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Extension of Vibrating-Wire Viscometry to Electrically Conducting Fluids and Measurements of Viscosity and Density of Brines with Dissolved CO₂ at Reservoir Conditions

Claudio Calabrese
Claudio Calabrese
Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
More by Claudio Calabrese
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Mark McBride-Wright
Mark McBride-Wright
Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
More by Mark McBride-Wright
,
Geoffrey C. Maitland
Geoffrey C. Maitland
Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
More by Geoffrey C. Maitland
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J. P. Martin Trusler*
J. P. Martin Trusler
Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
*E-mail: [email protected]
More by J. P. Martin Trusler
http://orcid.org/0000-0002-6403-2488

Cite this: J. Chem. Eng. Data 2019, 64, 9, 3831–3847

Publication Date (Web):August 16, 2019

https://doi.org/10.1021/acs.jced.9b00248

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Abstract

In order to design safe and effective storage of anthropological CO₂ in deep saline aquifers, it is necessary to know the thermophysical properties of brine–CO₂ solutions. In particular, density and viscosity are important in controlling convective flows of the CO₂-rich brine. In this work, we have studied the effect of dissolved CO₂ on the density and viscosity of NaCl and CaCl₂ brines over a wide range of temperatures from 298 to 449 K, with pressures up to 100 MPa, and salinities up to 1 mol·kg^–1. Additional density measurements were also made for both NaCl and CaCl₂ brines with dissolved CO₂ at salt molalities of 2.5 mol·kg^–1 in the same temperature and pressure ranges. The viscosity was measured by means of a vibrating-wire viscometer, while the density was measured with a vibrating U-tube densimeter. To facilitate the present study, the theory of the vibrating-wire viscometer has been extended to account for the electrical conductivity of the fluid, thereby expanding the use of this technique to a whole new class of conductive fluids. Relative uncertainties were 0.07% for density and 3% for viscosity at 95% confidence. The results of the measurements show that both density and viscosity increase as a result of CO₂ dissolution, confirming the expectation that CO₂-rich brine solutions will sink in an aquifer. We also find that the effect of dissolved CO₂ on both properties is sensibly independent of salt type and molality.

1. Introduction

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This paper addresses the challenge of measuring the changes in viscosity and density of concentrated brine solutions caused by dissolution of CO₂ under the extreme temperature and pressure conditions encountered in many industrial processes and in the subsurface storage of CO₂ as a method to ameliorate anthropogenic climate change. This is achieved through extending the theory underpinning the vibrating-wire (VW) viscometer technique to enable this highly accurate method to be used not just for brines but for a wide range of conducting liquids.

CO₂ is a fluid widely employed in the petrochemical and chemical industries. Carbon dioxide in its supercritical (sc) state is commonly used in processes of purification and extraction; (1) sc-CO₂ is also employed in environmental engineering for treating industrial waste liquids. (2) It plays an important role in petroleum engineering as a fluid for enhanced oil recovery (EOR) and enhanced coal bed methane recovery. (3−7) It is also used as a refrigerant fluid instead of chlorofluorocarbons which have higher global warming potential (GWP) compared to CO₂; (8) for the same reason, in the near future, it could also replace other refrigerants such as hydrofluorocarbons.

CO₂ is a trace gas naturally present in the Earth’s atmosphere and it dissolves in the ocean where it forms carbonic acid (H₂CO₃), and the ions bicarbonate (HCO₃^–) and carbonate (CO₃^2–). Although CO₂ has a relatively low GWP, it is classified as a greenhouse gas because of the huge quantities emitted annually by human activities and it is one of the primary agents driving climate change. (8) For this reason, large-scale CO₂ capture combined with storage in geological formations is considered crucial for reducing atmospheric CO₂ emissions. In this context, carbon capture and storage is an emerging technique capable of greatly reducing CO₂ emissions from large-scale industrial combustion of fossil fuels. Depleted oil and gas reservoirs and deep saline aquifers are potential sinks to store large quantities of CO₂ over a geological time scale.

When injected into a geological storage formation, CO₂ will contact the connate reservoir fluids, hydrocarbons and/or brines, present in the porous reservoir rocks. In order to design and operate safe and efficient carbon storage, it is therefore necessary to know the multiphase flow properties and the chemical and physical properties of mixtures of CO₂ with reservoir fluids. The distribution of CO₂ in the subsurface is a key element for successful carbon storage, and this is influenced by the relative permeability of the rock and the relation between saturation and capillary pressure. (9) Another important consideration is the injectivity of the wells through which the CO₂ enters the storage formation, which must be sufficient to cope with the desired flow rate. Injectivity is also dependent upon both the absolute and relative permeabilities, (10) and in turn, upon the thermophysical properties of the fluids and their mixtures. Finally, it is necessary to model the time scales of the different trapping mechanisms involved during geological carbon storage and these too are strongly influenced by thermophysical properties. (11)

The focus of the present work is on the viscosity and density of (CO₂ + brine) systems under conditions encompassing those of CO₂ storage in a deep saline aquifer. As shown by Pau et al. (12) and confirmed in this work, the density of homogenous (CO₂ + brine) solutions is higher than that of the original brine. As a consequence, once CO₂ has dissolved in the brine, the resulting solution tends to be transported toward the bottom of the reservoir by means of natural convective flows with viscous fingering. (13) The rate of this flow is strongly influenced by the density gradient and by the viscosity of the solution. This natural convection increases the rate of solubility trapping as fresh brine flows back to the top of the reservoir to contact undissolved CO₂. For these reasons, knowing the viscosity and density of the (CO₂ + brine) mixture as a function of temperature, pressure, and CO₂ mole fraction is vital for characterizing the reservoir behavior and developing predictive tools to model the processes of injection and subsequent evolution of the CO₂ plume. However, experimental data for the viscosity and density of (CO₂ + brine) systems at reservoir conditions are presently few in the literature. Tables 1 and 2 summarize the existing literature data for the viscosity and density of NaCl and CaCl₂ brine systems, with and without CO₂ addition, under high pressure conditions. An extensive study has been made by Al Ghafri et al. (14) of the density of CO₂-free NaCl(aq) and CaCl₂(aq) at temperatures between (283.15 and 473.15) K, pressures up 68.5 MPa, and various brine molalities. The effect of dissolved CO₂ on the density has been studied by Nighswander et al., (15) Yan et al. (16) and Song et al. (17) The latter study has an estimated expanded relative uncertainty of only 0.02% and but many of the data at high salt modalities appear to be oversaturated with CO₂ and hence not representative of homogenous states. In the case of viscosity, Kumagai and Yokoyama, (18) Bando et al., (19) and Fleury and Deschamps (20) studied the effect of CO₂ on the viscosity of NaCl(aq) at relatively low pressures and temperatures. The viscosity of CO₂-free NaCl(aq) solutions has been studied by Kestin et al. (21,22) over a temperature range from (293 to 423) K, pressures up to 35 MPa, and molalities up to 6 mol·kg^–1; Kestin et al. (21) also report a viscosity correlation in terms of temperature, pressure, and molality, with an uncertainty of 0.5%. No data are available for the [CO₂ + CaCl₂(aq)] systems but the viscosity of CO₂-free CaCl₂(aq) has been studied by Abdulagatov and Azizov, (23) Isono, (24) Wahab and Mahiuddin, (25) Gonçalves and Kestin, (26) and Zhang et al. (27)

Table 1. Available Experimental Data for Viscosity η and Density ρ of [xCO₂ + (1 – x)NaCl(aq)], at Temperatures T, Pressures p, and Salt Molalities m, with Relative Uncertainty U_r

references	property	T/K	p/MPa	x	m/(mol·kg^–1)	U_r (%)
Al Ghafri et al. (14)	ρ	298–473	0.9–68.4	0	1.06–6.00	0.05
Nighswander et al. (15)	ρ	353–473	2–10	≤0.015	0.173	0.65
Yan et al. (16)	ρ	323–413	5–40	≤0.022	1 and 5	0.1
Song et al. (17)	ρ	333–413	10–18	≤0.015	1, 2, 3 and 4	0.02
Kumagai and Yokoyama (18)	η	273–278	0.1–30	≤0.0162	0.34–0.86	0.8
Bando et al. (19)	η	303–333	10–20	saturation	0.00–0.53	2
Fleury and Deschamps (20)	η	308	8.5	≤0.0176	0.34–3.15	∼1.7
Kestin et al. (21)	η	293–423	0.1–35	0	0.00–6.00	0.5

Table 2. Available Experimental Data for Viscosity η and Density ρ of [xCO₂ + (1 – x)CaCl₂(aq)], at Temperatures T, Pressures p, and Salt Molalities m, with Relative Uncertainty U_r

references	property	T/K	p/MPa	m/(mol·kg^–1)	U_r, %
Al Ghafri et al. (14)	ρ	283–473	1.1–68.1	1.00–6.00	0.05
Abdulagatov and Azizov (23)	η	293–575	0.1–60	0.10–2.00	1.6
Isono et al. (24)	ρ, η	288–328	0.1	0.05–6.00	N/A
Wahab and Mahiuddin (25)	ρ, η	273–323	0.1	0.004–7.15	0.01, 0.5
Gonçalves and Kestin (26)	η	293–323	0.1	0.27–5.10	0.3
Zhang et al. (27)	ρ, η	298	0.1	0.02–7.87	0.01, 0.1

Obtaining accurate values of fluid thermophysical properties at high temperature and pressure (HTHP) presents particular challenges. Vibrating tube (VT) and VW techniques are particularly suited to HTHP adaptation, and in particular, a VW viscometer is probably the most accurate device for measuring fluid viscosity under extreme conditions, giving uncertainties of ±0.1% in the most favorable circumstances (gases) and routinely ∼±1% for dense gases and liquids. However, in the case of conducting fluids, we have ascertained that using the existing theory for nonconducting fluids can lead to significant errors, sometimes in excess of ±5%. It is therefore necessary to develop more accurate working equations for conducting fluids to enable high precision viscosity data to be obtained for conducting fluids, especially ionic systems. Addressing this issue is necessary for this study, but also has much wider implications for enabling accurate (±1–2%) determination of viscosity for a wide range of conducting fluids, especially under extreme conditions where other (less accurate) methods such as capillary flow become more difficult to implement.

In this paper, we present the improved working equation of the VW viscometer and report new viscosity and the density data for concentrated brines. The objectives of the work were fourfold: first, to develop a new working equation for the operation of a VW viscometer filled with a highly conductive solution; second, to study experimentally the effect of CO₂ on the viscosity and density of NaCl(aq) and CaCl₂(aq) solutions, over wide ranges of temperature and pressure, and at CO₂ mole fractions close to saturation; third, to test the hypothesis that the effect of CO₂ upon viscosity and density of a brine is independent of the salt type and molality; and finally, to provide an empirical model for both properties in terms of temperature, pressure, and CO₂ mole fraction. Furthermore, the present study provides densities for the [CO₂ + NaCl(aq)] and [CO₂ + CaCl₂(aq)] systems, in a range of conditions of interest for large-scale carbon storage and EOR processes. The viscosity measurements for [CO₂ + NaCl(aq)] extend in temperature from (333 to 449) K and in pressure from (30 to 100) MPa, while the [CO₂ + CaCl₂(aq)] systems are studied for the very first time over wide ranges of temperature and pressure.

2. Materials and Method

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2.1. Chemicals

The chemicals used in this work are detailed in Table 3. Pure deionized water was used for preparing all solutions and the salts were dried in an oven. Brine solutions were degassed by agitation under vacuum immediately prior to injection into the system.

Table 3. Chemical Samples Description Where w is Mass Fraction, x is Mole Fraction, and ρ_e is Electrical Resistivity at T = 298.15 K

chemical name	CAS number	source	purity	additional purification
calcium chloride dihydrate	10035-04-8	Sigma-Aldrich	w ≥ 0.990	none
carbon dioxide	124-38-9	BOC	x ≥ 0.99995	none
sodium chloride	7647-14-5	Sigma-Aldrich	w ≥ 0.995	none
water	7732-18-5	Millipore Direct-Q UV3	ρ_e > 18 MΩ·cm	vacuum degassed

2.2. Apparatus

The apparatus was described in detail in a previous paper, (28) and only a brief summary will be given here. In this work, the viscosity was measured with a VW viscometer, and the density was measured by means of a VT densimeter. Most of the wetted parts of the system were made of Hastelloy-C276 in order to avoid corrosion problems. The VW sensor was designed and built in-house in a configuration in which the VW was clamped at both ends. Figure 1 is a simplified diagram of the VW–VT apparatus, identical to that shown previously. (28) The viscometer and densimeter were connected with a circulation pump in a circuit that permitted mixtures to be homogenized in situ.

Figure 1. Simplified diagram of the VW–VT apparatus: (1) vacuum pumps, (2) aqueous brine solution, (3) CO₂ gas cylinder, (4) syringe pump, (5) circulating pump, (6) VW viscometer, (7) VT densimeter, (8) waste bottle, (V1 to V3) valves. (29)

The selection of the wire material was based on the following features: high density and melting temperature, adequate electrical conductivity and magnetic properties, high tensile strength, sufficient hardness, and resistance to corrosion. As a consequence, an alloy of platinum and iridium, containing 10 mass % Ir, was chosen for the wire. The density of the material at room temperature was ρ_w = 21560 kg·m^–3, (30) and the wire used was of 75 μm nominal radius.

The density of the fluid was measured by means of a high-pressure VT densimeter (Anton Paar DMA HPM) that was connected to an evaluation unit (mPDS 2000 V3) able to detect the period of oscillation with a resolution of 0.001 μs.

The temperature was regulated by circulating silicone oil from a thermostat bath through a heat exchanger within the densimeter module and an external jacket around the viscometer. Temperatures were measured by means of platinum resistance thermometers (PRTs). One was inserted into a thermowell in VT densimeter and a second was inserted into a thermowell in the pressure vessel containing the VW viscometer. Fluid pressure was controlled by the high-pressure syringe pump. Temperature stability was within ±0.05 K and pressure stability was within ±0.02 MPa, both measured over a 1 h period.

For all the other details regarding the viscosity sensor, the circulation pump, syringe pumps, and the other key components of the VW–VT apparatus, we refer the reader to a previous paper. (28)

3. New Semi-Empirical Working Equation for Highly Conductive Fluids

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3.1. Standard Equation for the VW Viscometer

The VW technique has been successfully employed in the past to study the viscosity of CO₂ with hydrocarbons (31) and with water. (28) In the steady-state VW technique, a tensioned metallic wire is immersed in the fluid of interest and placed in a permanent magnetic field perpendicular to its axis. A sinusoidal current is passed through the wire creating a Lorentz force that sets the wire into transverse motion. According to Faraday’s law, this motion induces a voltage across the wire which can be measured. (32) In this work, a lock-in amplifier was used to measure the complex voltage Φ as a function of the frequency f of the imposed current. The viscosity is obtained by analysis of the experimental resonance curve Φ(f) in terms of the following working equation

(1)

Here, Λ is the amplitude, and f₀ and Δ₀ are the resonance frequency and logarithmic decrement of the wire in vacuum; a, b, and c arise from the impedance of the stationary wire and any offsets in the lock-in amplifier (background term); finally, β and β′ are dimensionless parameters that account for the added mass and damping effect of the fluid surrounding the wire, respectively. These terms are given by (33,34)

(2)

where

(3)

K_n is the modified Bessel function of the second kind of order n, (35) ρ and η are the density and viscosity of the fluid, and ρ_s and R are the density and radius of the wire. The term icf in eq 1 is not always significant and can be neglected when, as in the present work, the viscosity is small and the resonance curve spans a narrow frequency range.

3.2. Revised Working Equation for Highly Conductive Fluids

The standard theory of the VW instrument does not account for the conductivity of the fluid surrounding the wire. Given the constraints upon the desired mechanical properties of the wire material, experiments with insulated wires have not been carried out and, instead, we aim to account for the electrical conductivity of the surrounding wire in the theory of the instrument. Figure 2a illustrates the physical situation that we seek to model, while Figure 2b is a simplified electrical equivalence circuit. Because the fluid surrounding the VW is conductive, it can be represented to a first approximation as additional impedance Z_b (or admittance G_b = 1/Z_b) in parallel with the VW. The electrical impedance of the VW itself may be written as the sum (Z_w + Z_m), where Z_w is the electrical impedance of the stationary wire, and Z_m is the additional impedance arising from damped motion of the wire in the presence of a magnetic field. The combined electrical impedance of this network is given by

(4)

Figure 2. Simplified schematics of the VW sensor: (a) physical arrangement; (b) electrical equivalence circuit; OSC, sine-wave oscillator (0.05–5 V rms); R_s, series resistor (1 kΩ), I, electric current; Z_w, electrical impedance of stationary wire; Z_m, additional electrical impedance due to wire motion in the magnetic field; Z_b, electrical impedance of brine; N and S, poles of the permanent magnet; A and B, differential signal terminals for connection to the lock-in amplifier.

If the admittance G_b is small, such that G_b(Z_w + Z_m)⁻¹ ≪ 1, then eq 4 may be approximated as follows

(5)

What is measured in an experiment is a voltage Φ given by

(6)

where I is the current and Φ_offset is a constant complex voltage offset set on the lock-in amplifier used to make the measurements. Accordingly, the recorded data are in the following form

(7)

Because the frequency range of the measurements is small, we assume that Z_w and G_b are constants and, because Z_w ≫ Z_m, we approximate G_b(Z_w + Z_m) as G_bZ_w to obtain

(8)

Equation 8 can be rewritten as

(9)

The factor (1 – G_bZ_w) is a complex constant which can be written in the form A·exp(iθ), where θ is a phase angle, and the term Z_mI is the usual VW resonance term (see eq 1). Hence, absorbing the terms in the square brackets appearing in eq 9 into the background terms, a revised working equation can be obtained as follows

(10)

where Λ′ = AΛ is a real valued constant. According to this relation, the effect of the stray impedance is to modify the resonance term by a scale factor and to rotate its phase by angle θ. A constant background term with real and imaginary parts remains. If G_b and Z_w were both real, then there would be no phase change. The main approximations made here are that all terms, except the resonance term, may be considered independent of frequency and that the product of the brine admittance and the impedance of the stationary wire is small compared with unity. The former is valid when the resonance data cover a narrow frequency band, that is, when the viscosity is small and the resonance curve is narrow. The latter is valid when Z_b ≫ Z_w. Both conditions appear to be satisfied experimentally.

Figure 3 shows an experimental resonance curve measured in NaCl(aq) at T = 448 K, p = 1.4 MPa, and m = 2.5 mol·kg^–1. This represents the most critical case considered in which we have the highest ratio of brine conductivity to viscosity. When the parameters of the standard working equation, eq 1, are fitted to these data significant discrepancies can be observed. However, eq 10 provides a high-quality fit. It is notable that, eqs 1 and 10 contain the same number of parameters, as we have dropped the term icf in eq 10. Unfortunately, the analysis leading to eq 10 is still incomplete because it neglects the possibility of leakage currents flowing between the wire and the surrounding brine, which gives rise to additional damping. As a consequence, the viscosity obtained when eq 10 is fitted to the data is over-estimated, compared with the literature, by some 12%.

Figure 3. Experimental resonance curve (components of the complex voltage Φ as a function of driving frequency f) in comparison with the standard and modified working equations: □, experimental in-phase voltage; ○, experimental quadrature voltage; green line, modified working equation; red line, standard working equation. Measurements carried out in NaCl(aq) at T = 448 K, p = 1.4 MPa, and m = 2.5 mol·kg^–1.

Electrical damping of the wire resonance can occur because the voltage per unit length induced in the wire is proportional to the velocity amplitude of the wire, which varies greatly along the length of the wire from zero at each end to a maximum amplitude at the midpoint. Therefore, a distributed potential difference arises between the wire and the surrounding brine giving rise to a distributed leakage current that causes additional damping of the resonance. If this term is not recognized then the viscosity of the fluid will be overestimated, as in the example mentioned above because the leakage-current damping will be included with the viscous damping in the analysis. Therefore, to account for the additional damping mechanism, we must include a term β″ in addition to the viscous damping term β′ in the working equation as follows

(11)

Equation 11 is the revised working equation that we have employed in this study.

3.3. Determination of the Additional Damping Term

A quantitative analysis of the additional damping is complicated because, in general, neither the exact current paths nor the brine conductivity are known. Therefore, in this work, we propose a semi-empirical approach. We first observe that the phase angle θ is easily obtained when fitting the experimental resonance curves. Furthermore, both θ and β″ are functions of the brine conductivity for a VW sensor of fixed geometry but the latter is unknown. Therefore, we seek an empirical relation β″(θ) between the additional damping and the phase angle, eliminating the conductivity from the problem, and we parameterize that relationship by means of measurements carried out in concentrated NaCl brines of known viscosity and density. For these brines, we make use of the reference data of Kestin et al. (21) for viscosity and Al Ghafri et al. (14) for density. The correlation for viscosity is based on the experimental results obtained with an oscillating-disk viscometer. (36) An overall uncertainty of 0.5% was attributed to the correlation based on a very detailed analysis of the experimental method. (36,37) The correlation has been validated in a temperature range from (293.15 to 423.15) K, a pressure from (0.1 to 30) MPa, and NaCl(aq) molalities up to 5.4 mol·kg^–1. Resonance-curve measurements were carried out for NaCl(aq) of molality m = (0.77 and 2.50) mol·kg^–1 and the experimental resonance curve data were then analyzed in terms of eq 11 with β′ calculated from eqs 2 and 3 using reference values of viscosity and density. The parameters so determined from each resonance curve were Λ′, θ, f₀, β″, a, and b. The results of these measurements for the additional damping term β″, as a function of the phase angle θ, are shown in Figure 4. We also show a quadratic polynomial fitted to the data which we used in the subsequent measurements to compute β″(θ). When this model was fitted to the reference values of viscosity, the standard deviation of the correlation was found to be 0.2%.

Figure 4. Additional damping β″ as a function of phase angle θ for NaCl(aq) with viscosity values constrained to literature data: (21) □, m = 0.77 mol·kg^–1; ○, m = 2.5 mol·kg^–1; —, quadratic correlation.

When the same resonance data were re-analysed with β″ replaced by the quadratic function of θ determined in Figure 4 and η treated as a free parameter, the resulting viscosities are found to be in close agreement with the correlation of Kestin et al. (21) This comparison is illustrated in Figure 5. The absolute average relative deviation between our experimental data and the correlation was 0.3%, while the maximum absolute relative deviation was 0.9%.

Figure 5. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp and calculated values η_calc from the correlation of Kestin et al. (21) for NaCl(aq) with molality m = 0.77 mol·kg^–1: ▲ 1 MPa, ×,15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa.

The theory behind this approach is based on general physical–chemical principles. Both the phase angle θ and the additional damping β″ arise specifically from the conductivity of the fluid. For this reason, the modified working equation should be applicable to any highly conductive fluid provided that a correlation between the additional damping term and the phase angle is established in the entire range of conductivity investigated. However, it should be recognized that, this relationship is specific to a given sensor.

4. Experimental Procedure

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4.1. Mixture Preparation

Before starting a new set of measurements, the system was carefully washed with deionized water in order to remove brine residues from the previous experiment. The cleaning process employed one of the syringe pumps for the water injection, activation of the circulation pump to flush the entire loop, and discharge to the waste line. The VT densimeter allowed simultaneous density measurements of the fluid in the system, and during the cleaning process, the density was observed to decrease over time toward that of water; at this point, the flushing process was stopped.

The system was evacuated through valves V2 and V3 (see Figure 1). In order to ensure isothermal filling, the temperature of the densimeter and the viscometer was controlled at the temperature of the laboratory (T = 295.15 K). CO₂(g) was admitted through valve V1 to an initial filling pressure calculated to give the desired mole fraction in the final aqueous solution. Knowing the system volume and the filling temperature and pressure, the amount of CO₂ was computed from the equation of state of Span and Wagner. (38) The initial pressure of CO₂ in the system was selected based on the model by Duan et al., (39,40) which is able to predict the solubility of CO₂ in aqueous NaCl and CaCl₂ solutions. Next, degassed brine solution of molality m was injected quantitatively from one of the syringe pumps until the pressure reached about 15 MPa. During this operation, the temperature of the syringe pump was controlled at 295.15 K. Several strokes of the pump were required to fill the system but all pump displacements were measured with the brine in the syringe compressed to a pressure of 15 MPa. The precise amount of brine injected was determined from the total injected volume measured at a pressure of 15 MPa, the pump temperature, and the corresponding brine density calculated from the correlation of Al Ghafri et al. (14)

4.2. Measurement Sequence

The viscosity and density measurements were carried out in the pressure range from (1 to 100) MPa, at nominal temperatures of (275, 296, 323, 348, 373, 398, 423, and 449) K. Simultaneous density and viscosity measurements were carried out for brine molalities of 0.77 mol·kg^–1 for NaCl(aq), and 1.00 mol·kg^–1 for CaCl₂(aq). Additionally, density measurements were made for both brine systems at m = 2.50 mol·kg^–1 in the same temperature and pressure ranges. The mole fractions of CO₂ in the NaCl(aq) system were x = (0, 0.0122, and 0.0159) at m = 0.77 mol·kg^–1, and x = (0, 0.0044, 0.0081, 0.0119) at m = 2.50 mol·kg^–1; at m = 0.77 mol·kg^–1, density measurements were additionally made at x = 0.0078. For the CaCl₂(aq), the mole fractions were x = (0, 0.0052, 0.0094, and 0.0137) at m = 1.00 mol·kg^–1, and x = (0, and 0.0061) at m = 2.50 mol·kg^–1. For each system, some combinations of salt-free mole fraction, pressure, and temperature were avoided to ensure that the mixtures remained in the homogeneous liquid region.

5. Calibration and Uncertainty Analysis

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The calibration procedures for the VW–VT apparatus were described previously, (28) and only a brief summary is given here.

5.1. Temperature

The temperatures of the VW viscometer and the VT densimeter were measured by means of two PRTs. The PRTs were calibrated against a standard PRT, which was in turn calibrated on ITS-90 with an expanded uncertainty of ≤0.015 K (k = 2). The calibration was carried out at temperatures from (273 to 473) K, in steps of 40 K; the Callendar–van Dusen equation was employed to represent the results. The standard uncertainty of the measured temperatures was 0.025 K.

5.2. Pressure

The pressure transducer (Honeywell TJE) was calibrated at pressures of (20, 40, 60, 80, and 100) MPa; the calibration was performed against a hydraulic pressure balance (DH Budenberg model 580 EHX) with an expanded relative uncertainty of 0.008% (k = 2). In order to correct for drift, the zero of the pressure sensor was re-adjusted periodically, by comparing (at atmospheric pressure) the measured pressure with the reading given by a digital barometer in the same laboratory. Taking this drift into account, the standard uncertainty of the pressure was estimated to be 0.1 MPa.

5.3. System Volume

The volume of the system was calibrated with pure deionized water at T = 298.15 K and it was found to be 44.09 cm³, with an overall standard uncertainty of 0.09 cm³. (28)

5.4. CO₂ Mole Fraction

Mixtures were prepared in situ as described below and the mole fraction x of CO₂ in the final homogeneous solution was determined from the amounts n_CO₂ of CO₂ and n_b of brine injected

(12)

The standard uncertainty u(x) of the CO₂ mole fraction depends upon the standard relative uncertainties u_r(n_CO₂) of n_CO₂ and u_r(n_b) of n_b as follows

(13)

The individual standard relative uncertainties appearing in eq 13 have been discussed previously (28) where it was shown that the uncertainty of the CO₂ filling pressure was the dominant term such that u(x) ≈ xu_r(p). This leads to a final value u(x) = 0.0004 for all the mixtures investigated.

5.5. Density

The density ρ(T,p) of the (CO₂ + brine) mixtures was determined from the period τ of the VT densimeter according to the simplified working equation

(14)

where A(T, p) is a function of temperature and pressure, while τ₀(T) is the temperature-dependent period of oscillation under vacuum. In order to determine A and τ₀, the strategy of Comuñas et al. (41) was employed with calibrations performed in pure deionized and degassed water at each nominal experimental pressure and temperature, and under vacuum conditions at each nominal experimental temperature. The quantity A(T,p) was then obtained from the following relation

(15)

where subscripts “w” and “0” refer to water and vacuum conditions, respectively. The densities of water at each experimental temperature and pressure were obtained from the IAPWS-95 equation of state of Wagner and Pruss. (42) Finally, the calibration functions were represented empirically as follows

(16)

(17)

The uncertainty analysis for density is exemplified in Table 4 for the [CO₂ + NaCl(aq)] system at salt molality m = 0.77 mol·kg^–1, and at the median temperature, pressure, and CO₂ mole fraction. The overall expanded relative uncertainty of 0.07% was attributed to all density measurements reported in this paper because the uncertainties varied very little over the range of conditions investigated.

Table 4. Uncertainty Analysis for the Density of CO₂ Solutions in NaCl(aq) with Salt Molality m = 0.77 mol·kg^–1 at the Median State Point in Terms of Standard Uncertainty u(X) of Dimensionless Parameters X and Arising Contribution u_r(ρ) to the Overall Standard Relative Uncertainty of Density

dimensionless parameter	X	u(X)	10²u_r(ρ)
p/MPa	50.22	0.1	0.004
T/K	373.24	0.025	0.002
m/(mol·kg^–1)	0.77	0.0019	0.006
x	0.0124	0.0004	0.016
τ₀/μs	2580.53	0.003	0.004
A/(kg·m^–3·μs^–2)	2.4902 × 10^–3	1.6 × 10^–7	0.006
τ/μs	2658.00	0.020^a	0.027
overall standard relative uncertainty			0.033

^{^a}

Repeatability uncertainty.

5.6. Viscosity

The key calibration parameter in both the standard and revised working equations is the radius R of the VW which was determined previously by calibration in pure deionized water. The overall standard uncertainty of the viscosity is related to the standard uncertainties of temperature, pressure, CO₂ mole fraction, density, logarithmic decrement in vacuum, additional damping term, wire radius, and thermal expansivity, and also the repeatability uncertainty. Table 5 shows the uncertainty analysis for the viscosity of the [CO₂ + NaCl(aq)] system at molality m = 0.77 mol·kg^–1 and at the median state point. Based on this, and the observation that the uncertainty varied only slightly over the range of conditions investigated, an expanded overall relative uncertainty of 3% was attributed to all viscosity measurements.

Table 5. Uncertainty Analysis for the Viscosity of CO₂ Solutions in NaCl(aq) with Salt Molality m = 0.77 mol·kg^–1 at the Median State Point in Terms of Standard Uncertainty u(X) of Dimensionless Parameters X and Arising Contribution u_r(ρ) to the Overall Standard Relative Uncertainty of Density

dimensionless parameter	X	u(X)	10²u_r(η)
p/MPa	50.22	0.1	0.01
T/K	373.24	0.025	0.03
m/(mol·kg^–1)	0.77	0.0019	0.02
x	0.0124	0.0004	0.01
ρ/(kg·m^–3)	1010.56	0.46	0.04
R/μm	73.20	0.18	0.50
10⁶Δ₀	29.9	15	0.03
α_w/(10^–6·K^–1)	8.7	0.4	0.01
10⁴β″	1.64	0.51	0.45
η/(mPa·s)	0.3303	0.0045^a	1.31
overall standard relative uncertainty			1.47

^{^a}

Repeatability uncertainty.

6. Results and Discussion

ARTICLE SECTIONS

Jump To

6.1. Experimental Results

The density results for the [xCO₂ + (1 – x)NaCl(aq)] system and the [xCO₂ + (1 – x)CaCl₂(aq)] system, are reported in Tables 6 and 7, respectively, while the corresponding viscosity results are given in Table 8 and 9.

Table 6. Experimental Densities ρ of [x CO₂ + (1 – x) NaCl(aq)] at Temperatures T, Pressures p, and Salt Molalities m^a

p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)
m = 0.77 mol·kg^–1
x = 0.0000
T = 274.83 K		T = 296.22 K		T = 323.33 K		T = 348.21 K
1.31	1033.05	1.38	1028.25	1.34	1017.80	1.38	1004.37
15.21	1039.38	15.22	1034.12	15.26	1023.47	15.26	1010.15
30.12	1045.95	30.11	1040.25	30.16	1029.36	30.18	1016.18
49.95	1054.41	49.93	1048.04	49.98	1036.98	50.00	1023.83
69.81	1062.53	69.81	1055.61	69.84	1044.30	69.88	1031.26
99.82	1074.13	99.84	1066.51	99.89	1054.90	99.92	1041.89
T = 373.25 K		T = 398.81 K		T = 423.73 K		T = 448.97 K
1.40	988.09	1.46	969.16	1.45	947.66	1.46	923.83
15.31	994.18	15.37	975.70	15.37	954.86	15.38	932.02
30.22	1000.44	30.26	982.49	30.27	962.29	30.29	940.31
50.06	1008.50	50.08	991.06	50.11	971.57	50.12	950.53
69.93	1016.20	69.95	999.13	69.96	980.32	69.98	960.05
99.96	1027.15	99.99	1010.69	100.00	992.59	100.00	973.43
x = 0.0078
T = 274.93 K		T = 296.22 K		T = 323.35 K		T = 348.20 K
15.20	1042.10	15.21	1036.82	15.23	1025.97	15.22	1012.34
30.11	1048.54	30.09	1042.90	30.14	1031.96	30.09	1018.37
49.98	1056.88	49.94	1050.70	50.01	1039.57	49.96	1026.19
69.86	1064.93	69.82	1058.23	69.89	1046.90	69.86	1033.63
99.90	1076.47	99.84	1069.13	99.87	1057.49	99.89	1044.33
T = 373.22 K		T = 398.38 K		T = 423.73 K		T = 448.95 K
15.27	995.79	15.29	976.70	15.30	955.13	15.30	931.45
30.15	1002.18	30.18	983.60	30.20	962.72	30.21	940.01
50.03	1010.37	50.06	992.35	50.07	972.37	50.08	950.72
69.91	1018.13	69.92	1000.65	69.94	981.27	69.94	960.53
99.91	1029.24	99.93	1012.39	99.93	993.88	99.94	974.22
x = 0.0122
T = 274.99 K		T = 296.20 K		T = 323.34 K		T = 348.19 K
15.26	1042.95	15.26	1037.62	15.26	1026.65	30.23	1018.84
30.15	1049.29	30.13	1043.57	30.17	1032.56	50.08	1026.61
50.04	1057.53	50.01	1051.36	50.04	1040.12	69.94	1034.12
69.90	1065.51	69.88	1058.94	69.92	1047.45	99.98	1044.82
99.95	1077.01	99.94	1069.76	99.93	1058.01
T = 373.24 K		T = 398.31 K		T = 423.62 K		T = 448.85 K
30.30	1002.42	30.29	983.55	30.29	962.25	30.30	938.95
50.22	1010.56	50.18	992.36	50.17	971.93	50.19	949.84
70.10	1018.40	70.08	1000.71	70.08	981.10	70.08	959.96
100.12	1029.50	100.10	1012.48	100.03	993.79	100.04	973.74
x = 0.0159
T = 274.98 K		T = 296.17 K		T = 323.32 K		T = 348.21 K
15.23	1046.29	15.20	1040.88	30.18	1035.45	50.24	1029.33
30.17	1052.59	30.08	1046.89	50.14	1043.09	70.10	1036.87
50.06	1060.79	50.11	1054.61	69.97	1050.47	99.99	1047.70
69.94	1068.70	69.84	1062.15	99.98	1061.04
99.99	1080.07	99.94	1072.95
T = 373.23 K		T = 398.29 K		T = 423.63 K		T = 448.83 K
50.24	1013.07	50.25	994.66	50.25	973.84	50.25	951.41
70.12	1020.96	70.11	1003.10	70.11	983.13	70.14	961.71
100.00	1032.18	99.99	1015.01	100.00	996.08	100.00	975.91
m = 2.50 mol·kg^–1
x = 0.0000
T = 274.95 K		T = 296.19 K		T = 323.30 K		T = 348.21 K
1.34	1098.36	1.33	1090.47	1.38	1077.94	1.36	1064.12
15.26	1103.81	15.24	1095.73	15.29	1083.20	15.27	1069.47
30.19	1109.50	30.16	1101.16	30.22	1088.58	30.20	1075.01
50.04	1116.83	50.02	1108.18	50.06	1095.53	50.06	1082.15
69.93	1123.92	69.88	1115.02	69.95	1102.24	69.96	1089.02
99.99	1134.12	99.98	1124.82	100.01	1111.99	100.02	1098.91
T = 373.22 K		T = 398.29 K		T = 423.62 K		T = 448.85 K
1.38	1047.69	1.39	1029.58	1.41	1009.24	1.41	987.39
15.31	1053.49	15.30	1035.58	15.33	1015.81	15.33	994.66
30.23	1059.36	30.23	1041.92	30.25	1022.75	30.26	1002.41
50.09	1066.79	50.08	1049.89	50.10	1031.25	50.11	1011.56
69.96	1073.94	69.98	1057.41	69.99	1039.38	69.99	1020.26
100.04	1084.13	100.05	1068.15	100.05	1050.77	100.05	1032.59
x = 0.0044
T = 274.88 K		T = 296.17 K		T = 323.30 K		T = 348.19 K
15.21	1105.65	15.22	1097.40	15.24	1084.14	15.26	1069.95
30.11	1111.39	30.17	1102.57	30.15	1090.05	30.17	1075.82
49.99	1118.74	50.02	1109.85	50.02	1097.17	50.04	1083.40
69.85	1125.78	69.90	1116.68	69.91	1104.02	69.93	1090.55
99.91	1135.93	99.94	1126.53	99.91	1113.77	99.95	1100.56
T = 373.22 K		T = 398.27 K		T = 423.61 K		T = 448.84 K
15.28	1053.33	15.30	1035.12	15.31	1015.02	30.28	1000.99
30.18	1059.51	30.20	1041.53	30.25	1021.92	50.14	1010.75
50.07	1067.45	50.08	1050.02	50.10	1030.95	70.02	1020.09
69.95	1074.88	69.96	1057.85	69.97	1039.25	99.97	1032.73
99.95	1085.53	99.97	1068.97	99.97	1051.18
x = 0.0081
T = 274.82 K		T = 296.17 K		T = 323.33 K		T = 348.19 K
15.23	1107.67	15.22	1099.22	15.23	1086.41	15.25	1072.35
30.12	1113.28	30.14	1104.51	30.15	1091.83	30.21	1077.96
49.99	1120.56	49.99	1111.65	50.02	1098.77	50.05	1085.14
69.87	1127.55	69.85	1118.42	69.90	1105.56	69.92	1092.02
99.89	1137.66	99.88	1128.22	99.90	1115.24	99.93	1101.93
T = 373.21 K		T = 398.27 K		T = 423.60 K		T = 448.85 K
30.24	1061.87	30.23	1043.86	30.24	1024.02	30.24	1003.16
50.09	1069.52	50.11	1052.07	50.11	1032.84	50.10	1012.72
69.96	1076.78	69.97	1059.94	69.99	1041.28	69.97	1021.84
99.92	1087.06	99.91	1070.72	99.90	1052.86	99.90	1034.31
x = 0.0119
T = 274.81 K		T = 296.16 K		T = 323.26 K		T = 348.18 K
15.21	1109.04	15.19	1100.61	50.05	1105.08	50.12	1086.39
30.10	1114.75	30.07	1106.11	69.85	1106.92	69.97	1093.31
49.97	1121.91	49.99	1113.09	99.82	1116.77	99.87	1103.30
69.82	1128.98	69.78	1119.81
99.78	1139.04	99.78	1129.64
T = 373.21 K		T = 398.26 K		T = 423.59 K		T = 448.82 K
50.20	1070.48	50.18	1052.89	50.17	1033.70	50.17	1013.13
70.00	1077.82	70.03	1060.74	70.03	1042.15	70.02	1022.50
99.85	1088.58	99.87	1071.64	99.87	1053.83	99.85	1035.18

^{^a}

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the density is u(ρ) = 0.00033·ρ.

Table 7. Experimental Densities ρ of [xCO₂ + (1 – x)CaCl₂(aq)] at Temperatures T, Pressures p, and Salt Molalities m^a

p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)	p/MPa	ρ/(kg·m^–3)
m = 1.00 mol·kg^–1
x = 0.0000
T = 274.87 K		T = 296.18 K		T = 323.31 K		T = 348.20 K
1.27	1088.12	1.28	1082.39	1.24	1071.60	1.30	1058.82
15.18	1094.18	15.17	1087.93	15.19	1077.19	15.22	1064.57
30.07	1100.27	30.07	1093.68	30.07	1082.81	30.10	1070.33
49.88	1108.27	49.90	1101.19	49.88	1090.06	49.93	1077.65
69.75	1115.89	69.75	1108.40	69.76	1097.04	69.79	1084.72
99.73	1126.88	99.73	1118.84	99.75	1107.20	99.77	1094.89
T = 373.22 K		T = 398.28 K		T = 423.60 K		T = 448.84 K
1.32	1042.78	1.32	1024.80	1.34	1004.42	1.36	982.19
15.23	1048.82	15.23	1031.20	15.25	1011.30	15.27	989.78
30.13	1054.88	30.12	1037.76	30.15	1018.56	30.16	997.78
49.94	1062.61	49.94	1045.99	49.95	1027.46	49.98	1007.39
69.79	1070.00	69.78	1053.70	69.82	1035.71	69.83	1016.54
99.79	1080.38	99.79	1064.71	99.81	1047.43	99.81	1029.19
x = 0.0052
T = 274.93 K		T = 296.18 K		T = 323.30 K		T = 348.17 K
15.23	1095.95	15.22	1089.50	15.25	1078.28	15.27	1065.06
30.10	1102.20	30.11	1095.40	30.14	1084.08	30.15	1071.00
49.96	1110.12	49.95	1102.90	49.98	1091.43	50.00	1078.60
69.81	1117.84	69.79	1110.07	69.83	1098.43	69.83	1085.75
99.77	1128.61	99.79	1120.45	99.77	1108.64	99.78	1096.01
T = 373.22 K		T = 398.23 K		T = 423.58 K		T = 448.84 K
15.27	1049.19	15.29	1031.24	15.29	1011.17	15.31	989.26
30.16	1055.45	30.18	1037.93	30.19	1018.37	30.19	997.10
49.99	1063.39	50.02	1046.43	50.03	1027.67	50.03	1007.25
69.85	1070.85	69.88	1054.29	69.86	1036.13	69.89	1016.39
99.81	1081.45	99.81	1065.50	99.81	1048.13	99.83	1029.42
x = 0.0094
T = 275.00 K		T = 296.22 K		T = 323.31 K		T = 348.17 K
15.24	1097.91	15.25	1091.33	15.26	1080.19	15.29	1067.02
30.13	1104.28	30.08	1097.05	30.15	1085.85	30.17	1072.80
49.98	1111.83	49.92	1104.48	50.01	1093.16	50.02	1080.25
69.82	1119.49	69.77	1111.60	69.86	1100.23	69.87	1087.40
99.79	1130.36	99.79	1122.03	99.83	1110.37	99.82	1097.65
T = 373.22 K		T = 398.24 K		T = 423.59 K		T = 448.85 K
15.31	1051.15	15.31	1033.21	15.32	1013.15	15.31	991.10
30.20	1057.23	30.20	1039.69	30.21	1020.20	30.21	998.83
50.04	1064.97	50.04	1048.04	50.05	1029.25	50.04	1008.86
69.88	1072.37	69.88	1055.85	69.88	1037.70	69.88	1017.95
99.81	1083.00	99.82	1066.96	99.82	1049.43	99.82	1030.76
x = 0.0137
T = 274.93 K		T = 296.21 K		T = 323.27 K		T = 348.15 K
15.17	1099.49	15.23	1092.96	30.06	1087.27	50.03	1081.44
30.07	1105.75	30.05	1098.64	49.99	1094.54	69.89	1088.69
49.90	1113.62	49.97	1105.96	69.77	1101.66	99.71	1099.04
69.74	1121.01	69.73	1113.19	99.68	1111.85
99.68	1131.95	99.71	1123.55
T = 373.20 K		T = 398.21 K		T = 423.57 K		T = 448.80 K
50.08	1066.09	50.09	1048.79	50.10	1029.65	50.11	1009.00
69.91	1073.59	69.91	1056.81	69.93	1038.30	69.95	1018.34
99.71	1084.28	99.73	1067.97	99.73	1050.48	99.76	1031.47
m = 2.50 mol·kg^–1
x = 0.0000
T = 274.98 K		T = 296.22 K		T = 323.23 K		T = 348.19 K
1.31	1201.94	1.31	1192.77	1.28	1179.30	1.32	1165.84
15.21	1207.74	15.24	1197.73	15.18	1184.63	15.22	1170.56
30.10	1212.77	30.13	1202.82	30.06	1189.89	30.11	1175.97
49.93	1219.37	49.96	1209.46	49.91	1196.52	49.95	1182.84
69.77	1225.90	69.78	1215.91	69.77	1202.94	69.79	1189.55
99.75	1235.53	99.74	1225.32	99.73	1212.15	99.79	1199.01
T = 373.20 K		T = 398.26 K		T = 423.60 K		T = 448.83 K
1.35	1151.73	1.36	1134.93	1.36	1116.33	1.36	1096.34
15.25	1156.76	15.27	1140.45	15.26	1122.22	15.25	1102.89
30.14	1161.97	30.16	1146.01	30.15	1128.37	30.15	1109.65
49.96	1168.74	49.97	1153.12	49.98	1136.00	49.97	1117.84
69.82	1175.25	69.82	1159.89	69.81	1143.19	69.82	1125.62
99.78	1184.69	99.80	1169.63	99.79	1153.51	99.83	1136.51
x = 0.0061
T = 275.25 K		T = 296.22 K		T = 323.28 K		T = 348.12 K
15.24	1208.37	15.21	1198.87	15.24	1185.89	15.26	1172.50
30.11	1213.62	30.09	1204.08	30.10	1190.97	30.17	1177.70
49.95	1220.48	49.94	1210.33	49.96	1197.57	50.01	1184.37
69.79	1227.11	69.79	1216.84	69.83	1203.93	69.87	1190.88
99.77	1236.71	99.79	1226.16	99.80	1213.12	99.79	1200.11
T = 373.21 K		T = 398.23 K		T = 423.56 K		T = 448.84 K
15.27	1157.31	15.28	1140.85	15.28	1122.76	15.30	1103.38
30.16	1162.72	30.17	1146.52	30.19	1128.81	30.18	1109.76
50.01	1169.65	50.02	1153.84	50.03	1136.63	50.03	1118.26
69.86	1176.32	69.86	1160.68	69.86	1144.01	69.86	1126.13
99.82	1185.83	99.80	1170.61	99.81	1154.33	99.82	1137.12

^{^a}

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the density is u(ρ) = 0.00033·ρ.

Table 8. Experimental Viscosities η of [xCO₂ + (1 – x)NaCl(aq)] at Temperatures T, Pressures p, and Salt Molality m = 0.77 mol·kg^–1^a

p/MPa	η/(mPa·s)	p/MPa	η/(mPa·s)	p/MPa	η/(mPa·s)
x = 0.0000
T = 274.65 K		T = 348.34 K		T = 373.31 K
1.4	1.748	1.4	0.412	1.4	0.310
15.3	1.718	15.3	0.416	30.2	0.318
30.2	1.704	30.2	0.421	50.0	0.323
50.1	1.700	50.0	0.429	69.9	0.329
		69.9	0.433	100.0	0.338
T = 398.18 K		T = 423.31 K		T = 448.27 K
1.4	0.247	15.3	0.206	30.3	0.181
15.3	0.251	30.2	0.212	50.1	0.185
30.2	0.256	50.1	0.216	70.0	0.190
50.1	0.260	70.0	0.220	100.0	0.197
70.0	0.265	100.0	0.228
100.0	0.273
x = 0.0122
T = 274.64 K		T = 348.36 K		T = 373.34 K
15.2	1.899	30.2	0.431	30.3	0.325
30.2	1.882	50.1	0.436	50.2	0.330
69.9	1.843	69.9	0.442	70.1	0.336
99.9	1.813			100.1	0.346
T = 398.24 K		T = 423.37 K		T = 448.33 K
30.3	0.260	30.3	0.213	30.3	0.183
50.2	0.265	50.2	0.219	50.2	0.187
70.1	0.269	70.1	0.224	70.1	0.193
		100.0	0.232	100.0	0.200
x = 0.0159
T = 274.63 K		T = 348.34 K		T = 373.29 K
15.2	1.961	50.2	0.443	50.2	0.335
30.2	1.942	70.1	0.449	70.1	0.341
100.0	1.872			100.0	0.351
T = 423.28 K		T = 448.23 K
50.2	0.222	50.3	0.190
70.1	0.227	70.1	0.195
100.0	0.235	100.0	0.202

^{^a}

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the viscosity is u(η) = 0.015·η

Table 9. Experimental Viscosities η of [xCO₂ + (1 – x)CaCl₂(aq)] at Temperatures T, Pressures p, and Salt Molality m = 1.00 mol·kg^–1^a

p/MPa	η/(mPa·s)	p/MPa	η/(mPa·s)	p/MPa	η/(mPa·s)
x = 0.0000
T = 274.75 K		T = 296.21 K		T = 323.40 K
1.3	2.142	30.1	1.224	1.3	0.736
49.9	2.117	99.7	1.237	15.2	0.734
99.7	2.096			30.1	0.732
				49.9	0.728
				69.8	0.725
T = 373.45 K		T = 398.33 K		T = 423.46 K
30.1	0.393	15.2	0.310	1.4	0.255
49.9	0.399	30.1	0.315	50.0	0.266
		49.9	0.321	69.8	0.272
T = 448.43 K
1.4	0.226
69.8	0.235
x = 0.0052
T = 274.87 K		T = 296.20 K		T = 323.30 K
15.2	2.194	15.2	1.264	30.1	0.732
		99.8	1.269	99.8	0.773
T = 373.36 K		T = 398.29 K		T = 423.45 K
15.3	0.391	15.3	0.316	15.3	0.260
30.2	0.403	30.2	0.321	50.0	0.269
50.0	0.410	69.9	0.334	69.9	0.273
T = 448.43 K
15.3	0.223
30.2	0.230
69.9	0.249
x = 0.0094
T = 296.24 K		T = 323.26 K		T = 373.23 K
15.2	1.277	15.3	0.737	30.2	0.410
30.1	1.281	50.0	0.757	50.0	0.419
		69.9	0.776
		99.8	0.793
T = 398.28 K		T = 423.42 K		T = 448.39 K
15.3	0.324	15.3	0.266	30.2	0.233
30.2	0.326	30.2	0.268	50.0	0.237
50.0	0.331	69.9	0.280	69.9	0.240
69.9	0.335	99.8	0.288
x = 0.0137
T = 274.93 K		T = 296.25 K		T = 323.21 K
15.2	2.298	30.0	1.297	30.1	0.759
30.1	2.293	99.7	1.327	49.9	0.771
69.7	2.275			99.7	0.804
T = 373.03 K		T = 398.28 K		T = 423.44 K
50.1	0.426	69.9	0.340	69.9	0.278
		99.7	0.371	99.7	0.292
T = 448.36 K
50.1	0.238
69.9	0.242
99.8	0.251

^{^a}

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the viscosity is u(η) = 0.015·η

6.2. Hypotheses

In analyzing the results, we wish to test the hypothesis that the influence of dissolved CO₂ on the density and viscosity of the brine solutions can be expressed in a way that is independent of both salt type and molality. Accordingly, in the following analysis, the terms pertaining to the effects of dissolved CO₂ will be identical with those determined earlier in connection with the (CO₂ + H₂O) system. (28)

We model the density according to the relation

(18)

where M_b = M_w(1 + mM_s)/(1 + mM_w) is the mean molar mass of the CO₂-free brine solution, M_w is the molar mass of water, M_s is the molar mass of salt, V_b = M_b/ρ_b is the molar volume of the CO₂-free brine, ρ_b is the brine density, M_CO₂ is the molar mass of CO₂, and V_CO₂ is the apparent molar volume of CO₂(aq). This last term was determined by McBride-Wright et al. for the (CO₂ + H₂O) system and correlated as a function of temperature and pressure as follows

(19)

the coefficients a_ij are reproduced in Table 10. (28) According to the hypothesis that we wish to test, the apparent molar volume CO₂(aq), V_CO₂, is identical with that determined in the (CO₂ + H₂O) system as represented by eq 19 and the coefficients in Table 10.

Table 10. Coefficients of Eq 19 for the Apparent Molar Volume of CO₂ in Aqueous Solution

a_0,0	a_1,0	a_2,0	a_0,1	a_1,1	a_2,1
51.19	–0.15575	3.2955 × 10^–4	–6.0708 × 10^–2	5.5026 × 10^–4	–1.2114 × 10^–6

In order to model the brine viscosity under CO₂ addition, we first require an accurate model for the viscosity of the CO₂-free brines as a function of temperature, pressure, and molality. To construct this, we first note the effect of pressure is generally very small for brine solutions and can be represented by a simple multiplicative factor such that

(20)

where

(21)

Here, κ_w is the viscosity pressure coefficient of pure water, which we take from Kestin and Shankland, (22) and κ^E is an excess pressure coefficient related to the salt type and molality, which we represent by the following three-parameter equation

(22)

We find that the Othmer model (43) provides a very effective means of correlating η₀(T,m). In this approach

(23)

where η_w(T) is the viscosity of pure saturated liquid water at temperature T, which we take from the IAPWS correlation. (44,45) The parameters A and B are expressed as cubic functions of molality for each brine system as follows

(24)

Finally, the viscosity of the CO₂-containing solution is given by

(25)

where the parameters e₁ and e₂ are identical to those determined previously for the (CO₂ + H₂O) system. (28) The nine parameters (A₁, A₂, A₃, B₁, B₂, B₃, c₁, c₂, and T₀) were determined by regression against the available literature data for the viscosity of NaCl and CaCl₂ brines. For NaCl, the parameters were fitted to the data of Kestin et al., (21,22) while for CaCl₂, we used the data of Abdulagatov and Azizov, (23) Isono, (24) Gonçalves and Kestin, (26) and Zhang et al. (27) (the data of Wahab and Mahiuddin (25) were found to be inconsistent with the other sources and were not used). Table 11 gives the parameters obtained for the two brine systems, together with the values of e₁ and e₂ determined previously. The correlations are valid for m ≤ 6 mol·kg^–1. The goodness of fit may be summarized by the average absolute relative deviation, defined as follows

(26)

where N is the total number of data points, η_i,exp is an experimental datum, and η_i,calc is the viscosity calculated from the model at the same state point. For the NaCl brines, N = 415 and Δ_AARD = 0.85% while, for CaCl₂ brines, N = 437 and Δ_AARD = 1.05%.

Table 11. Parameters in 20 for the Viscosity of CO₂–Brine Solutions

	NaCl	CaCl₂
A₁	8.6075 × 10^–2	2.6672 × 10^–1
A₂	2.3522 × 10^–3	1.1635 × 10^–2
A₃	3.5710 × 10^–4	5.7087 × 10^–4
B₁	–3.5198 × 10^–2	–7.2543 × 10^–2
B₂	5.4401 × 10^–3	2.0379 × 10^–2
B₃	–4.2694 × 10^–5	–7.8848 × 10^–4
c₁	–0.3974	–0.5511
c₂	0.6125	0.8314
T₀/K	142
e₁	65.560
e₂	2.468

The models presented for both density and viscosity are fully parameterized on the basis of independent data sources and are compared below with the present experimental data without further adjustment.

6.3. Density

Figure 6 shows the density as a function of mole fraction at constant pressure for the [xCO₂ + (1 – x)NaCl(aq)] system at a molality of 2.50 mol·kg^–1 and both the lowest and the highest temperatures investigated. Similarly, Figure 7 shows ρ(x) at constant p for the [xCO₂ + (1 – x)CaCl₂(aq)] system at m = 1.00 mol·kg^–1 for the lowest and highest temperatures. In these examples, and all other cases investigated, the density increases linearly with the mole fraction of CO₂. Plots of the molar volume V_m = M/ρ against x at constant T and p are also found to be linear functions of x such that

(27)

where A = V_b and B = (V_CO₂ – V_b). The linearity of these plots also implies that the apparent molar volume of CO₂(aq) is independent of x and, for practical purposes, practically identical with the partial molar volume at infinite dilution.

Figure 6. Densities ρ of [xCO₂ + (1 – x)NaCl(aq)] m = 2.50 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

Figure 7. Densities ρ of [xCO₂ + (1 – x)CaCl₂(aq)] with m = 1.00 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

In testing the hypothesis that the apparent molar volume of CO₂(aq) is independent of salt type and molality, we have evaluated the molar volume V_b of the CO₂-free brine from the correlation of Al Ghafri et al. (14) so that no parameters were fitted to the present data and a direct comparison was made between the experimental results and eq 18 with independent inputs for both V_b and V_CO₂. The correlation of Al Ghafri et al. (14) is strictly valid in the temperature range from (283 to 473) K at pressures up to 69 MPa and brine molalities up to 6.00 mol·kg^–1. However, for present purposes, we have extrapolated in temperature down to T = 275 K, and in pressure up to p = 100 MPa. The model represents the original experimental data upon which it was based to within ±0.25 kg·m^–3.

Figures 8 and 9 show the comparisons of our experimental data with the model for the [xCO₂ + (1 – x)NaCl(aq)] and [xCO₂ + (1 – x)CaCl₂(aq)] systems, respectively. These figures also include the densities at m = 0 reported previously. (28) Unsurprisingly, the model is in excellent agreement with the data at m = 0 because eq 19 was developed to fit those data. At finite salt molalities, there are small deviations within approximately ±2kg·m^–3 with absolute average relative deviations of 0.07% for the NaCl(aq) systems and 0.05% for the CaCl₂(aq) systems. From these comparisons, we conclude that the hypothesis that V_CO₂ is independent of salt type and molality is adequately confirmed.

Figure 8. Deviations Δρ = (ρ_exp – ρ_calc) between experimental densities ρ_exp of [xCO₂ + (1 – x)NaCl(aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of CO₂ mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg^–1; orange, m = 0.77 mol·kg^–1; green, m = 2.50 mol·kg^–1.

Figure 9. Deviations Δρ = (ρ_exp – ρ_calc) between experimental densities ρ_exp of [xCO₂ + (1 – x)CaCl₂ (aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of CO₂ mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg^–1; orange, m = 0.77 mol·kg^–1; green, m = 2.50 mol·kg^–1.

In Figure 10, we have shown the density of [xCO₂ + (1 – x)NaCl(aq)] reported by Yan et al. (16) and Song et al. (17) as deviations from our model as function of temperature, CO₂ mole fraction, and pressure. The results of Song et al. are plotted only for those states which, according to the solubility model of Spycher and Pruess, (46) are undersaturated with respect to CO₂. The literature data at NaCl molalities of (1 and 3) mol·kg^–3 mostly agree with our model to within ±1kg·m^–3 over all states, while those at molalities of 4 and 5 mol·kg^–1 tend to fall between (2 and 4) kg·m^–3 above the prediction of the model, although the data of Song et al. at m = 4 mol·kg^–1 only deviate by more than 1 kg·m^–3 at T = (393 and 413) K. It is notable that the deviations for each literature source and NaCl molality do not depend systematically upon either x or p. Yan et al. (16) calibrated their densimeter at each salt molality against the data of Rowe and Chou (47) and the observed deviations from our model at m = 5 mol·kg^–1 simply reflect the differences between the brine densities of Rowe and Chou and those of Al Ghafri et al. (14) used in this work. Overall, the agreement with the current model is quite satisfactory. The data of Nighswander et al. show much larger deviation from our model of between (4 and −27) kg·m^–3 and are not shown in Figure 10.

Figure 10. Deviations Δρ = (ρ_exp – ρ_calc) between experimental literature densities ρ_exp of [xCO₂ + (1 – x)NaCl(aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: □, Yan et al.; (16) ○, Song at al. (17) Colors indicate NaCl molality: red = 1 mol·kg^–1; green = 2 mol·kg^–1; blue = 3 mol·kg^–1; purple = 4 mol·kg^–1; orange = 5 mol·kg^–1.

6.4. Viscosity

Figures 11 and 12 illustrate the dependence of viscosity upon the mole fraction of dissolved CO₂ under conditions of constant temperature and pressure. The viscosity increases linearly and the slope is more pronounced at low temperature, as shown in Figure 11 where data for [xCO₂ + (1 – x)NaCl(aq)] are shown for the lowest and highest temperatures investigated. At the lowest temperature, addition of CO₂ to near saturation increases the viscosity of the mixture by just over 12%, whereas, at the highest temperature studied, the relative increment is just below 3%. Similar results are found for the viscosity of CaCl₂(aq) with molality of 1.00 mol·kg^–1. The hypothesis that we set out to investigate is that these slopes are the same as found in the (CO₂ + H₂O) system. To test this, we plot in Figure 13 the partial derivatives (∂ln η/∂x) determined in the (CO₂ + H₂O) system determined previously, (28) as well as the values determined from the present data at all states where three or more compositions were studied. Also shown is the same derivative according to eq 25: (∂ln η/∂x) = e₁ exp[−e₂(T/T₀ – 1)] with the parameters from Table 11. The data for (CO₂ + H₂O) were of course used to fit the parameters of the model and they follow eq 25 closely. The data for the two brine systems are more scattered and are generally larger than predicted by eq 25. The increased scatter reflects both the difficulty in measuring the viscosity of the brine solutions and the fact that the salting-out effect limits the amount of CO₂ that can be dissolved and hence restrict the precision with which the partial derivative (∂ln η/∂x) can be determined. The error bars show two standard deviations based on the linear regression statistics. From this graph, we conclude that the data do not strongly confirm our hypothesis.

Figure 11. Viscosities η of [xCO₂ + (1 – x)NaCl(aq)] with m = 0.77 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

Figure 12. Viscosities η of [xCO₂ + (1 – x)CaCl₂(aq)] with m = 1.00 mol·kg^–1 as a function of CO₂ mole fraction x at T = 373 K: ●, 30 MPa; ▲, 50 MPa. Solid lines are linear regression lines.

Figure 13. Partial derivative (∂ln η/∂x) of the natural logarithm of the viscosity η with respect to the mole fraction x of dissolved CO₂ as a function of temperature T: ●, CO₂ + H₂O; (28) ▲, CO₂ + NaCl(aq); ■, CO₂ + CaCl₂(aq). Solid line based on eq 25. Error bars show two standard deviations.

It is also notable that the viscosity increases linearly with increasing pressure at constant composition and temperature, except at T = 275 K where a linear decrease is observed. Figure 14 illustrates this decrement in the viscosity for the [xCO₂ + (1 – x)NaCl(aq)] system at T = 275 K. Similar behavior is observed for pure water. (45)

Figure 14. Viscosities η of [xCO₂ + (1 – x)NaCl(aq)] with m = 0.77 mol·kg^–1 as a function of pressure p at T = 275 K: ×, x = 0.000; ●, x = 0.0124; ▲, x = 0.0161. Solid lines are linear regression lines.

In Figure 15, we show the deviations of the present experimental viscosity results and of the literature data from eq 20 for the [xCO₂ + (1 – x)NaCl(aq)] system. Overall, the deviations of our data from the model are mostly within ±2% and we find Δ_AARD = 0.9%. Figure 15b shows that the deviations are essentially independent of x. Thus, while the individual slopes (∂ln η/∂x) at different state points do not conform very closely to eq 25, the overall prediction of viscosity in the CO₂–brine solutions is of good accuracy under our hypothesis. The dependence of viscosity upon the CO₂ mole fraction has also been reported in the literature for this system by Fleury and Deschamps, (20) Bando et al., (19) and Kumagai and Yokoyama. (18) Fleury and Deschamps (20) studied the effect of dissolved CO₂ on the viscosity of three NaCl(aq) systems, with salinities of (20, 80, and 160) g·L^–1, at T = 308.15 K and p = 8.5 MPa. Bando et al. (19) measured the viscosity of three different NaCl brines of mass fractions (0, 1, and 3) %, with dissolved CO₂ in a temperature range from (303.15 to 333.15) K and at pressures from (10 to 20) MPa. Kumagai and Yokoyama (18) measured the viscosity at temperatures between (273 and 278) K, and pressures up to 30 MPa, with CO₂ mole fractions up to 0.015. The results of Fleury and Deschamps (20) and Bando et al. (19) are in good agreement with eq 20, with most of the data within ±2% of the correlation. On the other hand, the data of Kumagai and Yokoyama (18) deviate increasingly with increasing CO₂ mole fraction and the absolute relative deviations reach about 6.5% at the highest values of x and p.

Figure 15. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp of [xCO₂ + (1 – x)NaCl(aq)], and viscosities η_calc calculated from eq 21 as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: ▲, this work; ◆, Kumagai and Yokoyama; (18) ●, Fleury and Deschamps; (20) *, Bando et al. (19)

Figure 16 shows the deviations of the present experimental viscosity results and of data from the literature from 20 for the [xCO₂ + (1 – x)CaCl₂(aq)] system. Overall, our data fall slightly below the model but the deviations, characterized by Δ_AARD = 2.3%, do not depend significantly on temperature, pressure, or the mole fraction of dissolved CO₂. Figure 16b, in particular, shows that in this system also the viscosity of the CO₂–brine solution is predicted adequately by the model. For this system, there are no published data for the brine viscosity with dissolved CO₂ and the comparison with literature is confined to x = 0. Viscosity data for CaCl₂(aq) solutions have been reported by Abdulagatov and Azizov, (23) Isono, (24) Wahab and Mahiuddin, (25) Gonçalves and Kestin, (26) and Zhang et al. (27) The study of Abdulagatov and Azizov (23) pertains to a molality of 2.00 mol·kg^–1 and is the only one that extends to high pressures (up to 60 MPa). In the case of Isono, (24) the measurements were made at atmospheric pressure, temperatures from (288.15 to 323.15) K, and molalities up to 6.00 mol·kg^–1. Wahab and Mahiuddin (25) studied the viscosity of pure CaCl₂(aq) at atmospheric pressure, temperatures from (273.15 to 323.15) K, and molalities up to 7.15 mol·kg^–1. Gonçalves and Kestin (26) covered a temperature range from (293.15 to 323.15) K, molalities up to 6.00 mol·kg^–1, and atmospheric pressure. Zhang et al. (27) performed measurements at the single temperature of 298.15 K and a pressure of 0.1 MPa with molalities up 7.88 mol·kg^–1. The viscosities measured by Abdulagatov and Azizov, (23) Isono, (24,25) Gonçalves and Kestin, (26) and Zhang et al. (27) are mostly represented by eq 21 to within ±2%, while those of Wahab and Mahiuddin (25) exhibit deviations that increase with temperature to around 4%. Overall, the observed agreement with the model is good.

Figure 16. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp of [xCO₂ + (1 – x)CaCl₂(aq)], and viscosities η_calc calculated from eq 21 as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: ▲, this work; ▲, Isono; (24) ●, Wahab and Mahiuddin; (25) ◆, Gonçalves and Kestin; (26) *, Zhang et al.; (27) +, Abdulagatov and Azizov. (23)

7. Conclusions

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A new semi-empirical working equation has been developed and validated for determining the viscosity of highly conductive fluids using the VW technique. This equation accounts for the conductivity of the fluid, and we note that large errors result if this factor is ignored. Viscosity and density measurements are reported for compositionally characterized homogeneous aqueous solutions of CO₂ and either NaCl or CaCl₂ at temperatures from (275 to 449) K, pressures up to 100 MPa, and salt molalities of 0.77 and 1.00 mol·kg^–1 for NaCl and CaCl₂, respectively. Additional density measurements were also made for both brines with dissolved CO₂ at salt molalities of m = 2.50 mol·kg^–1 in the same temperature and pressure ranges. The expanded relative uncertainties at 95% confidence are 0.07% for density, and 3% for viscosity.

These data were used to test the hypothesis that the influences of dissolved CO₂ is sensibly independent of salt type and molality. The density data were found to support this hypothesis clearly. For viscosity, the situation is less clear but, overall, the viscosity data could be represented well as a function of temperature, pressure, and CO₂ mole fraction by a correlation based on literature data for CO₂-free brines and a term to account for dissolved CO₂ developed previously for the (CO₂ + H₂O) system. This correlation is able to represent our experimental data with average absolute relative deviations of 0.9% for [CO₂ + NaCl(aq)] and 2.3% for [CO₂ + CaCl₂(aq)]. Satisfactory agreement was also observed with the available literature data.

For modeling the density of the (CO₂ + brine) systems, an equation based on the partial molar volume of CO₂ has been used. The latter has been correlated in terms of temperature and pressure, from the bubble pressure up to 100 MPa, and from (275 to 449) K. This equation was able to represent the experimental densities for the [CO₂ + NaCl(aq)] systems with an absolute average relative deviation of 0.07%, while the maximum absolute relative deviation was 0.31%; the corresponding figures for the [CO₂ + CaCl₂(aq)] systems were 0.05 and 0.30%, respectively. The experimental densities of the CO₂-free brine solutions were in good agreement with the current available literature data.

The equations given in this paper, along with a model for the solubility of CO₂, can be used to obtain both the viscosity and density of aqueous solutions containing both CO₂ and either NaCl or CaCl₂ over the ranges of temperature and pressure investigated, up to the CO₂ saturation limit. The model is also expected to be reliable for higher salt molalities but the salting-out effect means that the amount of CO₂ that can be dissolved in highly concentrated brines is very small, so that the effect of CO₂ saturation will diminish rapidly with increasing salinity.

Author Information

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Corresponding Author
- J. P. Martin Trusler - Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.; http://orcid.org/0000-0002-6403-2488; Email: [email protected]
Authors
- Claudio Calabrese - Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
- Mark McBride-Wright - Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
- Geoffrey C. Maitland - Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
Notes
The authors declare no competing financial interest.

Acknowledgments

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This work was carried out as part of the Qatar Carbonates and Carbon Storage Research Centre (QCCSRC). We gratefully acknowledge the funding of QCCSRC provided jointly by Qatar Petroleum, Shell, and the Qatar Science & Technology Park, and for supporting the present project, and the permission to publish this research.

References

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Combination of column adsorption and supercritical fluid extraction for recovery of dissolved essential oil from distillation waste water of Yulania liliiflora
Lei, Gaoming; Mao, Peizhi; He, Minqing; Wang, Longhu; Liu, Xuesong; Zhang, Anyun
Journal of Chemical Technology and Biotechnology (2016), 91 (6), 1896-1904CODEN: JCTBED; ISSN:0268-2575. (John Wiley & Sons Ltd.)
Arom. waste water is the main byproduct of industrial essential oil distn. To recover the dissolved essential oil from this distn. waste water, an approach combining column adsorption (CA) and supercrit. fluid extn. (SFE) was proposed. Yulania liliiflora was selected as a case study. Activated carbon of mixed porosity was employed and quant. desorption of the adsorbed oil was achieved using supercrit. carbon dioxide (SC-CO2). The optimized condition of CA-SFE was 18 MPa, 308 K, dynamic extn. for 60 min and CO2 flow rate of 3.6 g min-1. A recovery of 0.668 ± 0.050 g kg-1 (n = 3) was achieved for the dissolved oil from distn. waste water, significantly higher (P < 0.05) than that obtained by liq.-liq. extn. (LLE) (0.405 ± 0.032 g kg-1, n = 3). Yulania liliiflora recovered oil was rich in eucalyptol (52.6-55.2%), α-terpineol (15.2-18.1%) and terpinen-4-ol (8.1-8.7%). The CA-SFE approach is highly efficient and esp. suitable for large-scale application. The recovered essential oil is valued for being rich in organoleptically important and biol. active compds. © 2015 Society of Chem. Industry.
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Arif, M.; Barifcani, A.; Lebedev, M.; Iglauer, S. CO₂-Wettability of Low to High Rank Coal Seams: Implications for Carbon Sequestration and Enhanced Methane Recovery. Fuel 2016, 181, 680– 689, DOI: 10.1016/j.fuel.2016.05.053
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CO2-wettability of low to high rank coal seams: Implications for carbon sequestration and enhanced methane recovery
Arif, Muhammad; Barifcani, Ahmed; Lebedev, Maxim; Iglauer, Stefan
Fuel (2016), 181 (), 680-689CODEN: FUELAC; ISSN:0016-2361. (Elsevier Ltd.)
Coal seams offer tremendous potential for carbon geo-sequestration with the dual benefit of enhanced methane recovery. In this context, it is essential to characterize the wettability of the coal-CO2-water system as it significantly impacts CO2 storage capacity and methane recovery efficiency. Tech., wettability is influenced by reservoir pressure, coal seam temp., water salinity and coal rank. Thus a comprehensive investigation of the impact of the aforementioned parameters on CO2-wettability is crucial in terms of storage site selection and predicting the injectivity behavior and assocd. fluid dynamics. To accomplish this, we measured advancing and receding water contact angles using the pendent drop tilted plate technique for coals of low, medium and high ranks as a function of pressure, temp. and salinity and systematically investigated the assocd. trends. We found that high rank coals are strongly CO2-wet, medium rank coals are weakly CO2-wet, and low rank coals are intermediate-wet at typical storage conditions. Further, we found that CO2-wettability of coal increased with pressure and salinity and decreased with temp. irresp. of coal rank. We conclude that at a given reservoir pressure, high rank coal seams existing at low temp. are potentially more efficient with respect to CO2-storage and enhanced methane recovery due to increased CO2-wettability and thus increased adsorption trapping.
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Elsharkawy, A. M.; Poettmann, F. H.; Christiansen, R. L. Measuring Minimum Miscibility Pressure: Slim-Tube or Rising-Bubble Method?. SPE/DOE Enhanced Oil Recovery Symposium, 1992 Copyright 1992; Soc Petrol Eng Inc.: Tulsa, Oklahoma, 1992.
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Jaubert, J.-N.; Avaullee, L.; Pierre, C. Is It Still Necessary to Measure the Minimum Miscibility Pressure?. Ind. Eng. Chem. Res. 2002, 41, 303– 310, DOI: 10.1021/ie010485f
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Is It Still Necessary to Measure the Minimum Miscibility Pressure?
Jaubert, Jean-Noeel; Avaullee, Laurent; Pierre, Christophe
Industrial & Engineering Chemistry Research (2002), 41 (2), 303-310CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Gas injection processes are among the most effective methods for enhanced oil recovery. A key parameter in the design of a gas injection project is the min. miscibility pressure (MMP), the pressure at which the local displacement efficiency approaches 100%. From an exptl. point of view, the MMP is routinely detd. by slim tube displacements. However, because such expts. are very expensive (time-consuming), the question the authors want to answer in this article is as follows: Is this still necessary to measure the MMP. May other quicker, easier and cheaper gas injection expts. such as swelling test or multicontact test (MCT) substitute for slim tube test. This paper concludes that when the injected gas is not pure CO2 (and probably not pure N2 or pure H2S), it is enough to fit only two parameters of the equation of state on data including classical PVT data + swelling data + MCT data and then to predict the MMP. The accuracy obtained is similar to the exptl. uncertainty. It is thus possible to conclude that the slim tube test may be replaced by swelling tests and MCT, which are much cheaper.
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Neau, E.; Avaullée, L.; Jaubert, J. N. A New Algorithm for Enhanced Oil Recovery Calculations. Fluid Phase Equilib. 1996, 117, 265– 272, DOI: 10.1016/0378-3812(95)02962-1
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A new algorithm for enhanced oil recovery calculations
Neau, E.; Avaullee, L.; Jaubert, J. N.
Fluid Phase Equilibria (1996), 117 (1-2), 265-72CODEN: FPEQDT; ISSN:0378-3812. (Elsevier)
A method was proposed to calc. directly the min. miscibility pressure (MMP) in gas-injection enhanced petroleum recovery. The procedure consists of detg. directly the mechanism taking place (condensation or vaporization), and performing successive contacts (backward or forward) between a crude petroleum and an injection gas. Special efforts were devoted to decreasing the time of calcn. using optimal mixing proportions and a function (λp) that was esp. efficient at pressures close to the MMP. Moreover, when λp is a strictly increasing function of the contact no., a neg. flash algorithm was used. The continuous evolution of the estd. MMP in the case of the enrichment of an injection gas with a solvent illustrated the efficiency of the proposed method.
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Koottungal, L. General Interest: 2012 Worldwide EOR Survey. Oil Gas J. 2012, 110, 57– 69
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Houghton, J. T.; Ding, Y.; Griggs, D. J.; Noguer, M.; Linden, P. J. v. d.; Dai, X.; Maskell, K.; Johnson, C. A. Climate Change 2001: The Scientific Basis; Cambridge University Press: Cambridge, 2001.
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Saadatpoor, E.; Bryant, S. L.; Sepehrnoori, K. New Trapping Mechanism in Carbon Sequestration. Transp. Porous Media 2010, 82, 3– 17, DOI: 10.1007/s11242-009-9446-6
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New Trapping Mechanism in Carbon Sequestration
Saadatpoor, Ehsan; Bryant, Steven L.; Sepehrnoori, Kamy
Transport in Porous Media (2010), 82 (1), 3-17CODEN: TPMEEI; ISSN:0169-3913. (Springer)
The modes of geol. storage of CO2 are usually categorized as structural, dissoln., residual, and mineral trapping. Here we argue that the heterogeneity intrinsic to sedimentary rocks gives rise to a fifth category of storage, which we call local capillary trapping. Local capillary trapping occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer. When the rising CO2 plume encounters a region (10-2 to 10+1m) where capillary entry pressure is locally larger than av., CO2 accumulates beneath the region. This form of storage differs from structural trapping in that much of the accumulated satn. will not escape, should the integrity of the seal overlying the aquifer be compromised. Local capillary trapping differs from residual trapping in that the accumulated satn. can be much larger than the residual satn. for the rock. We examine local capillary trapping in a series of numerical simulations. The essential feature is that the drainage curves (capillary pressure vs. satn. for CO2 displacing brine) are required to be consistent with permeabilities in a heterogeneous domain. In this work, we accomplish this with the Leverett J-function, so that each grid block has its own drainage curve, scaled from a ref. curve to the permeability and porosity in that block. We find that capillary heterogeneity controls the path taken by rising CO2. The displacement front is much more ramified than in a homogeneous domain, or in a heterogeneous domain with a single drainage curve. Consequently, residual trapping is overestimated in simulations that ignore capillary heterogeneity. In the cases studied here, the redn. in residual trapping is compensated by local capillary trapping, which yields larger saturations held in a smaller vol. of pore space. Moreover, the amt. of CO2 phase remaining mobile after a leak develops in the caprock is smaller. Therefore, the extent of immobilization in a heterogeneous formation exceeds that reported in previous studies of buoyancy-driven plume movement.
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Burton, M.; Kumar, N.; Bryant, S. L. CO₂ Injectivity into Brine Aquifers: Why Relative Permeability Matters as Much as Absolute Permeability. Energy Procedia 2009, 1, 3091– 3098, DOI: 10.1016/j.egypro.2009.02.089
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CO2 injectivity into brine aquifers: why relative permeability matters as much as absolute permeability
Burton, McMillan; Kumar, Navanit; Bryant, Steven L.
Energy Procedia (2009), 1 (1), 3091-3098CODEN: EPNRCV; ISSN:1876-6102. (Elsevier)
For economic reasons operators of geol. storage projects are likely to inject CO2 at the largest possible rates into the smallest no. of wells. Thus a typical CO2 injection well is likely to run at the largest bottomhole pressure that is safe. Operators will also tend to prefer thicker, higher permeability target formations. However, a const.-pressure well exhibits a varying rate of CO2 injection for two reasons: classical multiphase flow effects, and long-term injection of CO2 removes water from the near-wellbore region. Drying ppts. dissolved salts, so the permeability of the dry rock need not equal the initial aquifer permeability. Mobility of CO2 in the dried rock and mobility of CO2 and brine the two-phase flow region det. the variation of injectivity with vol. of CO2 injected. We find a four-fold variation in injectivity when seven different CO2/brine relative permeability curves (Bennion and Bachu) are used, holding all other reservoir parameters the same. Since the product of formation permeability and formation thickness is relatively easy to measure, once a well has been drilled, uncertainty in relative permeability will therefore be a large contribution to uncertainty in achievable rates in CO2 storage projects. We develop anal. expressions for the injectivity variation in terms of phase mobilities and the speeds of satn. fronts. Classical theory (Buckley-Leverett) does not account for the drying front; using only Buckley-Leverett yields both quant. and qual. errors. The expressions are consistent with detailed reservoir simulations using com. software (CMG's GEM) that account for the full physics and complete phase behavior. The expressions can refine the estd. no. of wells needed for a target overall injection rate. This anal. also enables an operator to assess the value of retrieving core and measuring relative permeability in a prospective storage target.
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Benson, S. M.; Cole, D. R. CO₂ Sequestration in Deep Sedimentary Formations. Elements 2008, 4, 325– 331, DOI: 10.2113/gselements.4.5.325
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CO2 sequestration in deep sedimentary formations
Benson, Sally M.; Cole, David R.
Elements (Chantilly, VA, United States) (2008), 4 (5), 325-331CODEN: EOOCAG; ISSN:1811-5209. (Mineralogical Society of America)
A review. Carbon dioxide capture and sequestration (CCS) in deep geol. formations has recently emerged as an important option for reducing greenhouse emissions. If CCS is implemented on the scale needed to make noticeable redns. in atm. CO2, a billion metric tons or more must be sequestered annually-a 250 fold increase over the amt. sequestered today. Securing such a large vol. will require a solid scientific foundation defining the coupled hydrol.-geochem.-geomech. processes that govern the long-term fate of CO2 in the subsurface. Also needed are methods to characterize and select sequestration sites, subsurface engineering to optimize performance and cost, approaches to ensure safe operation, monitoring technol., remediation methods, regulatory overview, and an institutional approach for managing long-term liability.
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Pau, G. S. H.; Bell, J. B.; Pruess, K.; Almgren, A. S.; Lijewski, M. J.; Zhang, K. High-Resolution Simulation and Characterization of Density-Driven Flow in CO₂ Storage in Saline Aquifers. Adv. Water Resour. 2010, 33, 443– 455, DOI: 10.1016/j.advwatres.2010.01.009
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High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers
Pau, George S. H.; Bell, John B.; Pruess, Karsten; Almgren, Ann S.; Lijewski, Michael J.; Zhang, Keni
Advances in Water Resources (2010), 33 (4), 443-455CODEN: AWREDI; ISSN:0309-1708. (Elsevier Ltd.)
Simulations are routinely used to study the process of carbon dioxide (CO2) sequestration in saline aquifers. In this paper, we describe the modeling and simulation of the dissoln.-diffusion-convection process based on a total velocity splitting formulation for a variable-d. incompressible single-phase model. A second-order accurate sequential algorithm, implemented within a block-structured adaptive mesh refinement (AMR) framework, is used to perform high-resoln. studies of the process. We study both the short-term and long-term behaviors of the process. It is found that the onset time of convection follows closely the prediction of linear stability anal. In addn., the CO2 flux at the top boundary, which gives the rate at which CO2 gas dissolves into a neg. buoyant aq. phase, will reach a stabilized state at the space and time scales we are interested in. This flux is found to be proportional to permeability, and independent of porosity and effective diffusivity, indicative of a convection-dominated flow. A 3D simulation further shows that the added degrees of freedom shorten the onset time and increase the magnitude of the stabilized CO2 flux by about 25%. Finally, our results are found to be comparable to results obtained from TOUGH2-MP.
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Homsy, G. M. Viscous Fingering in Porous Media. Annual Review; Fluid Mechanics: Stanford, 1987; pp 271– 311.
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Al Ghafri, S.; Maitland, G. C.; Trusler, J. P. M. Densities of Aqueous MgCl₂(Aq), CaCl₂(Aq), KI(Aq), NaCl(Aq), KCl(Aq), AlCl₃(Aq), and (0.864 NaCl + 0.136 KCl)(Aq) at Temperatures between (283 and 472) K, Pressures up to 68.5 MPa, and Molalities up to 6 mol.kg^-1. J. Chem. Eng. Data 2012, 57, 1288– 1304, DOI: 10.1021/je2013704
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Densities of Aqueous MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), KCl(aq), AlCl3(aq), and (0.964 NaCl + 0.136 KCl)(aq) at Temperatures Between (283 and 472) K, Pressures up to 68.5 MPa, and Molalities up to 6 mol/kg-1
Al Ghafri, Saif; Maitland, Geoffrey C.; Trusler, J. P. Martin
Journal of Chemical & Engineering Data (2012), 57 (4), 1288-1304CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
We report the densities of MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), KCl(aq), AlCl3(aq), and the mixed salt system [(1 - x)NaCl + xKCl](aq), where x denotes the mole fraction of KCl, at temps. between (283 and 472) K and pressures up to 68.5 MPa. The molalities at which the solns. were studied were (1.00, 3.00, and 5.00) mol/kg-1 for MgCl2(aq), (1.00, 3.00, and 6.00) mol/kg-1 for CaCl2(aq), (0.67, 0.90, and 1.06) mol/kg-1 for KI(aq), (1.06, 3.16, and 6.00) mol/kg-1 for NaCl(aq), (1.06, 3.15, and 4.49) mol/kg-1 for KCl(aq), (1.00 and 2.00) mol/kg-1 for AlCl3(aq), and (1.05, 1.98, 3.15, and 4.95) mol/kg-1 for [(1 - x)NaCl + xKCl](aq), with x = 0.136. The measurements were performed with a vibrating-tube densimeter calibrated under vacuum and with pure water over the full ranges of pressure and temp. investigated. An anal. of uncertainties shows that the relative uncertainty of d. varies from 0.03% to 0.05% depending upon the salt and the molality of the soln. An empirical correlation is reported that represents the d. for each brine system as a function of temp., pressure, and molality with abs. av. relative deviations of approx. 0.02%. Comparing the model with a large database of results from the literature, we find abs. av. relative deviations of 0.03%, 0.06%, 0.04%, 0.02%, and 0.02% for the systems MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), and KCl(aq), resp. The model can be used to calc. d., apparent molar volume, and isothermal compressibility over the full ranges of temp., pressure, and molality studied in this work. An ideal mixing rule for the d. of a mixed electrolyte soln. was tested against our mixed salt data and was found to offer good predictions at all conditions studied with an abs. av. relative deviation of 0.05%.
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Nighswander, J. A.; Kalogerakis, N.; Mehrotra, A. K. Solubilities of Carbon Dioxide in Water and 1 Wt. % Sodium Chloride Solution at Pressures up to 10 MPa and Temperatures from 80 to 200 °C. J. Chem. Eng. Data 1989, 34, 355– 360, DOI: 10.1021/je00057a027
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Solubilities of carbon dioxide in water and 1 wt. % sodium chloride solution at pressures up to 10 MPa and temperatures from 80 to 200°C
Nighswander, John A.; Kalogerakis, Nicolas; Mehrotra, Anil K.
Journal of Chemical and Engineering Data (1989), 34 (3), 355-60CODEN: JCEAAX; ISSN:0021-9568.
Exptl. gas soly. data for the CO2-water and CO2-1 wt. % NaCl soln. binary systems are reported. Measurements were made at ≤10 MPa and 80-200°. A thermodn. model of these systems is also presented. The model employs the D. Peng-D. Robinson (1976) equation of state to represent the vapor phase and an empirical Henry's law const. correlation for the liq. phase. It is shown that the salting-out effect of the 1 wt. % NaCl soln. on CO2 soly. is small. Also described is a new exptl. app. consisting of a variable-vol. equil. cell enclosed in a const. temp. controlled oven and the procedure used in conducting the expts.
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Yan, W.; Huang, S.; Stenby, E. H. Measurement and Modeling of CO₂ Solubility in NaCl Brine and CO₂-Saturated NaCl Brine Density. Int. J. Greenhouse Gas Control 2011, 5, 1460– 1477, DOI: 10.1016/j.ijggc.2011.08.004
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Measurement and modeling of CO2 solubility in NaCl brine and CO2-saturated NaCl brine density
Yan, Wei; Huang, Shengli; Stenby, Erling H.
International Journal of Greenhouse Gas Control (2011), 5 (6), 1460-1477CODEN: IJGGBW; ISSN:1750-5836. (Elsevier Ltd.)
Phase equil. for CO2-NaCl brine is of general interest to many scientific disciplines and tech. areas. The system is particularly important to CO2 sequestration in deep saline aquifers and CO2 enhanced oil recovery, two techniques discussed intensively in recent years due to the concerns over climate change and energy security. This work is an exptl. and modeling study of two fundamental properties in high pressure CO2-NaCl brine equil., i.e., CO2 soly. in NaCl brine and CO2-satd. NaCl brine d. A literature review of the available data was presented first to illustrate the necessity of exptl. measurements of the two properties at high pressures. An exptl. method for measuring high pressure CO2 soly. in NaCl brine was then developed. With the method, CO2 solubilities in 0, 1, and 5 m NaCl brines were measured at 323, 373, and 413 K from 5 to 40 MPa. The corresponding d. data at the same conditions were also measured. For soly., two models used in the Eclipse simulator were tested: the correlations of Chang et al. and the Soreide and Whitson equation of state (EoS) model. The latter model was modified to improve its performance for high salinity brine. In the d. modeling, the correlations of Chang et al., Garcia's correlation, and five different EoS models were tested. Among these models, Garcia's correlation and the ePC-SAFT EoS generally give satisfactory agreement with the exptl. measurements. An anal. was also made to show that dissoln. of CO2 increases the brine d. only if the apparent mass d. of CO2 in brine is higher than the brine d. at the same conditions.
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Song, Y.; Zhan, Y.; Zhang, Y.; Liu, S.; Jian, W.; Liu, Y.; Wang, D. Measurements of CO₂-H₂O-NaCl Solution Densities over a Wide Range of Temperatures, Pressures, and NaCl Concentrations. J. Chem. Eng. Data 2013, 58, 3342– 3350, DOI: 10.1021/je400459y
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Measurements of CO2-H2O-NaCl Solution Densities over a Wide Range of Temperatures, Pressures, and NaCl Concentrations
Song, Yongchen; Zhan, Yangchun; Zhang, Yi; Liu, Shuyang; Jian, Weiwei; Liu, Yu; Wang, Dayong
Journal of Chemical & Engineering Data (2013), 58 (12), 3342-3350CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The d. of carbon dioxide + brine soln. under supercrit. conditions is a significant parameter for CO2 sequestration into deep saline formations. This paper has extended our previous study on d. measurements of CO2 + Tianjin brine to the CO2-H2O-NaCl soln. by using a magnetic suspension balance (MSB). The measurements were performed in the pressure range (10 MPa to 18 MPa) at a range of temps. (60 C to 140 C) with different concns. of NaCl (CNaCl = 1 mol·kg-1, 2 mol·kg-1, 3 mol·kg-1, 4 mol·kg-1) and different CO2 mass fractions (w = 0, 0.01, 0.02, 0.03). The effects of pressure, temp., CO2 mass fractions and NaCl concn. on the CO2-H2O-NaCl soln. d. were analyzed. The CO2-H2O-NaCl soln. d. increased almost linearly with an increase in the CO2 mass fraction when the NaCl concn. was less than 4 mol·kg-1 and the temp. was lower than 120 C. However, at a high concn. of NaCl (CNaCl = 4 mol·kg-1), the d. decreased with increasing mass fraction of CO2 when the temp. was over 120 C. The d. of the CO2-H2O-NaCl soln. with a high NaCl concn. decreased after dissolving CO2 at high temps., which caused the soln. to float over the saline layer and increased the risk of CO2 leakage. An empirical model was established to predict the soln. d. with high accuracy.
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Kumagai, A.; Yokoyama, C. Viscosities of Aqueous NaCl Solutions Containing CO₂ at High Pressures. J. Chem. Eng. Data 1999, 44, 227– 229, DOI: 10.1021/je980178p
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Viscosities of Aqueous NaCl Solutions Containing CO2 at High Pressures
Kumagai, Akibumi; Yokoyama, Chiaki
Journal of Chemical and Engineering Data (1999), 44 (2), 227-229CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
Viscosity measurements of aq. NaCl solns. contg. CO2 along three isotherms at 273 K, 276 K, and 278 K at pressures up to 30 MPa are reported. The measurements have been carried out within a falling capillary type viscometer and have an estd. uncertainty of ±0.8%. The exptl. values were correlated in terms of pressure, temp., and concns. of NaCl and CO2. The correlation reproduces the exptl. values to within ±1.3%.
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Bando, S.; Takemura, F.; Nishio, M.; Hihara, E.; Akai, M. Viscosity of Aqueous NaCl Solutions with Dissolved CO₂ at (30 to 60) °C and (10 to 20) MPa. J. Chem. Eng. Data 2004, 49, 1328– 1332, DOI: 10.1021/je049940f
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Viscosity of Aqueous NaCl Solutions with Dissolved CO2 at (30 to 60) °C and (10 to 20) MPa
Bando, Shigeru; Takemura, Fumio; Nishio, Masahiro; Hihara, Eiji; Akai, Makoto
Journal of Chemical and Engineering Data (2004), 49 (5), 1328-1332CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The viscosity of aq. NaCl solns. with dissolved CO2 was measured at conditions representing an underground aquifer at a depth of (1000 to 2000) m for the geol. storage of CO2 (i.e., (30 to 60) °C and (10 to 20) MPa at a mass fraction of NaCl between 0 and 0.03 by using a sedimenting solid particle type viscometer with an estd. uncertainty of ± 2 %). On the basis of this exptl. data, an empirical equation for predicting this viscosity as a function of the temp. and mole fraction of CO2 for these conditions was derived.
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Fleury, M.; Deschamps, H. Electrical Conductivity and Viscosity of Aqueous NaCl Solutions with Dissolved CO₂. J. Chem. Eng. Data 2008, 53, 2505– 2509, DOI: 10.1021/je8002628
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Electrical Conductivity and Viscosity of Aqueous NaCl Solutions with Dissolved CO2
Fleury, Marc; Deschamps, Herve
Journal of Chemical & Engineering Data (2008), 53 (11), 2505-2509CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The effect of dissolved CO2 on the elec. cond. and viscosity of three NaCl solns. covering the range of salinity usually encountered in potential CO2 storage geol. formations has been studied. At a const. temp. of 35 °C, the variations of cond. and viscosity are proportional to the mole fraction of dissolved CO2. For viscosity, the data obtained are in agreement with previous observations. The obsd. variations are small and are at max. on the order of 10 %. The variations of cond. and viscosity as a function of temp. up to 100 °C are not modified by the presence of CO2. A simple model is proposed to take into account the small modifications of cond. and viscosity as a function of the dissolved CO2 mole fraction and temp.
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Kestin, J.; Khalifa, H. E.; Correia, R. J. Tables of the Dynamic and Kinematic Viscosity of Aqueous NaCl Solutions in the Temperature Range 20–150°C and the Pressure Range 0.1–35 MPa. J. Phys. Chem. Ref. Data 1981, 10, 71– 88, DOI: 10.1063/1.555641
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Tables of the dynamic and kinematic viscosity of aqueous sodium chloride solutions in the temperature range 20-150°C and the pressure range 0.1-35 MPa
Kestin, Joseph; Khalifa, H. Ezzat; Correia, Robert J.
Journal of Physical and Chemical Reference Data (1981), 10 (1), 71-87CODEN: JPCRBU; ISSN:0047-2689.
Tabulated values of the dynamic and kinematic viscosity of aq. NaCl solns. are given. The tables cover the temp. range 20-150 °C, the pressure range 0.1-35 MPa and the concn. range 0-6 m. The accuracy of the tabulated values is ±0.5%. The correlating equations from which the tables were generated are given.
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Kestin, J.; Shankland, I. R. Viscosity of Aqueous NaCl Solutions in the Temperature Range 25–200 °C and in the Pressure Range 0.1–30 MPa. Int. J. Thermophys. 1984, 5, 241– 263, DOI: 10.1007/bf00507835
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Viscosity of aqueous sodium chloride solutions in the temperature range 25-200°C and in the pressure range 0.1-30 MPa
Kestin, J.; Shankland, I. R.
International Journal of Thermophysics (1984), 5 (3), 241-63CODEN: IJTHDY; ISSN:0195-928X.
New precise viscosity data are presented for aq. solns. of NaCl (0-6 mol/kg) at 25-200° and 0.1-30 MPa. The exptl. precision is ±0.5%; a comparison of the present results with data available in the literature indicated that the accuracy of the present data is also of the order of ±0.5%. Two empirical correlations that reproduce the data within the precision are given.
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Abdulagatov, I. M.; Azizov, N. D. Viscosity of Aqueous Calcium Chloride Solutions at High Temperatures and High Pressures. Fluid Phase Equilib. 2006, 240, 204– 219, DOI: 10.1016/j.fluid.2005.12.036
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Viscosity of aqueous calcium chloride solutions at high temperatures and high pressures
Abdulagatov, I. M.; Azizov, N. D.
Fluid Phase Equilibria (2006), 240 (2), 204-219CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
Viscosity of 6 (0.10, 0.33, 0.65, 0.97, 1.40, and 2.00) mol kg-1 binary aq. CaCl2 solns. was measured with a capillary-flow technique. Measurements were made at pressures ≤60 MPa. The range of temp. was from 293-575 K. The total uncertainty of viscosity, pressure, temp., and compn. measurements was estd. to be <1.6%, 0.05%, 15 mK, and 0.014%, resp. The effect of temp., pressure, and concn. on viscosity of binary aq. CaCl2 solns. was studied. The measured values of viscosity of CaCl2(aq) were compared with data, predictions, and correlations reported in the literature. The temp. and pressure coeffs. of viscosity of CaCl2(aq) were studied as a function of concn. and temp. The viscosity data were interpreted in terms of the extended Jones-Dole equation for the relative viscosity (η/η0) to accurate calc. the values of viscosity A- and B-coeffs. as a function of temp. The derived values of the viscosity B-coeffs. were compared with the values calcd. from the ionic B-coeff. data. The phys. meaning parameters V and E in the abs. rate theory of viscosity and hydrodynamic molar volume (effective rigid molar volume of salt) Vk were calcd. using present exptl. viscosity data. TTG model was used to compare predicted values of the viscosity of CaCl2(aq) solns. with exptl. values at high pressures.
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Isono, T. Density, Viscosity, and Electrolytic Conductivity of Concentrated Aqueous Electrolyte Solutions at Several Temperatures. Alkaline-Earth Chlorides, LaCl₃, Na₂SO₄, NaNO₃, NaBr, KNO₃, KBr, and Cd(NO₃)₂. J. Chem. Eng. Data 1984, 29, 45– 52, DOI: 10.1021/je00035a016
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Density, viscosity, and electrolytic conductivity of concentrated aqueous electrolyte solutions at several temperatures. Alkaline-earth chlorides, lanthanum chloride, sodium chloride, sodium nitrate, sodium bromide, potassium nitrate, potassium bromide, and cadmium nitrate
Isono, Toshiaki
Journal of Chemical and Engineering Data (1984), 29 (1), 45-52CODEN: JCEAAX; ISSN:0021-9568.
The ds., viscosities, and electrolytic conductivities of concd. aq. solns. of alk. earth chlorides, LaCl3, Na2SO4, NaNO3, NaBr, KNO3, KBr, and Cd(NO3)2 were measured at 15-55°. Temp. dependences of these properties are represented in terms of their thermal coeffs. at 25°.
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Wahab, A.; Mahiuddin, S. Isentropic Compressibility and Viscosity of Aqueous and Methanolic Calcium Chloride Solutions. J. Chem. Eng. Data 2001, 46, 1457– 1463, DOI: 10.1021/je010072l
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Isentropic Compressibility and Viscosity of Aqueous and Methanolic Calcium Chloride Solutions
Wahab, Abdul; Mahiuddin, Sekh
Journal of Chemical and Engineering Data (2001), 46 (6), 1457-1463CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
Speeds of sound and viscosities of aq. and methanolic calcium chloride solns. were measured as functions of concn. [0.0040 ≤ m/(mol·kg-1) ≤ 7.151 and 0.1903 ≤ m/(mol·kg-1) ≤ 3.252 for aq. and methanolic calcium chloride solns., resp.] and temp. (273.15 ≤ T/K ≤ 323.15). Isentropic compressibility isotherms of aq. calcium chloride solns. converge at 5.1 mol·kg-1. In the case of methanolic calcium chloride solns., isentropic compressibility isotherms vary smoothly with the increase in concn. and converge at 5.66 mol·kg-1 on extrapolation. Total solvation nos. of calcium chloride in water and methanol media were estd. to be 10.9 and 5.5, resp.
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Gonçalves, F. A.; Kestin, J. The Viscosity of CaCl₂ Solutions in the Range 20–50°C. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 24– 27, DOI: 10.1002/bbpc.19790830105
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The viscosity of calcium chloride solutions in the range 20-50°C
Goncalves, F. A.; Kestin, J.
Berichte der Bunsen-Gesellschaft (1979), 83 (1), 24-7CODEN: BBPCAX; ISSN:0005-9021.
The measurements at atm. pressure covered the entire range of compns. up to satn. The reproducibility was several parts per 10,000, and the accuracy ≤0.3%. An accurate correlation between molality and d. was obtained for 20.00 and 25.00°.
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Zhang, H.-L.; Chen, G.-H.; Han, S.-J. Viscosity and Density of H₂O + NaCl + CaCl₂ and H₂O + KCl + CaCl₂ at 298.15 K. J. Chem. Eng. Data 1997, 42, 526– 530, DOI: 10.1021/je9602733
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Viscosity and Density of H2O + NaCl + CaCl2 and H2O + KCl + CaCl2 at 298.15 K
Zhang, Hai-Lang; Chen, Geng-Hua; Han, Shi-Jun
Journal of Chemical and Engineering Data (1997), 42 (3), 526-530CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The viscosity and d. of water + sodium chloride + calcium chloride solns. and water + potassium chloride + calcium chloride solns. were measured over the entire concn. range at 298.15 K. The recently extended Jones-Dole equation still functions well for these systems up to a high concn. It has been empirically found that when a seventh term of molarity was further added to the extended Jones-Dole equation, the viscosity for calcium chloride solns. and the mixed electrolyte solns. with larger ionic strengths could be excellently represented up to their satd. concns. In consideration of the large soly. of calcium chloride and furthermore of its large ionic strength and of its large viscosity-concn. coeff. it could be supposed that the extended Jones-Dole equation in this work should fit many aq. electrolyte solns. to their rather high concns. or just to the satd. concns. At low concns., the calcd. viscosity values obtained by simple additivity are close to the exptl. values. Above a certain concn., the calcd. viscosities of NaCl + CaCl2 and KCl + CaCl2 mixts. are lower than the exptl. values and the difference becomes larger with increasing concn.
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McBride-Wright, M.; Maitland, G. C.; Trusler, J. P. M. Viscosity and Density of Aqueous Solutions of Carbon Dioxide at Temperatures from (274 to 449) K and at Pressures up to 100 MPa. J. Chem. Eng. Data 2015, 60, 171– 180, DOI: 10.1021/je5009125
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Viscosity and Density of Aqueous Solutions of Carbon Dioxide at Temperatures from (274 to 449) K and at Pressures up to 100 MPa
McBride-Wright, Mark; Maitland, Geoffrey C.; Trusler, J. P. Martin
Journal of Chemical & Engineering Data (2015), 60 (1), 171-180CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The viscosity and d. of aq. solns. of carbon dioxide having mole fractions of CO2 of 0.0086, 0.0168, and 0.0271 are reported. The measurements were made in the single-phase compressed liq. region at temps. between (294 and 449) K at pressures up to 100 MPa; addnl. d. measurements were also made at T = 274 K in the same pressure range. The viscosity was measured with a vibrating-wire viscometer while the d. was measured by means of a vibrating U-tube densimeter; both were calibrated with pure water and either vacuum or ambient air. The d. data have an expanded relative uncertainty of 0.07 % with a coverage factor of 2. From the raw data, the partial molar volume of CO2 in aq. soln. has been detd. and correlated as an empirical function of temp. and pressure. When combined with the IAPWS-95 equation of state of pure water, this correlation represents the measured densities of under-satd. solns. of CO2 in water within ± 0.04 %. The viscosity data have an expanded relative uncertainty of 1.4 % with a coverage factor of 2. A modified Vogel-Fulcher-Tamman equation was used to correlate the viscosity as a function of temp., pressure, and mole fraction of CO2 with an abs. av. relative deviation of 0.4 %. The viscosity and d. of satd. aq. solns. of CO2 may be calcd. by combining the correlations presented in this work with a suitable model for the mole fraction of CO2 at satn.
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29
McBride-Wright, M. Viscosity and Density of Aqueous Fluids with Dissolved CO₂; Imperial College London: London, 2013.
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30
Darling, A. S. Iridium Platinum Alloys: A Critical Review of Their Constitution and Properties. Platin. Met. Rev. 1960, 4, 18– 26
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Iridium-platinum alloys. Critical review of their constitution and properties
Darling, A. S.
Platinum Metals Review (1960), 4 (), 18-26CODEN: PTMRA3; ISSN:0032-1400.
32 references.
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31
Ciotta, F. Viscosity of Asymmetric Liquid Mixtures under Extreme Conditions; Imperial College London: London, 2010.
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Caudwell, D. R. Viscosity of Dense Fluid Mixtures; University of London, 2004.
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33
Retsina, T.; Richardson, S. M.; Wakeham, W. A. The Theory of a Vibrating-Rod Densimeter. Appl. Sci. Res. 1986, 43, 127– 158, DOI: 10.1007/bf00386040
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The theory of a vibrating-rod densimeter
Retsina, T.; Richardson, S. M.; Wakeham, W. A.
Applied Scientific Research (1986), 43 (2), 127-58CODEN: ASRHAU; ISSN:0003-6994.
A theory is presented of a device for the accurate detn. of the d. of fluids over a wide range of thermodn. states. The instrument is based upon the detn. of the characteristics of the resonance of a circular-section tube or rod, performing steady, transverse oscillations in the fluid. The theory accounts for the fluid motion external to the rod as well as the mech. motion of the rod and is valid over a defined range of conditions. A complete set of working equations and corrections is obtained for the instrument which, together with the limits of the validity of the theory, prescribe the parameters of a practical design capable of high accuracy.
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Retsina, T.; Richardson, S. M.; Wakeham, W. A. The Theory of a Vibrating-Rod Viscometer. Appl. Sci. Res. 1987, 43, 325– 346, DOI: 10.1007/bf00540567
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35
Abramowitz, M. S.; Stegun, I. A. Handbook of Mathematical Functions; Dover: New York, 1965.
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There is no corresponding record for this reference.
36
Kestin, J.; Khalifa, H. E.; Sookiazian, H.; Wakeham, W. A. Experimental Investigation of Effect of Pressure on Viscosity of Water in Temperature-Range 10-150 °C. Ber. Bunsen Ges. Phys. Chem. 1978, 82, 180– 188, DOI: 10.1002/bbpc.197800008
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37
Kestin, J.; Khalifa, H. E.; Abe, Y.; Grimes, C. E.; Sookiazian, H.; Wakeham, W. A. Effect of Pressure on Viscosity of Aqueous Nacl Solutions in Temperature-Range 20 °C - 150 °C. J. Chem. Eng. Data 1978, 23, 328– 336, DOI: 10.1021/je60079a011
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Effect of pressure on the viscosity of aqueous sodium chloride solutions in the temperature range 20-150°C
Kestin, Joseph; Khalifa, H. Ezzat; Abe, Yoshiyuki; Grimes, Clifford E.; Sookiazian, Heros; Wakeham, William A.
Journal of Chemical and Engineering Data (1978), 23 (4), 328-36CODEN: JCEAAX; ISSN:0021-9568.
The effect of pressure was studied on the viscosity of 0-5.4 m aq. NaCl solns. at 20-150 °. The viscosity was measured by the oscillating-disk method at 0-30 MPa at six concns. along a large no. of isotherms. The exptl. results have an estd. uncertainty of ±0.5%. The exptl. data were correlated in terms of pressure, temp., and concn. The correlation reproduces the original data to within the quoted uncertainty.
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Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509– 1596, DOI: 10.1063/1.555991
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A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa
Span, R.; Wagner, W.
Journal of Physical and Chemical Reference Data (1996), 25 (6), 1509-1596CODEN: JPCRBU; ISSN:0047-2689. (American Chemical Society)
This work reviews the available data on thermodn. properties of carbon dioxide and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data of the following properties: (a) thermal properties of the single-phase region (pρT) and (b) of the liq.-vapor satn. curve (ps, ρ', ρ") including the Maxwell criterion, (c) speed of sound w and (d) specific isobaric heat capacity cp of the single phase region and of the satn. curve, (e) specific isochoric heat capacity cυ, (f) specific enthalpy h, (g) specific internal energy u, and (h) Joule-Thomson coeff. μ. By applying modern strategies for the optimization of the math. form of the equation of state and for the simultaneous nonlinear fit to the data of all these properties, the resulting formulation is able to represent even the most accurate data to within their exptl. uncertainty. In the tech. most important region up to pressures of 30 MPa and up to temps. of 523 K, the estd. uncertainty of the equation ranges from ±0.03% to ±0.05% in the d., ±0.03% to ±1% in the speed of sound, and ±0.15% to ±1.5% in the isobaric heat capacity. Special interest has been focused on the description of the crit. region and the extrapolation behavior of the formulation. Without a complex coupling to a scaled equation of state, the new formulation yields a reasonable description even of the caloric properties in the immediate vicinity of the crit. point. At least for the basic properties such as pressure, fugacity, and enthalpy, the equation can be extrapolated up to the limits of the chem. stability of carbon dioxide. Independent equations for the vapor pressure and for the pressure on the sublimation and melting curve, for the satd. liq. and vapor densities, and for the isobaric ideal gas heat capacity are also included. Property tables calcd. from the equation of state are given in the appendix.
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Duan, Z.; Moller, N.; Weare, J. H. A High Temperature Equation of State for the H₂O-CaCl₂ and H₂O-MgC_l2 Systems. Geochim. Cosmochim. Acta 2006, 70, 3765– 3777, DOI: 10.1016/j.gca.2006.05.007
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A high temperature equation of state for the H2O-CaCl2 and H2O-MgCl2 systems
Duan, Zhenhao; Moller, Nancy; Weare, John H.
Geochimica et Cosmochimica Acta (2006), 70 (15), 3765-3777CODEN: GCACAK; ISSN:0016-7037. (Elsevier)
An equation of state (EOS) is developed for salt-water systems in the high temp. range. As an example of the applications, this EOS is parameterized for the calcn. of d., immiscibility, and the compns. of coexisting phases in the CaCl2-H2O and MgCl2-H2O systems from 523 to 973 K and from satn. pressure to 1500 bar. All available volumetric and phase equil. measurements of these binaries are well represented by this equation. This EOS is based on a Helmholtz free energy representation constructed from a ref. system contg. hard-sphere and polar contributions plus an empirical correction. For the temp. and pressure range in this study, the electrolyte solutes are assumed to be assocd. The water mols. are modeled as hard spheres with point dipoles and the solute mols., MgCl2 and CaCl2, as hard spheres with point quadrupoles. The free energy of the ref. system is calcd. from an anal. representation of the Helmholtz free energy of the hard-sphere contributions and perturbative ests. of the electrostatic contributions. The empirical correction used to account for deviations of the ref. system predictions from measured data is based on a virial expansion. The formalism can be used for generalization to aq. systems contg. insol. gases (CO2, CH4), alkali chlorides (NaCl, KCl), and alk. earth chlorides (CaCl2, MgCl2). The program of this model is available as an electronic annex (see EA1 and EA2) and can also be downloaded at: http://www.geochem-model.org/programs.htm.
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Duan, Z.; Sun, R. An Improved Model Calculating CO₂ Solubility in Pure Water and Aqueous NaCl Solutions from 273 to 533 K and from 0 to 2000. Chem. Geol. 2003, 193, 257– 271, DOI: 10.1016/s0009-2541(02)00263-2
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An improved model calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar
Duan, Zhenhao; Sun, Rui
Chemical Geology (2003), 193 (3-4), 257-271CODEN: CHGEAD; ISSN:0009-2541. (Elsevier Science B.V.)
A thermodn. model for the soly. of carbon dioxide (CO2) in pure water and in aq. NaCl solns. for temps. from 273 to 533 K, for pressures from 0 to 2000 bar, and for ionic strength from 0 to 4.3 m is presented. The model is based on a specific particle interaction theory for the liq. phase and a highly accurate equation of state for the vapor phase. With this specific interaction approach, this model is able to predict CO2 soly. in other systems, such as CO2-H2O-CaCl2 and CO2-seawater, without fitting exptl. data from these systems. Comparison of the model predictions with exptl. data indicates that the model is within or close to exptl. uncertainty, which is about 7% in CO2 soly.
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Comuñas, M. J. P.; Bazile, J.-P.; Baylaucq, A.; Boned, C. Density of Diethyl Adipate Using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements. J. Chem. Eng. Data 2008, 53, 986– 994, DOI: 10.1021/je700737c
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Density of Diethyl Adipate using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements
Comunas, Maria J. P.; Bazile, Jean-Patrick; Baylaucq, Antoine; Boned, Christian
Journal of Chemical & Engineering Data (2008), 53 (4), 986-994CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
New d. data for di-Et adipate (DEA) over 12 isotherms [(293.15 ≤ T ≤ 403.15) K] and 15 isobars [(0.1 ≤ p ≤ 140) MPa] are reported. This paper presents also the calibration procedure proposed for a new exptl. equipment. Data reliability has been verified over the pressure and temp. exptl. intervals by comparing our exptl. results for toluene and 1-butanol with previous literature data. A total of 732 exptl. data points have been measured in the framework of this work. The exptl. uncertainty is estd. to be ± 0.5 kg·m-3 (around 0.05 %). The pressure and temp. dependencies of di-Et adipate densities were accurately represented by the Tammann-Tait equation with std. deviations of 0.3 kg·m-3. These data were used to analyze the isothermal compressibility and the isobaric thermal expansivity for this fluid.
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Wagner, W.; Pruss, A. The Iapws Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387– 535, DOI: 10.1063/1.1461829
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The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use
Wagner, W.; Pruss, A.
Journal of Physical and Chemical Reference Data (2002), 31 (2), 387-535CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. In 1995, the International Assocn. for the Properties of Water and Steam (IAPWS) adopted a new formulation called "The IAPWS Formulation 1995 for the Thermodn. Properties of Ordinary Water Substance for General and Scientific Use", which we abbreviate to IAPWS-95 formulation or IAPWS-95 for short. This IAPWS-95 formulation replaces the previous formulation adopted in 1984. This work provides information on the selected exptl. data of the thermodn. properties of water used to develop the new formulation, but information is also given on newer data. The article presents all details of the IAPWS-95 formulation, which is in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data for the following properties: (a) thermal properties of the single-phase region (pρT) and of the vapor-liq. phase boundary (pσρ'ρ''T), including the phase-equil. condition (Maxwell criterion), and (b) the caloric properties specific isochoric heat capacity, specific isobaric heat capacity, speed of sound, differences in the specific enthalpy and in the specific internal energy, Joule-Thomson coeff., and isothermal throttling coeff. By applying modern strategies for optimizing the functional form of the equation of state and for the simultaneous nonlinear fitting to the data of all mentioned properties, the resulting IAPWS-95 formulation covers a validity range for temps. from the melting line (lowest temp. 251.2 K at 209.9 MPa) to 1273 K and pressures up to 1000 MPa. In this entire range of validity, IAPWS-95 represents the most accurate data to within their exptl. uncertainty. In the most important part of the liq. region, the estd. uncertainty of IAPWS-95 ranges from ±0.001% to ±0.02% in d., ±0.03% to ±0.2% in speed of sound, and ±0.1% in isobaric heat capacity. In the liq. region at ambient pressure, IAPWS-95 is extremely accurate in d. (uncertainty ≤ ±0.0001%) and in speed of sound (± 0.005%). In a large part of the gas region the estd. uncertainty in d. ranges from ±0.03% to ±0.05%, in speed of sound it amts. to ±0.15% and in isobaric heat capacity it is ±0.2%. In the crit. region, IAPWS-95 represents not only the thermal properties very well but also the caloric properties in a reasonable way. Special interest has been focused on the extrapolation behavior of the new formulation. At least for the basic properties such as pressure and enthalpy, IAPWS-95 can be extrapolated up to extremely high pressures and temps. In addn. to the IAPWS-95 formulation, independent equations for vapor pressure, the densities, and the most important caloric properties along the vapor-liq. phase boundary, and for the pressure on the melting and sublimation curve, are given. Moreover, a so-called gas equation for densities up to 55 kg m-3 is also included. Tables of the thermodn. properties calcd. from the IAPWS-95 formulation are listed.
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Correlating viscosity and vapor pressure of liquids
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Industrial and Engineering Chemistry (1945), 37 (), 1112-15CODEN: IECHAD; ISSN:0019-7866.
Straight lines are obtained when viscosity data are plotted on log paper against a temp. scale readily calibrated by using the vapor pressure of a reference substance such as H2O. In general the lines of such a plot must be isobaric. In some cases the viscosity data for a substance are best expressed as a series of 2 or 3 connecting straight lines. The breaks are due to changes in the phys. and often chem. nature of the material. H2O shows a break at about 40°. The equation for the straight line is log μ = - A log P + C, where μ is the viscosity of the material and P is the vapor pressure of any reference liquid, both being expressed in any desired units. A and C are consts. The use of a reduced temp. scale gives straight lines which in many cases tend to converge in a narrow range at the extrapolated points corresponding to the crit. Similar plots are obtained with fluidities.
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44
IAPWS Release on the Iapws Formulation 2008 for the Viscosity of Ordinary Water Substance , 2008.
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45
Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mareš, R.; Miyagawa, K. New International Formulation for the Viscosity of H₂O. J. Phys. Chem. Ref. Data 2009, 38, 101– 125, DOI: 10.1063/1.3088050
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Journal of Physical and Chemical Reference Data (2009), 38 (2), 101-125CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
The International Assocn. for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. This manuscript describes the development and evaluation of the 2008 formulation, which provides a correlating equation for the viscosity of water for fluid states up to 1173 K and 1000 MPa with uncertainties from less than 1% to 7% depending on the state point. (c) 2009 American Institute of Physics.
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46
Spycher, N.; Pruess, K. A Phase-Partitioning Model for CO₂–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO2-Enhanced Geothermal Systems. Transp. Porous Media 2010, 82, 173– 196, DOI: 10.1007/s11242-009-9425-y
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A Phase-Partitioning Model for CO2-Brine Mixtures at Elevated Temperatures and Pressures: Application to CO2-Enhanced Geothermal Systems
Spycher, Nicolas; Pruess, Karsten
Transport in Porous Media (2010), 82 (1), 173-196CODEN: TPMEEI; ISSN:0169-3913. (Springer)
Correlations are presented to compute the mutual solubilities of CO2 and chloride brines at temps. 12-300°C, pressures 1-600 bar (0.1-60 MPa), and salinities 0-6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO2-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on exptl. data from literature for phase partitioning between CO2 and NaCl brines, and extends the previously published correlations to higher temps. The model relies on activity coeffs. for the H2O-rich (aq.) phase and fugacity coeffs. for the CO2-rich phase. Activity coeffs. are treated using a Margules expression for CO2 in pure water, and a Pitzer expression for salting-out effects. Fugacity coeffs. are computed using a modified Redlich-Kwong equation of state and mixing rules that incorporate asym. binary interaction parameters. Parameters for the calcn. of activity and fugacity coeffs. were fitted to published soly. data over the P-T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual soly. model is presented for the case of a hypothetical, enhanced geothermal system where CO2 is used as the heat extn. fluid. In this simulation, dry supercrit. CO2 at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO2 displaces the formation water relatively quickly, but that the produced CO2 contains significant water for long periods of time. The amt. of water in the CO2 could have implications for reactivity with reservoir rocks and engineered materials.
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Pressure-volume-temperature-concentration relation of aqueous sodium chloride solutions
Rowe, Allen M., Jr.; Chou, James C. S.
Journal of Chemical and Engineering Data (1970), 15 (1), 61-6CODEN: JCEAAX; ISSN:0021-9568.
The derivs. ( v/ P)T,x of NaCl solns. have been exptl. detd. at 0-175° for NaCl concns. of 0-25 g per 100 g of soln. and pressures up to 350 kg/cm2. An interpolation formula which describes the pressure-vol.-concn. (P-v-T-x) relation has been developed to fit these exptl. results and the d. data from the literature.
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This article is cited by 3 publications.

Ali Aminian, Bahman ZareNezhad. Molecular Dynamics Simulations Study on the Shear Viscosity, Density, and Equilibrium Interfacial Tensions of CO2 + Brines and Brines + CO2 + n-Decane Systems. The Journal of Physical Chemistry B 2021, 125 (10) , 2707-2718. https://doi.org/10.1021/acs.jpcb.0c10883
Rui Sun, Zhigang Niu, Shaocong Lai. Modeling dynamic viscosities of multi-component aqueous electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl−, SO42− and dissolved CO2 under conditions of CO2 sequestration. Applied Geochemistry 2022, 142 , 105347. https://doi.org/10.1016/j.apgeochem.2022.105347
L M Zaripova, M S Gabdrakhimov. Well bottomhole cleaning device. IOP Conference Series: Materials Science and Engineering 2020, 952 (1) , 012067. https://doi.org/10.1088/1757-899X/952/1/012067

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Figure 1
Figure 1. Simplified diagram of the VW–VT apparatus: (1) vacuum pumps, (2) aqueous brine solution, (3) CO₂ gas cylinder, (4) syringe pump, (5) circulating pump, (6) VW viscometer, (7) VT densimeter, (8) waste bottle, (V1 to V3) valves. (29)
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Figure 2
Figure 2. Simplified schematics of the VW sensor: (a) physical arrangement; (b) electrical equivalence circuit; OSC, sine-wave oscillator (0.05–5 V rms); R_s, series resistor (1 kΩ), I, electric current; Z_w, electrical impedance of stationary wire; Z_m, additional electrical impedance due to wire motion in the magnetic field; Z_b, electrical impedance of brine; N and S, poles of the permanent magnet; A and B, differential signal terminals for connection to the lock-in amplifier.
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Figure 3
Figure 3. Experimental resonance curve (components of the complex voltage Φ as a function of driving frequency f) in comparison with the standard and modified working equations: □, experimental in-phase voltage; ○, experimental quadrature voltage; green line, modified working equation; red line, standard working equation. Measurements carried out in NaCl(aq) at T = 448 K, p = 1.4 MPa, and m = 2.5 mol·kg^–1.
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Figure 4
Figure 4. Additional damping β″ as a function of phase angle θ for NaCl(aq) with viscosity values constrained to literature data: (21) □, m = 0.77 mol·kg^–1; ○, m = 2.5 mol·kg^–1; —, quadratic correlation.
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Figure 5
Figure 5. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp and calculated values η_calc from the correlation of Kestin et al. (21) for NaCl(aq) with molality m = 0.77 mol·kg^–1: ▲ 1 MPa, ×,15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa.
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Figure 6
Figure 6. Densities ρ of [xCO₂ + (1 – x)NaCl(aq)] m = 2.50 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.
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Figure 7
Figure 7. Densities ρ of [xCO₂ + (1 – x)CaCl₂(aq)] with m = 1.00 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.
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Figure 8
Figure 8. Deviations Δρ = (ρ_exp – ρ_calc) between experimental densities ρ_exp of [xCO₂ + (1 – x)NaCl(aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of CO₂ mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg^–1; orange, m = 0.77 mol·kg^–1; green, m = 2.50 mol·kg^–1.
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Figure 9
Figure 9. Deviations Δρ = (ρ_exp – ρ_calc) between experimental densities ρ_exp of [xCO₂ + (1 – x)CaCl₂ (aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of CO₂ mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg^–1; orange, m = 0.77 mol·kg^–1; green, m = 2.50 mol·kg^–1.
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Figure 10
Figure 10. Deviations Δρ = (ρ_exp – ρ_calc) between experimental literature densities ρ_exp of [xCO₂ + (1 – x)NaCl(aq)], and densities ρ_calc calculated from eqs 18 and 19 with brine densities from ref (14) as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: □, Yan et al.; (16) ○, Song at al. (17) Colors indicate NaCl molality: red = 1 mol·kg^–1; green = 2 mol·kg^–1; blue = 3 mol·kg^–1; purple = 4 mol·kg^–1; orange = 5 mol·kg^–1.
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Figure 11
Figure 11. Viscosities η of [xCO₂ + (1 – x)NaCl(aq)] with m = 0.77 mol·kg^–1 as a function of CO₂ mole fraction x at (a) T = 275 K and (b) T = 449 K: ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.
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Figure 12
Figure 12. Viscosities η of [xCO₂ + (1 – x)CaCl₂(aq)] with m = 1.00 mol·kg^–1 as a function of CO₂ mole fraction x at T = 373 K: ●, 30 MPa; ▲, 50 MPa. Solid lines are linear regression lines.
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Figure 13
Figure 13. Partial derivative (∂ln η/∂x) of the natural logarithm of the viscosity η with respect to the mole fraction x of dissolved CO₂ as a function of temperature T: ●, CO₂ + H₂O; (28) ▲, CO₂ + NaCl(aq); ■, CO₂ + CaCl₂(aq). Solid line based on eq 25. Error bars show two standard deviations.
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Figure 14
Figure 14. Viscosities η of [xCO₂ + (1 – x)NaCl(aq)] with m = 0.77 mol·kg^–1 as a function of pressure p at T = 275 K: ×, x = 0.000; ●, x = 0.0124; ▲, x = 0.0161. Solid lines are linear regression lines.
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Figure 15
Figure 15. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp of [xCO₂ + (1 – x)NaCl(aq)], and viscosities η_calc calculated from eq 21 as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: ▲, this work; ◆, Kumagai and Yokoyama; (18) ●, Fleury and Deschamps; (20) *, Bando et al. (19)
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Figure 16
Figure 16. Relative deviations Δη/η = (η_exp – η_calc)/η_exp between experimental viscosities η_exp of [xCO₂ + (1 – x)CaCl₂(aq)], and viscosities η_calc calculated from eq 21 as a function of (a) temperature T, (b) CO₂ mole fraction x, and (c) pressure p: ▲, this work; ▲, Isono; (24) ●, Wahab and Mahiuddin; (25) ◆, Gonçalves and Kestin; (26) *, Zhang et al.; (27) +, Abdulagatov and Azizov. (23)
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References
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  Saadatpoor, Ehsan; Bryant, Steven L.; Sepehrnoori, Kamy
  Transport in Porous Media (2010), 82 (1), 3-17CODEN: TPMEEI; ISSN:0169-3913. (Springer)
  The modes of geol. storage of CO2 are usually categorized as structural, dissoln., residual, and mineral trapping. Here we argue that the heterogeneity intrinsic to sedimentary rocks gives rise to a fifth category of storage, which we call local capillary trapping. Local capillary trapping occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer. When the rising CO2 plume encounters a region (10-2 to 10+1m) where capillary entry pressure is locally larger than av., CO2 accumulates beneath the region. This form of storage differs from structural trapping in that much of the accumulated satn. will not escape, should the integrity of the seal overlying the aquifer be compromised. Local capillary trapping differs from residual trapping in that the accumulated satn. can be much larger than the residual satn. for the rock. We examine local capillary trapping in a series of numerical simulations. The essential feature is that the drainage curves (capillary pressure vs. satn. for CO2 displacing brine) are required to be consistent with permeabilities in a heterogeneous domain. In this work, we accomplish this with the Leverett J-function, so that each grid block has its own drainage curve, scaled from a ref. curve to the permeability and porosity in that block. We find that capillary heterogeneity controls the path taken by rising CO2. The displacement front is much more ramified than in a homogeneous domain, or in a heterogeneous domain with a single drainage curve. Consequently, residual trapping is overestimated in simulations that ignore capillary heterogeneity. In the cases studied here, the redn. in residual trapping is compensated by local capillary trapping, which yields larger saturations held in a smaller vol. of pore space. Moreover, the amt. of CO2 phase remaining mobile after a leak develops in the caprock is smaller. Therefore, the extent of immobilization in a heterogeneous formation exceeds that reported in previous studies of buoyancy-driven plume movement.
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10. 10
  Burton, M.; Kumar, N.; Bryant, S. L. CO₂ Injectivity into Brine Aquifers: Why Relative Permeability Matters as Much as Absolute Permeability. Energy Procedia 2009, 1, 3091– 3098, DOI: 10.1016/j.egypro.2009.02.089
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  10
  CO2 injectivity into brine aquifers: why relative permeability matters as much as absolute permeability
  Burton, McMillan; Kumar, Navanit; Bryant, Steven L.
  Energy Procedia (2009), 1 (1), 3091-3098CODEN: EPNRCV; ISSN:1876-6102. (Elsevier)
  For economic reasons operators of geol. storage projects are likely to inject CO2 at the largest possible rates into the smallest no. of wells. Thus a typical CO2 injection well is likely to run at the largest bottomhole pressure that is safe. Operators will also tend to prefer thicker, higher permeability target formations. However, a const.-pressure well exhibits a varying rate of CO2 injection for two reasons: classical multiphase flow effects, and long-term injection of CO2 removes water from the near-wellbore region. Drying ppts. dissolved salts, so the permeability of the dry rock need not equal the initial aquifer permeability. Mobility of CO2 in the dried rock and mobility of CO2 and brine the two-phase flow region det. the variation of injectivity with vol. of CO2 injected. We find a four-fold variation in injectivity when seven different CO2/brine relative permeability curves (Bennion and Bachu) are used, holding all other reservoir parameters the same. Since the product of formation permeability and formation thickness is relatively easy to measure, once a well has been drilled, uncertainty in relative permeability will therefore be a large contribution to uncertainty in achievable rates in CO2 storage projects. We develop anal. expressions for the injectivity variation in terms of phase mobilities and the speeds of satn. fronts. Classical theory (Buckley-Leverett) does not account for the drying front; using only Buckley-Leverett yields both quant. and qual. errors. The expressions are consistent with detailed reservoir simulations using com. software (CMG's GEM) that account for the full physics and complete phase behavior. The expressions can refine the estd. no. of wells needed for a target overall injection rate. This anal. also enables an operator to assess the value of retrieving core and measuring relative permeability in a prospective storage target.
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11. 11
  Benson, S. M.; Cole, D. R. CO₂ Sequestration in Deep Sedimentary Formations. Elements 2008, 4, 325– 331, DOI: 10.2113/gselements.4.5.325
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  11
  CO2 sequestration in deep sedimentary formations
  Benson, Sally M.; Cole, David R.
  Elements (Chantilly, VA, United States) (2008), 4 (5), 325-331CODEN: EOOCAG; ISSN:1811-5209. (Mineralogical Society of America)
  A review. Carbon dioxide capture and sequestration (CCS) in deep geol. formations has recently emerged as an important option for reducing greenhouse emissions. If CCS is implemented on the scale needed to make noticeable redns. in atm. CO2, a billion metric tons or more must be sequestered annually-a 250 fold increase over the amt. sequestered today. Securing such a large vol. will require a solid scientific foundation defining the coupled hydrol.-geochem.-geomech. processes that govern the long-term fate of CO2 in the subsurface. Also needed are methods to characterize and select sequestration sites, subsurface engineering to optimize performance and cost, approaches to ensure safe operation, monitoring technol., remediation methods, regulatory overview, and an institutional approach for managing long-term liability.
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12. 12
  Pau, G. S. H.; Bell, J. B.; Pruess, K.; Almgren, A. S.; Lijewski, M. J.; Zhang, K. High-Resolution Simulation and Characterization of Density-Driven Flow in CO₂ Storage in Saline Aquifers. Adv. Water Resour. 2010, 33, 443– 455, DOI: 10.1016/j.advwatres.2010.01.009
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  12
  High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers
  Pau, George S. H.; Bell, John B.; Pruess, Karsten; Almgren, Ann S.; Lijewski, Michael J.; Zhang, Keni
  Advances in Water Resources (2010), 33 (4), 443-455CODEN: AWREDI; ISSN:0309-1708. (Elsevier Ltd.)
  Simulations are routinely used to study the process of carbon dioxide (CO2) sequestration in saline aquifers. In this paper, we describe the modeling and simulation of the dissoln.-diffusion-convection process based on a total velocity splitting formulation for a variable-d. incompressible single-phase model. A second-order accurate sequential algorithm, implemented within a block-structured adaptive mesh refinement (AMR) framework, is used to perform high-resoln. studies of the process. We study both the short-term and long-term behaviors of the process. It is found that the onset time of convection follows closely the prediction of linear stability anal. In addn., the CO2 flux at the top boundary, which gives the rate at which CO2 gas dissolves into a neg. buoyant aq. phase, will reach a stabilized state at the space and time scales we are interested in. This flux is found to be proportional to permeability, and independent of porosity and effective diffusivity, indicative of a convection-dominated flow. A 3D simulation further shows that the added degrees of freedom shorten the onset time and increase the magnitude of the stabilized CO2 flux by about 25%. Finally, our results are found to be comparable to results obtained from TOUGH2-MP.
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13. 13
  Homsy, G. M. Viscous Fingering in Porous Media. Annual Review; Fluid Mechanics: Stanford, 1987; pp 271– 311.
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14. 14
  Al Ghafri, S.; Maitland, G. C.; Trusler, J. P. M. Densities of Aqueous MgCl₂(Aq), CaCl₂(Aq), KI(Aq), NaCl(Aq), KCl(Aq), AlCl₃(Aq), and (0.864 NaCl + 0.136 KCl)(Aq) at Temperatures between (283 and 472) K, Pressures up to 68.5 MPa, and Molalities up to 6 mol.kg^-1. J. Chem. Eng. Data 2012, 57, 1288– 1304, DOI: 10.1021/je2013704
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  14
  Densities of Aqueous MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), KCl(aq), AlCl3(aq), and (0.964 NaCl + 0.136 KCl)(aq) at Temperatures Between (283 and 472) K, Pressures up to 68.5 MPa, and Molalities up to 6 mol/kg-1
  Al Ghafri, Saif; Maitland, Geoffrey C.; Trusler, J. P. Martin
  Journal of Chemical & Engineering Data (2012), 57 (4), 1288-1304CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  We report the densities of MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), KCl(aq), AlCl3(aq), and the mixed salt system [(1 - x)NaCl + xKCl](aq), where x denotes the mole fraction of KCl, at temps. between (283 and 472) K and pressures up to 68.5 MPa. The molalities at which the solns. were studied were (1.00, 3.00, and 5.00) mol/kg-1 for MgCl2(aq), (1.00, 3.00, and 6.00) mol/kg-1 for CaCl2(aq), (0.67, 0.90, and 1.06) mol/kg-1 for KI(aq), (1.06, 3.16, and 6.00) mol/kg-1 for NaCl(aq), (1.06, 3.15, and 4.49) mol/kg-1 for KCl(aq), (1.00 and 2.00) mol/kg-1 for AlCl3(aq), and (1.05, 1.98, 3.15, and 4.95) mol/kg-1 for [(1 - x)NaCl + xKCl](aq), with x = 0.136. The measurements were performed with a vibrating-tube densimeter calibrated under vacuum and with pure water over the full ranges of pressure and temp. investigated. An anal. of uncertainties shows that the relative uncertainty of d. varies from 0.03% to 0.05% depending upon the salt and the molality of the soln. An empirical correlation is reported that represents the d. for each brine system as a function of temp., pressure, and molality with abs. av. relative deviations of approx. 0.02%. Comparing the model with a large database of results from the literature, we find abs. av. relative deviations of 0.03%, 0.06%, 0.04%, 0.02%, and 0.02% for the systems MgCl2(aq), CaCl2(aq), KI(aq), NaCl(aq), and KCl(aq), resp. The model can be used to calc. d., apparent molar volume, and isothermal compressibility over the full ranges of temp., pressure, and molality studied in this work. An ideal mixing rule for the d. of a mixed electrolyte soln. was tested against our mixed salt data and was found to offer good predictions at all conditions studied with an abs. av. relative deviation of 0.05%.
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15. 15
  Nighswander, J. A.; Kalogerakis, N.; Mehrotra, A. K. Solubilities of Carbon Dioxide in Water and 1 Wt. % Sodium Chloride Solution at Pressures up to 10 MPa and Temperatures from 80 to 200 °C. J. Chem. Eng. Data 1989, 34, 355– 360, DOI: 10.1021/je00057a027
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  15
  Solubilities of carbon dioxide in water and 1 wt. % sodium chloride solution at pressures up to 10 MPa and temperatures from 80 to 200°C
  Nighswander, John A.; Kalogerakis, Nicolas; Mehrotra, Anil K.
  Journal of Chemical and Engineering Data (1989), 34 (3), 355-60CODEN: JCEAAX; ISSN:0021-9568.
  Exptl. gas soly. data for the CO2-water and CO2-1 wt. % NaCl soln. binary systems are reported. Measurements were made at ≤10 MPa and 80-200°. A thermodn. model of these systems is also presented. The model employs the D. Peng-D. Robinson (1976) equation of state to represent the vapor phase and an empirical Henry's law const. correlation for the liq. phase. It is shown that the salting-out effect of the 1 wt. % NaCl soln. on CO2 soly. is small. Also described is a new exptl. app. consisting of a variable-vol. equil. cell enclosed in a const. temp. controlled oven and the procedure used in conducting the expts.
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16. 16
  Yan, W.; Huang, S.; Stenby, E. H. Measurement and Modeling of CO₂ Solubility in NaCl Brine and CO₂-Saturated NaCl Brine Density. Int. J. Greenhouse Gas Control 2011, 5, 1460– 1477, DOI: 10.1016/j.ijggc.2011.08.004
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  16
  Measurement and modeling of CO2 solubility in NaCl brine and CO2-saturated NaCl brine density
  Yan, Wei; Huang, Shengli; Stenby, Erling H.
  International Journal of Greenhouse Gas Control (2011), 5 (6), 1460-1477CODEN: IJGGBW; ISSN:1750-5836. (Elsevier Ltd.)
  Phase equil. for CO2-NaCl brine is of general interest to many scientific disciplines and tech. areas. The system is particularly important to CO2 sequestration in deep saline aquifers and CO2 enhanced oil recovery, two techniques discussed intensively in recent years due to the concerns over climate change and energy security. This work is an exptl. and modeling study of two fundamental properties in high pressure CO2-NaCl brine equil., i.e., CO2 soly. in NaCl brine and CO2-satd. NaCl brine d. A literature review of the available data was presented first to illustrate the necessity of exptl. measurements of the two properties at high pressures. An exptl. method for measuring high pressure CO2 soly. in NaCl brine was then developed. With the method, CO2 solubilities in 0, 1, and 5 m NaCl brines were measured at 323, 373, and 413 K from 5 to 40 MPa. The corresponding d. data at the same conditions were also measured. For soly., two models used in the Eclipse simulator were tested: the correlations of Chang et al. and the Soreide and Whitson equation of state (EoS) model. The latter model was modified to improve its performance for high salinity brine. In the d. modeling, the correlations of Chang et al., Garcia's correlation, and five different EoS models were tested. Among these models, Garcia's correlation and the ePC-SAFT EoS generally give satisfactory agreement with the exptl. measurements. An anal. was also made to show that dissoln. of CO2 increases the brine d. only if the apparent mass d. of CO2 in brine is higher than the brine d. at the same conditions.
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17. 17
  Song, Y.; Zhan, Y.; Zhang, Y.; Liu, S.; Jian, W.; Liu, Y.; Wang, D. Measurements of CO₂-H₂O-NaCl Solution Densities over a Wide Range of Temperatures, Pressures, and NaCl Concentrations. J. Chem. Eng. Data 2013, 58, 3342– 3350, DOI: 10.1021/je400459y
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  17
  Measurements of CO2-H2O-NaCl Solution Densities over a Wide Range of Temperatures, Pressures, and NaCl Concentrations
  Song, Yongchen; Zhan, Yangchun; Zhang, Yi; Liu, Shuyang; Jian, Weiwei; Liu, Yu; Wang, Dayong
  Journal of Chemical & Engineering Data (2013), 58 (12), 3342-3350CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The d. of carbon dioxide + brine soln. under supercrit. conditions is a significant parameter for CO2 sequestration into deep saline formations. This paper has extended our previous study on d. measurements of CO2 + Tianjin brine to the CO2-H2O-NaCl soln. by using a magnetic suspension balance (MSB). The measurements were performed in the pressure range (10 MPa to 18 MPa) at a range of temps. (60 C to 140 C) with different concns. of NaCl (CNaCl = 1 mol·kg-1, 2 mol·kg-1, 3 mol·kg-1, 4 mol·kg-1) and different CO2 mass fractions (w = 0, 0.01, 0.02, 0.03). The effects of pressure, temp., CO2 mass fractions and NaCl concn. on the CO2-H2O-NaCl soln. d. were analyzed. The CO2-H2O-NaCl soln. d. increased almost linearly with an increase in the CO2 mass fraction when the NaCl concn. was less than 4 mol·kg-1 and the temp. was lower than 120 C. However, at a high concn. of NaCl (CNaCl = 4 mol·kg-1), the d. decreased with increasing mass fraction of CO2 when the temp. was over 120 C. The d. of the CO2-H2O-NaCl soln. with a high NaCl concn. decreased after dissolving CO2 at high temps., which caused the soln. to float over the saline layer and increased the risk of CO2 leakage. An empirical model was established to predict the soln. d. with high accuracy.
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18. 18
  Kumagai, A.; Yokoyama, C. Viscosities of Aqueous NaCl Solutions Containing CO₂ at High Pressures. J. Chem. Eng. Data 1999, 44, 227– 229, DOI: 10.1021/je980178p
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  18
  Viscosities of Aqueous NaCl Solutions Containing CO2 at High Pressures
  Kumagai, Akibumi; Yokoyama, Chiaki
  Journal of Chemical and Engineering Data (1999), 44 (2), 227-229CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  Viscosity measurements of aq. NaCl solns. contg. CO2 along three isotherms at 273 K, 276 K, and 278 K at pressures up to 30 MPa are reported. The measurements have been carried out within a falling capillary type viscometer and have an estd. uncertainty of ±0.8%. The exptl. values were correlated in terms of pressure, temp., and concns. of NaCl and CO2. The correlation reproduces the exptl. values to within ±1.3%.
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19. 19
  Bando, S.; Takemura, F.; Nishio, M.; Hihara, E.; Akai, M. Viscosity of Aqueous NaCl Solutions with Dissolved CO₂ at (30 to 60) °C and (10 to 20) MPa. J. Chem. Eng. Data 2004, 49, 1328– 1332, DOI: 10.1021/je049940f
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  19
  Viscosity of Aqueous NaCl Solutions with Dissolved CO2 at (30 to 60) °C and (10 to 20) MPa
  Bando, Shigeru; Takemura, Fumio; Nishio, Masahiro; Hihara, Eiji; Akai, Makoto
  Journal of Chemical and Engineering Data (2004), 49 (5), 1328-1332CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The viscosity of aq. NaCl solns. with dissolved CO2 was measured at conditions representing an underground aquifer at a depth of (1000 to 2000) m for the geol. storage of CO2 (i.e., (30 to 60) °C and (10 to 20) MPa at a mass fraction of NaCl between 0 and 0.03 by using a sedimenting solid particle type viscometer with an estd. uncertainty of ± 2 %). On the basis of this exptl. data, an empirical equation for predicting this viscosity as a function of the temp. and mole fraction of CO2 for these conditions was derived.
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20. 20
  Fleury, M.; Deschamps, H. Electrical Conductivity and Viscosity of Aqueous NaCl Solutions with Dissolved CO₂. J. Chem. Eng. Data 2008, 53, 2505– 2509, DOI: 10.1021/je8002628
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  20
  Electrical Conductivity and Viscosity of Aqueous NaCl Solutions with Dissolved CO2
  Fleury, Marc; Deschamps, Herve
  Journal of Chemical & Engineering Data (2008), 53 (11), 2505-2509CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The effect of dissolved CO2 on the elec. cond. and viscosity of three NaCl solns. covering the range of salinity usually encountered in potential CO2 storage geol. formations has been studied. At a const. temp. of 35 °C, the variations of cond. and viscosity are proportional to the mole fraction of dissolved CO2. For viscosity, the data obtained are in agreement with previous observations. The obsd. variations are small and are at max. on the order of 10 %. The variations of cond. and viscosity as a function of temp. up to 100 °C are not modified by the presence of CO2. A simple model is proposed to take into account the small modifications of cond. and viscosity as a function of the dissolved CO2 mole fraction and temp.
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21. 21
  Kestin, J.; Khalifa, H. E.; Correia, R. J. Tables of the Dynamic and Kinematic Viscosity of Aqueous NaCl Solutions in the Temperature Range 20–150°C and the Pressure Range 0.1–35 MPa. J. Phys. Chem. Ref. Data 1981, 10, 71– 88, DOI: 10.1063/1.555641
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  21
  Tables of the dynamic and kinematic viscosity of aqueous sodium chloride solutions in the temperature range 20-150°C and the pressure range 0.1-35 MPa
  Kestin, Joseph; Khalifa, H. Ezzat; Correia, Robert J.
  Journal of Physical and Chemical Reference Data (1981), 10 (1), 71-87CODEN: JPCRBU; ISSN:0047-2689.
  Tabulated values of the dynamic and kinematic viscosity of aq. NaCl solns. are given. The tables cover the temp. range 20-150 °C, the pressure range 0.1-35 MPa and the concn. range 0-6 m. The accuracy of the tabulated values is ±0.5%. The correlating equations from which the tables were generated are given.
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22. 22
  Kestin, J.; Shankland, I. R. Viscosity of Aqueous NaCl Solutions in the Temperature Range 25–200 °C and in the Pressure Range 0.1–30 MPa. Int. J. Thermophys. 1984, 5, 241– 263, DOI: 10.1007/bf00507835
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  22
  Viscosity of aqueous sodium chloride solutions in the temperature range 25-200°C and in the pressure range 0.1-30 MPa
  Kestin, J.; Shankland, I. R.
  International Journal of Thermophysics (1984), 5 (3), 241-63CODEN: IJTHDY; ISSN:0195-928X.
  New precise viscosity data are presented for aq. solns. of NaCl (0-6 mol/kg) at 25-200° and 0.1-30 MPa. The exptl. precision is ±0.5%; a comparison of the present results with data available in the literature indicated that the accuracy of the present data is also of the order of ±0.5%. Two empirical correlations that reproduce the data within the precision are given.
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23. 23
  Abdulagatov, I. M.; Azizov, N. D. Viscosity of Aqueous Calcium Chloride Solutions at High Temperatures and High Pressures. Fluid Phase Equilib. 2006, 240, 204– 219, DOI: 10.1016/j.fluid.2005.12.036
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  Viscosity of aqueous calcium chloride solutions at high temperatures and high pressures
  Abdulagatov, I. M.; Azizov, N. D.
  Fluid Phase Equilibria (2006), 240 (2), 204-219CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
  Viscosity of 6 (0.10, 0.33, 0.65, 0.97, 1.40, and 2.00) mol kg-1 binary aq. CaCl2 solns. was measured with a capillary-flow technique. Measurements were made at pressures ≤60 MPa. The range of temp. was from 293-575 K. The total uncertainty of viscosity, pressure, temp., and compn. measurements was estd. to be <1.6%, 0.05%, 15 mK, and 0.014%, resp. The effect of temp., pressure, and concn. on viscosity of binary aq. CaCl2 solns. was studied. The measured values of viscosity of CaCl2(aq) were compared with data, predictions, and correlations reported in the literature. The temp. and pressure coeffs. of viscosity of CaCl2(aq) were studied as a function of concn. and temp. The viscosity data were interpreted in terms of the extended Jones-Dole equation for the relative viscosity (η/η0) to accurate calc. the values of viscosity A- and B-coeffs. as a function of temp. The derived values of the viscosity B-coeffs. were compared with the values calcd. from the ionic B-coeff. data. The phys. meaning parameters V and E in the abs. rate theory of viscosity and hydrodynamic molar volume (effective rigid molar volume of salt) Vk were calcd. using present exptl. viscosity data. TTG model was used to compare predicted values of the viscosity of CaCl2(aq) solns. with exptl. values at high pressures.
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24. 24
  Isono, T. Density, Viscosity, and Electrolytic Conductivity of Concentrated Aqueous Electrolyte Solutions at Several Temperatures. Alkaline-Earth Chlorides, LaCl₃, Na₂SO₄, NaNO₃, NaBr, KNO₃, KBr, and Cd(NO₃)₂. J. Chem. Eng. Data 1984, 29, 45– 52, DOI: 10.1021/je00035a016
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  24
  Density, viscosity, and electrolytic conductivity of concentrated aqueous electrolyte solutions at several temperatures. Alkaline-earth chlorides, lanthanum chloride, sodium chloride, sodium nitrate, sodium bromide, potassium nitrate, potassium bromide, and cadmium nitrate
  Isono, Toshiaki
  Journal of Chemical and Engineering Data (1984), 29 (1), 45-52CODEN: JCEAAX; ISSN:0021-9568.
  The ds., viscosities, and electrolytic conductivities of concd. aq. solns. of alk. earth chlorides, LaCl3, Na2SO4, NaNO3, NaBr, KNO3, KBr, and Cd(NO3)2 were measured at 15-55°. Temp. dependences of these properties are represented in terms of their thermal coeffs. at 25°.
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25. 25
  Wahab, A.; Mahiuddin, S. Isentropic Compressibility and Viscosity of Aqueous and Methanolic Calcium Chloride Solutions. J. Chem. Eng. Data 2001, 46, 1457– 1463, DOI: 10.1021/je010072l
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  Isentropic Compressibility and Viscosity of Aqueous and Methanolic Calcium Chloride Solutions
  Wahab, Abdul; Mahiuddin, Sekh
  Journal of Chemical and Engineering Data (2001), 46 (6), 1457-1463CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  Speeds of sound and viscosities of aq. and methanolic calcium chloride solns. were measured as functions of concn. [0.0040 ≤ m/(mol·kg-1) ≤ 7.151 and 0.1903 ≤ m/(mol·kg-1) ≤ 3.252 for aq. and methanolic calcium chloride solns., resp.] and temp. (273.15 ≤ T/K ≤ 323.15). Isentropic compressibility isotherms of aq. calcium chloride solns. converge at 5.1 mol·kg-1. In the case of methanolic calcium chloride solns., isentropic compressibility isotherms vary smoothly with the increase in concn. and converge at 5.66 mol·kg-1 on extrapolation. Total solvation nos. of calcium chloride in water and methanol media were estd. to be 10.9 and 5.5, resp.
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26. 26
  Gonçalves, F. A.; Kestin, J. The Viscosity of CaCl₂ Solutions in the Range 20–50°C. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 24– 27, DOI: 10.1002/bbpc.19790830105
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  26
  The viscosity of calcium chloride solutions in the range 20-50°C
  Goncalves, F. A.; Kestin, J.
  Berichte der Bunsen-Gesellschaft (1979), 83 (1), 24-7CODEN: BBPCAX; ISSN:0005-9021.
  The measurements at atm. pressure covered the entire range of compns. up to satn. The reproducibility was several parts per 10,000, and the accuracy ≤0.3%. An accurate correlation between molality and d. was obtained for 20.00 and 25.00°.
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27. 27
  Zhang, H.-L.; Chen, G.-H.; Han, S.-J. Viscosity and Density of H₂O + NaCl + CaCl₂ and H₂O + KCl + CaCl₂ at 298.15 K. J. Chem. Eng. Data 1997, 42, 526– 530, DOI: 10.1021/je9602733
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  27
  Viscosity and Density of H2O + NaCl + CaCl2 and H2O + KCl + CaCl2 at 298.15 K
  Zhang, Hai-Lang; Chen, Geng-Hua; Han, Shi-Jun
  Journal of Chemical and Engineering Data (1997), 42 (3), 526-530CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The viscosity and d. of water + sodium chloride + calcium chloride solns. and water + potassium chloride + calcium chloride solns. were measured over the entire concn. range at 298.15 K. The recently extended Jones-Dole equation still functions well for these systems up to a high concn. It has been empirically found that when a seventh term of molarity was further added to the extended Jones-Dole equation, the viscosity for calcium chloride solns. and the mixed electrolyte solns. with larger ionic strengths could be excellently represented up to their satd. concns. In consideration of the large soly. of calcium chloride and furthermore of its large ionic strength and of its large viscosity-concn. coeff. it could be supposed that the extended Jones-Dole equation in this work should fit many aq. electrolyte solns. to their rather high concns. or just to the satd. concns. At low concns., the calcd. viscosity values obtained by simple additivity are close to the exptl. values. Above a certain concn., the calcd. viscosities of NaCl + CaCl2 and KCl + CaCl2 mixts. are lower than the exptl. values and the difference becomes larger with increasing concn.
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28. 28
  McBride-Wright, M.; Maitland, G. C.; Trusler, J. P. M. Viscosity and Density of Aqueous Solutions of Carbon Dioxide at Temperatures from (274 to 449) K and at Pressures up to 100 MPa. J. Chem. Eng. Data 2015, 60, 171– 180, DOI: 10.1021/je5009125
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  28
  Viscosity and Density of Aqueous Solutions of Carbon Dioxide at Temperatures from (274 to 449) K and at Pressures up to 100 MPa
  McBride-Wright, Mark; Maitland, Geoffrey C.; Trusler, J. P. Martin
  Journal of Chemical & Engineering Data (2015), 60 (1), 171-180CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The viscosity and d. of aq. solns. of carbon dioxide having mole fractions of CO2 of 0.0086, 0.0168, and 0.0271 are reported. The measurements were made in the single-phase compressed liq. region at temps. between (294 and 449) K at pressures up to 100 MPa; addnl. d. measurements were also made at T = 274 K in the same pressure range. The viscosity was measured with a vibrating-wire viscometer while the d. was measured by means of a vibrating U-tube densimeter; both were calibrated with pure water and either vacuum or ambient air. The d. data have an expanded relative uncertainty of 0.07 % with a coverage factor of 2. From the raw data, the partial molar volume of CO2 in aq. soln. has been detd. and correlated as an empirical function of temp. and pressure. When combined with the IAPWS-95 equation of state of pure water, this correlation represents the measured densities of under-satd. solns. of CO2 in water within ± 0.04 %. The viscosity data have an expanded relative uncertainty of 1.4 % with a coverage factor of 2. A modified Vogel-Fulcher-Tamman equation was used to correlate the viscosity as a function of temp., pressure, and mole fraction of CO2 with an abs. av. relative deviation of 0.4 %. The viscosity and d. of satd. aq. solns. of CO2 may be calcd. by combining the correlations presented in this work with a suitable model for the mole fraction of CO2 at satn.
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  McBride-Wright, M. Viscosity and Density of Aqueous Fluids with Dissolved CO₂; Imperial College London: London, 2013.
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  Darling, A. S. Iridium Platinum Alloys: A Critical Review of Their Constitution and Properties. Platin. Met. Rev. 1960, 4, 18– 26
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  Iridium-platinum alloys. Critical review of their constitution and properties
  Darling, A. S.
  Platinum Metals Review (1960), 4 (), 18-26CODEN: PTMRA3; ISSN:0032-1400.
  32 references.
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  Ciotta, F. Viscosity of Asymmetric Liquid Mixtures under Extreme Conditions; Imperial College London: London, 2010.
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  Caudwell, D. R. Viscosity of Dense Fluid Mixtures; University of London, 2004.
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  Retsina, T.; Richardson, S. M.; Wakeham, W. A. The Theory of a Vibrating-Rod Densimeter. Appl. Sci. Res. 1986, 43, 127– 158, DOI: 10.1007/bf00386040
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  The theory of a vibrating-rod densimeter
  Retsina, T.; Richardson, S. M.; Wakeham, W. A.
  Applied Scientific Research (1986), 43 (2), 127-58CODEN: ASRHAU; ISSN:0003-6994.
  A theory is presented of a device for the accurate detn. of the d. of fluids over a wide range of thermodn. states. The instrument is based upon the detn. of the characteristics of the resonance of a circular-section tube or rod, performing steady, transverse oscillations in the fluid. The theory accounts for the fluid motion external to the rod as well as the mech. motion of the rod and is valid over a defined range of conditions. A complete set of working equations and corrections is obtained for the instrument which, together with the limits of the validity of the theory, prescribe the parameters of a practical design capable of high accuracy.
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34. 34
  Retsina, T.; Richardson, S. M.; Wakeham, W. A. The Theory of a Vibrating-Rod Viscometer. Appl. Sci. Res. 1987, 43, 325– 346, DOI: 10.1007/bf00540567
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  Abramowitz, M. S.; Stegun, I. A. Handbook of Mathematical Functions; Dover: New York, 1965.
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  Kestin, J.; Khalifa, H. E.; Sookiazian, H.; Wakeham, W. A. Experimental Investigation of Effect of Pressure on Viscosity of Water in Temperature-Range 10-150 °C. Ber. Bunsen Ges. Phys. Chem. 1978, 82, 180– 188, DOI: 10.1002/bbpc.197800008
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  Kestin, J.; Khalifa, H. E.; Abe, Y.; Grimes, C. E.; Sookiazian, H.; Wakeham, W. A. Effect of Pressure on Viscosity of Aqueous Nacl Solutions in Temperature-Range 20 °C - 150 °C. J. Chem. Eng. Data 1978, 23, 328– 336, DOI: 10.1021/je60079a011
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  Effect of pressure on the viscosity of aqueous sodium chloride solutions in the temperature range 20-150°C
  Kestin, Joseph; Khalifa, H. Ezzat; Abe, Yoshiyuki; Grimes, Clifford E.; Sookiazian, Heros; Wakeham, William A.
  Journal of Chemical and Engineering Data (1978), 23 (4), 328-36CODEN: JCEAAX; ISSN:0021-9568.
  The effect of pressure was studied on the viscosity of 0-5.4 m aq. NaCl solns. at 20-150 °. The viscosity was measured by the oscillating-disk method at 0-30 MPa at six concns. along a large no. of isotherms. The exptl. results have an estd. uncertainty of ±0.5%. The exptl. data were correlated in terms of pressure, temp., and concn. The correlation reproduces the original data to within the quoted uncertainty.
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38. 38
  Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509– 1596, DOI: 10.1063/1.555991
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  A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa
  Span, R.; Wagner, W.
  Journal of Physical and Chemical Reference Data (1996), 25 (6), 1509-1596CODEN: JPCRBU; ISSN:0047-2689. (American Chemical Society)
  This work reviews the available data on thermodn. properties of carbon dioxide and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data of the following properties: (a) thermal properties of the single-phase region (pρT) and (b) of the liq.-vapor satn. curve (ps, ρ', ρ") including the Maxwell criterion, (c) speed of sound w and (d) specific isobaric heat capacity cp of the single phase region and of the satn. curve, (e) specific isochoric heat capacity cυ, (f) specific enthalpy h, (g) specific internal energy u, and (h) Joule-Thomson coeff. μ. By applying modern strategies for the optimization of the math. form of the equation of state and for the simultaneous nonlinear fit to the data of all these properties, the resulting formulation is able to represent even the most accurate data to within their exptl. uncertainty. In the tech. most important region up to pressures of 30 MPa and up to temps. of 523 K, the estd. uncertainty of the equation ranges from ±0.03% to ±0.05% in the d., ±0.03% to ±1% in the speed of sound, and ±0.15% to ±1.5% in the isobaric heat capacity. Special interest has been focused on the description of the crit. region and the extrapolation behavior of the formulation. Without a complex coupling to a scaled equation of state, the new formulation yields a reasonable description even of the caloric properties in the immediate vicinity of the crit. point. At least for the basic properties such as pressure, fugacity, and enthalpy, the equation can be extrapolated up to the limits of the chem. stability of carbon dioxide. Independent equations for the vapor pressure and for the pressure on the sublimation and melting curve, for the satd. liq. and vapor densities, and for the isobaric ideal gas heat capacity are also included. Property tables calcd. from the equation of state are given in the appendix.
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39. 39
  Duan, Z.; Moller, N.; Weare, J. H. A High Temperature Equation of State for the H₂O-CaCl₂ and H₂O-MgC_l2 Systems. Geochim. Cosmochim. Acta 2006, 70, 3765– 3777, DOI: 10.1016/j.gca.2006.05.007
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  A high temperature equation of state for the H2O-CaCl2 and H2O-MgCl2 systems
  Duan, Zhenhao; Moller, Nancy; Weare, John H.
  Geochimica et Cosmochimica Acta (2006), 70 (15), 3765-3777CODEN: GCACAK; ISSN:0016-7037. (Elsevier)
  An equation of state (EOS) is developed for salt-water systems in the high temp. range. As an example of the applications, this EOS is parameterized for the calcn. of d., immiscibility, and the compns. of coexisting phases in the CaCl2-H2O and MgCl2-H2O systems from 523 to 973 K and from satn. pressure to 1500 bar. All available volumetric and phase equil. measurements of these binaries are well represented by this equation. This EOS is based on a Helmholtz free energy representation constructed from a ref. system contg. hard-sphere and polar contributions plus an empirical correction. For the temp. and pressure range in this study, the electrolyte solutes are assumed to be assocd. The water mols. are modeled as hard spheres with point dipoles and the solute mols., MgCl2 and CaCl2, as hard spheres with point quadrupoles. The free energy of the ref. system is calcd. from an anal. representation of the Helmholtz free energy of the hard-sphere contributions and perturbative ests. of the electrostatic contributions. The empirical correction used to account for deviations of the ref. system predictions from measured data is based on a virial expansion. The formalism can be used for generalization to aq. systems contg. insol. gases (CO2, CH4), alkali chlorides (NaCl, KCl), and alk. earth chlorides (CaCl2, MgCl2). The program of this model is available as an electronic annex (see EA1 and EA2) and can also be downloaded at: http://www.geochem-model.org/programs.htm.
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40. 40
  Duan, Z.; Sun, R. An Improved Model Calculating CO₂ Solubility in Pure Water and Aqueous NaCl Solutions from 273 to 533 K and from 0 to 2000. Chem. Geol. 2003, 193, 257– 271, DOI: 10.1016/s0009-2541(02)00263-2
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  An improved model calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar
  Duan, Zhenhao; Sun, Rui
  Chemical Geology (2003), 193 (3-4), 257-271CODEN: CHGEAD; ISSN:0009-2541. (Elsevier Science B.V.)
  A thermodn. model for the soly. of carbon dioxide (CO2) in pure water and in aq. NaCl solns. for temps. from 273 to 533 K, for pressures from 0 to 2000 bar, and for ionic strength from 0 to 4.3 m is presented. The model is based on a specific particle interaction theory for the liq. phase and a highly accurate equation of state for the vapor phase. With this specific interaction approach, this model is able to predict CO2 soly. in other systems, such as CO2-H2O-CaCl2 and CO2-seawater, without fitting exptl. data from these systems. Comparison of the model predictions with exptl. data indicates that the model is within or close to exptl. uncertainty, which is about 7% in CO2 soly.
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41. 41
  Comuñas, M. J. P.; Bazile, J.-P.; Baylaucq, A.; Boned, C. Density of Diethyl Adipate Using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements. J. Chem. Eng. Data 2008, 53, 986– 994, DOI: 10.1021/je700737c
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  Density of Diethyl Adipate using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements
  Comunas, Maria J. P.; Bazile, Jean-Patrick; Baylaucq, Antoine; Boned, Christian
  Journal of Chemical & Engineering Data (2008), 53 (4), 986-994CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  New d. data for di-Et adipate (DEA) over 12 isotherms [(293.15 ≤ T ≤ 403.15) K] and 15 isobars [(0.1 ≤ p ≤ 140) MPa] are reported. This paper presents also the calibration procedure proposed for a new exptl. equipment. Data reliability has been verified over the pressure and temp. exptl. intervals by comparing our exptl. results for toluene and 1-butanol with previous literature data. A total of 732 exptl. data points have been measured in the framework of this work. The exptl. uncertainty is estd. to be ± 0.5 kg·m-3 (around 0.05 %). The pressure and temp. dependencies of di-Et adipate densities were accurately represented by the Tammann-Tait equation with std. deviations of 0.3 kg·m-3. These data were used to analyze the isothermal compressibility and the isobaric thermal expansivity for this fluid.
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42. 42
  Wagner, W.; Pruss, A. The Iapws Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387– 535, DOI: 10.1063/1.1461829
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  The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use
  Wagner, W.; Pruss, A.
  Journal of Physical and Chemical Reference Data (2002), 31 (2), 387-535CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. In 1995, the International Assocn. for the Properties of Water and Steam (IAPWS) adopted a new formulation called "The IAPWS Formulation 1995 for the Thermodn. Properties of Ordinary Water Substance for General and Scientific Use", which we abbreviate to IAPWS-95 formulation or IAPWS-95 for short. This IAPWS-95 formulation replaces the previous formulation adopted in 1984. This work provides information on the selected exptl. data of the thermodn. properties of water used to develop the new formulation, but information is also given on newer data. The article presents all details of the IAPWS-95 formulation, which is in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data for the following properties: (a) thermal properties of the single-phase region (pρT) and of the vapor-liq. phase boundary (pσρ'ρ''T), including the phase-equil. condition (Maxwell criterion), and (b) the caloric properties specific isochoric heat capacity, specific isobaric heat capacity, speed of sound, differences in the specific enthalpy and in the specific internal energy, Joule-Thomson coeff., and isothermal throttling coeff. By applying modern strategies for optimizing the functional form of the equation of state and for the simultaneous nonlinear fitting to the data of all mentioned properties, the resulting IAPWS-95 formulation covers a validity range for temps. from the melting line (lowest temp. 251.2 K at 209.9 MPa) to 1273 K and pressures up to 1000 MPa. In this entire range of validity, IAPWS-95 represents the most accurate data to within their exptl. uncertainty. In the most important part of the liq. region, the estd. uncertainty of IAPWS-95 ranges from ±0.001% to ±0.02% in d., ±0.03% to ±0.2% in speed of sound, and ±0.1% in isobaric heat capacity. In the liq. region at ambient pressure, IAPWS-95 is extremely accurate in d. (uncertainty ≤ ±0.0001%) and in speed of sound (± 0.005%). In a large part of the gas region the estd. uncertainty in d. ranges from ±0.03% to ±0.05%, in speed of sound it amts. to ±0.15% and in isobaric heat capacity it is ±0.2%. In the crit. region, IAPWS-95 represents not only the thermal properties very well but also the caloric properties in a reasonable way. Special interest has been focused on the extrapolation behavior of the new formulation. At least for the basic properties such as pressure and enthalpy, IAPWS-95 can be extrapolated up to extremely high pressures and temps. In addn. to the IAPWS-95 formulation, independent equations for vapor pressure, the densities, and the most important caloric properties along the vapor-liq. phase boundary, and for the pressure on the melting and sublimation curve, are given. Moreover, a so-called gas equation for densities up to 55 kg m-3 is also included. Tables of the thermodn. properties calcd. from the IAPWS-95 formulation are listed.
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43. 43
  Othmer, D. F.; Conwell, J. W. Correlating Viscosity and Vapor Pressure of Liquids. Ind. Eng. Chem. 1945, 37, 1112– 1115, DOI: 10.1021/ie50431a027
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  Correlating viscosity and vapor pressure of liquids
  Othmer, Donald F.; Conwell, John W.
  Industrial and Engineering Chemistry (1945), 37 (), 1112-15CODEN: IECHAD; ISSN:0019-7866.
  Straight lines are obtained when viscosity data are plotted on log paper against a temp. scale readily calibrated by using the vapor pressure of a reference substance such as H2O. In general the lines of such a plot must be isobaric. In some cases the viscosity data for a substance are best expressed as a series of 2 or 3 connecting straight lines. The breaks are due to changes in the phys. and often chem. nature of the material. H2O shows a break at about 40°. The equation for the straight line is log μ = - A log P + C, where μ is the viscosity of the material and P is the vapor pressure of any reference liquid, both being expressed in any desired units. A and C are consts. The use of a reduced temp. scale gives straight lines which in many cases tend to converge in a narrow range at the extrapolated points corresponding to the crit. Similar plots are obtained with fluidities.
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44. 44
  IAPWS Release on the Iapws Formulation 2008 for the Viscosity of Ordinary Water Substance , 2008.
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45. 45
  Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mareš, R.; Miyagawa, K. New International Formulation for the Viscosity of H₂O. J. Phys. Chem. Ref. Data 2009, 38, 101– 125, DOI: 10.1063/1.3088050
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  New International Formulation for the Viscosity of H2O
  Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mares, R.; Miyagawa, K.
  Journal of Physical and Chemical Reference Data (2009), 38 (2), 101-125CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  The International Assocn. for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. This manuscript describes the development and evaluation of the 2008 formulation, which provides a correlating equation for the viscosity of water for fluid states up to 1173 K and 1000 MPa with uncertainties from less than 1% to 7% depending on the state point. (c) 2009 American Institute of Physics.
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46. 46
  Spycher, N.; Pruess, K. A Phase-Partitioning Model for CO₂–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO2-Enhanced Geothermal Systems. Transp. Porous Media 2010, 82, 173– 196, DOI: 10.1007/s11242-009-9425-y
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  A Phase-Partitioning Model for CO2-Brine Mixtures at Elevated Temperatures and Pressures: Application to CO2-Enhanced Geothermal Systems
  Spycher, Nicolas; Pruess, Karsten
  Transport in Porous Media (2010), 82 (1), 173-196CODEN: TPMEEI; ISSN:0169-3913. (Springer)
  Correlations are presented to compute the mutual solubilities of CO2 and chloride brines at temps. 12-300°C, pressures 1-600 bar (0.1-60 MPa), and salinities 0-6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO2-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on exptl. data from literature for phase partitioning between CO2 and NaCl brines, and extends the previously published correlations to higher temps. The model relies on activity coeffs. for the H2O-rich (aq.) phase and fugacity coeffs. for the CO2-rich phase. Activity coeffs. are treated using a Margules expression for CO2 in pure water, and a Pitzer expression for salting-out effects. Fugacity coeffs. are computed using a modified Redlich-Kwong equation of state and mixing rules that incorporate asym. binary interaction parameters. Parameters for the calcn. of activity and fugacity coeffs. were fitted to published soly. data over the P-T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual soly. model is presented for the case of a hypothetical, enhanced geothermal system where CO2 is used as the heat extn. fluid. In this simulation, dry supercrit. CO2 at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO2 displaces the formation water relatively quickly, but that the produced CO2 contains significant water for long periods of time. The amt. of water in the CO2 could have implications for reactivity with reservoir rocks and engineered materials.
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47. 47
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  Pressure-volume-temperature-concentration relation of aqueous sodium chloride solutions
  Rowe, Allen M., Jr.; Chou, James C. S.
  Journal of Chemical and Engineering Data (1970), 15 (1), 61-6CODEN: JCEAAX; ISSN:0021-9568.
  The derivs. ( v/ P)T,x of NaCl solns. have been exptl. detd. at 0-175° for NaCl concns. of 0-25 g per 100 g of soln. and pressures up to 350 kg/cm2. An interpolation formula which describes the pressure-vol.-concn. (P-v-T-x) relation has been developed to fit these exptl. results and the d. data from the literature.
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Extension of Vibrating-Wire Viscometry to Electrically Conducting Fluids and Measurements of Viscosity and Density of Brines with Dissolved CO2 at Reservoir Conditions

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Abstract

1. Introduction

2. Materials and Method

2.1. Chemicals

2.2. Apparatus

Figure 1

3. New Semi-Empirical Working Equation for Highly Conductive Fluids

3.1. Standard Equation for the VW Viscometer

3.2. Revised Working Equation for Highly Conductive Fluids

Figure 2

Figure 3

3.3. Determination of the Additional Damping Term

Figure 4

Figure 5

4. Experimental Procedure

4.1. Mixture Preparation

4.2. Measurement Sequence

5. Calibration and Uncertainty Analysis

5.1. Temperature

5.2. Pressure

5.3. System Volume

5.4. CO2 Mole Fraction

5.5. Density

5.6. Viscosity

6. Results and Discussion

6.1. Experimental Results

6.2. Hypotheses

6.3. Density

Figure 6

Figure 7

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Figure 10

6.4. Viscosity

Figure 11

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7. Conclusions

Author Information

Acknowledgments

References

Cited By

Abstract

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References

STEP 1:

STEP 2:

Extension of Vibrating-Wire Viscometry to Electrically Conducting Fluids and Measurements of Viscosity and Density of Brines with Dissolved CO₂ at Reservoir Conditions

5.4. CO₂ Mole Fraction