Foam flow investigation in 3D printed porous media: Fingering and gravitational effects

Flow in porous media investigations have shown foam injection have a higher sweep efficiency compare to gas injection. However, fingering of highly mobile gas into the foam bank and separation of fluids (gas and surfactant) resulted by gravity segregation can influence the performance of foam injection project. To the best of our knowledge, this phenomenon has not been investigated experimentally in the literature. In this study, foam injection experiments have been performed in a model oriented in a horizontal and perpendicular orientation with respect to gravity using also different flow rates. High resolution imaging tools were utilized to record displacement process of oil by gas/surfactant/foam. The recorded images enabled us to monitor gas fingering and foam flow dynamics at pore scale. The obtained results highlighted the adverse effect of fingering of highly mobile gas into the foam bank and fluids separation by gravity segregation in the performance of foam project.


INTRODUCTION
Displacement of fluids with gas and water is a common practice in many industrial applications such as soil remediation, enhanced oil recovery (EOR) and CO2 sequestration.
Gravity segregation due to the density difference between displaced and displacing fluids divides the porous medium into three zones I) override zone where only the phase with the lower density exists, II) underride zone where only the phase with the higher density exists and III) the mixed zone where both phases exist simultaneously 1 . This selective movement of fluids inside the porous media causes unstable displacement that influences the reservoir performance 2,3 . Foam which is a discontinuous gas phase separated by thin liquid films called lamellae can decrease mobility ratio between displacing and displaced fluids and address gravity segregation [4][5][6] . Foam modifies mobility ratio in two ways: first, the relative permeability of the displacing fluid ( K rD ) decreases by trapping gas in porous media, and second, by increasing the effective shear viscosity of the displacing fluid ( μ rD ) 7 . Increase in apparent viscosity by foam comes from three contributions: (1) surface tension gradient created when surfactant foaming agent migrates from the front of the bubbles and accumulates at their back, (2) the thin liquid slugs between bubbles, and wall and bubbles, and (3) resistance to deformation of air bubbles pass through the porous media that have smaller size than foam bubbles 8 . Foam forms inside the porous media by three mechanisms leave behind, snap-off, and lamellae division. Leave behind is the dominant mechanism of foam generation at lower flow rates. As gas invades into a media saturated with surfactant, the lamellae are left behind the gas 9 . Snap off mechanism is more important at high flow rate and can reduce the mobility of foam more significantly in comparison to the leave behind mechanism. Gas bubble expands as it moves through a pore throat to a pore body causing a decrease in capillary pressure and a pressure gradient in the liquid phase. Consequently, liquid accumulates in the pore throat and if the capillary pressure is large enough the liquid finally snaps off the gas bubble 10 . Lamellae division is similar to snap off and occurs at high flow rates. As a pre-existing lamellae approaches a branch point in porous media it divides into several lamellae 11 . Foam flows in porous media as a continuous phase or discontinuous phase 12 . Continuous flow occurs when gas goes through porous media without interruption by lamella. In discontinuous mode, gas is transferred as a chain of gas bubbles that are separated by lamella.
Foam can be placed in the reservoir by pre-generated foam injection, co-injection of gas and surfactant and surfactant-alternating-gas (SAG) injection. Surfactant must be used as the liquid phase to stabilize lamellae. Researches showed SAG injection in which alternating slugs of a surfactant solution and gas are injected into the reservoir is the optimum method for foam placing into the reservoir [13][14][15] . It reduces the contact of gas and water in surface facilities.
More importantly, foam weakens as the gas displaces water from the near well-region and the injectivity of gas increases and the possibility of reservoir fracturing decreases 5,16 . Holt and Vassenden 6 showed foam injection resulted in higher segregation length (i.e. a longer distance over which segregation occurs as a result of gravity) than gas and water. They showed that the segregation length ( L g ) in SAG injection process (the distance over which segregation occurs as a result of gravity): where Q( m 3 s ) is the total volumetric injection rate of gas and liquid, K (m 2 ) is the vertical permeability of the porous medium, ρ w and ρ g ( kg m 3 ) are liquid and gas density respectively, g( m s 2 ) is the gravity acceleration, D(m) is the thickness of the porous medium, and γ rt ) is the total relative mobility of the mixed gas-liquid zone. Here K rw and K rg are relative permeability of water and gas respectively, and μ w (Pa . s) and μ g (Pa . s) are the viscosity of water and gas respectively. Shi and Rossen 5 indicated high value of gravity numbers (e.g. ratio between viscous and gravity forces) defined as N g = ∆ ρ . g ∇ p promote gravity segregation in SAG injection process.
is the density differences between fluids and g( m s 2 ) is the gravity acceleration. Some other researchers studied the effect of gravity segregation in SAG injection process [18][19][20][21][22] . However, they did not consider the effect of showed in a simulation study that the fingering of highly-mobile gas into the foam bank may be unavoidable and causes instabilities in a foam injection process. This fingering can also distort the foam front, even when favorable mobility control creates in foam front. To the best of our knowledge, there is no experimental study to support these findings or refute them.
In this work, fingering of highly mobile gas into the foam bank and gravity segregation effects on fluids separation were studied in a foam injection process using a 2D micromodel system at a wide range of the injection rate.

Design and fabrication of porous media
Following the procedure described by Osei-Bonsu et al. 24 , the porous medium used in this research was designed with 'Rhinoceros' CAD software package for 3D illustrations. The pore network was created from a Voronoi diagram consisting of 660 polygons. Voronoi diagrams can be used to design homogenous and heterogeneous microfluidic and micromodel network that was used in many theoretical and numerical studies in the field of porous media and also commonly used in the foams literature [25][26][27] .
The model was populated with a random length pore throat size distribution ranging from 0.3 to 0.5 mm. The pore throat size can be defined as the radius of a circle fitting in the narrowest space that connect two adjacent pore bodies together. Plexiglas plate to prevent flow over the grains. Furthermore, two perforations (1 mm diameter) at opposite ends of the porous medium were placed to serve as the inlet and outlet.

Fluid properties and experimental procedure
In each run of the experiment, the printed porous medium was saturated with Isopar V (Brenntag, UK) referred to as 'oil' hereafter. The oil was stained red in order to enhance the visual contrast. Table 1 shows properties of the oil used in this study. The surfactant solution used for foam generation was prepared from a 1:1 blend of sodium dodecyl sulphate and cocamidopropyl betaine (2% active content) with 0.25M NaCl solution.

Image analysis
The recorded images were analyzed using in-house codes developed in MATLAB to distinguish the oil, grains (solid phase) and the injected fluids (see Osei-Bonsu et al. 24 for details of the segmentation algorithm). Additionally, Image J software was used to determine    The second flow regime occurred when the pressure gradient is large enough to produce fine textured foams generated mostly by snap-off mechanism and lamella division. The rate of lamellae generation and mobilization was large enough to make strong foam as can be seen in  model. In addition, Gas released from foam coalescence fingered through the oil phase in front of it and created some isolated oil blobs as can be seen in Figure 3 (d). In this flow regime, full oil recovery from the porous medium was attained after approximately 2.5 PV of injection.
At high flow rates, the displacement efficiency of foam injection decreased again as can be seen in Figure 2 (a) and Figure 3 (g). This is due to that at higher injection flow rate, more volume of gas fingers and subsequently more escaping gas occurred as can be seen in Figure   5. Visual observations also showed the volume of foam that existed as continuous phase increases by increasing flow rate. This continuous gas phase eventually fingered through the oil phase. Fingering more volume of gas caused instability in the displacement process and decrease in displacement efficiency. It may be expected that this gas fingering is due to dryout effect of foam at 85 foam quality. It can be said the dry-out effect is not relevant in our system with rather larger pores. Also, Kofi Osei-Bonsu et al 24 used the same surfactant and a porous media quite similar to what we used in our study and found the foam quality corresponds to the critical capillary pressure was 98. Therefore, we can be sure that in our system, it is presumably the presence of oil (rather than the dry out effect) which is what helps to destabilise foam. Complete oil displacement was occurred after about 3.5 PV of injection at 80 ml/hr flow rate.

Vertical orientation
Similar to the horizontal orientation, three distinct flow regimes were observed in the case of the vertical orientation. The first flow regime includes the lower end of injection rates (from 1 ml/hr to 5 ml/hr). Complete segregation of gas and surfactant was the dominant characteristic of this flow regime as depicted in Figure 3 (b). As Shi and Rossen proposed 5 large values of gravity number imply gravity segregation. Here gravity number ( N g = ∆ ρ . g ∇ P ) was calculated for different flow rates after 1 PV injection in Table 3 for the experiment conducted in vertical orientation.  The third regime in the case of vertical orientation corresponds to the higher injection rates.
In this flow regime, foam was generated in the mixed zone. However, similar to horizontal orientation, fingering of high volume of gas had adverse effect on foam displacement as can be seen in Figure 3 (h). Although, higher flow rates helped with addressing the effect of gravity segregation, but displacement efficiency decreases due to gas viscous fingering.

Quantitative analysis on foam saturation
The  In the vertical orientation, the saturation of foam was zero in the first flow regime (when the injection rate is low) due to complete segregation of gas and surfactant. In the second flow regime, the effect of gravity segregation decreased by increasing flow rate leading to increasing foam saturation (around 50 percent) followed by the third flow regime (when the injection rate is high) where the saturation of foam decreases to about 15 percent resulted from gas fingering.

Effects of the injection rate and gravity segregation on oil entrapment
Our results indicated that gas fingering and fluids separation by gravity segregation has  and Zone B (defined in Figure 1). However, this is not the case when the porous medium is placed vertically with most of the blobs trapped within Zone A (i.e. the upper part of the porous medium). As already illustrated, during injection through the vertical oriented porous medium, gas and surfactant solution moved to Zone A and Zone B, respectively due to the gravity segregation. Since the viscosity contrast between gas and oil is greater than viscosity contrast between surfactant and oil, Zone A is more prone to fingering and formation of isolated oil blobs. One can add to this the contribution of the fraction of gas escaping from Zone B toward Zone A due to the gravity.

Dynamics of foam displacement influenced by the gravity
In addition to the number and distribution of oil blobs, oil recovery and foam saturation, gravity segregation influences the dynamic of foam front displacement. As an example, During oil displacement in horizontal orientation, the front had a convex shape up to 1.2 PV injection followed by a gradual evolution into a concave front. The morphological evolution of the front is likely due to variations in the foam texture along the front. The insets in Figure   8 illustrating In vertical orientation, foam front adopted an 'S' shape after 1.7 PV injections. This is due to the gradual increase of the bubble density in the middle region and that a small part of Zone A caused high flow resistance (this is once again due to high bubble density) and changed flow orientations to other parts of the model. Subsequently, the foam front propagation in Zone B was faster than Zone A due to the presence of more liquid in Zone B (higher saturation) compared to Zone A as a result of the gravity segregation which led to a decrease in flow resistance in that region.