Membrane Flash Index: Powerful and Perspicuous Help for Efficient Separation System Design

There are different factors and indices to characterize the performance of a pervaporation membrane, but none of them gives information about their capabilities in the area of liquid separation compared to the most convenient alternative, which is distillation. Membrane flash index (MFLI) can be considered the first and only one that shows if the membrane is more efficient or not than distillation and quantifies this feature too. Therefore, the MFLI helps select the best separation alternative in the case of process design. In this study, the evaluation and capabilities of membrane flash index are comprehensively investigated in the cases of six aqueous mixtures: methyl alcohol–water, ethyl alcohol–water, isobutyl alcohol–water, tetrahydrofuran–water, N-butyl alcohol–water, and isopropanol–water. It must be concluded that the separation capacity of organophilic type membranes is remarkably lower than hydrophilic membranes in all cases of separation. The study of the MFLI is extended with the consideration of other binary interaction parameters like separation factor, permeation flux, selectivity, and pervaporation separation index (PSI) in order to find a descriptive relationship between them. For the same membrane material type, descriptive function can be determined between feed concentration and MFLI and PSI and separation factor, which can be used to calculate each other’s value. On the basis of the indices and especially the MFLI, a significant help can be given to the process design engineer to select the right liquid separation alternative and, in the case of pervaporation, find the most appropriate membrane.


INTRODUCTION
Flash distillation is a specific method within the whole of rectification and distillation processes, where a liquid mixture is warmed up and pumped into the distillation apparatus of reduced pressure with permanent stream. In steady-state operations, the combinations of two phases are permanent and in equilibrium. The liquid and vapor phases are fed into a decanter (phase separator) where they are treated separately. 1,2 Pervaporation is a current operation for the treatment of aqueous mixtures with organic content. The pervaporation (PV) technology is mostly applied for dehydration of organic substances, 3−9 separation of organic mixtures, 10−13 and takeout of low-concentration organic substances from their mixtures. 14−20 The separated mixture passes over a phase change in the thin film material (membrane) on account of the used vacuum at the product part that results in the permeate being in the vapor phase. 21−23 The mixture is separated by the sorption and diffusion features of a rather passing substance over a thin film membrane. 1 Depending on the passing substance, pervaporation is classified into two major categories: hydrophilic pervaporation (HPV) and organophilic pervaporation (OPV). 1,23−27 An enormous number of practical operations and publications represent the relevance of pervaporation as a separation process in the category of membranes. 28,29 The effectiveness and the slight functional circumstances make pervaporation a profitable process in the field of separation methods. 1,30 Inorganic zeolite and composite polydimethylsiloxane (PDMS) are the most used materials for organophilic pervaporation for discharge organic compounds from their mixtures. 31 Polyvinyl alcohol (PVA) is the generally used membrane type for hydrophilic pervaporation. 1,32 PV can be evaluated by various factors. Equation 1 describes the flux 33 as (1) where P i is the amount of substance i in the permeate side, A is the membrane surface area, and Δt is the duration of the separation process. 34 (2) where x i , x j and y i ,y j are concentrations of substances i and j in the feed side and the permeate side. It must be mentioned that the separation factor (α) is (dimensionless). 35 Equation 3 shows the calculation of the pervaporation separation index (PSI): Permeance can specify the performance of pervaporation membranes, which is normalized substance flux by the pressure divergence as impulsion: 1,36 The ratio of permeances gives the selectivity (β): 1 In the literature, the pervaporation separation index, flux, and separation factor are generally applied for ranking the separation performances of different pervaporations. 23 The listed factors are the functions of the inside attributions of the used material of membranes. However, the selectivity also depends on the functional circumstances, mainly permeate pressure, temperature, and compositions of feed. 23 It can be mentioned that the promising direction of evaluation pervaporation achievement is the determination of selectivity; 36 nevertheless, a few research papers describe this parameter.
It has to be mentioned that the literature do not show a comprehensive clear approach for the comparison of separation effectiveness of pervaporation and its separation alternative, which is distillation. 36 The relative vaporization in the distillation process is involved in the interpretation of selectivity by Baker. 1,29 Nevertheless, this comparison does not result in a direct and simple correlation between distillation and pervaporation for process engineers. Hinchliffe and Porter 37−39 have reported the cost-based comparison of membrane separation and distillation. Cost permeability has been defined and case studies have been plotted in the function of effective selectivity and this parameter. However, it is informative and really helpful for practice but very specific and difficult to generalize the comparison. Furthermore, the membrane prizes change quickly because this sector is innovative.
Considering pervaporation and flash distillation options, pervaporation can be compared to the characteristics of elementary flash distillation. Toth et al. 1 created a simply method, which is mainly based on the comparison of available theoretical maximum distillate compositions. The main formula of the so-called membrane flash index (MFLI) is as follows: where y i PV is the permeate concentration and y i D [VLE] is the equilibrium distillation value. The comparison perspective of the MFLI focuses only on the separation abilities of the distillation and pervaporation operations. The prime preference of the membrane flash index is simplicity and accuracy because only two practical (experimental) data (α i and x i F ) and the appropriate vapor−liquid equilibrium (VLE) data are enough for evaluation. The membrane flash index presents explicit comparison of distillation and pervaporation in the process and chemical engineering area. The separation achievement of PV is preferable than the application of flash distillation if the MFLI is above 1. 1 In our previous paper, 1 the calculation of the MFLI was described with one equilibrium model in detail. The purpose of this study is to evaluate the MFLI in the aspects of other descriptive quantities and to extend its calculation.

RESULTS AND DISCUSSION
In general, 10−15 assorted samples (membrane) with the highest membrane flash indexes are inspected in every case of the main group of membrane material types. Organophilic and  Table 1.
It can be concluded that PVA and other dehydration membranes are dominant in every hierarchy and organophilic pervaporation shows significantly worse separation efficiency than methanol dehydration. Table 2 introduces the highest results of MFLIs in the case of the different membrane types for which selectivity values were available in the research paper. The best three selectivities are introduced. In addition, the corresponding separation factors and PSI values are given to the comparison. The complete data set can be seen in Supporting Information, Part II/3.
It must be mentioned that there is no accordance between separation factor and PSI, e.g., the highest separation factor of the membrane type is not the highest in PSI value. In contrast, the membrane with the highest MFLI value has also the highest selectivity.   Table 3 introduces the MFLI of pervaporation membranes of ethyl alcohol−water mixtures.
It can be mentioned that the parameters of dehydration membranes are dominant as seen with methanol−water separation. The highest values of MFLIs in the case of organophilic and hydrophilic types for which selectivity values were available in the research paper can be seen in Table 4. Separations and PSI values were added; the complete data set can be seen in Supporting Information, Part III/3.
It can be said that the highest MLFIs have the highest selectivities too and there is no accordance between MFLIs and PSI values. The Supporting Information contains the    It must be mentioned that there is remarkably less OPV and HPV membrane type for separation of heterogeneous azeotropic compounds from water. Table 5 introduces the MFLIs of membranes in the organophilic and hydrophilic pervaporations of isobutanol−water mixture. Table 6 shows the comparison of the main descriptive quantities of IBU−water mixture.
Same tendencies and experience can be determined in separation of IBU−water binary mixture as in the case of ethyl alcohol and methyl alcohol. The Supporting Information contains a functional relationship between isobutanol feed weight fractions and PSIs and MFLIs in the case of PDMS and PVA membranes in the part of IV/3.
2.4. Separation of Tetrahydrofuran−Water Mixture. The comparison of separation factors, MFLIs, and PSIs of tetrahydrofuran−water mixture is summarized in Table 7.
2.5. Separation of N-Butanol−Water Mixture. Table 8 summarizes the comparison of separation factors, MFLIs, and PSI of N-butanol−water mixture.
2.6. Separation of Isopropanol−Water Mixture. Table  9 summarizes the comparison of separation factors, MFLIs, and PSI of isopropanol−water mixture.

CONCLUSIONS
In the case of process synthesis, the final decision about the design of a liquid separation system has to consider environmental impacts, cost elements of methods, controllability, etc., in many cases. Membrane flash index (MFLI) gives preliminary information about the selection between pervaporation and distillation methods to help find the appropriate separation method. Moreover, if the membrane flash index value is relative high, the membrane separation should be preferred by far. So, a high value of MFLI shows not only the priority of pervaporation but gives also a heuristic judgment how far it is better. As our examples show that the MFLI can be only a bit higher than 1, showing that pervaporation could be better, but the MFLI can be several orders of magnitude higher than 1 shows a superior performance of pervaporation over the distillation. On the contrary, if the membrane flash index is low, that is, near 1, flash distillation should be selected because that seems to be the better choice.
The separation capacities of six binary, aqueous mixtures are investigated. MFLIs, separation factors, total fluxes, pervaporation separation indices, and selectivity values are evaluated. Three thermodynamic models are introduced for the calculation of MFLIs to generalize the description. It can be determined that the dehydration type membranes have remarkably higher separation capacities in all investigated cases than the organophilic membranes.
To harmonize the MFLI with the other membrane parameters/indices, it is necessary to find the connection between these evaluation parameters to give support for         with the other membrane characterizing parameters. Therefore, an algorithm is presented for the calculation of the different membrane characterizing parameters for the efficient support of chemical process design. First, the calculation of the MFLI is suggested to determine the selection between pervaporation and distillation. If the MFLI suggests one to use pervaporation, the determination of selectivity is recommended for the recognition of optimal operating parameters, pressure, temperature, etc. Lastly, the calculation of PSI can summarize the information of purity with separation factor value, yield, and fluxes. Figure 7 introduces the possible operating boundaries of flash distillation.

COMPUTATIONAL METHODS
The available theoretical maximum vapor data (y max ) is the equilibrium composition of the feed, and the corresponding y i D data has to be established as a function of x i F , as can be seen in Figure 7.
Refereed vapor−liquid equilibrium data has to be applied to find the appropriate y i D . Information can be found in the Vapor−Liquid Equilibrium (VLE) Data Collection from DECHEMA 56 in the database of flowsheet simulators (ChemCAD, Aspen Plus, Aspen Hysys, etc.). In most of the cases, enough exact VLE data is not available. Thus, regression processes of thermodynamic models are offered for the definition of accurate and appropriate y i D . Three thermodynamic models are described, which is offered for the calculation of y i D in the case of the determination of MFLIs. The paper extends the calculation of MFLI with this presentation.
The activity coefficient model presented by Wilson 57 aims to incorporate two adjustable interaction parameters and clean constituent's molar volumes and to specify the excess Gibbs energy of binary solution, therefore modeling equilibrium. The activity coefficients can be calculated by eq 7: 58 where the values of Λ ij can be calculated from liquid molar volumes of clean constituents (V i , V j ) and λ ij and λ ij are interaction parameters of the Wilson model given in cal/g·mol: The main equation of the "non-random two-liquid model" (NRTL) 59 (9) where and (11) B ij , B ji , and α ij are used by the NRTL equation under the regression of binary interaction parameters (BIPs) in the flowsheet simulator, e.g., ChemCAD. 1 The "universal quasichemical model" (UNIQUAC) 60 combines together an enthalpic (residual contribution) term and an entropic (also called combinatorial contribution) term for the determination of activity coefficients. The combinato-

ACS Omega
http://pubs.acs.org/journal/acsodf Article rial term is the effect coming from the molecule shape (that could be calculated from group contributions), the residual term from interactions between molecules: 58  (14) where τ ij =exp( − Δu ij /RT), where Δu ij is the binary interaction parameter. The values are defined as Δu ij = u ij − u ii , incorporating the interactions between different and similar molecules. 58 It must be mentioned that the applied thermodynamic model has to be remarked in every cases.
The selection of the model should be confirmed in the literature. Using eq 15, y i PV can be calculated easily: It has to be also mentioned that the comparison is based on the best available permeate concentration. The main permeable component has to be distributed by each other: organic concentration in the permeate product at organophilic PV with an appropriate equilibrium organic concentration and, in contrast, water concentration in the permeate product at hydrophilic pervaporation with an appropriate equilibrium water concentration. Figure 8 introduces the general determination process of membrane flash index (MFLI). 1 The Supporting Information contains an example of the determination of MFLIs in Part I. Figures 9 and 10 Table 10). In the case of vapor−liquid equilibrium data, the "non-random two-liquid model" (NRTL) thermodynamic model 59 is applied.
The comparison of PV and flash distillation is studied only for such separation cases, where the target is not azeotrope fractionation. 1 It can be mentioned that improved separation achievement can be gained by applying rectification, although pervaporation is often the preferred solution in the case of the treatment of the azeotropic mixtures. 31,62 ■ ASSOCIATED CONTENT
Example calculation for membrane flash index (MFLI), separation of methanol and water, separation of ethanol and water, separation of isobutanol and water, separation of tetrahydrofuran and water, separation of N-butanol and water, separation of isopropanol and water, nomenclature, and references (PDF)