Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
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This achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
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We are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
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Thank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
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1. Introduction
Both polymeric and ceramic membranes have been the center of interest for their tremendous contribution in water treatment industry. Despite their advantages, these synthetic membranes have limitations in terms of performance and durability. Over the years, researchers have been trying to combine the effective features of both, polymeric and ceramic, materials in one new material called mixed matrix membrane (MMM) or hybrid membrane. The sole purpose of developing new materials has been to associate the advantageous characteristics of the two types of membranes boosting the overall process efficacy. Conventionally, objectives such as enhancement in permeability or selectivity, reduction in fouling and removal of specific contaminants have been attained either by combining two or more processes or by developing an integrated filtration process. However, material advancement in membrane technology and nanotechnology has made it possible to fine tune the process efficiency and have successfully paved the way for the synthesis of MMMs for different applications. Apart from the water purification applications, the advent of MMMs has revolutionized other areas also where separation or purification is of great significance. Some of these potential applications reported in literature include water purification, medical industry, catalytic, and gas separation. Nevertheless, MMMs have not yet crossed the lab-scale barrier because the MMM technology is still in a developmental phase and only a few lab-scale developments have been reported so far.
2. Types of MMMs
MMMs can be defined as incorporation of dispersed nanomaterials such as zeolite, carbon molecular sieve, and carbon nanotubes incorporated in a continuous polymer phase. Figure 1 presented a schematic of an ideal MMM structure including the dispersed phase and the polymer matrix [1].
Figure 1.
Schematic diagram of an ideal MMM structure [1].
MMM could offer the physicochemical stability of a ceramic material and the membrane forming ease of polymeric materials while promising the desired morphology with higher permeability, selectivity, higher hydrophilicity, high fouling resistance, high thermal, mechanical, and chemical strength over a wider temperature and pH range [2, 3, 4, 5, 6, 7].These types of MMMs are named as inorganic filler-based MMMs, organic filler-based MMMs, biofiller-based MMMs, and hybrid filler-based MMMs, depending on the type of the dispersed fillers in the polymer matrix, as presented in Figure 1 [1]. This chapter will focus on inorganic filler-based MMM, especially zeolite-MMM.
2.1. Inorganic filler-based MMMs
The field of inorganic filler-based membrane is a promising type of membrane, which has been explored extensively over the recent years. In the polymeric matrix, the inorganic fillers attach themselves to support materials by covalent bonds, van der Waals forces, or hydrogen bonds. These inorganic fillers are prepared through processes such as sol gel, inert gas condensation, pulsed laser ablation, spark discharge generation, ion sputtering, spray pyrolysis, photothermal synthesis, thermal plasma synthesis, flame synthesis, low-temperature reactive synthesis, flame spray pyrolysis, mechanical alloying/milling, mechano-chemical synthesis, and electrodeposition. Currently, different types of inorganic fillers have been added to the polymeric phases. Some of these fillers are zeolite [8], silica [9], TiO2 [10], carbon nanotubes [11], and silver [12]. There are two methods to incorporate inorganic fillers into membrane structure by blending with the solution or by attaching the fillers to the surface through different techniques [4]. Inorganic-based filler MMMs have been employed in water industry for the adsorptive removal of pollutants, disinfection and/ or microbial control, catalytic degradation, and desalination [13]. They also have potentials to provide both high gas superior selectivity and the desirable mechanical and economical properties. Researchers believe that a suitable combination of polymers and inorganic fillers should offer superior permeability and selectivity compared to simple materials. In this review, zeolite-MMM will be comprehensively studied, as a promising membrane for several applications.
2.1.1. Zeolite-MMMs
Zeolites are microporous crystalline aluminosilicate materials with uniform pore and channel size, thus they are used in various fields such as catalysts in the petrochemical industry, ion-exchangers, and absorbents for softening and purification of water [14, 15, 16]. Incorporation of zeolites into a polymer matrix has attracted great attention in membrane technology, due to several excellent advantages such as permeability improvement of the selective component, in addition to the enhancement of the thermal stability and the mechanical strength of a polymeric membrane, [17] and its molecular sieving property, thermal resistance and chemical stability [18, 19, 20]. On the other hand, zeolites are expensive. Limitation in both polymeric and zeolite offers the need to synthesize the novel polymer–zeolite MMM. The interaction of zeolites in the membrane matrix and its shape-selective catalytic properties could improve permeability and selectivity separations [21]. There have been numerous attempts to incorporate zeolite particles in polymer matrices for gas separation due to its superior separation and size exclusion and in water purification applications [22, 23].
Rezakazemi et al. [24] studied the gas transport properties of zeolite-reinforced polydimethylsiloxane (PDMS) MMM. They evaluated the feasibility of this zeolite-MMM for hydrogen purification and natural gas sweetening, and also the permeation rates of CH4, H2, C3H8, and CO2 were assessed. The filler was dispersed homogenously in the matrix without any voids at the zeolite–polymer interface. It was confirmed that the homogenous incorporation of filler in the matrix resulted in higher gas permeability for the MMM, as compared with the polymeric membranes.
Ciobanu et al. [25] reported that zeolite-polyurethane membranes demonstrated improved properties. The good interaction between the polymer and the zeolite at the interface was confirmed and the membrane swelling was reduced. Consequently, the water flux through membrane increased with increasing zeolite concentration.
Hoek [26] studied the formation of mixed matrix reverse osmosis membranes by the interfacial polymerization of thin film nanocomposite polysulfone supports impregnated with zeolites. Figure 2 represents the cross-section image of zeolite nanocomposite reverse osmosis membrane, which is utilized for water purification through desalination process. It was found that increasing the zeolite nanofillers concentrations resulted in smoother, more hydrophilic, and more negatively charged MMM. As a consequence, the MMM membrane demonstrated high flux and a slight improvement in salt rejection compared to TFC membrane without zeolite nano-particles due to changes of membrane morphology.
Figure 2.
Schematic cross-section of zeolite nanocomposite membrane (zeolite-MMM) [26].
3. Interfacial morphology of zeolite-MMMs
To obtain the optimum interfacial morphology between the zeolites and polymer, several key roles should be considered. The first one is to promote the adhesion between polymer matrix and molecular sieve phases by modifying the zeolite surface with silane coupling agents [27, 28, 29]. The second one is to introduce low molecular weight materials to fill the voids between polymer and molecular sieve phases [30, 31]. The third one is to apply high processing temperatures close to glass transition temperature (Tg) of polymeric materials to maintain the polymer chain flexibility during the membrane formation [32]. The fourth one is to prime the surface of zeolites by polymer [33].
The polymer matrix plays an important role for permeability and the inorganic filler has a controlling factor for the selectivity of the separation process. As a result, interfacial compatibility between the two phases has profound impact on the separation performance for such membranes. The addition of inorganic fillers has key impacts on the interfacial void formation, aggregation, pore blockage of the morphology, and the transport phenomenon. Consequently, the impregnation of zeolites has a significant influence on the overall performance of the newly developed MMMs. The formation of these interfacial voids is attributed to two main phenomena, the interaction between the polymer phase and the filler and the stress exerted during preparation [1, 32]. The presence of interfacial voids creates additional channels that allow the solvent to pass through the membrane [34]. However, mechanical strength and rejection rate are also concerned by the channel density [35].
Figure 3 represents various structures at the polymer/zeolite interface region [36]. Figure 3a demonstrates a homogenous blend of polymer and sieve, indicating an ideal interphase morphology. Figure 3b shows polymer chains rigidification due to the shrinkage stresses generated during solvent removal. Figure 3c confirmed poor compatibility between zeolite and polymer matrix morphology, due to the formation of voids at the interfacial region. Figure 3d indicates sealing surface pores of zeolites by the rigidified polymer chains. Overall, the interaction between polymer and zeolite is related to chemical nature of the polymer and sieve surfaces, and the stress encountered during material preparation, which are the critical factors to form the interphase.
Figure 3.
Illustration of various structures at the polymer/zeolite interface region [36].
These features are a challenge and should be controlled or avoided for the synthesis of the targeted zeolite-MMM for several applications. The formation of relatively nonselective defects at the interface between the zeolite particles and the polymer medium will result in MMMs, which fail to demonstrate their performance [37]. Therefore, despite the good properties of the polymer-zeolite membranes MMMs, they still face some challenges to overcome.
4. Interfacial modification of zeolite-MMMs
Several strategies have been offered to improve the polymer–zeolite interaction; hence to avoid nonselective voids. These methods are included incorporation of a plasticizer into the polymer solution that can decrease the polymer glass transition temperature (Tg) [32]. Consequently, polymer chain flexibility maintains during membrane preparation either by annealing the membranes above glass transition temperature of polymer [38, 39] or external surface of zeolites can be modified by coupling agents. The surface-initiated polymerization is a most frequent technique to improve the polymer−filler adhesion in polymer-zeolite MMMs [40]. Furthermore, adding the low molecular-weight (LMWAs) to the membrane formulation can act as a compatibilizer or a third component to prepare glassy polymer/ LMWAs blend membranes [31, 41], priming method can be also used to reduce the stress at the polymer-particle interface, and to minimize agglomeration of the particles. Consequently, the interfacial interaction between the two components will be improved through coating the surface of the filler particles with a dilute polymer dope [31], to minimize the zeolite-solvent/nonsolvent interaction, especially for the use of modified zeolite in asymmetric membranes [42]. Therefore, the obtained hydrophobic surface can suppress the zeolite particles from acting as nucleating agents. As a result, it will minimize the voids induced by the unfavorable interaction between polymer and zeolite particles.
4.1. Interfacial modification with silane agents
Silane coupling agents were commonly proposed to modify the zeolite surface in order to improve the compatibility of the inorganic filler with the polymeric matrix [43, 44]. It is known from literatures related to the silanation of zeolites that silane coupling agents have two types of reactive groups. First, the hydroxyl groups of zeolites, which could make hydrogen bonds with the amino silane agent [43]. Second, the organo functional group, such as amino and epoxy, which could be used to bond polymer chains to the zeolite. Therefore, improving adhesion between the zeolite and the bulk polymer phase in the membrane was achieved [42]. Figure 4 shows a schematic silanation of zeolite surface with 3-aminopropyldimethylethoxysilane (APDMES) coupling agent [42].
Figure 4.
Schematic of the envisioned coupling reaction [42].
Koros [45] indicated that the glass transition temperature of MMMs is influenced by silane modification. In other words, the Tg of the zeolite-MMMs increased with the increasing of silane concentration on the surface of the zeolite particles. As a result, the silane modification of zeolite affects the mechanical properties of continuous phase due to the formation of the hydrogen bonding between the zeolite particles and polymer matrix and the movement reduction of the polymer chains [29, 41].
Leo [46] investigates the effects of silane-grafting on the separation performance of MMM for gas permeation. The 3-aminopropyltrimethoxysilane (APMS) was added to modify SAPO-34 zeolite before the impregnation into the asymmetric polysulfone (PSf) MMMs through dry–wet phase inversion method. Both PSf/modified SAPO-34 membranes showed great enhancement in terms of selectivity and permeability, compared to the original PSf membrane. The increment of CO2 selectivity and permeability was correlated to the diminishing of the interfacial voids, when SAPO-34 zeolite was modified using APMS in ethanol.
Pechar et al. [47] studied the use of 3-aminopropyltrimethoxysilane (APTMS) influence to modify ZSM-2 zeolite to synthesize polyimide MMMs. Although micrographs showed the absence of voids, however, the modified ZSM-2-MMMs performance for CO2 selectivity and permeability was dropped relatively, similarly, to the performance of pure polymeric membrane, due to the pore blockage of the ZSM-2 zeolite [48].
In order to overcome this problem, other researchers such as Li et al [28] modified zeolite 3A, 4A, and 5A using 3-aminopropylmethyldiethoxysilane (APMDES) in toluene solvent. Hence, rigidification of polymer chain and partial pore blockage reduced through this modification process. As a result, they showed high improvement for both of the selectivity and permeability of CO2 than those MMMs containing zeolite without the modification and without major blockage the zeolite pores. Therefore, in some cases, surface modification by the silane coupling agents was recommended to enhance interfacial adhesion but hardly improve permselectivity.
4.2. Addition of low molecular weight materials (LMWMs)
Adding low molecular weight additives (LMWAs) to the membrane formulation acts as a compatibilizer or a third component to improve the compatibility between zeolite and polymer matrix. The low molecular weight materials induce a hydrogen bond with hydroxyl and carbonyl moiety. In addition, the formation of hydrogen bond confirms its solubility in the solvent used to make the polymer dope solution. It should be noted that LMWMs should be solid at room temperature, in order to prevent their evaporation during membrane fabrication, and consequently losing their ability of forming interfacial voids [31]. Once hydrogen bonds are formed between polymer chains and LMWMs, the free volume of polymers decreases, which results in a decrease in their gas permeability whereas increase in their gas permselectivity.
Yilmaz [49] reported mixed matrix membranes for the use in gas separation by blending polycarbonates (PC) with an additive p-nitroaniline (pNA) and incorporating zeolite 4A particles as filler. The permeability of all gases was measured using differential scanning calorimetry (DSC) analysis through PC/(pNA)/zeolite 4A membranes, which were lower than those through pure PC membrane. The incorporation of pNA was essential, since pNA acts as a facilitator for provision of better interaction between rigid, glassy polymer PC and zeolite 4A particles. Therefore, the incorporation of a molecular-weight additive with functional groups into zeolite-MMMs can be used as a tool to improve the structure and performance properties of the membranes.
One of the examples of LMWMs is 2,4,6-triaminopyrimidine (TAP) that contained three primary amine groups, which are able to form hydrogen bonds with both hydroxyl and carbonyl groups [31]. Furthermore, it had been reported that the carbonyl groups of polyimides (PI) could interact with amine groups of urethanes through the hydrogen bond formation.
Park [31] used TAP to obtain the interfacial void-free PI membranes filled with zeolites. TAP enhanced the contact of zeolite particles with polyimide chains presumably by forming the hydrogen bonding. As a consequence, the void-free PI/zeolite 13X/TAP membrane showed the higher gas permeability for He, N2, O2, CO2, and CH4 with little expense of selectivity compared to the PI/TAP membrane having the same PI/TAP ratio, while the PI/zeolite 4A/TAP membrane showed the lower permeability but higher permselectivity. The difference between both membranes was influenced by the pore size of zeolites. In addition, the molecular sieving effect of zeolites seemed to take place when the kinetic diameter of gas penetrants approached the pore size of zeolites.
4.3. Annealing
One of the largest challenges in designing zeolite-MMMs is the poor contact between polymer and zeolite defects. Many efforts made to overcome to this problem associated with the zeolite-MMMs through the annealing of zeolite-MMMs above the glass transition temperature (Tg) [32]. In other words, Tg is considered as a qualitative estimation to compare the polymer chain rigidity of mixed matrix membranes at different zeolite types with simple polymer membrane and it also leads to better contact between zeolite and polymer chain [50]. Annealing process at temperature above the Tg results in the formation of stronger bond between polymer matrix and zeolite. Despite advantages of annealing in relaxing the stress imposed to the hollow fiber membrane, it results in higher packing density of polymer chains. Therefore, there are drawbacks associated with annealing. In addition, it did not lead to significant improvement in the morphology of the membranes. Annealing at high Tg formed sieve-in-a-cage morphology, which will be difficult to create a good contact between the polymer and the sieve [32]. In order to overcome to this disadvantage of annealing, incorporation of a plasticizer into the polymer solution can decrease the polymer Tg and thus maintain polymer chain mobility and flexibility during membrane fabrication [51]. Therefore, to develop membrane fabrication technology, a quench method after annealing membranes above Tg can be effective in gas separation process by forming frozen polymer chains quickly [52]. Therefore, it will have a higher free volume in the polymer matrix and subsequently higher gas permeability without the loss of selectivity.
4.4. Priming method
The dilute polymers are the same as the bulk polymers used for the preparation of MMMs. Coating the surface of the filler particles with a dilute polymer dope is known as the priming method [45]. The agglomeration is considered as responsible for defects between polymer matrix and zeolite particle phases [53]. Since more agglomeration occurs in the polymer matrix when smaller particles are used, especially at high particle loadings, and large zeolite particles are used to form practical mixed matrix membranes. Therefore, zeolite particles were primed by increasing amount of polymer. It should be considered that polymer effectively coats the zeolite particles before adding remaining bulk polymer and mixing with the priming polymer [54]. The purpose of priming is to reduce stress at the polymer-particle interface, increase the compatibility between zeolite and polymer in MMMs, and to minimize agglomeration of zeolite particles [55, 56].
5. Applications of zeolite-MMM
The advent of zeolite-MMMs enhances the separation or purification performance of the membranes significantly. The review represents various applications of zeolite-reinforced polymeric membranes. Some of these potential applications reported in literature include water purification, gas separation, medical, catalytic, and biomedical applications.
5.1. Zeolite-MMM for water purification
Water treatment is increasingly important to remove water pollutants and solve water problems. Drinking water may compose of hazardous substances such as toxins and endocrine disrupting compound. Therefore, it would be urgent to invent more sustainable and reliable treatment process to remove water contaminations and to regulate the quality of drinking water. The development of cost-effective membranes is in a great need to effectively replace the conventional water treatment technologies to produce water that meet or exceed stringent standards.
Recent studies have demonstrated that the zeolite-MMMs were applied to design reverse osmosis membrane to enhance the membrane properties such as permeability, selectivity, stability, surface area, or catalytic activity in water purification and separation processes [57, 58]. Nevertheless, there are only few studies performed on zeolite-MMMs for water treatment, it is determined that the size of zeolite was designed to match the expected polyimide active film thickness, thereby providing a preferential flow path through the nanochannels of zeolites [26, 59].
For example, thin film nanocomposite (TFN) reverse osmosis (RO) membranes have been used by incorporating zeolite particles into the PA rejection layer. It has shown that the incorporation of zeolite in a PA layer could improve its water permeability without significant loss of salt rejection under high pressure during RO process [60]. Main reason for that is nanochannels of zeolites with great sub-nanometer pores in zeolite nanoparticles that behave as preferential flow channels for water molecules. The zeolite-PA-based TFN membranes are considered as superior separation performance for RO applications due to their enhanced water permeability of active layer [61].
Tanga [61] provided an additional study to confirm that thin film nanocomposite membranes can significantly improve FO water flux significant with a relatively low zeolite loading due to both the surface and intrinsic separation properties of TFN membranes. Compared with TFC membrane, the TFN membrane is potentially more favorable during the application of treating feed solutions with relative higher salinity water under AL-FS orientation.
Sridhar [62] studied reactive separation of lactic acid (LA) using a microporous hydrophobic H-beta zeolite/polyvinylidene fluoride (PVDF) mixed matrix membrane from aqueous streams. Experiments were conducted using a stirred cell assembly consisting of two bell-shaped glass pipe reducers containing aqueous LA separated by the membrane from an organic solution of tri-noctylamine (TOA) carrier in alcoholic medium. The interfacial concentrations of species adjacent to the membrane in aqueous and organic chambers are influenced by mass transfer coefficients, the concentration of TOA in organic phase and the zeolite loading, and forward extraction rates. Overall, the mass transfer rates were improved with the zeolite addition, due to the kinetics of complex formation and diffusion. The continuous separation of LA by a membrane contactor could enhance the fermentation yield of the acid, which is inhibited by LA through deactivating of the lactate dehydrogenase enzyme of Lactobacillus bulgaricus microorganism used in the production of LA.
5.2. Zeolite-MMM for gas separation
Membrane technologies, such as pervaporation and gas separation, are recognized as highly promising approaches to reduce the energy consumption of industrial processes. Compared with polymeric membranes that show Robeson upper bound between selectivity and permeability, MMM are attracting research attention, due to their high permeability and selectivity.
It is known that the permeability of a gas through an MMM depends on several factors such as intrinsic properties of the filler and polymer, the filler loading, and the filler–polymer matrix interface, and the filler loading [58]. For designing a mixed matrix system for separating a certain gas pair, the molecular sieving phase must provide precise size and shape discrimination ability to distinguish the molecules. Moreover, zeolites with three-dimensional networks are generally preferred for gas separation since they offer less restricted diffusion paths. As a result, the attractive polymer matrix materials are generally glassy with relatively lower permeability and much higher selectivities. Indeed, addition of zeolites or another highly selective media would only improve the already industrially acceptable properties, if defects can be eliminated.
Pechar et al. [63] used silanated zeolite L filler modified with 3-aminopropyltriethoxysilane (APTES) and a glassy polyimide as polymer matrix for fabricating MMMs for gas separations. Both CO2 selectivity and permeability of the modified MMM dropped relatively to the neat membrane, due to the blocked zeolite pores by APTES.
Furthermore, metal–organic frameworks (MOFs), as porous fillers possessing molecular sieving properties, have been combined with polymers to give MMM with substantial enhanced separation performance of CO2/CH4 for natural gas sweetening or CO2/N2 in flue [64]. MOF-74 series recently have demonstrated superior CO2 adsorption capacities, due to the presence of open metal sites. This finding positions the materials as a very promising candidate for CO2 capture from flue gas. Figure 5 represents MIL-101/PSF membranes at different MOF loadings. It was found that the CO2 permeability increases from about 5 to over 35 barrer from pure PSF to 24 wt % MIL-101/PSF. The increase for CO2 also raises the ideal selectivity for CO2/N2 and CO2/CH4 from about 20 to 25 [65].
Figure 5.
SEM image of a MIL-101/PSF MMMs shows a homogenous distribution of MOF particles in the polymer matrix at different load [65].
5.3. Zeolite-MMM for catalysis
Recently, many reports demonstrated catalytic activity of polymer–zeolite MMM, because the interaction of materials in the membrane matrix and the shape-selective catalytic properties of zeolites can improve permselective separations. Membrane also functions as a separator in gas phase between different gaseous molecules. Thus, membrane should be permeable enough to give efficient separation. For liquid phase separation, metal organic complexes and inorganic filler such as zeolite have been used [66]. It is well presented mostly that polydimethylsiloxane (PDMS) is incorporated as a polymer matrix because of high permeability, affinity for reagents, thermal, mechanical, and chemical stability [67].
Langhendries and Baron [68] studied the catalytic activity of zeolite-filled poly(dimethylsiloxane) polymer membranes. The incorporation of zeolite-encaged iron-phthalocyanine partial oxidation catalysts into a dense hydrophobic polymer membrane results in a substantial improvement in catalyst performance. Both mathematical model and kinetics determined exact concentrations in polymer and catalyst, and subsequently, the resulting catalyst activity and selectivity. Their results also indicate that hydrophobic poly-(dimethylsiloxane) is an attractive polymer for the incorporation of the hydrophilic zeolite-encaged iron-phthalocyanine catalyst. As a result, diffusion through composite catalytic membranes can be predicted using the mass transfer coefficients of pure zeolite and pure polymer material, and a tortuosity factor based on the zeolite loading as a catalyst.
Another study, Jia and Peinemann [69] investigated the incorporation of polydimethylsiloxane (PDMS) into a polymer matrix and silicalite-1, a hydrophobic zeolite in order to study the permeation of various gases. In their study, only a couple of very high zeolite loadings were investigated, and they indicated that zeolite played the role of a molecular sieve in the membrane by facilitating the permeation of smaller molecules while it prevents the permeation of larger ones.
5.4. Zeolite-MMM for biomedical application
Combination of polymer materials with zeolite particles has been attracted attention not only due to enhanced mechanical and thermal properties, but also because of antibacterial properties. Polymer hosting can provide the enhanced antibacterial activity. There are three methods such as, production of reactive oxygen species (ROS) MMM, mixed matrix membrane direct damage to cell membrane; uptake of ions from mixed matrix membrane followed by DNA replication; and disruption of adenosine triphosphate (ATP) production [70].
Siddiq [71] studied the antibacterial effects of polysulfone/polyimide (PSf/PI) mixed matrix membranes fabricated by incorporation of modified zeolite (MZ) particles through solution casting method. The antibacterial property of fabricated zeolite-MMMs against Gram-negative bacteria (Klebsiella pneumonia, Salmonella typhi) and gram positive bacteria (Staphylococcus aureus, Bacillus subtilis) were also investigated. The MMM showed good antibacterial activity and a highest activity by PSf/PI/MZ mixed matrix membrane. Therefore, the combination effect of polysulfone/polyimide and modified zeolite sufficiently increased the antibacterial effect of mixed matrix membranes.
6. Challenges and future prospects
Recently, novel zeolite-MMMs have attracted great attention in membrane technology, due to the excellent advantages such as improvement in the permeability, selectivity, thermal stability, mechanical strength of a polymeric membrane. Furthermore, the recent developments demonstrated that gas separation as well as water treatment has significantly benefited from membrane technology so far and advancements in these areas are still in progress in order of their wider use can become a reality. However, the comprehensive understanding of organic–inorganic interfaces is in a great need. Zeolite-MMMs performance suffers from defects caused by poor contact at the molecular sieve/polymer interface, the complexity of the synthesis process, high cost, identification of compatible inorganic particles, agglomeration, inorganic particle concentration, phase separation, control of morphology and structural defects. Moreover, some zeolite-MMMs for water purification application is considered a potential hazard to humans and environmental, which also needs to more study to determine the hazardous character of these nanoparticles and mechanism of nanoparticles embedded membrane fouling in industrially water purification in the future.
One of most difficulties associated with membrane technology is fouling for a long time. Although, several strategies such as incorporation of antifouling nanoparticles, and surface modification have been used to overcome this problem, intensive investigations are needed to stop regeneration of microbial colonies on membrane surface and to reduce the leaching of filler. The next generation MMM should be developed with producing nano-size fillers without aggregation to improve their separation properties for membrane industry especially MMMs. There are several reasons to produce nano-size fillers, especially zeolite fillers such as more polymer/particle interfacial area and enhanced polymer–filler interface contact by smaller particles. The potential of incorporating fillers such as zeolite particles has not been attained up to the expectation of zeolite-MMMs performance, due to the smaller sizes, homogeneous distribution, agglomeration, price, availability, compatibility with polymer interface, their relation with water chemistry, better interfacial contact, and stability.
Despite many novel MMMs and fillers are being investigated so far but their performances are restricted due to limited synthesis processes. Previously process fails to demonstrate their performance due to the formation of relatively nonselective defects at the interface between the zeolite particles and the polymer medium on laboratory scale. Therefore, other major issue related to MMM is the interface defects that can lead to isolating zeolite fillers from the transport processes. Therefore, new techniques to achieve a perfect interface between inorganic fillers and polymers in membranes without compromising performance and scaling up these novel membranes under industrially relevant conditions is greatly needed [72].
In addition, many of these novel MMMs reported so far have been only tested on a laboratory scale and need further research to use commercially in industry. It is required to produce novel materials that can have high selectivity as well as nano-sized fillers with incredibly small sizes. There are limitations on developing novel materials due to high prices or expensive synthesis processes. The molecular dynamic simulations (MD) of mixed matrix materials could be effective approach to predict diffusive performance of MMM, especially zeolite-MMMs, and to provide experimental guidelines for tuning the membrane permeability at the molecular level without high costs. Although there are previously predicted models for predicting the processes contributing to membrane separations, however, studies in MMMs showed inadequate suitable models. Therefore, MD will be essential and effective to predict the morphology and intrinsic properties of these fillers and its interaction of the polymeric matrix.
Last but not least factor, is changing and membrane morphology could change properties of membranes, and subsequently will influence the membrane performance. Therefore, improving membrane performance in real conditions such as high temperature, high pressure, and with incorporating of a plasticizer into the polymer solution would be possible and essential in order to provide better thermally and chemically zeolite-MMMs at different operating conditions.
Although there is development success of the synthesis and the application of MMMs impregnated with zeolites for gas, water separation, and other applications, however, the mechanisms behind these phenomena require intensive investigations for more advanced MMM technology.
7. Conclusion
Mixed matrix membranes with zeolite fillers has attracted a lot of attention in membrane technology research due to its excellent advantages, such as high permeability and improved selectivity. Zeolite-MMMs could be considered an ideal candidate for purification industry since it combines the properties of polymeric matric and zeolite inorganic fillers. Application and fabrication techniques of zeolite reinforced polymeric membranes have been comprehensively reviewed in this article with the aim of optimizing interfacial interaction between the zeolite and the polymeric matrix. Compatibility between zeolite and polymer matrix can be improved with a number of methods, such as: by applying high processing temperature during membrane formation, the silane modification, and priming on the particle’s surface, annealing that can relax the stress imposed to hollow fiber and result in higher packing density of polymer chains, and the introduction of a LMWA agent between the polymer matrix and inorganic particles.
There have been numerous attempts to incorporate zeolite particles in polymer matrices in water purification applications and for gas separation due to its superior separation properties and size exclusion. Applications of zeolite-MMMs were re-evaluated for a variety of industrial processes, including water purification, medical industry, catalytic, and gas separation. However, despite its advantages, there are still issues and difficulties associated with zeolite-MMMs that have restricted their wider applications.
It can be concluded that the advancements in the application and fabrication of zeolite-MMM needs further intensive investigations. Future research should be conducted with the aim of developing new techniques that provide better understanding of zeolite incorporation into polymer structures. New materials should also be considered as a way of reducing the fouling concerns. Additional study is necessary for an improved understanding of the basic transport mechanism occurring through the MMMs. The next generation MMMs must be developed with nano-size fillers and without aggregation so as to improve their separation properties severely needed in the membrane industry. Some results indicate that the nanosize zeolite particles incorporated in MMMs offer better performance in comparison with micron size particles. New additives and modification agents should be produced to improve adhesion between polymer and inorganic fillers. In conclusion, despite of all the identified problems, MMM technology with zeolites could be considered a strong candidate for modern purification industry due to the remarkable properties of polymeric and inorganic zeolite materials.
Acknowledgments
The authors would like to acknowledge the Department of Chemical and Biological Engineering at the University of Saskatchewan for the support provided.
\n',keywords:"mixed matrix membrane, filler, zeolites, hydrophilicity, interfacial, morphology",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/59283.pdf",chapterXML:"https://mts.intechopen.com/source/xml/59283.xml",downloadPdfUrl:"/chapter/pdf-download/59283",previewPdfUrl:"/chapter/pdf-preview/59283",totalDownloads:880,totalViews:469,totalCrossrefCites:2,totalDimensionsCites:8,hasAltmetrics:0,dateSubmitted:"October 2nd 2017",dateReviewed:"January 11th 2018",datePrePublished:"November 5th 2018",datePublished:"June 27th 2018",dateFinished:"February 10th 2018",readingETA:"0",abstract:"Mixed matrix membranes (MMMs) could provide a solution to the permeability and selectivity trade-off in polymeric membranes and bridge the gap with inorganic membranes. MMM could offer the physicochemical stability of a ceramic material while ensuring the desired morphology with higher permeability, selectivity, hydrophilicity, fouling resistance, as well as greater thermal, mechanical, and chemical strength over a wider temperature and pH range. Zeolites are fascinating and versatile materials, vital for a wide range of industries due to their unique structure, greater mechanical strength, and chemical properties. This chapter focused on zeolite-MMM and characterized various zeolite-reinforced polymeric membrane types and applications. Several key rules in the synthesis procedures have been comprehensively discussed for the optimum interfacial morphology between the zeolites and polymers. Furthermore, the influence of the zeolite filler incorporation has been discussed and explored for a range of applications. This chapter provided a broad overview of the MMM’s challenges and future improvement investigative directions.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/59283",risUrl:"/chapter/ris/59283",book:{slug:"zeolites-and-their-applications"},signatures:"Mahboobeh Maghami and Amira Abdelrasoul",authors:[{id:"151521",title:"Dr.",name:"Amira",middleName:null,surname:"Abdelrasoul",fullName:"Amira Abdelrasoul",slug:"amira-abdelrasoul",email:"amira.abdelrasoul@usask.ca",position:null,institution:{name:"University of Saskatchewan",institutionURL:null,country:{name:"Canada"}}},{id:"239836",title:"Mrs.",name:"Mahboobeh",middleName:null,surname:"Maghami",fullName:"Mahboobeh Maghami",slug:"mahboobeh-maghami",email:"mam539@mail.usask.ca",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Types of MMMs",level:"1"},{id:"sec_2_2",title:"2.1. Inorganic filler-based MMMs",level:"2"},{id:"sec_2_3",title:"2.1.1. Zeolite-MMMs",level:"3"},{id:"sec_5",title:"3. Interfacial morphology of zeolite-MMMs",level:"1"},{id:"sec_6",title:"4. Interfacial modification of zeolite-MMMs",level:"1"},{id:"sec_6_2",title:"4.1. Interfacial modification with silane agents",level:"2"},{id:"sec_7_2",title:"4.2. Addition of low molecular weight materials (LMWMs)",level:"2"},{id:"sec_8_2",title:"4.3. Annealing",level:"2"},{id:"sec_9_2",title:"4.4. Priming method",level:"2"},{id:"sec_11",title:"5. Applications of zeolite-MMM",level:"1"},{id:"sec_11_2",title:"5.1. Zeolite-MMM for water purification",level:"2"},{id:"sec_12_2",title:"5.2. Zeolite-MMM for gas separation",level:"2"},{id:"sec_13_2",title:"5.3. Zeolite-MMM for catalysis",level:"2"},{id:"sec_14_2",title:"5.4. Zeolite-MMM for biomedical application",level:"2"},{id:"sec_16",title:"6. Challenges and future prospects",level:"1"},{id:"sec_17",title:"7. 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Effect of nanoparticles on gas sorption and transport in poly (1-trimethylsilyl-1-propyne). Macromolecules. 2003;36:6844'},{id:"B38",body:'Ismail AF, Rahim RA, Rahman WAWA. Characterization of polyethersulfone/Matrimid® 5218 miscible blend mixed matrix membranes for O2/N2 gas separation. Separation and Purification Technology. 2008;63:200'},{id:"B39",body:'Li Y, Chung TS, Huang Z, Kulprathipanja S. Dual-layer polyethersulfone (PES)/BTDA-TDI/MDI co-polyimide (P84) hollow fiber membranes with a submicron PES–zeolite beta mixed matrix dense-selective layer for gas separation. Journal of Membrane Science. 2006;277:28'},{id:"B40",body:'Hu CC, Liu TC, Lee KR, Ruaan RC, Lai JY. Zeolite-filled PMMA composite membranes: influence of coupling agent addition on gas separation. Desalination. 2006;193:14'},{id:"B41",body:'Karatay E, Kalıpçılar H, Yılmaz L. Preparation and performance assessment of binary and ternary PES-SAPO 34-HMA based gas separation membranes. Journal of Membrane Science. 2010;364:75'},{id:"B42",body:'Husain S, Koros WJ. Mixed matrix hollow fiber membranes made with modified HSSZ-13 zeolite in polyetherimide polymer matrix for gas separation. Journal of Membrane Science. 2007;288:195'},{id:"B43",body:'Xu L, Rungta M, Koros WJ. Matrimid® derived carbon molecular sieve hollow fiber membranes for ethylene/ethane separation. Journal of Membrane Science. 2011;380:138'},{id:"B44",body:'Khan AL, Cano-Odena A, Gutie’ rrez B, Minguillo’ n C, Vankelecom IFJ. Hydrogen separation and purification using polysulfone acrylate–zeolite mixed matrix membranes. Journal of Membrane Science. 2010;350:340'},{id:"B45",body:'Vu DQ, Koros WJ, Miller SJ. Mixed matrix membranes using carbon molecular sieves: I. Preparation and experimental results. Journal of Membrane Science. 2003;211:311'},{id:"B46",body:'Junaidi MUM, Khoo CP, Leo CP, Ahmad A. The effects of solvents on the modification of SAPO-34 zeolite using 3-aminopropyl trimethoxy silane for the preparation of asymmetric polysulfone mixed matrix membrane in the application of CO2 separation. Microporous and Mesoporous Materials. 2014;192:52'},{id:"B47",body:'Pechar TW, Tsapatsis M, Marand E, Davis R. Preparation and characterization of a glassy fluorinated polyimide zeolite-mixed matrix membrane. Desalination. 2002;146:3'},{id:"B48",body:'Pechar TW, Kim S, Vaughan B, Marand E, Tsapatsis M, Jeong HK, Cornelius CJ. Fabrication and characterization of polyimide–zeolite L mixed matrix membranes for gas separations. Journal of Membrane Science. 2006;277:195'},{id:"B49",body:'Şen D, Kalıpçılar H, Yılmaz L. Gas separation performance of polycarbonate membranes modified with multifunctional low molecular-weight additives. Separation Science and Technology. 2006;41:1813'},{id:"B50",body:'Li Y, Chung TS, Cao C, Kulprathipanja S. The effects of polymer chain rigidification, zeolite pore size and pore blockage on polyethersulfone (PES)-zeolite A mixed matrix membranes. Journal of Membrane Science. 2005;260:45'},{id:"B51",body:'Kulprathipanja S, Charoenphol J. U.S. Mixed Matrix Membrane for Separation of Gases, Patent 6,726,744, 2004'},{id:"B52",body:'Dolveck JY, Dai GH, Moser P, Pineri M, Aldebert P, Escoubes M, Avrillon R, Mileo JC. Materials Science Forum. 1992 1549, 105'},{id:"B53",body:'Li Y, Krantz WB, Chung TS. A novel primer to prevent nanoparticle agglomeration in mixed matrix membranes. AIChE Journal. 2007;53:2470'},{id:"B54",body:'Hillock AMW, Mille SJ, Koros WJ. Crosslinked mixed matrix membranes for the purification of natural gas: Effects of sieve surface modification. Journal of Membrane Science. 2008;314(1-2):193'},{id:"B55",body:'Chen XY, Ghaffari, Nik O, Rodrigue D, Kaliaguine S. Polymer. 2012;3:3269'},{id:"B56",body:'Ward JK, Koros WJ. Crosslinkable mixed matrix membranes with surface modified molecular sieves for natural gas purification: I. Preparation and experimental results. Journal of Membrane Science. 2011;377:75'},{id:"B57",body:'Tin PS, Chung TS, Jiang LY, Kulprathipanja S. Carbon–zeolite composite membranes for gas separation. Carbon. 2005;43:2025'},{id:"B58",body:'Zimmerman CM, Singh A, Koros WJ. Tailoring mixed matrix composite membranes for gas separations. Journal of Membrane Science. 1997;137:145'},{id:"B59",body:'Lind ML, Ghosh AK, Jawor A, Huang X, Hou W, Yang Y, Hoek EMV. Influence of zeolite crystal size on zeolite-polyamide thin film Nanocomposite membranes. Langmuir. 2009;25 10139'},{id:"B60",body:'Kim SH, Kwak SY, Sohn BH, Park TH. Design of TiO2 nanoparticle self-assembled aromatic polyamide thin-film-composite (TFC) membrane as an approach to solve biofouling problem. Journal of Membrane Science. 2003;211:157'},{id:"B61",body:'Maa N, Weia J, Liao R, Tanga CY. Zeolite-polyamide thin film nanocomposite membranes: Towards enhanced performance for forward osmosis. Journal of Membrane Science. 2012;405:149'},{id:"B62",body:'Madhumala MS, Sankarshan D, Sridhar S. Selective extraction of lactic acid from aqueous media through a hydrophobic H-Beta zeolite/PVDF mixed matrix membrane contactor. Industrial and Engineering Chemistry Research. 2014;53 17770'},{id:"B63",body:'Pechar T, Kim W, Vaughan S, Marand B, Baranauskas E, Riffle V, Jeong HK. Preparation and characterization of a poly(imide siloxane) and zeolite L mixed matrix membrane. Journal of Membrane Science. 2006;277:210'},{id:"B64",body:'Dechnik J, Sumby CJ, Janiak C. Enhancing mixed-matrix membrane performance with metal–organic framework additives. Crystal Growth & Design. 2017;17:4467'},{id:"B65",body:'Harold B, Jeazet T, Koschine T, Staudt C, Raetzke K, Janiak C. Correlation of gas permeability in a metal-organic framework MIL-101(Cr)–Polysulfone mixed-matrix membrane with free volume measurements by positron annihilation lifetime spectroscopy (PALS). Membranes. 2013;3:331'},{id:"B66",body:'Wales MD, Joos LB, Traylor WA, Pfromm P, Rezac M. Composite catalytic tubular membranes for selective hydrogenation in three phase systems. Catalysis Today. 2015. DOI: 10.1016/j.msec.2016.02.025'},{id:"B67",body:'Gu Y, Emin C, Remigy JC, Favier I, Gomez M, Noble RD, Lahitte JF. Hybrid catalytic membranes: Tunable and versatile materials for fine chemistry application. Materials Today Proceedings. 2016;3:419'},{id:"B68",body:'Langhendries G, Baron GV. Mass transfer in composite polymer-zeolite catalytic membranes. Journal of Membrane Science. 1998;141:265'},{id:"B69",body:'Jia M, Peinemann KV. Molecular sieving effect of zeolite filled silicone rubber membranes. Journal of Membrane Science. 1991;57:289'},{id:"B70",body:'Marambio-Jones C, Hoek EM. A review of the antibacterial effects of silver nanomaterials and potential implications for human health and the environment. Journal of Nanoparticle Research. 2010;12:1531'},{id:"B71",body:'Muntha ST, Siddiq M, Kausar A, Khan K. Mixed matrix membranes of polysulfone/polyimide reinforced with modified zeolite based filler: Preparation, properties and application. Chinese Journal of Polymer Science. 2018;36:65'},{id:"B72",body:'Wind JD, Paul DR, Koros WJ. Natural gas permeation in polyimide membranes. Journal of Membrane Science. 2004;228:227'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Mahboobeh Maghami",address:null,affiliation:'
Department of Chemical and Biological Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Department of Chemical and Biological Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
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1. Introduction
Performance and design of closed power and refrigeration cycles are basically driven by the thermodynamic properties of their working fluids. This is the reason why, since the early 1900s, many researchers have been stressing over the importance of optimizing the working fluid of these cycles and of selecting a proper thermodynamic model to accurately calculate their properties.
Two approaches are currently applied to seek the optimal working fluid. The first strategy consists in considering a limited number of existing pure fluids, the “physical fluid screening.” Alternatively, authors apply a product design approach, consisting in considering the molecular parameters of the working fluid as optimization variables; the resulting optimal fluid is thus fictive and is named here “fictive fluid screening.”
The application of the “physical fluid screening” is preferably associated with the use of equations of state whose accuracy has been properly validated over experimental data of the considered set of existing fluids (see, e.g., [1, 2, 3, 4, 5]). The preferred modeling option lies in the use of multi-parameter equations of state such as Helmholtz energy-based equations of state optimized by NIST (e.g., the GERG [6], the Span and Wagner [7], and so on), m-Benedict-Webb-Rubin (BWR) [8], Bender [9], and so on. Despite being highly accurate, these equations of state require the availability of a huge number of fluid-specific parameters, and their optimal values are thus provided by the model developer. An interesting chapter [10] has been recently published by Bell and Lemmon to spread the use of multi-parameter equations of state in the ORC community. However, at their current state of development, these models are thus not sufficiently flexible to be used in a screening approach extended to a population of hundreds of existing pure fluids and mixtures. For the same reason, the use of these multi-parameter models in a “fictive fluid screening” approach is inappropriate. To provide the reader with an order of magnitude, more than 1000 of fluids could be considered in this physical fluid screening procedure. The Design Institute for Physical Properties (DIPPR) currently provides accurate experimental data in a database (DIPPR 801) for 2330 pure fluids. Refprop 10.0 (NIST) [11] currently allows for the accurate representation of only 147 fluids.
To extend the range of considered fluids, studies present in the literature also consider the use of more flexible equations of state, that is, models characterized by a low number of parameters. If we focus on studies about closed power cycles, the equations of state, which have mainly been applied, are as follows: PC-SAFT-based model [12, 13] (which requires three molecule-specific parameters) in [14, 15, 16], BACKONE equation of state [17] (with four molecule-specific parameters) in [18], and the standard Peng-Robinson equations of state [19, 20] (with three parameters for each pure fluid) in [21, 22, 23]. These authors considered a different number of fluids. The one counting the highest considered number of fluids is the study by Drescher and Brüggemann [21], with 700 pure fluids. To our knowledge, all the other studies count less than 100 fluids (generally between 10 and 30). Peng-Robinson equation of state is currently the most flexible model to perform an extensive “physical fluid screening” of power and refrigeration working fluids. One of the main conclusions of authors who applied and compared different thermodynamic models (which is, unfortunately, rarely the case—we just found one study) is that the use of the Peng-Robinson equation of state is reliable in comparison with more accurate—but less flexible—multi-parameter equations of state [23].
Since 2004, Jaubert and co-workers have started publishing an improved version of the Peng-Robinson equation of state (version of the year 1978, PR78), the “Enhanced-Predictive-Peng-Robinson-78” (E-PPR78) [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]. Differently from PR78, this model is entirely able to predict the properties of mixtures without the need for its preliminary calibration over experimental data; moreover, the adjective enhanced has been juxtaposed to its previous name (PPR78) in 2011 [41] to highlight the improved accuracy in calculating mixing enthalpies and heat capacities (with respect to the original PPR78 model).
This model is widely used in the Chemical Engineering community but, inexplicably, remains unknown in the Energy Engineering one. The aims of this chapter are thus to present this model, to outline the proper way to apply it according to the latest advancements over pure fluid modeling [42, 43, 44, 45, 46], and to perform the screening of pure and/or multicomponent working fluids for power and refrigeration cycles.
2. From Peng-Robinson to E-PPR78 equation of state
The E-PPR78 model is an improved version of the equation of state published in 1978 by Peng and Robinson, the PR78 equation of state. This model has been developed to allow for the accurate and predictive (i.e., without the need for its optimization over experimental data) application of the Peng-Robinson equation of state to multi-component mixtures. We thus start with introducing the forerunner PR78 equation of state:
P=RTv−b−avv+b+bv‐bE1
When applied to the ith pure component, a in Eq. (1) corresponds to the pure-component cohesive parameter, ai, and b to its co-volume, bi. We will refer to a and b to indicate the mixture cohesive and co-volume parameters. We will detail in the following section how to calculate pure fluid ai and bi (Section 2.1) and mixture a and b (Section 2.2). Before continuing, it is worth warning the reader of the fact that the original E-PPR78 model degenerates into the standard PR78 equation of state when considering pure fluids.
2.1 PR78: the application to pure fluids
When applied to pure fluids, the standard Peng-Robinson equation of state requires the definition of parameters ai and bi, calculated as reported in the following:
However, in the last 4 years, two improved (i.e., thermodynamically consistent [42, 48] and very accurate) α-functions have been developed and published [44, 46]: a fluid-specific α-function and a generalized one, respectively, based on the model Twu91 [49] and Twu88 [50]. The application of the fluid-specific α-function Twu91 optimized in [46] guarantees the highest accuracy and requires three parameters (L, M, and N) for each pure fluid (reported by Pina-Martinez et al. [46] for 1721 molecules):
αiT=TTc,iNiMi−1⋅expLi1−TTc,iMiNi2E4
The generalized version of Twu88 [46] requires, similar to the Soave α-function, the knowledge of the acentric factor of each pure fluid and takes the following form:
The alternative use of the three α-functions recalled above leads to different accuracies in the calculation of thermodynamic properties. A comparison is reported in Table 1 between the PR equation of state incorporating the three different α-functions and pseudo-experimental data made available by DIPPR [51]. Piña-Martinez et al. also showed [46] that the modification of the α-function affects in a very negligible way the accuracy on volume calculations. To improve volumes, a further modification is required, as explained in Section 2.3.
Comparison of the mean average percentage errors (MAPEs) calculated with PR incorporating either the Soave α-function or the generalized Twu88 α-function or fluid-specific Twu91 α-function.
2.2 From PR78 to E-PPR78: the application to mixtures
The application of the PR equation of state to a mixture requires the selection of mixing rules for calculating mixture cohesive and co-volume parameters, a and b. Classical Van der Waals one-fluid mixing rules are used in the original PR78 model:
aTz=∑i=1N∑j=1NzizjaiTajT1−kijbz=∑i=1NzibiE6
The kij parameter is the so-called binary interaction parameter characterizing the molecular interactions between molecules i and j. The most accurate application of the original PR78 model requires the empirical optimization of the kij parameter over, at least, vapor-liquid equilibrium experimental data.
In 2004, Jaubert and Mutelet [24] proposed a model to predictively calculate the kij parameter by means of the application of a group contribution method. This method allows to estimate and predict the kij parameter by combining the molecular characteristics of elementary groups in which each molecule can be subdivided. This model is the most physically grounded model to determine the kij binary interaction parameters of PR-78 equation of state, and its use is extremely recommended to predictively calculate thermodynamic properties of multi-component mixtures. The expression provided by this model to predictively calculate the binary interaction parameter is as follows:
where ai and bi are the energy and co-volume parameters of the ith molecule, given in Eq. (2); Ng is the number of different groups defined by the method; and αik is the fraction of molecule i occupied by group k (occurrence of group k in molecule i divided by the total number of groups present in molecule i). Akl and Bkl, the group-interaction parameters, are symmetric, Akl = Alk and Bkl = Blk (where k and l are two different groups), and empirically determined by correlating experimental data. Also, Akk = Bkk = 0. The inclusion of this predictive expression for kij in the PR78 equation of state results in the Predictive-PR78 (PPR78).
It is worth recalling the historical development of the process of optimization of Akl and Bkl provided by the model developers. These parameters have initially been optimized over only vapor-liquid equilibrium data of binary mixtures. The model resulting from the use of these so-optimized group contribution parameters is called PPR78 (Predictive-Peng-Robinson equation of state). Lately, authors recognized that the inclusion of enthalpy and heat capacity data in the optimization process does not affect the accuracy in modeling VLE properties but improves extraordinarily the accuracy in calculating enthalpies and heat capacities of mixtures. So, starting from the year 2011 [41], published Akl and Bkl have been obtained by minimizing the errors between model calculations and experimental data relative to VLE, mixing enthalpy and heat capacity properties. The model resulting from the inclusion of these group contribution parameters is called Enhanced-Predictive-PR78 equation of state (E-PPR78). The last optimized values of Akl and of Bkl are reported in Table S1 of Supplementary Material of [39] for 40 molecular groups.
The optimization of these parameters has been performed over more than 150,000 experimental data and developed over more than 15 years. Even if preferable, that would be quite time-expensive if there was the need to re-optimize these group contribution parameters when changing any feature of the cubic equation of state (e.g., the α-function) or the cubic equation of state itself. Thankfully, it has been demonstrated [52] that it is possible to rigorously determine kij of any equation of state, knowing those of the original E-PPR78. In particular, it is possible to easily replace the Soave α-function, originally present in E-PPR78, with one of the improved functions presented in Section 2.1 (Eqs. (4) and (5)) and to use Akl and Bkl parameters of the Soave-based E-PPR78 by applying, instead of Eq. (7):
With respect to Eq. (7), this expression incorporates the pure component energy parameters calculated from the modified α-function. If we consider Twu α-function, we will thus use aimod given by:
aimodT=ac,iαimodTE9
It is worth observing that for the systems for which the Soave α-function is already very accurate (i.e., mean average percentage errors of the order of 1% for saturation pressures and of 2% for vaporization enthalpies and liquid heat capacities), the kij in Eq. (7) (i.e., the standard E-PPR78 model, with the Soave function) is able to provide the best reproduction of mixture data. The alternative use of a more accurate α-function (which thus improves pure fluid calculations) and Eq. (8), to enable the use of original Akl and Bkl group contribution parameters optimized with the original Soave-based E-PPR78, slightly deteriorates the results on mixtures (e.g., in the case of mixtures of alkanes). Clearly, the best would consist in re-optimizing all group contribution parameters using the best α-function directly in Eq. (7) instead of using the less-time-consuming Eq. (8) to derive the modified kij(T) parameters. However, even adopting the simplified approach consisting in using Eq. (8), the predictive capability of this model remains very accurate for modeling closed power cycle working fluids and refrigerants (see the examples reported in Figure 1).
Figure 1.
Isobar vapor-liquid equilibrium phase diagrams for the system n-butane (1)–n-hexane (2) (a) and isothermal vapor-liquid equilibrium phase diagrams for the system 1-butene (1)-R610 (2) (b), CO2 (1)-R134a (2) (c), R116 (1)-ethylene (2) (d). Lines represent calculations with E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Black points represent calculated pure component saturation pressures. (a) P (bar) = 10.132 (continuous line), 25.855 (long-dashed line), 32.75 (long- and short-dashed line), and 37.921 (short-dashed line); (b) T (K) = 312.92 (continuous line), 327.93 (long-dashed line), and 342.93 (short-dashed line); (c) T (K) = 252.95 (continuous line), 329.60 (long-dashed line), 339.10 (long- and short-dashed line), and 354.00 (short-dashed line); and (d) T (K) = 251.00 (continuous line) and 275.00 (short-dashed line).
However, there are systems for which the Soave model is very inaccurate and the use of Twu α-function with Soave-based E-PPR78 Akl and Bkl parameters highly improves results. By way of example, we present a pivotal binary mixture, benzene-cyclohexane, for which the standard PR equation of state (i.e., with the Soave α-function) does predict in a very inaccurate way of pure component saturation pressures. The original E-PPR78 equation of state, based on standard PR, is thus not very accurate in predictively modeling mixture saturation pressures because of the basic incapacity of the PR equation of state in modeling pure fluid properties (see in Figure 2a). However, if the Soave α-function is replaced with a more accurate α-function (given, e.g., by Eq. (4)) and if we then use Eq. (8) (with the Soave-based E-PPR78 Akl and Bkl parameters reported in [39]) to represent benzene (formed by six groups CHaro) and cyclohexane (formed by six groups CH2,cyclic), we obtain the graph as shown in Figure 2b. The accuracy is thus strongly improved without the need of re-optimizing any parameter.
Figure 2.
Isothermal VLE diagrams of the benzene (1)–cyclohexane (2) system, at 298.15 K. Lines represent calculations with standard E-PPR78 (a) and E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Green points represent calculated pure components saturation pressures.
Considering the above remarks, we suggest the replacement of the Soave α-function with the Twu one, in E-PPR78, thus applying Eq. (8) and Soave-based E-PPR78 group contribution Akl and Bkl parameters.
2.3 Volume correction
It is well known that one of the main limitations of cubic equations of state is their inaccuracy in high predicting liquid densities. Péneloux et al. [53] showed that it was possible to come up with this problem by adding a translation term to the volume. This translation consists in correcting the volume resulting from the resolution of the cubic equation of state (Eq. (1)) as follows:
In case of pure fluids:
vitTP=viTP−ciE10
In case of mixtures:
vtTPz=vTPz−cc=∑iNcci⋅zilinearmixingruleforcE11
In a recent publication, some accurate generalized (i.e., predictive) expressions for the translation term are optimized over 475 compounds, available in the DIPPR. For the Peng-Robinson equation of state, it is provided as follows:
ci=RTc,iPc,i0.1975−0.7325⋅zRA,iE12
A databank of Rackett compressibility factors, zRA, for 1489 components is available in Supplementary Material of [46]. The application of this translation has been observed to greatly improve the mean average percentage errors on calculated volumes. Considering the same 1489 pure fluids, the authors attested, in the same work, that the error in calculating the volume of the liquid phase at saturation condition is reduced from 8.7% (PR without translation) to 2.2% (PR with translation in Eq. (12)). If zRA is not available, authors suggested the use of the following expression, where the translation term is only a function of the acentric factor.
ci=RTc,iPc,i0.0096+0.0049⋅ωiE13
Jaubert et al. [45] were able to demonstrate that entropy (s), internal energy (u), Helmholtz energy (a), constant pressure and constant volume heat capacity (cp and cv), vapor pressure (Psat), and all properties change of vaporization (∆vapH, ∆vapS, ∆vapU, ∆vapA, ∆vapCp, and ∆vapCv) of pure fluid properties are not influenced by a temperature-independent volume translation.
It can be thus deduced that the addition of a translation term and the modification of the α-function have unlinked effects: the utilization of a volume translation improves volume calculations without affecting the abovementioned thermodynamic properties, while the use of an improved α-function improves subcritical and supercritical properties without deteriorating density calculations (see Conclusion reported in Section 2.1).
The application of both the consistent-Twu α-function (either Eq. (4) or Eq. (5)) and the volume translation in Eq. (12) results in the most accurate generalized cubic equation of state available in the literature.
For completeness, we would like to observe that, other than volume, also enthalpy and speed of sound are affected by the inclusion of a temperature-independent volume translation term (see [45]). However, the impact of such a translation on the calculation of enthalpy differences and of speed of sound is really negligible. In fact, it can be mathematically demonstrated from the use of relations presented in [45] that the enthalpy variation calculated with the translated cubic equation of state, ∆ht, and the one calculated with the nontranslated form, ∆h0, are related by the following relation:
So, first, it can be observed that isobar enthalpy variations are not affected by the inclusion of a volume translation term. Moreover, it can be shown that, in general, for temperature and pressure conditions relevant for power and refrigeration cycle applications, the term ci⋅P1−P2/Δh0 is much lower than 0.001 for gaseous systems and lower than 0.005 for liquid systems. As regards the speed of sound, it can be mathematically derived that ratio between the speed of sound determined with the translated cubic equation of state, wt, and the one calculated with the nontranslated EoS, w0, is given by:
wtTPw0TP=1−cvTPE15
which generally varies between 0.990 and 1.020 for liquid systems and is equal to 1.000 for vapor systems. These quantifications have been performed considering toluene, R134a, butane, propane, and ammonia.
3. Conclusion
Despite its simplicity and flexibility, E-PPR78 is a model that guarantees one of the most reliable predictive determinations of the thermodynamic properties of working fluids for power and refrigeration cycles. Being by definition a predictive model, its use is highly suggested to look for the best working fluid candidate over thousands of pure and multi-component fluids.
In this chapter, we presented the model and suggested to modify the Soave-based-original-E-PPR78 model by using the Twu α-function, to allow for the more precise representation of systems for which the Soave one is not sufficiently accurate. Finally, we recalled that the inclusion of a volume translation term in the E-PPR78 model highly improves the errors in the calculation of densities without affecting the rest of the, already accurate, properties.
\n',keywords:"thermodynamic cycle, pure working fluid, mixture, thermodynamic models, translated-E-PPR78",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/71837.pdf",chapterXML:"https://mts.intechopen.com/source/xml/71837.xml",downloadPdfUrl:"/chapter/pdf-download/71837",previewPdfUrl:"/chapter/pdf-preview/71837",totalDownloads:312,totalViews:0,totalCrossrefCites:0,dateSubmitted:"February 5th 2019",dateReviewed:"March 18th 2020",datePrePublished:"April 20th 2020",datePublished:"May 13th 2020",dateFinished:"April 20th 2020",readingETA:"0",abstract:"This chapter presents the features of the Enhanced-Predictive-PR78 equation of state (E-PPR78), a model highly suitable to perform “physical fluid screening” in power and refrigeration cycles. It enables, in fact, the accurate and predictive (i.e., without the need for its preliminary optimization by the user) determination of the thermodynamic properties of pure and multicomponent fluids usable in power and refrigeration cycles: hydrocarbons (alkanes, alkenes, alkynes, cycloalkane, naphthenic compounds, and so on), permanent gases (such as CO2, N2, H2, He, Ar, O2, NH3, NO2/N2O4, and so on), mercaptans, fluorocompounds, and water. The E-PPR78 equation of state is a developed form of the Peng-Robinson equation of state, which enables both the predictive determination of binary interaction parameters and the accurate calculation of pure fluid and mixture thermodynamic properties (saturation properties, enthalpies, heat capacities, volumes, and so on).",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/71837",risUrl:"/chapter/ris/71837",signatures:"Silvia Lasala, Andrés-Piña Martinez and Jean-Noël Jaubert",book:{id:"7659",title:"Organic Rankine Cycles for Waste Heat Recovery",subtitle:"Analysis and Applications",fullTitle:"Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications",slug:"organic-rankine-cycles-for-waste-heat-recovery-analysis-and-applications",publishedDate:"May 13th 2020",bookSignature:"Silvia Lasala",coverURL:"https://cdn.intechopen.com/books/images_new/7659.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-78985-474-9",printIsbn:"978-1-78985-473-2",pdfIsbn:"978-1-83880-376-6",editors:[{id:"190049",title:"Dr.",name:"Silvia",middleName:null,surname:"Lasala",slug:"silvia-lasala",fullName:"Silvia Lasala"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. From Peng-Robinson to E-PPR78 equation of state",level:"1"},{id:"sec_2_2",title:"2.1 PR78: the application to pure fluids",level:"2"},{id:"sec_3_2",title:"2.2 From PR78 to E-PPR78: the application to mixtures",level:"2"},{id:"sec_4_2",title:"2.3 Volume correction",level:"2"},{id:"sec_6",title:"3. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manag. 2009;50(3):576-582'},{id:"B2",body:'Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic Rankine cycles. Energy. 2010;35(2):1033-1099'},{id:"B3",body:'Martelli E, Capra F, Consonni S. Numerical optimization of combined heat and power organic Rankine cycles—Part A: Design optimization. Energy. 2015;90(P1):310-328'},{id:"B4",body:'Astolfi M, Alfani D, Lasala S, Macchi E. Comparison between ORC and CO2 power systems for the exploitation of low-medium temperature heat sources. Energy. 2018;161:1250-1261'},{id:"B5",body:'Walraven D, Laenen B, D’haeseleer W. Comparison of thermodynamic cycles for power production from low-temperature geothermal heat sources. Energy Conversion and Management. 2013;66:220-233'},{id:"B6",body:'Kunz O, Klimeck R, Wagner W, Jaeschke M. The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures [Internet]. 2007. pp. 1–555. Disponible sur: http://www.gerg.eu/publications/technical-monographs'},{id:"B7",body:'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. Journal of Physical and Chemical Reference Data. 1996;25(6):1509-1596'},{id:"B8",body:'Benedict M, Webb GB, Rubin LC. An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures II. Mixtures of methane, ethane, propane, and n-butane. The Journal of Chemical Physics. 1942;10(12):747-758'},{id:"B9",body:'Bender E. The calculation of phase equilibria from a thermal equation of state (Engl. Transl.) [PhD thesis]. Bochum: Ruhr University; 1971'},{id:"B10",body:'Bell IH, Lemmon EW. Organic fluids for organic Rankine cycle systems: Classification and calculation of thermodynamic and transport properties. In: Organic Rankine Cycle (ORC) Power Systems: Technologies and Applications. Woodhead Publishing; 2016. pp. 91-119'},{id:"B11",body:'Lemmon EW, Huber ML, Bell IH, McLinden MO. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 10.0. Standard Reference Data Program. Gaithersburg: National Institute of Standards and Technology; 2018'},{id:"B12",body:'Gross J, Sadowski G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial and Engineering Chemistry Research. 2001;40(4):1244-1260'},{id:"B13",body:'Papaioannou V, Lafitte T, Avendaño C, Adjiman CS, Jackson G, Müller EA, et al. Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments. Journal of Chemical Physics. 2014;140(5):054107'},{id:"B14",body:'Hattiangadi A. Working Fluid Design for Organic Rankine Cycle (ORC) Systems. 2013. Disponible sur: https://repository.tudelft.nl/islandora/object/uuid%3A492ce6c0-ab22-42d0-ba00-3cf3702eb873'},{id:"B15",body:'Lampe M, Stavrou M, Buecker HM, Gross J, Bardow A. Simultaneous optimization of working fluid and process for organic Rankine cycles using PC-SAFT. Industrial and Engineering Chemistry Research. 2014;53(21):8821-8830'},{id:"B16",body:'White MT, Oyewunmi OA, Chatzopoulou MA, Pantaleo AM, Haslam AJ, Markides CN. Computer-aided working-fluid design, thermodynamic optimisation and thermoeconomic assessment of ORC systems for waste-heat recovery. Energy. 2018;161:1181-1198'},{id:"B17",body:'Müller A, Winkelmann J, Fischer J. Backone family of equations of state: 1. Nonpolar and polar pure fluids. AIChE Journal. 1996;42(4):1116-1126'},{id:"B18",body:'Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low-temperature organic Rankine cycles. Energy. 2007;32(7):1210-1121'},{id:"B19",body:'Peng D-Y, Robinson DB. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals. 1976;15(1):59-64'},{id:"B20",body:'Peng D-Y, Robinson DB. The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs. Gas Processors Association. Edmonton, Alberta, Canada: University of Alberta; 1978'},{id:"B21",body:'Drescher U, Brüggemann D. Fluid selection for the Organic Rankine Cycle (ORC) in biomass power and heat plants. Applied Thermal Engineering. 2007;27(1):223-228'},{id:"B22",body:'Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Applied Thermal Engineering. 2007;27(1):100-110'},{id:"B23",body:'White MT, Sayma AI. Simultaneous cycle optimization and fluid selection for ORC systems accounting for the effect of the operating conditions on turbine efficiency. Frontiers in Energy Research. 2019;7:50'},{id:"B24",body:'Jaubert J-N, Mutelet F. VLE predictions with the Peng-Robinson equation of state and temperature-dependent kij calculated through a group contribution method. Fluid Phase Equilibria. 2004;224(2):285-304'},{id:"B25",body:'Jaubert J-N, Vitu S, Mutelet F, Corriou J-P. Extension of the PPR78 model (predictive 1978, Peng–Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilibria. 2005;237(1):193-211'},{id:"B26",body:'Vitu S, Privat R, Jaubert J-N, Mutelet F. Predicting the phase equilibria of CO2 + hydrocarbon systems with the PPR78 model (PR EoS and kij calculated through a group contribution method). Journal of Supercritical Fluids. 2008;45(1):1-26'},{id:"B27",body:'Vitu S, Jaubert J-N, Mutelet F. Extension of the PPR78 model (predictive 1978, Peng-Robinson EoS with temperature-dependent kij calculated through a group contribution method) to systems containing naphtenic compounds. Fluid Phase Equilibria. 2006;243(1–2):9-28'},{id:"B28",body:'Privat R, Jaubert J-N, Mutelet F. Addition of the nitrogen group to the PPR78 model (predictive 1978, Peng Robinson EOS with temperature-dependent kij calculated through a group contribution method). Industrial and Engineering Chemistry Research. 2008;47(6):2033-2048'},{id:"B29",body:'Privat R, Mutelet F, Jaubert J-N. Addition of the hydrogen sulfide group to the PPR78 model (predictive 1978, Peng-Robinson equation of state with temperature dependent k(ij) calculated through a group contribution method). Industrial and Engineering Chemistry Research. 2008;47(24):10041-10052'},{id:"B30",body:'Privat R, Jaubert J-N, Mutelet F. Addition of the sulfhydryl group (−SH) to the PPR78 model (predictive 1978, Peng-Robinson EoS with temperature-dependent kij calculated through a group contribution method). The Journal of Chemical Thermodynamics. 2008;40(9):1331-1341'},{id:"B31",body:'Privat R, Jaubert J-N. Addition of the sulfhydryl group (SH) to the PPR78 model: Estimation of missing group-interaction parameters for systems containing mercaptans and carbon dioxide or nitrogen or methane, from newly published data. Fluid Phase Equilibria. 2012;334:197-203'},{id:"B32",body:'Qian J-W, Privat R, Jaubert J-N. Predicting the phase equilibria, critical phenomena, and mixing enthalpies of binary aqueous systems containing alkanes, cycloalkanes, aromatics, alkenes, and gases (N2, CO2, H2S, H2) with the PPR78 equation of state. Industrial and Engineering Chemistry Research. 2013;52(46):16457-16490'},{id:"B33",body:'Qian J-W, Jaubert J-N, Privat R. Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model. Fluid Phase Equilibria. 2013;354:212-235'},{id:"B34",body:'Qian J-W, Jaubert J-N, Privat R. Phase equilibria in hydrogen-containing binary systems modeled with the Peng-Robinson equation of state and temperature-dependent binary interaction parameters calculated through a group-contribution method. Journal of Supercritical Fluids. 2013;75:58-71'},{id:"B35",body:'Qian J-W, Privat R, Jaubert J-N, Coquelet C, Ramjugernath D. Fluid-phase-equilibrium prediction of fluorocompound-containing binary systems with the predictive E-PPR78 model [Prévision en matière d’équilibre des phases de fluide des systèmes binaires contenant des fluorocomposés avec le modèle prédictif E-PPR78]. International Journal of Refrigeration. 2017;73:65-90'},{id:"B36",body:'Plee V, Jaubert J-N, Privat R, Arpentinier P. Extension of the E-PPR78 equation of state to predict fluid phase equilibria of natural gases containing carbon monoxide, helium-4 and argon. Journal of Petroleum Science and Engineering. 2015;133:744-770'},{id:"B37",body:'Xu X, Privat R, Jaubert J-N. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the E-PPR78 model. Industrial and Engineering Chemistry Research. 2015;54(38):9494-9504'},{id:"B38",body:'Xu X, Lasala S, Privat R, Jaubert J-N. E-PPR78: A proper cubic EoS for modeling fluids involved in the design and operation of carbon dioxide capture and storage (CCS) processes. International Journal of Greenhouse Gas Control. 2017;56:126-154'},{id:"B39",body:'Xu X, Jaubert J-N, Privat R, Arpentinier P. Prediction of thermodynamic properties of alkyne-containing mixtures with the E-PPR78 model. Industrial and Engineering Chemistry Research. 2017;56(28):8143-8157'},{id:"B40",body:'Qian JW, Privat R, Jaubert JN, Duchet-Suchaux P. Enthalpy and heat capacity changes on mixing: Fundamental aspects and prediction by means of the PPR78 cubic equation of state. Energy & Fuels. 2013;27(11):7150-7178'},{id:"B41",body:'Qian J. Développement du modèle E-PPR78 pour prédire les équilibres de phases et les grandeurs de mélange de systèmes complexes d’intérêt pétrolier sur de larges gammes de températures et de pressions. Nancy: Institut National Polytechnique de Lorraine; 2011'},{id:"B42",body:'Le Guennec Y, Lasala S, Privat R, Jaubert J-N. A consistency test for α-functions of cubic equations of state. Fluid Phase Equilibria. 2016;427:513-538'},{id:"B43",body:'Le Guennec Y, Privat R, Lasala S, Jaubert JN. On the imperative need to use a consistent α-function for the prediction of pure-compound supercritical properties with a cubic equation of state. Fluid Phase Equilibria. 2017;445:45-53'},{id:"B44",body:'Le Guennec Y, Privat R, Jaubert J-N. Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and super-critical domains. Fluid Phase Equilibria. 2016;429:301-312'},{id:"B45",body:'Jaubert JN, Privat R, Le Guennec Y, Coniglio L. Note on the properties altered by application of a Péneloux-type volume translation to an equation of state. Fluid Phase Equilibria. 2016;419:88-95'},{id:"B46",body:'Pina-Martinez A, Le Guennec Y, Privat R, Jaubert J-N, Mathias PM. Analysis of the combinations of property data that are suitable for a safe estimation of consistent Twu α-function parameters: Updated parameter values for the translated-consistent tc-PR and tc-RK cubic equations of state. Journal of Chemical Engineering Data. 2018;63(10):3980-3988'},{id:"B47",body:'Soave G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science. 1972;27(6):1197-1203'},{id:"B48",body:'Lasala S. Advanced cubic equations of state for accurate modelling of fluid mixtures. In: Application to CO2 Capture Systems. Italy: Politecnico di Milano; 2016'},{id:"B49",body:'Twu CH, Bluck D, Cunningham JR, Coon JE. A cubic equation of state with a new alpha function and a new mixing rule. Fluid Phase Equilibria. 1991;69:33-50'},{id:"B50",body:'Twu CH. A modified Redlich-Kwong equation of state for highly polar, supercritical systems. In: International Symposium on Thermodynamics in Chemical Engineering and Industry. 1988'},{id:"B51",body:'DIPPR 801 Database [Internet]. Disponible sur: https://www.aiche.org/dippr/events-products/801-database'},{id:"B52",body:'Jaubert J-N, Privat R. Relationship between the binary interaction parameters (kij) of the Peng–Robinson and those of the Soave–Redlich–Kwong equations of state: Application to the definition of the PR2SRK model. Fluid Phase Equilibria. 2010;295(1):26-37'},{id:"B53",body:'Péneloux A, Rauzy E, Fréze R. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilibria. 1982;8(1):7-23'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Silvia Lasala",address:"silvia.lasala@univ-lorraine.fr",affiliation:'
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