4.3 CONCLUSION: HOW TO CHOOSE A MODEL The right questions Ionic liquids What is the property of interest?

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1 Chapter 4 From Phases to Method (Models) Selection Ionic liquids Ionic liquids are a new kind of solvent receiving considerable attention in the research community. These solvents are in fact organic salts which remain liquid at room temperature. Like all salts, they are composed of a cation and an anion. The difference from the usual salts is that these ions consist of organic chains, which may have different molar masses. Due to their ionic character, they do not evaporate, and therefore remain in the liquid phase. A liquid-liquid phase split may be observed, however, especially in the presence of water or organic material. A large number of possible cation-anion combinations exist, so they can be customised to the intended application. It is out of the scope of this book to discuss this topic. Several review papers exist in the literature, and the interested reader is invited to consult the relevant papers directly [271, 272]. It may be of use to mention that an UNIFAC method has been dedicated to ionic liquids [273]. 4.3 CONCLUSION: HOW TO CHOOSE A MODEL The right questions The practicing engineer requires a simple, unique model that will predict all possible types of fluid behaviour. Hopefully, the discussions in this book will have convinced him that the state of knowledge today does not allow such a simple approach. In the absence of a simple model, the engineer will request a clear answer on which model to choose for his/her application: some kind of expert system that provides a unique answer, obviously including the appropriate parameters. Again, he/she may be faced with disappointment: often, several methods are possible, and no best choice can be identified. The only universal recommendation that can and should be made is that any model must be compared with experimental data: these are to be taken as a guideline for the choice of any theoretical approach. In the same way as has been proposed in the past [274], this book suggests several entry points to answer the question: What is the property of interest? This is extensively discussed in chapter 2. We may identify two types of properties: Single phase properties, discussed in the first section of this fourth chapter. Figure 1.9 page 18, in the very first chapter of this book also illustrates which model can be used depending on the process pressure-temperature location with respect to the phase envelope. Phase equilibrium properties, discussed in the second part of this fourth chapter. This second type of property is generally much more difficult to calculate accurately. te that the simulation tools generally offer property packages that contain a pre-defined selection of property-model combinations. An example of such combinations is

2 326 Chapter 4 From Phases to Method (Models) Selection provided in table 4.7 hereinafter. This combination is often thermodynamically inconsistent as it is rarely possible to have the same accuracy for different properties using the same model. Yet, this situation is most often acceptable What is the fluid composition? This issue is extensively discussed in the third chapter of this book, since the choice of model parameters is directly related to the system composition. More specifically, one must be able to distinguish entropic deviations from ideality (related to size asymmetry) and enthalpic deviations (which are due to differing polarities and/or hydrogen bonding). In this fourth chapter, a number of typical systems that may be of industrial interest have been investigated What are pressure and temperature conditions of the process? There are two main families of fluid phase models: activity coefficient and equation of state). Although equations of state can describe all fluid phase conditions (vapour, liquid, supercritical), the use of activity coefficient models may have some practical advantages. As discussed in section (p. 52), the use of activity coefficients implies a heterogeneous approach for calculating distribution coefficients, while a homogeneous approach is used with equations of state. Table 4.6, taken from de Hemptinne and Behar [275], summarises some advantages and disadvantages of both approaches. Table 4.6 Heterogeneous and homogeneous approaches for vapour liquid distribution coefficients calculation (taken from [275]) Advantages Disadvantages Homogeneous approach y Ki = i K i L x i = ϕ i ϕ V i High pressures. Phase envelope calculation, including the near-critical region Limited by the choice of an appropriate mixing rule Heterogeneous approach i PT, σ Pi T ϕσ i T γi x, T Ki P ϕv i ( y, PT, ) Improved accuracy because of the large choice of models, in particular for non-ideal mixtures Limited to pressures below 1.0 MPa* phase envelope calculation Requires the asymmetric convention in case of supercritical components Unable to take into account free-volume effects in polymer-solvent systems = ( ) ( ) ( ) ( ) * there is no truly theoretical reason for this limit to 1.0 MPa: use of a Poynting correction can enlarge the validity domain up to 1.5 MPa, but above this pressure, one of the components is often supercritical, resulting in the need to use the asymmetric convention. The use of the heterogeneous approach, although very powerful for non-ideal mixtures, is in principle limited to low pressure applications. It requires the use of: Pure component property correlations. For database components, accurate correlations exist. Otherwise, other methods should be employed, as discussed in section (p. 109). A clear difficulty exists when one of the components is supercritical Henry s

3 Chapter 4 From Phases to Method (Models) Selection 327 law should be used in this case, leading to the much more complex asymmetric convention as explained in section A (p. 63). An activity coefficient model. In this case, a distinction is made between predictive models (less accurate, but can be used without data, like the regular solution or the Flory models) and correlative models (require many experimental data, or, equivalently, a well-furnished parameter database, e.g. NRTL or UNIQUAC). This is discussed in section (p. 188). te that UNIFAC is a very powerful alternative when no data exist, and that COSMO-RS or COSMO-SAC can now be used to create quite accurate pseudo-experimental values for liquid phase activity coefficients. Today, there is a clear trend in favour of the homogeneous approach, both because it allows a coherent description of all fluid phases (and thus describes critical points), and because new, powerful equations of state have become available: The traditional limitations of the cubic equations of state have been overcome by the G E -based mixing rules (section E.b, p. 214). This approach requires a large number of data for fitting and validation. The PSRK method, which uses UNIFAC can be considered predictive. The approach, which uses a Van Laar type G E model is also predictive but can only be applied to mixtures of non-polar compounds and supercritical gases. Molecular based equations offer improved predictivity (SAFT is discussed as an example here, in section , p. 216). Its use with group contributions is now extensively studied by several research groups, and it is expected that this method will become increasingly used in the future Decision tree Nevertheless, it may be useful to provide a decision tree for vapour-liquid phase equilibrium calculations, as has already been attempted by other authors [275, 276]. It might help the beginning engineer in his search. In the figure 4.59, we aim at finding an approach that is suited for pre-studies. For more advanced studies, a full analysis of key components as discussed in chapter 3, yielding a more accurate method, is needed. In figure 4.59, the reader will be guided through a number of key questions, labelled with a greek letter, and further explained below (comments to figure 4.59). At the end of each selection process, the letter helps positioning the reader in table 4.7 for additional elements regarding the choice of the thermodynamic method. This table provides some complementary information regarding the choice of single-phase properties. For cubic EoS (CEOS), the importance to verify either the alpha function or the mixing rule parameters is stressed using either the α or k ij symbol followed by an exclamation mark. Some cases, that are particularly difficult to model, are indicated with a red arrow inviting the engineer to search for additional data. The meaning of the colours is as follows: yellow means heterogeneous approach, green means homogeneous approach (with an equation of state). Generally, the high pressure (equation of state, green) approaches are more complex, but also applicable at low pressure. The significance of the keywords used, both in table 4.7 and in figure 4.59, is provided in table 4.8.

4 328 Chapter 4 From Phases to Method (Models) Selection α1: only HC? hydrocarbons and their associated gases β1: size Enthalpic asymmetry? Entropic β2: size asymmetry? Supercritical gases γ1: water+ HC? γ3: azeotropy? δ1: electrolyte? Close boiling δ3: close to critical Salts no salts δ2: γ2: Critical ε2: P > 0.1 MPa Low pressure ε1: reactive? Low pressure High Low pressure High ζ1: pseudo? A S B S C S D S E S F S G S H S I S J S K S L S M S e-nrtl e-uniquac e-unifac Pitzer Henry Pitzer SW CEOS-GE CPA SRKKD UNIQUAC NRTL UNIFAC CEOS-GE SAFT PSRK GCA Flory UNIQUAC SAFT Lattice-Fluid Free Volume CEOS alpha; kij! CEOS kij! CEOS BK10 CEOS alpha! GS CEOS kij(t)! Risk for LLE? Risk for LLE? watch for data watch for data watch for data Figure 4.59 Decision tree for vapour-liquid equilibrium calculations.

5 Chapter 4 From Phases to Method (Models) Selection 329 Question Label Explanation α1: only HC? β1: size asymmetry? β2: size asymmetry? γ1: water+ HC? γ2: γ2: γ3: azeotropy? δ1: electrolyte? δ1: electrolyte? M F G H B C The first, basic, question is related to the presence of other than hydrocarbons (except gases) in the mixture. The branch on the right corresponds to non-polar systems where the three parameter corresponding states principle can be applied. This branch is also well adapted to petroleum cuts. n-hydrocarbons gases (CO 2, H 2 S ) may also be described on the hydrocarbon branch. For mixtures that contain non-hydrocarbons (that include heteroatoms, i.e. O, S, N ), the other branch should be chosen. When it is attested that the mixture is non-ideal, a distinction should be made between enthalpic and entropic deviations from ideality (discussion in section , page 173). Entropic deviations results from mixtures with molecules of strongly different sizes or shapes (size asymmetry); enthalpic deviation is related to different interaction energies between the species. This question refers to the presence of supercritical gases in the system (see section 4.2.3, page 288). The answer is yes when a significant amount of H 2, N 2 is present in the system. If so, the traditional wisdom is to recommend the Grayson-Streed (GS) method, but it is generally safer (especially for equilibria with heavy ends) to use a cubic EoS on the condition that temperature-dependent interaction parameters (k ij ) are available. Methane can in some cases be considered as strongly supercritical (especially at high temperature), but may also lead to close-to-critical conditions, as discussed in G below, when temperature is low. Water hydrocarbon mixtures are complex mixtures because of their very different chemical affinities. The properties of the aqueous phase require specific models (choose yes), as explained in detail in section (p. 293). If other strongly polar components are present, mutual solubilities between the hydrocarbon and aqueous liquids strongly increase, and the right branch should be chosen (choose no), as discussed in section (p. 316). For mixtures that exhibit entropic non-idealities and moderate pressures, below 1 MPa, the Flory theory provides a fully predictive scheme, but it is most often combined with a local composition model, as in the UNIQUAC theory (which requires interaction parameters). The equations of state in item G is also adequate in this case. For mixtures that exhibit entropic non-idealities at high pressure conditions, an equation of state that takes into account free volume is required, as liquid-liquid phase split may be observed. The SAFT or Lattice-Fluid EoS (Sanchez-Lacombe) are designed for these systems. Close boiling systems often lead to the presence of azeotropes (useful or not). This is discussed in section (p. 271) and requires validation on experimental data. The cubic EoS, which can be recommended in this case, must be well-tuned to both pure component vapour pressures (the so-called alpha function) and mixture bubble pressures (key binaries), as discussed in some details in section (p. 204). The presence of electrolytes (salts) will strongly affect the result: in the presence of these ionic species, electrolyte models, briefly introduced in section (p. 186), can be used with some success (Pitzer is most often used for complex electrolyte systems). At high pressures, an equation of state should be used. The Soreide and Whitson equation (SW) is here recommended although it can only handle NaCl salt, and no other polar component than water. An aqueous phase is present, that contain no other polar component, and no salt. In some applications, it may be considered pure water (use a decant option). This will still let water dissolve in the other phases, but the aqueous phase is approximated as a pure component. In some cases, it may be important to know the true composition of the aqueous phase, in which case the empirical or Henry-constant models discussed in section (p. 293) can be used. The CPA EoS is well-suited for this problem. Yet, any cubic EoS can also be used here, provided that the alpha function is validated and a complex mixing rule (at least two binary interaction parameters: kij and kji as in the SRKKD Eos or a GE-based mixing rule as discussed in section E.b (p. 214). These models are also used for physical treatment of acid gases (section , p. 310). Comments to figure 4.59.

6 330 Chapter 4 From Phases to Method (Models) Selection Question Label Explanation δ2: δ2: δ3: close to critical ε1: reactive? D E I A In the presence of a mixture of very polar components (as for example discussed in section 4.2.6, p. 316), it is generally recommended to use an activity coefficient model, with well-documented binary interaction parameters, on the condition that pressure is not too high. UNIQUAC and NRTL are often used indifferently, and UNIFAC (section C, p. 184: the Dortmund version is considered better) is preferred when no parameters are available. te that it is often possible to fill automatically the UNIQUAC or NRTL parameter matrix using UNIFAC. In case of risk of liquid-liquid phase split, it is essential to validate the model with experimental data, because a slight change in conditions may have a great effect on LLE. The vapour phase is often considered ideal, but the Hayden-O Connell virial coefficient can be needed for hydrogen-bonding systems. Sometimes, special approaches are required (hexamer forming of HF, for example). The equations of state discussed under label E are increasingly used for low pressure calculations. In the presence of a mixture of very polar components (as for example discussed in section 4.2.6, p. 316), the activity coefficient models are limited in pressure. At pressures higher than 1 MPa, an equation of state should be used. A cubic EoS can do the job if an appropriate activity coefficient model is included in the GE-type mixing rule (as in the case of the PSRK EoS). The SAFT model is increasingly used in this context. The process may be focusing on components that are close to their critical points (either gases, as CO 2 or H 2 S, or light hydrocarbons). Only a homogeneous method with an equation of state can be used. Cubic EoS are particularly well-suited because their very construction makes that the pure component critical point is exact. For mixtures, the prediction should be used with caution. The EoS has been designed for this type of problems. The other properties (enthalpic or density), require a high quality virial EoS (as recommended by NIST, see also section , p. 199). In some cases, chemical reactions in the aqueous phase strongly affect the vapour-liquid equilibrium (e.g. amine treatment). Specific packages (that include simultaneous phase and chemical equilibrium calculations) must be used for these reacting systems. They very often use the electrolyte version of NRTL or UNIQUAC as discussed in section (p. 186). Some simulators propose a special sour gas package for acid gas + water mixtures. ε2: P > 0.1 MPa J If pressure is larger than 0.1 MPa, and no specific azeotropic condition is feared, the traditional cubic EoS can be used without great danger. This is the case for stabilization columns, for example. ζ1: pseudo? K In some cases, very low pressure calculations are needed, which means that the liquid is a heavy component. Very often, petroleum pseudo-components are used (typically for vacuum distillation). In this case, the automated API nomograph BK10 (which is nothing but an improved Raoult s law) is traditionally recommended. ζ1: pseudo? L In the case the heavy end is paraffinic, for example (wax treatment), it is recommended to use a cubic EoS, for which the validity of the alpha function has been extended to heavy components (as in PR78). Comments to figure 4.59 (cont d).

7 Chapter 4 From Phases to Method (Models) Selection 331 A B C Table 4.7 Model Choice depending on the Result of the Selection Process in Figure 4.59 Fugacity (equilibrium) e-nrtl, e-uniquac e-unifac Special Sour Packages Pitzer SW CEOS -GE CPA CEOS with specific mixing rules Enthalpy/entropy Density Comments + include excess Specific CEOS -GE CPA CEOS with specific mixing rules D UNIQUAC, NRTL + include excess properties UNIFAC E F G Specific Specific Aqueous phase: use water; hydrocarbon phase: use API Watch for parameters Predictive other polar component than water Only NaCl; no other polar component than water Requires parameter fit Good for mixed solvents Most simulators offer specific solutions (e.g. SRKKD) for water + hydrocarbons Watch for parameters, especially when using excess enthalpy CEOS -GE CEOS -GE Requires parameter fit SAFT SAFT SAFT Group contribution methods may make this model predictive GCA GCA Often used for biofuel applications VTPR VTPR VTPR Predictive, hence less accurate; more recent version of PSRK PSRK Predictive, hence less accurate UNIQUAC, Flory LLE Group contribution SAFT SAFT SAFT methods may make this model predictive Lattice Fluid (Sanchez-Lacombe) UNIFAC Free Volume Group contribution methods may make this model predictive Predictive

8 332 Chapter 4 From Phases to Method (Models) Selection Table 4.7 Model Choice depending on the Result of the Selection Process in Figure 4.59 (cont d) H CEOS Lee Kesler Lee Kesler (API) Lee Kesler Lee Kesler (API) I CEOS alpha, k ij Lee Kesler, MBWR J CEOS, Lee Kesler Lee Kesler MBWR Lee Kesler (API) K BK10 Lee Kesler Lee Kesler (API) L M Fugacity (equilibrium) PR (SRK), alpha Enthalpy/entropy Density Comments Lee Kesler Lee Kesler (API) PR (SRK), k ij Lee Kesler Lee Kesler GS Lee Kesler Lee Kesler Check alpha parameter on vapour pressures; Evaluate mixing rules (k ij ) on mixture data Close to the critical point, it is extremely difficult to have accurate predictions of the single phase properties Check alpha parameter on vapour pressures; Evaluate mixing rules (k ij ) on mixture data For pseudo-components only Check alpha parameter on vapour pressures Evaluate mixing rules (k ij ) on mixture data (a temperature dependent k ij is often essential) t for hydrogen solubility in heavy components

9 Chapter 4 From Phases to Method (Models) Selection 333 Table 4.8 Keywords for Models API Keyword Aqueous phase: use water BK10 Description API correlations: these are very similar to those presented in section Specific water density correlation, as proposed by NIST (steam tables) Improved Antoine correlations Section of this book Page C 200 CPA Cubic Plus Association B 218 e-nrtl, Electrolyte NRTL e-unifac Electrolyte UNIFAC e-uniquac Electrolyte UNIQUAC Flory Flory activity coefficient model B 180 GS Grayson Streed GCA Group Contribution with Association equation of state B 218 Lattice Fluid (Sanchez-Lacombe) Lattice fluid Equation of State Lee Kesler Lee & Kesler method C 202 When considering the liquid phase, it may be interesting to use library correlations for the pure component, with an ideal mixing rule (see section , p. 60). Most simulators offer well-validated correlations include excess (UNIQUAC, NRTL) In addition to using library correlations, for strongly non-ideal mixtures, the excess property must be added, as calculated using NRTL or UNIQUAC and eq (2.101), p. 62 MBWR Modified Benedict Webb & Rubin EoS C 203 NRTL Activity coefficient model C 177 Pitzer Activity coefficient model Predictive Peng-Robinson with temperature dependent k ij. (Van Laar introduced in the PR EoS, using a g E -mixing rule) E 214 CEOS Cubic Equation of State: Peng Robinson or Soave-Redlich Kwong equations of state are used indifferently CEOS alpha CEOS k ij It is important to validate the alpha function of cubic equations of state. The Twu correlation generally improves the results A simple mixing rule can do it, but well-adjusted binary interaction parameters are needed B E 212

10 334 Chapter 4 From Phases to Method (Models) Selection Table 4.8 Keywords for Models (cont d) Keyword CEOS -GE Description A complex mixing rule is needed, possibly using several k ij, but a G E -type mixing rule is best Section of this book Page E 212 PSRK Predictive SRK (UNIFAC introduced in the SRK EoS, using a G E mixing rule) E 212 SAFT Statistical Associating Fluid Theory A 216 Soreide&Whitson Equation of State special Sour packages Special, simulator-dependent, packages specific Special, simulator-dependent, packages SRK Soave Redlich Kwong (see above) SRKKD SRK with the Kabadi-Danner mixing rule UNIFAC Activity coefficient model C 184 UNIFAC Free Volume Activity coefficient model UNIQUAC Activity coefficient model B 183 VTPR Volume Translated Peng Robinson E 212 REFERENCE LIST [1] de Swaan Arons, J. and de Loos, T. Phase Behavior: Phenomena, Significance and Models ; Ed. Sandler, S. I.; Marcel Dekker, Inc., [2] Kiran, E. and Levelt Sengers, J. M. H. Supercritical Fluids; Fundamentals for Applications ; Kluwer Academic Publishers, [3] Sadus, R. J. High Pressure Phase Behaviour of Multicomponent Fluid Mixtures ; Elsevier Science Publisher: Amsterdam, [4] Poling, B. E., Prausnitz, J. M. and O Connell, J. P. The Properties of Gases and Liquids 5th Ed.; McGraw-Hill: New York, [5] Reid, R. C., Prausnitz, J. M. and Sherwood, T. K. The Properties of Gases and Liquids ; McGraw-Hill Book Company: New York, [6] Reid, R. C., Prausnitz, J. M. and Poling, B. E. The Properties of Gases and Liquids 4th Ed. McGraw-Hill Book Company: New York, [7] Domb, C. Phase Transitions and Critical Phenomena, Academic Press, [8] Anisimov, M. A. and Sengers, J. V. Critical Region in Equations of State for Fluids and Fluid Mixtures; Ed. Sengers, J. V., Kayser, R. F., Peters, C. J. and White, H. J. Jr; Experimental Thermodynamics; Elsevier: Amsterdam, [9] Maxwell, J. B. Data Book on Hydrocarbons ; Van strand Company, Inc: London New York Toronto, [10] API Technical Data Book Petroleum Refining, 3rd Ed. 6; American Petroleum Institute: Washington, D.C., [11] Wuithier, P. Le Pétrole: Raffinage et Génie Chimique (Tome 1) Ed. Technip: Paris, 1972.

Overall: 75 ECTS: 7.0

Course: Chemical Engineering Thermodynamics Language: English Lecturer: Prof. dr. sc. Marko Rogošić TEACHING WEEKLY SEMESTER Lectures 3 45 Laboratory 1 15 Seminar 1 15 Overall: 75 ECTS: 7.0 PURPOSE: Within