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XT, P,y)
(8) (9)
K, = r/(T^)ps-(T)/P
(10)
K,=ps'{T)/P
(11)
K, = y/ (T,x')/ri"(T,x")
(12)
Eq. 8 uses an equation of state to obtain the fugacity coefficients, ^>,. p o r both phases while Eqs. 9 - 1 1 involve varies approximations for activity coefficients, y,, and vapor pressures, P '. For liquid-liquid equilibria, Eq. 12 would be used. Figure 1 highlights the work-flow and data-flow with respect to the service role of the properties (and property models). Note that for a TP-flash simulation, first the mass balance Eq. 1 together with the constraint (equilibrium condition) Eq. 3 is solved; for each evaluation of Eqs. 1 & 3, the property models are called. When convergence is achieved, the property models are called one more time for the evaluation of the energy balance. In this case, since T and P are fixed, the energy balance computes Q (the energy added/removed) needed to make the operation possible.
Figure 1: The service role of properties and property models This is a typical simulation problem where the property models (Eqs. 4-12) are used in the service role because every time an evaluation of Eqs. 1-3 needs to be made, there is a request
31 for the properties, for which Eqs. 4-7 are called. Another example of the service role is to ask for the density, either to convert the composition in mole fractions to moles/cm or to calculate the volume of the (separation) tank or the height of the liquid in a tank. In each case, only Eq. 7 will be called. 2.2.2 Service/Advice Role In process design and synthesis, property values are often regarded as explicit or implicit target values for a synthesis/design algorithm to satisfy by finding values for the unknown intensive variables. In section 2.2.1, the problem definition assumed (or specified) that a two phase system would exist at the specified T and P. Consider now that we do not know if a two phase system would exist at the specified T and P and also that we are only interested in removing a chemical through precipitation (crystallization). At any assumed (or specified) T, P, and z, we check if the liquid stream F would be stable at T & P. If not, there would be two phases, at least. Also, if the assumed T is above the melting point of at least one of the chemicals (for example, chemical A) in the system and below the melting point of the others, then there is a good chance that this chemical would precipitate, such as if the assumed T is below the saturation temperature of the feed mixture. The advice role here is to determine if solid-liquid based separation is feasible and also which chemical would be obtained as a solid. The design problem is to determine the temperature T of operation that would match the amount of separation (or recovery) that is desired. Figures 2a and 2b show two examples of this advice role. In each case, a solid-liquid equilibrium based saturation diagram is shown for an aqueous electrolyte system and a non-electrolyte system. It should be noted that the feed composition, z, and temperature, T, indicate which solid chemical would be separated.
Figure 2a: Saturation point compositions of naphthalene in a binary mixture of naphthalene-benzene as a function of temperature (y-axis)
Figure 2b: Saturation point compositions of sodium chloride in an aqueous solution as a function of temperature
32
Another example of the advice role can be found in solvent design, where the properties have explicit target values such as solubility and selectivity for a particular solute at a specific condition of operation. Here, the chemical structure of candidate solvents is manipulated until the solution properties match the target values. The process design problem (defined above) and the chemical product (solvent) design problem may be solved as part of a two-step procedure (irrespective of whether they are solved sequentially or simultaneously): Step I - generate alternatives {e.g., T'or solvent) Step II - determine properties (e.g., number of phases, solubility, or selectivity) and screen/verify alternatives through simulation. In Step I (generation), properties play a service/advice role while in Step II (verification) properties play only a service role. Strategies for the advice role attempt to eliminate infeasible solutions, or at least reduce the size of the search space and/or mathematical problem of a given situation, by providing the necessary insight. For example, an initial list of candidate solvents may be generated by searching for substances having similar solubility parameters as the solute. For each candidate solvent-solute combination, solid solubility diagrams (see Figures 2a-2b) would provide advice for selection of the operating temperature. The list of solvents would be reduced as candidates which do not meet the criteria are identified. For final verification, a simulation is needed (that is, solving Eqs. 1-6 for solidliquid equilibrium systems). Other examples of the advice role can be found in Gani & O'Connell[l]. The service/advice role is highlighted in Figure 3. Based on the problem specification, advice role in the generation step checks for feasible solid-liquid separation. If yes, then the service role is played for the verification (simulation) step. Note that the advice role also helps to design the condition of operation (choice of temperature and amount of solvent to be added or removed). Computer-aided molecular design techniques [2] are an example of properties used in their service/advice role, that employs different versions of the product model are employed.
Figure 3: Service/advice role of properties (property models) Often the advice role for properties is less demanding on the property models than is the service role. For example, sometimes the advice role for different product models can be
33
played with only pure component or infinite dilution properties of the compounds present in the mixture; the service role usually needs properties over the entire composition range. 2.2.3 Integration Role The most comprehensive role for properties in the solution of process-product design problems is that of integration. In process/tools integration and in graphical (visual) design techniques, properties actually can define an integrated solution strategy. Typical examples of this role can be traced back to graphical design techniques for separation processes (see for example, Henley and Seader [3] who describe various types of graphical design techniques) and for heat integration based on pinch technology [4]. In the case of distillation column design, the mass balance equation (Eq. 1) and the constraint equation (Eq.3) are represented in a two-dimensional plot of saturation vapor composition on the y-axis and the corresponding liquid composition in the x-axis. Each data point corresponding to the constraint equation represents a liquid in equilibrium with the vapor at the system pressure (usually constant) and temperature which varies over the column. In the case of heat integration, only Eqs. 2, 5 & 6 are needed. The two variables considered are the cumulative enthalpies for the hot and cold streams and the corresponding temperature. In the case of distillation design, the relation between saturation temperature and composition provides integration while in the case of heat integration, the relation between temperature and enthalpy does the integration. Using the process model defined by Eqs. 1-6, the integration role can be visualized through the following simple problem: • •
Given a contaminated product stream with a flowrate of F kmol/h having a composition fc of contaminant (for example, 0.02 mole fraction of phenol), Design a process through which the product stream becomes essentially free of the contaminant (mole fraction of phenol less than l.OxlO"6).
Through the traditional service or service/advice roles, the problem would be solved as follows - find candidate solvents that will create another liquid (solvent) phase and includes as much as possible of the phenol. For each solvent candidate, simulations are made to establish the process design. Now consider the following alternative solution technique called the reverse approach 1. Use Eq. 1 to calculate the required (or design target) solubility. Since the problem information actually provides both inlet and outlet concentrations of the product stream, this must be feasible. Note that since solubility (property) is actually the known variable, the solution of this separation problem does not require a property model. 2. Use Eqs. 3,11 and appropriate activity coefficient models to estimate solubilities for a solute in candidate solvents at selected temperatures. As long as the solubilities match the desired (target) values from step 1, the mass balance equation does not need to be solved.
34
It is interesting to note that in the traditional solution approach, using the generation and test paradigm, a simulation problem needs to be solved for every alternative. For many alternatives, however, a property model may not be available as part of the process model. If the generate and test steps are performed simultaneously (that is, include the simulation as part of an optimization loop), only one process model can be used, thereby severely restricting the application range since only one property model can also be used (unless multiple optimization problems are solved). With the reverse (integrated) approach, however, any number of property models can be used for step 2 while in step 1, property models are not needed at all. The procedure is to first solve a reverse simulation problem to determine the design target in terms of a set of properties, and then solve a reverse property estimation problem to determine the solvents and the operating conditions (for example, temperature). Multiple solutions are obtained, which only need to be ordered according to a performance index to identify the optimal solution. The property (in this case, solubility) plays the integration role to connect the simulation and design problems. On the other hand, from a point of view of the solution of the model equations, it plays the role of decomposition (separation of the balance and constraint equations from the constitutive equations). More details on this reverse approach can be found in [5, 6]. Figure 4 highlights the principal difference between the traditional or forward approach and the reverse approach (with the integration role for properties). Recently, Bek-Pedersen and Gani [7] have defined a driving force which is also a function of the saturation temperature and the corresponding phase compositions. Using the driving force for integration, Bek-Pedersen and Gani [7] have shown how simultaneous design and simulation can be performed for any two-phase separation process. Here, the property model plays all roles; service, advice and integrated solution of the simulation and design problem. The use of the driving force to integrate simulation and design is highlighted in Figure 5.
Figure 4: Integration role of properties and property models.
35
Note that in Figure 5, once the maximum driving force has been located at Fm and a reflux ratio (RR) is selected, by making the two operating lines to intersect on the D-Dx vertical line, the number of stages and the column profile (T, x & y_) can be back-calculated [7]. This means that the design and simulation of the distillation column correspond to the property target (maximum driving force). By definition, at the maximum driving force, the energy consumption is the minimum because this is the external medium that creates the twophase system. In the above examples, the relations among thermodynamic properties and intensive variables generated the integrated algorithm or solution strategy in addition to providing the solutions. "Intelligent" manipulation of the process and property model equations and variables using physicochemical and mathematical insights identified a small number of intensive variables as the unknown process model variables to represent the essential information about the problem. This tools integration, which is most valuable in applying integrated algorithms for synthesis, design and/or control, can be appreciated by considering the roles of properties in different process-product engineering problems through their independent, intensive variables (Table 1).
2.2 PROPERTY ROLES AND PROPERTY MODEL SELECTION In all three roles of properties, the proper selection of property models is important. Depending on the type of the problem, the consequences of property model choice can differ, even for the same property. The use of an inappropriate property model and/or model parameters may not be limited to only wrong numerical results that cause bottlenecking and over-sizing; even wrong process configurations can be found [8, 9].
Figure 5: Driving force based simulation and design (integrator is the driving force, a function of Py (T, P, x, y_) providing integration.
36 Table 1: Relationship between problems and properties in process-product engineering. Purpose
Problem
Determine
Remarks
Synthesis
Generate feasible process alternatives
Effects of T, P, x on process model
Design
Obtain condition of operation
Values of T, P, x that satisfy constraints
Properties affect process model results and play all roles, depending on the solution approach Properties provide target values and can play all the roles, depending on the solution approach
Control
Design control system
T, P,x sensitivities
Property models provide derivative information via service and advice roles
Energy analysis Environmental impact
Determine energy needs Verify that environmental constraints are satisfied
Enthalpies from T, P, x Component flows in effluent streams
Property models are essential via service and advice roles
Economy
Minimize cost of operation and equipment
Cost as a function of capital and operation
Property models affect process model results via service and advice roles
Property models are needed via service and advice roles
Often the user of a property model does not have the knowledge and experience to choose "wisely" among the myriad of options. The selection is commonly based on familiarity, hearsay or ease of accessibility. However, consideration of the numerous property models and comprehension of the complexities of current and future property models can be difficult even for the experienced user. Issues associated with this aspect are discussed by Gani and O'Connell [10]). 2.3.1 Service Role Since property models provide requested property values for quantitative evaluations of conservation of mass and energy, their quantitative accuracy must be evaluated. Some of the important issues related to the choice of the appropriate property model are the following: problem type, system (mixture) type, availability of property model parameters and computational complexities. Note that the estimation of the secondary and/or functional properties such as fugacity or activity coefficients, mixture densities, mixture enthalpies, etc., generally require pure component single value primary properties along with secondary/functional properties. Also, when the property model is used in the service role for a simulation problem, the derivatives of the properties with respect to the unknown variables (usually also the intensive variables T, P and/or composition) are needed when numerical methods like Newton-Raphson are used. Because of the importance of quantitative accuracy, tuning of the model parameters is an issue, especially since it depends on the availability of experimental data. In this case, a sensitivity analysis, that is, variations of the property of interest with respect to changes in
37
model parameters is valuable to fine-tune a small number of parameters. This is particularly useful when only limited experimental data are available. Such analyses show that pure component vapor pressures make a significant difference in the estimated vapor-liquid equilibrium (VLE) compositions for non-ideal systems, while the pure component critical (primary) properties are important for high pressure VLE calculations. Solid-liquid equilibrium (SLE) calculations are very sensitive to heats of fusion. The ratios of the activity coefficients of each component in the two liquid phases have direct impact on liquid-liquid equilibrium (LLE) compositions. Errors in densities effect the equipment sizing (volume and area) parameters. Since only one property model for each property may be used in process models such as the one represented by Eqs. 1-3, only carefully selected property models with fine-tuned model parameters and continuous derivative properties within a wide range of intensive variable values, should be used. Note that in the service role, only one property model may be used for the necessary properties during any simulation; this can be a disadvantage during simultaneous simulation and optimization of process-product problems since process and product models are solved simultaneously. For simulation problems from section 2.2.1 involving only the mass balance (Eq. 1) and the equilibrium condition (Eq.3), it can be noted that any one of Eqs. 8-12 may be appropriate for the equilibrium constant, Kh depending on the type of the problem, system, etc. Interesting issues with respect to the choice of models for Kt are the computational scale and time. If the fugacity and/or activity coefficients need to use complex relations based on groups at the atomic level (such as the SAFT EOSfll]), the models are usually computationally intensive and expensive. On the other hand, interactions at molecular levels (such as the SRK EOS[12]) are commonly less computationally intensive and relatively inexpensive. Consequently, calculation schemes where repetitive solution of Eqs. 1 & 3 are needed, computationally cheap models are usually preferred while for schemes where only a few calculations of Eqs. 1 & 3 are needed, and quantitative accuracy is important, computationally intensive models may be implemented. One alternative in this case is to use the reference and local models. The properties are generated by a reference model {e.g., SAFT EOS) and then matched with a computationally cheaper local model {e.g., the SRK EOS) to create a local, system-problem specific model. This idea is similar to property model simplification techniques proposed some time ago [13, 14]. The difference is that simplified local models needed to be generated for every iteration of a simulation. Here, system/problem specific local models need to be generated only once and can be used for all types of simulation problems for the same chemical system and properties. 2.3.2 Service/Advice Role In addition to the service role, for properties to play the advice role, the corresponding property model must be qualitatively as well as quantitatively correct. This is because the design problem (where advice is needed) usually involves generation and screening of different alternatives and verification of the feasibility of a desired operation (separation or reaction). Therefore, there is more emphasis on the qualitative accuracy. Of course, when the condition of operation (such as the temperature of operation) is to be found, quantitative accuracy is also essential.
38 In the case of equilibrium based separation processes, the advice role depends on the known (or generated) phase equilibrium (needing the solution of Eqs. 3 and 4 only). While these need to be calculated only once for each case, there can be many different chemical systems. Therefore, the choice of the property models (for Eqs. 8-12) needs to consider the application range not only in terms of intensive variable values but also in terms of chemical systems. This is particularly important for designing molecules with desired properties, where the selected property model needs to be predictive with respect to chemical systems to generate and screen large numbers of feasible alternatives. Unfortunately, if solvent selection is done simultaneously with the optimization of the process performance, only one property model per property can be used, restricting the search space for the problem solution. The best property model selection strategy is to choose a group or atomic contribution method (see chapters 3-4) for the advice role because of both predictive ability and qualitatively correctness for a wide range of chemical systems. Then, when a chemical system has been selected by such a method, measured and/or generated data should be used to regress (or fine tune) the model parameters of a local model with limited predictive capabilities. The last step also validates the property model for use in the service role. 2.3.3 Integration Role An important issue in the integration role of properties is how to bring together the special features of property models for process model-based calculation schemes. That is, it is necessary to identify the appropriate properties and the intensive variables. For a number of separation processes, including all of the 2-phase equilibrium separation processes, a driving force has been identified as the integrator (figure 5 and Section 2.2.3). Then the process model equations can be decoupled for integration of simulation and design. Note that the driving force can be calculated from physical equilibrium constants (as in Eqs. 8-12) and the location of the maximum is a function of the intensive variables for the same physical equilibrium constant values. The chemical identities provide an estimate of the chemical equilibrium constants from which the driving force diagram is calculated. Since the design target of minimum energy consumption (or solvent rate, etc.) can only be achieved if the design is based on the maximum driving force, the choice of property models and their accuracy in representing the variations of properties on the intensive variables is very important. In the context of the reverse approach, any number of property models can be used, so it is possible to select the appropriate property model based on their application range. This means that the design and simulation results based on the location of the maximum driving force and the driving force values would be valid for any number of separation problems (chemical systems).For reactive systems (with or without separation), a similar definition of driving force can also be employed to generate a similar diagram as the one showed in Figure 5. Hildebrandt et al. [15] call this driving force-based diagram the attainable region, which forms the basis for reactor design and simulation. Another useful feature of the reverse approach is that it often allows the use of the property models under the same conditions they have been developed and verified. That is, property models are usually validated by model developers through comparison with measured experimental phase equilibrium data not
39 through process simulation results. The driving force diagram involves precisely the same information.
2.3 DERIVATIVE ANALYSIS: A CONNECTION BETWEEN MODEL GENERATORS AND MODEL USERS One final issue, which enters into all property roles, is the question of the derivatives of properties with respect to the intensive variables which illustrates the differences between developers and users. Consider the problem shown in Figure 6. The numerical solution of this simulation/optimization based design problem requires the following derivatives (where 6 is any property and % is any intensive variable):
Figure 6: Simulation & optimization of a PT-flash operation (minimize the amount of heat to be added/removed, keeping the ratio of V/F constant while manipulating the operating temperature and pressure) If the selected property model, i.e., Eqs. 4, 5, 6, have not been tested for the existence of these derivatives, convergence failures are likely to occur. If the derivatives are inconsistent, the Gibbs-Duhem conditions (see chapter 1) will not be satisfied and so the numerical results will not be thermodynamically consistent, even when all other solution criteria may be
40
satisfied. Model developers (generators and implementers) need to recognize this issue and test derivatives for existence and consistency and to provide this information to users. Because the objectives, organizations and styles of property model generators, implementers and users are not usually the same, their interconnections are typically weak. In particular, generators usually seek generalized models to have as large an application range as possible, while they ignore computational speed and derivative issues . On the other hand, property model users commonly implement models having high computational efficiency and as wide spectrum of applications as possible. But they usually do not provide developers with much information on the limitations of their models. Better communication is needed between property model generators and users to deal with these concerns for the most effective impact of models in process-product design applications.
2.4 CONCLUSIONS Three different roles for properties and their corresponding models have been highlighted. Property models can play a much wider role than the traditional service role, for which they are mostly known (or receive credit for). Using them in the advice role can improve the design, widen the search space and increase the efficiency of the solution method. When property models become difficult to use in forward simulation approaches because of complexity, possibilities of using a reverse approach should be investigated. In most design and/or simulation problems, the "exit" conditions are usually known but not actually used in the simulation; they merely verify the simulation results or the design. By using both the known "inlet" and "exit" conditions, property integration can be identified and target values assigned. Many interesting process-product design problems can be solved more easily through this reverse approach. Finally, for property models to play their roles efficiently and for more advanced models to find applications in process-product design, better communication between property model generators, implementers and users is necessary.
REFERENCES 1. R. Gani, J. P. O'Connell, Computers & Chemical Engineering, 25 (2000) 3. 2. J. P. O'Connell, M. Neurock, "Trends in property estimation for process and product design", in: Proceedings of FOCAPD'99, Breckenridge, USA, 1999. 3. J. D. Seader, E. J. Henley, Separation Process Principles, John Wiley & Sons, Inc., New York, USA, 1998. 4. B. Linhoff, J. R. Flower, AIChE J., 24 (1978) 633-642. 5. R. Gani, E. N. Pistikopoulos, Fluid Phase Equilibria, 194-197 (2002) 43-59. 6. M. R. Eden, S. B. Jorgensen, R. Gani, M. M. El-Halwagi, Chemical Engineering & Processing, 43(2004) 595-608. 7. E. Bek-Pedersen, R. Gani, Chemical Engineering & Processing, 43 (2004) 251-262. 8. Y. Xin, B. W. Whiting, Ind & Eng Chem Res, 39 (2000) 2998.
41 9. E. A. Brignole, R. Gani, J. A. Romagnoli, Ind & Eng Chem Process Des & Develop, 24 (1985) 42-48. 10. R. Gani, J.P. O'Connell, Comp. Chem. Eng., 13, (1989) 397-404. 11. J. Gross, G. Sadowski, Ind & Eng Chem Res, 41 (2002) 1084-1093. 12. G. Soave, Chem Eng Sci., 27 (1972) 1197. 13. S. Macchietto, E. H. Chimowitz, T. F. Andersen, L. F. Stutzman, Ind Eng Chem Process Des Develop, 25 (1986) 674-682. 14. J. Perregaard, E. L. Sorensen, Computers & Chemical Engineering, 16S (1992) 247254. 15. D. Hlidebrandt, D. Glasser, C. Crowe, Ind & Eng Chem Res, 29 (1990), 49.
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Part II: Models for Properties
3. Pure component property estimation^ Models & databases Jorge Marerro & Rafiqul Gani 4. Models for liquid phase activity coefficients-UNIFAC Jens Abildskov, Georgios M. Kontogeorgis & Rafiqul Gani 5. Equations of state with emphasis on excess Gibbs energy mixing rules Epaminondas C. Voutsas, Philippos Coutsikos & Georgios M. Kontogeorgis 6. Association models — The CPA equation of State Georgios M. Kontogeorgis 7. Models for polymer solutions Georgios M. Kontogeorgis 8. Property estimation for electrolyte systems Michael L. Pinsky & Kiyoteru Takano 9. Difussion in multieomponent mixtures Alexander Shapiro, Peter K. Davis, J. L. Duda 10. Modeling of phase equilibria in systems with organic solid solutions Joao Coutinho, Jerome Pauly, Jean-LucDaridon 11. An introduction to modeling of gas hydrates Eric Hendriks & Henk Meijer
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Computer Aided Property Estimation for Process and Product Design G.M. Kontogeorgis and R. Gani (Editors) © 2004 Elsevier B.V. All rights reserved.
45
Chapter 3: Pure Component Property Estimation: Models & Databases Jorge Marrero and Rafiqul Gani 3.1 INTRODUCTION Pure component properties are needed for many process and product design calculations. They may be needed to study the behavior of the product (such as the solubility of drug in water), behavior of a chemical under the conditions of operation of a process (heat of vaporization of a refrigerant or process fluid in a closed cycle), dimensioning of equipment (density of the chemical in a tank), the physical state of the product (melting point and/or boiling point to identify solid, liquid or vapor state) and many more. For the estimation of mixture properties also, the pure component properties are employed in different mixture property models. For example, the well-known SRK equation of state employs the critical properties while an ideal mixing model for liquid density employ only the pure component liquid densities of each chemical species present in the mixture. The objective of this chapter is to provide the reader with a set of pure component property models for a corresponding set of frequently used properties in process-product design. These models have been tested and evaluated against a wide range of chemical species by the authors. A good collection of pure component property models can also be found in many specialized property estimation books, journal papers, commercial software and databases. It is beyond the scope of this chapter to name all the references as well as methods. The calculation methods outlined in each section of this chapter should provide some guidance in terms of the important steps related to estimation of a pure component property.
3.2 MODELS FOR PRIMARY PROPERTIES As described in Chapter 1, primary properties are classified as those, which can usually be determined only from the molecular structural information and have a single unique value. In this chapter, only a set of primary properties that are needed for a wide range of processproduct design calculations are presented through one property estimation approach. This does not mean that the property models used below are the best or have the highest accuracy. These models are, however, frequently used and their details, including the model parameter tables, are readily available. The property model presented below can be classified as an additive method using a group-contribution+ approach. The property estimation methods will be highlighted through the molecular structure of Glycine (CAS No. 000056-40-6). Only the estimated primary and the secondary properties of
46 Glycine are given. When the estimated value for a secondary property for Glycine is not given, it means that not all the dependent properties are available. When experimental data for the property is available, it is also given. The chemical formula, group assignment and 3D molecular structure is given in Figure 1.
Figure 1: Molecular structural details for Glycine 3.2.1
Primary Property Models
All the properties listed below are only functions of the molecular structural information described in terms of first-order, second-order and third-order groups. Note that all molecules must be completely described by first-order groups and may or may not have second- and third-order groups. The estimation steps are as follows: 1. 2. 3. 4.
Identify the groups (first-, and if necessary, second- and third-order groups) Determine how many groups of each type are needed to represent the molecule Retrieve the parameters from the model parameter tables for the property of interest Sum the contributions and use the corresponding property model function
Properties & Models The following property models have been proposed by Marrero and Gani [1,2]. In each case, the summation terms having the following expression Contribution of first-order groups, Sum.Groups.I = £i ni C; for i = 1, NCi Contribution of second-order groups, Sum.Groups.II = Ej rrij Dj for j = 1, NC2 Contribution of third-order groups. Sum.Groups.Ill = Zk Ok Ek for k = 1, NC3
(1) (2) (3)
In the above equations, n;, rrij, Ok are the number of first-, second- and third-order groups of types i, j and k, respectively. Q, Dj and E^ are the contributions for the selected property for first-, second- and third-order groups of types i, j and k, respectively. NCi, NC2 and NC3 are the total numbers of different types of first-, second- and third-order groups representing the molecule. Critical temperature, K Tc = 231.239*Iog(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)
(4)
47
Glycine: 1028.0 K (experimental: 1028) Critical pressure, bar Pc = l/(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III + 0.108998)2 + 5.9827
(5)
Glycine: = 67.4 bar (experimental: 67.4) Critical volume, cm3/mol Vc = 7.95 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III
(6)
Glycine: = 234.01 cmVmol (experimental: 234.0) Normal melting point, K T m = 147.450*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)
(7)
Glycine: = 535.63 K (experimental: 535.15) Normal boiling point, K Tb = 222.543*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)
(8)
Glycine: = 710.97 K Standard Gibbs free energy of formation. kJ/mol Gf = -34.967 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III
(9)
Glycine: -300.1 kJ/mol (experimental: -300.1) Standard Enthalpv of formation at 298 K, kJ/mol H r = 5.549 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (10) Glycine: -388.49 kJ/mol (experimental: -392.1) Enthalpv of vaporization at 298 K. kJ/mol Hv = 11.733 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (11) Enthalpv of vaporization at TH, kJ/mol HVb - a + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (12) Glycine: = 43.0 kJ/mol Heatoffusionat298K, kJ/mol HfuS = -2.806 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (13) Glycine: 28.4 kJ/mol (experimental: 28.4)
48 3.3 MODELS FOR SECONDARY PROPERTIES As defined in Chapter 1, secondary properties are those that cannot be explicitly calculated only from structural information and usually require the knowledge of other properties. Most of these models have been derived from the principle of corresponding states, although, a number of empirical correlations also exist. There is available, a wide range of methods for prediction of secondary properties. Many books and handbooks provide methods for calculating these properties. Poling el al. [3] provides a good collection of many of the needed methods. Horvath [4] also provides a large number of methods for primary as well as secondary properties. In this section, a set of pure component properties that have a single value is listed together with a corresponding property estimation method. 3.2.1 Secondary Property Models The following steps may be followed in the estimation of pure component secondary properties. 1. For the secondary property of interest, select an estimation method 2. For the selected estimation method, identify the properties (data) needed to use the model and verify the application range of the method in terms of chemical species (type) 3. Retrieve from a database or predict the necessary properties (to be used as input) 4. Calculate the property through the selected method For the secondary properties listed below, the following properties are needed as input. All these properties are also defined below. For each property, first the generic form of the equation in terms of dependency on other properties/variables is given, followed by the method for calculation, the model equations, and finally, the calculated value for the chemical used as an example. Hfus (kJ/mol). Tb (K), Tc (K), Pc (bar), Vc (cmVmol), SolPar (MPa°5), Ss (MPa°5), nD, Dm (debye), ps(bar), Mw (g/mol), Ws (mg/L) Properties & Models For each property, the name of the property, the representation of the property in terms of its dependence on other properties, the method used and the equations involved are presented. Heat of Vaporization at Th. HVb= f(Tj,, Tc, Pc) Method: Correlation (Equation 7-11.5 in Reid et. al. [5]) tr = Tb/Tc X = 0.37691 - 0.37306*tr+ 0.15075/(Pc*tr2) Y = (0.4343*log(Pc) - 0.69431+ 0.89584*tr)/X
49 Hvb = Tb*0.008314*Y (14) Not recommended for Glycine Pitzer's Acentric Factor, co = f(Tb, Tc, Pc) Method: Lee-Kesler Correlation (2-3.4 in Reid et. al. [5])) / Constantinou & Gani [6] 0 = Tb/Tc a = -log(Pc*0.98692327) - 5.92714 + 6.09648/0 + 1.28862*log(6) - 0.169347*96 P = 15.2518 - 15.6875/9 - 13.4721 *log(9) + 0.43577*96 co = a / p (15) Glycine: 0.747 Lee-Kessler 0.673 Constantinou & Gani [6] Critical Compressibility Factor, Zc = f(Tc, Pc, Vc) Method: Theoretical (Equation) Definition ZC = (PC*VC)/(83.14*TC) (16) Glycine: 0.185 Liquid Volume at Tb, Vb =f(Vc), cm3/mol Method: Tyn and Calus Correlation (3-10.1 in Reid et. al. [5]) Vb = 0.285*Vcli)48 (17) Glycine: 86.5 cm /mol Liquid Volume at 298 K, Vm = f(Tc, Pc, co), cmVmol Method: Rackett Modified Correlation t r =1.0-298.15/T c Zra = 0.29056-0.08775*co W=l+(l-trf28571 Vm = (83.14*T0*Zrallunc)/Pc (18) Refractive Index, no = f(Soli>ar) Method: Correlation [4] nD = (0.48872*SolPar+5.55)/9.55 (19) Glycine: 1.8 Molar Refraction, Rm = f(nn, Vm) Method: Correlation [4] Rm = (((nD)2-l)*Vm*1000)/((nD)2 + 2) (20) Surface Tension at 298 K, a = f(Sol|>ar, Vm), dyne/cm Method: Correlation [4]
50 CT = 0.01707*(Sol Par ) 2 *(V m ) 0333333 (21) Entropy of Fusion. Sfus = f(HfUS, T m ), J/(mol*K) Method: Theoretical (Equation) Definition S rus =1000*H fus /T m
(22)
Glycine: 53.07 J/(mol*K) Closed Flash Temperature. Tfc = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tfc = -2.03*(Sum.Groups.Ic G ) + 0.659*T b + 20.00
(23)
Open Flash Temperature, Tfo = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tf0 = 3.63*(Sum.Groups.Ic G ) + 0.409*T b + 88.43
(24)
Glycine: 414 K Hansen Dispersive Solubility Parameter, 8s - f(GCcG, V m ), MPa 0 5 Method: Constantinou and Gani [6] 8s = (Sum.Groups.IcG)/Vm
(25)
Glycine: 17.74 MPa 0 5 Hansen Polar Solubility Parameter, 8 P = f(GC C o, V m ), MPa 0 ' 5 Method: Constantinou and Gani [6] 8 P = [(Sum.Groups.I C G) 05 ]/V m (26) Glycine: 12.16 MPa 0 5 Hansen Hydrogen Bonding Solubility Parameter, 8 H B = f(GCCG, V m ), MPa 0 5 Method: Constantinou and Gani [6] SUB = [(Sum.Groups.IcG)/V m ]° 5 (27) Glycine: 17.38 MPa 0 5 Dipole Moment. D m = f(8 s , V m ), debye Method: Correlation [4] D m = 0.02670*8 s *(V m )° 5 (28) Dielectric Constant, DH = F(Solpar, no, D m ) Method: Correlation [4] I f n D < 0.001. DK = (n D ) 2
51 Else, DE = (SolPar*0.48871-7.5)/0.22 (29) Henry Constant of a gas in water at 298 K, Hhenr), = (pS(298), Mw, Ws), bar*m3/mol Method: Theoretical (Equation) Definition Hhenry = ps(298)*Mw/Ws
(30)
3.3.1 Secondary Properties modeled as Primary Property For a number of secondary of secondary properties, it is sometimes possible to model them as primary properties. That is, it is possible to predict the property only as a function of the molecular structural information. Recently, Marrero and Gani [2] have developed models for Octanol-water partition coefficients, Solubility of a chemical in water at 298 K, and the Hildebrand solubility parameter. Also, the method of Martin and Young [7] for the measure of toxicity in terms of 50% mortality of Fathead Minnow after 96 hours of exposure has been adapted to the Marrero and Gani method. As in the case of primary properties listed in section 3.2, the prediction of the following properties also follow the same steps Octanol-water partition coefficient (LogKow) LogKow = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (31) Glycine: -3.41 (experimental:-3.21) Water Solubility, Ws, Log(mg/L) LogWs = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (32) Glycine: 5.41
(experimental: 5.39)
Hildebrand solubility parameter at 298 K, Solpar, M(Pa) Solpar = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (33) Glycine: 23.9 MPa03 Acute Toxicity (96-h LC50) to Fathead Minnow, mol/L -Log(LC50) = Sum.Groups.I (34) Glycine: 2.82
3.4 FUNCTIONAL PROPERTIES As defined in Chapter 1, pure component functional properties are those that depend on the specific value of temperature and/or pressure. Most prediction methods employ a suitable equation of state, the principle of corresponding states or a specially fitted correlation. In this
52
section, a set of functional properties and a corresponding property model is presented. Note that as in secondary properties, functional properties may also require other properties as input data. Note also that many temperature dependent functional properties are available in databases where the coefficients for the correlation of each property and chemical are stored. These correlation functions are discussed in section 3.4 of this chapter. The following steps may be employed in the estimation of functional properties. 1. For the property of interest, select an appropriate property model. 2. Verify the applicability of the model in terms of chemical species as well as the temperature (and/or pressure) limit of the method. 3. Retrieve or estimate the necessary properties to be used as input data 4. Calculate the property of interest at the condition (temperature and/or pressure) of interest using the selected method 3.4.1 Properties & Models For each property, the name of the property, the functional dependence, the units of measure, the method and the model equations are presented. Diffusion coefficient of component at infinite dilution in water, Dab = f(Vb, Tb, T) cm2/s Method: Modified Tyn & Calus Correlation (11-9.5 in Reid et. al. [5]) X = exp(-24.71 + 4209/T + 0.04527T - 0.00003376*T2) for 273.15 < T < 643.15 Dab = 0.01955/[(Vb)0433]*(T/X) (34) See also Chapter 9 for other prediction methods. Liquid Density,CTL= f(Tc, Pc, co, T), g/cm3 Method: Modified Rackett correlation (3-11.10 in Reid et. al. [5]) Zra = 0.29056-0.08775*© Tfimc = 1 + (1-T/Tcf285714 for T/Tc < 0.9 a, = (83.14*Tc*(Zra)Tfunc)/Pc (35) Thermal Conductivity, Tcon = f(Tb, Tc, T, Mw) W/m*K Method: Correlation (10-9.5 in Reid et. al. [5]) Tr = T/Tc Tbr = Tb/Tc Tcon = [l.ll/[(Mw) 05 ]*(3 + 20*(l-Tr)06666)]/[(3 + 20*(l-Tbr)06666)] (36) forT r 300 K and a melting point < 250 K. B. Find all compounds having a boiling point > 300 K, a melting point < 250 K and the Hildebrand solubility parameter between 25 and 27 MPa . 3.5.2
References for Databases
In this section, a few of the well-known databases found on the internet are listed below in Table 1, while references where useful data can be found are given in Table 2. Table 1: List of well-known databases Name API TECH Database CambridgeSoft ChemFinder
Address & Comments Pure component, petroleum characterization, etc. http://www.epcon.com Searchable data and hyperlink index for thousands of compounds - the ideal starting point for internet "data-mining" http://chemfinder.cambridgesoft.com/
56 Table 1 continued CRC Handbook of Chemistry and Physics DECHEMA Chemistry Data Series DETHERM DIPPR Electrolytes GPSA Data Book IUPAC-NIST SDS Knoval Science and Engineering Resources PDB PPDS TAPP The NIST Webbook
Library Network Database (http://www.hbcpnetbase.com/) A 15 volume data collection Comprehensive collection of thermophysical and mixture properties data, includes Dortmund DDB and ELDAR DDB http://www.dechema.de/f-infsys-e.htm7englisch/dbMain.htm Critically evaluated thermophysical data http://www.aiche.org/dippr/vision.htm IVC-SEP database for properties of electrolyte systems www. i vc- sep .kt. dtu.dk/databank GPSA Engineering Data Book —section 23 (physical properties) & 24 (thermodynamic properties) http://www.gasprocessors.com Solubility Data Series http://www.unileoben.ac.at/~eschedor Library Network Database (International Critical Tables, Polymers -Property Database, Handbook of Thermodynamic and Physical Properties of Chemical Compounds, etc.) Protein Data Bank — Processing and distribution of 3-D biological and macromolecular structural data http://pdb.ccdc.cam.ac.uk/pdb/ Physical Properties Data Service http://www.tds-tds.com/fs_ppds.htm Thermochemical and Physical Properties Database http://www.chempute.com/tapp.htm An excellent source of physical and chemical data http://webbook.nist.gov
3.6 CONCLUSIONS Pure component properties are needed in the solution of various types of process-product design problems as well as input in many models for estimation of mixture properties. Usually, they are stored (experimental data) in databases, at least, the single value properties and the temperature dependent functional properties. The problem, however, is that even though the database may contain thousands of compounds, not all data is available for all the listed compounds. Also, in process-product design, new chemicals may be synthesized, which would not be present in the database. For this reason, property models for estimation of pure component properties are needed. In this respect, the chapter provides the reader a
57 quick guide in terms of the most commonly used pure component properties and a representative set of property models. Table 2: References for data Biochemistry & Biotechnology Drugs- Phase diagrams Octanol-water partition coefficients Polymer Data Solubility data Solubility data Water infinite dilution activity coefficients
Thermodynamic data for biochemistry and biotechnology, Hans-Jurgen Hinz, Editor, Springer-Verlag, 1986 J. Phys Chem Res Data, 1999, 28(4), 889-930 J. Phys Chem Res Data, 1989, 18(3) 1111-1229 Polymer DIPPR 881 Project High&Danner, 1992 Barton Handbook, CRC Press 1990 J. Marrero & J. Abildskov, Solubility and realted properties of large complex molecules. Part 1, Chemistry Data Series, Vol XV, DECHEMA, 2003 Voutsas & Tassios, Ind Eng Chem Res, 1996, 35, 1438 supporting material
REFERENCES 1. J. Marrero, R. Gani, Fluid Phase Equilibria, 183-184 (2001) 183. 2. J. Marrero, R. Gani, Industrial Engineering & Chemistry Research, 41 (2002) 6623. 3. B. E. Poling, J. M. Prausnitz, J. P. O'Connell, "The Properties of Gases and Liquids", McGraw-Hill, New York, 5th Edition, 2000. 4. A. L. Horvath, "Molecular Design", Elsevier, Amsterdam, The Netherlands, 1992. 5. R. Reid, J. M. Prausnitz, B. E. Poling, "The Properties of Gases and Liquids", McGraw-Hill, New York, 4th Edition, 1987. 6. L. C. Constantinou, R. Gani, AIChE J, 40 (1994) 1697 7. T. M. Martin, D. M. Young, Chem. Res. ToxicoL, 14 (2001), 1378 8. T. L. Nielsen, J. Abildskov, P. M. Harper, I. Papaeconomou, R. Gani, J. Chem Eng Data, 46 (2001) 1041.
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Computer Aided Property Estimation for Process and Product Design G.M. Kontogeorgis and R. Gani (Editors) © 2004 Elsevier B.V. All rights reserved.
59
Chapter 4: Models for Liquid Phase Activity Coefficients - UNIFAC Jens Abildskov, Georgios M. Kontogeorgis and Rafiqul Gani 4.1 INTRODUCTION Computer-optimized design of the separation processes, e.g. distillation, absorption and extraction, typically encountered in the chemical industry, requires thermodynamic models, which can be applied to a variety of chemicals. The investment (capital costs) for the separation steps is often in the neighborhood of 50-70 % of the total cost, and energy costs for separations can be up to 90 % of the total cost. Measured phase-equilibrium data are typically employed at the later design stages. However, for preliminary design, at the earlier stages and for screening purposes i.e. for testing alternative separation techniques, approximate models, which can be widely applicable, are of interest. Such models can provide rapid estimation of phase equilibria over a wide range of conditions. In addition to the case of the forward property prediction problem (chemical system is known but property values need to be calculated or retrieved), the reverse property prediction problem (property values are known but the chemical system is not known) is also of interest. These are typically problems related to the design of molecules/mixtures/blends such as solvents, process fluids, etc., where the desired properties of the chemical are known but the identity of the chemicals or their mixtures are not. Finding a system with properties close to a specified set also requires rapid predictions of phase equilibria for many mixtures. In this latter case, the use of predicted data is probably the only way in which the problem becomes solvable and forms the basis for computer-aided molecular/mixture design techniques. The need of process-product design techniques for rapid estimation of phase equilibria for a wide variety of systems, conditions and problems has been the driving force behind the development of the UNIFAC and other group contribution models. Statistical thermodynamics has not as yet reached a stage where rigorous solution theories of general applicability are available, although some results of limited practical use have been reported1 (see also chapter 12). Semi-empirical methods are, thus, of interest. Of the most well-known semi-empirical methods useful for predictions of phase equilibria, the group contribution concept is possibly the most widely used. They are usually simple, easy to use and are at least qualitatively correct for many systems where no experimental data is available. Examples of such group contribution methods are the analytical solution of groups, ASOG2 and UNIFAC3, both providing the liquid phase activity coefficients for the compounds present in the solution. Despite their limitations (see section 4.3.3), such group contribution methods have found widespread application in engineering design calculations due to their relative simplicity, their predictive power and analytical form.
60 Several reviews have appeared since the 1980s summarizing the developments of these models4"8. This chapter gives a short overview of the most well-established UNIFAC methods, including the most recent developments and their efficient computer-based use. Table 1: Partial list of different versions of the UNIFAC model. UNIFAC Models UNIFAC-VLE
Special Feature 1 -parameter for group interactions
UNIFAC-LLE
1 -parameter for group interactions
Modified UNIFAC Lyngby
3-parameters for group interactions
Modified Dortmund UNIFAC
3-parameters for group interactions
Linear-UNIFAC
2-parameters for group interactions
Linear Dortmund UNIFAC
2-parameters for group interactions
KT-UNIFAC
lst-order (Linear UNIFAC) & 2ndorder group contribution terms
Remarks - Reference Original version with parameter tables [1977]3'9'" Parameters regressed from LLEdata[1981]'2 Changes in model equations & new parameter tables [1987113 Changes in model equations & new parameter tables [1987]14 Changes in model equations & new parameter tables [1992]15 Changes in model equations & new parameter tables [1992]16 Changes in model equations & new 1 st-order and 2nd-order group parameter tables [2002]10
4.2 THE UNIFAC METHOD Since its development in 19759, a number of different versions of the UNIFAC groupcontribution method for the estimation of liquid phase activity coefficients have been developed. The first UNIFAC method will be called here as the UNIFAC-VLE. One of the latest versions of UNIFAC, the KT-UNIFAC, has been developed by Kang et alw. Table 1 gives a partial list of different versions of UNIFAC that will be discussed in this chapter. The characteristic feature of all UNIFAC methods is that all versions are based on the group contribution approach where the liquid phase activity coefficient of component i in solution with one or more components is calculated as a sum of contributions of all groups representing the mixture (solution). These contributions are divided into two terms - a combinatorial term that accounts for the contributions due to differences in size and shape and are based on the group surface area and volume parameters, and a residual term accounting for the energetic differences, which includes the interaction parameters between the groups. With respect to the intensive variables, the UNIFAC method is dependent only on
61 temperature and composition but not pressure. The combinatorial term is dependent on composition only (in addition to the group surface area and volume parameters) while the residual term depends on the temperature, the composition and the group parameters (surface area, volume and interactions). With the exception of KT-UNIFAC, all UNIFAC methods employ lst-order functional groups to represent the compounds present in the liquid mixture. KT-UNIFAC employs both lst-order and 2nd-order functional groups to represent the compounds present in the liquid mixture. Therefore, the combinatorial and residual contributions have first-order and secondorder terms if 2nd-order groups are present. Two examples of representation of molecules with the UNIFAC groups are given below in Table 2. Note that each group is characterized by a main group, a sub-group, the sub-group surface area (Rf), the sub-group surface volume (Qf) and the main-group/main group interaction parameters anmo, amn,o, amn,o- Each compound therefore is represented by NSG number of sub-groups and a corresponding number of main-groups. A total of NMG maingroups are needed to describe all the compounds in the mixture. Table 2: Representation of molecular structures with different types of groups Ethanol (NSG=3, NMG=2) Sub-Groups: 1 CH3, 1 CH2, 1 OH Main-Groups: CH2, OH 2nd-Order groups: None
2-Butanol (NSG=4, NMG=2, NSOG=1) Sub-Groups: 2CH3, 1 CH2, 1 CH, 1 OH Main-groups: CH2, OH 2nd-Order groups: CHOH
4.2.1 General Model Equations (lst-order) The UNIFAC GC-method for the estimation of the liquid phase activity coefficient of component i in a solution consist of a combinatorial and a residual contribution: lny=lny\+lny":
(1)
The combinatorial term (In y/) includes entropic effects due to molecular size and shape differences while the residual term (In j,R) involves the intermolecular interactions. The different versions of the UNIFAC GC-method differ in their formulation of the combinatorial term and the expression of the temperature dependence of the residual part. Combinatorial Term - In j \ C The combinatorial term is written as17 /«r;;=/-j,+/«j,-^,(/--+/«-! * v Li Li) with
(2)
62 L> = ^ — /_, x,
