Thermodynamics model parameters

Gorak and Vogelpohl (1985) present an experimental study of ternary distillation in a packed column. The system used was methanol(l)-2-propanol(2)-water(3) and the column was 0.1 m wide and filled with Sulzer CY packing. Use the nonequilibrium model to simulate their experiments. Investigate the sensitivity of the simulation results to the thermodynamic model parameters. Write an article in the format required by Separation Science Technology that summarizes your calculations. 

In this chapter, a few important examples of industrial interest in the field of separation processes are discussed. In the case ofthe design of distillation processes, the quality of the thermodynamic model parameters has a great influence on the rehabihty of the results. Therefore, the parameters used for the calculation of pure component properties, phase equilibria, and so on, should be checked carefully prior to process simulation. 

In this chapter, the background of phase equilibrium was reviewed. The useful binary and ternary tools in Aspen were also illustrated with examples. Data regression capability in Aspen for obtaining thermodynamic model parameters from experimental data was also demonstrated. For the cases where there is no experimental data, how to use UNIFAC to estimate physical properties was also given in this chapter. 

There are no experimental thermodynamic data for ternary alloys. [1991Kau] reported thermodynamic model parameters of several phases within CALPHAD formalism. Thermodynamic model parameters were obtained by primarily matching the available experimental phase equilibria. 

Thermodynamic consistency requites 5 1 = q 2y but this requirement can cause difficulties when attempts ate made to correlate data for sorbates of very different molecular size. For such systems it is common practice to ignore this requirement, thereby introducing an additional model parameter. This facihtates data fitting but it must be recognized that the equations ate then being used purely as a convenient empirical form with no theoretical foundation. 

Whiting, W.B., TM. Tong, and M.E. Reed, 1993. Effect of Uncertainties in Thermodynamic Data and Model Parameters on Calculated Process Performance, Industiial and Engineeiing Chemistiy Reseaieh, 32, 1993, 1367-1371. (Relational model development)... 

Estimation of parameters. Model parameters in the selected model are then estimated. If available, some model parameters (e.g. thermodynamic properties, heat- and mass-transfer coefficient, etc.) are taken from literature. This is usually not possible for kinetic parameters. These should be estimated based on data obtained from laboratory expieriments, if possible carried out isothermal ly and not falsified by heat- and mass-transport phenomena. The methods for parameter estimation, also the kinetic parameters in complex organic systems, and for discrimination between models are discussed in more detail in Section 5.4.4. More information on parameter estimation the reader will find in review papers by Kittrell (1970), or Froment and Hosten (1981) or in the book by Froment and Bischoff (1990). 

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... 

Even if we make the stringent assumption that errors in the measurement of each variable ( >,. , M.2,...,N, j=l,2,...,R) are independently and identically distributed (i.i.d.) normally with zero mean and constant variance, it is rather difficult to establish the exact distribution of the error term e, in Equation 2.35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and in the treatment of potentiometric titration data (Sutton and MacGregor. 1977 Sachs. 1976 Englezos et al., 1990a, 1990b). 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993)... 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

Parameter Estimation in Activity Coefficients Thermodynamic Models... 

Table 5.2 Model parameters used in the thermodynamic description of liquid Si.

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

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