Calculation of gas solubility

For the calculation of gas solubilities for physical absorption processes both approaches discussed in Section 5.1 (Eqs. (5.9) and (5.10)) for VLE calculations can be applied. 

While there is no difference for the calculation of gas solubilities in comparison to VLE in the case of the equation of state (approach A), for approach B, there is the problem that the standard state (pure liquid at system temperature and system pressure) used for VLE calculations cannot be used anymore, since supercritical compounds are not existent as liquid. This means an alternative standard fugacity is required for the y —y)-approach. 

An alternative is the usage of the Henry constant H,j as standard fugacity Using the Henry constant as standard fugacity, the following expression is obtained for the calculation of gas solubilities in a binary system ... 

The quality of all model calculations with respect to solvent activities depends essentially on the careful determination and selection of the parameters of the pure solvents, and also of the pure polymers. Pure solvent parameter must allow for the quantitative calculation of pure solvent vapor pressures and molar volumes, especially when equation-of-state approaches are used. Pure polymer parameters strongly influence the calculation of gas solubilities, Henry s constants, and limiting solvent activities at infinite dilution of the solvent in the liquid/molten polymer. Additionally, the polymer parameters mainly determine the occurrence of a demixing region in such model calculations. Generally, the quantitative representation of liquid-liquid equilibria is a much more stringent test for any model, what was not discussed here. To calculate such equilibria it is often necessary to use some mixture properties to obtain pure-component polymer parameters. This is necessary because, at present, no single theory is able to describe correctly the properties of a poly-... 

What main conclusions can we draw from the three examples discussed here First, although van t Hoff plots should involve Km rather than Kc data, the use of the latter may afford sensible and possibly accurate thermochemical values (always under the assumption of ideal solutions ), particularly if the density term of equation 14.5 is considered in the calculation of the reaction entropy. Second, due to the lack of gas solubility data, the second law method is much... 

The tentative equation summarized in Table V allows the calculation of the solubility at one atmosphere gas partial pressure which is numerically equal to the inverse of Henry s constant (equation 1). Although Henry s law may be adequate up to moderate pressures, it requires some corrections for the solubilities at higher pressures. Table VI summarizes some approaches that have been used to correlate solubility pressure isotherms. These have been discussed in many places including references [,21 and 22]. ... 

In the following discussion, only the basic equations that allow the calculation of the solubility of a solid material (solute, component 2) in a dense gas will be reported. The equilibrium condition for component 2 is ... 

Careful consideration was taken in the parameterization process to insure that the parameters were deemed reasonable for the atom types, using the OPLS-AA force field atom types as a comparison. As one of the goals of this project was to ensure that robustness was achieved in many different calculated properties of the newly developed model, several sets of simulations were also performed to ensure that the parameters could achieve a reasonable agreement with experiment. Some of the properties calculated included the gas phase density, the partial molar volume in aqueous solution, and the bulk solvent structure as well. The calculation of the solubility was discussed in the previous section for the parameterization process and the viewing of these results, the solubility will be reported in log S values, as many of the literature values are reported as log S values, and therefore, the comparison would not lose any sensitivity due to rounding error from the log value. 

It is possible to determine C quantitatively using Hildebrand s theory of microsolutes. An example of the accuracy that can be achieved is provided by the calculation of the solubilities of a series of p-aminobenzoate esters in hexane (17,18). Michaels, et al. (19) used this approach to estimate the solubility of steroids in various polymers. The solubilities of seven steroids in six polymers were calculated from the steroid melting points, heats of fusion, and solubility parameters. Equation 8 was derived, where Jjj is the maximum steady state flux, h is the membrane thickness, x is the product of V, the molar volume of the liquid drug, and the square of the difference in the solubility parameters of the drug and polymer, p is the steroid density, T is melting point (°K), T is the temperature of the environment, R is the gas constant, and AH and ASf are the enthalpy and entropy of fusion, respectively. 

It should be pointed out that the gas solubility could be calculated using the laws of solution behavior previously described in Chapter 5, provided sufficient data are available. It is necessary to have not only data for the overall composition of the system hut complete and accurate equilibrium constant data as well. These data are seldom, if ever, available for a crude-oil system and values of gas solubility must be obtained either experimentally or by estimation. However, to illustrate the complexity of computations of this type the method is outlined below for a two-component system of known overall composition. 

We consider application of Eqs. (I.6-16)-(1.6-I8) to (he calculation of the solubility of naphthalene (component 2) in carbon dioxide (component I) at 3S°C and at high pressures. Data for these conditions (Tsekhanskaya et al.T) are shown as open circles in Fig. 1.6-2. Particularly noteworthy is the dramatic enhancement In solubility—several orders of magnitude—that occurs with increasing pressure near foe critical pressure of foe solvent gas. The solubility enhancement, which obtains for temperatures slightly higher than the critical temperature of a solvent gas (the critical temperature of COi is 3l°C), is the basis for certain "supercritical extraction processes ase Paulaitis et a1.Ba for discussions of fols topic. 

In the study of the solubility of a gas in a liquid one is interested in the equilibrium when the mixture temperature T is greater than the critical temperature of at least one of the components in the mixture, the gas. If the mixture can be described by an equation of state, no special difficulties are involved, and the calculations proceed as described in Sec. 10.3. Indeed, a number of cases encountered in Sec. 10.3 were of this type (e.g., ethane in the ethane-propylene mixture at 344.3 K). Consequently, it is not necessary to consider the equation-of-state description of gas solubility, as it is another type of equation-of-state vapor-liquid equilibrium calculation, and the methods described in Sec. 10.3 can be used. 

However, the description of gas solubility using activity coefficient models does require some explanation, and this is what is discussed in this section. The activity coefficient description is of interest because it is applicable to mixtures that are not easily describable by an equation of state, and also because it may be possible to make simple gas solubility estirnates using an activity coefficient model, whereas a computer program is required for equation-of-state calculations. 

For He, Ne, Ar, and Kr, Weiss (1970, 1971) and Weiss and Kyser (1978) gave empirical equations that directly yield the atmospheric solublity equilibrium concentrations Ci,eq at a total pressure of 1 atm. While this form of gas solubilities is very convenient in practice, it should be noted that such equilibrium concentrations are—as shown by Equations (2) and (3)—not directly proportional to P. The correct way to calculate the equilibrium concentrations at any pressure from those at Po = 1 atm is ... 

In the current study we are mainly interested in describing the gas solubility in pure water, under two-phase equilibrium (H-L ) conditions. The gas of primary interest to the study is methane. To this purpose we use different published thermodynamic models that are based on Equations of State (EoS) forfugacity calculations that are coupled with the van der Waals-Platteeuw theory from Statistical Thermodynamics, and models of gas solubility in the aqueous phase. 

Maassen, S., Arlt, W., and Klamt, A. (1995) Prediction of gas solubilities and partition coefficients on the basis of molecular orbital calculations (COSMO) with regard to the influence of solvents. Chem. Ing. Tech., 67 (4), 476-479. 

In Approach A, the fugacity coefficients of the liquid (pf and vapor phase are needed. They describe the deviation from ideal gas behavior and can be calculated with the help of equations of state, for example, cubic equations of state and reliable mixing rules. In Approach B, besides the activity coefficients s value for the standard fugacity is required. In the case ofVLE usually the fugacity of the pure liquid at system temperature and system pressure is used as standard fugacity. For the calculation of the solubilities of supercritical compounds Henry constants are often applied as standard fugacity (see Section 5.7). 

For the calculation of the solubility y2 reliable sublimation pressures are required. For the calculation of the Poynting factor, additionally the molar volume of the solid compound is required. Then the equation of state only has to describe the fugacity coefficient in the gas phase 02 as a function of pressure. 

Phase and chemical equilibrium calculations are essential for the design of processes involving chemical transformations. Even in the case of reactions that cannot reach chemical equilibrium, the solution of this problem gives information on the expected behaviour of the system and the potential thermodynamic limitations. There are several problems in which the simultaneous calculation of chemical and phase behaviour is mandatory. This is the case, for example, of reactive distillations where phase separation is used to shift chemical equilibrium. Also, the calculation of gas and solid solubility in liquids of high dielectric constants requires at times the resolution of chemical equilibrium between the different species that are formed in the liquid phase. Several algorithms have been proposed in the literature to solve the complex non-linear problem however, proper thermodynamic model selection has not received much attention. 

A requirement for modeling gas-liquid reactors is that the gas and liquid diffusion coefficients and mass transfer coefficients are known. For an estimation of the diffusion coefficients in the gas and liquid phases, see Appendices 4 and 6, respectively. Estimation of mass transfer coefficients is considered in Appendices 5 and 7, and methods for calculating the gas solubilities are discussed in Appendix 8. 

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