Subroutines

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

This subroutine, in turn, utilizes subroutine BUS to evaluate... 

Evaluation of the activity coefficients, (or y for noncondensable components),is implemented by the FORTRAN subroutine GAMMA, which finds simultaneously the coefficients for all components. This subroutine references subroutine TAUS to obtain the binary parameters, at system temperature. 

The computation of pure-component and mixture enthalpies is implemented by FORTRAN IV subroutine ENTH, which evaluates the liquid- or vapor-phase molar enthalpy for a system of up to 20 components at specified temperature, pressure, and composition. The enthalpies calculated are in J/mol referred to the ideal gas at 300°K. Liquid enthalpies can be determined either with... 

The bubble and dew-point temperature calculations have been implemented by the FORTRAN IV subroutine BUDET and the pressure calculations by subroutine BUDEP, which are described and listed in Appendix F. These subroutines calculate the unknown temperature or pressure, given feed composition and the fixed pressure or temperature. They provide for input of initial estimates of the temperature or pressure sought, but converge quickly from any estimates within the range of validity of the thermodynamic framework. Standard initial estimates are provided by the subroutines. 

Figure 7-1. Incipient equilibrium vapor-phase compositions calculated with subroutine BUDET.

Equations (7-8) and (7-9) are then used to calculate the compositions, which are normalized and used in the thermodynamic subroutines to find new equilibrium ratios,. These values are then used in the next Newton-Raphson iteration. The iterative process continues until the magnitude of the objective function 1g is less than a convergence criterion, e. If initial estimates of x, y, and a are not provided externally (for instance from previous calculations of the same separation under slightly different conditions), they are taken to be... 

Again, Equations (7-8) and (7-9) are then used to calculate new compositions. These compositions, normalized, and the new value for T are utilized in thermodynamic subroutine calls to find equilibrium ratios and enthalpies for use in the next iteration. 

Both vapor-liquid flash calculations are implemented by the FORTRAN IV subroutine FLASH, which is described and listed in Appendix F. This subroutine can accept vapor and liquid feed streams simultaneously. It provides for input of estimates of vaporization, vapor and liquid compositions, and, for the adiabatic calculation, temperature, but makes its own initial estimates as specified above in the absence (0 values) of the external estimates. No cases have been encountered in which convergence is not achieved from internal initial estimates. 

Examples of Vapor-Liquid Separation Calculations Conducted with Subroutine FLASH... 

This computation procedure has been implemented by FORTRAN IV subroutine BLIPS, which is described and listed in Appendix G. This subroutine provides for designation of "solvent" components if not designated, they are determined internally. 

Each iteration requires only one call of the thermodynamic liquid-liquid subroutine LILIK. The inner iteration loop requires no thermodynamic subroutine calls thus is uses extremely little computation effort. 

Examples of Liquid-Liquid Equilibrium Saturation Calculations Conducted with Subroutine ELIPS... 

Figure 7-2. Conjugate liquid phase compositions for water-acrylonitrile-acetonitrile system calculated with subroutine ELIPS for feeds shown by . ...

The calculational procedure employed in BLIPS, when used with the particular initial phase-composition estimated included in the subroutine, has converged satisfactorily for all systems we have encountered (except very near plait points as noted). 

The subroutine is well suited to the typical problems of liquid-liquid separation calculations wehre good estimates of equilibrium phase compositions are not available. However, if very good initial estimates of conjugate-phase compositions are available h. priori, more effective procedures, with second-order convergence, can probably be developed for special applications such as tracing the entire boundary of a two-phase region. 

Subroutine PRDTA2. This subroutine reads the pure-component and binary parameters required for the various correlations describing the liquid and vapor phases. All input parameters are printed for verification. 

Subroutine VLDTA2. VLDTA2 loads the binary vapor-liquid equilibrium data to be correlated. If the data are in units other than those used internally, the correct conversions are made here. This subroutine also reads the estimated standard deviations for the measured variables and the initial parameter estimates. All input data are printed for verification. 

Subroutine OUTDAT. OUTDAT prints the estimated parameters and other statistical results obtained during the regression. 

This subroutine also prints all the experimentally measured points, the estimated true values corresponding to each measured point, and the deviations between experimental and calculated points. Finally, root-mean-squared deviations are printed for the P-T-x-y measurements. 

Subroutine REGRES. REGRES is the main subroutine responsible for performing the regression. It solves for the parameters in nonlinear models where all the measured variables are subject to error and are related by one or two constraints. It uses subroutines FUNG, FUNDR, SUMSQ, and SYMINV. 

Subroutine SYMINV. This subroutine inverts a symmetric matrix. 

Subroutine FUNG. This subroutine evaluates the constraint... 

Subroutine FUNDR. This subroutine calculates the required derivatives for REGRES by central difference, using EVAL to calculate the objective functions. 

Subroutine EVAL. This subroutine calculates and returns... 

Subroutine VPLQK. VPLQK calculates K factors (K = for given values of pressure, temperature, liquid and vapor compositions, and the adjustable parameters. The K factors are calculated from the following relation (Prausnitz, 1969) ... 

Subroutine VPLQK uses subroutines MVOLM, ACTIV2, REFUG, and PHIS2. 

Subroutine REFUG. This subroutine calculates the liquid reference fugacities. Three options are possible. First, an equation of the form... 

Subroutine MVOLM. MVOLM calculates the liquid molar volume at a given temperature using the modified Rackett equation... 

Subroutine ACTIV2. This subroutine calculates the activity coefficients using one of the liquid-phase equations discussed in the previous section. 

Subroutine MULLER. MULLER iteratively solves the equilibrium relations and computes the equilibrium vapor composition when organic acids are present. These compositions are used by subroutine PHIS2 to calculate fugacity coefficients by the chemical theory. 

Subroutine BIJS2. This subroutine calculates the pure-component and cross second virial coefficients for binary mixtures according to the method of Hayden and O Connell (1975). 

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