Marcelo F. Alfradique

Modeling and simulation of reactive distillation columns using computer algebra

Abstract This work presents an extension of a computer algebra (CA) program, Thermath , originally developed for the automatic implementation of physical property calculations, to generate computer codes in Fortran for the simulation of steady-state reactive distillation columns. The adopted procedure requires the simultaneous solution, using the Newton–Raphson method, of mass and energy balances, phase equilibrium equations, chemical equilibrium or rates of reaction equations and an additional equation needed to match the number of degrees of freedom. The Thermath program was used to obtain Fortran subroutines that implement these equations and their derivatives with respect to the process variables and the equation of state and/or excess Gibbs free energy model used in the simulation. The results are in excellent agreement with those available in the literature. By using Thermath , it was possible to reduce the time and effort needed to implement the mathematical models of multistage reaction–separation equipment.

Automatic generation of procedures for the simulation of multistage separators using computer algebra

We successfully extended a computer algebra program (Thermath), orginally developed for the automatic computer implementation of physical property calculations, in order to perform the global phase stability test and to generate code for the steady state simulation of multistage separators. Analytical derivatives of the modeling equations and of the thermodynamic properties were rapidly obtained and automatically implemented in Fortran 77 using Thermath. Even though the final assembly of the code was doen manually, the largest portion of the program corresponds to automatically generated code. A program for the simulation of extraction columns was developed and showed excellent agreement with results available in the literature. The global phase stability program was tested in the identification of liquid-liquid phase transitions, showing results coherent with those from the extraction column program. Quadratic convergence rates in the Newton-Raphson method were obtained with both programs, as should be expected when the functions and their derivatives are correctly implemented.

Automatic Generation of Matlab Functions Using Mathematica and Thermath

The program tool Thermath now lets researchers automatically generate complete, ready-to-use Matlab functions. The examples here deal with critical-point calculations and the development of equipment models for separations in the chemical industry, but the ability to automatically generate Matlab functions is useful in many areas of science and engineering.