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

Abstract

We successfully extended a computer algebra program (Thermath), originally 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 done manually, the largest portion of the programs 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.

Computer Simulation of Biodiesel Production By Hydro-esterification

“…The modeling of the esterification step is based on considerations of Chen et al (2000), Alfradique and Castier (2005) and Machado et al (2013) for the simulation of reactive distillation columns. The scheme of the generic plate adopted in this work is shown in Figure 2: Figure 2: Configuration of stage j in reactive distillation column (Alfradique and Castier, 2005).…”

“…The scheme of the generic plate adopted in this work is shown in Figure 2: Figure 2: Configuration of stage j in reactive distillation column (Alfradique and Castier, 2005).…”

“…The mathematical formulation was implemented using the programming language FORTRAN 77. Additional details about the solution method are available in the work of Alfradique and Castier (2005).…”

Modeling and simulation of supercritical extraction columns using computer algebra

“…These columns may be modeled using various levels of detail, ranging from models that take into account mass transfer and hydrodynamics in the column [2] to models that assume phase equilibrium at each stage [3]. This work follows the latter assumption and uses the Newton-Raphson method in the simultaneous solution of the model equations [3][4][5][6].…”

“…For example, Thissel and Mills [7] used the CA package Macsyma ® for simulating a simple extraction column and Alfradique et al [6] used Mathematica ® in the development of a Fortran code for the simulation of isothermal extraction columns. For other applications in chemical engineering, CA programs such as Maple ® and Mathematica ® are being increasingly used [6,[8][9][10][11][12][13][14][15][16][17], because they provide symbolic, numerical and graphical capabilities in a single computation environment. For example, Castier [11] the Thermath package using the Mathematica ® programming language.…”