# Accession Number:

## ADA012989

# Title:

## Chemical Equilibrium Problems Treated by Geometric and Transcendental Programming

# Descriptive Note:

## Technical rept.

# Corporate Author:

## STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH

# Personal Author(s):

# Report Date:

## 1975-04-01

# Pagination or Media Count:

## 216.0

# Abstract:

The chemical equilibrium problem--finding the equilibrium composition of a multiphase, multicomponent system--is of interest in the study of chemical systems in general, with many potential applications in biochemistry and biomedicine. The problem can be posed as a nonlinear program, where a convex free energy function is minimized, subject to linear mass balance equations. There is an associated dual chemical problem, equivalent to a geometric program when the system is ideal. This work studies the chemical duality and applies the existing theory of geometric programming to analyze and solve chemical problems. Some general characteristics of free energy functions are developed and are used to analyze the properties of equilibrium solutions. Chemical duality is applied to formulate and solve a class of related problems which are of a different nature than the original chemical equilibrium problem. A dual cutting- plane algorithm is adapted from a method developed for geometric programs and is tested and compared to a standard chemical equilibrium code. Geometric programming theory is extended to include forms having variables as exponents. The resulting transcendental geometric programs are shown to be a generalization of chemical problems, where the system is not ideal.

# Descriptors:

# Subject Categories:

- Physical Chemistry
- Operations Research