THE DEVELOPMENT OF TECHNIQUES FOR THE SOLUTION OF LARGE CHEMICAL ENGINEERING PROBLEMS

A digital simulation language called the General Equation Modeling System, GEMS, has been created which efficiently solves large systems of simultaneous algebraic and differential equations. This package was designed to solve large, stiff, and nonlinear problems which are commonly found in Chemical Engineering. In addition, special functions were designed to permit simulations involving time delays, hard limiters, and sampled data systems. The resulting simulation language is widely applicable to potential users in many areas because of its ease of use, and because of the novel and efficient techniques which have been incorporated into its design.; The set of simultaneous equations defining the problem to be solved is entered in standard mathematical notation for the convenience of the user, and these equations are then converted into a proper state variable form by the GEMS package. There are often several alternate techniques available for producing such a state variable representation, and the overall stability of the simulation depends to a large degree on the representation selected. Several situations which can cause stability problems are identified, and a procedure for generating a state variable representation is proposed which avoids these situations.; As stiff systems often occur in practice, an implicit integration algorithm is employed. Such algorithms require that the Jacobian matrix of the state equations be evaluated at various points. In order to improve the speed and accuracy of this process, a set of symbolic arithmetic manipulation routines is used to generate analytical expressions for as many elements of the state matrix as possible. A set of rules is proposed for algebraic simplification, and it is shown that they can produce a substantial degree of simplification with essentially no increase incomputational effort.; A difficulty often arises in systems which contain several variables which are defined by sets of simultaneous nonliner algebraic equations. The system as a whole can be solved only if such sets of simultaneous equations can be solved. A new technique is developed which can solve certain sets of algebraic equations with extreme ease. This technique is combined with Newton-Raphson iteration and the method of imbedding to produce a method which is fast and stable, and which has a large radius of convergence.; Several example problems indicate some of the capabilities of the GEMS simulation language. The results demonstrate the significant improvements realized in the solution of stiff problems. Future additions to the integration options available will allow the user to quickly and accurately solve large and complex problems with a choice of the most sophisticated algorithms currently available.