Process Simulation

Process simulation is the solution of process models. This chapter focuses on simple and effective numerical methods that are widely used in process simulation to solve algebraic equations, ordinary differential equations, and partial differential equations. In process modeling, algebraic equations typically result from the steady state description of processes with lumped parameters. The chapter describes the numerical solution of linear algebraic equations, which forms the basis for the solution of non-linear algebraic equations. Newton-Raphson method is a computational algorithm to solve non-linear algebraic equations based on derivative information. Frequently encountered in process models, differential equations describe the change in system properties with space and time. Ordinary differential equations typically describe temporal property changes in uniform, or lumped-parameter parameters. Explicit Runge-Kutta methods have been used widely to solve ordinary differential equations. Accurate solutions of certain differential equations require very small step sizes with explicit methods in general. Such equations are called stiff equations.