Application of continuation and modeling methods to phase equilibrium, steady state, and dynamic process calculations

Recently, globally convergent continuation methods have been used successfully to find a solution to systems of nonlinear equations used to model multicomponent, multistage separation processes. This study deals with applications of continuation methods to steady-state processes, which may contain multiple stationary solutions, and dynamics of interlinked separation system.; For steady-state processes, the following topics are covered: (a) A Newton-type homotopy method with the deflated decomposition technique and the den Heijer and Rheinboldt step-size algorithm is used to locate all real roots of interlinked separation columns from an arbitrary starting point at a specified reflux ratio. (b) Solution branches of a Petlyuk tower system, with reflux ratio as a free parameter, are traced out by a modified AUTO code, based on pseudo-arclength continuation method. Two turning points and a few bifurcation points, which have special physical meaning, are found. Thermodynamic efficiencies for all four operational conditions are the same at a specified reflux ratio. (c) An algorithm that can switch branches between real and complex domains is proposed to locate all real zeros of nonlinear equations involving algebraic and transcendental functions, but no operators such as differentiation and integration, by using a Newton homotopy, where the starting point can be easily estimated by an experience criterion. An alternative method, called mapped continuation, based on a fixed-point homotopy, is also developed to locate all zeros. (d) Another application of the continuation method, called the successive continuation algorithm of Doedel, is applied where the system is reformulated as an optimal form. An unreported tie line to a binary system of n-butyl acetate and water was found by the isoactivity method with this successive continuation algorithm. The classical Williams-Otto process is used to illustrate the application of this algorithm to a flowsheeting problem. (e) A few new features are implemented into the COFRAC program, which is an extremely flexible program originally developed by Wayburn to handle interlinked separation columns with highly non-ideal mixtures.; For modeling dynamics of interlinked separation system, it is found that unspecified interlink flow rates, which produces a higher index to the DAE system, are the main reason for failure of the variable-size, variable-order BDF algorithm, DASSL. This phenomenon does not occur in dynamic modeling of conventional columns.