Simultaneous modular algorithm for steady-state flowsheet simulation and design

The sequential modular algorithm has been used widely for steady-state simulation and design. Consequently, a considerable body of computer programs tailored for such applications exists today. Most of the current research in steady-state calculations, however, is oriented towards simultaneous solution of the entire set of system equations. An unfortunate consequence of this approach is that the software developed for sequential modular calculations can not be employed.The simultaneous modular algorithm offers many of the advantages of an equation-solving procedure while using the existing sequential modular software. This work presents theoretical analysis and experimental results of various implementations of the simultaneous modular algorithm.The split fraction model of a unit behavior (y = ax) is shown to have worse convergence properties than Wegstein's algorithm in a sequential modular procedure. Indeed. it is quite a fortuitous set of circumstances when such a model exhibits stable convergence behavior.The difference split fraction model (dy = adx) is shown to be equivalent to Wegstein's algorithm for a flowsheet with a single recycle loop. On systems with multiple recycle loops, the model exhibits better convergence than Wegstein's algorithm.The simultaneous modular algorithm can also be implemented as a sparse quasi-Newton procedure to solve systems of non-linear equations. Such implementation allows simultaneous solution of design specifications and flowsheet balances. An initial estimate of the stream variables is obtained by one or more sequential passes through a flowsheet. The system Jacobian matrix is approximated by the difference split fraction unit models. Subsequent Jocobian matrices are obtained by a sparse update procedure.Covergergence properties of various implementations are demonstrated by examples.