A robust solution method for flowsheeting equation systems

A robust solution method for the large-scale nonlinear algebraic equation systems involved in steady-state process flowsheeting is presented.; The method described here retains rapid local convergence by embedding Newton's method within a branch and bound framework providing rigorous global convergence. The combined strategy will simply apply Newton's method, on problems for which that will work. Otherwise, progressively more involved computations, entailing the solution of linear programs that combine local Jacobian and global bounding information to generate corrected search directions and assess region feasibility, are invoked as needed. Interval analysis techniques are employed to automatically generate bounding functions from the analytical expressions for the equations. Adaptive domain partitioning and a branch and bound structure provide a formal back-tracking mechanism.; Details of the algorithm are described, and the results of tests on both small problems and flowsheeting systems in several thousand variables are presented. These results demonstrate effective performance on a variety of process modelling problems.