| Nonlinear equations arise in many chemical engineering applications. Hence, a reliable and efficient nonlinear equation solver would be highly desirable. A comprehensive test of iterative nonlinear equation solution techniques has been performed in this study, in particular the techniques used for computing the correction step, for evaluating sparse Jacobian matrices, for updating sparse Jacobian matrices, and for solving sparse linear equations. The modified Powell's dogleg method, quasi-Newton method, damped quasi-Newton method, discrete Newton's method were combined and were implemented in two codes: NEQM for full matrix systems and SPNLQ for sparse matrix systems. They were tested using ten small problems and thirteen large problems collected from a broad spectrum of chemical engineering applications. Implicit function scaling or function and variable scaling was found to be effective. The modified Powell's dogleg method was found to perform the best on the combined basis of efficiency and reliability.; The Curtis, Powell, and Reid's method in evaluating the initial sparse Jacobian matrices proved to be very competitive with the Coleman and More's method in finding optimal groupings of Jacobian columns. The Bogle's least relative change Jacobian update was found to be the most effective, especially in conjunction with the modified Powell's dogleg method. It was found that 60% of the total CPU time was taken in the linear equation section. Results indicated that the continuous back-substitution method (CBS) performed far more superior than the modified Gaussian elimination method (LU) while an improved rank-one BTS method (RANKI) was competitive. |
