Developing a fast and robust numerical method for the simulation of cocurrent hollow fiber gas separation membranes for process flowsheet synthesis

Membrane separation technology has become an important part of process flowsheet synthesis in which it can be combined with other unit operations for enhanced separation of gasses and liquids. Since process flowsheet synthesis requires computationally efficient numerical algorithms, in this work, an accurate, fast, and robust computer model for the simulation of cocurrent hollow fiber membranes is proposed. The algorithm is based on a modified shooting method with quadratic interpolation, which requires no derivative computations versus classical optimization methods. Moreover, for solving the set of differential equations, three different integration methods were employed and compared over wide range of operating conditions. Based on both speed and robustness, the best method was found to be the variable order numerical differentiation formula as it succeeded in solving the problem fast and accurately under all tested points. The maximum computational time was 3.4 s, while the maximum absolute permeate outlet pressure estimation error was 0.37%, which is remarkable. Also, the method was validated with both experimental and simulation studies in the literature. Hence the proposed algorithm is suitable for process flowsheet synthesis, process design, and optimization studies.