A Robust Numerical Framework for Hollow-Fiber Membrane Module Simulation and Solver Performance Analysis

Area of Science:

• Chemical Engineering
• Computational Science

Background:

• Robust numerical frameworks are crucial for simulating, designing, monitoring, and controlling membrane-based separation units.
• Industrially relevant conditions often involve highly nonlinear operating parameters.

Purpose of the Study:

• To develop and validate a comprehensive phenomenological and numerical framework for simulating hollow-fiber membrane modules.
• To investigate the performance of steady-state and pseudotransient numerical solution strategies for real-time applications.

Main Methods:

• Governing equations for coupled mass, momentum, and energy transport were discretized using orthogonal collocation.
• Two numerical solution strategies were compared: Newton-Raphson (steady-state) and pseudotransient formulation.
• A novel numerical treatment for energy balance at boundaries with zero permeate flow was introduced.

Main Results:

• The steady-state Newton-Raphson approach demonstrated superior computational efficiency, robustness, and accuracy with appropriate initial estimates.
• A linear initial guess and four collocation points provided an optimal balance for convergence speed and accuracy.
• The pseudotransient formulation served as a reliable auxiliary strategy under extreme operating conditions.

Conclusions:

• The proposed framework offers a reliable basis for simulation and assessing computational feasibility for in-line and real-time monitoring.
• The steady-state Newton-Raphson method is recommended for most monitoring applications due to its efficiency.
• Further work will explore digital-twin integration, online parameter updating, and closed-loop control.