Vector Acceleration Methods for Faster Convergence of Cyclic Steady State in Adsorption Process Simulations

Area of Science:

• Chemical Engineering
• Computational Chemistry
• Separation Science

Background:

• Simulations of fixed-bed adsorption processes with in situ regeneration are computationally intensive due to repeated nonlinear partial differential equation solutions.
• Reaching cyclic steady state (CSS) in these simulations requires iterative methods, often leading to significant time consumption and optimization challenges.

Purpose of the Study:

• To systematically investigate Steffensen's vector acceleration methods for expediting CSS convergence in adsorption process simulations.
• To evaluate the effectiveness of these methods across diverse adsorption cycle dynamics, including vacuum swing adsorption (VSA), temperature swing adsorption (TSA), and vacuum temperature swing adsorption (VTSA).

Main Methods:

• Applied variants of Steffensen's vector acceleration methods, specifically noting the Graves-Morris extrapolator.
• Tested these methods on simulations of a four-step VSA cycle for CO2 capture, a six-step TSA cycle for CO2 capture, and a three-step VTSA cycle for CH4 upgrading.
• Focused on methods requiring no prior knowledge of first derivatives (Jacobian).

Main Results:

• Steffensen's methods, particularly the Graves-Morris extrapolator, consistently enhanced CSS convergence rates across all tested adsorption processes.
• Achieved significant reductions in computational time: up to 75% for VSA, up to 70% for TSA, and up to 35% for VTSA compared to successive substitution.
• Demonstrated the potential for simple, code-agnostic modifications to accelerate simulations.

Conclusions:

• Steffensen's vector acceleration methods offer a computationally efficient approach to simulating fixed-bed adsorption processes with in situ regeneration.
• These methods provide substantial time savings, making simulations and optimization of adsorption-based separations more feasible.
• The findings highlight a practical strategy for improving the performance of adsorption process modeling.