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Development of a fourth-order compact finite difference scheme for simulation of simulated-moving-bed process
Chuanyi Yao1,2, Yanjuan Zhang3, Jinliang Chen4
1Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, China. cyao@xmu.edu.cn.
Scientific Reports
|May 10, 2020
Summary
A new finite difference scheme accurately simulates simulated moving bed (SMB) processes for separations. This method improves computational efficiency by 45%, offering faster and reliable results for chemical separations.
Area of Science:
- Chemical Engineering
- Numerical Analysis
- Separation Science
Background:
- Simulated Moving Bed (SMB) chromatography is crucial for industrial separations.
- Solving SMB models requires efficient numerical methods, especially with dynamic boundary conditions.
- Existing methods may face challenges with time-varying boundary conditions in SMB simulations.
Purpose of the Study:
- To develop a high-accuracy, fourth-order compact finite difference scheme for SMB model equations.
- To address challenges posed by time-updated, non-explicit boundary conditions in SMB simulations.
- To validate the scheme's accuracy and efficiency for industrial separation processes.
Main Methods:
- Developed a fourth-order compact finite difference scheme.
- Implemented direct and pseudo grid point methods for dynamic boundary conditions.
- Validated the scheme using an advection-diffusion equation with a known solution.
- Applied the scheme to glucose-fructose separation and 1,1'-bi-2-naphtol enantioseparation in SMB.
Main Results:
- The developed scheme demonstrated high accuracy in solving the advection-diffusion equation.
- Simulations of glucose-fructose separation and enantioseparation showed excellent agreement with experimental data.
- Combining the scheme with continuous prediction reduced computational time by approximately 45%.
Conclusions:
- The fourth-order compact finite difference scheme is accurate and effective for SMB simulations.
- The proposed methods for handling dynamic boundary conditions are robust.
- The enhanced computational efficiency makes the method suitable for large-scale industrial applications.
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