Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, China.
The Key Lab for Synthetic Biotechnology of Xiamen City, Xiamen University, Xiamen, 361005, China.
Sci Rep. 2020 May 8;10(1):7820. doi: 10.1038/s41598-020-64562-8.
A fourth-order compact finite difference scheme was developed to solve the model equation of simulated moving bed, which has a boundary condition that is updated along the calculation process and cannot be described as an explicit function of time. Two different methods, direct method and pseudo grid point method, were proposed to deal with the boundary condition. The high accuracy of the two methods was confirmed by a case study of solving an advection-diffusion equation with exact solution. The developed compact finite difference scheme was then used to simulate the SMB processes for glucose-fructose separation and enantioseparation of 1,1'-bi-2-naphtol. It was found that the simulated results fit well with the experimental data. Furthermore, the developed method was further combined with the continuous prediction method to shorten the computational time and the results showed that, the computational time can be saved about 45%.
为了解决模拟移动床模型方程，开发了一种四阶紧致有限差分格式，该格式具有沿计算过程更新的边界条件，不能表示为时间的显式函数。提出了两种不同的方法，即直接法和伪网格点法，来处理边界条件。通过对具有精确解的对流扩散方程的案例研究，验证了这两种方法的高精度。然后，将开发的紧致有限差分格式用于模拟葡萄糖-果糖分离和 1,1'-联萘-2,2'-二醇对映体分离的 SMB 过程。结果表明，模拟结果与实验数据吻合良好。此外，还进一步将所开发的方法与连续预测方法相结合，以缩短计算时间，结果表明，可以节省约 45%的计算时间。
