Dynamic Simulation of a Pilot Scale Vacuum Gas Oil Hydrocracking Unit by the Space‐Time CE/SE Method

Abstract

This work introduces a modified space-time conservation element/solution element (CE/SE) method for the simulation of the dynamic behavior of a pilot-scale hydrocracking reactor. With this approach, a four-lump dynamic model including vacuum gas oil (VGO), middle distillate, naphtha and gas is solved. The proposed method is capable of handling the stiffness of the partial differential equations resulting from the hydrocracking reactions. To have a better judgment, the model is also solved by the finite difference method (FDM), and the results from both approaches are compared. Initially, the absolute average deviation of the cold dynamic simulation using the CE/SE approach is 8.98 %, which is better than that obtained using the FDM. Then, the stability analysis proves that for achieving an appropriate response from the dynamic model, the Courant number, which is a function of the time step size, mesh size and volume flow rate through the catalytic bed, should be less than 1. Finally, it is found that, following a careful selection of these parameters, the CE/SE solutions to the hydrocracking model can produce higher accuracy than the FDM results.

Combination of space–time conservation element/solution element method and continuous prediction technique for accelerated simulation of simulated moving bed chromatography

“…Recently, the application of CE/SE method had been extended to simulation of explosive [23,24], aeroacoustics [25], crystallization [26], heat conduction [27], relativistic hydrodynamics [28,29], chemical reaction [30,31], et al Lim et al [18,19] utilized the CE/SE method to solve SMB model equations and found the accuracy and computational efficiency to be simultaneously improved.…”

A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

“…Therefore, the space-time domain is discretized two times by: a rhomboid mesh and a rectangular mesh. The theoretical framework of the CE-SE method for the nonfractional case is well established and it has been applied to a large number of real problems with successful results [26][27][28][29][30][31][32][33]. An important property of the fractional differential operators is the nonlocality which is achieved with the discretization of the integral associated with the fractional derivative.…”