Chemical Engineering Science, Vol.84, 276-291, 2012
Mathematical modeling of high-pressure oil-splitting reactor using a reduced population balance model
A reduced non-equilibrium bivariate population balance model is developed to model simultaneous reversible chemical reaction and extraction of an industrial scale high-pressure oil-splitting reactor with a first-order reversible kinetics. The model includes details about the reacting mixture by considering the discrete (particulate) nature of the dispersed phase. This, however; increases the mathematical complexity of the model and results in a coupled system of partial differential equations (PDE) of hyperbolic type with nonlinear source terms. The characteristics analysis shows that these hyperbolic PDEs have two dominant and distinct characteristic speeds: The mean droplet speed and the mean continuous phase (oil) speed. This generates a set of contact waves moving along the reactor height in opposite directions. Therefore, modern numerical methods based on CFD literature are applicable to provide a numerical solution of the developed model. As a first step in the numerical investigation, a finite volume method with a first-order upwind scheme is developed and implemented. Also, sufficient conditions of stability are derived and implemented. The numerical model is validated against analytical solution of a special case, where numerical convergence in the sense of l(2)-norm is established. Numerical simulation results showed that the unreacted oil concentration profile decreased exponentially along the reactor height. On the other hand, the glycerine concentration in the oil phase passes through a maximum due to the simultaneous reaction and extraction processes. Three operating parameters: temperature, mean droplet diameter and excess water flow rate were studied to highlight their effect on the reactor performance. The most important parameter was the reactor operating temperature, where 240 degrees C was found sufficient for complete oil conversion. This agrees with the operating temperature in industrial practice. (C) 2012 Elsevier Ltd. All rights reserved.