Mathematical modeling of high-pressure oil-splitting reactor using a reduced population balance model

Splitting Triglycerides with a Counter-Current Liquid–Liquid Spray Column: Modeling, Global Sensitivity Analysis, Parameter Estimation and Optimization

In this work we present the model of a counter-current spray column in which a triglyceride (tripalmitic triglyceride) is hydrolyzed by water and leads to fatty acid (palmitic acid) and glycerol. A finite volume model (FVM) of the column was developed to describe the reactive extraction process with a two-phase system and validated with an analytical model from the literature with the given data set encompassing six experimental runs. Global, variance-based (Sobol) sensitivity analysis allowed assessment of the sensitivity of the sweet water glycerol content in respect to liquid density, overall mass-transfer coefficient, reaction rate coefficient and the equilibrium ratio to rank them accordingly. Furthermore, parameter estimation with a differential evolution (DE) algorithm was performed to obtain among others the mass transfer, backmixing and reaction rate coefficients. The model was used to formulate and solve a process design problem regarding economic and sustainable performance. Multi-criteria optimization was applied via DE to minimize total annual cost (TAC) and the Eco99 indicator by varying the steam inlet flow rate and distribution over the two steam inlets as the independent variables. The model and analysis was implemented in Fortran and Python where the Fortran model can also be embedded in a process simulator such as PRO/II or Aspen.