Nonlinear Model Predictive Control for Gas Antisolvent Recrystallization Process

Abstract

Crystallization techniques have been played an important role for several decades in producing various chemical products such as polymers, dyes, pharmaceuticals, and explosives. It is also essentially used in separation and purification stages of petrochemical and fine-chemical industries. Conventional crystallization processes, however, have practical problems in that toxic waste solvent streams are inevitably produced in the process and some substances are contaminated with the solvent, deteriorating the purity. In this reason, novel crystallization processes using supercritical fluids have recently attracted much attention. They are environmentally acceptable due to the use of benign solution such as CO2, applicable to various solutes, and operated at mild conditions, 25℃ and 5-100 bar. These include rapid expansion of supercritical solution (RESS), gas antisolvent (GAS) process, and particles from gas-saturated solutions (PGSS). It is well known that GAS crystallization process attains a very rapid, essentially uniform and very high supersaturation upon reduction of the solid solubility in its solution with dissolution of antisolvent CO2. This owes to the two way mass transfer of CO2 and solvent, for dissolution of CO2 and evaporation of solvent, respectively. This facilitates uniform nucleation and almost instantaneous crystallization, which make the antisolvent crystallization a unique process resulting in the formation of ultra-fine particles with a narrow particle size distribution and controlled morphology. In this work, a dynamic model for GAS process is presented and control approach to obtain a desired particle size distribution (PSD) is proposed. At first, a mathematical model from a population balance model (PBM) is developed to describe PSD of GAS process. The developed GAS model consists of a partial differential equation (PDE), a set of ordinary differential equations (ODE), and algebraic equations associated with it. Thus, it requires a numerical discretization method to solve the PDE. A high resolution (HR) scheme is presented since it is rather simple to implement and more accurate than other discretization methods. Simulation results show the effect of CO2 addition rate on the final particle size distribution in the process. Control issues in GAS processes are quite challenging since the system is highly nonlinear and includes complex crystallization kinetics, nucleation and growth. Researchers have investigated the control of liquid antisolvent crystallization process to find optimal input profile, but the control for gas antisolvnet process has not been much tried yet. It is generally more difficult to control GAS process than liquid antisolvent process since the liquid-vapor phase equilibrium should be considered in the system model. A nonlinear model predictive control (MPC) strategy is proposed to control the particle size distribution of GAS process. Linear MPC, successive linearized MPC are applied to the system and the control results are compared.