Jeffrey D. Ward

Population balance modeling in Simulink: PCSS

In this work we develop, demonstrate, and distribute the code for a new Simulink block that models the dynamic evolution of the population density function for a physical system which can be modeled by a population balance equation. The name of the block is PCSS, for population balance modeling using the conservation element/solution element method in Simulink. The block interfaces with an auxiliary user-defined function that allows the user to specify arbitrary expressions for growth and generation/loss terms, as well as an arbitrary number of inputs, outputs and auxiliary states for the block. The versatility of the block allows a wide variety of physical systems to be modeled, and the implementation in Simulink facilitates rapid model development and permits the use of pre-existing MATLAB/Simulink packages for system identification and control.

Plantwide dynamics and control of processes with crystallization

Abstract Recently Ward et al. [Ward, J. D., Doherty, M. F., & Yu, C. C. (2007). Plantwide operation and control of processes with crystallization. AIChE Journal , 53 , 2885–2896] presented new shortcut expressions for the steady-state operation of plantwide processes with crystallization. The method allows the engineer to predict the steady-state gain between the production rate and certain other key process variables for various choices of controlled variables. The result is a simple analytical model that shows how the process operates for various choices of control structure. The previous work of Ward et al. considered only steady-state process operation. In this contribution we apply the method and results from our previous work to develop plantwide control structures, and test the structures using a rigorous non-linear dynamic process model. We demonstrate that the method produces workable plantwide control structures, and that the steady-state behavior of the dynamic process is consistent with the predictions of our previous work.

Comparison of objective functions for batch crystallization using a simple process model and Pontryagin’s minimum principle

Abstract In this contribution different objective functions based on the moments of the product crystal size distribution are compared using optimal control theory to solve for the optimal batch trajectory for each objective. For a simple crystallization process model with only nucleation and ordinary crystal growth, and neglecting the contribution of the nucleated mass to the nucleation rate and material balance, mostly analytic expressions are obtained for the optimal control vector. Different objective functions lead to different final values for the costates, which lead to different sets of coupled differential and algebraic equations which must be solved to determine the values of constants numerically. The results of nine different objective functions for three crystal systems are presented. The objective functions based on the lower moment of the nucleated crystals lead to late-growth trajectories while the objective functions based on the higher moment of the nucleated crystals lead to early-growth trajectories, consistent with previous findings. The effect of seed loading is also investigated.

Design of a Pressure-Swing Distillation Process for the Separation of n-Hexane and Ethyl Acetate Using Simulated Annealing

Abstract A pressure-swing distillation process for the separation of n-hexane and ethyl acetate, which form a minimum boiling azeotrope, is proposed and optimized using simulated annealing and simulation-optimization. The design variables considered are the two column pressures, the feed stages and total number of stages of both columns. The optimal process design is somewhat more expensive than the optimal extractive distillation process (designed separately) but the pressure-swing process benefits from the fact that no additional component is introduced.

Empirical trajectories for batch crystallization control with constraints

Optimization of batch crystallization is studied with tight constraints on the maximum rate of change of batch temperature or maximum rate of evaporation. It is observed that under tight constraints, the constraint has the greatest effect on the shape of the batch trajectory. Three crystallization systems are simulated for different values of the batch time and crystal yield. The resulting temperature or evaporation rate trajectories are plotted in dimensionless coordinates and fit to an empirical equation. The empirical equation performs similar to other convex trajectories recommended in the literature and much better than the linear trajectory.

Control of two batch crystallization processes with apparent growth-rate dispersion

Control of batch crystallization processes is studied for two experimental systems: potassium aluminum sulfate and adipic acid. Both systems showed significant broadening of the crystal size distribution during the batch operation, which was attributed to growth-rate dispersion. Models for crystal nucleation and growth, including growth-rate dispersion, were developed to describe both processes.

Controllability of three types of dividing wall columns

Abstract We investigated the pairing of controlled and manipulatd variables and the overall controllability of three types of dividing wall columns (with the dividing wall in the upper, lower and middle section of the column; DWCL, DWCU and DWCM, respectively) using steady-state and dynamic controllability measures. Dividing wall columns were designed for the separation of a mixture of three species with constant relative volatilities, for different values of the relative volatilities and feed compositions. The steady-state processes were simulated in Aspen Plus and the relative gain arrays, non-square relative gain array and condition number were determined for each case using the steady-state model. Finally, the dynamic responses of the processes were simulated in Aspen dynamics and an integral error criteria was used to compare the performance of different control structures. The results indicate that generally DWCL is favorable if the intermediate-boiling species is most plentiful in the feed, and DWCU is preferable in other cases.