The research done by the group centers around the development and application of concepts in optimization theory, operations research, and numerical methods for process design, analysis, and control.

Topic: Optimization Superstructure Development for Rigid Polyols

Rigid polyols are defined as polyether polyols formed by catalyzed alkoxylation of initiators. These polyols react with isocyanates to manufacture closed cell foams which are used in the production of refrigerators and freezers, building and construction insulation, etc. Demand has doubled in the last 10 years and is expected to double again in the next 10 years. Rigid polyols are currently produced in semi-batch reactors. As product demand grows, the business is faced with investing in more or larger semi-batch reactors which will reduce the capital cost per production, but this is still too high for re-investment relative to other products. Lower capital cost solutions, such as transfer the production from existing semi-batch units to continues process, are needed to help sustain growth. Continuous reactors can decrease the capital cost if a scheme can be devised to produce similar products. In order to determine if this is possible, simulation and optimization can be used with reaction kinetics to determine the required number, type and size of reactors to achieve product specifications with minimal cost.

Topic: Non-Smooth Process Optimization using Complementarity Constraints.

Process Intensification is currently the most important aspect for chemical industry to decrease energy consumption and harmful gas emissions. As more complex and rigorous process models are developed to achieve this goal, there is a need to develop solution strategies for optimizing these process models. Most process models suffer from discontinuities and non-differentiability making it difficult to solve them using common optimization solvers. We model these non-smooth equations using complementarity constraints. Mathematical Programming with Complementarity Constraints(MPCC) and Nonlinear programming(NLP) are powerful tools to solve optimization problems without introducing complex integer variables. We use various methods from MPCC literature and implement in solving large scale chemical process models. Currently, we are using finite element heat exchanger model to optimize refrigeration cycles. The phase change inside the heat exchangers is modeled by complementarity constraints. The MPCC problem is reformulated and solved successively as a NLP. In future, we will integrate this MPCC solution framework into more complicated models.

Topic: Optimization for continuous multiple product processes.

Continuous multiple product processes are commonly observed in the chemical industry such as halogenation of aromatics. The process has the following two aspects. One is the process usually consists of multiphase reactors such as bubble columns, and several separation units such as distillations, absorbers, and crystallizers. This aspect leads to large-scale process modeling which contains Differential Algebraic Equations (DAEs). Another is the process should be optimized for the balance of product demand which could vary from time to time. The demand also usually includes uncertainty. From these characteristics, the goals of the project are to model the large-scale process and to optimize the process under uncertainty of its product demand. So far, the detailed model of a bubble column reactor is established. The optimization of the entire process under demand uncertainty has been investigated with an ideal reactor model. The current study is the optimization with surrogate modeling to implement the detailed bubble column model in the entire process model.

Topic: Modeling, simulation, estimation, and control of multiple-timescale systems.a

Many physical-chemical processes, described by highly nonlinear dynamic systems of partial differential and algebraic equations (PDAEs), exhibit multiple-timescale behavior. Such systems are difficult to simulate and optimize using Newton-like methods because of their extreme sensitivity to discretization strategy, initial conditions, and input parameters. My research attempts to alleviate these difficulties by providing computational tools for the analysis, initialization, and pseudo-steady reduction of such systems, and by demonstrating their application to chemical looping combustion (CLC) processes. Part of the IDAES project.

Topic: Model Reformulation and Index Reduction for Flue Gas Desulfurization

The primary source of sulfur dioxide emissions is flue gas from fossil fuels-based power plants. Several emissions reduction technologies have been incorporated in power plants, of which the most common is the Limestone-Gypsum Wet Flue Gas Desulfurization (FGD) system. Due to fast cycling of power plants, it can be very difficult to satisfy SO2 emission standards at the outlet of FGD units. Furthermore, specifications of gypsum must also be satisfied during load following operation. A rigorous dynamic FGD model is helpful in satisfying these challenging performance conditions. A number of rate-limiting mechanisms occur in the limestone droplets, while the mechanisms at the scrubber bulk also play a critical role. Therefore, a multiscale dynamic model is desired. Due to fast ionic reactions and presence of a large number of ionic and molecular species, the system of equations are stiff, highly nonlinear, not well-posed and sometimes non-smooth, and therefore challenging to solve reliably during dynamic simulation.

A complementarity formulation is a way to deal with non-smooth decisions in dynamic process models. This method was used to reformulate a simple 0-D scrubber model to simulate the precipitation and dissolution of solids in the scrubber in an automatic way under various input conditions. Index reduction is a systematic way of reformulating an ill-posed, high-index Differential-Algebraic Equation (DAE) FGD models. A generic index reduction technique was customized and applied to the DAE model describing the absorption of SO2 in a limestone slurry droplet. The droplet model was thus reformulated to a well-posed index-1 model. For our near-term goals, we plan to develop a multiscale dynamic FGD model by incorporating the droplet model within the scrubber bulk model, calibrate and validate our results using data from our Industry partner, and incorporate the models into the flowsheet.