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: Reduced Order Model (ROM)-based optimization for energy systems

As multi-scale modeling and advanced simulation technologies mature, it is desirable to utilize their predictive power in process design and optimization. However, these models present unique challenges for traditional optimization frameworks. A popular approach is to fit an algebraic surrogate model to these complex functions. However, small errors in the regression can result in a large deviation from the true optimum. We are developing trust region algorithms capable of adaptively controlling this error during the optimization process to provably converge to the true optimum.

Our current system of interest is the oxycombustion power generation process. In this process, the boiler is not easily described by algebraic models, so will model it use a hybrid zonal boiler model that integrates the radiation equation in 3D. This boiler model will be integrated into an equation oriented process optimization framework using trust region methods.

Topic: Dynamic Real-Time Optimization (DRTO)

Model predictive control (MPC) is an optimization based form of control that has many applications in the chemical industry. The mathematic programming formulation of the problem allows for an easy way to handle multiple-input-multiple-output systems, as well as state and control variable constraints. Furthermore, nonlinear model predictive control (NMPC) extends MPC to make use of a nonlinear dynamic model in order to ensure accuracy across a wider range of states.

Our goal is to ensure good performance when this technology is applied to large-scale chemical processes. In particular, we are interested in the stability of NMPC in the presence of disturbances. Specific areas of research include calculating predictive state trajectory bounds in order to quantify robust stability, as well as reformulations of the nonlinear programming (NLP) optimization problems that allow for robust stability even in pathological cases.

We are also interested in economic nonlinear model predictive control (e-NMPC) in which the process economics are optimized directly. This modification leads to new complications in the stability analysis, and there are many open questions in this area.

Topic: Pressure swing adsorption optimization strategies for CO2 capture

Pressure swing adsorption (PSA) has received recent attention as a potential process for economically removing CO2 from flue and/or shifted syngas for carbon capture and storage. We apply state-of-the-art methods for PSA optimization using a superstructure-based approach; this allows simultaneous selection of PSA cycle steps and optimization of operating parameters (feed flow rate, recycle fractions, bed pressures, etc.). The partial differential equation bed models are discretized with finite volumes in space and two flux limiters are compared. Sparse linear solvers are implemented to accelerate the integration of bed models and direct sensitivity equations, which are interfaced to MATLAB. The PSA optimization approach is demonstrated on CO2/H2 separation case studies for an integrated gasification combine cycle power plant, and solved by sequential quadratic programming solvers.

Topic: Modeling and optimal grade transitions for polypropylene processes in fluidized bed reactors

Gas phase polymerizations using fluidized bed reactors are widely implemented in industry. We present a set of differential and algebraic equations to simulate this process for producing polypropylene. Kinetic models based on multisite catalysts (Ziegler-Natta) are used for propylene and ethylene copolymerization. This work will lead to the grade transition optimization, shortening the transition time by manipulating operation conditions.

Topic: Advanced Optimal Control Strategies for Bubbling Fluidized Beds

Bubbling Fluidized Bed (BFB) models have been previously created for CO2 capture. Such models contain Partial Differential Equations to model the mass and energy balances for different regions inside the bed. Additionally there are Algebraic Equations to model the hydrodynamics, equations of state, etc. This leads to a system of Partial Differential Equations (PDAE) that can be handled through an implicit high order discretization scheme like collocation.

The availability of such models and new algebraic modeling languages like Pyomo, make possible the implementation of Non-Linear Model Predictive Control (NMPC) strategies for the BFB.

The goals of the project are to generate steady and dynamic state models for the BFB with generic discretization schemes and to implement fast NMPC and state estimation strategies.

Topic: Multistage Nonlinear Model Predictive Control under Uncertainty

Model Predictive Control (MPC) has been widely used in process control industry mainly because it can deal with constraints and multiple-input-multiple-output. However, the system performance deteriorates under the influence of uncertainty. The current robust MPC techniques are often shy of applications due to either model conservativeness or formidable computational effort. In order to improve this situation, we present a multistage nonlinear model predictive control (NMPC) to serve as a non-conservative robust NMPC scheme. Multistage NMPC models the uncertainty evolution with a scenario tree structure that exploits the degree of freedom by allowing future control inputs to adjust accordingly to future available information.

Currently, our case study is based on a nonlinear CSTR example with a setpoint tracking objective with one uncertain parameter. The performance of multistage NMPC has been compared to standard NMPC and no-recourse robust NMPC, and the result shows that multistage NMPC is a promising framework to account for plant uncertainty. The effect of different robust horizons has also been discussed.

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.