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: 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.

Topic: Nonlinear Model Predictive Control of the Hydraulic Fracturing Process

Hydraulic fracturing draws more attention over the past decade since it can recover great amount of crude oil and natural gas from shale deposits and bring considerable economic benefits. However, high operating pressure and environmental concerns are critical issues in this process. Therefore, we need an accurate dynamic model and a well-performed controller to be aware of these issues. In my work, a dynamic model is built by modeling the fracture propagation, mass transport of chemicals, and wellhead pressure. In addition, the process is controlled by Nonlinear Model Predictive Controller (NMPC), which has been widely used because it can deal with constraints and multiple-input-multiple-output systems. We also use multistage NMPC, considering the uncertainty evolution with a scenario tree to provide a promising approach to control this process under the influence of uncertain parameters of rock properties.

Topic: Nonlinear Mixed Effects Modeling

For researchers in reaction kinetics, parameter estimation plays an important role, where the parameters of interest often relate to reaction rate laws. To estimate those parameters, researchers often replicate an experiment under similar conditions to ensure they are achieving a repeatable result. During each experiment, there are sources of error that occur which fall into one of two categories: fixed and random effects. Fixed effects describe the relationship between the dependent variable and predictor variables whereas random effects usually represent disturbances and local deviations from the relationships described by fixed effects. Mixed effects models are used for chemical kinetics because they account for both the variable error within an individual experiment as well as across a set of experiments, preventing bias in the estimation of the fixed parameters. For a given repeated set of experiments, there are parameters that are unique to an individual data set and those which are shared among all data sets.These represent local and global parameters, respectively. As the number of experiments that needs to be analyzed increases, so does the number of parameters, giving rise to a computationally expensive and difficult nonlinear parameter estimation problem. We are currently developing and applying a nested Schur decomposition (NSD) approach to handle large scale nature of this problem.