Carnegie Mellon University
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Algorithms for modeling and optimization of discretized differential algebraic equations with application to chemical looping combustion

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posted on 2023-02-28, 22:02 authored by Robert B. Parker

Nonlinear dynamic optimization is a powerful tool for control and estimation in chemical engineering for its ability to respect an equation-based model, satisfy inequality constraints, and converge quickly with large-scale systems. Recent software development has made formulating nonlinear dynamic optimization problems involving chemical processes a tractable task. However, nonlinear dynamic model are difficult to analyze and sometimes do not converge reliably. This thesis addresses these issues by developing tools for the analysis of nonlinear dynamic optimization models, implementing an algorithm to solve differential-algebraic equation (DAE) optimization problems with a reduced-space implicit function formulation, and demonstrating the application of nonlinear dynamic optimization, and these tools in particular, on chemical looping combustion (CLC) models.

Chemical looping combustion is an advanced hydrocarbon combustion technology in which fuel and air react in separate chambers via a solid oxygen carrier intermediate. The separation of fuel and air reactions yields a carbon dioxide-water product that can easily be separated for capture and storage. Chapter 4 of this thesis describes chemical looping and presents a chemical looping reactor model that will form the basis for much of the work presented. Chapter 5 applies multi-scenario nonlinear dynamic optimization to parameter estimation from experimental data for a detailed shrinking core kinetic model of an oxygen carrier reduction process, yielding kinetic parameters that predict conversion over time with less than 5% root-mean-squared error. 

The remainder of this thesis focuses heavily on modeling tools and algorithms for nonlinear dynamic optimization. In Chapter 6, matching and partitioning algorithms from graph theory are applied to analyze a singular CLC reactor model and identify the cause of singularity in terms of 90 underconstrained variables and 60 overconstrained variables in a process model with over 10,000 variables and constraints total. The decomposition exploits knowledge of the DAE structure of the model to partition based on time indices and differential and algebraic equations, then applies the Dulmage-Mendelsohn partition to subsystems to identify overconstrained and underconstrained variables. This decomposition represents a significant improvement in the specificity with which a singularity may be identified. 

In Chapter 7, the discretization stability of the reactor model is analyzed and confirmed, and an NMPC simulation is performed with the tractable model. Finally, in Chapter 8, an implicit function formulation is presented and applied to dynamic optimization problems with the reactor model. In this formulation, algebraic equations are removed from the optimization problem formulation and converged separately in an implicit function. Algebraic variables, along with their derivatives calculated by the implicit function theorem, are used to solve the optimization problem in a reduced space. The implicit formulation improves convergence reliability, solving 24% more problem instances over two parameter sweeps of dynamic optimization problems. 




Degree Type

  • Dissertation


  • Chemical Engineering

Degree Name

  • Doctor of Philosophy (PhD)


Lorenz (Larry) Biegler

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