(596a) Nonlinear Programming Strategies for Optimization of Dynamic Chemical Looping Reactor Models

Nonlinear Programming (NLP) is an important tool for many chemical engineering applications where design and operating variables can have significant impacts on process efficiency. This is especially important in the energy industry, where efficiency directly translates to the societal goal of having reliable electric power infrastructure with a small carbon footprint. In this industry, simulations of optimal operation of carbon-based power generators allow practitioners to make informed decisions when evaluating alternatives for construction and investment. One such alternative is chemical looping combustion (CLC), a combustion process conducive to carbon capture in which oxygen is transferred from air to fuel through a solid oxygen carrier that continually loops between oxidation and reduction reactions that occur in separate reaction beds.

CLC reactors are modeled as systems of partial differential and algebraic equations, discretized to form large systems of nonlinear equations that are the equality constraints of nonlinear optimization problems. These equations include material and energy balances in the gas and solid phases, hydrodynamic equations for pressure drop across the reactor, Shomate equations for thermodynamic properties, and nonlinear transfer correlations. The large and highly nonlinear nature of these system makes them very difficult to solve due to poor scaling of the nonlinear system and starting points that are not close to local optimum. Because of these challenges, optimal simulations of these processes are not widely available. This work presents equation-oriented NLP strategies necessary to overcome these challenges for optimal control of moving bed and bubbling fluidized bed chemical looping combustion reactors.

The two-phase nature of these processes leads to variables and constraint expressions of significantly different orders of magnitude and thus ill-conditioned constraint Jacobian matrices, which at feasible points have condition numbers upwards of 10²⁰. While linear system scaling methods are well-established and effective for reducing error introduced during a linear system solve, scaling of the nonlinear system is equally important for convergence of NLP algorithms, but systematic methods for scaling general nonlinear systems have not been established. Here we introduce a systematic scaling strategy for variables and constraints based on our knowledge of these processes and investigate the impact on condition numbers and convergence of NLP algorithms.

We also investigate strategies to promote convergence of interior point nonlinear optimization solvers in the presence of poorly conditioned nonlinear systems. To avoid small steps due to ill-conditioning and to keep search directions close to Newton directions when possible, we take a conservative approach to regularization of the KKT matrix, performing more refactorizations in order to prevent regularization coefficents from becoming unnecessarily large. To promote convergence of feasibility restoration, we use an l₁-penalty restoration phase that guarantees satisfaction of constraint qualifications (Thierry, 2019).

The co-dependence of these NLP strategies is investigated as well as the trade-off between computation time and robustness. We synthesize these results to present a class of NLP algorithms tailored to perform dynamic optimization of CLC reactor models. Several real-world examples are presented to demonstrate the effectiveness of these approaches.