(434d) Nonlinear Model Predictive Control for Flue Gas Desulfurization

Sulfur dioxide (SO₂) emissions are known to not only cause health issues, but also have an adverse effect on the environment in various ways. SO₂ is known to be a precursor of acid rain and plays a major role in the surface reactions that lead to the depletion of the ozone layer. The primary source of SO₂ emissions is flue gas from fossil fuels-based power plants. Several flue gas desulfurization (FGD) technologies have been incorporated in power plants. These include limestone scrubbing, sodium scrubbing, magnesia scrubbing and a few others. Of these, the most popular technology is the limestone slurry-based system known as the wet limestone FGD (WFGD), primarily because of its high SO₂ removal capacity and low capital and operating costs. Several types of scrubbers such as spray scrubbers, venturi scrubbers and packed beds are used for limestone scrubbing. The most widely used system is the counter-current spray scrubber. In this system, flue gas enters from the bottom and the limestone slurry in the form of droplets is introduced from the top through nozzles distributed over several spray headers. SO₂ from the flue gas reacts with limestone to form calcium sulfite, which is oxidized at the bottom of the scrubber to form the byproduct gypsum.

Due to fast cycling of power plants and variabilities in the sulfur content in the coal, 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. In addition, efficiency of the FGD units should be maximized. A rigorous dynamic model of the FGD unit can be 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. For instance, the instantaneous reactions comprise of dissociation of species (e.g. SO₂, sulfites, bisulfites, bicarbonates etc.) and finite rate processes involve limestone dissolution, sulfite oxidation and crystallization. These processes have to be coupled with the scrubber bulk hydrodynamics and considered simultaneously. Therefore, a multi-scale dynamic model is required to capture the interactions among a large number of ions and complex thermodynamic and chemistry. Due to the fast ionic reactions in the limestone droplet and presence of many ionic and molecular species, the highly nonlinear system of equations is stiff and ill-posed, and is therefore challenging to solve reliably as a dynamic simulation.

In this work, we present an implementation of FGD simulation for the limestone scrubbing unit. It is a multiscale model. At the slurry droplet scale, we solve a two-point boundary value problem (BVP) to characterize the absorption of SO₂ in a slurry droplet. This is a Differential-Algebraic Equation (DAE) model based on penetration theory and, as such, requires rigorous analysis and reformulation to obtain and solve a so-called index-1 DAE model. At the scrubber bulk scale, the physical processes include complex factors such as velocity, size distribution, collision and coalescence between the slurry droplets which play a significant role in the SO₂ absorption at the droplet scale. We integrate the droplet model into the scrubber bulk to characterize SO₂ scrubbing in the absorption zone. Finally, we develop a dynamic oxidation reactor model for the oxidation reaction yielding gypsum. The dynamic FGD scrubber model integrates the droplet phase, the scrubber bulk phase and the oxidation reactor. We simulate the multi-scale model at various operating conditions and demonstrate its validity by comparing it with plant measurements from the partner power-plant. Having validated the multi-scale dynamic FGD model off-line, we apply nonlinear model predictive control (NMPC) strategies to demonstrate optimal control of the scrubber to maximize efficiency and meet emissions regulations while efficiently rejecting dynamic load and concentration changes.

We use Pyomo, an open source framework for modeling and optimization, to implement the spray scrubber model. We demonstrate the performance of this multi-scale dynamic model for the limestone WFGD system. First, we show that the BVP associated with SO₂ absorption is an ill-posed, high-index DAE model and present a systematic reformulation procedure to obtain a well-posed, index-1 DAE model that lends to a tractable numerical solution. Second, we simulate dynamic SO₂ scrubbing operations for the base line loadings of a coal-fired power plant. Using multi-level spray flowrates as decision variables we also demonstrate the optimization of operating costs and efficiency. Using the NMPC framework, we demonstrate the dynamic optimization of the FGD operation for maximizing efficiency and minimizing deviations in the gypsum quality specifications, under transient plant conditions such as ramp up and ramp down in SO₂ concentration and flowrates.