Optimal control strategies for gas cooling systems using geometric design and model predictive control

Abstract

This thesis presents a theoretical approach on designing the geometry of a gas cooling system unit and its application with the multivariable optimal control technique based on the dynamic mathematical models with a motivation to enhance the cooling efficiency. The gas cooling system can be defined as a process that cools down the exterior heat or solid microparticles introduced to a confined volume space by injecting inert cooling gas stream that absorbs the released heat. Two example cooling processes that are discussed in this study and come under this definition are the CO2 storage tank pre-cooling process and the microparticle cooling process. Although both processes are included in a same process category, the individual process characteristics and their ultimate goals which need to be achieved are significantly different. Hence, such factors requiring the main consideration are discussed for the design of the cooling process units. These apply also on developing the optimal controller scheme for the gas cooling systems. Rigorous dynamic modelings are derived for each process based on the first principles which are further used in the development of appropriate model predictive control (MPC) schemes. The result produced by these optimal controllers are later compared with base cases using the proportional-integral (PI) controllers, which illustrate that the multivariable optimal control is able to enhance the stability and the efficiency of both processes. First example is the pre-cooling process of CO2 storage tanks. The design of CO2 storage tanks are determined in advance considering the maximization of the available loading amount. The tank system must be cooled before loading cryogenic liquid CO2 to prevent physical and thermal damage to the tank wall. The pre-cooling process gasifies a fraction of the liquid CO2 cargo and injects the resulting gas into the storage tank until the tank reaches the target temperature and pressure. Thus an MPC approach for optimizing the injection flowrate of CO2 gas to reduce the loss of liquid CO2 cargo and CO2 capturing and compression cost is proposed. The process is mathematically formulated into a nonlinear multi-input-multi-output (MIMO) gas-phase system in which the injection mass flowrate and the outlet purging mass flowrate of CO2 gas act as control inputs. Then, a finite-horizon linearized model predictive control (MPC) scheme is designed to make the tank system reach the target state within a designated operation time limit. A terminal penalty is suboptimally approximated by solving a modified discrete Lyapunov stability condition and added to the control objective function in order to provide a theoretical finite-horizon stability and enhance the process termination. For the microparticle cooling process which is the second example, a systematical procedure for selecting a favorite design of a cylinder-on-cone cooling chamber that provides sufficient cooling residence time for spherical polymer particles produced by a prototype polymer meltspray nozzle is suggested. First, calculations on the particle residence time required for cooling is carried out using a lumped particle model to determine the chamber height. Second, dynamic responses with a step input of the hot air injection rate and the overall air flow streamlines inside the case examples with different chamber structures are obtained with computational fluid dynamics (CFD) simulations. The simulation results suggest that the cone height and the diameters of the cylinder and the outlet interact each other, influencing the mixing and the heat transfer of the gas phase inside the cooling chamber. A chamber design with less instability and good mixing in the air flow is selected among the case designs. CFD simulation results show that polymer droplets are sufficiently cooled in the selected chamber geometry. Lastly, an adaptive MPC structure controlling the air temperature inside the spray cooling chamber and the flowrate of the purging air out from the chamber outlet simultaneously by manipulating the injection flowrates of cold air and normal air streams is devised. The idea is based on the fact that significant portion of microparticle products depend their moving trajectories on the gravity and the flowrate of the surrounding air stream, which make these two variables the main operation parameters influencing the efficiencies of the follow-up units which collect the microparticles according to their sizes. We demonstrate that both control variables are well-managed near given setpoints through the MPC application, rejecting three possible scenarios of step disturbances added on the process parameters including the setpoint of the air temperature inside the spray cooling chamber, the surrounding air temperature and the injection mass flowrate of the melt feed stream.