Advanced Optimization Strategies for Periodic Adsorption

Periodic Adsorption Processes (PAPs) have gained increasing commercial importance as an energy-efficient separation technique over the past two decades. Based on fluid-solid interactions, these systems never reach steady state. Instead they operate at cyclic steady state, where the bed conditions at the beginning of the cycle match with those at the end of the cycle. Nevertheless, optimization of these processes remains particularly challenging, because cyclic operation leads to dense Jacobians, whose computation dominates the overall cost of the optimization strategy. In order to efficiently handle these Jacobians during optimization and reduce the computation time, this work presents new composite step trust-region algorithms based on sequential quadratic programming and interior point methods for the solution of minimization problems with both nonlinear equality and inequality constraints. Instead of forming and factoring the dense constraint Jacobian, these algorithms approximate the Jacobian of equality constraints with a specialized quasi-Newton method. Hence, they are well suited to solve optimization problems related to PAPs. In addition to allowing inexactness of the Jacobian and its null-space representation, the algorithm also provides exact second order information in the form of Hessian-vector products to improve the convergence rate. The resulting approach also combines automatic differentiation and more sophisticated integration algorithms to evaluate the direct sensitivity and adjoint sensitivity equations. Numerical performance iv results on small scale PAP problems and CUTEr problems show significant reduction in computation time. Furthermore, we propose a systematic methodology to design PSA cycles using a superstructure based approach. The superstructure is rich enough to predict a number of different PSA operating steps, and their optimal sequence is obtained by solving an optimal control problem. PSA is a potential technology for pre-combustion CO2 capture because of low operating costs and high performance. We utilize the superstructure approach to synthesize PSA cycles for this purpose which can separate both H2 and CO2 at high purity and operate with a low power consumption of 86 kWh/tonne of CO2 captured.