Advanced Optimization Strategies for Periodic Adsorption Processes

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 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.