Integrated simulation and optimization of distillation-based flowsheets

The present thesis is motivated by chemical engineering: process simulation and optimization with a focus on distillation-based flowsheets. In this context, a process consists of a number of unit operations connected by streams. Such a structure can be represented by a so-called flowsheet. In general, the process should be designed in a way that certain engineering demands are fulfilled, e.g. product purities, product yield, or maximum costs. The design of a process in steady state includes the choice of units in combination with their respective connections and also the choice of values for the specific design variables for each unit. Within the scope of this work, we assume that the layout of the flowsheet is given and we focus on choosing the design variables for each unit. The steady state behavior of a distillation-based flowsheet is modeled by default via a large system of nonlinear equations that reflect conservation and thermodynamic laws, whereas the number of degrees of freedom is small. These large nonlinear systems of equations cannot be solved analytically. Therefore, they are solved numerically with iterative methods after fixing the degrees of freedom, most often by use of Newton-type methods. Convergence failures occur quite often and, in that case, the user has to come up with new guesses for the fixed process variables until convergence is reached. This potentially turns the simulation and optimization of a flowsheet into a time-consuming procedure. In this thesis, we address the problems introduced above and present an approach that facilitates robust, flexible, and simultaneous steady state process simulation and optimization of distillation-based flowsheets. For that purpose, we use the well-understood asymptotic limiting case of distillation columns with an infinite reflux ratio and infinite number of stages, the socalled ∞/∞-model, as starting point and generate ideas that can be transferred to distillation columns with a finite reflux ratio and a finite number of stages. Such distillation columns are then calculated via upward or downward stage-to-stage calculations, where the transition from one stage to the next is formulated as a fixed-point problem. In the limiting case of infinitely large reflux ratio it is immediately possible to guarantee convergence for the corresponding fixed-point iteration. By application of the Banach fixed-point theorem we can also guarantee convergence of stage-to-stage calculations for suitable input variables in case the reflux ratio is finite. Furthermore, process simulation is embedded in an optimization problem with a typically small number of optimization variables and constraints. The input variables for stage-to-stage calculations, which serve as optimization variables, can be adapted in the outer optimization loop such that a feasible or even optimal solution is finally found. In the limiting case of distillation columns with an infinite number of stage, this procedure is similar to applying the shooting method to ordinary differential equations. Using the ∞/∞-model we can generate excellent initial guesses for the optimization variables.