Collocation models for distillation units and sensitivity analysis studies in process optimization

Abstract

<p>This thesis examines problems in two related subject areas.</p> <p>The first subject area involves the development orthogonal collocation on finite elements (OCFE) models for stagewise distillation processes for use in steady-state optimization. The OCFE model formulation divides the column sections into smaller subdomains (finite elements) in order to track irregularities in the column profiles. Stages that have feed or sidestreams entering or leaving the column are modeled as discrete equilibrium stages in the OCFE model. An adaptive element breakpoint placement procedure determines an element partition for each column section so that a solution of improved accuracy is obtained. The element partition is based on the equidistribution of the material and energy balances residuals around envelopes in the column. OCFE models converge to the same optimal solution as tray-by-tray models in less computational time, but have similar sensitivity at the optimum with respect to major model parameters.</p> <p>The second area involves the study of parametric sensitivity analysis in process optimization. A sensitivity analysis procedure is developed that calculates the behaviour of the optimal solution for changes in one independent parameter using continuation methods. A procedure is proposed to modify the equation set which allows the study of the effects of multiple simultaneous parameter variations along specified directions in the optimal solution. Special attention is given to the detection and analysis of singularities in the optimal solution path caused by violation of either the strict complementarity, linear independence or second-order optimality conditions. The methodology provides information to determine the range of parameter estimate variation for which the active constraint set or the characteristics of the optimal solution remain unchanged. The adjustment of the independent variables in a multiple unit flowsheet, so that optimality is maintail'ed, is investigated in the presence of model parameter variation.</p>