Dynamic Optimization of Multi-Unit Systems Under Failure Conditions

Abstract

Shutdowns in a chemical processing plant are detrimental both to plant economics and critical product characteristics. These situations can be due to routine maintenance, or due to the more extreme case of equipment failure due to wear. Nevertheless, both are cases of non-normal plant operation, and are often unavoidable. These situations are complicated further when many units are linked, and subjected to a high degree of integration. In this case, the shutdown of any unit within the plant can have immediate and potentially severe impacts on other areas of the operation. Since these events are unavoidable, the challenge is to minimize their economic impact through careful design of operating practices, and potentially plant design retrofits. This thesis focuses on developing generic and systematic methods of determining economically optimal operating policies and plant designs in the face of failures in multi-unit operations. This includes determining the optimal trajectory of critical plant variables (flows through units, flows between units, buffer tank levels, etc.), as well as determining whether plant design changes would improve plant economics during such events. Such ventures lead to mixed-integer dynamic optimization (MIDO) problems. A dynamic model of the process is presented, accounting for the major flows of process materials through units, between units, as well as the accumulation of these in the intermediate buffer capacities. The approach used was to assume that the processing units operated at pseudo-steady-state, with dynamics confined to the intermediate buffer capacities. All models developed were based on a combination of empirical and fundamental elements. For use of the model in an optimization study, a simultaneous approach, in which the differential equations are discretized and included as equality constraints, was employed. This yielded a nonlinear optimization problem involving only algebraic equations. Optimal responses to scenarios involving planned maintenance shutdowns, as well as unplanned shutdowns (unit failures) were computed, with plant economics used as the merit function. Sensitivity to parameters such as preparation time, shutdown length, and restoration time were studied. In all cases, it was desired to maximize plant economics, while maintaining a smooth operation. While several methods are available for use in a multi-criterion optimization problem, a two-tiered approach was developed and applied in which the plant economics were maximized first, and input usage subsequently minimized as a secondary objective. After identifying key failure scenarios through a review of industrial data and downtime reports, a multiple-model formulation was developed involving the probability distribution of failure scenarios. Optimal steady-state operating levels for the buffer capacities were computed. This formulation is then extended to a mixed-integer programming problem in which the addition of extra buffer capacity is included as a decision variable.