Optimal production and scheduling of a process with decaying catalyst

Abstract

A multiperiod mixed-integer nonlinear programming (MINLP) optimization model is presented to schedule catalyst changeovers and determine the best operating policy for a chemical process with decaying performance. Two solution strategies are proposed to reduce the effect of nonconvexities and to reduce the solution time: (1) a search strategy that relies on partitioning the time horizon and (2) a strategy that makes use of the Generalized Benders Decomposition (GBD).Keywords: catalyst deactivation, production planning, mixed integer planning, optimization IntroductionThe operation of chemical processes with catalysts having decaying performance over time gives rise to a challenging modeling and optimization problem (for example, see Xiong and Jutan, 2003). As the catalyst activity decays over time, process shutdowns for catalyst changeovers must be planned to restore the process performance. It is therefore necessary to develop a kinetic model that can predict the production, taking into account the catalyst deactivation. Process operations are optimized based on the deactivation and process economics. The trade-off is between the high production rates achieved from maintaining frequently renewed, high-functioning catalyst loads, and the loss in production and maintenance costs arising from catalyst changeovers.Catalyst deactivation has received attention with kinetic studies at the reactor level (Ho, 1984;Kittrel, 1982) and at the pilot-plant level (Krishnaswamy and Kittrel, 1979). Deactivation kinetic models are determined based on data sets consisting of declining conversion at constant temperature or of increasing temperature at constant conversion. Sapre (1997) proposed an alternate technique where space velocity is adjusted to maintain constant conversion. This technique, at constant temperature, gives more reliable rate information for both the catalyst deactivation and the primary catalytic reaction. The empirical kinetic models are used to determine the temperature-time relationship required under various process constraints to maintain constant conversion.The development of optimization models for planning and scheduling of chemical processes has received significant attention over the last 10 years . The problem of scheduling multiple feeds on parallel units with decaying performance has been addressed by Jain and Grossmann (1998 (2003) formulated a multiperiod optimization model for the production and scheduling of catalyst changeovers in a process with decaying performance for short time horizons over which the demand varies. This model is a nonconvex mixed-integer nonlinear programming (MINLP) problem and therefore may lead to suboptimal solutions. The model proposed later makes more extensive use of disjunctive constraints and can handle much longer time horizons. In addition, two solution strategies, partitioning and Generalized Benders Decomposition, are presented to tackle the problem of nonconvexities and to reduce the solution time. The efficiency of both strategies is discussed in the section ...

An optimal control approach to scheduling and production in a process using decaying catalysts

“…The elements of the problem set up here are similar to that in Houze et al (2003) and Bizet et al (2005). However, those publications did not reveal any parameters used in their studies, citing confidentiality reasons.…”

“…1. The number of catalyst loads considered in Bizet et al (2005) was either or 3. If that number was increased, the number of combinations involved in their solution methodology would increase exponentially and so, obtaining good solutions would require a very large amount of computational e↵ort.…”

“…2. In Bizet et al (2005), the flow rate, temperature and sales are decisions to be taken on a monthly basis, whereas in this work, those controls are optimised on a weekly basis. The smaller problem size enabled by the MSMIOCP approach facilitates producing solutions which are more informative compared to the former.…”

“…The smaller problem size enabled by the MSMIOCP approach facilitates producing solutions which are more informative compared to the former. If decisions were taken on a weekly basis in Bizet et al (2005), the problem size would have increased almost 4-fold, thus accentuating the di culties in obtaining solutions.…”

“…Houze et al (2003) formulated a model using the big-M formulation to schedule catalyst changeovers and plan production to meet seasonal demand for 2-year and 4-year horizons. Bizet et al (2005) modified the model in Houze et al (2003) by using convex hull formulations instead of the big-M formulations wherever possible, which enabled solutions for longer time horizons of 74-months and 9-years. Further, they claim, without rigorous proof, to overcome the non-convexities of that model to obtain global optimality by using two di↵erent approaches: a partitioning search strategy and the Generalized Benders Decomposition (Geo↵rion, 1972).…”