Measurement of plant flexibility

Abstract

Operational flexibility is an important consideration when designing and operating a chemical plant. Very often, flexibility is concerned with the problem of insuring feasible steady-state operation over a variety of operating uncertainties. To quantify how flexible a process is, various metrics have been developed. Grossmann and his co-workers[1,2] first introduced the flexibility index (FIG) which quantifies the smallest percentage of the uncertain parameters' expected deviation that the process can handle. Another metric named resilience index (RI) was adopted by Saboo et al.[3] However, these two measurements require identification of the nominal point which must locate within the feasible region. In addition, these measurements just consider the critical uncertainty. This may cause serious flexibility under-estimation or neglect the ability of the process to handle other process uncertainties. To solve this problem, Pistikopoulos and Mazzuchi[4] proposed the stochastic flexibility (SF). Although SF accounts for the chance that the process can operate feasibly, the probability distribution of all the uncertain parameters may not be available at the design stage. Even though the probability distributions are obtainable, the calculation of SF is usually tedious. This paper aims at introducing a new process flexibility metric. Flexibility is reckoned as the size of the feasible space (Sf) in which the uncertain parameters can be feasibly handled. A new flexibility index (FIV) is defined as the size ratio of Sf to the overall space (So) bounded by the uncertain parameters' expected limits. A process with FIV = 1 indicates that it can run feasibly with all the expected values of the uncertain parameters. Alternatively, a process with FIV = 0 implies that none of the expected uncertainties can be handled feasibly. Unlike FIG, FIV measures the entire space where all uncertain parameters can be freely moved. This paper will provide an algorithm used for estimating Sf and the newly defined FIV. Examples will be presented to demonstrate the applications of this new FIV and compare this with the other flexibility measurements.