Flexibility study for a MSF by Monte Carlo simulation

Abstract

Traditionally, processes and controllers are designed sequentially. Firstly, the process configurations (structures) and parameters are designed to satisfy the economic objectives, such as maximum profit or minimum operational costs. The designs are based on steady state models, and they are subjected to the operational constraints. Then, the controllers are designed, with a focus on rejecting the possible effects of external disturbances and process uncertainties, and achieving the desired dynamic performance. This approach carries a risk in that it may end up choosing the cheapest process design that can prove difficult to control. It may also miss out a slightly less economic but easier to control design, the one that might be more profitable in the long run (Weitz & Lewin, 1996). Operability properties of a process determine how process dynamics affect the quality of a process control design. These include flexibility, controllability, optimality, stability, selection of measurements and manipulated variables. The flexibility is defined as ‘the ability to maintain the process variables within the feasible operational region, despite the presence of uncertainties’ (Grossman et al., 1983). Flexibility is often considered simultaneously with the economic objectives and hence the optimality issue is raised. As a consequence, flexibility studies are dominated by numerous optimization strategies. Those studies aim at the determination of flexible operational spaces and flexibility measurements. The analysis generally involves two complementary tasks, the calculation of the flexibility index and the flexibility test. Operational flexibility is an important issue when designing and operating a chemical plant. Very often, flexibility is concerned with the problem of ensuring a feasible steady-state operation over a variety of operating uncertainties. To quantify how flexible a process is many metrics have been developed. Grossmann et al. (1983) 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. (1985). These two measurements -FIG and RI– require identification of the nominal point, which must be located within the feasible region. These measurements however only take the critical uncertainty into account. 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 (1990) proposed an index called stochastic flexibility, SF, that is determined from the probability distribution of all the uncertain parameters. 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 can be obtained, the calculation of SF is usually tedious. To avoid this difficulty, Lai and Hui (2007) proposed the index FIV. This was calculated as the size ratio of the feasible space to the overall space bounded by the expected limits of the uncertain parameters. The feasible space is the subspace of the overall space in which the uncertain parameters can be feasibly handled. The index SF and FI belong to the interval [0, 1]; a higher value means a higher flexibility. In this work several flexibility indexes for a multi-stage flash (MSF) desalination plant were estimated. To mimic the plant operation a stationary simulator was developed, and the determination of the feasible space was carried out with Monte Carlo simulation (Metropolis & Ulam, 1949; Rubinstein & Kroese, 2007). This approach does not involve an optimization model, but only a simulation one; hence the implementation is more simple and robust than other approaches. Finally, the proposed method yields additional information besides the flexibility indexes, and the relevance of this additional information shows the potential of this approach.