Scheduling of Parallel Furnaces Shutdown under Uncertainty

ERICA P. SCHULZ; M. SOLEDAD DIAZ

San Francisco, USA

Congreso; AIChE annual meeting; 2006

American Institute of Chemical Engineers

This work addresses optimal scheduling and process optimization under uncertainty for cracking furnaces shutdowns in an ethylene plant. A two-stage stochastic model is formulated, which is transformed into a deterministic mixed integer nonlinear (MINLP) one. Cracking furnaces are typical units that operate in parallel and exhibit decaying performance due to coke deposition inside coils, which has negative effects on ethylene yield. In this paper, the model, which is based on a discrete time representation, takes into account the interactions between the entire process plant operation and the furnace performance through the inclusion of nonlinear correlations for both the furnaces and the entire plant to account for an important recycle stream, which is part of the furnaces feed, at each time period. The decay in furnaces performance throughout operating time has been modelled by means of two sets of binary variables and several continuous time varying variables (Schulz et al., 2006). The main one is coils’ roughness, an empirical linearly increasing continuous variable in each time period, whose dependence on time has been determined through rigorous simulations and checked with plant data. The model includes feed and product storage level determination, as well as sales for varying product demand throughout a given time horizon. In this way, there are first stage decisions associated to manufacturing variables that include production levels, process units operating conditions and furnaces run lengths. Second stage decisions are related to logistics; they include inventory levels, product sales, shortage of product and deviation from target inventory levels. The objective function is to minimize expected cost and it is composed of two terms. The first term captures the costs associated to the manufacturing phase, i.e., the sum of the first-stage costs, which are deterministic and include fixed and variable production charges, cost of raw material purchase. The second term comprises the expected value of the second-stage costs, which quantify the costs associated to inventory holding charges, safety stock violation penalties and penalties for lost sales. They are related to logistics decisions. This second term is obtained by applying the expectation operator to an embedded optimization problem.  A distribution-based approach is adopted  to model product demand as normally distributed with a specified mean and standard deviation. An analytical expression is derived for the expected value of the solution of the inner optimization problem, as proposed by Gupta and Maranas (2003), and the resulting reformulated MINLP problem has been solved in GAMS (Brooke et al., 1992) using DICOPT++ (Viswanathan and Grossmann, 1990).