Heat integration of multipurpose batch plants using a continuous-time framework

Presented in this paper is a continuous-time mathematical formulation for optimization of heat integrated batch chemical plants. This formulation is applicable to both multipurpose and multiproduct facilities in which opportunities for direct heat integration exist. It is assumed that thermal driving forces and heat duties between operations identified as potential heat integration candidates are sufficient. These operations can either belong to the same batch plant or distinct batch facilities within the same site. Two scenarios are explored in this paper. The first scenario entails a situation where energy requirement is dependent on batch size, which is allowed to vary with distinct task occurrences within the time horizon of interest. The second scenario is based on fixed batch sizes in which the duty requirement is specified as a parameter. In the first scenario, the resulting formulation is initially cast as a nonconvex mixed integer nonlinear program (MINLP), which is linearized exactly to yield a convex MILP problem. This linearization is not necessary in the second scenario, as the resulting model is readily an MILP problem. A literature example and a case study are used to demonstrate the effectiveness of the formulation.