Global Optimization of the Design of Shell-and-Tube Heat Exchangers Considering Fouling Modelling

Abstract

Heat exchangers are equipment responsible for altering the temperature and/or physical state of process streams. During the operation, these equipment are subjected to fouling phenomenon, what causes a decrease in heat transfer, increasing the operational and maintenance costs. The approach used to deal with this problem during the heat exchanger design is to insert additional thermal resistances when calculating the overall heat transfer coefficient. However, these additional resistances, represented as fouling resistances, ignore the fact that the fouling rate is affected by the thermo-fluid dynamic conditions in the interior of the equipment. Therefore, each alternative for the design solution is associated to a different fouling rate. Concluding, the present thesis presents an investigation of how the fouling models can be inserted in the heat exchanger design optimization problem. Through applying mathematical programming techniques, formulations of the problem are proposed considering two types of fouling models: (i) a model in which the fouling resistance depends on the flow velocity, typically applied to systems involving water streams and (ii) a fouling rate model that depends on flow velocity and temperature, applied to crude oil streams in preheat trains in atmospherically distillation units in refineries. The first formulation results in an integer linear programming problem (ILP) and the second one in a mixed integer linear programing problem (MILP). The linear nature of both formulations allows the identification of the global optimum, even when using conventional optimization algorithms. The formulations proposed are able to identify the feasible solutions for the heat exchanger design with lower cost than those obtained through the conventional design considering constant fouling resistances.