Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

A new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD-based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD-based design model for one-shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.