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.

中文翻译：

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带有详细交换器设计的热交换器网络综合：第1部分。管壳式热交换器设计的离散微分代数方程模型

通过建立耦合的差分热方程以及设计变量的代数方程，提出了一种用于管壳式换热器详细设计的新方法。换热器设计组件（通道，折流板和壳体）用于离散微分方程，并与代数设计方程同时求解。耦合微分代数方程（DAE）系统适合于数值优化，因为它代替了非平滑对数平均温度差（LMTD）项。通过迭代求解基于LMTD的方法，可以确定关于壳体数量，流体分配，管尺寸和挡板数量的离散决策。然后将所得的换热器拓扑用于离散详细的DAE模型，通过改变管长来最小化经济目标函数，将其作为非线性规划模型进行求解，以获得详细的交换器设计。DAE模型还在详细设计的同时提供了交换器内部的料流温度曲线。可以观察到，对于具有恒定流特性的单壳热交换器，DAE模型的结果几乎与基于LMTD的设计模型相等，但是当允许流特性随温度变化或增加壳数时，则显示出显着差异。解决方案的准确性和所需的计算成本表明，该模型非常适合解决热交换器网络综合问题并结合详细的交换器设计，这在本文的第2部分中得到了证明。