The simulation of a multi-pass shell-and-tube reactor requires the solution of a nonlinear two-point boundary-value problem. Six nonlinear ordinary differential equations describing the production of ethanolamines in 1–2 and 1–4 shell-and-tube reactors are solved numerically using both a quasi-linearization algorithm and a classical shooting method. Despite the presence of five unknown initial values, the shooting-method approach proved superior for this particular problem. The simulation revealed that for exothermic reactions the optimum tube-side temperature profile (and therefore the minimum-size reactor) was most closely approached by designing for the lowest overall heat transfer coefficient and cooling-water flow rate and highest inlet cooling-water temperature, subject to the constraint of a maximum-reaction mixture temperature.

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