Dynamics of Steam Heated Shell and Tube Heat Exchangers: Non-Linear Model Derivation, Solution and Validation

The dynamics of steam heated shell and tube heat exchangers with one passage in the shell and one or more passages in the tubes are governed by a non-linear system of Integro Hyperbolic Partial Differential Equations (HIPDAE) when longitudinal dispersion effects are neglected and finite vapor, wall and fluid capacitances, real fluid properties accounted for. Their non-linear behaviour is described with a theoretical Hammerstein model with delays and non-linear dynamics of vapor phase. Though several variable transformations are used, the solutions are obtained in original variables by the characteristic, Laplace transform and difference equation methods (CLD) without numerical quadratures neither convolutions and are valid for any dependence of heat transfer coefficients and capacitances from input variables. These solutions are also valid for generic non-zero initial conditions and any combination of stepwise and a sequence of stepwise variations of inputs, namely flow rate of steam and temperature and flow rates of cold fluid. The calculations are carried out with the aid of a double grid framework on physical domain in order to allow for an arbitrary selection of sampling time and spatial coordinates. The results of the calculations are compared with those obtained by finite element method (FEM) with adaptive quadrature, by a model of Hammerstein type with adaptive dynamic as well and by the numerical inversion of the Laplace domain solutions. The approximate solutions compare very well with rigorous solutions at the expense of much minor efforts. Other similar systems, governed by the same differential equations, could be easily simulate with the aid of the procedure developed in this study.