Reliable compartmental models for double-pipe heat exchangers: An analytical study

Abstract

In this work, the analytical properties of the heat exchanger infinite-dimensional dynamic model are discussed. More importantly, those of a 2nd-order lumped-parameter model using the logarithmic mean temperature difference (LMTD) as driving force are derived and shown to agree with those of the former. Three essential aspects are focused: existence and uniqueness of solutions, equilibrium states, and stability properties. The results developed in this work are intended to supply a solid support for the reliability on the use of the kind of simple compartmental model that is treated. This is specially addressed to works where it is not the quantitative solutions but the qualitative behavior that is important, like modelling and simulation of heat exchanger networks and complex industrial processes where heat exchangers are involved.

A bounded positive non-linear PI control law for double-pipe heat exchangers

“…(see for instance [17], [15]). The control objective consists in the regulation of the process (hot) fluid outlet temperature, T ho , towards a (prespecified) desired value, T hd , through the cold fluid flow rate, F c , as input variable, taking into account the restricted range and unidirectional nature of such an input flow rate (according to Assumption A10).…”

“…(2) has been used for control design for instance in [10]. It has actually been used as a suitable dynamics representation of double-pipe heat exchangers for numerous purposes, as pointed out in [17].…”

“…The hot fluid flow rate, F h , is kept constant, while the value of the cold fluid flow rate, F c , can be arbitrarily varied within a compact interval F c [F cl , F cu ], for some positive constants F cl < F cu . Under these assumptions, and taking the whole exchanger as one bi-compartmental cell, a simplified but suitable lumpedparameter dynamical model for a double-pipe heat exchanger is (see for instance [17]):…”

Model based predictive control for a solar-thermal system

“…For simulation purposes to test the controller it will be kept as a function of the mass flow rates and therefore be time-dependent. ∆T mean which corresponds to the logarithmic mean temperature difference can be expressed by (3) as shown in [18] and [19].…”

An Integrated FDD Approach for an Intensified HEX/Reactor

“…Developments of dynamic models for HEX and continuous reactor have received considerable attention. The lumped model, also called cell-based model in the literature, is very often used, by which each cell is modelled by means of the energy and mass balances; see, for example, [13][14][15][16][17][18]. Among these models, the heat transfer coefficient will be assumed either constant or slowly decreasing.…”