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In process plants incorporating heat exchanger networks (HENs) for heat recovery, deposits building up on heat transfer surfaces may lead to increased energy consumption and in certain cases also undesirable plant stoppages for heat exchanger cleaning. Such problems can be avoided if online cleaning of the individual exchangers is applied.

In this article, the scheduling of cleaning operations is considered assuming a priori knowledge of the time behaviour of the thermal resistance of deposits R’fj(t) in the individual exchangers (j=1..p), gained by measuring and recording operating parameters of the HEN over longer production periods.

First, the mathematical model of the influence of fouling on heat exchanger and HEN operation is introduced and illustrated by an example of its application. The model makes it possible to predict fouling-induced changes as well the consequences of heat exchanger cleaning in HEN performance, including energy recovery.

On this basis, a decision-making model is proposed for optimisation of the cleaning schedule, taking its economic effects into account, and an example of optimal scheduling of cleaning operations in an HEN comprising 10 heat exchangers is presented.

The modelling of the influence of fouling on HEN operation stems from earlier work by Markowski and co-workers,^1–3 who observed that the detrimental effect of fouling can be reduced by adopting appropriate measures in HEN design. The choice of the following is important:

• HEN structure affecting interactions between the individual exchangers and thus influencing heat recovery – the more interactions occur, the better the compensation of negative fouling effects; and
• local parameters relating to deposit build-up in each single exchanger – ? (Biot factor) and ΔT_minc (minimum temperature difference in the absence of deposits); at low values of ? and ΔT_minc , the exchanger is less sensitive to fouling.

In the literature, various methods for the optimisation of cleaning schedules for a single equipment unit have been proposed.^4,5 For complex HENs, Muller-Steinhagen proposed an integrated approach for developing alternative fouling mitigation strategies based on both experimental and modelling work.⁶ Smaili et al. analysed cleaning synchronisation of HENs for continuous processes subject to fouling (taking sugar manufacturing as an example) and arrived at the mathematical problem of mixed integer non-linear programming.⁷ Georgiadis et al. considered a general mathematical framework for optimal periodic cleaning and energy management problems in HENs.⁸ Economic trade-offs between the total number and timings of cleaning operations and the cost and availability of the hot utility in the plant were illustrated.

Mathematical Modelling of the Influence of Fouling on Heat Exchanger Network Operation
Interaction Between Heat Exchangers
Fouling build-up on the heat transfer surface of a heat exchanger operated in the HEN brings about a change in the exchanger capacity as well as changes in the outlet temperatures of process streams. The operation of the exchanger can also be affected by other exchangers serving the same process streams (‘antecedent exchangers’; examples of such exchangers in a specific HEN are given below). As deposits build up on the heat transfer surfaces of the antecedent exchangers, the temperatures of the process streams at the exchanger inlet change. The knowledge of these temperatures is a prerequisite for analysing exchanger operation and identifying the effects of fouling on its heat transfer surface. This is illustrated in Figure 1A, where fouling-induced changes in the temperature distribution, assuming unchanged temperature values at inlet, are indicated. In order to determine how the build-up of deposits in an HEN affects a specific heat exchanger, its interaction with antecedent exchangers should be studied.

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