Research PaperQuantifying the ‘implementation gap’ for antifouling coatings
Introduction
Fouling is a chronic problem in many process heat transfer systems. The presence of unwanted deposit layers causes increased resistance to heat transfer and can cause blockage. The associated losses in thermal and hydraulic performances over time directly impact the sustainability of systems affected by fouling. It also introduces the need to clean heat exchangers on a regular basis. Cleaning is rarely instantaneous, requiring the unit to be taken out of service. This incurs further energy losses or capital expenditure in order to maintain a backup facility to cover the absent unit. Cleaning operations also introduce further, non-thermal environmental impacts and wider sustainability considerations associated with consumption and disposal of cleaning chemicals and wasted product.
The decision of when and how to clean an exchanger is an optimisation problem, considering the cost of energy losses due to fouling over an operating period of length t and those incurred as a result of cleaning (taking time τ). Figure 1 illustrates the problem for a single heat exchanger. This ‘fouling-cleaning cycle’ problem was first described by Ma and Epstein [1] and a practical example and further analysis was presented by Cosado [2]. A dimensional analysis of the problem, including the effects of ageing, was shown by Ishiyama et al. [3].
Methods for identifying the optimal fouling–cleaning cycle period, i.e., t + τ, have been identified for different operating scenarios [3], as well as cases where there is a choice of cleaning method [4]. The objective function to be optimised for scenarios involving a single heat exchanger is the time-averaged operating cost, ϕop, given bywhere Q is the heat duty, cE is the cost of energy and Ccl is the cost of a cleaning operation. The calculations require knowledge of the fouling behaviour over time, Q(t'). If this is available, it allows the operator and the designer to determine the optimal configuration and operating strategy for the unit. This is a classical example of a trade-off between capital investment, linked to the design of the unit, and operating costs, linked to time in service. Different designs can then be compared.
The use of antifouling coatings to delay the onset of fouling or to hinder fouling (maintain Q near Qcl), as well as to enhance cleaning (reduce τ and/or Ccl), has been actively pursued in several industrial sectors. Such ‘non-stick’ coatings often incur additional capital spending related to the cost and manufacturing of coated surfaces. There can also be a reduction in heat transfer coefficient when the layer has a relatively low thermal conductivity. The financial attractiveness (i.e. the economic sustainability) of installing a coated heat exchanger then depends on the trade-off between capital and operating costs over the lifetime of the unit. In practice the lifetime of the unit is likely to be determined by the effectiveness of the layer, as the layer is likely to degrade or otherwise suffer reduced performance over time. The balance between these costs will differ between a new system and a revamped or retrofitted one. In the latter case, an existing exchanger is replaced and the extra capital outlay needs to be recovered from improved operation.
These financial considerations – which can include CO2 taxes – effectively set bounds on the price of antifouling coatings, determined by comparing manufacturing costs and the maximum saving that can be achieved from fouling mitigation, in a ‘value pricing’ calculation. Order of magnitude estimates for different applications can establish the potential attractiveness of antifouling coatings for a given scenario. This concept was outlined by Gomes da Cruz et al. [5], who applied it to three cases with different operating and cost bases. They assumed simple fouling behaviour, i.e. where the fouling resistance, Rf, increased linearly with time at constant fouling rate b, viz.where U is the overall heat transfer coefficient and Ucl the value after cleaning. Linear Rf -t' behaviour, as described by (2), is often not observed in practice as (i) there may be an induction time, tind, before noticeable effects of fouling appear, and (ii) the rate of increase in Rf varies with time owing to changes in surface temperature, deposit strength etc. Asymptotic fouling behaviour is often reported, wherein Rf approaches a limit at long times. This is often described mathematically by the Kern-Seaton model [6]:
Here t'-tind is written as t* for convenience: tind is the induction period where there is negligible deposition, tf is the characteristic timescale (the kinetic parameter), and Rf∞ is the asymptotic fouling resistance. The latter parameter is frequently employed in overdesigning heat exchangers subject to fouling, even though this approach tends to promote fouling in a ‘self-fulfilling prophecy’ [7]. The Kern-Seaton model is employed here: other expressions may also be used, but the results obtained in Section 2.3 may not apply.
This paper develops the ‘value pricing’ concept for heat exchangers subject to asymptotic fouling, extending the numerical analysis in [5] to one type of fouling behaviour which is of direct relevance to industrial practice. Criteria determining when an exchanger should be cleaned are identified. We have identified one case, that of equal heat capacity flow rates, where a semi-analytical result can be obtained which does not require tedious calculation. Its use is illustrated with a case study based on data reported by Oldani et al. [8], comparing water crystallisation fouling on stainless steel tubes and ones with a perfluoropolyether (PFPE) coating.
Section snippets
The operating cost
The time to clean, τ, is assumed to be independent of processing history. This assumption is expected to be valid if the exchanger has to be disassembled for cleaning. τ is likely to be reduced if cleaning-in-place is used and the antifouling coating promotes cleaning. Inspection of Equation (1) shows there will be an optimal processing time, topt, if dϕop/dt = 0, which requires
This statement of the optimal processing criterion requires the operating cost at topt to
Illustrative case study
A case study, based on data taken from the literature, is used to illustrate the quantifying of the financial benefit of anti-fouling coatings. Oldani et al. [8] reported the performance of a single-pass counter-current shell-and-tube unit with constant flow rates and approach temperatures. The process and utility streams were both aqueous, and the unit was subject to crystallisation fouling. The Rf − t' data sets in Fig. 3 were interpreted to exhibit asymptotic fouling behaviour and were
Case study: quantifying the financial attractiveness of a PFPE coating
The effect of operating period length on the time-averaged operating cost, calculated using Equation (11), as well as the thermal cost penalties, for the uncoated and coated SS units are presented in Fig. 4. The optimal time to operate the uncoated unit before cleaning is 64 days and for the coated SS unit it is 100 days. It can be seen that the minimum in ϕop is not symmetrical, so that the penalty for cleaning early is slightly larger than that for cleaning later. The optimised operating
Conclusions
The attractiveness of using anti-fouling coatings to mitigate fouling in a heat exchanger subject to asymptotic fouling behaviour has been assessed using a techno-economic analysis of the performance of the exchanger over a fouling and cleaning cycle. The methodology allows the financial attractiveness of an anti-fouling coating and the associated optimal cleaning strategy to be quantified.
For the special case of a counter-current exchanger with equal heat capacity flow rates, a standard
Acknowledgement
A PhD studentship for OMM from Du Pont/Chemours is gratefully acknowledged.
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