Statistical aspects of fouling processes

Abstract Fouling in heat exchangers is traditionally characterized by deterministic (linear or nonlinear) kinetic models of fouling deposition and removal processes. This deterministic approach to fouling does not reflect the real situation of heat exchangers subject to fouling. The observations in a real situation of fouling of heat exchangers, when compared with the results obtained from predictive models, show a large discrepancy. This discrepancy in the fouling literature is normally referred to as uncertainty of the process. In this paper an attempt is made to model this uncertainty by characterizing the fouling as a correlated random process. The deterministic kinetic models (available in the literature) are randomized by treating their parameters as random quantities. Three fouling patterns are characterized by Rf(t) = Bt for the linear process, Rf(t) = mtn for the power law process with a falling rate (0 n ≤ 1) and Rf(t) = Rf∗[1 − exp (—t/τ)] for an asymptotic process, where t > 0 and B, m, Rf∗ and τ are the random process parameters with associated distributions. Fouling causes the performance loss of heat exchangers which can be tolerated up to a certain limit (i.e. critical level of fouling, Rfc), and thus it is of interest to find P[R(t) ≤ Rfc] = P(T > t) where T is the time to reach Rfc. Such distributions are developed in this paper, which are validated against the available data in the literature. It is demonstrated that alpha, modified alpha and Weibull are the most appropriate models to characterize the time to reach a critical level of fouling, if the underlying random fouling growth laws are linear, power law and asymptotic respectively. Knowledge of these distributions and the methods to determine their parameters is useful for devising appropriate maintenance and cleaning schedules in a probabilistic framework.