MODELLING THE FOULING INDUCTION PERIOD

A fouling process is often preceded by an induction period in which no significant fouling is observed. In this paper, a simple lumped parameter model based on fractional surface coverage θ has been developed to correlate experimental data in the induction period. The model assumes that active foulant species stick to the surface and gradually cover it, the rate of change of surface coverage dθ/dt being proportional to the fractional free surface (1-θ). It is further assumed that the foulant already on the surface acts as a seed, attracting more foulant in a micro-growth manner such that the growth rate is proportional to θ. The two assumptions are combined to obtain the relationship dθ/dt = kθ(1θ) where k is the lumped rate constant. The fouling layer grows on the covered surface and the fouling rate can be expressed as θRf′ where Rf′ can be any established fouling rate expression. Experimental data, including the data during induction periods, have been successfully correlated for systems including crude oil, crystallization and whey protein fouling. The physical meanings of the model parameters are discussed. The model supports experimental observations in which shorter induction periods are found with higher surface temperatures. INTRODUCTION A fouling process is commonly preceded by an induction period in which no significant fouling is observed. The induction period could be from a few minutes in a laboratory experiment to a month or so in refinery plants. A number of researchers have addressed this phenomenon, including in particular, the factors that can influence the induction period. For protein fouling, Belmar-Beiny et al. (1993) observed a much shorter induction period for a plate heat exchanger than for a tubular heat exchanger. They considered that this was due to the higher turbulence in the former. BelmarBeiny and Fryer (1993) analysed the first layer of deposit, which was thought to be formed during the induction period and found that it was made of proteinaceous materials rather than minerals. More recently, Augustin et al. (2007) investigated the effect of surface treatments on protein fouling and reported the effect of surface temperature on the induction period. For crystallization fouling, Troup and Richardson (1978) discussed nucleation time which is closely related to the induction period phenomenon. More recently, Geddert et al. (2007) investigated the effects of surface coatings and attempted to correlate the induction with the surface roughness and surface tension but did not reach any quantitative conclusion. In spite of many observations and investigations of induction phenomena, the induction period has not been studied in a substantially quantitative manner especially for crude oil fouling. The main reason for this can be attributed not only to the complexity of the fouling behaviour in the induction period but also to the fact that no additional experimental information can be gained as the induction period proceeds since it appears from thermal measurements as an apparently steady state operation. Most fouling models are focused on the fouling rate in the period when the heat transfer resistance is increasing (e.g. Wilson et al., 2005). Few models have addressed the induction period. Vatistas (1987) reported a stochastic model for the induction step in particulate fouling. This model can predict the effect of friction velocity on the induction time but was found to be difficult to use in correlating the experimental data. Malayeri and MüllerSteinhagen (2007) developed a phenomenological model for the prediction of fouling resistance of calcium sulphate solutions during boiling heat transfer, including an empirical estimation of the induction time. However, this model, as they stated, is limited only to the fouling period and it was recommended that one should endeavour to correlate data within the initial period. Neural network techniques can be, and have been, successfully utilized to correlate the data during the entire fouling process (Malayeri and MüllerSteinhagen, 2007; Radhakrishnan et al. 2007). The drawback of this approach is that it is, in essence, a black box technique which does not offer any physical understanding of the process. Fahiminia et al. (2005) derived a relationship between delay time (i.e. induction period) and supersaturation ratio at any given fluid velocity and surface temperature based on classical nucleation theory. They also showed that for any given fluid velocity Proceedings of International Conference on Heat Exchanger Fouling and Cleaning VIII 2009 (Peer-reviewed) June 14-19, 2009, Schladming, Austria Editors: H. Müller-Steinhagen, M.R. Malayeri and A.P. Watkinson