Comments on analogies for correlated heat and mass transfer in turbulent flow

The Colburn analogy is a well-known analogy for predicting the heat and masstransfer coefficients in turbulent pipe flow. However, this analogy (or other heat-mass transfer analogies) is not applicable for predicting the mass transfer rate in turbulent flows, where the concentration field is correlated to the temperature field. An example of such a situation is frost formation on the cold surfaces of heat exchangers that are exposed to moist air (Lee et al., 1997). Another example, is that of paraffin deposition in cold pipelines, which is a multimillion dollar problem faced during the transportation of “waxy” crude oils (Anonymous, 2001). In both of these processes, a temperature gradient is directly responsible for establishing a concentration gradient. In the latter process, paraffin molecules precipitate and deposit on the walls of cold pipelines restricting the flow of oil. It is necessary to quantify the convective mass flux of paraffin molecules while modeling this phenomenon. In this article, an approach based on solubility is developed to predict the convective mass-transfer rate. Although this article specifically describes the paraffin deposition process, the results shown here can be used for any process, where the heat and mass transfer are correlated. Crude oil is a complex mixture consisting of paraffins, aromatics, naphthenics, resins, asphaltenes, and other impurities. The solubility of high-molecular-weight paraffins (interchangeably referred to as “waxes” in this article) in crude oil decreases drastically with decreasing temperature. At off-shore reservoir temperatures (70–150) and pressures, the solubility of these waxes is sufficiently high to keep them fully dissolved in the crude oil. However, as the oil is transported through subsea pipelines, where the ambient temperatures can be about 4°, the waxes precipitate out, due to their decreased solubility and deposit on the cold pipe walls. The enormous economic impact of this problem has led to several studies of the paraffin deposition process (Bern et al., 1980; Brown et al., 1993; Burger et al., 1981; Holder and Winkler, 1965; Majeed et al., 1990; Patton and Casad, 1970; Prasad, 1987; Singh et al., 2000). A number of mechanisms have been considered, and in our previous work we have found that molecular diffusion, enhanced by convective mass flux, is the dominant mechanism responsible for wax deposition (Singh et al., 2000). In two of our previous articles published in the AIChE Journal (Singh et al., 2000, 2001), we have explored the wax deposition phenomenon using laboratory flow-loops, and developed a mathematical model to predict the deposition under the laminar flow regime. It is necessary to extend the results of wax deposition under laminar flow conditions to deposition under turbulent flow, because many oil pipelines operate under turbulent flow conditions. One of the challenges that arise when developing a model for turbulent flow deposition, is the determination of the mass-transfer coefficient of paraffin molecules. As explained later, analogies, such as the Colburn analogy, can not be used to predict the mass-transfer rate in this situation. Hence, the mass-transfer coefficient has to be derived by different means.