Comments on Analogies for Correlated Heat and Mass Transfer in Turbulent Flow (R&D Note)
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.
Modelling of Paraffin Wax in Oil Pipelines
As warm oil or condensate from the reservoir flow through a pipeline on the cold sea bottom, wax often precipitate and deposit on the wall. To predict the rate of the deposition, wax modeling is important. The main mechanism contributing to deposition, molecular diffusion, is driven by a radial concentration gradient. The concentration gradient is driven by the radial temperature gradient. When precipitation of wax crystallites occurs in the bulk of the flow, it affects the concentration gradient, which again affects the rate of deposition. The current thesis gives an elucidation of this particularity. Fundamental heat and mass transport equations are solved numerically in Matlab and the result shows that the concentration profiles become slighter as the precipitation become larger. This decreases the mass flux due to molecular diffusion. A term “shear dispersion” was introduced in 1980’s to describe particle deposition of wax. The term has been used in several wax deposition models, but the mechanisms behind are not well explained in the literature. An elucidation of both a shear induced lift force and shear induced diffusion are investigated.
Correlations for prediction of molecular diffusivities in liquids
New correlations have been developed for diffusivities in liquids at infinite dilution for normal paraffin solutions, for aqueous solutions, as well as generally for polar and non-polar solutions. The molar volume, parachor and radius of gyration for both solute and solvent were used as correlating parameters. The new correlations represent a significant improvement in accuracy for predicted diffusivities.