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.
A fundamental model of wax deposition in subsea oil pipelines
Wax deposition in subsea pipelines is a significant economic issue in the petroleum industry. A mathematical model has been developed to predict the increase in both the deposit thickness and the wax fraction of the deposit using a fundamental analysis of the heat and mass transfer for laminar and turbulent flow conditions. It was found that the precipitation of wax in the oil is a competing phenomenon with deposition. Two existing approaches consider either no precipitation (the independent heat and mass transfer model) or instantaneous precipitation (the solubility model) and result in either an overprediction or an underprediction of deposit thickness. By accounting for the kinetics of wax precipitation of wax in the oil (the kinetic model), accurate predictions for wax deposition for both lab-scale and pilot-scale flow-loop experiments with three different oils were achieved. Furthermore, this kinetic model for wax precipitation in the oil was used to compare field-scale deposition predictions for different oils. V C 2011 American Institute of Chemical Engineers AIChE J, 57: 2955–2964, 2011
Effect of stress conditions on collapse deformation behavior of a rockfill material
A set of saturated and dry-saturated large-scale triaxial tests were conducted in order to explore the effects of stress conditions on the saturation-induced collapse deformation behavior of a rockfill material. Specimens were tested in different confining pressures and for dry-saturated tests the specimens were submerged in various shear stress levels. The results indicate that in all of the dry-saturated tests a sudden reduction in the volume of the specimens was observed during the submerging process. The ratio of the minimum axial strength of a submerged specimen (at the end of the saturation process) to the shear strength of the specimen before saturation is defined as the coefficient of stress recovery, Csr. Results of the dry-saturated tests showed that this ratio increases as the confining pressure increases and decreases by increasing the shear stress level. According to the results of dry-saturated tests the values of internal friction angle reduction caused by saturation (Δϕc), the ratio of the elasticity modulus of the material after saturation to its elasticity modulus in dry condition, i.e., Ewet/Edry, and also the saturation induced sudden volumetric strain (εvc) decrease as the confining pressure increases. However the shear stress level does not have any meaningful effect on the variation of Dfc, Ewet/Edry and (εvc).