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.
Study of Paraffin Wax Deposition in Seasonally Pigged Pipelines
Waxy crude oil pipelines are pigged periodically to scrape the adhered wax deposit from the pipe wall and remove it from the pipeline. If wax deposition on the pipe wall is not too severe and there is not much change in pipeline throughput due to wax deposition in winter, a pigging operation in winter is inadvisable because a “paraffin blockage” may occur during pigging due to a lower operating temperature. Seasonal pigging of this pipeline is advisable if the crude oil is piped at ambient temperature in summer and the wax deposit on the pipe wall accumulated during winter is eroded by the oil flow. The pipeline should be pigged during high temperatures in summer rather than in winter. A semi-empirical wax deposition model developed by our laboratory is used to predict the wax deposit distribution along the pipeline in different seasons and the volume of pre-pigging deposit on the pipe wall, and a seasonal pigging program is recommended. An experimental method consisting of determination of the gel point of wax-contaminated oil ahead of the pig is developed to calculate the volume of wax deposits removed by the pipeline pigging operation under actual field conditions to test the model. The wax content in the crude oil is determined from the gel point. The relative discrepancy between the predicted and the field experimental pigging operation data is 12.3%.
Slotted Waveguide Antenna With Two Radiation Nulls
A design of a linear array antenna having two radiation nulls and otherwise omnidirectional radiation pattern is reported. A new configuration of a waveguide broad wall longitudinal slot doublet with positive and negative offsets with respect to the waveguide center line is used to design the array. This type of doublet produces two radiation nulls. Each of the null directions can be shifted at least up to plusmn25deg by proper choice of slot offset. Resonance and radiation characteristics of the proposed doublet are also presented. Finally, one linear array antenna consisting of seven doublets has been fabricated. Measurements show that the 15 dB null widths are 14.2deg and the null depths are at least 24.8 dB. Maximum gain ripple in the omnidirectional region is 1.75 dB.