Comment pubs.acs.org/EF
Comments on “The Effect of Operating Temperatures on Wax Deposition” by Huang et al. Hamid O. Bidmus† and Anil K. Mehrotra* Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada The above-referenced paper by Huang et al.,1 published recently in Energy & Fuels, reported the predictions from a wax deposition model for the rate of wax deposition at different temperatures of oil and coolant. The model, derived on the basis of mass-transfer considerations or mass flux, uses the mass driving force and solubility curve to predict wax deposition. They used their model predictions to conclude that the thermal driving force, defined as the difference between the oil temperature (Toil) and the coolant temperature (Tcoolant), is not as important for the wax deposition process. In particular, they compared the experimental results by Bidmus and Mehrotra2 to their predictions obtained from the wax deposition model. The purpose of this comment is to point out several omissions and inconsistencies that we have observed in the paper by Huang et al.1 Huang et al.1 attributed erroneously an incorrect generalization to Bidmus and Mehrotra,2 which was that the deposit thickness decreases as the thermal driving force decreases. As explained later in this comment, this observation is true only under a specific set of conditions. Apparently, Huang et al.1 did not distinguish correctly between the results from two sets of wax deposition experiments with the model oil, as reported by Bidmus and Mehrotra.2 One set of deposition experiments was performed under ‘hot flow’ conditions, in which the temperature of the model oil was maintained higher than the wax appearance temperature (WAT).2 For these experiments performed with T oil > WAT and a constant coolant temperature, Tcoolant < WAT, it was shown that the wax deposition increased with a decrease in the thermal driving force.2 Such an effect of the thermal driving force has also been reported in numerous other studies performed under ‘hot flow’ conditions, including Bott and Gudmundsson,3 Ghedamu et al.,4 Creek et al.,5 Bidmus and Mehrotra,6 and Paso and Fogler.7 In fact, Mehrotra and Bidmus8 pointed out that wax deposition can be prevented altogether if the flowing crude oil could be maintained at a very high temperature. That is, as an extreme case, no deposition could occur with a high oil temperature, even though it would involve a large thermal driving force. The effect of the thermal driving force on wax deposition has not been interpreted correctly in sections 1.B and 1.C of the paper by Huang et al.,1 which is like many earlier publications on this topic. It is now commonly accepted that the overall thermal driving force, (Toil − Tcoolant), does not affect wax deposition in a direct manner. Indeed, it has been shown that wax deposition could not occur without a difference between the average temperatures of the oil and coolant;6 this was found to be the case even when wax crystals were suspended in the oil in the ‘cold flow’ experiments.2 Several previous studies from our laboratory have addressed the importance of the thermal driving force in detail.6,9−12 We © 2012 American Chemical Society
wish to clarify the actual role of the thermal driving force in influencing the thickness of the wax deposit. All of the important temperatures in the wax deposition process are shown schematically in Figure 1, where xd denotes the deposit
Figure 1. Illustration of temperatures across various thermal resistances during wax deposition in a pipe.
thickness and ri and ro denote the inside and outside pipe radii, respectively. Following an analysis of the heat-transfer mechanism involved in wax deposition, it was shown that the relative magnitudes of the temperature differences across the four individual thermal resistances in series, when wax deposition occurs inside a tube [namely, (Toil − Tinterface), (Tinterface − Twall‑in), (Twall‑in − Twall‑out), and (Twall‑out − Tcoolant)], are more important than the overall thermal driving force, (Toil − Tcoolant).6,10 This observation was arrived at by equating the rate of heat transfer through the two conductive and two convective thermal resistances, as shown in Figure 1, which are present in series at steady state.6,10 For example, the Received: March 21, 2012 Revised: May 11, 2012 Published: May 22, 2012 3963
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experimental results, plotted in Figure 7 of the paper by Parthasarathi and Mehrotra,10 showed that wax deposition can vary significantly for the same value of the overall thermal driving force, (Toil − Tcoolant), when all other variables are held constant. In other words, even though (Toil − Tcoolant) provides the overall thermal driving force for heat transfer, it is not a controlling parameter for wax deposition. In a simplified form, rather than (Toil − Tcoolant), the wax deposition tendency was explained in terms of two temperature differences, namely, (Toil − WAT) and (WAT − Tcoolant), with (WAT ≈ Tinterface) during the deposition process.10 The wax deposit mass has been shown to increase with a decrease in (Toil − WAT) and with an increase in (WAT − Tcoolant).6,9−12 That is, wax deposition, under ‘hot flow’ conditions, will increase as Toil is lowered to approach the WAT and/or Tcoolant is decreased further to a value much lower than the WAT. Thus, contrary to the observations in sections 1.B and 1.C of the paper by Huang et al.,1 the wax deposition, under ‘hot flow’ conditions, has been shown to decrease with an increase in Toil and/or Tcoolant. In this regard, the fractional temperature difference (or the fractional thermal resistance) across the deposit layer, (Tinterface − Twall‑in)/(Toil − Tcoolant), is more significant for the wax deposition process than (Toil − Tcoolant).6,8,10−12 The second set of deposition experiments, reported by Bidmus and Mehrotra,2 were performed under ‘cold flow’ conditions, in which the oil temperature was held below the WAT throughout the experiment. In these ‘cold flow’ experiments, as expected with Toil < WAT, wax crystals were observed to be suspended in the model oil during the deposition experiments such that the flowing oil was actually a suspension or slurry.2 The objective of the ‘cold flow’ experiments was to investigate whether oil slurries flowing at lower temperatures, with wax crystals suspended in the oil, would lead to reduced wax deposition, as was suggested in a comprehensive review by Merino-Garcia and Correra.13 For these experiments, a systematic stepwise cooling protocol was developed to lower the model oil temperature below its WAT, while preventing any wax deposition on the cooling surfaces, before commencing the deposition experiments.2 From the data obtained at constant values of Tcoolant, it was concluded that a decrease in the oil temperature, Toil, decreased the amount of wax deposited.2 That is, wax deposition, under ‘cold flow’ conditions, decreases with a decrease in Toil and an increase in Tcoolant. Huang et al.1 examined the results from the ‘cold flow’ experiments by Bidmus and Mehrotra,2 while not distinguishing them from the ‘hot flow’ experimental results. Huang et al.1 also reported their flow loop deposition experiments carried out on a North Sea oil sample, with a WAT of about 30 °C. They compared the wax solubility data for the North Sea oil sample, in Figure 2 of their paper, to that for the model oil (similar to that used by Bidmus and Mehrotra2), in Figure 4 of their paper. The solubility data were obtained at a relatively fast cooling rate of 1 °C/min, for which the supercooling effects in the crystallization process might be more dominant. They noted, in section 2.B of their paper, that the solubility curve for the North Sea oil sample is more temperature-sensitive than that for the model oil. However, both the ordinate and abscissa scales used in their Figures 2 and 4 were substantially different. When both sets of solubility data are plotted using the same scales, as shown in Figure 2 of this comment, the solubility curve for the model oil is seen to be actually more temperature-sensitive (i.e., having a larger slope) than that for the North Sea oil sample. Thus, the solubility data
Figure 2. Comparison of solubility curves of North Sea oil and model oil reported by Huang et al.1
by Huang et al.1 do not support their own observation and the associated conclusion. Huang et al.1 used the results from their deposition experiments with the North Sea oil sample to conclude that the wax deposition increases with a decrease in the thermal driving force at a constant coolant temperature. This trend is opposite of that observed by Bidmus and Mehrotra2 for the ‘cold flow’ experiments, but it is in agreement with the ‘hot flow’ deposition results. The North Sea oil deposition experiments were carried out at oil temperatures ranging from 15 to 35 °C using a coolant temperature of 5 °C. With a WAT of 30 °C for the North Sea oil sample,1 the experiments with oil temperatures between 15 and 35 °C would include both ‘hot flow’ and ‘cold flow’ conditions. Most of the experiments were, however, at oil temperatures below the WAT of the North Sea oil sample or under ‘cold flow’ conditions. Evidently, wax crystals will form in the liquid phase when the oil temperature is held below the WAT. These wax crystals could deposit or ‘stick’ to the cooling surface as well as possibly remain suspended in the oil, depending upon the cooling approach used. Huang et al.1 did not clarify this important issue. Their experimental method, as described in the paper, did not explain how the North Sea oil sample was cooled to the oil temperature for their deposition experiments. Without a complete description of the experimental protocol, especially the oil cooling rate and method employed, it is difficult to understand and reproduce their experimental results. The details of the oil cooling protocol are important if their results are to be compared directly to those obtained from the ‘cold flow’ experiments of Bidmus and Mehrotra.2 In using a mass-transfer-based model for predicting wax deposition, Huang et al.1 assumed, in section 3.A of their paper, that wax molecules only precipitate in the deposit but not in the oil phase. For the ‘cold flow’ deposition experiments, where the bulk oil temperature is below the WAT, this assumption is questionable. Moreover, precipitation of wax crystals will also lower the WAT of the residual liquid phase of the oil. An important question is as follows: What would happen to all of 3964
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the wax crystals that precipitate out of the oil at temperatures below the WAT (as shown by the solubility curve)? Did Huang et al.1 assume all of the precipitated wax crystals to become entrained in the deposit? Again, on the basis of the solubility curve and the described experimental setup, this would not appear to be a justifiable assumption. These are serious concerns relating to the model predictions reported by Huang et al.1 for wax deposition from the North Sea oil sample. The model predictions for North Sea oil deposition reported by Huang et al.1 in their Table 1 show certain inconsistencies. The wall temperature, Twall, is important for predicting wax deposition in the mass-transfer approach; however, the predicted values of Twall in Table 1 appear to be high considering that the deposit layer, with typical thermal conductivity in the range of 0.12−0.35 W m−1 K−1, would serve as an insulation between the hot oil and (cooler) pipe wall.14 It is difficult to estimate Twall accurately for their data because of a lack of sufficient information on the properties of the North Sea oil sample along with the coolant flow rate and the heat-transfer coefficient. The reported Twall values seem to correspond to the pre-deposition stage; however, it would be incorrect to assume that Twall would remain the same after the deposition process begins, because it would introduce another significant thermal resistance as a result of the deposit layer, thereby changing Twall. Finally, an important assumption involved in the mass diffusion model, employed by Huang et al.,1 is that the temperature at the oil−deposit (i.e., liquid−solid) interface is taken to increase from Twall initially to the WAT as the depositlayer grows to a steady-state value. To the best of our knowledge, this assumption relating to a variable (and increasing) oil−deposit interface temperature has not been validated by experimental measurements of the interface temperature during the deposit growth phase. On the contrary, wax deposition experiments involving the cooling of a batch of model oil, under both static and sheared conditions, have shown the interface temperature to remain approximately equal to the WAT, while the deposit layer grows.15,16 In the heattransfer-dominated wax deposition modeling approach (for both laminar and turbulent flows), which involves a moving boundary formulation to account for heat transfer with phase change, the interface temperature is assumed to be held at the WAT throughout the deposition process,17−21 which has been supported by experimental measurements.15,16 It is noted that this moving boundary modeling approach was also used recently by Mehrotra et al.22 to obtain a satisfactory match of the wax deposition data under static cooling conditions.15 It would be interesting to compare similar predictions from the mass diffusion model, which assumes a variable oil−deposit interface temperature.
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Tcoolant = average temperature of the coolant (°C) Tinterface = average temperature at the oil−deposit interface (°C) Toil = average or bulk temperature of the oil (°C) Twall = average temperature at the tube or pipe wall (°C) Twall‑in = average temperature at the tube or pipe inside wall (°C) Twall‑out = average temperature at the tube or pipe outside wall (°C) WAT = wax appearance temperature (°C) xd = deposit thickness (m)
REFERENCES
(1) Huang, Z.; Lu, Y.; Hoffmann, R.; Amundsen, L.; Fogler, H. The effect of operating temperatures on wax deposition. Energy Fuels 2011, 25, 5180−5188. (2) Bidmus, H. O.; Mehrotra, A. K. Solids deposition during “cold flow” of wax−solvent mixtures in a flow-loop apparatus with heat transfer. Energy Fuels 2009, 23, 3184−3194. (3) Bott, T. R.; Gudmundsson, J. S. Deposition of paraffin wax from kerosene in cooled heat exchanger tubes. Can. J. Chem. Eng. 1977, 55, 381−385. (4) Ghedamu, M.; Watkinson, A. P.; Epstein, N. Mitigation of wax buildup on cooled surfaces. In Fouling Mitigation of Industrial HeatExchange Equipment; Panchal, C. B., Bott, T. R., Somerscales, E. F. C., Toyama, S., Eds.; Begel House: New York, 1997; pp 473−489. (5) Creek, J. L.; Lund, H. J.; Brill, J. P.; Volk, M. Wax deposition in single phase flow. Fluid Phase Equilib. 1999, 158−160, 801. (6) Bidmus, H. O.; Mehrotra, A. K. Heat-transfer analogy for wax deposition from paraffinic mixtures. Ind. Eng. Chem. Res. 2004, 43, 791−803. (7) Paso, K.; Fogler, H. S. Bulk stabilization in wax deposition systems. Energy Fuels 2004, 18, 1005−1013. (8) Mehrotra, A. K.; Bidmus, H. O. Heat-transfer calculations for predicting solids deposition in pipeline transportation of ‘waxy’ crude oils. In Heat Transfer Calculations; Kutz, M., Ed.; McGraw-Hill: New York, 2005; Chapter 25. (9) Mehrotra, A. K. Comments on: Wax deposition of Bombay high crude oil under flowing conditions. Fuel 1990, 69, 1575−1576. (10) Parthasarathi, P.; Mehrotra, A. K. Solids deposition from multicomponent wax−solvent mixtures in a benchscale flow-loop apparatus with heat transfer. Energy Fuels 2005, 19, 1387−1398. (11) Fong, N.; Mehrotra, A. K. Deposition under turbulent flow of wax−solvent mixtures in a bench-scale flow-loop apparatus with heat transfer. Energy Fuels 2007, 21, 1263−1276. (12) Tiwary, R.; Mehrotra, A. K. Deposition from wax−solvent mixtures under turbulent flow: Effects of shear rate and time on deposit properties. Energy Fuels 2009, 23, 1299−1310. (13) Merino-Garcia, D.; Correra, S. Cold flow: A review of a technology to avoid wax deposition. Pet. Sci. Technol. 2008, 26, 446− 459. (14) Cole, R. J.; Jessen, F. W. Paraffin deposition. Oil Gas J. 1960, 58 (38), 87−91. (15) Bidmus, H.; Mehrotra, A. K. Measurement of the liquid−deposit interface temperature during solids deposition from wax−solvent mixtures under static cooling conditions. Energy Fuels 2008, 22, 1174− 1182. (16) Bidmus, H.; Mehrotra, A. K. Measurement of the liquid−deposit interface temperature during solids deposition from wax−solvent mixtures under sheared cooling. Energy Fuels 2008, 22, 4039−4048. (17) Bhat, N. V.; Mehrotra, A. K. Modeling of deposit formation from ‘waxy’ mixtures via moving boundary formulation: Radial heat transfer under static and laminar flow conditions. Ind. Eng. Chem. Res. 2005, 44, 6948−6962. (18) Bhat, N. V.; Mehrotra, A. K. Modeling of deposition from ‘waxy’ mixtures in a pipeline under laminar flow conditions via moving boundary formulation. Ind. Eng. Chem. Res. 2006, 45, 8728−8737.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address †
WorleyParsons Canada, Calgary, Alberta T2W 4X9, Canada.
Notes
The authors declare no competing financial interest.
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NOMENCLATURE ri = inside radius of pipe (m) ro = outside radius of pipe (m) 3965
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(19) Mehrotra, A. K.; Bhat, N. V. Modeling the effect of shear stress on deposition from ‘waxy’ mixtures under laminar flow with heat transfer. Energy Fuels 2007, 21, 1277−1286. (20) Bhat, N. V.; Mehrotra, A. K. Modeling the effect of shear stress on the composition and growth of the deposit layer from ‘waxy’ mixtures under laminar flow in a pipeline. Energy Fuels 2008, 22, 3237−3248. (21) Mehrotra, A. K.; Bhat, N. V. Deposition from ‘waxy’ mixtures under turbulent flow in pipelines: Inclusion of a viscoplastic deformation model for deposit aging. Energy Fuels 2010, 24, 2240− 2248. (22) Mehrotra, A. K.; Bidmus, H. O.; Bhat, N. V.; Tiwary, R. Modelling the gelling behaviour of wax−solvent mixtures under static cooling. Trends Heat Mass Transfer 2010, 11, 17−31.
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