- Email: [email protected]
Wax deposition in single phase flow
Fluid Phase Equilibria 158–160 Ž1999. 801–811
Wax deposition in single phase flow J.L. Creek a
a, )
, Hans Jacob Lund b , James P. Brill
b,1
, Mike Volk
b
Department of Physical and Chemical Measurements, CheÕron Petroleum Technology, 1300 Beach BouleÕard, La Habra, CA, 90631-6374 USA b Department of Petroleum Engineering, UniÕersity of Tulsa, 600 S. College AÕenue, Tulsa, OK 74104 USA Received 22 March 1998; accepted 18 December 1998
Abstract A series of experiments on wax deposition from oil have been performed in a 50-m long by 43.4 mm ID jacketed flow loop at Tulsa University. Tests were performed on a 358API crude oil from the Gulf of Mexico with a wax appearance temperature ŽWAT. of 1208F. The series of tests were designed to determine temperature and flow rate effects on the deposition rate and fraction of oil in the deposit. The deposit thickness in the flow loop was determined using five methods; pressure difference, energy balance, the spool piece volume change ŽLDLD., ultrasonic transit time, and direct measurement in a test section. Samples of the deposits were analyzed at the conclusion of each test for included oil. The effect of the difference in temperature between the oil and pipe wall showed a simple increasing deposition rate with temperature difference. The change in deposition rate was a weak function of oil temperature relative to WAT. The variation in deposition rate with flow velocity gave large differences between laminar and turbulent flow. Deposit oil contents decreased with increasing flow velocity. The fraction of oil in the deposit decreased with time in turbulent flow tests but did not change in laminar tests. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Data; Diffusion coefficient; Solid–fluid equilibria
1. Introduction New petroleum production horizons at water depths greater than 500 m have driven industry to discover new technologies for preventing and controlling the deposition of petroleum wax. Traditional methods of management, prevention, and remediation have been established for many years w1,2x. The
) 1
Corresponding author. Tel.: q1-562-694-7664; fax: q1-592-684-7565; e-mail: [email protected] E-mail: [email protected].
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 0 6 - 5
802
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
greater water depths mean lower temperatures, and longer and fewer production lines available in deeper water make economic solutions to prevention, management, and remediation key to economic development of these new deep water resources. It has been shown for example that the cost of remediation increases with water depth to the extent that the cost is on the order of $200,000 when the depth is 100 m, but on the order of $1,000,000 when the remediation occurs in depths near 400 m. The cost is proportionally greater as development depth increases w3x. The Tulsa University Fluid Flow Projects on Wax Deposition is a Joint Industry Project Ž JIP. comprised of a research staff at the University of Tulsa and 37 oil and gas companies and government agencies. The purpose of the JIP is to study wax deposition in multiphase flowing petroleum systems. Prerequisite to multiphase testing is a thorough understanding of deposition from single phase flow. This work reports the experimental program and results of single phase deposition experiments for a Gulf of Mexico crude oil. A single phase flow facility was donated to the JIP by the Alberta Research Council and Petro-Canada. A series of experiments have been performed in the 50-m long by 43.4-mm internal diameter ŽID. jacketed single phase flow loop after the loop was installed and refurbished at the University of Tulsa. Key features of the facility are temperature and pressure measurement stations every 5 m along the flow loop, a glycol-water filled temperature control jacket over the full 50-m length of the loop, and mass flow meters to determine the flow of fluid and coolant. The loop is configured as a horizontal ‘U’ tube with two removable test sections Žspools.. One is located 20 m from the entrance and a second 5 m from the end of the flow loop. An experimental program has been executed to gain an understanding of wax deposition from single phase flow prior to experimentation on deposition from multiphase flow. A thorough review of the existing literature on the theory of deposition from single phase flow has been reported by Matzain w4x. Fig. 1 shows a schematic problem description. The general consensus of the petroleum industry is that once a radial temperature gradient is established between the oil and pipe wall, and the oil temperature is below the wax appearance temperature Ž WAT. of the oil, deposition occurs. The solubility of paraffin in the oil is a single valued decreasing function of temperature. The difference in the temperature between the oil and pipe wall produces a composition gradient corresponding to solubility of paraffin species in oil. This gradient results in an imbalance in the chemical potential and hence a Fick’s law mass flow.
Fig. 1. Pipeline deposition scenario.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
803
According to Cussler w5x, Fick’s law states that the flux Ji of diffusing species in a given volume is related to the concentration gradient by a diffusion constant Di . Ji s ADi Ec irE z . Ž1. Rygg et al. w6x have taken Eq. Ž1. and related the volume of diffusing species into the deposition zone for a multi-component system to the volume of deposit as Vdep s Ž 2p rL . Ý Ž Di MWr i r i .Ž Ec irET . ETrEr
4
Ž2.
i
where r the radius has been substituted for z and the deposit area is given by 2p rL, Di is the diffusion coefficient, c i is the concentration of species i in moles per unit volume, MWi and r i are the molecular weight and the density of species i. We propose that deposition occurs in the laminar boundary layer for turbulent flow and in the low velocity ‘boundary’ in laminar flow. An initial soft deposit is formed through relief of the local supersaturation of the wax species in solution. The size of the deposit depends in part on the thickness of the boundary because of the mechanical strength of the deposit. We also propose that the deposit further rearranges and hardens with time to the deposits recovered from pipelines. Examination of Eq. Ž2. shows two quantities that need to be tested if this equation is correct. The first of these is effectively heat flux which is related to w ETrEr x and the second depends only on the fluid being tested, Ý i Di Ž Ec irET . . The available correlations for predicting diffusion coefficients are suited for binary mixtures only. Cussler w5x describes the difficulty in predicting the diffusion coefficients for multicomponent mixtures. A second reason for concern over the diffusion coefficient for the system is that classical mass diffusion is an isothermal, quiescent process that may not directly apply for flowing, non-isothermal systems. The deposition scenario is a non-isothermal flowing system and appears to be driven by the heat flow term, w ETrEr x. The appropriate flux coefficient may be a combination of mass and thermal diffusion. This conclusion is reasonable when one considers the close similarity among the transfers of mass, heat, and momentum. This is summarized by the Reynolds Analogy, which states that when heat, mass, and momentum are supplied to the fluid in corresponding ways the resulting rates of transfer relative to the corresponding driving force are equivalent for all three forces. Perry and Chilton w7x have summarized this in Eq. Ž 3. as krG M s hrc p G s fr2 Ž3. where k is the molar mass transfer coefficient, G M is the molar velocity, h is the heat transfer coefficient, c p is the specific heat, G is the mass velocity, and f is the friction factor. This is illustrated in Fig. 1. The temperature difference leads to a concentration gradient through differential solubility of wax components in the oil. This in turn leads to a chemical potential driving force but can also leads to a thermal diffusion driving force. The term Ý i Di , the diffusion coefficient is usually ‘fitted’ to experimental data w4x. 2. Test program The first portion of the test program is to confirm the performance of the test facility and also confirm known results. The second part was used to study the effects of flow and time on wax deposition. The first series of tests were conducted to verify that the temperature gradient factor in
804
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Eq. Ž2., w ETrEr x should be directly proportional to the deposition rate. This was studied by varying the temperature difference between the oil and jacket glycol under both laminar and turbulent conditions for temperature differences from 8.3 Ž158F. to 258C Ž458F. . The second series of tests were conducted to determine the effect of oil temperature on the deposition rate. In this part of the work the temperature difference between the oil and glycol-water jacket fluid was maintained at 8.38C Ž158F. while the oil temperature varied from a few degrees about the WAT of 48.88C Ž 1208F. to 29.48C Ž858F. . These experiments were designed to test the sensitivity of deposition rate to the Dwd crdT x term in Eq. Ž2. . Hamouda and Davidsen w8x, and Eaton and Weeter w9x have clearly shown that the shear dispersion mechanism discussed previously by Burger et al. w10x, Bern et al. w11x, and Weingarten and Euchner w12x is not significant. We verified that deposition through shear dispersion did not contribute to our system. A more interesting result of these two studies w8,9x was the variation of deposition rate with flow rate. Similar results were presented by Grung w13x in 1995. We, therefore, included a series of tests to attempt to quantify the effect of flow rate on deposition rate. The last area studied arose from the earlier work of Hunt w1x who indicated that the fraction of wax in the deposit increased with time from about 20% for experiments on the order of a day to near 60% for tests lasting several hundred hours. Eaton and Weeter w9x reported that deposits that were initially gelled oil became hard over a 240-h deposition period for rotational velocities that correspond to laminar flow. Tests were included to study the effect of deposit aging for both laminar and turbulent flow by conducting tests for both 24 and 120 h. 3. Description of experiments Tests were performed on a 358API crude oil from the Gulf of Mexico donated by the Mobil Oil Corporation. The WAT for the subject oil was 48.898C Ž1208F.. The experiments were performed in the flow loop described in Section 1. A 50:50 water–ethylene glycol mixture was circulated in a thermostatic jacket fluid counter current to the oil flow. Temperature and pressure taps were located at the entrance and exit of the flow loop as well as every 5 m along the flow loop. The oil and glycol–water Ž ‘glycol’. coolant flow rates were determined with mass flow meters. The pressure and temperature for the oil and the temperature of the glycol were determined at each measurement station located at 5-m intervals along the flow loop. The magnitude of the deposit in the flow loop could be determined using five methods; pressure difference, energy balance based on temperature difference, internal volume changes in the test sections Ž LDLD., ultrasonic transit time, and direct measurement. A thorough discussion of these deposit determination techniques is given elsewhere w14x. The ultrasonic deposition measurement device was the result of a joint effort among Norsk Hydro Research and Christian Michelsen Research of Bergen Norway and Chevron Petroleum Technology Company. The device tested was a prototype based on the speed of sound and will not be discussed here. Samples of the deposits from each spool piece were collected and analyzed at the conclusion of each test to determine the included oil content of the deposit. The fraction of included oil present in the deposit was determined by high temperature gas chromatography. Samples of each deposit were dissolved in carbon disulfide and injected into a high temperature gas chromatograph. The weight percent paraffin was determined for each sample. Comparison of the deposit analysis with the original oil analysis gave the oil fraction in the deposit.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
805
4. Discussion of results The first target of the study was the effect of the temperature difference between the oil and the pipe wall. This is conveniently represented as the difference in the temperatures of the oil and the ‘glycol’ as they enter the flow loop. The results of this series of tests are given in Fig. 2 for laminar flow and Fig. 3 for turbulent flow. The wax thickness was difficult to determine, even with the number of techniques used. The laminar flow deposits were extremely soft and were found to contain typically from 80% to 90% oil by weight. These deposits had the consistency of gelatin with imbedded wax crystals. It was noted that in one case after a shut down, starting the pumps sheared off the deposit. The shearing off of the deposit was also observed when the flow rate was increased from 24 to 240 m3 of oil per day. Notice also that the thickness determined by removing the test spools and measuring the spool volume with water ŽLDLD. are much lower than the results of other techniques. The softness of this deposit in the laminar flow case could cause deposit loss when the oil is removed from the loop prior to removing the test spools. The deposit from the greatest temperature difference between the ‘glycol’ and oil also gives among the softest deposits. This could possibly account for the apparent maximum in the laminar deposition case shown in Fig. 2. Earlier tests at similar conditions gave a deposit that did not have enough mechanical strength to support itself without the oil being present in the spool piece. The line termed Simulation in the figures was computed with a deposition simulator prepared by T.S. Brown of Multiphase Solutions, Inc. This simulator, based on his earlier work w15x, was optimized to simulate the flow loop used in these tests. The effect of Ž ETrEr . for the turbulent flow tests is shown in Fig. 3. A linear increase of deposit thickness with temperature difference can be seen in Fig. 3. The turbulent flow deposits had a consistency similar to ‘shoe polish.’ These deposits were strong compared to the very soft laminar deposits. The deposits formed at the higher temperature differences are softer than those formed at smaller temperature differences. This is thought to be caused by a greater concentration of high molecular weight species in these deposits since the actual minimum temperature of deposition is higher and lower melting species are not precipitated at the pipe wall. An error analysis of the deposit measurement techniques has shown that the ‘energy balance’ method was more appropriate for laminar flow conditions and the pressure difference method was
Fig. 2. Effect of temperature difference between oil and wall for laminar flow.
806
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Fig. 3. Effect of temperature difference between oil and wall for turbulent flow.
more appropriate for the turbulent flow tests. The deposition in turbulent flow was far less than for laminar flow which is in agreement with Grung w13x. The deposition simulator did capture the general trend of the experimental data. Fig. 4 shows the effect of initial oil temperature on deposition rate. These tests were conducted under laminar flow conditions with an 8.38C Ž158F. temperature difference between the oil and ‘glycol.’ The abscissa in Fig. 4 is the difference in temperature between the WAT for the oil and the experimental inlet temperature. The data are quite scattered due to the soft deposits formed. Fig. 5 shows the quantity Ž C1rm .U Ž EcrET . for the subject oil varies little with temperature. This is consistent with the experimental results in Fig. 4. The Simulation curve in Fig. 4 shows a trend with the oil temperature because the WAT is less than the 51.78C Ž1258F. oil temperature. The conclusion for this oil is that the deposition over 24 h does not depend on the changing initial temperature. This conclusion supports the idea of an oil specific deposition tendency discussed by Bern et al. w11x and Hsu and Brubaker w16x as a significant parameter for scaling laboratory deposition rates to field deposition rates.
Fig. 4. Effect of initial oil temperature.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
807
Fig. 5. Product of the diffusion constant and d crdT with oil temperature.
Fig. 6 shows the effect of flow rate on deposition rate. Five flow rates between 8 and 320 m3rday of oil were studied at a temperature difference of 8.38C Ž 158F. between the ‘glycol’ and oil and an oil inlet temperature of 40.558C Ž1058F.. The lowest two flow rates shown in Fig. 6 have Reynolds numbers less than 1000. The deposition rates for the three experiments at the highest flow rates are approximately the same for these 24-h tests. The Simulation results show deposition rates that have the inverse behavior of the measured data with increasing flow rate. Our data are consistent with earlier work by Hamouda and Davidsen w8x, Eaton and Weeter w9x and Grung w13x. This suggests either a different mechanism or that sloughing becomes an important consideration as flow rates increase. Fig. 7 shows the gross differences between turbulent and laminar deposition rates at similar temperature differences. This was indicated in Figs. 2 and 3 and confirms earlier reports w13x. The laminar case flow rate is one tenth that of the turbulent cases. We did not observe the deposit aging in laminar flow that had been reported earlier w8x. The turbulent flow tests produced a significantly harder deposit with a lower oil content after 120 h than the 24-h test. The 120-h turbulent flow deposit had to be melted or chipped from the test spool. The consistency of this deposit was similar to candle wax. We determined these deposits contained between 60 and 80% wax. This is consistent with Hunt’s w1x result. The deposit from the 24-h test at the same flow and deposition conditions was more like shoe polish and could be wiped from the test spool.
Fig. 6. Effect of flow rate on deposition.
808
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Fig. 7. Deposition as a function of time.
Fig. 8 examines the turbulent flow deposit vs. time data from Fig. 7 more closely. The computed deposit thickness from pressure drop and energy balance methods diverge after about 40 h. The energy balance thickness determination shows the deposit thinning with time whereas the pressure drop thickness determination is very slowly increasing. The pressure drop result has been confirmed with the ultrasonic device, the volume of wax technique Ž LDLD. , and physical observation. The decrease in the energy balance thickness can be attributed to changes in the deposit composition since the oil and paraffin in the deposit have different thermal conductivities. Our estimates are that the wax thermal conductivity is two to three times that of the oil. The insulation effect of the deposit is decreased with increasing wax content in the deposit, giving an indication that the apparent wax thickness is decreasing with time. The mechanism thought to be responsible for the aging is analogous to Ostwald ripening or the self organization of the wax molecules in the deposit. The proposed mechanism for wax hardening Ž a very slow process. based on this ripening process is as follows: Initially, wax is deposited as an agglomerate of many small crystals which have a large surface area relative to their volume. This primary deposition is relatively fast because wax precipitates at the pipeline wall from oil which has a relatively high supersaturation of precipitating species. Mass transport occurs mainly by convection
Fig. 8. Comparison of calculated wax thickness from pressure and temperature differences.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
809
Ži.e., by turbulence. and diffusion Ž through the thin laminar layer near the wall. . Because the supersaturation is high, solid wax will be thermodynamically more stable than dissolved wax, even for small wax crystals having a relatively large surface area. As a consequence, the ‘open’ wax initially deposited is mostly very small crystals with oil included in the pore spaces between the small wax crystals. Stated otherwise, because of the high supersaturation, ‘open’ wax crystals are formed in a regime in which the decrease in the bulk free energy Žper unit volume of deposited wax. associated with the conversion of dissolved wax into solid wax, is much larger than the increase in surface free energy Žper unit area of deposited wax. which is associated with the formation of a waxroil interface. Loosely stated, in this regime the crystals don’t care about the size of their interfacial area with the oil. After ‘open’ wax has been formed a much slower and much subtler process will occur. Wax deposition from the stagnant oil, included in the cavities of the open wax, will continue until the wax dissolved in the oil is in thermodynamic equilibrium with the solid wax deposit. However, if the oil is in thermodynamic equilibrium with a crystal having a small surfacervolume ratio Žfor example, a large compact crystal., then the oil is undersaturated in wax content with respect to a crystal having a large surfacervolume ratio Žfor example, a small porous crystal. . Wax from small and porous crystals will dissolve into the oil, which will subsequently deposit wax on larger crystals or fill the existing pores, thereby replacing some of the oil. This process will stop only after a solid layer of wax has been formed. Because differences in the crystal area only result in very small differences in supersaturation with respect to the oil, and also because mass transfer is diffusion controlled, the conversion of open wax into compact wax by Ostwald ripening can be an extremely slow process w17x. This is tenable since the time scale for initial crystal formation is fractions of seconds while the reorganization of the crystal is on the order of days. The diffusion of these species within the solid phase is slower than in the liquid phase, but does occur. The stochastically deposited paraffin should eventually reorganize into a lower energy lattice. The wax content of the deposit continued to increase at the expense of the thickness of the deposit. The only explanation for the ripening in the turbulent case and not the laminar case is the difference in the amount of heat that passes through the deposit per unit time in the turbulent case compared to the laminar case. The turbulent deposits are thinner and the flow and heat throughput for the system is about 10 times greater for the laminar case. Sloughing was also observed during the 120-h tests with the ultrasonic probe. The observations with the probe were almost continuous. The apparent thickness would drop to zero only to grow back to the long term magnitude over a period of 3–4 h. This happened three different days during the 120-h test. This is consistent with the observations of Hsu et al. w18x. One additional deposition test was performed with the oil and ‘glycol’ temperatures identical. This provided a zero point check and a test of the shear dispersion mechanism as a contributor to deposition. Hamouda and Davidsen w8x have shown that deposition under the zero heat flux condition does not occur. Tests were performed with the inlet oil and glycol temperature the same within experimental error. Some deposition was observed in the top part of the spool pieces when the operating temperature approached a temperature where the subject oil exhibited non-Newtonian flow. The test temperature was increased 13.98C Ž258F. and the experiment was repeated. Negligible deposition was observed. The first two cases reported were in laminar flow. One test was performed for turbulent flow conditions at the initial temperature. No deposition was observed in the turbulent case. It was concluded that the apparent deposition was caused by a temperature anomaly due to the
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
810
fine temperature controllers on the flow loop. The temperature at the wall in some parts of the flow loop is higher than the temperature at the centerline of the flow loop. Another potential problem is the gelling behavior of this crude below 26.78C Ž808F.. This gelling could give an apparent deposit that is actually gelled oil.
5. Conclusions 1. The greater the temperature difference between the oil and the wall, the greater the deposition rate. 2. The initial temperature of the oil does not significantly alter the deposition rate. The factor of C1rmU Žd crdT . is nearly constant with temperature variation. 3. The deposition rate decreases with increasing flow rate rather than increasing as indicated by present deposition simulation tools. 4. The oil content of the deposits in turbulent flow was significantly lower than the oil content of the deposits in laminar flow. 5. Deposit aging was observed and documented by the change in heat transfer characteristics of the deposit and the change in oil content of the deposits.
6. Nomenclature A c r f m D C1 k GM G h cp T V z r
Area, m2 Molar concentration, molesrm3 Radius, m Friction factor Viscosity, mPa sŽcP. Coefficient of diffusion, mrs 2 Diffusion constants DUm , cP mrs 2 Molar mass transfer coefficient, molesrm2 s Molar velocity, molesrm2 s Mass velocity, kgrs m2 Film heat transfer coefficient, Jrm2 s K Specific heat at constant pressure, Jrkg K Temperature, T, K Volume, m3 Distance, m Density, kgrm3
Subscripts i o p M w dep
ith component oil pressure moles wax deposit
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
811
Acknowledgements This work was supported by the member companies of the Tulsa University Paraffin Deposition JIP, which are: AGIP, Amoco, ARC, ARCO, BG, BHP, BP, Chevron, Conoco, DOE, ELF, Exxon, Fisher-Rosemount, GRI, JNOC, Kerr-McGee, Marathon, Micro Motion, MMS, Mobil, MSI, NalcoExxon, Natco, NKK, Norsk Hydro, ONGC, PEMEX, Petro-Canada, Petrolite, Petronas, Phillips, Robbins and Myers, Shell, Statoil, Texaco, Total, and Unocal. The authors wish to thank the Flow Loop and Deposition Studies Committee of the JIP for their valuable suggestions and Emmanuel Delle Case, Mandar Apte, and Bazlee Matzain for their helpful discussions.
References w1x B.E. Hunt Jr., Laboratory Study of Paraffin Deposition, SPE J. Pet. Technol., Ž1962. 1259–1269. w2x F.W. Jessen, J.N. Howell, Effect of Flow Rate on Paraffin Accumulation in Plastic, Steel, and Coated Pipe, Petroleum Trans., AIME Ž1958. 80–84. w3x C.B. Pate, MMSrDeepstar Workshop on Produced Fluids, Offshore Technology Conference, Houston, TX, May 4, 1995. w4x A. Matzain, Single Phase Liquid Paraffin Deposition Modeling, MS Thesis, The University of Tulsa, Tulsa, OK, 1996. w5x E.L. Cusssler, Diffusion; Mass Transfer in Fluid Systems, Cambridge Univ. Press, 1987. w6x O.B. Rygg, A.K. Rydahl, H.P. Ronnigsen, Wax Deposition in Offshore Pipeline Systems, BHRG Multiphase Technology Conference, Banff, Alberta, Canada, June 9–11, 1998. w7x R.H. Perry, C.H. Chilton, Chemical Engineer’s Handbook, 5th edn., McGraw-Hill, 1973. w8x A.A. Hamouda, S. Davidsen, An Approach for Simulation of Paraffin Deposition in Pipelines as a Function of Flow Characteristics With a Reference to Teesside Oil Pipeline, SPE 28966, SPE International Symposium on Oilfield Chemistry, San Antonio, TX, February 14–17 Ž1995.. w9x P.E. Eaton, G.Y. Weeter, Paraffin Deposition in Flow Lines, 76-CSMErCSChE -22, 16th National Heat Transfer Conference, St. Louis, MO, August 8–11 Ž1976.. w10x E.D. Burger, T.K. Perkins, J.H. Striegler, Studies of Wax Deposition in the Trans Alaska Pipeline, SPE J. Pet. Technol., Ž1981. 1075. w11x P.A. Bern, V.R. Withers, R.J.R. Cairns, Wax Deposition in Crude Oil Pipelines, EUR 206, 1980 European Offshore Petroleum Conference and Exhibition, London, England, Oct. 21–24. w12x J.S. Weingarten, J.A. Euchner, Methods for Predicting Wax Precipitation and Deposition, SPE J. Production Eng. Ž1988. 121–126. w13x K.E. Grung, Norsk Hydro’s Collaborative Studies for Multiphase Production Systems Related to Produced Fluid Properties Strategy for Wax Studies, Deepstar 900 Meeting, ARCO E&P, Plano, TX, October 27 Ž1995.. w14x X.T. Chen, T.M. Butler, M. Volk, J.P. Brill, Techniques for Measuring Wax Thickness During Single and Multiphase Flow, SPE 38773, SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 5–8 Ž1997.. w15x T.S. Brown, V.G. Niesen, D.D. Erickson, Measurement and Prediction of the Kinetics of Paraffin Deposition, SPE 26548, SPE Annual Technical Conference and Exhibition, Houston, TX, Oct. 3–6 Ž1993.. w16x J.J.C. Hsu, J.P. Brubaker, Wax Deposition Scale-Up Modeling for Waxy Crude Production Lines, OTC 7778, 1995 Offshore Technology Conference, Houston, TX, May 1–4. w17x Ulfert Klomp, personal communication, Oct. 21, 1997. w18x J.J.C. Hsu, M.M. Santamaria, J.P. Brubaker, Wax Deposition of Waxy Live Crudes under Turbulent Flow Conditions, SPE 28480, SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 25–28 Ž1994..
Wax deposition in single phase flow J.L. Creek a
a, )
, Hans Jacob Lund b , James P. Brill
b,1
, Mike Volk
b
Department of Physical and Chemical Measurements, CheÕron Petroleum Technology, 1300 Beach BouleÕard, La Habra, CA, 90631-6374 USA b Department of Petroleum Engineering, UniÕersity of Tulsa, 600 S. College AÕenue, Tulsa, OK 74104 USA Received 22 March 1998; accepted 18 December 1998
Abstract A series of experiments on wax deposition from oil have been performed in a 50-m long by 43.4 mm ID jacketed flow loop at Tulsa University. Tests were performed on a 358API crude oil from the Gulf of Mexico with a wax appearance temperature ŽWAT. of 1208F. The series of tests were designed to determine temperature and flow rate effects on the deposition rate and fraction of oil in the deposit. The deposit thickness in the flow loop was determined using five methods; pressure difference, energy balance, the spool piece volume change ŽLDLD., ultrasonic transit time, and direct measurement in a test section. Samples of the deposits were analyzed at the conclusion of each test for included oil. The effect of the difference in temperature between the oil and pipe wall showed a simple increasing deposition rate with temperature difference. The change in deposition rate was a weak function of oil temperature relative to WAT. The variation in deposition rate with flow velocity gave large differences between laminar and turbulent flow. Deposit oil contents decreased with increasing flow velocity. The fraction of oil in the deposit decreased with time in turbulent flow tests but did not change in laminar tests. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Data; Diffusion coefficient; Solid–fluid equilibria
1. Introduction New petroleum production horizons at water depths greater than 500 m have driven industry to discover new technologies for preventing and controlling the deposition of petroleum wax. Traditional methods of management, prevention, and remediation have been established for many years w1,2x. The
) 1
Corresponding author. Tel.: q1-562-694-7664; fax: q1-592-684-7565; e-mail: [email protected] E-mail: [email protected].
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 0 6 - 5
802
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
greater water depths mean lower temperatures, and longer and fewer production lines available in deeper water make economic solutions to prevention, management, and remediation key to economic development of these new deep water resources. It has been shown for example that the cost of remediation increases with water depth to the extent that the cost is on the order of $200,000 when the depth is 100 m, but on the order of $1,000,000 when the remediation occurs in depths near 400 m. The cost is proportionally greater as development depth increases w3x. The Tulsa University Fluid Flow Projects on Wax Deposition is a Joint Industry Project Ž JIP. comprised of a research staff at the University of Tulsa and 37 oil and gas companies and government agencies. The purpose of the JIP is to study wax deposition in multiphase flowing petroleum systems. Prerequisite to multiphase testing is a thorough understanding of deposition from single phase flow. This work reports the experimental program and results of single phase deposition experiments for a Gulf of Mexico crude oil. A single phase flow facility was donated to the JIP by the Alberta Research Council and Petro-Canada. A series of experiments have been performed in the 50-m long by 43.4-mm internal diameter ŽID. jacketed single phase flow loop after the loop was installed and refurbished at the University of Tulsa. Key features of the facility are temperature and pressure measurement stations every 5 m along the flow loop, a glycol-water filled temperature control jacket over the full 50-m length of the loop, and mass flow meters to determine the flow of fluid and coolant. The loop is configured as a horizontal ‘U’ tube with two removable test sections Žspools.. One is located 20 m from the entrance and a second 5 m from the end of the flow loop. An experimental program has been executed to gain an understanding of wax deposition from single phase flow prior to experimentation on deposition from multiphase flow. A thorough review of the existing literature on the theory of deposition from single phase flow has been reported by Matzain w4x. Fig. 1 shows a schematic problem description. The general consensus of the petroleum industry is that once a radial temperature gradient is established between the oil and pipe wall, and the oil temperature is below the wax appearance temperature Ž WAT. of the oil, deposition occurs. The solubility of paraffin in the oil is a single valued decreasing function of temperature. The difference in the temperature between the oil and pipe wall produces a composition gradient corresponding to solubility of paraffin species in oil. This gradient results in an imbalance in the chemical potential and hence a Fick’s law mass flow.
Fig. 1. Pipeline deposition scenario.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
803
According to Cussler w5x, Fick’s law states that the flux Ji of diffusing species in a given volume is related to the concentration gradient by a diffusion constant Di . Ji s ADi Ec irE z . Ž1. Rygg et al. w6x have taken Eq. Ž1. and related the volume of diffusing species into the deposition zone for a multi-component system to the volume of deposit as Vdep s Ž 2p rL . Ý Ž Di MWr i r i .Ž Ec irET . ETrEr
4
Ž2.
i
where r the radius has been substituted for z and the deposit area is given by 2p rL, Di is the diffusion coefficient, c i is the concentration of species i in moles per unit volume, MWi and r i are the molecular weight and the density of species i. We propose that deposition occurs in the laminar boundary layer for turbulent flow and in the low velocity ‘boundary’ in laminar flow. An initial soft deposit is formed through relief of the local supersaturation of the wax species in solution. The size of the deposit depends in part on the thickness of the boundary because of the mechanical strength of the deposit. We also propose that the deposit further rearranges and hardens with time to the deposits recovered from pipelines. Examination of Eq. Ž2. shows two quantities that need to be tested if this equation is correct. The first of these is effectively heat flux which is related to w ETrEr x and the second depends only on the fluid being tested, Ý i Di Ž Ec irET . . The available correlations for predicting diffusion coefficients are suited for binary mixtures only. Cussler w5x describes the difficulty in predicting the diffusion coefficients for multicomponent mixtures. A second reason for concern over the diffusion coefficient for the system is that classical mass diffusion is an isothermal, quiescent process that may not directly apply for flowing, non-isothermal systems. The deposition scenario is a non-isothermal flowing system and appears to be driven by the heat flow term, w ETrEr x. The appropriate flux coefficient may be a combination of mass and thermal diffusion. This conclusion is reasonable when one considers the close similarity among the transfers of mass, heat, and momentum. This is summarized by the Reynolds Analogy, which states that when heat, mass, and momentum are supplied to the fluid in corresponding ways the resulting rates of transfer relative to the corresponding driving force are equivalent for all three forces. Perry and Chilton w7x have summarized this in Eq. Ž 3. as krG M s hrc p G s fr2 Ž3. where k is the molar mass transfer coefficient, G M is the molar velocity, h is the heat transfer coefficient, c p is the specific heat, G is the mass velocity, and f is the friction factor. This is illustrated in Fig. 1. The temperature difference leads to a concentration gradient through differential solubility of wax components in the oil. This in turn leads to a chemical potential driving force but can also leads to a thermal diffusion driving force. The term Ý i Di , the diffusion coefficient is usually ‘fitted’ to experimental data w4x. 2. Test program The first portion of the test program is to confirm the performance of the test facility and also confirm known results. The second part was used to study the effects of flow and time on wax deposition. The first series of tests were conducted to verify that the temperature gradient factor in
804
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Eq. Ž2., w ETrEr x should be directly proportional to the deposition rate. This was studied by varying the temperature difference between the oil and jacket glycol under both laminar and turbulent conditions for temperature differences from 8.3 Ž158F. to 258C Ž458F. . The second series of tests were conducted to determine the effect of oil temperature on the deposition rate. In this part of the work the temperature difference between the oil and glycol-water jacket fluid was maintained at 8.38C Ž158F. while the oil temperature varied from a few degrees about the WAT of 48.88C Ž 1208F. to 29.48C Ž858F. . These experiments were designed to test the sensitivity of deposition rate to the Dwd crdT x term in Eq. Ž2. . Hamouda and Davidsen w8x, and Eaton and Weeter w9x have clearly shown that the shear dispersion mechanism discussed previously by Burger et al. w10x, Bern et al. w11x, and Weingarten and Euchner w12x is not significant. We verified that deposition through shear dispersion did not contribute to our system. A more interesting result of these two studies w8,9x was the variation of deposition rate with flow rate. Similar results were presented by Grung w13x in 1995. We, therefore, included a series of tests to attempt to quantify the effect of flow rate on deposition rate. The last area studied arose from the earlier work of Hunt w1x who indicated that the fraction of wax in the deposit increased with time from about 20% for experiments on the order of a day to near 60% for tests lasting several hundred hours. Eaton and Weeter w9x reported that deposits that were initially gelled oil became hard over a 240-h deposition period for rotational velocities that correspond to laminar flow. Tests were included to study the effect of deposit aging for both laminar and turbulent flow by conducting tests for both 24 and 120 h. 3. Description of experiments Tests were performed on a 358API crude oil from the Gulf of Mexico donated by the Mobil Oil Corporation. The WAT for the subject oil was 48.898C Ž1208F.. The experiments were performed in the flow loop described in Section 1. A 50:50 water–ethylene glycol mixture was circulated in a thermostatic jacket fluid counter current to the oil flow. Temperature and pressure taps were located at the entrance and exit of the flow loop as well as every 5 m along the flow loop. The oil and glycol–water Ž ‘glycol’. coolant flow rates were determined with mass flow meters. The pressure and temperature for the oil and the temperature of the glycol were determined at each measurement station located at 5-m intervals along the flow loop. The magnitude of the deposit in the flow loop could be determined using five methods; pressure difference, energy balance based on temperature difference, internal volume changes in the test sections Ž LDLD., ultrasonic transit time, and direct measurement. A thorough discussion of these deposit determination techniques is given elsewhere w14x. The ultrasonic deposition measurement device was the result of a joint effort among Norsk Hydro Research and Christian Michelsen Research of Bergen Norway and Chevron Petroleum Technology Company. The device tested was a prototype based on the speed of sound and will not be discussed here. Samples of the deposits from each spool piece were collected and analyzed at the conclusion of each test to determine the included oil content of the deposit. The fraction of included oil present in the deposit was determined by high temperature gas chromatography. Samples of each deposit were dissolved in carbon disulfide and injected into a high temperature gas chromatograph. The weight percent paraffin was determined for each sample. Comparison of the deposit analysis with the original oil analysis gave the oil fraction in the deposit.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
805
4. Discussion of results The first target of the study was the effect of the temperature difference between the oil and the pipe wall. This is conveniently represented as the difference in the temperatures of the oil and the ‘glycol’ as they enter the flow loop. The results of this series of tests are given in Fig. 2 for laminar flow and Fig. 3 for turbulent flow. The wax thickness was difficult to determine, even with the number of techniques used. The laminar flow deposits were extremely soft and were found to contain typically from 80% to 90% oil by weight. These deposits had the consistency of gelatin with imbedded wax crystals. It was noted that in one case after a shut down, starting the pumps sheared off the deposit. The shearing off of the deposit was also observed when the flow rate was increased from 24 to 240 m3 of oil per day. Notice also that the thickness determined by removing the test spools and measuring the spool volume with water ŽLDLD. are much lower than the results of other techniques. The softness of this deposit in the laminar flow case could cause deposit loss when the oil is removed from the loop prior to removing the test spools. The deposit from the greatest temperature difference between the ‘glycol’ and oil also gives among the softest deposits. This could possibly account for the apparent maximum in the laminar deposition case shown in Fig. 2. Earlier tests at similar conditions gave a deposit that did not have enough mechanical strength to support itself without the oil being present in the spool piece. The line termed Simulation in the figures was computed with a deposition simulator prepared by T.S. Brown of Multiphase Solutions, Inc. This simulator, based on his earlier work w15x, was optimized to simulate the flow loop used in these tests. The effect of Ž ETrEr . for the turbulent flow tests is shown in Fig. 3. A linear increase of deposit thickness with temperature difference can be seen in Fig. 3. The turbulent flow deposits had a consistency similar to ‘shoe polish.’ These deposits were strong compared to the very soft laminar deposits. The deposits formed at the higher temperature differences are softer than those formed at smaller temperature differences. This is thought to be caused by a greater concentration of high molecular weight species in these deposits since the actual minimum temperature of deposition is higher and lower melting species are not precipitated at the pipe wall. An error analysis of the deposit measurement techniques has shown that the ‘energy balance’ method was more appropriate for laminar flow conditions and the pressure difference method was
Fig. 2. Effect of temperature difference between oil and wall for laminar flow.
806
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Fig. 3. Effect of temperature difference between oil and wall for turbulent flow.
more appropriate for the turbulent flow tests. The deposition in turbulent flow was far less than for laminar flow which is in agreement with Grung w13x. The deposition simulator did capture the general trend of the experimental data. Fig. 4 shows the effect of initial oil temperature on deposition rate. These tests were conducted under laminar flow conditions with an 8.38C Ž158F. temperature difference between the oil and ‘glycol.’ The abscissa in Fig. 4 is the difference in temperature between the WAT for the oil and the experimental inlet temperature. The data are quite scattered due to the soft deposits formed. Fig. 5 shows the quantity Ž C1rm .U Ž EcrET . for the subject oil varies little with temperature. This is consistent with the experimental results in Fig. 4. The Simulation curve in Fig. 4 shows a trend with the oil temperature because the WAT is less than the 51.78C Ž1258F. oil temperature. The conclusion for this oil is that the deposition over 24 h does not depend on the changing initial temperature. This conclusion supports the idea of an oil specific deposition tendency discussed by Bern et al. w11x and Hsu and Brubaker w16x as a significant parameter for scaling laboratory deposition rates to field deposition rates.
Fig. 4. Effect of initial oil temperature.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
807
Fig. 5. Product of the diffusion constant and d crdT with oil temperature.
Fig. 6 shows the effect of flow rate on deposition rate. Five flow rates between 8 and 320 m3rday of oil were studied at a temperature difference of 8.38C Ž 158F. between the ‘glycol’ and oil and an oil inlet temperature of 40.558C Ž1058F.. The lowest two flow rates shown in Fig. 6 have Reynolds numbers less than 1000. The deposition rates for the three experiments at the highest flow rates are approximately the same for these 24-h tests. The Simulation results show deposition rates that have the inverse behavior of the measured data with increasing flow rate. Our data are consistent with earlier work by Hamouda and Davidsen w8x, Eaton and Weeter w9x and Grung w13x. This suggests either a different mechanism or that sloughing becomes an important consideration as flow rates increase. Fig. 7 shows the gross differences between turbulent and laminar deposition rates at similar temperature differences. This was indicated in Figs. 2 and 3 and confirms earlier reports w13x. The laminar case flow rate is one tenth that of the turbulent cases. We did not observe the deposit aging in laminar flow that had been reported earlier w8x. The turbulent flow tests produced a significantly harder deposit with a lower oil content after 120 h than the 24-h test. The 120-h turbulent flow deposit had to be melted or chipped from the test spool. The consistency of this deposit was similar to candle wax. We determined these deposits contained between 60 and 80% wax. This is consistent with Hunt’s w1x result. The deposit from the 24-h test at the same flow and deposition conditions was more like shoe polish and could be wiped from the test spool.
Fig. 6. Effect of flow rate on deposition.
808
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
Fig. 7. Deposition as a function of time.
Fig. 8 examines the turbulent flow deposit vs. time data from Fig. 7 more closely. The computed deposit thickness from pressure drop and energy balance methods diverge after about 40 h. The energy balance thickness determination shows the deposit thinning with time whereas the pressure drop thickness determination is very slowly increasing. The pressure drop result has been confirmed with the ultrasonic device, the volume of wax technique Ž LDLD. , and physical observation. The decrease in the energy balance thickness can be attributed to changes in the deposit composition since the oil and paraffin in the deposit have different thermal conductivities. Our estimates are that the wax thermal conductivity is two to three times that of the oil. The insulation effect of the deposit is decreased with increasing wax content in the deposit, giving an indication that the apparent wax thickness is decreasing with time. The mechanism thought to be responsible for the aging is analogous to Ostwald ripening or the self organization of the wax molecules in the deposit. The proposed mechanism for wax hardening Ž a very slow process. based on this ripening process is as follows: Initially, wax is deposited as an agglomerate of many small crystals which have a large surface area relative to their volume. This primary deposition is relatively fast because wax precipitates at the pipeline wall from oil which has a relatively high supersaturation of precipitating species. Mass transport occurs mainly by convection
Fig. 8. Comparison of calculated wax thickness from pressure and temperature differences.
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
809
Ži.e., by turbulence. and diffusion Ž through the thin laminar layer near the wall. . Because the supersaturation is high, solid wax will be thermodynamically more stable than dissolved wax, even for small wax crystals having a relatively large surface area. As a consequence, the ‘open’ wax initially deposited is mostly very small crystals with oil included in the pore spaces between the small wax crystals. Stated otherwise, because of the high supersaturation, ‘open’ wax crystals are formed in a regime in which the decrease in the bulk free energy Žper unit volume of deposited wax. associated with the conversion of dissolved wax into solid wax, is much larger than the increase in surface free energy Žper unit area of deposited wax. which is associated with the formation of a waxroil interface. Loosely stated, in this regime the crystals don’t care about the size of their interfacial area with the oil. After ‘open’ wax has been formed a much slower and much subtler process will occur. Wax deposition from the stagnant oil, included in the cavities of the open wax, will continue until the wax dissolved in the oil is in thermodynamic equilibrium with the solid wax deposit. However, if the oil is in thermodynamic equilibrium with a crystal having a small surfacervolume ratio Žfor example, a large compact crystal., then the oil is undersaturated in wax content with respect to a crystal having a large surfacervolume ratio Žfor example, a small porous crystal. . Wax from small and porous crystals will dissolve into the oil, which will subsequently deposit wax on larger crystals or fill the existing pores, thereby replacing some of the oil. This process will stop only after a solid layer of wax has been formed. Because differences in the crystal area only result in very small differences in supersaturation with respect to the oil, and also because mass transfer is diffusion controlled, the conversion of open wax into compact wax by Ostwald ripening can be an extremely slow process w17x. This is tenable since the time scale for initial crystal formation is fractions of seconds while the reorganization of the crystal is on the order of days. The diffusion of these species within the solid phase is slower than in the liquid phase, but does occur. The stochastically deposited paraffin should eventually reorganize into a lower energy lattice. The wax content of the deposit continued to increase at the expense of the thickness of the deposit. The only explanation for the ripening in the turbulent case and not the laminar case is the difference in the amount of heat that passes through the deposit per unit time in the turbulent case compared to the laminar case. The turbulent deposits are thinner and the flow and heat throughput for the system is about 10 times greater for the laminar case. Sloughing was also observed during the 120-h tests with the ultrasonic probe. The observations with the probe were almost continuous. The apparent thickness would drop to zero only to grow back to the long term magnitude over a period of 3–4 h. This happened three different days during the 120-h test. This is consistent with the observations of Hsu et al. w18x. One additional deposition test was performed with the oil and ‘glycol’ temperatures identical. This provided a zero point check and a test of the shear dispersion mechanism as a contributor to deposition. Hamouda and Davidsen w8x have shown that deposition under the zero heat flux condition does not occur. Tests were performed with the inlet oil and glycol temperature the same within experimental error. Some deposition was observed in the top part of the spool pieces when the operating temperature approached a temperature where the subject oil exhibited non-Newtonian flow. The test temperature was increased 13.98C Ž258F. and the experiment was repeated. Negligible deposition was observed. The first two cases reported were in laminar flow. One test was performed for turbulent flow conditions at the initial temperature. No deposition was observed in the turbulent case. It was concluded that the apparent deposition was caused by a temperature anomaly due to the
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
810
fine temperature controllers on the flow loop. The temperature at the wall in some parts of the flow loop is higher than the temperature at the centerline of the flow loop. Another potential problem is the gelling behavior of this crude below 26.78C Ž808F.. This gelling could give an apparent deposit that is actually gelled oil.
5. Conclusions 1. The greater the temperature difference between the oil and the wall, the greater the deposition rate. 2. The initial temperature of the oil does not significantly alter the deposition rate. The factor of C1rmU Žd crdT . is nearly constant with temperature variation. 3. The deposition rate decreases with increasing flow rate rather than increasing as indicated by present deposition simulation tools. 4. The oil content of the deposits in turbulent flow was significantly lower than the oil content of the deposits in laminar flow. 5. Deposit aging was observed and documented by the change in heat transfer characteristics of the deposit and the change in oil content of the deposits.
6. Nomenclature A c r f m D C1 k GM G h cp T V z r
Area, m2 Molar concentration, molesrm3 Radius, m Friction factor Viscosity, mPa sŽcP. Coefficient of diffusion, mrs 2 Diffusion constants DUm , cP mrs 2 Molar mass transfer coefficient, molesrm2 s Molar velocity, molesrm2 s Mass velocity, kgrs m2 Film heat transfer coefficient, Jrm2 s K Specific heat at constant pressure, Jrkg K Temperature, T, K Volume, m3 Distance, m Density, kgrm3
Subscripts i o p M w dep
ith component oil pressure moles wax deposit
J.L. Creek et al.r Fluid Phase Equilibria 158–160 (1999) 801–811
811
Acknowledgements This work was supported by the member companies of the Tulsa University Paraffin Deposition JIP, which are: AGIP, Amoco, ARC, ARCO, BG, BHP, BP, Chevron, Conoco, DOE, ELF, Exxon, Fisher-Rosemount, GRI, JNOC, Kerr-McGee, Marathon, Micro Motion, MMS, Mobil, MSI, NalcoExxon, Natco, NKK, Norsk Hydro, ONGC, PEMEX, Petro-Canada, Petrolite, Petronas, Phillips, Robbins and Myers, Shell, Statoil, Texaco, Total, and Unocal. The authors wish to thank the Flow Loop and Deposition Studies Committee of the JIP for their valuable suggestions and Emmanuel Delle Case, Mandar Apte, and Bazlee Matzain for their helpful discussions.
References w1x B.E. Hunt Jr., Laboratory Study of Paraffin Deposition, SPE J. Pet. Technol., Ž1962. 1259–1269. w2x F.W. Jessen, J.N. Howell, Effect of Flow Rate on Paraffin Accumulation in Plastic, Steel, and Coated Pipe, Petroleum Trans., AIME Ž1958. 80–84. w3x C.B. Pate, MMSrDeepstar Workshop on Produced Fluids, Offshore Technology Conference, Houston, TX, May 4, 1995. w4x A. Matzain, Single Phase Liquid Paraffin Deposition Modeling, MS Thesis, The University of Tulsa, Tulsa, OK, 1996. w5x E.L. Cusssler, Diffusion; Mass Transfer in Fluid Systems, Cambridge Univ. Press, 1987. w6x O.B. Rygg, A.K. Rydahl, H.P. Ronnigsen, Wax Deposition in Offshore Pipeline Systems, BHRG Multiphase Technology Conference, Banff, Alberta, Canada, June 9–11, 1998. w7x R.H. Perry, C.H. Chilton, Chemical Engineer’s Handbook, 5th edn., McGraw-Hill, 1973. w8x A.A. Hamouda, S. Davidsen, An Approach for Simulation of Paraffin Deposition in Pipelines as a Function of Flow Characteristics With a Reference to Teesside Oil Pipeline, SPE 28966, SPE International Symposium on Oilfield Chemistry, San Antonio, TX, February 14–17 Ž1995.. w9x P.E. Eaton, G.Y. Weeter, Paraffin Deposition in Flow Lines, 76-CSMErCSChE -22, 16th National Heat Transfer Conference, St. Louis, MO, August 8–11 Ž1976.. w10x E.D. Burger, T.K. Perkins, J.H. Striegler, Studies of Wax Deposition in the Trans Alaska Pipeline, SPE J. Pet. Technol., Ž1981. 1075. w11x P.A. Bern, V.R. Withers, R.J.R. Cairns, Wax Deposition in Crude Oil Pipelines, EUR 206, 1980 European Offshore Petroleum Conference and Exhibition, London, England, Oct. 21–24. w12x J.S. Weingarten, J.A. Euchner, Methods for Predicting Wax Precipitation and Deposition, SPE J. Production Eng. Ž1988. 121–126. w13x K.E. Grung, Norsk Hydro’s Collaborative Studies for Multiphase Production Systems Related to Produced Fluid Properties Strategy for Wax Studies, Deepstar 900 Meeting, ARCO E&P, Plano, TX, October 27 Ž1995.. w14x X.T. Chen, T.M. Butler, M. Volk, J.P. Brill, Techniques for Measuring Wax Thickness During Single and Multiphase Flow, SPE 38773, SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 5–8 Ž1997.. w15x T.S. Brown, V.G. Niesen, D.D. Erickson, Measurement and Prediction of the Kinetics of Paraffin Deposition, SPE 26548, SPE Annual Technical Conference and Exhibition, Houston, TX, Oct. 3–6 Ž1993.. w16x J.J.C. Hsu, J.P. Brubaker, Wax Deposition Scale-Up Modeling for Waxy Crude Production Lines, OTC 7778, 1995 Offshore Technology Conference, Houston, TX, May 1–4. w17x Ulfert Klomp, personal communication, Oct. 21, 1997. w18x J.J.C. Hsu, M.M. Santamaria, J.P. Brubaker, Wax Deposition of Waxy Live Crudes under Turbulent Flow Conditions, SPE 28480, SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 25–28 Ž1994..