Energy & Fuels 2006, 20, 2531-2536
2531
Flow Behavior of Daqing Waxy Crude Oil under Simulated Pipelining Conditions Jianlin Ding,† Jinjun Zhang,*,†,‡ Hongying Li,†,‡ Fan Zhang,†,‡ and Xiaojing Yang†,‡ Department of Petroleum Storage and Transportation, China UniVersity of PetroleumsBeijing, China, and Beijing Key Laboratory of Urban Oil and Gas Distribution Technology ReceiVed April 6, 2006. ReVised Manuscript ReceiVed July 24, 2006
Daqing oilfield is the largest oilfield in China. This crude oil is a typical waxy crude oil, with a wax content of 26% and a gel point of 32 °C. Flow behaviors of waxy crude oils at temperatures near the gel point/pour point are vital for both pipeline hydraulic calculation and evaluation on restartability of a shutdown pipeline. In this study, experimental simulation was conducted by using a stirred vessel with the energy dissipation of viscous flow as the shear simulation parameter. Crude oil specimens were taken from the stirred vessel at different temperatures during flow simulation, and the DSC (differential scanning calorimetry) curves and rheological properties, such as viscosity, gel point, yield stress, and thixotropy, were measured. The viscosity under simulated pipelining conditions was found to be much less than that measured under quiescent cooling conditions, and the gel point decreased with decreasing temperature of sampling, i.e., the end temperature of the dynamic cooling process. The DSC curves of crude oil specimen captured at different sampling temperatures and from different positions such as the bulk of crude oil and the wall of the stirred vessel showed no difference, which indicated the depletion of wax due to wax deposition during the shear simulation was not responsible for viscosity and gel point reduction in the dynamic cooling measurement. Therefore, this reduction is attributed to shear disturbance on the developing wax crystal structure, called the shear history effect. At sampling temperatures above 35 °C, which is 3 °C above the gel point measured under quiescent cooling conditions, both the yield stresses and the thixotropic parameters showed little dependence on the shear history. However, at lower sampling temperatures, remarkable shear history dependence was found. Empirical correlations were developed between the yield stress and the sampling temperature as well as the measurement temperature and between the thixotropic parameters and the sampling temperature. These correlations provide not only quantitative information on the shear history effect of waxy crude but also accurate rheological properties for assessment of the operation state and restartability of pipelines transporting this crude oil.
1. Introduction The Daqing oilfield is the largest oilfield in China. Crude oil annually produced in this oilfield has been about 50 million tons, accounting for about one-third of China’s total crude oil production. This crude oil is a typical waxy crude oil, with a wax content of 26%, a wax appearance temperature (WAT) of 43 °C, and a gel point of ∼32 °C. It is known that, at temperatures above the WAT, wax is dissolved into the crude oil as molecules and the wax crude behaves as a Newtonian fluid. However, at temperatures below the WAT, with precipitation of more and more wax crystals, the crude oil changes from the Newtonian to the non-Newtonian fluid at a temperature called the abnormal temperature1 and exhibits complex rheological behaviors such as pseudoplasticity, thixotropy, yield stress, and viscoelasticity as the oil cools. When 2% to 3% of wax is crystallized, a spongy structure of wax crystals will form and the crude oil undergoes gelation.2-4 For pipeline transportation, the apparent viscosity/rheological model, thixotropic model, and yield stress as well as the gel point/ pour point are of great importance to both pipeline hydraulic * Corresponding author. Tel./Fax: 86-10-89734627. E-mail: zhangjj@ cup.edu.cn. † China University of PetroleumsBeijing. ‡ Beijing Key Laboratory of Urban Oil and Gas Distribution Technology. (1) Yan, D.; Luo, Z. Rheological properties of Daqing crude oil and their application in pipeline transportation. SPE Prod. Eng. 1987, 11, 267-276.
calculation and evaluation on restartability of a shutdown pipeline. It is also known that the flow behaviors of wax crude oils are also characterized by their shear and thermal history dependence, called the shear and thermal history effect.5-9 This effect is mainly shown at temperatures below the abnormal temperature. This shear and thermal effect can be attributed to the effect of shear and heating/cooling on the morphology and (2) Holder, G. A.; Winkler, J. Wax crystallization from distillate fuels. J. Inst. Pet. 1965, 5, 228-252. (3) Rønningsen, H. P.; Bjφrndal, B.; Hansen, A. B.; Pedersen, W. B. Wax precipitation from North Sea crude oils: 1. Crystallization and dissolution temperatures, and Newtonian and non-Newtonian flow properties. Energy Fuels 1991, 5, 895-908. (4) Li, H.; Zhang, J.; Yan, D. Correlations between the pour point/gel point and the amount of precipitated wax for waxy crudes. Pet. Sci. Technol. 2005, 23, 1313-1322 (5) Wardhaugh, L. T.; Boger, D. V. Flow characteristics of waxy crude oils: application to pipeline design. AIChE J. 1991, 37, 871-885. (6) Matveenko, V. N.; Kirsanov, E. A.; Remisov, S. V. Rheology of highly paraffinaceous crude oil. Colloids Surf., A 1995, 101, 1-7. (7) El-Gamal, I. M.; Gad, E. A. M. Low-temperature rheological behavior of Umbarka waxy crude and influence of flow improver. Colloids Surf., A 1998, 131, 181-191. (8) El-Gamal, I. M. Combined effects of shear and flow improvers: The optimum solution for handling waxy crudes below pour point. Colloids Surf., A 1998, 135, 283-291. (9) Chanda, D.; Sarmah, A.; Borthakur, A.; Rao, K. V.; Subrahmanyam, B.; Das, H. C. Combined effect of asphaltenes and flow improvers on the rheological behaviour of Indian waxy crude oil. Fuel 1998, 77, 11631167.
10.1021/ef060153t CCC: $33.50 © 2006 American Chemical Society Published on Web 09/26/2006
2532 Energy & Fuels, Vol. 20, No. 6, 2006
Ding et al.
structure of wax crystals.3,10,11 Wardhaugh and Boger5 studied the shear history effect of waxy crude oils and suggested a socalled locus of equilibrium viscosities to replace the rheological model in hydraulic calculations of steadily operating pipelines. Recently, Kane´ et al.11 studied the relation between rheology and structure of waxy crude oils cooled under quiescent and shearing conditions. However, few studies to establish a quantitative relation between the rheological parameters and the shear history of a waxy crude oil, which is necessary for pipeline hydraulic calculation, have been published. The objective of this study was to investigate, under conditions of simulated pipeline flow, the effect of shear history on flow behaviors of the Daqing crude oil, including the gel point, the apparent viscosity, the yield stress, and the thixotropic model, to provide quantitative rheological information for assessment of the operation state and restartability of pipelines transporting this crude oil.
φ ) Kγ˘ n+1
where K is the consistency coefficient, Pa‚sn, and n is the flow behavior index. On the basis of this consideration, the energy dissipation, which is the amount of energy dissipated in a flow process or over a period of time due to the viscous force and is usually easily calculated for most of flow processes, could be an ideal parameter for shear simulation and has been verified for waxy crude oils beneficiated with pour-point-depressants.12 The energy dissipation in flowing through a distance of pipeline is actually the frictional pressure drop across this section of pipeline. In practice, the controlled parameter in shear simulation is the average shear rate, which can be calculated based on the relationship between the shear rate and the energy dissipation rate. For pipe flow of the power-law fluid, the average shear rate is as follows,13,14
2. Theoretical Basis for Pipeline Flow Simulation It is well-known that, in pipe flow, the shear rate varies with the radius position, with the shear rate being maximal at the pipe wall and zero at the center. Besides, the profile of shear rate across the section of a pipe varies for different fluids, Newtonian and non-Newtonian. To simulate the shear history experienced by each layers of fluid flowing at different radius positions, Wardhaugh and Boger5 sheared the crude oil specimen with a constant shear rate in each experiment but varied the shear rate in different experiments by using the rotational rheometer, to obtain equilibrium non-Newtonian viscosities corresponding to various shear histories (shear rate) at different radius positions, and to further form the locus of equilibrium viscosities. This method may be valid for pure laminar flow in straight pipes. However, most crude oil pipelines are operated in turbulent flow. For this case, they suggested use of shear rate at the pipe wall for shear simulation. But one should note that, in turbulent flow, fluid particles moves chaotically. Shearing the crude oil with the shear rate at the pipe wall, which is the maximum shear rate within the pipe, is obviously unreasonable and makes the oil oversheared. Essentially, the effect of shear on structure of fluids depends not only on the rate of shear but also on the shear stress. The energy dissipation rate in fluid mechanics is such a quantity that combines these two factors. It is defined as
(3)
γ˘ )
( ) 2fFV h3 Kd
1/n + 1
(4)
where f is the Fanning friction factor; F is the density of the fluid, kg/m3; V h is the cross-sectional average velocity of the fluid, m/s; and d is the diameter of the pipeline. Equation 4 is valid for both laminar and turbulent flows. 3. Experimental Section 3.1. Shear-Simulation Device. A tight stainless steel cylindrical tank with the inner diameter of 200 mm and the height of 265 mm was used for shear simulation. Temperature of the crude oil sample was controlled by a HAAKE C25P water bath. The crude oil was stirred by a four-blade propeller with a diameter of 140 mm. Figure 1 shows a sketch of the shearsimulation device. The average shear rate in stirred vessels can also be determined based on the same principle of relation between the shear rate and the energy dissipation rate.15 In our case, the average shear rate of the fluid in the shear simulation vessel was calibrated as
γ˘ ) 0.468 49N1.3993K-0.4182n - 1.8822V-0.3795 (1.5 L < V < 5.0 L) (5)
where τ is the shear stress and γ˘ is the shear rate. This is valid for both Newtonian and non-Newtonian fluids. For the powerlaw fluids, according to eq 2, one yields
where N is the speed of agitation, r/min, and V is the volume of fluid in the vessel, L. 3.2. Basic Data for Simulation. The Tieling-Dalian pipeline transporting Daqing crude oil was simulated in this study. Parameters of the simulated pipeline were as follows: pipeline diameter, 720 mm; flow rate of the pipeline, 9.70 million tons annually; heating temperature of the crude oil, 45 °C; and ground temperature, 2.4 °C. 3.3. Experimental Procedure. First, 4.3 L of crude oil was filled into the stirred vessel, and then the vessel was sealed tightly. To remove memory of the crude oil, it was pretreated by heating to 80 °C and kept isothermally for 2 h, and then it
(10) Vinckier, I.; Moldenaers, P.; Mewis, J. Relationship between rheology and morphology of model blends in steady shear flow. J. Rheol. 1996, 40, 613-63. (11) KanEÄ , M.; Djabourov, M.; Volle, J. L. Rheology and structure of waxy crude oils in quiescent and under shearing conditions. Fuel 2004, 83, 1591-1605. (12) Zhang, J.; Zhou, S.; Li, H.; Li, Y.; Tu, H.; Huang, Q.; Yan, D. Entropy generation as a parameter to simulate the shear history effect of the beneficiated waxy crude oils. In Proceedings of the XIV International Congress on Rheology, Seoul, Korea, Aug 22-27, 2004.
(13) Zhang, J.; Yan, D. Calculation of average shear rate in pipe flow based on energy dissipation rate. Acta Pet. Sin. 2002, 23, 88-90 (in Chinese). (14) Zhang, J.; Zhang, F.; Huang, Q.; Yan, D. Experimental simulation of the effect of shear on rheological properties of beneficiated waxy crude oils: theoretical basis and application. In Proceedings of the 4th Pacific Rim Conference on Rheology, Shanghai, China, Aug 7-11, 2005. (15) Zhang, J.; Huang, Q.; Yan, D. Estimation of average shear rate in stirred vessels for pipelining shear simulation. Acta Pet. Sin. 2003, 24, 9496 and 100 (in Chinese).
φ ) τ:D
(1)
where φ is the energy dissipation rate, W/m3; τ is the stress tensor, Pa; and D is the tensor of deformation rate, s-1. In laminar pipe flow, the energy dissipation rate simplifies to
φ ) τγ˘
(2)
Flow BehaViors of Waxy Crude Oil
Figure 1. Sketch of the shear simulation device.
was left to cool quiescently and kept at room temperature for 48 h before the shear-simulation experiment. After the pretreatment, the crude oil was heated to 45 °C and kept at this temperature for 0.5 h. The temperature in heating stations of the simulated pipeline was 45 °C. Then, 300 mL of crude oil was sampled from the sampling valve at the bottom of the stirred vessel for measuring the gel point and viscosity vs temperature curves under quiescent conditions. Then the crude oil in the stirred vessel was cooled at a rate determined by referring to the pipeline operation, and during cooling, the crude oil was sheared at the shear rate of pipeline transportation determined according to eq 4. It should be noted that, for heated oil pipelines, the average pipe flow shear rate is not a constant at different axial positions of the pipeline because of the oil temperature change during flow, resulting in changing rheological properties and, thus, the friction factor in eq 4. Therefore, the agitation speed of the vessel was adjusted according to the pipe flow shear rate. When the crude oil was cooled to the prescribed sampling temperatures, ∼220 mL of crude oil specimen was taken out for measuring the gel point, viscosity, yield stress, thixotropy, and DSC (differential scanning calorimetry) curve. 3.4. Measurement of DSC Curves and Rheological Properties of the Specimen. 3.4.a. DSC. All DSC tests and analyses on thermal characteristics of the crude oil specimen were performed using a computer-controlled TA2000/MDSC2910 DSC apparatus. Calibration for temperature and heat flow determination was carried out using the melting point and the heat of melting of high-purity metal indium. Dry N2 gas is purged through the DSC cell, and cooling is accomplished with a liquid-nitrogen cooling accessory. A 4-8 mg crude oil specimen was transferred into an aluminum crucible, which was then sealed and weighed. Experiments were carried out by heating the crucible to 80 °C and keeping it at the temperature for 1 min, then cooling it at a cooling rate of 5 °C‚min-1 from 80 to -30 °C. 3.4.b. Viscosity. The viscosity of the specimen was characterized with the coaxial cylinder sensor system MVDIN of HAAKE VT550 rheometer. The crude oil specimen taken from the stirred vessel was loaded into the coaxial cylinder system preheated to the prescribed sampling temperature, and a viscosity measurement was started after 5 min to make the specimen temperature at the required measurement temperature. 3.4.c. Gel Point. The gel point of the specimen was determined according to the Chinese Standard Petroleum Test Method SY/T 0541-94. The crude oil specimen was transferred to the gel-point test tube that had been made at the prescribed sampling temperature, then cooled at a rate of 0.5-1.0 °C‚min-1. Flowability of the specimen was checked at every 2
Energy & Fuels, Vol. 20, No. 6, 2006 2533
°C. The gel point is defined as the highest temperature at which movement of the specimen surface cannot be observed when the tube is held horizontally for 5 s. 3.4.d. Yield Stress. The yield stress measurement was made with the coaxial cylinder sensor system Z41Ti of HAAKE RS-150H controlled-stress rheometer. The crude oil specimen was loaded into the sensor system preheated to the prescribed sampling temperature, and then it was cooled to the measured temperature at the rate of 0.5 °C‚min-1. The yield stress measurement was made after keeping the specimen statically for 30 min. 3.4.e. Thixotropy. The thixotropy of the specimen was also characterized with the coaxial cylinder sensor system MVDIN of HAAKE VT550 rheometer. The crude oil specimen was loaded into the coaxial cylinder system preheated to the prescribed sampling temperature, and then it was cooled to the measurement temperature, 29 °C in this study, at the rate of 0.5 °C‚min-1. The thixotropy measurement was started after the specimen was kept isothermally for 30 min. 4. Results and Discussions 4.1. DSC Curves. DSC is well-documented as a powerful technique for investigating the thermal characteristics of crude oils.16-21 By analyzing the thermal fingerprint of specimens, the concentration of precipitated wax and the total wax content of a crude oil can be deduced, which is based on the fact that the concentration of precipitated wax is proportional to its crystallization heat flow.20,21 It is well-known that wax particles start appearing in the crude oil when the bulk temperature drops to the WAT. During the shear-simulation experiment, wax deposition on the vessel wall may occur because of thermal gradients. If so, the characteristics of crude oil may change as a result of wax depletion in the bulk crude oil. To investigate the possible impact of wax depletion due to wax deposition during cooling and shearing, specimens of crude oil at different positions were captured when the temperature of the crude oil was below 32 °C and tested by the DSC. Figure 2 shows the results of specimens taken from the bulk fluid through the sampling valve at various temperatures from 37 to 30 °C, and Figure 3 shows the results of five specimens taken at 30 °C from the surface of the bulk fluid, the center of the bulk fluid, the bottom and the wall of the vessel, as well as ordinarily from the sampling valve. The crude oil specimens at the vessel wall and at the bottom were taken by first draining away bulk fluid in the vessel after the flow simulation was finished. The specimen on the wall, which is the possible wax deposit, was scraped by using a spoonlike tool. It can be seen that the characteristics of the crude oil specimens (16) Claudy, P.; Letoffe, J. M.; Benoit, C.; Jean, O. Crude oils and their distillates: Characterization by differential scanning calorimetry. Fuel 1988, 67, 58-61. (17) Hansen, A. B.; Larsen, E.; Pedersen, W. B.; Nielsen, A. B.; Rønningsen, H. P. Wax precipitation from sea crude oils. 3. Precipitation and dissolution of wax studied by differential scanning calorimetry. Energy Fuels 1991, 5, 914-923. (18) Claudy, P.; Garcin, M.; Vollet, J. L. Evaluation of crystallized fractions of crude oils by differential scanning calorimetry: Correlation with gas chromatography. Fuel 1995, 74, 92-95. (19) Letoffe, J. M.; Claudy, P.; Kok, M. V.; Garcin, M.; Vollet, J. L. Crude oils: Characterization of waxes precipitated on cooling by D. S. C. (differential scanning calorimetry) and thermomicroscopy. Fuel 1995, 74, 810-817. (20) Li, H.; Huang, Q.; Zhang, F.; Zhang, J. Determination of wax content in crude oils using DSC. J. UniV. Pet. 2003, 27, 60-62 (in Chinese). (21) Chen, J.; Zhang, J.; Li, H. Determining the wax content of waxy crude oils using differential scanning calorimetry. Thermochim. Acta 2004, 410, 23-26.
2534 Energy & Fuels, Vol. 20, No. 6, 2006
Ding et al.
Figure 2. DSC curves of bulk crude oil sampled at different temperatures.
Figure 3. DSC curves of specimens captured at different positions at 30 °C.
Figure 4. Comparison of viscosities under quiescent and simulated flow condition.
Figure 5. Yield stress measured at different temperatures vs the sampling temperature.
Table 1. WAT and Crystallization Enthalpy of Test Specimens sampling temperature (°C)
sampling position
WAT (°C)
crystallization enthalpy (J/g)
37 35 34 33 32 31
sampling valve
42.8 41.9 42.0 42.1 42.6 43.0 43.7 43.0 43.0 42.6 43.5 42.2 42.4 42.7 43.1
27.99 25.55 26.03 28.92 29.12 29.78 30.11 30.31 27.19 29.85 28.95 29.70 28.29 30.20 30.08
30
bulk surface bulk center sampling valve vessel wall vessel bottom volume surface volume center sampling valve vessel wall vessel bottom
had little change during the cooling and shearing processes, and the characteristics of the specimens from different positions were just the same. Table 1 provides quantitative information of the WAT and crystallizion enthalpy of the tested specimens. These DSC results illustrated that wax depletion due to wax deposition on the vessel wall did not exist. Actually, the wax deposition process can be described by five steps,22 with the first step being gelation of wax oil on the cold wall and formation of an incipient gel layer, followed by aging of the gel layer with diffusion of waxes into and through the layer and finally deposition. That is, wax content of the deposition layer increases with deposition time, and the wax content may not be much higher than the bulk crude oil, because a significant amount of oil may be trapped in the 3-D network structure of the wax crystals that behave as a porous medium.22 (22) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. Formation and aging of incipient thin film wax-oil gels. AIChE J. 2000, 46, 10591074.
Figure 6. Measured yield stress vs predicted yield stress from eq 6. Table 2. Gel Point Measured by Sampling at Different Temperatures sampling temp (°C) gel point (°C)
37 32
35 31
34 31
33 31
32 31
31 30
30 29
29 29
28 28
4.2. Viscosity Versus Temperature Chart. Figure 4 compares the viscosity vs temperature curves of the Daqing waxy crude oil measured under quiescent and simulated pipelining conditions. It can be seen that, at temperatures above the WAT, 43 °C for this crude oil, the viscosities measured under quiescent cooling and simulated pipelining conditions shows little difference; however, below the WAT, the difference becomes larger with decreasing temperature. The viscosities under quiescent cooling conditions were higher than those under simulated pipelining conditions. At 35 °C, the former was 154% higher than the latter (both referring to a shear rate of 20 s-1). Since the compositions of crude oil specimens remain unchanged during cooling and shearing, this viscosity difference can be attributed to the disturbance of shear on the forming structure of wax crystals in the crude oil.
Flow BehaViors of Waxy Crude Oil
Energy & Fuels, Vol. 20, No. 6, 2006 2535
Table 3. Thixotropic Parameters at Different Sampling Temperature (Measurement Temperature 29 °C) parameter value referring to different sampling temperature parameter
30°C
31 °C
32 °C
33 °C
35 °C
37 °C
40 °C
τy0 (Pa) τy1 (Pa) τy2 (Pa) K (Pa‚sn) ∆K1 (Pa‚sn) ∆K2 (Pa‚sn) n m1 m2 a1 (s-1) b1 (sm1-1) b2 (sm2-1)
6.3497 20.9649 6.6338 1.2484 0.3312 1.4341 0.6125 0.0224 0.0334 0.1257 0.0481 0.0306
6.2969 22.1019 5.8968 1.6153 0.5436 1.0025 0.5421 0.0198 0.0362 0.1282 0.0377 0.0304
6.2194 24.4038 4.0010 1.8477 1.1558 0.6725 0.5271 0.0213 0.0344 0.1308 0.0428 0.0391
6.1458 26.7993 2.4580 2.1695 1.6694 0.4680 0.5098 0.0233 0.0364 0.1321 0.0467 0.0337
5.9689 27.2975 1.7440 2.2835 1.9921 0.2680 0.4678 0.0267 0.0340 0.1283 0.0487 0.0318
6.0100 27.5894 1.8124 2.1436 1.8923 0.2821 0.4715 0.0254 0.0351 0.1378 0.0416 0.0300
5.9748 26.9547 1.6452 2.3169 1.9874 0.2593 0.4634 0.0215 0.0340 0.1423 0.0451 0.0299
4.3. Gel Point. For the same reason, the gel point decreased with decreasing sampling temperature; see Table 2. Because the gel-point measurement was conducted under quiescent cooling conditions after sampling from the shear simulation vessel and without specimen reheating, the change of the gel point with the sampling temperature indeed indicates the effect of shear history, i.e., the dynamic cooling process and the end temperature of dynamic cooling (the sampling temperature). In the gel-point measurements referring to the sampling temperature of 29 °C, the specimen was kept at 29 °C after being transferred into the test tube instead of being cooled directly; the specimen was found to start gelling after 10 min. Similarly, after 9 min, the specimen sampled at 28 °C became a gel. This clearly indicates that, though pumping waxy crude oils at temperatures below the gel point is possible, the crude oil will start gelling rapidly after pipeline shutdown. Therefore, it is dangerous to pump a waxy crude oil below its gel point. In China, the lowest operation temperature in the pipeline is required to be 3 °C above the gel point in order to ensure a sufficient safety margin. 4.4. Yield Stress. Yield stresses from 31 to 27 °C were measured for a crude oil specimen sampled at different temperatures; see Figure 5. It is found that, at sampling temperatures above 35 °C, the yield stress at all measurement temperatures showed no relation with the sampling temperature, but below 35 °C, the measured yield stresses declined with decreasing sampling temperature. This is also attributed to the disturbance of shear to formation of the wax crystal structure. According to the experimental data, the yield stress as a function of the sampling temperature and the measurement temperature can be described by the following empirical model,
partial reversibility of the thixotropic structure of the waxy crude oil:27
τ ) τy0 + λ1τy1 + λ2τy2 + (K + λ1∆K1 + λ2∆K2)γn dλ1 ) a1(1 - λ1) - b1λ1γ˘ m1 dt
(7)
dλ2 ) -b2λ2γ˘ m2 dt where τy0 is the permanent part of the yield stress, Pa; τy1 is the reversible part of the yield stress, Pa; τy2 is the irreversible part of the yield stress, Pa; K is the consistency coefficient, Pa‚sn; ∆K1 is the reversible part of the gel consistency, Pa‚sn; ∆K2 is the irreversible part of consistency, Pa‚sn; n is the flow behavior index; λ1 is the reversible structure parameter; λ2 is the irreversible structure parameter; m1 is the reversible structure parameter; m2 is the irreversible structure parameter; a1 is the building-up parameter of the reversible structure, s-1; b1 is the breaking-down parameter of the reversible structure, sm1-1; and b2 is the irreversible structure, sm2-1. Figure 7 shows the measured and predicted thixotropic curves by using eq 7. Parameters of eq 7 for the crude oil specimen at
τy ) 0.6442Ts e-0.6869(T-Tg) - 19.272 e-0.6841(T- Tg) (30 °C e Ts e 35 °C) (6) where τy is the yield stress, Pa; T is the measurement temperature, °C; Ts is the sampling temperature, °C; and Tg is the gel point measured under quiescent cooling conditions. The average deviation of the predicted value by eq 6 from the experimental data is 16.04%. Comparison of the measured and predicted values is shown in Figure 6. 4.5. Thixotropy. The thixotropic model is indispensable for accurate prediction of the restart pressure of a waxy crude oil pipeline. The Houska model was usually used for describing thixotropy of the waxy crude oil.23-26 We put forward a better but more complex model which takes into consideration the (23) Sestak, J.; Charles, M. E.; Cawkwell, M. G.; Houska, M. Start-up of Gelled Crude Oil Pipeline. J. Pipelines 1987, 6, 15-24. (24) Cawkwell, M. G.; Charles, M. E. An Improved Model for Start-up of Pipelines Contained Gelled Crude Oil. J. Pipelines 1987, 7, 41-52.
Figure 7. Measured and predicted thixotropic curves by using eq 7 (dashed line, predicted; solid line, measured).
29 °C but under various conditions of sampling temperature (i.e., the end temperature of dynamic cooling) are shown in Table 3. At sampling temperatures above 35 °C, the parameters τy0, τy1, τy2, K, ∆K1, ∆K2, and n show no dependence on the (25) Cawkwell, M. G.; Charles, M. E. Characterization of Canadian Arctic thixotropic gelled crude oils utilizing an eight-parameter model. J. Pipelines. 1989, 7, 251-264. (26) Chang, C.; Nguyen, Q. D.; Rønningsen, H. P. Isothermal Start-up of Pipeline Transporting Waxy Crude Oil. J. Non-Newtonian Fluid Mech. 1999, 87, 127-154. (27) Zhang, F.; Zhang, J.; Yang, X. Comparison of thixotropic models of waxy crude oil. In Proceedings of the XIV International Congress on Rheology, Seoul, Korea, August 22-27, 2004.
2536 Energy & Fuels, Vol. 20, No. 6, 2006
Figure 8. Parameters τy0, τy1, τy2, K, ∆K1, ∆K2, and n vs sampling temperature.
sampling temperature, but at temperatures below 35 °C, these parameters vary with the sampling temperature approximately linearly; see Figure 8. It is valuable to note that parameters representing the reversible structure, i.e., τy1 and ∆K1, decrease with decreasing sampling temperature, which essentially implies that the shear disturbance to the structure becomes greater with more shear imposed; meanwhile, the parameters representing the irreversible structure, i.e., τy2 and ∆K2, increase with decreasing sampling temperature, implying that the contribution of the irreversible structure becomes more significant with more shear imposed. The other five parameters, m1, m2, a1, b1, and b2, show no tendency of variation with the sampling temperature. 5. Conclusions Flow behaviors of Daqing waxy crude oil have been investigated through shear-simulation experiments, which were
Ding et al.
conducted by using a stirred vessel and taking the energy dissipation of viscous flow as the shear-simulation parameter. It was found that, below the WAT, the viscosity under simulated pipelining conditions was much less than that measured under quiescent cooling conditions, e.g., at 35 °C, the latter was 154% higher than the former (both referring to a shear rate of 20 s-1). To investigate the possible impact of wax depletion in the bulk fluid due to wax deposition, crude oil specimens were captured at different sampling temperatures and different positions and then tested by DSC. Little difference in the DSC curve had been observed, indicating that wax depletion can be excluded from the reason of viscosity reduction in the flow simulation. Shear disturbance to the forming wax crystal structure is determined to be responsible for this viscosity reduction. For the same reason, the gel point decreased with decreasing temperature of sampling, i.e., the end temperature of the dynamic cooling process. At sampling temperatures above 35 °C, both the yield stresses measured at temperatures from 27 to 31 °C and the thixotropic parameters showed no dependence on the sampling temperature, indicating that shear at temperatures when precipitated wax was not so much (1.42% at 35 °C in this case) showed little effect on wax crystal structure at lower temperatures. However, at sampling temperatures below 35 °C, both the yield stress and the thixotropic parameters were remarkably dependent on the shear history. Empirical correlations were developed for relationship between the yield stress and the sampling temperature as well as the measurement temperature. Because of the importance of the rheological parameters, particularly those below the WAT, to safe and economic operation of waxy crude oil pipelines, results of this study strongly suggest the necessity of pipelining simulation when determining rheological parameters of waxy crude oils. Acknowledgment. Financial support from the Key Research Project (No. 104118) of the Ministry of Education, the People’s Republic of China, is greatly appreciated. The authors would also like to acknowledge Mr. Zhu Yingru, Mrs. Sun Jishu, Mr. Han Shanpeng, Mr. Wang Haifeng, and Miss Chen Jinghua for their assistance in some of the experiments. EF060153T
