Gelation Behavior of Model Wax–Oil and Crude Oil ... - ACS Publications

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Gelation Behavior of Model Wax−Oil and Crude Oil Systems and Yield Stress Model Development Yansong Zhao,*,† Lalit Kumar,† Kristofer Paso,† Jamilia Safieva,† Mior Zaiga B. Sariman,‡ and Johan Sjöblom† †

Ugelstad Laboratory, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway ‡ Petronas, 50088 Kuala Lumpur, Malaysia ABSTRACT: An experimental investigation of waxy oil gelation behavior is performed using the methods of rheometry, optical analysis, tensiometry, and microscopy. Thermal history, shear history, asphaltene content, and chemical additives influence the gelation process. Consequently, the final gel state is strongly correlated to the gelation conditions. Various model wax−oil systems are prepared, including 5 wt % microcrystalline wax or 5 wt % macrocrystalline wax in dodecane, as well as 5 wt % macrocrystalline wax in Primol 352. Real waxy crude oils UL-YS1 and Se-7-E06 are also investigated. A new yield stress model is developed on the basis of experimental results and a modified Eyring theory to provide gel strength predictions for petroleum transport pipelines. In the absence of shear during gelation, the yield stress can be correlated with the thermal history. However, for non-quiescent gelation conditions, the gel strength is also dependent upon the imposed shear history during the gelation process. The imposed shearing influences the growth process of a volume-spanning crystal network. Finally, pressure wave propagation calculations are performed following the Rønningsen convention, highlighting the impact of yield stress on startup lag times associated with wax gelation in field transport pipelines.

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INTRODUCTION Successful shut-in and restart of waxy crude oil pipelines is an important criterion for flow assurance within the petroleum industry.1−3 Physical wax gels may form during low-temperature shut-in processes, resulting in solid-like plugs, which can fill an entire pipeline volume. Subsequently, during the restart process, a formed paraffin wax plug requires a large applied pressure at the pipe inlet to rupture the internal gel structure and afford steadystate flow.4−8 Therefore, both gel formation and gel breakage processes are highly relevant for crude oil transportation strategies. Waxy oil gelation mechanisms have been investigated by several researchers.9−11 It is reported that a number of factors influence the gelation process, including shear history, thermal history, and fluid composition.11−13 In the pipeline, both gelation and gel breakage processes influence local gel states as well as axial and radial fluid property profiles. The yield stress value is an important parameter for estimating the necessary restart pressure in a subsea transport pipeline.4,7,8,14,15 An equation to calculate the inlet gauge pressure required to overcome the yield stress is8,16 ΔPpredicted ≥

breakage model was established to predict the mechanical response of wax gels at various shear and thermal histories.19 It was shown that a simple rheological model can be applied to correlate the deformation and flow behavior of model wax−oil gels. In addition, the model provides an excellent correlation of the rheology of a crude oil UL-YS1. The mechanical response model accounts for only the gel breakage process, providing excellent correlation of stress profiles at constant shearing conditions, spanning the entire strain regime from Hookean behavior at low strains to equilibrium slurry flow at the infinite strain limit. The current work is performed to extend the validity of the modeling efforts to a broader range of shear and thermal history conditions. In this work, experiments are performed to assess the effects of thermal history, shear history and composition on the gelation process. Various methods are used to study the gelation process, including optical analysis, tensiometry, rheology, and microscopy. The effect of the temperature, asphaltene composition, and additive composition is investigated using a bubble pressure tensiometer. A yield stress model is established according to a modified Eyring theory and corroborated by the experimental results. The model may be used to correlate the strength of waxy oil gels with the formation conditions. Finally, yield front propagation calculations are performed following the model by Davidson et al.,7 demonstrating the impact of the rheometric measurements on field pipeline startup processes.

4τyL (1)

D

where τy denotes yield stress and L and D are pipeline length and diameter, respectively. It is necessary to develop a model to predict waxy oil yield stress values, accounting for shear history and thermal history within gel formation and breakage processes. The yielding behavior of waxy oil has been investigated by several researchers.11,16−18 It has been demonstrated that the yield stress of waxy oils is influenced by thermal history, shear history, baric history, and fluid composition. In previous work, a novel gel © 2012 American Chemical Society

Received: July 25, 2012 Revised: September 20, 2012 Published: September 21, 2012 6323

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Surface Tension. The effect of the temperature, asphaltene, and additive composition on surface tension is investigated using a bubble pressure tensiometer (BP 100, KRÜ SS GmbH, Germany). Temperature effects are investigated from 29 to 61 °C using a sample containing 5 wt % macrocrystalline wax in dodecane. The influence of additives is investigated at 29 °C using a sample consisting of 1000 ppm A5 in 5 wt % macrocrystalline wax in dodecane. Similarly, the influence of asphaltenes is investigated at 29 °C using a sample containing o-xylene to partially dissolve the asphaltenes. The sample contains 0 or 0.02 wt % asphaltene A in a solution of macrocrystalline wax in o-xylene and dodecane (5:30:65 weight ratio). Microscopy. A microscope (Nikon Eclipse ME600) is used to investigate wax crystal formation in model wax−oil fluids. The microscopy protocol is as follows: A sample of model wax−oil is loaded on a glass slide. Before loading, the sample is heated to a temperature above the WAT to ensure complete dissolution of solids. The sample is maintained at 50 °C for 5 min. Subsequently, the sample is cooled to 20 °C at a cooling rate of 1 °C/min. Finally, the temperature is maintained at 20 °C for 5 min, and the micrograph is acquired.19

EXPERIMENTAL SECTION

Materials. The chemicals used in this work are obtained from SigmaAldrich, Sasol Wax GmbH, ExxonMobil, and Champion Technologies, Inc. Mass fraction purities of dodecane (CAS registry number 112-40-3) and o-xylene (CAS registry number 95-47-6) are ≥0.990 and ≥0.980, respectively. Primol 352 is obtained from ExxonMobil. Physical properties of Primol 352 are tabulated in a previous reference.19 Macrocrystalline wax (Sasolwax 5405) and microcrystalline wax (Sasolwax 3971), asphaltenes A and B, additives (A1, A2, A3, A4, and A5 from Champion Technologies, Inc.), crude oil UL-YS1 (proprietary), and crude oil Se-7-E06 (proprietary) are also used in this work. Asphaltene A is precipitated by n-hexane. The elemental composition of asphaltene A is as follows: C, 78.7 wt %; H, 7.78 wt %; N, 0.70 wt %; O, 1.54 wt %; S, 10.26 wt %. Asphaltene B is extracted from waxy crude oil Se-7-E06 using n-hexane according to the Nenningsland procedure.20 Sample Preparation. Three kinds of samples, including 5 wt % macrocrystalline wax in dodecane, 5 wt % microcrystalline wax in dodecane, and 5 wt % macrocrystalline wax in Primol 352, are prepared. Samples are prepared with 0, 0.02, 0.04, 0.05, and 0.08 wt % asphaltene A in a solution of macrocrystalline wax, o-xylene, and dodecane (mass fraction ratio of macrocrystalline wax, o-xylene, and dodecane is 5:30:65). Similarly, samples are prepared with 0.02, 0.04, 0.06, and 0.08 wt % asphaltene B in a solution of macrocrystalline wax, o-xylene, and dodecane (5:30:65 weight ratio). To investigate additives, samples of 100 ppm of A1, A2, A3, A4, and A5 in 5 wt % macrocrystalline wax in dodecane are prepared. Samples of 100 ppm A1, A2, A3, and A4 in crude oil UL-YS1 are also prepared. Rheological Experiments. Rheometric experiments are performed using an Anton Paar (Austria) Physica 301, equipped with a 4 cm diameter 2° cone and plate geometry.19 The following protocols are used. (a) Thermal history protocol: A sample of oil is loaded between the cone and plate. Prior to loading, the sample and geometry are maintained at a temperature of at least 20 °C above the wax appearance temperature (WAT) to ensure a liquid paraffin state. The sample is cooled to 40 °C (45 °C for 5 wt % macrocrystalline wax in Primol 352) at a cooling rate of 20 °C/min. Subsequently, the sample is cooled to 4 °C at 1 °C/min. The sample is maintained at a constant 4 °C for 10 min to ensure solid−liquid equilibrium prior to gel breakage. Finally, the formed gel is broken at a constant shear rate of 0.1 s−1. Thermal history experiments are performed at various cooling rates ranging from 1 to 20 °C/min. Investigations probing the effect of the gelation temperature follow the same protocol; however, the final constant gel formation and breakage temperature ranges from 4 to 20 °C. Experiments probing asphaltene and additive content follow protocol a. (b) Shear rate history protocol: The protocol is similar to protocol a. During the first and second cooling stages, a single shear rate is imposed on the sample. Imposed shear rates range from 0.0001 to 10 s−1. In addition, shearing may be imposed during the thermal equilibration stage. (c) Shear stress history protocol: The protocol is similar to protocol a. During the cooling stage from a temperature of 40 °C (45 °C) to the final gel formation temperature, a single shear stress is imposed on the sample.19 The imposed shear stress ranges from 0 to 40 Pa. Optical Analysis. Wax precipitation is investigated by optical transmittance using a Turbiscan MA2000 (Formulaction, Inc., France) instrument. The samples investigated include 5 wt % microcrystalline wax in dodecane, 5 wt % macrocrystalline wax in dodecane, and 5 wt % macrocrystalline wax in Primol 352. In addition, experiments are performed with samples of 0, 0.02, 0.04, 0.06, and 0.08 wt % asphaltene A in a solution of macrocrystalline wax, o-xylene, and dodecane (5:30:65 weight ratio). Light transmittance is recorded as a function of time. Optical transmittance decreases with time because of turbidity imparted by gel formation. The method has previously been used to obtain estimates of asphaltene precipitation rates.21 Experiments are performed by first allowing a vial filled with model fluid to equilibrate in an external oven at 60 °C for a minimum time of 30 min. Subsequently, the vial is quickly transferred to the temperature-controlled Turbiscan cell, and optical transmittance measurements are acquired continuously. During the experiments, the Turbiscan cell is maintained at a constant temperature within the range of 15−35 °C.

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RESULTS AND DISCUSSION Rheological Experiments. Effect of the Imposed Shear Rate on Model Wax−Oil Gelation. The role of shear history on the paraffin wax gelation process is illustrated in Figure 1. The gel

Figure 1. Effect of the imposed shear rate on 5 wt % macrocrystalline wax in dodecane.

strength decreases monotonically with imposed shearing during the gel formation process, demonstrating the role of shear forces in disrupting the formation of a volume-spanning crystal−crystal network. The black data points (squares) indicate a protocol in which a shear rate is imposed during the entire cooling process from a temperature of 20 °C above the WAT to the final gel formation temperature. The shearing is also imposed during the isothermal equilibration stage. On the other hand, red data points (circles) indicate a protocol in which a shear rate is imposed only during the isothermal equilibration stage. Yield stresses of the sample decrease with an increasing imposed shear rate from 0.0001 to 10 s−1. Effect of the Imposed Shear Stress on Model Wax−Oil Gelation. The role of imposed shear stress on the paraffin wax gelation process is illustrated in Figure 2. The sample is 5 wt % macrocrystalline wax in dodecane. The black line indicates a protocol in which a shear stress of 0.2 Pa is imposed during the entire cooling process from a temperature of 20 °C above the WAT to the final gel formation temperature. A shear stress of 0.2 6324

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Table 1. Shear History for Experiments with 5 wt % Macrocrystalline Wax in Primol 352

number

imposed shear stress (Pa, from 65 to 45 °C, 20 °C/min)

imposed shear stress (Pa, from 45 to 4 °C, 1 °C/min)

imposed shear stress (Pa, 4 °C for 10 min)

1 2 3 4 5 6 7 8

0.5 0 0.5 5 0 10 0 10

0.5 0 0.5 5 0 10 0 10

0.5 0.5 0 5 5 10 10 0

Figure 2. Effect of the imposed shear stress on model wax−oil gelation: (a) dissimilar shear histories imposed during gelation of 5 wt % macrocrystalline wax in dodecane and (b) dissimilar shear histories (Table 1) imposed during gelation of 5 wt % macrocrystalline wax in Primol 352.

Pa is also imposed during the isothermal equilibration stage. The red line indicates a protocol in which a shear stress of 0.2 Pa is imposed during the entire cooling process. Similar curves are obtained in both cases. The effect of the imposed shear stress (0−10 Pa) is also investigated for 5 wt % macrocrystalline wax in Primol 352. Imposed shear stress conditions are shown in Table 1. Experimental results performed with an imposed shear stress of 0.5 Pa result in a high gel strength, as shown in Figure 2b. Applying a stress of 5 or 10 Pa during the gel formation process results in a significantly weaker gel. The formation of a volumespanning crystal network is hindered by the imposed shear stress. However, if a strong gel is allowed to form during the cooling stages, an imposed stress of 10 Pa during the equilibration stage will not significantly weaken the final gel structure. Effect of the Thermal History on Model Wax−Oil Gelation. The role of the temperature on the paraffin wax gelation process is illustrated in Figure 3. The samples used are 5 wt % macrocrystalline wax in dodecane and 5 wt % macrocrystalline wax in Primol 352. As shown in Figure 3a, the macrocrystalline

Figure 3. Effect of the temperature on yield stress of model wax−oil gels: (a) 5 wt % macrocrystalline wax in dodecane and (b) 5 wt % macrocrystalline wax in Primol 352.

yield stress value decreases with increasing temperatures from 4 to 20 °C at quiescent gel formation conditions. A similar trend is observed in Figure 3b for the macrocrystalline wax in Primol 352, exhibiting excellent reproducibility. The solubility of paraffin wax increases with an increasing temperature. Therefore, at equilibrium conditions of gel breakage, the gels formed at higher 6325

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temperatures exhibit lower solid fractions. Pristine gels with lower solid contents typically exhibit lower yield strength values. The role of the cooling rate on the paraffin wax gelation process is illustrated in Figure 4. The samples used are 5 wt %

Figure 4. Effect of the cooling rate on the yield stress of 5 wt % macrocrystalline wax in Primol 352.

macrocrystalline wax in dodecane and 5 wt % macrocrystalline wax in Primol 352. As shown in Figure 4, the yield stress decreases with an increasing cooling rate at quiescent gel formation conditions. Paraffin crystal sizes increase at lower cooling rates because of the promotion of crystal growth processes over nucleation processes, correlating to stronger gel networks. Cooling rate trends are in good agreement with previous work.19 Effect of Additives on Model Wax−Oil and Crude Oil Gelation. The influence of additives is investigated using a model fluid as well as a real crude oil. The samples used are 5 wt % macrocrystalline wax in dodecane and the crude oil UL-YS1. Gel breakage plots are shown in panels a and b of Figure 5. Yield stress values decrease with the presence of pour point depressant additives. However, the various additives clearly show dissimilar performance activity in the model fluid. Wax additives may influence nucleation, crystal growth, morphology, network structure, or interfacial conditions, via mechanisms of heterogeneous nucleation, co-crystallization, adsorption, or steric hindrance. In the real produced crude oil, however, similar gel breakage plots are obtained with all additives. Effect of Asphaltene on Model Wax−Oil Gelation. The role of asphaltenes on the paraffin wax gel formation process is investigated using a model oil that contains an aromatic solvent. The samples used contain asphaltene A or B at a concentration up to 0.08 wt %. Gel breakage plots are shown in panels a and b of Figure 6, respectively, for the model fluids containing asphaltene A and B. In both cases, the increasing presence of asphaltenes causes a progressive reduction in yield stress. The active mechanism of yield stress reduction may include heterogeneous nucleation, adsorption, or steric hindrance. However, asphaltenes are amorphous hydrocarbons and are unable to cocrystallize with paraffin wax. Optical Analysis. Paraffin molecular structure and solvent composition influence optical transmission profiles because of solubility effects. The microcrystalline fluid exhibits the lowest solubility conditions, resulting in rapid precipitation during cooling (Figure 7). In addition, the macrocrystalline wax shows a

Figure 5. Effect of additives on the yield stress of 5 wt % macrocrystalline wax in dodecane and crude oil UL-YS1: (a) 5 wt % macrocrystalline wax in dodecane and (b) crude oil UL-YS1.

lower solubility in Primol than in dodecane, resulting in faster precipitation. Solubility conditions also dictate the temperature variation of the transmission profiles shown in Figure 8. At temperatures of 25 °C and above, optical turbidity is not evident in the samples. Low solubility conditions at 15 °C result in fast wax precipitation. Optical transmission measurements on asphaltene-containing samples (Figure 9) are complicated by the inherent opacity of the asphaltenes. However, the presence of asphaltenes may delay the onset of transmission reduction from about 10 to 15−20 min. Surface Tension. Figures 10 and 11 show the effects of the temperature and composition on surface tension. Surface tension values are shown to stabilize after about 200 ms. The surface tension of 5 wt % macrocrystalline wax in dodecane decreases with an increasing temperature. As is shown in Figure 10b, the average surface tension versus temperature of model wax−oil can be described as follows: γ = aT + b

(2)

Linear surface tension correlations with temperature have been previously observed for other types of fluid systems.22 Figure 11 6326

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Figure 8. Effect of the temperature on optical transmission profiles of 5 wt % macrocrystalline wax in dodecane.

Figure 6. Effect of asphaltene on the gelation of model wax−oil fluid: (a) asphaltene A and (b) asphaltene B.

Figure 9. Effect of asphaltene A on optical transmission profiles of 5 wt % macrocrystalline wax in dodecane.

investigations relating to liquid−air interface dynamics of waxy petroleum fluids. Microscopy. Micrographs of 100 and 1000 ppm additive A1 in 5 wt % macrocrystalline wax in dodecane are obtained at 20 °C after cooling at 1 °C/min. Figure 12 illustrates that crystal sizes decrease with an increasing concentration of additive A1. The additive likely suppresses the crystal growth process via an adsorption or co-crystallization mechanism. Therefore, a higher crystal number density is achieved, and the formed crystals are smaller in size. As shown in panels a and b of Figure 5, the inhibited systems form weaker gels. Yield Stress Modeling. Shear stress profiles obtained at constant shear rate conditions can be described as19 ⎡ 1 ⎢ τ=⎢ ⎣ (n − 1)kγ + Figure 7. Effect of the wax and solvent type on optical transmission profiles of model wax−oils.

+ τs

1 (λ 0 − λe)n − 1

⎤n / n − 1 ⎡ ⎤ τs ⎥ ⎢hγ − n⎥ ⎥ (λ 0 − λe) ⎦ ⎣ ⎦ (3)

where τ, τs, γ, λ0, λe, h, k, and n denote shear stress, equilibrium shear stress, strain, initial intact crystal−crystal bond fraction, equilibrium intact crystal−crystal bond fraction, Hookean

shows that asphaltenes and additives reduce surface tension. Dynamic surface tension results may prove to be useful for 6327

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Figure 12. Micrographs of various content of additive A1 in 5 wt % macrocrystalline wax in dodecane: (a) 100 ppm and (b) 1000 ppm.

constant, breakdown constant, and breakdown order, respectively. The yield stress (τy) is the maximum value of shear stress. ⎤1/1 − n n ⎡ k(n − 1)τs h ⎥ ⎢ τy = + + τs hk ⎣ (λ 0 − λe)n (λ 0 − λe)n − 1 ⎦

(4)

Equation 4 only considers the gel breakage process. Therefore, it is necessary to establish a model for the gel breakage process that also accounts for the impact of gel formation processes in addition to the specific gel breakage conditions. Yield stress is a complex function of shear history and thermal history

Figure 10. Effect of the temperature on surface tension of 5 wt % macrocrystalline wax in dodecane: (a) dynamic surface tension at various temperatures and (b) average surface tension versus temperature. a = −0.1119, b = 30.00, and R2 = 0.9989.

τy = f (γh , Th)

(5)

where γh and Th denote shear history and thermal history during the gelation and breakage process. A yield stress model is developed as follows. The effect of shear history and thermal history on yield stress in the gel breakage process is investigated. The temperature dependence of viscosity can be correlated by a modified Eyring theory as follows:23 η=

2 ⎛ (ε + εS) ⎞ hN ⎛⎜ δ ⎞⎟ exp⎜ 0 ⎟ ⎝ RT ⎠ V ⎝a⎠

(6)

where h is the Planck constant, N is the Avogadro number, V is the molar volume of the system, ε0 represents an activation energy associated with the stress-activated viscosity, while εS accounts for changes in total solid−liquid interfacial area arising from thermodynamic solubility effects, R is the ideal gas constant, T is absolute temperature, and δ and a are length parameters representing distances between molecules.23 Hence, the modified Eyring theory accounts for thermodynamic solubility

Figure 11. Effect of asphaltene A and additive A5 on the surface tension of 5 wt % macrocrystalline wax in dodecane.

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effects within a single heuristic equation, instead of requiring a constant solid fraction. To apply the modified Eyring theory to physical gel rupture, the value of the pre-factor hN/V(δ/a)2 changes with strain during the gel breakage process. Straindependent viscosity may be considered independent of the shear rate below 0.1 s−1 based on the work by Paso et al.24 for macrocrystalline model fluid systems. Hence, for the current investigation performed with a shear rate of 0.1 s−1 and considering τ = ηγ̇, the yield stress at the yielding point is correlated by τy = k exp(E /RT ) 1

(7)

where τy1 represents the yield stress value that considers thermal and shear history during the gel breakage process. Equation 7 can be rewritten as ln τy = E /RT + C1 1

(8)

For the experiments shown in Figure 3a, the gels form under quiescent conditions with identical cooling rates. However, the gel breakage temperature (equivalent to the final gelation temperature) varies, demonstrating that yield stress is primarily dependent upon the temperature. Experimental results are in good agreement with fitting results using eq 8 and are shown in Figure 13a. The effect of the cooling rate during gelation is also investigated. The sample used is 5 wt % macrocrystalline wax in Primol 352. The crystal form may create a strong gel during the cooling process from 45 to 4 °C. The gel formation process is shown to be highly time-dependent. Low cooling rates afford sufficient time for the volume-spanning crystal−crystal network to form and may allow for strong crystal−crystal bonds to form via slow diffusion processes involving crystals and/or individual molecules. Specifically, crystals formed during cooling from 45 °C to the final gel formation temperature form the strongest gel at the lowest cooling rate of 1 °C/min. According to the experiments shown in Figure 13b, the relationship between the cooling rate and yield stress can be obtained as follows:

(9)

Figure 13. Comparison of experimental and fitted yield stress values of model wax−oils at different thermal histories: (a) 5 wt % macrocrystalline wax in dodecane (R2 = 0.9669) and (b) 5 wt % macrocrystalline wax in Primol 352 (R2 = 0.9818).

where τy2 represents the yield stress value that considers thermal and shear history during the gelation process. ΔT is 41 °C, and cooling rates range from 1 to 20 °C/min for the data in Figure 13b, representing the second cooling step in the rheometric protocol. Equation 9 can be used to predict the yield stress with different cooling rates for quiescent gelation processes. However, the attained correlation may be invalid in the very high or very low cooling rate regimes. Yield Front Propagation. Pressure wave propagation and yield front calculations are performed to demonstrate the impact of gelling and rheological behavior on real petroleum production operating processes. During the pipeline restart process, various pressure waves may propagate along the length of the pipeline prior to full-scale flow at the pipe outlet. An initial inertial acoustic wave proceeds at a high velocity along the axial length of the pipeline. For Newtonian fluids, full-scale flow will commence at the pipeline outlet after the acoustic wave transgresses the line. However, for gelling fluids, which attain a yield stress during the pipeline shut-in process, the acoustic wave may be rapidly attenuated and may not reach the pipe outlet. Therefore, the behavior of the acoustic wave is completely omitted in the

current modeling investigation. In addition to an acoustic wave, a viscous compression wave may transgress the pipeline during the flow initiation process. The viscous wave likely travels at a slower velocity than the acoustic wave. Finally, a pressure wave may form along the axial length of the pipeline because of changes in rheological properties, resulting from imposed flow. In practical pipeline applications, the viscous and gel degradation pressure waves are likely coupled, because of the fast onset of gel degradation associated with deformation. The gel degradation measurements performed in this work demonstrate yielding that occurs at an absolute imposed strain magnitude on the order of 10−2. Yield front propagation calculations are performed following the Rønningsen convention, in which the gel breakdown process is assumed to commence only after a shear stress is applied to a given fluid element in the pipeline. The time at which shearing commences for a local fluid element is denoted by the symbol ty. In the current modeling efforts, the viscous and gel degradation waves are assumed to be entirely decoupled and the calculated yield front propagation is driven entirely by time-dependent gel

⎛ ⎞ 1 ln τy = A⎜ln + ln(ΔT )⎟ + C 2 ⎝ dT /dt ⎠

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Figure 14. Yield front propagation calculations for the model wax−oil: (a) λ = 10−4, (b) λ = 10−3, (c) λ = 10−2, and (d) λ = 10−1.

Values of the breakdown parameter λ can, in principle, be estimated using small-scale rheometric measurements. However, fitted values of λ strongly depend upon the conditions of gel breakage. For example, at imposed shear rate conditions of 0.1 s−1, best fit values of λ are observed to be on the order of unity based on Figure 5a. However, fitted values of λ are directly proportional to imposed shear rate conditions, because of the strong strain dependence of the breakdown process, in which the gel state can be accurately represented as a point function of the absolute imposed strain on gel. In real pipeline conditions, shear rates may be very low during the pressure wave propagation process, on the order of 10−4 s−1. Therefore, appropriate values of the breakdown parameter λ may be on the order of 10−3 s−1 and certainly less than unity. As a first approximation, calculations are performed for a short model pipeline and a low applied pressure to demonstrate the relevance of the time-dependent pressure wave propagation process on startup lag times, even in the absence of compressibility effects. Figure 14 shows yield front progression profiles for cases in which the breakdown parameter λ varies from 10−4 to 10−1 s−1. For slow gel breakdown characterized by λ = 10−4, full-scale flow at the 1 km pipe outlet is delayed by over 800 h. On the other hand, fast gel breakdown (λ = 10−1) affords pipeline restart within 50 min, demonstrating the impact of rheology, yield stress, and gelling on the pipeline restart process.

breakdown. The yield stress of a gel element is assumed to follow a simple function of the time elapsed subsequent to stress application at the local fluid element position. Extensional stresses are not considered in the current analysis. The equation used to calculate yield stress is as follows: τB − τA τy = τA + 1 + λ (t − t y ) (10) where τB is the pristine yield stress and τA is the residual yield stress of the gel slurry. The term t − ty represents the shearing duration of a local fluid element. The parameter λ is expressed in units of inverse time and characterizes the gel degradation rate.7 Pressure profiles behind the yielding front are computed on the basis of local yield stress conditions, providing accurate estimation of the position and velocity of the gel degradation yielding front. Compression and viscous flow effects are neglected in the current modeling efforts. Future modeling efforts will focus on appropriately coupling the viscous and gel degradation pressure waves for compressible fluids. Yield front calculations are performed for the case of 5 wt % macrocrystalline wax in dodecane. On the basis of the experimental work (Figure 14), the yield stress is assumed to be 289 Pa, with a residual cold slurry yield stress of 5 Pa. A model pipeline is assumed with a length of 1000 m and an inner diameter of 30 cm. A total of 1 bar of pressure is assumed to be applied at the pipe inlet. Computations are performed with four different values of λ to demonstrate the impact of timedependent gel rheology on the pipeline restart hydrodynamics. 6330

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(8) Davidson, M. R.; Dzuy Nguyen, Q.; Chang, C.; Rønningsen, H. P. A model for restart of a pipeline with compressible gelled waxy crude oil. J. Non-Newtonian Fluid Mech. 2004, 123 (2−3), 269−280. (9) Lionetto, F.; Coluccia, G.; D’Antona, P.; Maffezzoli, A. Gelation of waxy crude oils by ultrasonic and dynamic mechanical analysis. Rheol. Acta 2007, 46 (5), 601−609. (10) Paso, K.; Senra, M.; Yi, Y.; Sastry, A. M.; Fogler, H. S. Paraffin polydispersity facilitates mechanical gelation. Ind. Eng. Chem. Res. 2005, 44 (18), 7242−7254. (11) Tinsley, J. F.; Jahnke, J. P.; Dettman, H. D.; Prud’home, R. K. Waxy gels with asphaltenes 1: Characterization of precipitation, gelation, yield stress, and morphology. Energy Fuels 2009, 23 (4), 2056−2064. (12) Aiyejina, A.; Chakrabarti, D. P.; Pilgrim, A.; Sastry, M. K. S. Wax formation in oil pipelines: A critical review. Int. J. Multiphase Flow 2011, 37 (7), 671−694. (13) Alcazar-Vara, L. A.; Garcia-Martinez, J. A.; Buenrostro-Gonzalez, E. Effect of asphaltenes on equilibrium and rheological properties of waxy model systems. Fuel 2012, 93 (0), 200−212. (14) Frigaard, I.; Vinay, G.; Wachs, A. Compressible displacement of waxy crude oils in long pipeline startup flows. J. Non-Newtonian Fluid Mech. 2007, 147 (1−2), 45−64. (15) Vinay, G.; Wachs, A.; Agassant, J. F. Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils. J. Non-Newtonian Fluid Mech. 2006, 136 (2−3), 93− 105. (16) Oh, K.; Jemmett, M.; Deo, M. Yield behavior of gelled waxy oil: Effect of stress application in creep ranges. Ind. Eng. Chem. Res. 2009, 48 (19), 8950−8953. (17) Venkatesan, R.; Nagarajan, N. R.; Paso, K.; Yi, Y. B.; Sastry, A. M.; Fogler, H. S. The strength of paraffin gels formed under static and flow conditions. Chem. Eng. Sci. 2005, 60 (13), 3587−3598. (18) Jia, B.; Zhang, J. Yield behavior of waxy crude gel: Effect of isothermal structure development before prior applied stress. Ind. Eng. Chem. Res. 2012, 51 (33), 10977−10982. (19) Zhao, Y.; Kumar, L.; Paso, K.; Ali, H.; Safieva, J.; Sjöblom, J. Gelation and breakage behavior of model wax−oil systems: Rheological properties and model development. Ind. Eng. Chem. Res. 2012, 51 (23), 8123−8133. (20) Nenningsland, A. L.; Gao, B.; Simon, S.; Sjöblom, J. Comparative study of stabilizing agents for water-in-oil emulsions. Energy Fuels 2011, 25 (12), 5746−5754. (21) Pereira, J. C.; Delgado-Linares, J.; Briones, A.; Guevara, M.; Scorzza, C.; Salager, J. L. The effect of solvent nature and dispersant performance on asphaltene precipitation from diluted solutions of instable crude oil. Pet. Sci. Technol. 2011, 29 (23), 2432−2440. (22) Firooz, A.; Chen, P. Effect of temperature on the surface tension of 1-hexanol aqueous solutions. Langmuir 2011, 27 (6), 2446−2455. (23) Macías-Salinas, R.; Durán-Valencia, C.; López-Ramírez, S. n.; Bouchot, C. Eyring-theory-based model to estimate crude oil viscosity at reservoir conditions. Energy Fuels 2008, 23 (1), 464−470. (24) Paso, K.; Kompalla, T.; Oschmann, H. J.; Sjöblom, J. Rheological degradation of model wax−oil gels. J. Dispersion Sci. Technol. 2009, 30 (4), 472−480.

CONCLUSION In this work, the effect of shear history, thermal history, asphaltenes, and additives on the gelation behavior of model wax−oil and crude oils is investigated. Yield stress values of model waxy oils decrease with an increasing temperature and cooling rate and also decrease with the addition of asphaltenes and additives. The experimental results of optical analysis show that wax precipitation decreases with an increasing temperature. In addition, the experimental results obtained with a tensiometer show that surface tension of model waxy oils decrease with an increasing temperature and the addition of an asphaltene and an additive. It illustrates that temperature, asphaltene, and additive influence the surface tension of model wax−oils. As shown in microscopy, the wax crystal size is reduced at relatively high additive contents. A yield stress model is obtained on the basis of a modified Eyring theory and experimental results. It is shown that the yield stress of a formed gel can be predicted according to a modified Eyring theory. Finally, yield front propagation is calculated according to the Rønningsen convention, demonstrating the impact of time-dependent gel rheology on pipeline restart hydrodynamics.

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AUTHOR INFORMATION

Corresponding Author

*Address: Ugelstad Laboratory, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Sem Sælands vei 4, Trondheim 7491, Norway. E-mail: [email protected] or [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge The Research Council of Norway, Champion Technologies, Petronas, and Statoil ASA for the financial support. All yield front propagation calculations were performed using a computer program developed at the Institute for Energy Technology (Kjeller, Norway) by Peter Borg, Chris Lawrence, and Olaf Skjæraasen.

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REFERENCES

(1) Phillips, D. A.; Forsdyke, I. N.; McCracken, I. R.; Ravenscroft, P. D. Novel approaches to waxy crude restart: Part 1: Thermal shrinkage of waxy crude oil and the impact for pipeline restart. J. Pet. Sci. Eng. 2011, 77 (3−4), 237−253. (2) Phillips, D. A.; Forsdyke, I. N.; McCracken, I. R.; Ravenscroft, P. D. Novel approaches to waxy crude restart: Part 2: An investigation of flow events following shut down. J. Pet. Sci. Eng. 2011, 77 (3−4), 286−304. (3) Magda, J. J.; El-Gendy, H.; Oh, K.; Deo, M. D.; Montesi, A.; Venkatesan, R. Time-dependent rheology of a model waxy crude oil with relevance to gelled pipeline restart. Energy Fuels 2008, 23 (3), 1311−1315. (4) de Souza Mendes, P. R.; de Abreu Soares, F. S.; Ziglio, C. M.; Gonçalves, M. Startup flow of gelled crudes in pipelines. J. NonNewtonian Fluid Mech. 2012, 179−180 (0), 23−31. (5) Alcazar-Vara, L. A.; Buenrostro-Gonzalez, E. Characterization of the wax precipitation in Mexican crude oils. Fuel Process. Technol. 2011, 92 (12), 2366−2374. (6) Ismail, L.; Westacott, R. E.; Ni, X. On the effect of wax content on paraffin wax deposition in a batch oscillatory baffled tube apparatus. Chem. Eng. J. 2008, 137 (2), 205−213. (7) Davidson, M. R.; Nguyen, Q. D.; Rønningsen, H. P. Restart model for a multi-plug gelled waxy oil pipeline. J. Pet. Sci. Eng. 2007, 59 (1−2), 1−16. 6331

dx.doi.org/10.1021/ef3012454 | Energy Fuels 2012, 26, 6323−6331