Study on Two-Phase OilâWater Gelling Deposition Behavior in Low

Article pubs.acs.org/EF

Study on Two-Phase Oil−Water Gelling Deposition Behavior in LowTemperature Transportation Zhihua Wang,*,†,§ Yang Liu,†,§ Jiexun Li,‡ Xianglong Zhuge,‡ and Lei Zhang† †

Key Laboratory for Enhanced Oil & Gas Recovery of the Ministry of Education, Northeast Petroleum University, Daqing, Heilongjiang 163318, People’s Republic of China ‡ Daqing Oilfield Company Limited, Daqing, Heilongjiang 163002, People’s Republic of China S Supporting Information *

ABSTRACT: The waxy crudes gelling and the wax depositing on the inner walls of crude oil pipelines present a costly problem in low-temperature transportation processes. This study focuses on a physical understanding of the gelling deposition during flow of two-phase oil−water in the pipelines. A method for evaluating the gelation characteristic of two-phase oil−water is established, and the effect of emulsified water on gelation is discussed. As the physical properties description, the two-phase diffusion coefficient is found to be a strong function of the water cut. The potential models developed from single-phase flow wax deposition models are proposed spontaneously, and the deposition behavior of two-phase flow in pipelines is predicted under a range of flow conditions in low-temperature transportation. The predictions show that the gelling deposition rate of two-phase oil−water flow is closely related to the pipe flow temperature, external temperature, water cut, and flow rate. The mechanisms of kinetic resistance for diffusion and gelation nucleation related to emulsification are non-negligible under the low-temperature condition. The prediction models are then verified by deposition experiments that are conducted in the laboratory flow loop. This study is not only beneficial to provide a robust and rigorous way to predict two-phase oil−water gelling deposition under the condition of the low-temperature transportation but also significant to well understand the deposition process in oil−water flow. Besides, the study further accelerates the simplification and optimization of petroleum industry production engineering as well.

1. INTRODUCTION Transportation of oil, water, and gas from producing wells to separation units via pipelines with heat tracing is a traditional product gathering pattern in oil fields.1,2 This common pattern ensures a nonstop energy supply downstream, besides the provided heat tracing source and temperature property of products determine the flowing performance, operation cost, and even the transportation safety. In view of the fact that the “pour point”3,4 is not sufficient to delineate the flowing behavior of waxy crudes, an important concept, “gelation temperature”, has been explained and applied to deal with the gelling deposition process of waxy oil under flow conditions.5 Visintin et al.6 observed a sharp increase in pour point, yield stress, and shear viscosity for waxy crude oil emulsions when the volumetric water content was above 25%, which is obtained from the experimental data of dispersed water volume within 70%. Commonly, the peak of the curve between water cut and apparent viscosity of emulsion is defined as the phase inversion point. Although the inversion point has fluid dependency, a stable water-in-oil (W/O) emulsion can be observed at water cuts before the phase inversion point, and an unstable multiple emulsion of water-in-oil in water (W/O/W) can be observed after the point.7,8 At this point, maybe the 70% volume fraction of the dispersed phase was critical value of phase inversion occurred in the distinctive phenomenon observed by Visintin et al.4 With the water cut increasing continually, low-temperature flowing performance of the mixtures would be improved by the activation effect from large amounts of free water inevitably. And then transporting the produced liquid without heat tracing © XXXX American Chemical Society

has prospect, which profit from the efficient utilization of the high water cut adequately, this is so-called multiphase cooling transportation.9,10 As a simplification and optimization process, the multiphase cooling transportation pattern has already been practiced in water flooding wells and polymer flooding wells of Daqing oil field, which is located in an extremely cold area.11,12 The transporting temperatures of these wells are close to the pour point of waxy crudes with high water cut, few of them are even lower than the waxy crudes pour point. Practice indicates that it is beneficial to reduce the budget for building the product gathering system and minimizing the operation cost of surface parts in oil fields.2 However, the two-phase flow patterns identification, the gelling characteristic, and deposition mechanism understanding during the flow of two-phase oil− water in pipelines have all obtained sufficient attention with several operational problems emerged, such as single wells production fluctuated, the effective flow area of the pipeline reduced, and partial or complete blockage appeared eventually. Many numerical models have been proposed and developed to date for the flow of waxy crudes and the associated deposition of waxy crystals within pipelines.13−22 In addition, a few of them are about two-phase oil-gas flow,13,16,17 most of the models may focus on single-phase oil or two-phase oil−water flow.14,15,18−22 In 2004, Paso and Fogler introduced the conception of paraffin components depletion in wax deposiReceived: February 4, 2016 Revised: May 19, 2016

A

DOI: 10.1021/acs.energyfuels.6b00294 Energy Fuels XXXX, XXX, XXX−XXX

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dominated by water. As the previous findings about singlephase oil flow that higher deposit thickness and lower wax fraction in deposit would be caused when it contains lower velocities. Hoffmann et al.20 observed the gelation in two-phase oil−water flow and considered it as a major mechanism for the formation of wax deposits in stratified oil−water flow. The gelation degree strengthened with the deposit thickness increases, and the carbon number distribution characteristic of the deposits in stratified flow region was the same as it is formed in gelation process.20,34 Furthermore, the change in the position of the oil−water interface was considered and addressed the first time, and the wax deposition behavior under nonisothermal oil−water stratified flow conditions was studied by numerical methods.21 The results revealed that the presence of water would relieve the wax deposition significantly by changing the mass and heat transfer characteristics. In addition, there is a much longer period which trebled the time of single-phase oil flow to reach the point of blockage when water phase accompanied in the model channel.21 In this study, the effect of emulsified water on gelation for oil−water mixtures conditions is investigated by the characterization of viscoelasticity using a controlled-stress rheometer and a waxy crude oil from Daqing Oilfield (China). The wax precipitation as a function of temperature is obtained from differential scanning calorimeter (DSC) thermogram, and the phase inversion tests of the waxy crudes are conducted as well. Taking the thermal characteristics and phase inversion behavior of waxy crudes into consideration, the thermodynamic and hydrodynamic computational models developed from singlephase flow wax deposition models are proposed, respectively, and the deposition during the flow of two-phase oil−water dispersions in pipelines are predicted under a range of lowtemperature transportation conditions. Oil−water deposition experiments have been carried out in flow loops device, and the availability of the models is validated by the experimental results. The deposition process is further understood for twophase oil−water flow conditions.

tion.23 However, the paraffin deposition process with oil−water flow conditions is still not well understood. This is because of the difficulty in obtaining consistent results with oil−water mixtures and the higher complexity of the problem with the addition of the water phase. Nevertheless, gas-oil ratio is decreasingly common in everyday field operations, and the water fraction produced by oil wells increasingly common over their lifetime generally, so it would be very useful to account for the increasing impact of emulsified water on crude oil gelling deposition behavior during continued production and operation, especially in the process of multiphase cooling transportation. The presence of water over a threshold value can promote viscous wax-oil gel emulsions accumulation and gel formation.24 These emulsions may be further stabilized by the presence of polar compounds, such as resins and asphaltenes, and it could have about 70% of water cuts.25 Rheological analysis is a traditional method for evaluating the stability and viscoelasticity of waxy emulsions with non-Newtonian behavior.26,27 In 1999, an investigation was carried out with controlled-stress rheometer for exploring how the effect of the shear stress and the cooling rate act on the gelation of a wax-oil mixture. The gel point was defined, and a physical understanding of the effect of thermal and shear histories on the gelation phenomenon of a wax-oil mixture was built.28 In 2000, the rheological structure of crude oil was predicted by Li et al. using the viscoelastic parameters,29 and the feasibility of oscillate shearing experiment for evaluating the modification effect of crude was verified. Cole and Jessen30 performed large scale laboratory experiments under laminar conditions with a deposition cell consisting of a cold plate through which the oil−water mixtures could flow and where the wax deposition would appear, and the effect of the pipe inner wall wettability on wax deposition was also discussed. The results indicated that wax deposition on the more-water-wet surface was significantly reduced with the presence of water, but no difference in deposition was identified for the oil-wet surfaces. In agreement with the results of Cole and Jessen, Hsu et al.31 conducted high-pressure flow-loop experiments with waxy crudes to investigate the effect of water on wax deposition under turbulent-flow conditions. Couto et al.32 established a coldfinger device and conducted oil−water wax-deposition tests with crude oil from the Gulf of Mexico, fresh water and brine for various emulsion characteristics, deposition periods, and temperature gradients. The results showed that the amount of deposit decreases almost exponentially with increasing water cuts, and the emulsion characteristics did not affect the deposition process for the conditions tested. A model of oil−water wax-deposition was developed by modifying the TUWAX (The University of Tulsa’s paraffin deposition software) single-phase deposition model for physical properties and solubility of the mixtures as functions of water cut. But the pioneering investigation assumed that the oil and water phase mixed well with no free oil or free water, and the phase inversion point prediction was not sufficiently considered in the model. Bruno et al.33 conducted a series of oil−water deposition tests using a small-scale flow loop. The results showed a decreasing trend of deposit thickness with increasing water cut for both the different physical properties crude oil tests, the preliminary oil− water wax deposition model developed by Couto et al.32 was validated against the experimental data, and several modifications were proposed to account for water content in the deposit and changes in the diffusion coefficient for flows which were

2. EXPERIMENTAL SECTION 2.1. Thermal Analysis. The experiments are performed using the waxy crude oil from Daqing Oilfield. According to SY/T 0541-200935 (equivalent to ASTM D5853-1136) and SY/T 7550-201237 (in accordance with ASTM D6560-2000 (2005)38), the pour point and wax content was measured as 35.3 °C and approximately 25%, respectively. The onset of waxes crystallization and the crystallization rate is measured by DSC. The temperature can be determined as wax appearance temperature (WAT) when obvious heat effects associated with this change in the crystallization of waxes occur. Details about DSC employed are presented elsewhere.12 The WAT of the waxy crude oil was 48.6 °C based on the DSC thermogram. 2.2. Rheological Measurements. Phase inversion characteristic of the waxy crude is first measured with the actual produced water which was also sampled from Daqing Oilfield. The measurement experiments are conducted in accordance with ASTM D 4440-2015.39 And the emulsifying structure is further confirmed by microscopic method. Then, the oscillatory shearing experiments are conducted for distinguishing the gelation behavior by controlled-stress rheometer. Exerting a dynamic stress which changes according to the time variable of sine function to two-phase oil−water: τ = τ0sin(2πft )

(1)

where, τ is dynamic stress, Pa; τ0 is the amplitude of dynamic stress, Pa; and f is the oscillation frequency, Hz. The measured strain related to time is B


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Figure 1. Schematic illustration of the flow loop device. γ = γ0sin(2πft + δ)

conditions. Details about the calculation equation of wax thickness and deposition rate in pipe wall are used in the differential pressure method which are presented elsewhere.46,47 As shown in Figure 1, both the closed horizontal test section and closed reference section have the same internal diameter as 2 in. and the same length as 16 feet long of the steel tubing. Both of the sections have taps connected to temperature transducers and differential pressure transducers every 8 feet, and a data acquisition system records the flow parameters of the fluid in the test section as well as the reference section. The closed installation can be operated at the pressure of 300 psi. In the operation, the waxy crudes and produced water sampled from Daqing Oilfield are poured into the oil tank and the water tank respectively, and are heated to 50−55 °C at first. Then, oil and water are pumped into the stirred tank in turn, which the temperature condition is maintained identically. Meanwhile, the twophase systems water cut are regulated by controlling the flow rate, and the sufficient mix and emulsification are realized. During a typical run, a specified oil−water mixture with a certain flow rate is pumped from the stirred tank through the test section which is cooled by a controlled temperature bath, the mixture is then returned to the stirred tank again, and the stirred tank is real-time maintained with the outlet temperature of the fluid in the test section identically. By the cycle repeating, the flow parameters of this condition are recorded. Furthermore, the simulation of pipeline operating environment in cold weather is realized using high-power refrigeration system in controlled temperature bath. Then, flow loop experiments which use the same properties of oil−water mixture in the reference section are conducted as well, and the stirred tank temperature is controlled above the WAT of waxy crude oil. The gelling deposition on the wall of the test section will be determined reasonably from the increase in the pressure drop as measured.

(2)

where, γ is dynamic strain, γ0 is amplitude of dynamic strain, and δ is phase angle between stress and strain. For pure elastic solid, phase angle between stress and strain is 0°; for pure viscosity species, δ = 90°; for viscoelastic species, 0° < δ < 90°. The energy storage and loss of the species can be characterized as storage modulus (G′) and loss modulus (G″), respectively. Thus, the storage modulus can be described as G′ = G*cos δ, and relating to the strength of the elasticity. The loss modulus can be described as G″ = G*sin δ, and relating to the degree of the viscosity. And G* is an absolute complex modulus (G* = τ0/γ0).40 The two-phase systems are created with the actual produced water, and volumetric water cut is 60%, 70%, 80%, 90%, and 95%, respectively. The oscillation frequency is 1 Hz, dynamic stress is 0.125 Pa, temperature scanning region range from 50 to 10 °C, and the cooling rate is 0.25 °C/min. The storage modulus (G′) and the loss modulus (G″) are measured under different oil−water conditions. Alternatively, the relationship between viscoelastic modulus and temperature is established. 2.3. Flow Loops Experiments. The methods for the determination of deposit thickness can be categorized as direct and indirect methods.41 As for the indirect methods, pressure drop method, heat transfer method, and liquid displacement-level detection (LD-LD) method are three online wax measurement techniques which have been used to measure the deposition thickness of single-phase or multiphase flow pipelines.42 And the LD-LD method was used in the published literature to study both circumferential and longitudinal distributions of wax thickness during gas−liquid two-phase flow in vertical and horizontal pipelines.42 Although an error analysis of the deposit measurement techniques has shown that the heat transfer method is more appropriate for laminar flow condition and the pressure drop method is more appropriate for turbulent flow condition.43−45 The pressure drop method, which cannot impose any effects on the heat transfer process, consumes less time and requires lower experimental cost, etc., is still recognized in the paraffindeposition experimental study when there are no slug flow and stratified flow patterns of two-phase oil−water in low-temperature.46−48 Differential pressure method, as a expansion of the pressure drop method, is used in the flow loops experiments. This method is based on the principle that the extra increase of frictional pressure drop over the pipe section stems from the reduction of the hydraulic diameter when wax deposition appears. Thus, the deposition rate can be determined by contrasting the frictional pressure drop of test pipe sections and reference pipe sections under the same

3. COMPUTATIONAL MODELS Under the low-temperature condition of typical non-Newtonian fluids, wax precipitation undoubtedly plays a predominant role in two-phase deposition behavior. So, there are potential solutions to establish computational models by modifying the existing single-phase flow wax deposition model15,22,49−52 for physical properties of the two-phase as functions of water cut. 3.1. Thermodynamic Model. The mathematical principle of thermodynamic method is classic and simple, which focus on explaining the molecular diffusion mechanism. When the shear C


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k τm w

1+n 1 ⎛ dCd ⎞⎛ dT ⎞ ⎜ ⎟⎜ ⎟ f wp μo − w ⎝ dT ⎠⎝ drd ⎠

Jdow = −Dow ρd × ϕ(M wow )

dCd dT

× L

dT drd

L

(6)

where 2 ⎛ ⎞−1 α 2M wow ⎟ ϕ(M wow ) = ⎜1 + 1 − M wow ⎠ ⎝

(3)

where, Wo−w is gelling deposition rate in two-phase flow, g/ (m2·h); τw is flowing shear stress of two-phase, Pa; f w is mass water cut of two-phase, %; μo−w is apparent viscosity of twophase, Pa·s; dCd is waxy crystals solubility coefficient, °C1−; dT is

and Jcow is convective mass flux from bulk to interface in twophase flow, kg/(m2·s); Jdow is diffusive mass flux into gelling deposition in two-phase flow, kg/(m2·s); Dow is diffusion

drd

dT

(7)

radial temperature gradient, °C/m; and k, m, n, p are coefficients and indices related to paraffin-deposition behavior. In the model of eq 3, when p = 0, it turns to be a single-phase paraffin deposition model, and its universality has been verified by Huang et al.53 τw and μo−w can be measured from rheological experiments. dCd can be obtained from the conversion of DSC dT thermogram for waxy precipitations which is a function of temperature. Operating eq 3 using denary logarithm, then the values of fitting parameters can be determined by multiple linear regression using Statistical Product and Service Solutions (SPSS) software with experimental data of physical properties, thermal analysis, and rheological measurements. Furthermore, unlike steady state process, effective diameters of pipelines change with the increase of deposit thickness, so dT can be

coefficient of wax in oil, m2/s;

determined by FLUENT software using the finite volume discretization method, and the governing equations, the twodimensional unstable heat conduction differential equations and the boundary conditions are summarized in detail in Supporting Information. 3.2. Hydrodynamic Model. Assuming that the deposition layer is immobile, and the densities of the waxy crude oil and deposition species are approximately equal, as eq 4 demonstrated, a single-phase paraffin deposition model has been proposed by Hernandez15 which developed from the Singh et al.54 model.

Where, is gelling deposition thickness change rate in twophase oil−water flow, m/s, and Jsow is shear removal flux of gelling deposition in two-phase flow, kg/(m2·s). Thus, the hydrodynamic mathematical model used to describe the deposition behavior of two-phase flow in pipelines is established.

dT drd

L

is radial temperature gradient in two-phase flow with a certain position, °C/m; ρd is density of gelling deposition in two-phase flow, kg/m3; Mwow is wax fraction in gelling deposition of twophase oil−water flow, %; α is aspect ratio of wax crystals. Substitution of eqs 5, 6, and 7 into eq 4 yields dh = dt

−Dow

dCd dT L

×

dT drd

L

× [1 − ϕ(M wow )] − Jsow ρ−d 1 M wow (8)

dh dt

4. RESULTS AND DISCUSSION 4.1. Thermal Property. The DSC thermogram of the waxy crude oil reveals a 210 J/g average value of paraffin crystallization heat is extracted. For the convenience of determining the solubility coefficient of waxy crystals, the relevant calculation with experimental data of latent heat is performed, and the conversion of DSC thermogram for wax precipitation as a function of temperature is realized and shown in Figure 2. It can be observed that the wax precipitation of crude oil has a stepped rise with the temperature dropping, which presents a small and narrow peak at around 45 °C, and a

(4)

Where, δ is deposition thickness, m; t is time, s; Jc is convective mass flux from bulk to interface, kg/(m2·s); Jd is diffusive mass flux into deposition, kg/(m2·s); Js is shear removal flux, kg/(m2· s); Mw is wax fraction in deposition, %; and ρw is wax density, kg/m3. Although W/O emulsions and W/O/W emulsions are heterogeneous multiphase dispersion systems at the micro level, the oil−water mixtures can be assumed as pseudo singlephase fluids when investigating the flowing problems with continuum theory or macro-approach. To some certain crude oil, the wax is only soluble in oil phase, and the solubility which varies with temperature is a constant with the water cut change. Then, the hydrodynamic deposition model15 expanded from the diffusion explanation and the diffusivity definition55 is expected to be used in two-phase oil−water for understanding the gelling deposition behavior in low-temperature transportation. The equation between convective mass flux and diffusive mass flux can be established as follows: Jcow =

is waxy crystals solubility

coefficient in two-phase flow with a certain position, °C1−;

drd

J − Jd − Js dδ = c dt ρw M w

dCd dT L

Jdow ϕ(M wow )

(5)

Figure 2. Wax precipitation as a function of temperature for crude oil. D


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Energy & Fuels large and broad peak at around 20 °C. With the further cooling, the temperature drops below 20 °C, the mass percent of wax precipitation appears to have a linear decline. This indicates that an obvious heating effect related to wax crystal precipitation occurs at about 45 °C, and a major exotherm is exhibited near 20 °C. This can be concluded that paraffin crystallization characteristic of the crude oil is affected by molecular weight, carbon number distribution, as well as the structure and branching degree of paraffin molecular. Wax with greater carbon number starts to precipitate in the temperature region which relates to the narrow peak, and the wax with lower carbon number tends to precipitate in the temperature region corresponding to the broad peak. The synergistic effects of the strong thermal dependence and the complexity of crude oil composition on wax precipitation are revealed. This is also in agreement with the shift feature of the peak in deposit carbon number distribution obtained under different coolant temperature and oil flow rate conditions.34 4.2. Phase Inversion Property. Figure 3 shows the results from phase inversion property test. It indicates that under the

Figure 4. Microscopic observation of emulsions at 35 °C. The water fractions in (a), (b), (c), and (d) are 55%, 65%, 75%, and 90%, respectively.

take over as the continuous phase, and this is also confirmed by the transition which will be mentioned below from stable laminar flow as the water cut increases toward the phase inversion point to core-annular flow regime at 85−95% water cuts in two-phase oil−water flow-loop experiments. 4.3. Effect of Emulsified Water on Gelation. As shown in Figure 5, the relationship between viscoelastic modulus of two-phase and temperature under different oil−water conditions is established. It reveals that the presence of water phase would not weaken gel formation. Instead, it can promote viscous gel emulsions formation. The close correlation is presented when the two-phase system water cut is above the phase inversion point. During the cooling process, the twophase exhibits a certain degree of viscoelasticity, this can be attributed to the aggregation of waxy crystals, emulsified water and several kinds of polar compounds, and the gradual growth of waxy crystals which is precipitated from crude oil. After the storage modulus (G′) associates with the loss modulus (G″), the viscoelastic modulus would have a sharp increase with the temperature dropping, and the gelation behavior will aggravate until the modulus tends to be stable. Then, the thermal dependence of the two-phase decreases gradually, and the solidity feature of gelation is sufficiently formed. Under the same cooling condition, the fluctuant impact from free water on viscoelastic modulus could be observed when the water cut continues to increase. The method of evaluating the oil−water gelation process can be developed spontaneously. During the cooling process of two-phase oil−water, the temperature can be defined as the gel point when the storage modulus (G′) and the loss modulus (G″) are equal, and this temperature corresponds to initial line intersection of rheological curves. And when the elasticity of two-phase oil−water takes the predominant role, the temperature, which corresponds to the storage modulus (G′) that tends to be stable, can be defined as lower limit of the gel point. Furthermore, the strength of gelation can be characterized quantitatively by the storage modulus (G′), it can be used for explaining the shearing deformation resisting ability and the internal structure yield property of waxy crudes which are affected by emulsified water. By means of this method, the gelation characteristic parameters of two-phase oil−water can

Figure 3. Phase inversion test (35 °C).

condition of low-temperature near to the pour point of the waxy crude oil, the apparent viscosity of the two-phase increases with the addition of water until it reaches the peak of water cut at 60−65%. It is evident that W/O emulsions have been formed under the conditions, and it reaches the phase inversion point after 65%. With the further addition of water, because of the formation of multiple emulsions of W/O/W, the apparent viscosity of the two-phase system drops sharply, and the viscosity readings tend to fluctuate above and below. Microscopic observation of the two-phase at different water cuts further reveals the mechanism of phase inversion behavior. The smaller and more uniform droplet size distribution of the dispersed water phase seems to exist for emulsion at 65% (Figure 4b), the microstructure of W/O and the aggregation of wax crystals can be observed clearly for emulsion at 55% (Figure 4a). In Figure 4c and d, the multiple emulsifying structure regarding water as continuous phase starts to present for two-phase after inversion point, droplet sizes also grow as water cut increases, and coarse droplets can be observed at higher water cut of 90%. Besides, the emulsions show a shear thinning non-Newtonian behavior before and after the inversion point, and a more noteworthy effect of shear rate on the apparent viscosity can be observed as the dispersed phase fraction increases. Furthermore, the stability of the emulsion breaks down after inversion point, the water begins to E


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Figure 5. Relationship between viscoelastic modulus and temperature.

functions of water cut, and the computational model of deposition rate in two-phase flow is established:

be determined in Table 1. The results indicate that, like the description of single-phase gelation behavior, rheological Table 1. Experimental Results of Gelation Characteristic Parameters water cut of two-phase (%)

gel point (°C)

equilibrium value of G′ (Pa)

60 70 80 90

33.4 33.2 32.7 32.0

28000 8520 4830 3000

Wo − w = 826.35τ−w0.4239f w−0.3806

0.6373 1 ⎛ dC ⎞⎛ dT ⎞ ⎜ ⎟⎜ ⎟ μ ⎝ dT ⎠⎝ dr ⎠ o−w

(9)

Under different conditions, the gelling deposition rate can be calculated by extracting physical parameters and thermal property data simultaneously. As shown in Figure 6, the gelling deposition rate predicted from thermodynamic model reaches a maximum just at the gel point, and then gradually decreases as the flow temperature drops. The behavior could be attributed to the flux of species toward the pipe wall which is affected by both molecular diffusion and thermal diffusion. The driving force for the former is the concentration gradient (dC/dT), and the driving force for the latter is the temperature gradient (dT/ dr). The role of the two gradients would not be proportional in the gelling deposition layer. This shows excellent agreement with the previously obtained understandings about the effects of thermal diffusion and molecular diffusion in wax deposition predictions reported by Hussein et al.57 Figure 7 shows the effect of water cut on gelling deposition, it exhibits that there are two different slopes in the functional relationship, the water cut which is represented by the intersection of slopes equals the phase inversion point, and the gelling deposition drastically decreases with the water cut increases. It indicates that the existence of the emulsified water would further promote gelling deposition behavior in low-temperature transportation, and the water-annulation around pipe wall is formed much easier in the

measurements are also suitable to the physical understanding of two-phase gelation characteristic in low-temperature transportation. The gel point of two-phase is lower than the pour point of crude oil itself. However, a depression in the gel point and a decrease in the gelation network strength are observed with a higher water cut. It is significant to take the effect of emulsified water on gelation into consideration, and the gel network would be developed by the aggregation of waxy crystals and water at low-temperature conditions. This shows a reasonable agreement with previously established correlations and experimental data for a wax-oil gel emulsion reported by Paso et al.56 4.4. Deposition Behavior of Two-Phase Flow in Pipelines. 4.4.1. Prediction with Thermodynamic Method. As mentioned above, the correlation coefficients are determined by the multiple linear regression with experimental data, the physical properties of the oil−water mixture are obtained as F


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Figure 6. 85% water cut gelling deposition rate as a function of temperature.

Figure 7. 4.08 m3/h flow rate gelling deposition rate as a function of water cut.

Figure 8. Gelling deposition rate under the low-temperature of 33 °C as a function of flow rate.

high water cut two-phase flow, thus inhibiting the species precipitation. The results are in well agreement with the twophase oil−water rheological measurements data above. Figure 8 reveals that the gelling deposition rate decreases as the flow rate increases, and the amount of deposition reduces at higher flow rate in the same period. And this is consistent with the conclusion of single-phase flow that an increase in flow rate resulted in a decrease in the amount of paraffin deposition.41,43,54,58−61 However, differ from the fact that wax deposits formed in single-phase flow at higher flow rates are considerably harder than those formed at lower flow

rates,43,46,54,62−66 since the effect of emulsified water on gel network, the deposition species obtained at different flow rates of two-phase flow on pipe walls are loose, and shape like a porous medium. Similarly, there are two different slopes in the functional relationship, the flow rate which represented by the intersection point of slopes is about 1.35 m3/h. When below this flow rate, the gelling deposition behavior which is affected by the shear stripping mechanism may be neglected reasonably. In addition, from the results above, in identical working conditions of two-phase low-temperature transportation, when the external temperature has a significant decrease, which G


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Figure 9. 85% water cut gelling deposition rate as a function of temperature.

Figure 10. 4.08 m3/h flow rate gelling deposition rate as a function of water cut.

means that the differential temperature between the oil−water and the pipe wall increases, the gelling deposition rate would be multiplied. 4.4.2. Prediction with Hydrodynamic Method. As mentioned above, the physical properties of the two-phase oil− water flow are all functions of water cut which can be determined. In the hydrodynamic model of eq 8 above, Mwow and ρ d can be directly measured after the flow-loop experiments. Regard the solubility of paraffin in two-phase systems as a fundamental physical property, the value of waxy crystals solubility coefficient

dCd dT L

Dow = 13.3 × 10−8 ×

V A0.71

(11)

where, T is pipe flow temperature, °C, and μo−w is apparent viscosity, mPa·s. Molar volume of paraffin molecules VA can be valued as 435 cm3/mol and γ = 10.2/VA + 2.209. The Dow at water cuts after the inversion point can be calculated as follows: Dow = Do(1 − fw )

(12)

where, f w is water cut, %; Do is diffusion coefficient of wax in oil without water phase; and the details about correlated value of the coefficient are consistent with the investigation of Singh et al.54 The previous data obtained from the single-phase oil flow loop have revealed that the shear removal flux may be constant with time for the same flow conditions.67 Thus, the shear removal flux of gelling deposition in two-phase oil−water flow can be defined as μ τw Jsow = k′ o − w Q ρo − w γ̇w (13)

can also be obtained from

the conversion of DSC thermogram for waxy precipitations, which is a function of temperature. As the previous findings from Singh et al. about the aspect ratio which is a much weaker function of the pipe wall temperature,54 α depicted as a function of flow rate in low-temperature transportation, can be estimated from α = −9.44 ln Q + 148.95

(T + 273.15)1.47 μoγ − w

(10)

where, Q is two-phase flow rate, m3/s. And based on the development of correlations for prediction of molecular diffusion coefficient in liquids, the determination of Dow at water cuts before the inversion point can use the following equation:

where, ρo−w is density of oil-wax mixture, kg/m3; γ̇w is shear rate, 1/s; Q is two-phase flow rate, m3/s; k′ is a constant related to shearing and stripping, can be determined in the similar way with the regression of correlation coefficient in thermodynamic model above by extracting physical parameters, loop experiH


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Figure 11. Gelling deposition rate under the low-temperature of 33 °C as a function of flow rate.

Newtonian fluid,42,44 the two-phase in this experiments is treated as a non-Newtonian fluid in consideration of the high wax content of 25% and the oil−water emulsification. The Reynolds numbers in the experimental simulations are shown in Figure 12, it is evident that the dispersed phase volume

ments data, and the equivalent rheological measurements data at gel point of two-phase. Furthermore,

dT drd

can also be determined by FLUENT L

software using the finite volume discretization method, and the details are summarized in the Supporting Information. Hence the deposition rate computational model of two-phase flowing which develops from the hydrodynamic method can be expressed as dh = dt

−Dow × 10−4

−4.06 ×

dCd dT L

×

dT drd

L

× [1 − ϕ(M wow )]

0.35 μ τ 10−8 Q oρ−w γ̇w ρ−d 1 o−w w

0.35

(14)

Also, according to the details about the procedure of determining all these constants and variables mentioned above, combining the experiment results with large-scale calculations, all the parameters in eq 14 can be obtained, and the gelling deposition rate under different conditions can be calculated. From Figure 9, the gelling deposition rate would gradually increase while the temperature of two-phase flow in pipe decreases. When below the gel point, the deposition rate decreases in a degree. The result also indicates that these two mechanisms of molecular diffusion and thermal diffusion have no specific ratio in contribution to the gelling deposition behavior. As shown in Figure 10, the gelling deposition rate decreases with the two-phase water cut increases, in particular, it would have a significant decrease when the water cut exceeds 70%. It can be attributed to the diffusion coefficient (Dow) decrease in this model when the water cut increases. Also, the water-annulation around pipe wall is formed much easier as explained above. Figure 11 shows the predictions of gelling deposition rate as a function of flow rate with hydrodynamic method. The gelling deposition behavior mitigate with the flow rate of two-phase increase under low-temperature conditions. It can be concluded that the flow rate change may cause the variation of shear stripping flux and aspect ratio of waxy crystals, which can be utilized for explaining the mechanism reasonably. 4.4.3. Availability Verification. The flow-loop experiments with the differential pressure principle have been performed, and differ from the fact that the non-Newtonian behavior of low wax crudes is not appreciable and it is commonly treated as

Figure 12. Reynolds numbers as a function of water cut at different flow rates of the two-phase.

fraction and flow rate affect the transition from laminar flow to turbulent flow. In the present work, this transition toward turbulent flow occurs as the water fraction is higher than 90% and the flow rate is over 0.31m/s. And as mentioned above, the extra increase of pressure drop over the pipe section depends on the reduction of the hydraulic diameter resulting from wax deposition appears, so the average thickness deposition rate can be obtained by contrasting the pressure drop of test sections and reference sections in simulation experiments. The results for the experimental simulations are shown in Figure 13, the differences in the deposition rate obtained for both conditions are within 20% error band of the measurements. Furthermore, the transition of flow regimes is identified as water cut increases over the phase inversion point, and the core-annular flow regimes are completely formed in the flow-loop experiments when the water cut of two-phase is at 85−95%. Comparison between quantitative predictions and measured data in flow-loop experiments of the gelling deposition rate is also presented in Figure 13. Both of the predicted results obtained by the two computational methods closely match the large-scale flow-loop data. However, the deviation of hydrodynamic method is much lower, the mean relative deviations in I


Article

Energy & Fuels

Figure 13. Deviation of gelling deposition rate obtained by simulation and prediction.

existing deposition in two-phase oil−water flow, a kinetic resistance for the diffusion is non-neglectable either. This finding provides an expanded explanation for the existing paraffin deposition theory from single-phase flow,68−70 and the mechanisms of diffusion, shearing, and gelation are concomitant in two-phase flow. The molecular diffusion is still a primary deposition mechanism, but the driving force related to

various typical conditions are about 10%, which means that the predicted data and experimental data agree fairly well. It indicates that as the driving force for molecular diffusion in the two-phase flow, the interfacial concentration is different from the equilibrium concentration at the low-temperature interface. Besides considering that part of the bulk flux will contribute to new deposition growth and the rest will be diffused into the J


Article

Energy & Fuels radial temperature gradient is not balanced because of the presence of water, and the transition of flow conditions which is caused by the dispersed water phase strengthens the shearing dispersion and shear stripping mechanism. Furthermore, it can be concluded that the gelation nucleation related to emulsification is a particular deposition mechanism of twophase flow in pipelines, and the paraffin adsorbed on dispersed phase surface and the polar components accumulate gradually and form a network structure at low-temperature, this nuclearlike gel network set with emulsified water deposits with the changes of flow conditions and surface properties of pipelines, and the porous deposits are formed. This mechanism of gelation nucleation which related to emulsification is more suitable for the explanation of local gelling deposition behavior in two-phase flow. Also, this understanding shows good agreement with single-phase paraffin deposition model improved by Hernandez.15 So, it is available to utilize the hydrodynamic method which developed from single-phase flow wax deposition model for further understanding the two-phase gelling deposition behavior, and provide a robust and rigorous way for reliable predicting the two-phase gelling deposition under a range of flow conditions in low-temperature transportation.

As the emulsions between waxy crude oil and water may be stabilized by the presence of polar compounds, such as asphaltenes and resins, future work should focus on extending the existing knowledge of the polar compounds impact on gelling deposition at single-phase flow to multiphase flow.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.6b00294. Solving equations of radial temperature gradient in twophase flow (DOC)

■

AUTHOR INFORMATION

Corresponding Author

* Telephone: 86-459-6503-102; Fax: 86-459-6503-482; E-mail: [email protected]. Author Contributions §

Z.H.W. and Y.L. contributed to the work equally.

Notes

The authors declare no competing financial interest.

■

5. CONCLUSIONS In this work, simulation experiments and model predictions were carried out to investigate the gelling deposition behavior of oil−water in low-temperature transportation. First, the thermal property and phase inversion point of the waxy crude oil were determined. The DSC thermogram reveals that wax precipitation has a stepped rise with the temperature dropping, and it is consistent with the conclusions from the previous studies, which show that the peak of wax deposit carbon number distribution shifts toward higher carbon numbers as the temperature increases.34 W/O and W/O/W emulsions are formed before and after the inversion point respectively, and the stability of the emulsions breaks down after inversion point. Then, a method which uses rheological measurements for evaluating the gelation characteristic of two-phase oil−water was established. It was found that the gelation behavior is significantly affected by the emulsified water, and the gel network would be developed by the aggregation of crudes, waxy crystals, and emulsified water at low-temperature conditions. Potential thermodynamic and hydrodynamic computational models developed from single-phase flow wax deposition models were proposed, respectively, and the deposition behavior of two-phase flow in pipelines was predicted under a range of flow conditions in low-temperature transportation. The prediction results show that two-phase oil−water flow gelling deposition rate is closely related to the pipe flow temperature, external temperature, water cut, and flow rate. The gelling deposition experiments identify the flow regimes transition from stable laminar flow to core-annular flow regime which completely emerges at 85−95% water cuts as the water cut increases over the phase inversion point, and further confirmed that the hydrodynamic method could be better for understanding the two-phase gelling deposition behavior scientifically. It is concluded that in addition to diffusion and shearing mechanism, gelation nucleation related to emulsification is another coexistent deposition mechanism, and this also provides an alternative explanation for the existing wax deposition mechanisms in oil−water flow.20

ACKNOWLEDGMENTS This work was financially supported by the State Key Program of National Natural Science Foundation of China (Grant No. 51534004) and the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (Grant No. UNPYSCT-2015074).

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