Energy Fuels 2011, 25, 753–761 Published on Web 02/17/2011
: DOI:10.1021/ef101195a
Modeling Formation Damage due to Asphaltene Deposition in the Porous Media Bahram S. Soulgani,*,† Bahman Tohidi,‡ Mohammad Jamialahmadi,§ and Davood Rashtchian† †
Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran 11155-9465, Iran, ‡ Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom, and § Petroleum University of Technology, Ahwaz 63431, Iran Received September 4, 2010. Revised Manuscript Received November 30, 2010
Asphaltene deposition in a reservoir severely reduces the effective permeability and results in a reduction in oil production. The main term in asphaltene deposition modeling in the porous media is pore surface deposition. Previous models do not describe the effects of different parameters (i.e., concentration, velocity, and temperature) on the pore surface deposition term. We report the results of a series of experiments carried out to study the effects of the above parameters on the surface deposition term using an accurate thermal method. Based on these data, a new expression for the surface deposition term has been developed and implemented in asphaltene deposition modeling. The developed model was used in simulating formation damage due to asphaltene deposition in porous media. The results are very promising and the calculated permeabilities are in very good agreement with the experimental data reported in the literature.
such as miscible injection, natural gas injection, or CO2 injection, as they may intensify the asphaltene deposition problem in reservoir. There are various techniques to prevent and/or remove asphaltene from the wellbore, tubing, and surface facilities. They include inhibitor injection and chemical washing. Deposited asphaltene could be remove by applying various remedial treatments such as solvent soaks with aromatic solvent and/or aromatic solvent blended with dispersants, and/or physical removal.6 Modeling asphaltene deposition could play a major role in estimating the amount and location of asphaltene deposits and/ or resulting formation damage, as well as frequency of treatment. Most of the existing asphaltene deposition models are based on the Gruesbeck and Collins7 work which considered porous media as two different parallel pathways with small and large pore sizes. They explained the mechanism of solid deposition with three terms that include surface deposition, entrainment, and pore plugging. The first two terms occur in the large pores and the last one occurs in the small pores. Civan8 reported the first model for the asphaltene deposition in porous media by improving the Gruesbeck and Collins7 model. Ali and Islam9 provided a model for asphaltene deposition in porous media that incorporated asphaltene adsorption using the surface excess theory of Sircar10 with the original model of parallel pathways. They have performed a series of experiments with artificial carbonated core and a mixture of crude oil and asphaltene with 60:40 volume ratio
1. Introduction Asphaltenes are the heaviest fraction of crude oils which are generally defined as the fraction that is soluble in aromatic solvents such as benzene or toluene, and insoluble in normal alkanes such as n-pentane or n-heptane.1 Asphaltenes are polyaromatic structures or molecules, containing heteroatoms (i.e., S, O, N) and metals (e.g., Va, Ni) that exist in petroleum fluids in an aggregated state.2 These aggregates are stabilized in solution by resins and aromatics, which act as peptizing agents.3 In terms of physical appearance, asphaltenes are dark brown to black friable solids with no definite melting point. Asphaltenes and resins are in thermodynamic equilibrium at static reservoir condition. However changes in thermodynamic conditions such as pressure, temperature, or composition during oil production may cause stabilized asphaltenes to precipitate out of fluid and they could deposit in the reservoir, wellbore, wellstring, pipelines, and surface processing facilities.4 The precipitation and deposition of asphaltene in a reservoir can severely reduce the oil production due to permeability impairment, changes in the rock wettability, or increase in the produced fluid viscosity; the first of these (i.e., permeability damage) appears to be the dominant mechanism of formation damage.5 Asphaltene deposition may have an adverse effect on some enhanced oil recovery processes *To whom correspondence should be addressed. E-mail:
[email protected]. (1) Speight, J. G. The Chemistry Technology of Petroleum, 3rd ed.; Marcel Dekker: New York, 1999. (2) Civan, F. Reservoir Formation Damage-Fundamentals, Modelling, Assessment, Mitigation; Gulf Publication: Houston, TX, 2000. (3) Bunger, J. W.; Li, N. C. Chemistry of Asphaltene; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1981. (4) Khalil, C. N.; Rocha, N. O.; Silva, E. B. Detection of Formation Damage Associated to Paraffin in Reservoirs of the Reconcavo Baiano, Brazi; Society of Petroleum Engineers: Houston, TX, 1997. (5) Leontaritis, K. J.; Arnaefule, J. O.; Charles, R. E. SPEJ, Soc. Pet. Eng. J. 1994, 9 (3), 157–164. r 2011 American Chemical Society
(6) Allenson, S. J.; Walsh, M. A. A Novel Way to Treat Asphaltene Deposition Problems Found in Oil Production; Society of Petroleum Engineers: Houston, TX, 1997. (7) Gruesbeck, C.; Collins, R. E. SPEJ, Soc. Pet. Eng. J. 1982, 22 (6), 847–856. (8) Civan, F. Modeling and Simulation of Formation Damage by Organic Deposition; Int. Symp. Colloid Oil Prod.: Rio de Janeiro, 1995. (9) Ali, M. A.; Islam, M. R. SPEJ, Soc. Pet. Eng. J. 1997, 13, 178–183. (10) Sircar, S.; Novosad, J.; Myers, A. L. Ind. Eng. Chem. Fundam. 1972, 11, 249–254.
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11
as injected fluids. Wang et al. presented an improved modeling of asphaltene and wax deposition simultaneously. They verified their model, using the data reported by Minssieux12 on asphaltene deposition in core. There are few models for asphaltene deposition in the near wellbore area. Leontaritis13 developed a simplified model for predicting formation damage and productivity decline due to asphaltene deposition in under-saturated asphaltenic oil reservoirs. Almehaidab14 presented a model for asphaltene deposition near wellbore. Kocabas et al.15 modeled asphaltene deposition near wellbore based on the previous Ali and Islam deposition modeling. In all the above models the surface deposition term (which is the most important term16 is based on the Gruesbeck and Collins7 experiments for fine mineral solid deposition and not asphaltene deposition. Therefore, the above models do not use basic asphaltene deposition data and the related parameters (i.e., temperature and velocity). Although the near wellbore region is more accessible with respect to remedial action, formation damage due to asphaltene deposition plays a major role in well inflow performance. Therefore, it is crucially important to develop a reliable model for predicting such formation damage, hence frequency of treatment and/or remedial actions. There are some important parameters that could play a major role in asphaltene deposition, including temperature, velocity, and concentration. Temperature is generally constant in a reservoir, however, there could be a significant temperature change near the wellbore due to JouleThomson effect and fluid evaporation, as a result of higher pressure drop near the wellbore. Velocity could also increase sharply near the wellbore, due to an increase in volumetric flow rate (as a result of pressure drop) and a reduction in flow area. The above two parameters could also contribute to a change in asphaltene concentration which in turn could affect asphaltene deposition. Therefore, it is crucially important to take into account these parameters while modeling asphaltene deposition near the wellbore. This paper presents a comprehensive model for surface asphaltene deposition, using a new term for surface deposition. The new term has been optimized using experimental data generated in this laboratory. The experimental work included a series of tests for determination of asphaltene deposition on the internal surface of a flow tube carried out by using accurate thermal technique. The developed model was used to predict permeability reduction due to asphaltene deposition in a core sample. The results are in excellent agreement with the literature experimental data of Minssieux.12
tated asphaltene could result in an increase in the fluid viscosity, whereas deposited asphaltene could reduce the flow conduit. There are limited data available on asphaltene deposition and permeability damage using core flooding experiments. However, these tests are very relevant with respect to estimating permeability reduction due to asphaltene deposition. Core flooding could be considered as one-dimensional linear flow with negligible gravity effect. The capillary effect could also be ignored as single-phase oil is used in most core flooding experiments. Therefore, for modeling core flooding one can ignore the effect of gravity and capillary forces. This will reduce the model to a mass balance for oil and asphaltene, a momentum balance, and a relation between porosity and permeability. The mass balance for the oil phase is given by D D φFL wO þ F uL wO ¼ 0 ð1Þ Dt Dx L The mass balance for the asphaltene is given by D D φC A FA þ φFL wA þ FL uL wSA þ FL uL wA Dt Dx :
¼ - FA V AD
ð2Þ
As discussed before, different models have been developed for calculating the rate of asphaltene deposition (i.e., V_ AD) in the porous media. The momentum balance equation is given by Darcy’s law. u ¼
k dp μ dx
ð3Þ
Gruesbeck and Collins7 developed the theory to describe deposition and entrainment of fines in porous media. They assumed porous media as two different parallel pathways with smaller pore size that can be eventually plugged completely and larger pore size that cannot be completely plugged. Civan8 improved the formulation of Gruesbeck and Collins7 and provided a model based on the three terms surface deposition, entrainment, and plugging without applying parallel pathways. Wang et al.17 proposed eq 4 for the net rate of asphaltene deposition in porous media. : V AD ¼ RA S L C A φ - βA V A υL - υcr, L þ γAi ð1 þ σ A V A ÞuL S L C
ð4Þ
The first expression is a surface deposition term which is the dominating term in rate of asphaltene deposition. This term describes the amount of asphaltene deposition on the surface of pores which is based on Gruesbeck and Collins’7 experiments on fine mineral particles. They concluded this term is only proportional to the concentration of fine particles. However, one should note that the experiments have been conducted using fine mineral particles and not asphaltene. In our opinion this is major shortcoming with respect to modeling asphaltene deposition and the main aim of this work is to improve this term, as detailed later in this article. The second term represents the entrainment due to high fluid velocity. Deposited asphaltenes on the surface of the pore throats reduce the available diameter for flow, as a result the interstitial velocity increases. When the interstitial velocity exceeds the critical velocity, some of the deposits dislodge
2. Formulation of Asphaltene Deposition in Porous Media Under different thermodynamic and hydrodynamic conditions a portion of asphaltenes may precipitate out of solution. Some of the precipitated asphaltenes may deposit. The precipi(11) Wang, S.; Civan, F.; Strycker, A. R. Simulation of Paraffin and Asphaltene Deposition in Porous Media; Society of Petroleum Engineers: Houston, TX, 1999. (12) Minssieux, L. Core Damage from Crude Asphaltene Deposition; Society of Petroleum Engineers: Houston, TX, 1997. (13) Leontaritis, K. J. Asphaltene Near-Wellbore Formation Damage Modelling; Society of Petroleum Engineers: Lafayette, LA, 1998. (14) Almehaideb, R. A. J. Pet. Sci. Eng. 2004, 42, 157–170. (15) Kocabas, I.; Islam, M. R.; Modarress, H. JPSE, J. Pet. Sci. Eng. 2000, 26, 19–30. (16) Al-Ruhaimani, F. A. Predicting Asphaltene Deposition and Assessing Formation Damage; Society of Petroleum Engineers: The Hague, 2003.
(17) Wang, S.; Civan, F. Productivity Decline of Vertical and Horizontal Wells by Asphaltene Deposition in Petroleum Reservoirs; Society of Petroleum Engineers: Houston, TX, 2001.
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Figure 1. Schematic drawing of experimental apparatus.
from the pore surface and are entrained by flow. The entrainment coefficient (i.e., βΑ) is valid when the interstitial velocity is greater than critical velocity, otherwise entrainment coefficient is set to zero. The last term is the pore throat plugging rate which is also valid when asphaltene particle sizes are greater than the pore throat diameter. Porosity is reduced by the amount of fractional pore volume occupied by asphaltene depositions. Hence, instantaneous porosity could be given by φ ¼ φi - V AD
ð5Þ
The instantaneous, local permeability impairment is given by18 3 φ k ¼ f pki ð6Þ φi 3. Deposition Experiments and Modeling An experimental apparatus was constructed for calculating the mass of asphaltene deposited as a function of time by measuring the changes in heat transfer coefficient (or thermal resistance) due to asphaltene deposition. Figure 1 shows the schematic diagram of the recirculation loop apparatus consisting of a 50-L supply tank with an internal cooling coil, pump, an orifice plate that was used for the flow measurement, and finally the testing section which is an external heated stainless still pipe. The test section is shown in Figure 2. The important dimensions of the test section are as follows:
Figure 2. Schematic diagram of test section.
adjusted to represent the temperature on the internal surface of the pipe. This involved determining a correlation value to be subtracted from the wall thermocouple temperature, which accounted for the temperature drop due to conduction from the thermocouples location to the internal surface of pipe. The temperature drop between the thermocouple and surface can be calculated from : s ð7Þ T s ¼ T th - q λs
inside diameter of pipe 23.8 mm heated length 160 mm heated length to thermocouples location 95 mm.
Heat was supplied to the test section by a Thermocoax stainless steel sheathed resistance heater which was fitted into a thread outside the pipe. The ratio between the distance (of the thermocouples from the surface) and the thermal conductivity of the heating rod material (s/λs) was determined for each thermocouple by
The test section contained a resistance heater and four thermocouples located near the heated surface to monitor the surface temperature. The thermocouples readings are (18) Civan, F.; Knapp, R. M.; Ohen, H. A. J. Pet. Sci. Eng 1989, 3, 65– 79.
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calibration measurements using a Wilson plot technique. A typical value of s/λs was 1.4 10-4 m2K/W. The local heat transfer coefficient R was calculated from : q ð8Þ R ¼ Ts - Tb Due to material and design limitations of the Thermocoax heater, temperatures and heat fluxes of the test section were limited to 200 °C and 150,000 W/m2, respectively. During the tests the fluid was pumped at a constant volumetric flow rate into the heated pipe and recirculated. When the fluid flowed over the hot internal pipe surface its temperature increased and surface temperature decreased. As a result, unstable asphaltene particles deposited on the internal surface of the pipe. This increased the thermal resistance to heat flow. The resistance can be described as follows: : q ð9Þ R0 ¼ 0 Ts - Tb
Figure 3. Typical measured variation of different parameters of asphaltene deposition.
Equation 9 shows that if no deposition is formed on the surface, as long as the flow rate, bulk temperature, and heat flux are kept constant the heat transfer coefficient R0 will also remain constant and does not change with time. But if asphaltene deposits on the surface it acts as a thermal resistance to transfer of heat and as a consequence the heat transfer coefficient decreases with time. Therefore, if the heat flux is maintained constant, the surface temperature Ts increases. The heat transfer coefficient at any given time could be calculated from the following equation: : q ð10Þ Rt ¼ t Ts - Tb
Figure 4. Schematic of asphaltene deposition process.
internal surface of pipe, which acts as thermal resistance to heat flow. The thermal resistance of deposited asphaltene layer can be calculated from the initial heat transfer coefficient when the surface is still clean and the actual heat transfer coefficients from eq 11. The clean heat transfer coefficient R0 is calculated from the Gnielinski21 correlation. The change in the amount of asphaltene deposited per unit area vs time can be obtained by substituting eq 11 into eq 12 1 1 ð13Þ md ¼ Fd λd Rt R0
The thermal resistance of the deposited asphaltene on the surface is equal to (i.e., Jamialahamdi and M€ ullerSteinhagen,19) 1 1 ð11Þ RtA ¼ Rt R0 The mass of asphaltene deposit on the surface corresponding to this thermal resistance is equal to (i.e., Jamialahmadi and M€ uller-Steinhagen,20) mtd ¼ Fd λd RtA ð12Þ
Various mechanisms could be involved in asphaltene deposition once they become unstable due to an increase in the system temperature. As shown in Figure 4 there are two competing mechanisms for asphaltene deposition. The high wall temperature encourages deposition whereas fluid flow may remove asphaltene particles. The latter depends on the sticking of asphaltenes and hydrodynamic flow condition which include share forces, turbulent bursts, resolution, and erosion. Two different mechanisms of mass transfer and chemical reaction (i.e., formation of asphaltene) are believed to be the main factors in the process of asphaltene deposition on the surface. The experiments were designed to determine which one of the above mechanisms controls the deposition process. Deposited asphaltene may remove from the surface. It depends on the strength of asphaltene bond with the pipe surface in comparison with hydrodynamic conditions, including shear forces, turbulent bursts, and erosion, as well as resolution.
Therefore, if a well-defined test rig is designed to measure the variations of surface temperature with time as a result of asphaltene deposition, it allows us to calculate the forced convective heat transfer coefficient, the thermal resistance, and its corresponding mass of deposit formed on the surface as a function of time from eqs 10, 11, and 12, respectively. 3.1. Asphaltene Deposition Experiments. A series of experiments has been conducted to measure asphaltene deposition as function of time for heat fluxes ranging from 25 000 to 86 000 W/m2, flocculated asphaltene concentration of 3.5 kg/m3, oil velocity varying from 0.35 to 1.56 m/s, and bulk temperature of 85 °C. Figure 3 shows typical heat transfer coefficient, heat flux, and surface and bulk temperatures. Initially, the heat transfer coefficient is almost constant at 2.45 kW/m2K. Then, it declined almost linearly with time. This is due to the deposited asphaltene layer on the (19) Jamialahmadi, M.; Muller-Steinhagen, H. Heat Trans. Eng. J. 1991, 12, 19–26. (20) Jamialahmadi, M.; Muller-Steinhagen, H. IChemE J. 2007, 85, 1–11.
(21) Gnielinski, V. W€ arme€ ubertragung in Rohren, VDI-W€ ameatlas, 6th ed.; VDI-Verlag: D€usseldof, 2002.
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Figure 7. Velocity effect on the asphaltene deposition.
Figure 5. Typical deposition-removal time curve.
increase in the fouling resistance with time, in the range of specified oil velocity. This indicates that during the fist few weeks of deposition process the thickness of asphaltene deposit formed on the surface is small and there is no significant removal from the surface and, therefore, the rate of deposition is almost constant. This could explain asphaltene blockage across the production wells and surface facilities, especially at low flow rates. However, it may be postulated that after a long time, when a substantial thickness of deposit on the surface is reached, hence a localized high velocity, some deposit may come off by the mechanism of shear-related removal. Oil velocity, flocculated asphaltene concentration, and surface temperature were found to be the three main parameters affecting the rate of deposition. 3.1.1. Effect of Oil Velocity. Studying the effect of velocity is vital in determining asphaltene deposition mechanism. If asphaltene deposition process is controlled by transport of precipitated asphaltenes particles onto the pipe surface, its rate of deposition is expected to increase with an increase in the fluid velocity at constant surface and bulk temperatures. Our experimental results show that the rate of asphaltene deposition is reduced with an increase in fluid velocity, indicating that mass transfer is not the controlling parameter. To identify the controlling mechanism, asphaltene deposition rate was determined over a wide range of oil velocities at constant concentration, bulk and initial surface temperatures. The results of these measurements are summarized in Figure 6. The deposition rates obtained from the slope of these curves are plotted as a function of oil velocity number in Figure 7. As shown in the figure, the rate of asphaltene deposition decreases significantly with an increase in oil velocity. Assuming insignificant deposit erosion this can only mean that the sticking potential of particles reaching the surface must decrease with an increase in flow velocity. This hypothesis was already discussed in detail for particulate fouling by M€ uller-Steinhagen22 and Epstein.23 In particulate processes, the rate of deposition is inversely proportional to the fluid velocity: : 1 ð15Þ md µ j v
Figure 6. Heat transfer coefficient corresponding to mass of deposited asphaltene.
The sum of the above mechanisms represents the rate of the asphaltene deposition on the surface. In mathematical terms the net rate of growth of asphaltene deposition may be regarded as the difference between the rate of deposition and removal of flocculated asphaltene particles from the surface. In more precise mathematical terms it can be presented as : : dm ð14Þ ¼ md - mr dt Equation 14 shows that the asphaltene deposition is a dynamic process and it changes with time in a manner determined by the rate of deposition and removal. Equation 14 can be represented as a net mass of deposition-time curve, as illustrated in Figure 5. The shape of the curve is indicative of the phenomena occurring during the deposition process. If the deposit is sticky (i.e., has a very strong bond with the pipe surface) the rate of removal of deposited asphaltene particles can be ignored and the rate of deposition increases linearly with time, as shown in Figure 5. Asymptotic deposition is generally a characteristic of soft and weak asphaltene deposits, which flake off easily due to the shearing force of the fluid flow. This behavior is observed if the deposition rate is constant and the removal rate is proportional to the thickness of the deposit, as shown by the bottom curve in Figure 5. The falling rate behavior shown by the middle curve in Figure 5 would result from a falling deposition rate or from a falling deposition rate and an increasing removal rate. Comparing our experimental results presented in Figure 6 with theoretical deposition behavior in Figure 5 shows a linear
Depending on the controlling mechanism, the reported values of j are in the range 0.35-2. The present results indicate that the (22) M€ uller-Steinhagen, H. Mitigation of heat exchanger fouling, Conf. Fouling in Heat Exch.; University Auckl, 1998. (23) Epstein, N., Fouling Sci. Tech.; Kluwer Academic Publisher, 1998.
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Figure 8. Temperature effect on asphaltene deposition.
Figure 9. Concentration of precipitation effect on the rate of asphaltene deposition.
deposition rate of flocculated asphaltene particles on the surface is almost inversely proportional to the oil velocity to the power of one (i.e., j = 1). 3.1.2. Effect of Surface Temperature. To investigate the effect of temperature on the asphaltene deposition process, experiments have been carried out at three different inlet bulk temperatures;75, 80, and 85 °C;with fixed initial surface temperature and velocity. It has been observed that the heat transfer coefficient decreases faster with increasing temperature and, therefore, the rate of asphaltene deposition is increased .The effect of temperature on the rate of asphaltene deposition is shown in Figure 8. These results indicate that the rate of asphaltene particle deposition on the surface depends strongly on the temperature. This is a clear indication of the dominating role of chemical reaction in asphaltene deposition. Generally, in chemical reaction processes the effect of temperature is expressed by the Arrhenius equation, i.e., : ð16Þ md Re - Ea =RT
directly proportional to the concentration of flocculated asphaltene. 3.2. Asphaltene Surface Deposition. The results of this study can be summarized in eq 18. This equation has been developed based on parameters investigated in this work, i.e., temperature, velocity, and precipitated asphaltene concentration. : K d - Ea =RT e C AS ð18Þ md ¼ v 4. Asphaltene Precipitation Modeling In the literature, two thermodynamics models have been introduced for modeling asphaltene precipitation from live oil. The first model is based on real solutions which assume asphaltene is completely soluble in oil.24-27 In this model, precipitation of asphaltene as solid phase is described by reducing its solubility in oil phase. Furthermore, asphaltene precipitation is assumed to be a reversible process. The second model is the colloidal model which considers asphaltene molecules dispersed and suspended as colloids in oil that is peptized by resins.28,29 Based on this model asphaltene molecules flocculate if resins concentration is reduced. The colloidal model considers asphaltene precipitation an irreversible process. Numerous experiments have been carried out to study the reversibility of asphaltene precipitation. Hirschberg et al.24 showed the reversibility of asphaltene at high temperature with pressure depletion. Rassamdana et al.30 applied titration method with n-hexane and found partial reversibility of asphaltene precipitation with respect to composition changes at room temperature. Asphaltene dissolution is a kinetically slow process, and therefore may need longer time to reach complete dissolution.31
where E is activation energy, R is the Universal gas constant, and T is the system temperature in K. Plot of asphaltene deposition rate versus term of 1/T gives the activation energy (i.e., Figure 8). The value of activation energy calculated from the results of this work is 65.3 kJ/mol. 3.1.3. Effect of Flocculated Asphaltene Concentration. Several experiments were performed to determine the role of precipitated asphaltene concentration on the deposition process. The primary cause of asphaltene deposition is the concentration of flocculated asphaltene in the flowing oil. If the removal rate can be ignored (i.e., low velocities) and all particles arriving at the surface are deposited, the rate of deposition can be expressed as : ð17Þ md ¼ kðC As Þn
(24) Hirschberg, A.; De Jong, L. N. J.; Schipper, B. A.; Meyers, J. G. SPEJ, Soc. Pet. Eng. J. 1989, 24 (3), 283–293. (25) Boer, R. B.; Leerlooyer, K.; Elgner, M. R. P.; van Bergen, A. R. D. SPEJ, Soc. Pet. Eng. J. 1995, 10 (1), 55–61. (26) Nghiem, L. X.; Coombe, D. A.; Ali, F. Compositional Simulation of Asphaltene Deposition and Plugging; Society of Petroleum Engineers: New Orleans, LA, 1998. (27) Zhou, X.; Thomas, F. B.; Moore, R. G. J. Can. Pet. Technol. 1996, 35 (10), 37–45. (28) Leontaritis, K. J.; Mansoori, G. A. Asphaltene Flocculation During Oil Production and Processing: A Thermodynamic Collodial Model; Society of Petroleum Engineers: San Antonio, TX, 1987. (29) Mansoori, G. A. J. Pet. Sci. Eng. 1997, 17 (2), 101–111. (30) Rassamdana, H.; Dabir, B.; Nematy, M.; Farhani, M.; Sahimi, M. AIChE J. 1996, 42, 10–22.
where CAs is the flocculated asphaltene concentration at the surface conditions. Order of term CAs determines the effect of precipitated asphaltene concentration on the deposition rate. If it is a zero order reaction, the precipitated asphaltene concentration has no effect on the rate of asphaltene deposition. The observed effect of flocculated asphaltene concentration at a velocity of 1.25 m/s and constant bulk and surface temperature is shown in Figure 9. The results indicate that the heat transfer coefficient decreases and rate of asphaltene deposition increases as the concentration is increased and at the experimental conditions it is almost 758
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Results of high pressure microscope (HPM) and particle size analysis (PSA) show that precipitated solid asphaltene due to pressure change redissolves in live oil.32 Several solubility thermodynamic models have been developed. Hirschberg et al.24 introduced an approach for thermodynamic modeling of asphaltene by combining Flory-Huggins theory for polymer solution with Hildebrand Solubility Concept. In this approach vapor-liquid equilibrium is determined by applying EOS. Then liquid phase is divided into two components, a component that corresponds to asphaltene and the other component that represents the remaining oil (deasphaltened oil). Hirschberg obtained the following equation: VA VA -1ðδA - δL Þ2 ð19Þ φA ¼ Exp VL RT Figure 10. Asphaltene precipitation modeling of Weyburn reservoir fluid.
where φA is the volume fraction of dissolved asphaltene in the crude oil and VA is the molar volume of asphaltene. The molar volume VL and solubility parameter δL are calculated for the deasphaltened oil mixture by using EOS. Molar volume of asphaltene depends on the molecular weight and density of asphaltene. On the other hand, molecular weight of asphaltene depends on its aggregation.33,34 Therefore, the maximum solubility cannot be calculated accurately. Hence asphaltene molar volume is used as tuning parameter. The solubility parameter can be estimated by titration with solvent and can be represented by a linear relation with respect to temperature ð20Þ δA ¼ a þ bT
Table 1. Compositions of Crude Oil Used in the Experiment of Asphaltene Precipitation
where a and b are constants. The parameter b is negative as the solubility parameter decreases with an increase in temperature.35 5. Modeling Asphaltene Deposition in Porous Media
component
Hassi-Messouad composition (mol%)
weyburn composition (mol%)
N2 CO2 C1 C2 C3 IC4 NC4 IC5 NC5 FC6 FC7þ
1.8 1.32 33.15 13.95 9.91 1.29 4.66 1.4 2.48 3.59 26.45
0.57 2.46 36.37 3.47 4.05 0.59 1.34 0.74 0.83 1.62 47.96
The length and diameter of core samples were between 0.05 and 0.07 and 0.023 m. Core dimensions were chosen to achieve large pore volume fluid injection within a reasonable time period. The porosity and permeability of samples varied from 0.071 to 0.247 and 0.67 10-15 to 107 10-15 m2, respectively. The injection flow rates for different core samples were set between 2.20 10-8 and 1.38 10-8 m3/s. The experiments were carried out at constant temperature (i.e., 50 and 80 °C) and back pressure (10.342 bara). Minssieux12 used dead oils of Weyburn and Hassi-Messaoud with asphaltene content 5.3% and 0.15%, respectively. Minssieux12 has not report the composition of the dead oils. Therefore, we used published compositional data in the literature for modeling asphaltene precipitation. Burke et al.36 conducted experiments on Weyburn fluid and reported composition and asphaltene precipitation data which have been used by other researchers17,37. Figure10 shows the asphaltene precipitation modeling using eq 19 for the Weyburn oil. Haskett et al.38 have reported composition of Hassi-Messaoud crude oil. The composition data of the two crude oils used in experiments are given in Table 1. Partial differential equations and other constructive relationships were solved to determine pressure and asphaltene concentration along the core samples. The Rung-Kutta fourth order scheme has been applied to calculate the volume fraction of asphaltene deposition (i.e., eq 4). Numerical
As detailed earlier, we have conducted a series of experiments, investigating the asphaltene deposition rate by thermal method. The results of this work were used in developing a more reliable term for surface deposition of asphaltene. The new surface deposition term developed in this work was used in improving asphaltene deposition modeling in porous media. Equation 4 which describes the kinetic of asphaltene deposition in porous media has been improved by introducing the new surface deposition term developed in this work. The resulting improved kinetic model for asphaltene deposition in porous media was used to describe the asphaltene deposition test results in core flow experiments. Minssieux12 has reported extensive asphaltene core flooding experiments which are the most reliable and referred data in the literature. Hence, his core flooding experiments have been used for verifying asphaltene deposition model. The experiments were performed with four cores selected from Hassi-Messaoud reservoir and three consolidated sandstone outcrop samples of Fontainebleau, Vosgas, and Palatinat. (31) Huanquan, P.; Firoozabadi, A. Soc. Pet. Eng. 1998, 13 (2), 118– 127. (32) Mullins, O. C.; Sheu, E. Y.; ,Hammami, A.; Marshall, A.G. Asphaltenes, Heavy Oils Petroelomics, 1st ed.; Springer: New York City, 2007. (33) Anderson, S. I.; Speight, J. G. J. Pet. Sci. Technol. 1999, 22, 53– 66. (34) Kohse, B. F.; Nghiem, L. X.; Maeda, H.; Ohno, K. Modeling Phase Behaviour Including the Effect of Pressure and Temperature on Asphaltene Precipitation; Society of Petroleum Engineers: Australia, 2000. (35) Nghiem, L. X. PhD thesis. Phase Behaviour Modelling and Compositional Simulation of Asphaltene Deposition in Reservoir; University of Alberta: Edmonton, Alberta, Canada, 1999.
(36) Burke, N. E.; Hobbs, R. E.; Kashon, S. F. J. Pet. Technol. 1990, 42, 1440–1446. (37) Kohse, B. F.; Nghiem, L. X. Modeling Asphaltene Precipitation and deposition in Compositional reservoir Simulator; Society of Petroleum Engineers: Oklahoma, 2004. (38) Haskett, C. E.; Tartera, M. A. Soc. Pet. Eng. 1965, 17 (4), 387–391.
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Energy Fuels 2011, 25, 753–761
: DOI:10.1021/ef101195a
Soulgani et al. Table 2. Core Flooding Data
core formation oil density (kg/m3) asphaltene content viscosity (20 °C) porosity (%) permeability (m2) length (m) diameter (m) injection flow rate (m3/s) temperature (°C) back pressure (bar)
GF1
GF3
GV10
GV5
GP9
HMD26
Fontainebleau Weyburn 882 5.3 0.013 13.1 107 10-15 0.06 0.023 1.38 10-8 50 10.342
Fontainebleau Weyburn 882 5.3 0.013 13.7 77.4 10-15 0.06 0.023 2.76 10-9 50 10.342
Vosgas Weyburn 882 5.3 0.013 24.3 18 10-15 0.06 0.023 2.76 10-9 50 10.342
Vosgas Weyburn 882 5.3 0.013 24.7 29 10-15 0.06 0.023 2.76 10-9 50 10.342
Palatinat HMD 811 0.15 0.0015 22.6 1.1 10-15 0.06 0.023 2.76 10-9 80 10.342
HMD HMD 811 0.15 0.0015 7.1 6.7 10-16 0.06 0.023 2.20 10-9 80 10.342
Figure 11. Asphaltene deposition modeling for sample GF3.
Figure 14. Asphaltene deposition modeling for sample GP9.
Figure 12. Asphaltene deposition modeling for sample GV10.
Figure 15. Asphaltene deposition modeling for sample GF1.
Figure 13. Asphaltene deposition modeling for sample GV5.
Figure 16. Asphaltene deposition modeling for sample HMD.
760
Energy Fuels 2011, 25, 753–761
: DOI:10.1021/ef101195a
Soulgani et al.
Table 3. Result of Core Flooding Modeling parameter 2
kd (m/s) β (1/m) Vcr (m/s) γ (1/m) σ fp
GF1 4.65 10 0 0 13.391 35 1
GF3 -5
GV10 -5
5.12895 10 0.756 0.00007 0 0 1
GV5 -5
8.68 10 0.43 0.00005 0 0 1
solution for calculating asphaltene concentration is accomplished using Crank-Nicholson finite-difference scheme. The Crank-Nicholson method is based on central difference in space and trapezoidal rule in time, giving second order convergence in time. Therefore, it is numerically stable. Numerical simulation was carried out in a linear grid system of 50 grid blocks. Time was discretized with a Δt of 50 s. The number of grid blocks and time were set after a series of trial runs to improve accuracy. Numerical simulation runs were conducted for six experiments that were denoted as GF1, GF3, GV5, GV10, GP9, and HMD26. Table 2 gives experimental conditions for various samples. Permeability damages due to asphaltene deposition in core were simulated using the improved kinetic model of asphaltene deposition. The surface deposition, entrainment, and plugging coefficients were adjusted to achieve best match with the experimental data. The best match was found with adjusting the surface deposition and entrainment coefficients for samples GF3, GV5, GV10, and GP9. It was found that the plugging term has no role in permeability damages on these samples. For experiments GF1 and HMD26 the best results were achieved by adjusting surface deposition and pore throat plugging coefficients. It was found that the entrainment term has no effect on GF1 and HMD26 samples. Figures 11-16 and Table 3 show the experimental and predicted formation damage for the core flooding experiments. As shown in the figures, the predictions of the model developed in this work are in excellent agreement with the experimental results. The results showed that the main term in modeling kinetics of asphaltene deposition is surface deposition.
GP9 -5
3.1 10 0.3 0.0000421 0 0 1
HMD26 -5
5.53699 10 0.6 0.00005 0 0 1
3.07094 10-5 0 0 5.934 0 1
fp [-] pore connectivity parameter k [m2] instantaneous permeability ki [m2] initial permeability k [-] constant m [kg/m2] mass of deposit per unit area · m [kg/m2s] rate of deposition or removal P [bar] pressure · q [W/m2] heat flux, R [1.987 cal/(mol K)] universal gas constant RA [m2K/W] thermal resistance of deposit asphaltene SL [-] oil phase saturation, fraction s [m] distance between thermocouple location and heat transfer surface t [s] time T [K] temperature u [m/s] superficial velocity v [m/s] interstitial oil velocity vL [m/s] interstitial velocity of oil phase vcr [m/s] critical interstitial velocity for entrainment VAD [-] volume fraction of deposited asphaltene VA [m3/mol] molar volume of asphaltene VL [m3/mol] molar volume of oil phase wo [-] mass fraction of oil in the oil phase wA [-] mass fraction of dissolved asphaltene wSA [-] mass ratio of asphaltene precipitates suspended in oil to the phase Greek symbols RA [1/s] surface deposition rate coefficient for asphaltene R [W/m2K] heat transfer coefficient βA [1/m]entrainment rate coefficient γAi [1/s] instantaneous plugging deposition rate coefficient for asphaltene λ [W/m 3 K] thermal conductivity δA [(bar)0.5] solubility parameter of asphaltene δL [(bar)0.5] solubility parameter of oil phase, M [N 3 s/m2] viscosity F [kg/m3] density σA [cons.] snow-ball effect rate coefficient for asphaltene φA [-] volume fraction of asphaltene soluble in the crude oil φ [-] instantaneous porosity, fraction φi [-] initial porosity, fraction
6. Conclusions This study presented a new comprehensive model for surface deposition based on a series of experiments carried out with asphaltene. The results of the experiment showed that surface deposition rate increases with increasing temperature and asphaltene precipitation concentration. Surface deposition rate is inversely proportional to oil velocity and decreases as oil velocity is increased. Based on the results of the tests conducted in this work a new surface deposition term was developed. The new term was used in modeling the kinetic of asphaltene deposition porous media. The new kinetic model was used in simulating core flooding tests reported in the literature. The predictions of the new kinetic model are in excellent agreement with the experimental data, demonstrating the reliability of the developed kinetic model in predicting formation damage due to asphaltene deposition.
Subscripts-Superscripts A asphaltene b bulk cr critical d deposit L liquid o oil r removal s surface t at time t th thermocouple 0 at time t = 0
Nomenclature a and b [-] constants CA [-] asphaltene concentration in oil phase Ea [J/mol] attachment activation energy 761
