Data-driven comparison between solid model and PC-SAFT for modeling asphaltene precipitation

Accepted Manuscript Data-driven comparison between solid model and PC-SAFT for modeling asphaltene precipitation Ali Abouie, Hamed Darabi, Kamy Sepehrnoori PII:

S1875-5100(17)30215-9

DOI:

10.1016/j.jngse.2017.05.007

Reference:

JNGSE 2176

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 25 October 2016 Revised Date:

7 March 2017

Accepted Date: 3 May 2017

Please cite this article as: Abouie, A., Darabi, H., Sepehrnoori, K., Data-driven comparison between solid model and PC-SAFT for modeling asphaltene precipitation, Journal of Natural Gas Science & Engineering (2017), doi: 10.1016/j.jngse.2017.05.007. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Abstract

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Selecting an appropriate equation of state (EOS) to model asphaltene precipitation in compositional wellbore and reservoir simulators is still unclear in the literature. Recent studies have shown that the PC-SAFT model is more appropriate for modeling asphaltene precipitation compared to the commonly used solid model. The main objective of this paper is to compare the solid and PC-SAFT models in both static and dynamic asphaltene modeling. Through fluid characterization, the capabilities of both models are compared to reproduce precipitation experimental data.

Introduction

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The results show that both solid and PC-SAFT models are capable of predicting the amount of asphaltene precipitation with high accuracy. Although the matching process using the PCSAFT model is much easier, the properly tuned solid model is also able to reproduce the experimental data with the same quality as the PC-SAFT model. The simulation results show that the PC-SAFT model is superior to the solid model in terms of the extrapolation accuracy when the experimental data are not available for the simulation conditions (i.e., variation in temperature, pressure, and fluid composition in the reservoir/wellbore). However, both models are applicable for interpolation when the experimental data cover the entire range of the simulation condition. The wellbore simulations show that although the trend of asphaltene deposition is similar for both models, the solid model using Peng-Robinson EOS overestimates the amount of asphaltene precipitation and deposition in the wellbore compared to the PC-SAFT model. On the other hand, the simulation procedure using the PC-SAFT model takes much more computational time as this model uses an iterative solution to obtain the density roots and the phase equilibrium calculation.

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Asphaltene deposition is known to be one of the major problems in the oil industry. Asphaltene precipitation and deposition from the reservoir fluid cause serious formation damage problems (i.e., pore throat plugging and wettability alteration) in the near wellbore region where maximum pressure drop occurs (Darabi 2014). Furthermore, asphaltene precipitation and deposition can occur in the wellbore and result in partial or total plugging. These factors affect the project economics by lowering the production rate and requiring frequent remediation jobs. Additionally, miscible gas flooding with CO2, N2, and natural gas might reduce the asphaltene solubility in the crude oil and enhance the probability of asphaltene precipitation and deposition in the reservoir and wellbore (Gonzalez et al. 2005). By classic definition, asphaltene is the heaviest and most polarizable component of the crude oil. Asphaltene is characterized as insoluble in paraffins such as n-pentane and soluble in aromatic solvents such as benzene (Srivastava and Huang 1997). The carbon number of asphaltene macromolecules is in the range of 40 to 80 with a typical H/C ratio of 1.1 to 1.2. The typical range of asphaltene density is around 1.12 to 1.2 g / cm3 (Gonzalez et al. 2005). Hence, the crude oil with more asphaltene content has higher viscosity and density. Creek (2005) reported that removal and reduction of asphaltene deposits cost about 0.5 and 3 million US dollars for onshore and offshore fields, respectively, and the loss of production may rise up to 1.2 million US dollars per day assuming the oil price of $30 per barrel. Therefore, prevention of asphaltene precipitation and deposition is more favorable in terms of easiness and

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costs compared to the removal procedure. Hence, it is essential to have an insight into the precipitation mechanisms to minimize the deposition rate through optimizing the field operating conditions (e.g., injection rate, composition of the injection gas, operating conditions of the production wells). Moreover, this knowledge helps us recommend the best schedule time for remediation jobs (Darabi and Sepehrnoori 2015).

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Modeling asphaltene precipitation is the initial step for predicting asphaltene deposition in the reservoir and wellbore. From the precipitated asphaltene in the reservoir and wellbore, a portion would deposit on the rock surface and tubing and the remainder would flow with the fluid stream. Therefore, it is necessary to estimate asphaltene precipitation in order to determine the deposition rate. In the following section, the commonly used precipitation models are explained.

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Precipitation Models. Various thermodynamic models have been developed in the past few years to predict the asphaltene phase behavior and the solubility of asphaltene in the crude oil. These models can be categorized into four main groups: solubility model, solid model, thermodynamic micellization model, and thermodynamic model based on PC-SAFT equation of state (EOS). Each model is briefly described in the following section:

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1. Solubility model: This approach considers asphaltene stability in terms of reversible solution equilibrium. According to Flory-Huggins theory, equality of the chemical potential is the basic condition for chemical equilibrium (Flory 1942). In addition, this model considers a chemical equilibrium condition between the asphaltene-rich phase and the solvent-rich phase. Examples of solubility models in the literature are Hirschenberg (Hirschenberg et al. 1984), Cimino (Cimino et al. 1995), and Nor-Azlan (Nor-Azlan and Adewumi 1993) models. Although implementation of these models is fairly easy, the results are not predictive.

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2. Solid model: This model assumes that asphaltene is a single component in the solid phase. The oil and gas phases are also modeled with a cubic EOS. The equilibrium condition is based on the equality of the fugacities for each component in all phases. Examples of solid models are Gupta (Gupta 1986), Thomas (Thomas et al. 1992), and Ngheim (Ngheim et al. 1993) models. Nghiem model assumes that the heaviest component in the oil phase splits into non-precipitating and precipitating components. All properties of these two components (e.g., critical properties, acentric factors, and parachors) are identical except for the binary interaction coefficients with lighter components. 3. Thermodynamic-colloidal model: the colloidal model assumes that asphaltenes are suspended solid particles that are peptized by resins in a colloidal system. Victorov and Firoozabadi (1996) proposed that asphaltene particles are micelles in the crude oil. These micelles consist of asphaltene as a core, surrounded by layers of resins. As long as these micelles are stable, asphaltene precipitation would not occur. However, if the thermodynamic equilibrium is disturbed, these protective shells can cause asphaltene precipitation (Leontaritis and Mansoori 1987; Leontaritis 1988; Allenson and Walsh 1997; Pan and Firoozabadi 1998). 4. Thermodynamic model based on PC-SAFT EOS: Recently, new molecular based EOSs

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were developed where the effect of large molecular size difference on the fluid phase behavior is included. Statistical Associating Fluid Theory (SAFT) has shown promising results in predicting the phase behavior of mixtures with high difference in size and shape, such as the fluids containing asphaltene particles (Gonzalez et al. 2007, Gonzalez et al. 2008, Vargas et al. 2009). Chapman et al. (1990) derived SAFT EOS by extending the Wetherim’s first order perturbation theory (Wetherim 1984; Wetherim 1986) to chain molecules to predict the effects of large molecular size differences. Gross and Sadowski (2001) modified SAFT EOS to include a hard chain reference and developed the perturbed chain SAFT (PC-SAFT) EOS to predict the phase behavior of complex associating fluids and high molecular weight fluids similar to asphaltene molecules. Ting et al. (2003) also used PC-SAFT to model asphaltene precipitation.

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The conventional cubic equation of state (CEOS) and PC-SAFT EOS are the most popular and common EOSs for modeling the asphaltene phase behavior. Due to the simplicity and reasonable prediction of the mixture behavior, cubic EOSs are often used in compositional reservoir and wellbore simulations. However, CEOS predictions are believed not to be accurate enough for mixtures containing complex molecules and wide-range molecular sizes. In addition, CEOS predictions for liquid densities are usually poor. This poor prediction encouraged Peneloux et al. (1982) to propose volume correction factor to provide more accuracy without affecting the phase equilibrium simulation results. The other problem with CEOS is that asphaltene parameters (i.e., critical properties, acentric factor, parachor, and molecular weight) are not defined clearly and specifically.

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On the other hand, PC-SAFT EOS has shown promising results for predicting the phase behavior of mixtures with a wide range of molecular sizes. Although PC-SAFT EOS is believed to be more accurate compared to CEOS in modeling the phase behavior of these mixtures, several problems are attributed to PC-SAFT EOS such as the computational time. PC-SAFT EOS has shown to require much higher computational time compared to CEOS. Mohebbinia et al. (2014) showed that CPU time of a compositional reservoir simulation with PC-SAFT takes about 1.5-2.1 more time than using the PR EOS. Furthermore, PC-SAFT EOS requires detailed fluid information such as SARA (Saturate, Aromatic, Resin, and Asphaltene) analysis, chromatography composition analysis for the gas and liquid phases, and the gas-oil ratio value which are not usually available. Therefore, there is still an ongoing debate whether to choose the more predictive or simpler model in compositional simulators. Recently, multiphase flow simulators in the wellbores have been developed that can address flow assurance issues such as asphaltene deposition. For instance, Ramirez-Jaramillo et al. (2005) proposed a multiphase, multi-component wellbore model to predict asphaltene deposition in stand-alone wells. They also discussed an asphaltene deposition model along with the effect of asphaltene particles on the rheology of the flowing fluid. Vargas et al. (2010) also developed a simulation tool to predict the asphaltene precipitation and deposition in pipelines. In this work, a single phase flow model was developed that accounts the kinetics of asphaltene deposition, precipitation, and aggregation. Vargas et al. (2010) showed relatively good agreement between the simulation results, field observation, and experimental data. Eskin et al. (2011) also discussed the detailed analysis of asphaltene particle deposition in the turbulent flow streams. They showed a theoretical model and experimental results performed in a Couette device. Eskin et al. (2011) further developed a model for asphaltene particles size distribution and the mechanism of

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particle transport from fluid bulk to the pipe surface. Shirdel (2013) also developed a onedimensional, multiphase, multicomponent, non-isothermal wellbore model with the capability of modeling asphaltene precipitation and deposition in the wellbore. Kor et al. (2016) also integrated several tools and field data to predict asphaltene deposition in an oil well. They used a commercial phase behavior package to perform the equilibrium flash calculation for the solid model. Afterwards, hydrodynamic data of the wellbore and several depositional mechanisms were used to predict the profile of asphaltene deposition in a Kuwait oil well.

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The objective of this work is to study the capabilities of the PC-SAFT and Peng-Robinson (PR) EOSs for asphaltic fluids over a wide range of pressure and temperature to compare the prediction capability, which includes asphaltene phase behavior and asphaltene precipitation curves. Two different crude oils were used in this work for comparison studies. Afterwards, dynamic simulations are performed to compare the predicted profile of asphaltene deposition in the wellbore.

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Model Development

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In the development section, the PC-SAFT EOS has been implemented into UTWELL, The University of Texas at Austin Wellbore Simulator (Shirdel 2013; Abouie et al. 2016) with the capability of performing three-phase flash calculation (i.e., vapor phase, oil phase, and asphaltene-rich phase) based on the thermodynamic conditions (i.e., fluid composition, pressure, and temperature). Water also exists as the fourth phase for which flow equations are solved. However, it is assumed that there is no mass transfer between the water phase and any of the hydrocarbon phases. Based on the thermodynamic equilibrium condition (i.e., pressure and temperature), asphaltene may precipitate as the asphaltene-rich phase. In other words, if the equilibrium condition falls in the area between upper and lower onset pressures, asphaltene starts to form from the crude oil. The upper asphaltene onset pressure is defined as a pressure at which the least soluble asphaltenes start to precipitate. The lower onset pressure is also defined as the pressure at which asphaltene redissolves into the oil phase. The asphaltene-rich phase is assumed to be a liquid phase in a micro-aggregate form with some amounts of other components. Therefore, the average properties of the oil and asphaltene-rich phases are used as the liquid phase properties in all flow equations in the wellbore, if necessary. The main assumptions in the PC-SAFT precipitation model can be briefly described as below: 1) Asphaltene precipitation is considered as a thermodynamically reversible process. 2) Association term of the PC-SAFT EOS is neglected since the molecular size and Van der Waals interactions can sufficiently model the asphaltene phase behavior. 3) Only the asphaltene component in the asphaltene-rich phase precipitates and might deposit on the rock surface and in the wellbore. Identification of the hydrocarbon phases is also necessary in UTWELL to determine the gas, oil, and asphaltene-rich phases. Therefore, the thermodynamic equilibrium algorithm of Perschke (1988) is used which consists of a stability analysis to predict the number of phases present in each grid block followed by flash calculation to determine the distribution of the hydrocarbon components in different phases. In addition, tracking the phases is also added to label the phases consistently during the simulation. Another aspect of the developed model is the linkage between the borehole and reservoir

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fluid flow domains. Sequential borehole-formation coupling was developed by Frooqnia et al. (2011) to ensure the conservation of mass between the two domains while securing the stability and numerical convergence. This advancement permitted them to numerically simulate and interpret the cross-communication of adjacent layers through the borehole using production logs (Frooqnia et al. 2016). More details of the development and implementation of the PC-SAFT and PR EOSs for modeling asphaltene precipitation in the reservoir and wellbore can be found in Shirdel (2013), Mohebbinia et al. (2014), Abouie (2015), and Abouie et al. (2016). Results

Phase Behavior Modeling

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This section presents the phase behavior modeling of two asphaltic crude oil samples (i.e., Fluid A and Fluid B) using both PC-SAFT and PR EOSs. Case 1 (Fluid A) investigates asphaltene precipitation during primary production. Case 2 (Fluid B) studies asphaltene precipitation during lean gas injection. In this case, 10% lean gas is injected and mixed with the reservoir fluid to increase the production rate. Finally, a dynamic case of asphaltene precipitation and deposition in the wellbore is presented to compare the trend of asphaltene deposition with the PC-SAFT and PR EOSs.

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This section studies the asphaltene phase behavior and amount of asphaltene precipitation in a wide range of pressure and temperature in comparison with the experimental data. Both PCSAFT and PR EOSs were tuned using gas chromatography and SARA data to reproduce the bubble point and asphaltene onset pressures of the crude oils. It should be noted that the characterization and tuning procedures are different for the PC-SAFT and PR EOSs. Several methods have been proposed to characterize the oil in order to use the PC-SAFT model (Ting et al. 2003, Pedersen and Hadsbjerg 2007, Pangunati et al. 2012). In this work, we used the characterization method of Pengunati et al. (2012) to characterize Fluids A and B. Nine components (i.e., N2, CO2, C1, C2, C3, heavy gas, saturates, aromatics + resins, and asphaltene) are considered in the characterization procedure. All these components are considered to be nonassociating components. The properties of each component are defined based on three parameters: m (number of segments per molecule), σ (temperature-independent segment diameter), and ε/k (segment-segment interaction energy). These parameters are determined by fitting the pure component properties to the saturated liquid density and vapor pressure data (Gross and Sadowski 2001, Ting et al. 2003). Furthermore, the pseudo-component properties can be determined based on the average molecular weight and degree of aromaticity (Gonzalez et al. 2007). For tuning purposes, the molecular weight of the plus fraction in stock tank oil, aromaticity, binary interaction coefficient, and the three parameters of the asphaltene component (i.e., m, σ, and ε/k) were manipulated. On the other hand, characterizing the fluid for the PR EOS requires a different procedure (Darabi 2014, Abouie et al. 2015). In this case, the number of lumped components, binary interaction coefficients, volume shift parameters, and molar volume of asphaltene are used as the tuning parameters. Case Study 1: Primary Production

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This case investigates asphaltene precipitation from an asphaltic reservoir fluid (Oil A). The sample fluid is a live oil taken from a Middle Eastern reservoir which is known to have asphaltene precipitation problem during primary production (Panuganti et al., 2012). Most wells in this reservoir are subjected to a high amount of asphaltene deposition and some of these wells were completely plugged few weeks after cleanup.

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The characterized composition and fluid properties of Fluid A for the PC-SAFT EOS are summarized in Tables 1 and 2, respectively. The binary interaction parameters for this system are also reported in Table 3. Figure 1 presents the asphaltene precipitation envelope (APE) for this crude oil that is generated by implementing the PC-SAFT EOS. The upper onset, bubble point, and lower onset pressures are plotted from 100°F to 400°F. As can be observed, the PC-SAFT EOS predicted the onset and bubble point pressure with high accuracy. For crude Oil A, the chance of asphaltene formation and precipitation is lower at temperature ranges from 225°F to 275°F since the upper onset and lower onset pressures curves nearly coincide with each other. In other words, the amount of asphaltene precipitation is considerably smaller if the production conditions such as pressure and temperature fall into the range between the upper and lower onset pressures and temperatures. Therefore, the amount of asphaltene precipitation, and consequently, deposition at the reservoir condition (200 ºF) is low during the primary production. However, as mentioned previously, the fluid goes through significant changes in pressure and temperature in the wellbore from the reservoir condition to the surface condition. Hence, the chance of asphaltene precipitation in the wellbore is higher compared to the reservoir condition.

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The reservoir Fluid A is also characterized using the solid model (e.g., PR EOS) to predict the asphaltene precipitation envelope. The tuning procedure was performed to match the bubble point and upper onset pressures of the initial fluid. Tables 4 and 5 present the characterized fluid and binary interaction coefficient for Fluid A, respectively. As shown in Table 5, the binary interaction coefficients are larger between asphaltene and lighter hydrocarbon components compared to the non-precipitating plus fraction. The molar volume of asphaltene is set around 11.85 ft 3 / lbmol for this crude oil. The APE using PR EOS is also plotted in Figure 1. It is worth mentioning that the linear interpolation is used to predict the AOPs between the available AOP’s experimental data to estimate at different temperatures. As can be observed, both PR and PCSAFT EOSs predicted the upper onset and bubble point pressures with high accuracy within the available range of experimental data. However, the difference in simulation results between these models becomes significant outside the range of experimental data.

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Figure 2 presents the asphaltene precipitation as a function of pressure at three different temperatures generated by the PC-SAFT EOS using UTWELL and a commercial phase behavior software (PVTsim Nova 2015). Good agreement is observed between UTWELL and the commercial PVT package with only a slight difference below the bubble point pressure at 130°F. This minor difference can be attributed to the small deviation in the results of the flash calculations in UTWELL and the commercial software. Based on APE, it is obvious that the range and amount of precipitation is higher at 130°F compared to 165°F and 254°F. Figure 3 shows the generated precipitation curve using PR EOS. The trend of simulation results with the PR EOS is similar to the PC-SAFT EOS. However, the precipitation percentage is different among these models due to the fact that the characterization method (especially molecular weight of the asphaltene component) is different. Hence, the mole fraction of asphaltene component is different among these models. If the mole fraction of the precipitated asphaltene in the mixture is used as the y-axis, Figure 4 would be observed. Figure 4 illustrates that the PR

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EOS can predict asphaltene precipitation with a really good approximation compared to the PCSAFT EOS. At 254°F, the experimental results show that upper asphaltene onset pressure is 2419 psi. For this case, the PR EOS is exact while the PC-SAFT EOS predicts the onset pressure equal to 2126 psi associated with 13.8% error. Nevertheless, the amount of asphaltene precipitation is small at this temperature.

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Case Study 2: Lean Gas Injection This case study presents lean gas injection into a reservoir to improve oil recovery. As a part of this project, it is necessary to evaluate the risk of asphaltene formation, generated by the contact of the lean gas with the reservoir fluid. During primary production, observations showed that asphaltene precipitation was not a significant problem for production wells. However, the laboratory experiments using the transmittance of an optimized laser light in the near infrared wavelength showed that asphaltene instability occurs by mixing the reservoir fluid with the lean gas. The lean gas mainly consists of methane (72%), ethane (12%), propane (7.5%), and carbon dioxide (4%). Table 6 presents the fluid composition and the PC-SAFT parameters after characterizing the fluid mixture to be used in the PC-SAFT EOS. The binary interaction coefficient for this system is similar to Fluid A (Table 3). The PC-SAFT EOS prediction and comparison of the mixed fluid with experimental data points are shown in Figure 5. As can be seen, there is a good agreement between the PC-SAFT model and the experimental data. Figure 6 presents the asphaltene precipitation curves at three different temperatures and compares the prediction of the implemented PC-SAFT EOS in UTWELL and the commercial PVT simulator. As shown, excellent agreement is observed between UTWELL and the commercial software. Notably, at 130°F, 70% asphaltene precipitation occurs. Similar to the previous case, the fluid was characterized and tuned using the PR EOS. Tables 7 and 8 present the properties of the characterized fluid and binary interaction coefficients, respectively. The molar volume of asphaltene is considered equal to 16.97 ft 3 / lbmol . Figure 7 presents the results of the PR EOS modeling of precipitation curves at three experimental temperature points. Again, similar trend is observed compared to the PC-SAFT EOS. Furthermore, it can be observed that asphaltene precipitation reaches the maximum value around the bubble points. Finally, the mole fraction of the precipitated asphaltene calculated by the PC-SAFT and PR EOSs are plotted in Figure 8. As shown, there is a good agreement between these two models. At 130°F, a slight difference can be observed where the PC-SAFT EOS overestimates the onset pressure point. At this point, the PC-SAFT EOS predicts the onset pressure of 5510 psi, while the experimental investigation showed that the onset pressure point is 4692 psi. Dynamic Asphaltene Modeling In this section, we performed simulation studies with Fluid A to compare the profile of asphaltene deposition using both PR and PC-SAFT EOSs. The simulation input data is presented in Table 9. As can be seen, there is a 3000 ft well which is in the stage of primary production. This well is in a reservoir with initial pressure of 2100 psi and operates with the constant wellhead pressure of 800 psi. As shown previously in Figure 1, this well is known to have flow assurance problems under these conditions. Therefore, a multiphase flow simulation is performed to predict the profile of asphaltene deposition in the well. Figure 9 shows the amount of asphaltene deposition in the wellbore using two different EOSs after one, three, and six

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months of production. As can be seen, the trend of deposition is similar for both models. However, the amount of asphaltene deposition becomes different after six month of production. This difference is attributed to the changes in mole fraction of components in the wellbore. As asphaltene starts to deposit on the surface of the wellbore, less asphaltene remains to flow. Consequently, the mole fraction of the components and the phase behavior of the mixture would change. Hence, it is possible that asphaltene-rich phase does not form based on the PC-SAFT EOS prediction, as the fluid flows towards the wellhead. Figure 10 shows the effect of reduction in asphaltene mole fraction on the asphaltene phase behavior. As shown, a reduction in asphaltene mole fraction shrinks the asphaltene precipitation envelope, and consequently, there would be lower chance of asphaltene formation as asphaltene starts to deposit. In other words, even a small amount of asphaltene deposition stabilizes the crude oil composition and reduces the probability of precipitation. Figure 11 shows the same phenomenon for crude Oil B as asphaltene gradually starts to deposit. It should be noted that the solid model using the PR EOS uses constant onset pressures during the simulation and does not consider the effect of the composition variations on onset pressures. By tuning the PR model for several compositions, it is possible to include the effect of the composition variation on the bubble point and onset pressures.

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Figure 12 also shows the results after 1, 3, and 6 months of simulation for the following changes: (a) pressure; (b) temperature; (c) oil superficial velocity; and (d) gas superficial velocity. As can be seen in Figure 12a, asphaltene deposition changes the pressure profile over time. It can be observed that as time progresses, the bottom-hole pressure increases which results in smaller pressure difference between the reservoir and wellbore. Hence, less fluid goes into the wellbore and the performance of the reservoir and wellbore is decreased. The temperature profile also shows a decreasing trend at the surface due to the dynamic effects of pressure, phase velocities, and asphaltene thickness. Figures 12c and 12d also show the velocity profiles along the wellbore. Since bottom-hole pressure increases over time, less fluid comes into the wellbore, and consequently, the velocities and production rate are decreased. The velocity is only increased at the locations where severe asphaltene deposition occurs (e.g., the smaller flow area). Since the velocities of the hydrocarbon phases decrease over time, there would be more time for heat transfer between the fluid and formation. This can also clarify the reason for temperature drop along the wellbore over time.

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Moreover, Figure 13 compares the CPU times of the PC-SAFT and PR EOSs. As shown, the PR EOS is much faster compared to the PC-SAFT EOS by a CPU time reduction factor of 2.2. Our study showed that this reduction factor is in the same range (1.5-2.2) independent of the number of grid blocks. The higher computational time in UTWELL compared to the simple multiphase flow simulation is due to the three phase flash calculation, deposition rate calculation, and changes in wellbore dimeter/boundary condition at each time step. Summary and Conclusions This study compared the performance of the PR and PC-SAFT EOSs in both static and dynamic asphaltene modeling in order to shed some lights on selecting an appropriate EOS to model asphaltene precipitation in compositional wellbore and reservoir simulators. The following is the summary and conclusions of this study:

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The static asphaltene phase behavior modeling using the PR and PC-SAFT EOSs showed that both EOSs are capable of regenerating the experimental data. There is a good agreement between the PR and PC-SAFT EOSs results with the experimental data. The PC-SAFT EOS showed more accuracy at conditions outside the experimental range. The PR and PC-SAFT EOSs were implemented in a non-isothermal compositional wellbore simulator to model the asphaltene precipitation and deposition over a wide range of conditions (i.e., pressure, temperature, and fluid composition). Dynamic modeling comparison through the wellbore simulation showed that both PR and PC-SAFT EOSs predict the asphaltene deposition profile in the wellbore with a similar trend. However, the thickness of the deposited asphaltene was different. This observation can be described by the fact that asphaltene mole fraction changes as deposition occurs. As a result, the fluid composition and the phase behavior would change which cannot be captured by the PR EOS. Comparison of the simulation CPU time showed that the PC-SAFT EOS is computationally more expensive compared to the PR model in the compositional simulator. For the investigated case, multiphase flow simulation with the PC-SAFT EOS was slower with a factor of 2.2.

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Nomenclature

Asphaltene Onset Pressure

APE

Asphaltene Precipitation Envelope

EOS

Equation of State

SAFT

Statistical Associating Fluid Theory

PC-SAFT

Perturbed Chain Statistical Associating Fluid Theory

PR

Peng-Robinson

STO

Stock Tank Oil

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AOP

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Acknowledgments

This work was supported by Abu Dhabi National Oil Company (ADNOC) and by the Reservoir Simulation Joint Industry Project, at the Center for Petroleum and Geosystems Engineering of The University of Texas at Austin. We express our gratitude to Dr. Mahdi Haddad for his review, comments, and discussion of this article. References Abouie, A. 2015. Development and Application of a Compositional Wellbore Simulator for Modeling Flow Assurance Issues and Optimization of Field Production, M.Sc. Thesis, The University of Texas at Austin, Austin, Texas, USA. Abouie, A., Shirdel, M., Darabi, H., and Sepehrnoori, K. 2015. Modeling Asphaltene Deposition in the

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Wellbore During Gas Lift Process. Presented in SPE Western Regional Meeting, Garden Grove, California, USA. Abouie, A., Rezaveisi, M., Mohebbinia, S., and Sepehrnoori, K. 2016. Static and Dynamic Comparison of Equation of State Solid Model and PC-SAFT for Modeling Asphaltene Phase Behavior. Presented in SPE Western Regional Meeting, Anchorage, Alaska, USA. Allenson, S. J., and Walsh, M. A. 1997. A Novel Way to Treat Asphaltene Deposition Problems Found in Oil Production, Presented in International Symposium on Oilfield Chemistry, Houston, Texas, USA. Chapman, W. G., Gubbins, K. E., Jackson, G., and Radosz, M. 1990. New Reference Equation of State for Associating Liquids. Industrial & Engineering Chemistry Research, 29(8), 1709-1721. Cimino, R., Correra, S., Sacomani, P. A., and Carniani, C. 1995. Thermodynamic Modelling for Prediction of Asphaltene Deposition in Live Oils. Presented in SPE International Symposium on Oilfield Chemistry, San Antonio, Texas, USA. Creek, J. L. 2005. Freedom of Action in the State of Asphaltenes: Escape from Conventional Wisdom. Energy & fuels, 19(4), 1212-1224. Darabi, H. 2014. Development of a non-isothermal Compositional Reservoir Simulator to Model Asphaltene Precipitation, Flocculation, and Deposition and Remediation, PhD dissertation, The University of Texas at Austin, Austin, Texas, USA. Darabi, H., and Sepehrnoori, K. 2015. Modeling and Simulation of Near-Wellbore Asphaltene Remediation Using Asphaltene Dispersants. Presented in SPE Reservoir Simulation Symposium, Houston, Texas, USA. Fallahnejad, G., and Kharrat, R. 2015. Fully Implicit Compositional Simulator for Modeling of Asphaltene Deposition During Natural Depletion. Fluid Phase Equilibria, 398, 15-25. Flory, P. J. 1942. Thermodynamics of High Polymer Solutions. The Journal of chemical physics, 10(1), 51-61. Frooqnia, A., Torres-Verdín, C., Sepehrnoori, K. A-Pour, R. 2016. Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs. SPE Journal. SPE-183628-PA, 22 (1): 389 - 406. http://dx.doi.org/10.2118/183628-PA. Frooqnia, A. 2014. Numerical Simulation and Interpretation of Borehole Fluid-Production Measurements. Ph.D. Dissertation, The University of Texas at Austin, Austin, Texas. Frooqnia, A., A-Pour, R., Torres-Verdín, C., Sepehrnoori, K. 2011. Numerical Simulation and interpretation of Production Logging Measurements using a New Coupled Wellbore-Reservoir Model, Paper VV presented at SPWLA 52nd International Logging Symposium, Colorado Springs, Colorado, 14-18 May. Gonzalez, D. L., Ting, P. D., Hirasaki, G. J., and Chapman, W. G. 2005. Prediction of Asphaltene Instability under Gas Injection with the PC-SAFT Equation of State. Energy & fuels, 19(4), 12301234. Gonzalez, D. L., Hirasaki, G. J., Creek, J., and Chapman, W. G. 2007. Modeling of Asphaltene Precipitation due to Changes in Composition Using the Perturbed Chain Statistical Associating Fluid Theory Equation of State. Energy & fuels, 21(3), 1231-1242. Gonzalez Rodriguez, D. L. 2008. Modeling of Asphaltene Precipitation and Deposition Tendency Using the PC-SAFT Equation of State, PhD dissertation, Rice University, Houston, Texas, USA. Goudarzi, A., Delshad, M., and Sepehrnoori, K. 2013. A Critical Assessment of Several Reservoir Simulators for Modeling Chemical Enhanced Oil Recovery Processes. Presented in SPE Reservoir Simulation Symposium, Woodlands, Texas, USA. Gross, J., and Sadowski, G. 2001. Perturbed-chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Industrial & engineering chemistry research, 40(4), 1244-1260. Gupta, A. K. 1986. A Model for Asphaltene Flocculation Using an Equation of State, M.Sc Thesis, University of Calgary, Calgary, Canada. Hirschberg, A., DeJong, L. N. J., Schipper, B. A., and Meijer, J. G. 1984. Influence of Temperature and Pressure on Asphaltene Flocculation. Society of Petroleum Engineers Journal, 24(03), 283-293. Kor, P., Kharrat, R., and Ayoubi, A. (2016). Comparison and evaluation of several models in prediction

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of asphaltene deposition profile along an oil well: a case study. Journal of Petroleum Exploration and Production Technology, 1-14. Korrani, A. K. N. 2014. Mechanistic Modeling of Low Salinity Water Injection, PhD dissertation, The University of Texas at Austin, Austin, Texas, USA. Kurup, A. S., Vargas, F. M., Wang, J., Buckley, J., Creek, J. L., Subramani, H. J., and Chapman, W. G. 2011. Development and Application of an Asphaltene Deposition Tool (ADEPT) for Well Bores. Energy & Fuels, 25(10), 4506-4516. Leontaritis, K. J., and Mansoori, G. A. 1987. Asphaltene Flocculation During Oil Production and Processing: A Thermodynamic Collodial Model. Presented inSPE International Symposium on Oilfield Chemistry, San Antonio, Texas, USA. Leontaritis, K. J. 1988. Asphaltene Deposition: a Thermodynamic-Colloidal Model. PhD dissertation, University of Illinois, Chicago, IL, USA. Mohebbinia, S., Sepehrnoori, K., Johns, R. T., and Kazemi Nia Korrani, A. 2014. Simulation of Asphaltene Precipitation during Gas Injection Using PC-SAFT EOS. Presented in SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands. Nghiem, L. X., Hassam, M. S., Nutakki, R., and George, A. E. D. 1993. Efficient Modelling of Asphaltene Precipitation. Presented in SPE Annual Technical Conference and Exhibition, Houston, Texas, USA. Nor-Azlan, N., and Adewumi, M. A. 1993. Development of Asphaltene Phase Equilibria Predictive Model. Presented in SPE Eastern Regional Meeting, Pittsburgh, PA, USA. Pan, H., and Firoozabadi, A. 1998. A Thermodynamic Micellization Model for Asphaltene Precipitation: Part I: Micellar Size and Growth. SPE Production & Facilities, 13(02), 118-127. Panuganti, S. R., Vargas, F. M., Gonzalez, D. L., Kurup, A. S., and Chapman, W. G. 2012. PC-SAFT Characterization of Crude Oils and Modeling of Asphaltene Phase Behavior. Fuel, 93, 658-669. Pedersen, S.K., and Hasdbjerg, C. 2007. PC-SAFT Equation of State Applied to Petroleum Reservoir Fluids. Presented in SPE Annual Technical Conference and Exhibition, Anaheim, California, USA. Péneloux, A., Rauzy, E., and Fréze, R. 1982. A Consistent Correction for Redlich Kwong Soave Volumes. Fluid Phase Equilibria, 8(1), 7-23. Perschke, D. R. 1988. Equation of State Phase Behavior Modeling for Compositional Simulation, PhD dissertation, The University of Texas at Austin, Austin, Texas, USA. PVTsim Nova software. 2015. Calsep A/S, Lyngby, Denmark. Schou Pedersen, K., and Hasdbjerg, C. 2007. PC-SAFT equation of state applied to petroleum reservoir fluids. Presented in SPE Annual Technical Conference and Exhibition, Anaheim, California, USA. Shirdel, M. 2013. Development of a Coupled Wellbore-Reservoir Compositional Simulator for Damage Prediction and Remediation, PhD dissertation, The University of Texas at Austin, Austin, Texas, USA. Srivastava, R. K., and Huang, S. S. 1997. Asphaltene Deposition During CO2 Flooding: a Laboratory Assessment. Presented in SPE Production Operations Symposium, Oklahoma City, Oklahoma, USA. Thomas, F. B., Bennion, D. B., Bennion, D. W., and Hunter, B. E. 1992. Experimental and Theoretical Studies of Solids Precipitation from Reservoir Fluid. Journal of Canadian Petroleum Technology, 31(01). Ting, P.D., Hirasaki, G. J., and Chapman, W. G. 2003. Modeling of Asphaltene Phase Behavior with the SAFT Equation of State. Petroleum Science and Technology, 21(3-4), 647-661. Vargas, F. M., Gonzalez, D. L., Hirasaki, G. J., and Chapman, W. G. 2009. Modeling Asphaltene Phase Behavior in Crude Oil Systems Using the Perturbed Chain Form of the Statistical Associating Fluid Theory (PC-SAFT) Equation of State. Energy & Fuels, 23(3), 1140-1146. Victorov, A. I., and Firoozabadi, A. 1996. Thermodynamics of Asphaltene Precipitation in Petroleum Fluids by a Micellization Model. AIChE J, 42, 1753-1764. Wertheim, M. S. 1984. Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics. Journal of statistical physics, 35(1-2), 19-34. Wertheim, M. S. 1986. Fluids with Highly Directional Attractive Forces. IV. Equilibrium

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Polymerization. Journa of statistical physics, 42(3-4), 477-492.

ACCEPTED TableMANUSCRIPT 1 Component

Mole%

MW

N2

PC-SAFT parameters m

σ (A)

ε/k (K)

28.04

1.206

3.313

90.96

1.944

44.01

2.073

2.785

169.21

C1

33.590

16.04

1.000

3.704

150.03

C2

7.557

30.07

1.607

3.520

191.42

C3

6.742

44.10

2.002

3.618

208.11

Heavy Gas

8.198

65.49

2.530

3.740

228.51

Saturates

31.743

167.68

5.150

3.900

249.69

Aromatics + Resins

9.907

253.79

6.410

3.990

285.00

Asphaltene

0.133

1700.00

32.998

4.203

353.50

Table 6 MW

N2

0.185

28.01

CO2

2.248

44.01

C1

37.954

C2

7.982

C3

6.367 7.764

Saturates

29.948

Aromatics + Resins

7.544

Asphaltene

0.0086

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m

σ (A)

ε/k (K)

1.21

3.31

90.96

2.07

2.79

169.21

16.04

1.00

3.70

150.03

30.07

1.61

3.52

191.42

44.10

2.00

3.62

208.11

66.75

2.53

3.74

228.51

181.19

5.50

3.91

250.72

230.86

5.71

4.00

300.57

1700.00

35.60

4.40

400.00

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Heavy Gas

PC-SAFT parameters

SC

Mole%

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Component

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0.163

CO2

ACCEPTED MANUSCRIPT

Table 4 Component N2

3

Mole %

PC(psi)

TC(°R)

VC(ft /lbmol)

MW

Acentric Factor

Parachor

Volume Shift

0.163

492.31

227.16

1.434

28.01

0.04

41.00

0.000

1.941

1069.86

547.56

1.506

44.01

0.23

78.00

0.000

H2 S

0.000

1296.18

671.76

1.578

34.08

0.10

80.10

0.000

C1

33.531

667.19

343.08

1.586

16.04

0.01

77.00

0.000

C2

7.659

708.34

549.72

2.371

30.07

0.10

108.00

0.000

RI PT

CO2

7.271

615.76

665.64

3.252

44.10

C4-C5

11.757

520.17

793.63

4.451

64.30

C6-C7

9.426

486.66

957.74

5.648

90.24

C8-C13

14.169

371.13

1121.70

8.283

133.82

0.43

380.34

0.029

C14-C20

6.080

248.05

1332.30

13.657

228.02

0.70

608.88

0.104

C21-C29

3.263

179.77

1486.60

19.066

328.62

0.95

810.52

0.185

C30+A

3.772

122.34

1629.72

23.401

557.57

1.18

1032.69

0.149

Asphaltene

0.969

122.34

1629.72

23.401

557.57

1.18

1032.69

0.149

MW

Acentric Factor

Parachor

Volume Shift

M AN U

SC

C3

0.15

150.30

0.000

0.21

205.66

0.000

0.28

262.10

0.004

Component

Mole %

PC(psi)

TC(°R)

0.1838

492.31

227.16

CO2

2.2575

1069.86

547.56

C1

38.0006

667.19

343.08

C2

8.1311

708.34

VC(ft /lbmol)

EP

N2

TE D

Table 7

549.72

3

1.434

28.01

0.04

41.00

0.000

1.506

44.01

0.23

78.00

0.000

1.586

16.04

0.01

77.00

0.000

2.371

30.07

0.10

108.00

0.000

6.9816

615.76

665.64

3.252

44.10

0.15

150.30

0.000

C4-C5

10.4980

521.13

791.83

4.438

64.04

0.21

204.80

0.000

5.814

91.16

0.29

264.72

0.000

AC C

C3

C6-C7

7.0656

465.73

947.23

C8-C13

13.1525

367.59

1123.49

8.357

135.53

0.42

384.62

0.019

C14-C20

6.8615

255.54

1354.00

13.362

231.33

0.62

616.37

0.091

C21-C29

4.0492

196.87

1530.77

18.152

339.91

0.85

829.55

0.172

C30-C35

1.2620

143.66

1605.24

22.334

450.21

1.05

995.66

0.141

C36+A

1.5281

99.07

1870.94

28.449

638.17

1.54

1153.92

0.220

Asphaltene

0.0285

99.07

1870.94

28.449

638.17

1.54

1153.92

0.220

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Table 3 N2

C1

C2

C3

Heavy Gas

Saturates

Aromatic+Resins

Asphaltene

0 0 0.0678

0

0.03

0.05

0.062

0

0.04

0.097

0.058

0

0

RI PT

0 0.09

0.1

0.053

0

0

0

0.12

0.07

0.03

0.02

0.015

0

0.14

0.13

0.09

0.03

0.012

0.01

0.005

0.158

0.1

0.015

0.029

0.025

0.01

0.012

0.007

0

0.16

0.1

0.015

0.07

0.06

0.01

0.01

-0.004

0

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0.06 0.075

EP

Heavy Gas Saturates Aromatic+Resins Asphaltene

H2S

AC C

N2 CO2 H2S C1 C2 C3

CO2

0

0

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Table 5 N2

H2S

C1

C2

C3

Table 2 C4-C5

C6-C7

C8-C13

C14-C20

C21-C29

C30+A

0

Crude oil A GOR(scf/stb)

-0.020

0

H2S

0.176

0.096

0

C1

0.031

0.103

0.08

0

C2

0.042

0.130

0.07

0

0

C3

0.091

0.135

0.07

0

0

0

C4-C5

0.095

0.128

0.06

0

0

0

0

C6-C7 C8-C13

0.106

0.131

0

0

0

0

0

0

0.114

0.143

0

0

0

0

0

0

0

C14-C20 C21-C29

0.120

0.150

0

0

0

0

0

0

0

0

0.120

0.150

0

0

0

0

0

0

0

0

0

C30+A

0.025

0.031

0

0

0

0

0

0

0

0

0

0

Asphaltene

0.025

0.031

0

0.2

0.2

0.2

0.2

0

0

0

0

0

N2

CO2

C1

C2

C3

C4-C5

C6-C7

C8-C13

C14-C20

C21-C29

C30-C35

Table 8

0.000

0

C1

0.025

0.105

0

C2

0.010

0.130

0

0

C3

0.090

0.125

0

0

0

C4-C5

0.099

0.116

0

0

0

0

C6-C7

0.110

0.115

0

0

0

0

0

C8-C13

0.112

0.123

0

0

0

0

0

0

C14-C20

0.120

0.150

0

0

0

0

0

0

0

C21-C29

0.120

0.150

0

0

0

0

0

0

0

C30-C35

0.120

0.150

0

0

0

0

0

0

0

C36+A

0.120

0.150

0

0

0

0

0

0

0

Asphaltene

0.120

0.150

0.2

0.2

0.2

0.2

0

AC C

EP

0

0

Asphaltene

0

0

0

0

0

0

0

0

TE D

CO2

C36+A

M AN U

0

0

SC

CO2

N2

Asphaltene

RI PT

N2

CO2

0

0

787

MW of reservoir fluid (g/mol)

97.75

MW of flashed gas (g/mol)

29.064

MW of STO(g/mol)

193

STO density (g/cc)

0.823

Saturates(wt%)

66.26

Aromatics(wt%)

25.59

Resins(wt%)

5.35

Asphaltene(wt%)

2.8

ACCEPTED MANUSCRIPT Table 9 Well Data

Reservoir and Fluid Data

3000 ft

Net pay zone

100 ft

Well TVD

3000 ft

Reservoir pressure

2100 psi

Max grid size

20 ft

Reservoir temperature

160 °F

Ambient temperature at top

60 °F

Ambient temperature at bottom

160 °F

Total heat transfer coefficient

1.0 Btu/ft2.hr.°F

Tubing ID

0.085 ft

Oil productivity index

0.15 ft3/psi.ft.day

Wellhead pressure

800 psi

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Well MD

M AN U

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ACCEPTED MANUSCRIPT

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Figure 1: APE curve for crude oil 'A' generated using PC-SAFT and PR EOSs

Figure 2: Comparison of asphaltene precipitation curves using PC-SAFT EOS at three different temperatures by UTWELL and PVTsim for crude oil 'A'

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Figure 3: Asphaltene precipitation curves for crude oil 'A' at various temperatures using PR EOS

Figure 4: Comparison of the normalized precipitation curves at three different temperatures using PR and PC-SAFT EOSs for crude oil 'A'

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Figure 5: APE curve for crude oil 'B' generated using PC-SAFT and PR EOSs

Figure 6: Comparison of asphaltene precipitation curves using PC-SAFT EOS at three different temperatures by UTWELL and PVTsim for crude oil 'B'

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Figure 7: Asphaltene precipitation curves for crude oil 'B' at various temperatures using PR EOS

Figure 8: Comparison of the normalized precipitation curves at three different temperatures using PR and PC-SAFT EOSs for crude oil 'B'

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Figure 9: Comparison of the thickness of deposited asphaltene in the wellbore after one, three, and six months of production using Peng-Robinson and PC-SAFT EOSs

Figure 10: Effect of reduction in asphaltene mole fraction on asphaltene phase behavior (crude oil 'A')

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Figure 11: Effect of reduction in asphaltene mole fraction on asphaltene phase behavior (crude oil 'B')

(a)

(b)

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(c) (d) Figure 12: (a) pressure, (b) temperature, (c) oil superficial velocity, (d) gas superficial velocity profiles along the wellbore after 1, 3, and 6 months

Figure 13: CPU time comparison of Peng-Robinson and PC-SAFT EOSs

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•

PC-SAFT equation of state is implemented into the compositional wellbore model to perform three-phase flash calculation and determine asphaltene precipitation in the wellbore. The performances of Peng-Robinson and PC-SAFT EOSs are compared in both static and

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dynamic asphaltene modeling. •

Static results illustrated that both equations of state have the capability of modeling asphaltene precipitation envelope with relatively high accuracy.

•

Dynamic modeling comparison through wellbore simulation showed Peng-Robinson

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EOS would overestimates the amount of asphaltene precipitation and deposition in the wellbore.

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Comparison of simulation CPU time showed that PC-SAFT is computationally slower compared to the PR model in the compositional simulator (slower by a factor of 2.2) due

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to the iterative process of finding the density roots for phase equilibrium calculation.

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