Regular Article
Prediction of asphaltene precipitation upon injection of various gases at nearwellbore conditions: A simulation study using PCSAFT EoS
^{1}
Department of Petroleum Engineering, School of Chemical and Petroleum Engineering, Shiraz University, 7134851154 Shiraz, Iran
^{2}
Enhanced Oil Recovery (EOR) Research Centre, IOR/EOR Research Institute, Shiraz University, 7134851154 Shiraz, Iran
^{3}
Institut für Verfahrenstechnik und Umwelttechnik, Technische Universität Dresden, 01062 Dresden, Germany
^{*} Corresponding author: rparsaei@shirazu.ac.ir
Received:
8
March
2019
Accepted:
29
May
2019
The depletion of oil reservoirs and increased global oil demand have given impetus to employ various secondary and tertiary oil recovery methods. Gas injection is widely used in both secondary and tertiary modes, though the major problem associated with this process is the precipitation and deposition of asphaltene, particularly at nearwellbore conditions. Indepth knowledge of asphaltene phase behavior is therefore essential for the prediction of asphaltene precipitation. Previous studies reported the impact of gas injection on asphaltene phase behavior, but the knowledge of precipitation of asphaltene as a function of different mole fractions of injected gas is also imperative. In this study, the thermodynamic model of PCSAFT EoS is used to discern the phase equilibrium of asphaltene by analyzing the asphaltene dropout curve during gas injection. Asphaltene dropout curves of two different live oil samples are analyzed by injecting CO_{2}, CH_{4}, and N_{2} gases at different mole percentages and temperatures. The results revealed that PCSAFT EoS can serve as a reliable tool for estimating bubble pressure and asphaltene onset pressure for a wide range of temperatures, pressures, and compositions. The simulation results for the injection of CO_{2}, CH_{4}, and N_{2} also showed that CO_{2} gas gives minimum asphaltene precipitation. It reduces the size of the dropout curve or moves it toward higher pressures. CH_{4} and N_{2} expand the dropout curve by raising the upper onset point. CH_{4} increases the maximum point of the dropout curve for two types of oil studied (A and B) at two different temperatures. N_{2} raises the maximum point of oil type “A” by approximately 57% at 395 K, while it has no effect on the maximum point of oil type “B”. In addition, reducing the temperature resulted in either decrease or increase of asphaltene solubility, demonstrating that the impact of temperature on asphaltene precipitation is closely related to the composition of the crude.
© S. Mahmoudvand et al., published by IFP Energies nouvelles, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nomenclature
: Reduced Helmholtz free energy, (–)
d_{i}: Temperaturedependent segment diameter of component i, Å
g^{hs}: Hardsphere radial distribution function, (–)
m_{i}: Number of segments in a chain of component i
U^{r}: Residual internal energy, J
v_{m}: Molar volume, cm^{3}/mole
N: Total number of molecules, (–)
Z: Compressibility factor, (–)
ε^{AB}: Association energy between site A and site B, J
κ^{AiBi}: Association volume parameter, (–)
: Abbreviation (n = 0, …, 3) defined by equation (7), Å^{ n−3}
φ_{k}: Fugacity coefficient of component k, (–)
δ: Hildebrand solubility parameter, (J/cm^{3})^{0.5}
ε: Depth of square well potential, J
ρ: Total number density of molecules, 1/Å
σ: Temperature independent segment diameter, Å
Superscripts
disp: Contribution due to dispersive attraction
hc: Hardchain system residual contribution
hs: Hardsphere system residual contribution
Abbreviations
APE: Asphaltene Phase (or precipitation) Envelope
AARD: Absolute Average Relative Deviations
1 Introduction
Asphaltene is the heaviest and the most polar component of crude oil. Currently, the most common definition of asphaltene is based on its solubility. Asphaltene is soluble in aromatic solvents like benzene, toluene and insoluble in lightparaffinic solvents such as npentane or nheptane. Asphaltene is also composed of complex polynuclear aromatic components, which include alkyl groups. It consists primarily of oxygen, nitrogen, sulfur and metals such as vanadium, and nickel [1–6]. Asphaltene molecule is very complex and its properties would profoundly vary from one crude to another [7]. To recognize asphaltene properties in molecular level several technologies such as fieldionization mass spectrometry [8], electrospray ionization, Fourier transform ion cyclotron resonance mass spectrometry [9], atmospheric pressure photoionization mass spectrometry [10], fielddesorption/field ionization mass spectrometry [11], laser desorption ionization [12], and timeresolved fluorescence depolarization [7] are employed nowadays. Exploiting these techniques in the last decade has provided us with a clearer perspective of asphaltene. For instance, these methods give an average molecular weight of about 750 g/mol for asphaltene within a range of 300–1400 g/mol [13]. However, large molecular weights reported for asphaltenes in some older reports by vapor pressure osmometry or size exclusion chromatography are most likely due in part to the measurement of aggregate weight, not molecular one.
Asphaltene can cause severe problems in various sectors of the oil industry from reducing the reservoir permeability to plugging the respective facilities such as wellheads, separators, and pipelines [14, 15]. Different mechanical and chemical methods have been proposed for mitigation of asphaltene deposition, but these methods are costly. On the other hand, some of the damages caused by asphaltene are permanent, thus prevention of asphaltene precipitation and deposition are more critical than repairing facilities [16, 17]. In addition, the removal of asphaltene from the reservoir rock surface is even more complex than the surface facilities. Accordingly, the knowledge of asphaltene behavior, as well as developing a tool to predict its precipitation are essential [2, 18]. It is also known that asphaltene precipitation would precede the deposition but there are other factors involved in this phenomenon such as flow regime, rheology, twophase flow patterns, and surface characteristics [5, 19, 20]. When the condition changes and asphaltene is no longer soluble in the oil phase, it starts to precipitate from reservoir fluid which would, in turn, increase the oil density. In later stages, the precipitated particles may deposit on the rock surface, which causes pore plugging and formation damage.
The most important step in developing a tool for prediction of asphaltene deposition is an accurate estimation of asphaltene precipitation onset. This is commonly evaluated by thermodynamic models. Asphaltene thermodynamic models are classified into two main categories namely, solubility and colloidal models. In the colloidal approach, the crude is divided into the polar and nonpolar subsets. Models based on the colloidal approach assume asphaltenes as suspended solid particles, which are peptized by resins in a colloidal system [21]. This approach assumes that asphaltenes exist in the oil as solid particles; and, describes the stability of asphaltenes in terms of micelle formation where asphaltene selfassociates into aggregates to make a core. Then, resins adsorb onto the core (based on polarpolar interactions) to form a steric shell. Asphaltene colloidal stability was first introduced by Nellsteyn and then was modified by Pfeiffer and Saal [22]. While colloidal models of asphaltene were beneficial in the early stages of understanding asphaltene behavior, but they cannot describe reversibility of asphaltene precipitation. Although numerous works have been done using this model and several modifications have been implemented, the colloidal models require many parameters to be tuned prior to prediction [23–26].
Solubility theory assumes asphaltene molecules as part of the oil mixture and asphaltene precipitation is modeled as a liquidliquid or solidliquid equilibrium [27]. In this approach, solution theories and Equations of State (EoS) are the two main parts of solubility theory [28–31]. In particular, cubic EoS is used to describe asphaltene phase behavior since it provides a reliable match with the experimental results although its prediction of liquidliquid equilibrium is questionable [32]. Furthermore, the cubic EoS contains many parameters, which make the calculations tedious and timeconsuming [32].
Association EoS such as CPA and SAFT can be used for modeling complex fluid phase behavior like mixtures containing asphaltene. By extending Wertheim’s first order perturbation theory to chain molecules, the statistical association fluid theory equation of state was developed by Chapman et al. [33]. Among different modifications of SAFT EoS, PCSAFT EoS was developed by Gross and Sadowski [34] to account for the chain length effects. This EoS is reported to accurately model different mixtures (containing hydrogen bond mixtures) and pure compounds [34].
Many researchers have modeled asphaltene phase behavior using PCSAFT EoS. They investigated the effects of injection of different gases on asphaltene phase behavior, the results of these works are in line with the experimental data [35–39]. Several works in the literature also present group contribution methods to predict phase envelope or solubility of gases in the heavy fraction of oils [40, 41]. In this work, it is intended to study the amount of precipitated asphaltene upon pressure drop and also injection of different mole percentages of various gases including CO_{2}, N_{2}, and CH_{4}, at different temperatures. The latter is imperative since to the best of our knowledge no research has been conducted to investigate the impact of temperature on asphaltene precipitation. In oil reservoirs, usually, the temperature remains constant but otherwise is expected near the injection well.
A simple and robust algorithm based on RachfordRice equation using PCSAFT EoS for fugacity coefficient calculations is used in this work to eliminate the complexity of asphaltene phase behavior prediction by minimizing the Gibbs free energy of the threephase system. This algorithm is validated using experimental data of Asphaltene Phase Envelope (APE) upon the injection of different gases at various pressures and temperatures. This simple Vapor–Liquid–Liquid Equilibrium (VLLE) algorithm may also be used in conjunction with other EOSs. To explain it briefly, at first, a conventional twophase flash calculation (VLE) is performed. Then, the stationary point method by Michelsen [42] is used to have initial guesses for the stability analysis which is crucial for algorithms in multiphase equilibrium calculations. Stability analysis is done to check the stability of the liquid phase resulted from the VLE. If the presence of a new liquid phase, such as asphaltene phase is verified, the threephase split calculation is performed next by solving RachfordRice equations for the vapor phase and a second liquid phase (asphaltene phase).
2 Theoretical calculations
2.1 PCSAFT EoS
In phase equilibrium, the computation of fugacity coefficients of each component is of prime importance. Different EoSs use various methods to calculate the fugacity coefficient. Using PCSAFT EoS usually includes two stages for thermodynamic equilibrium models: (i) Helmholtz free energy, and (ii) fugacity coefficient calculation. The PCSAFT EoS is based on Helmholtz free energy. By extending Helmholtz free energy for the fugacity coefficient, the PCSAFT EoS is then used for thermodynamic equilibrium. The mixture Helmholtz free energy of the nonassociating fluid in PCSAFT EoS is defined as
(2)where , , are the residual, hard chain and dispersion contributions for the mixture Helmholtz free energy, respectively. In equation (2), A is Helmholtz free energy, N is the total number of molecules, k is the Boltzmann constant and T is absolute temperature. The PCSAFT EoS describes the fugacity coefficient (φ_{k}) of component k as
(3)where Z, and v are the compressibility factor, the mole fraction of component k and the molar volume, respectively.
2.2 The hard chain contribution
Hard sphere and chain formation constitute the hard chain contribution as follows:
(4)where , , and are the mean segment number, the number of segments in a chain of species i in the mixture and the hardsphere radial distribution function, respectively. The required equations are expressed as:
(9)where ρ is the total number density of molecules, d_{i} is the temperaturedependent segment diameter of component i, σ_{i} is the temperature independent segment diameter and ε_{i} is the depth of square well potential of component i.
2.3 The dispersion contribution
There are attractive forces between molecular segments that interact with each other. The attractive forces between chains with the same and different lengths are defined as dispersion contribution using the following equations:
(10)where the variables C_{1}, , and are described as
(13)where η is the packing fraction (reduced density), which is equal to [18, 34]. Other equations for calculation of required derivatives such as and are given elsewhere [18, 43].
3 Oil characterization for PCSAFT EoS
The PCSAFT EoS needs five parameters of fluid characterization: (1) the number of segments in the molecule (i.e., chain length), m, (2) a size parameter, σ, (3) a segment energy parameter, ε, (4) the volume of association, κ^{AiBi}, and (5) the energy of association, ε^{AiBi}. The last two parameters are required only for the molecules that are selfassociating. Previous studies have shown that asphaltene phase stability is controlled by van der Waals forces, hence m, σ and ε are enough for modeling asphaltene phase behavior [27, 32]. These parameters are in general obtained based on regression to vapor pressure and saturated liquid densities for pure components [34].
Two asphaltenic oil samples “A” and “B” were studied in this work. They were taken from reservoirs that experienced asphaltene precipitation problem during primary oil recovery [44]. The composition and PCSAFT parameters of these oil samples are given in Tables 1 and 2, respectively. Experimental studies were implemented by Jamaluddin et al. [44] to evaluate asphaltene precipitation from crude oil “A” under N_{2} injection [44], also, they characterized this oil as a recombined oil to obtain PCSAFT EoS parameters [35, 45]. They considered the separator gas as a fourcomponent fluid (i.e., N_{2}, CO_{2}, C_{1}, and light nalkanes) and recombined it with the stock tank oil which was characterized by three subfractions of saturates, aromatics plus resins and asphaltenes. They used PCSAFT EoS and modeled this crude oil APE. Gonzalez et al. [45] showed that the experimental data of asphaltene precipitation for crude oil “A” [44] are well described by the PCSAFT EoS model. For oil “B” the composition of monophasic reservoir fluid is available. Hence, Tavakkoli et al. [46] flashed it to atmospheric conditions by PCSAFT EoS to obtain flashed gas and liquid compositions. They recombined these compositions and tuned the aromaticity value (γ) for C_{7+} and nhexane to find the characterized composition of oil “B” for the PCSAFT equation. PCSAFT parameters of all of the components of oil “B” after characterization are reported in Table 2. Binary interaction coefficients are available in the main references [45, 46].
Tavakkoli et al. [46] divided the asphaltene fraction into two subfractions of nC_{5−7} and nC_{7+} asphaltenes, based on the experimental amount of asphaltenes precipitated by nC_{5} and nC_{7} to investigate the effect of asphaltene polydispersity. They fitted the aromaticity value for the aromatics + resins component to reproduce both the experimental stock tank oil density and bubble point pressure. The aromaticity value and molecular weight of asphaltene subfractions are fitted to the experimental upper onset pressure at different temperatures. Aromaticity values are reported in Table 2 for oil “B”. To highlight the diverse impact of gas injected to the reservoir on the dropout curve of asphaltene, in this study, we predicted the amount of asphaltene that precipitates upon the injection of different gases under wellbore operating conditions. We also studied the effect of change in the temperature near the wellbore. The asphaltene drop out curves for oil with and without different gases is regenerated in this research assuming that the precipitation occurs in the Liquid–Liquid Equilibrium (LLE) between the upper onset and bubble point region and VLLE between the bubble point and lower onset pressure. This study proves that careful scrutiny is essential for EOR/IOR methods which involve additional gas.
4 Results and discussion
Figure 1 shows the APE for the crude oil “A”. To interpret this figure, one needs to check the asphaltene solubility parameter. The solubility parameter given by Hildebrand is calculated by δ = (−U^{ r } /v_{m})^{0.5} [47]. This parameter is the square root of Cohesive Energy Density (CED), the term in parentheses, is the energy required for removing a molar volume of the component from its neighbors to infinite separation. This relation is often used for nonpolar and slightly polar systems with no hydrogen bonding. It is worth mentioning that asphaltene has the highest solubility parameter among the components of crude oil [48]. Decreasing the pressure increases the molar volume and hence, lowers the asphaltene solubility. Asphaltene starts to precipitate at an upper onset pressure and reaches its maximum around the bubble pressure. For pressures below the bubble point, lighter components are released by which the molar volume of the liquid phase drops and consequently asphaltene solubility increases. Then, precipitation of asphaltene stops at a pressure called lower onset pressure. Temperature changes may have two diverse effects on the APE of crude oils. Higher temperature results in higher molar volumes and higher oil entropy. The overall decrease or increase in CED is determined by a competitive increase in numerator and denominator of the fraction. At lower temperatures, the effect of oil entropy is more than density and causes lower solubility for asphaltene, which means lower upper onset and higher lower onset pressures, but at the higher temperature, the oil density effect is prominent.
Fig. 1 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressures for oil “A” prior to gas injection. 
In Figure 1, Absolute Average Relative Deviations (AARD) for prediction of the upper onset and bubble pressures are 5.36% and 2.14%, respectively. These values for Figure 2 are 3.63% and 2.01%, respectively that confirm the applicability of the algorithm used in this work. Figure 3 reveals that increasing injection of N_{2} enhances asphaltene onset pressures, bubble pressures and the difference between the asphaltene onset pressure and the bubble point pressure. This is because of low polarizability and low molecular weight of N_{2} which cause lower solubility parameter and more asphaltene precipitation and finally the higher difference between upper and lower pressures. In fact, lighter oil has a lower solubility parameter for asphaltene and so produces more asphaltene precipitation. In this figure, AARD values for estimation of upper onset and bubble pressures are 6.75% and 7.73%, respectively.
Fig. 2 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressures for oil “B” prior to gas injection. 
Fig. 3 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressure upon the injection of N_{2} at 420 K for oil “A”. 
As shown in Figures 1–3, a good agreement exists between the model and experimental data for discerning the impact of operational conditions such as temperature, type of injection gas, and the amount of injection gas.
The main parameters that affect the oil APE are m, σ, and ε/k of the pseudocomponents and their respective binary interaction coefficients with other components. Panuganti et al. [32] and Gonzalez Rodriguez [35] proposed several methods based on sensitivity analysis to fit the experimental data with predictions of the PCSAFT EoS. The bubble point pressure curve is tuned initially, and then the upper and lower onset curves are matched with the laboratory data by tuning the asphaltene parameters (i.e., m, σ, and ε/k) in their methods. Analyzing the sensitivity of the APE to all of these parameters is beyond the scope of this study. Therefore, we only examined the sensitivity of the APE curves to m, σ, and ε/k of asphaltene and the result for crude oil “A” is plotted in Figure 4a–4c, respectively.
Fig. 4 Sensitivity analysis for asphaltene parameters on APE of crude oil “A”. (a): m, (b): σ, and (c): ε/k. 
4.1 Effect of injection of various mole fractions of CO_{2}, CH_{4,} and N_{2} on precipitation of asphaltene
Figure 5 shows the impact of different mole fractions of CO_{2} on asphaltene dropout curve of oil “A” at a typical temperature of the wellbore, 355 K and 395 K. Comparing Figures 5a and 5b reveals the effect of temperature on the asphaltene dropout curve due to CO_{2} injection. In fact, there is a crossover temperature under which CO_{2} increases crude oil solubility parameters and stabilizes asphaltene that results in a narrower asphaltene dropout curve as CO_{2} concentration increases and over which carbon dioxide reduces solubility parameters and makes asphaltene to be unstable at higher pressures. This is shown by calculating the upper onset pressure of asphaltene for oil “A” in Figure 6. This figure depicts that CO_{2} injection enlarges the APE by elevating the upper onset curve in temperatures a little higher than 370 K. While this curve is dropped at lower temperatures. An expanded APE means when a live oil gets depressurized, asphaltene destabilizes at higher pressures. As shown in Figure 7a, CO_{2} injection into oil “B” extenuates asphaltene precipitation by making the dropout curve smaller. The same behavior can be seen in Figure 5a, although adding CO_{2} to this oil at 395 K shows a different influence. Increasing the mole percent of CO_{2} injected to Oil “B” does not give a monotonic increase of upper onset pressure in contrary to the addition of CO_{2} into oil “A” at 395 K that grows the upper onset pressure continuously. Thus, the CO_{2} injection effect on asphaltene is a function of oil type and reservoir temperature.
Fig. 5 The amount of asphaltene precipitation for oil “A” upon injection of various mole fractions of CO_{2} at (a) T = 355 K and (b) T = 395 K. 
Fig. 6 Effect of CO_{2} on the APE for crude oil “A”. 
Fig. 7 The amount of asphaltene precipitation for oil “B” upon injection of various mole fractions of CO_{2} at (a) T = 355 K and (b) T = 395 K. 
Figure 8 clearly shows that CO_{2} injection decreases and then increases the upper onset curve of asphaltene for oil “B” at 395 K. Although a monotonic decrease in the upper onset pressure is seen at 355 K.
Fig. 8 Effect of CO_{2} on the upper onset curve of oil “B” at 395 K and 355 K. 
CH_{4} injection displaces the bubble point and upper onset pressures more sharply in comparison with CO_{2}. Results of this injection for both oils at 355 K are drawn in Figure 9. This effect is more severe in the case of N_{2} injection that is depicted in Figure 10. As more CH_{4} and N_{2} are injected, higher upper onset pressures and bubble pressures are observed. Nonetheless, for the CO_{2} injection scenario at 355 K, its behavior was different. Moreover, the quantities of increased bubble point and upper onset pressures upon N_{2} injection are more than the cases of CH_{4} injection. This can be attributed to the density and polarizability of the injected gases.
Fig. 9 The amount of asphaltene precipitation upon injection of various mole fractions of CH_{4} into oils “A” and “B” at T = 355 K. 
Fig. 10 The amount of asphaltene precipitation upon the injection of various mole fractions of N_{2} into oils “A” and “B” at T = 355 K. 
Adding N_{2} to the oil lowers the internal energy of the whole system based on Hildebrand solubility parameter and so decreases the asphaltene solubility parameter. This would, in turn, lead to more asphaltene precipitation. The knowledge of bubble point and asphaltene onset pressures is important to prevent two and three phase flows near the wellbore when the asphaltene would drop out of the liquid phase.
4.2 Effect of temperature on precipitation of asphaltene due to the injection of various gases
The temperature change near the wellbore would affect asphaltene precipitation, particularly, during the gas lifting process. Temperature change would have two effects on crude oil. The elevated temperature would result in lower oil density and higher oil entropy. These two effects counteract each other in terms of promoting asphaltene precipitation. Lower oil density causes more asphaltene precipitation, while higher oil entropy causes less asphaltene precipitation. Temperature effect on destabilization of asphaltene during CO_{2} injection is a matter of debate and needs a precise evaluation of the oil. This was explained earlier in Figures 5–8. As shown in Figure 11, it is obvious that, for N_{2} and CH_{4} injection, higher temperature causes a lower amount of asphaltene precipitation. This is because the effect of oil entropy for the temperature range of 355 K–395 K is more pronounced than density, but for various types of injected gas, the effect of temperature on asphaltene precipitation is different. The effect of temperature for N_{2} injection is more noticeable than for CH_{4} and CO_{2}.
Fig. 11 The amount of asphaltene precipitation upon injection of 10 mole % of CH_{4} and N_{2} into oils “A” and “B” at different temperatures. 
4.3 Effect of injected gas type on precipitation of asphaltene at a constant temperature
To discern the impact of the type of injecting gas on asphaltene precipitation, the calculations were performed using 10 mole % of different gases at two temperatures. The results are presented in Figure 12. As shown in these figures, CO_{2} lowers the maximum precipitation of asphaltene in oil “A” at 355 K by 10.2% but the effect is very little at 395 K. However, CH_{4} and N_{2} intensify the asphaltene precipitation in this type of oil by elevating the maximum dropout of asphaltene. CH_{4} and N_{2} raise the maximum point of the drop out curve by 6.1% and 12.3% at 355 K and by 36.7% and 57.1% at 395 K, respectively. The effects are totally different in oil “B”. CO_{2} decreases the maximum point at 355 K and 395 K by 17.1% and 11.3%, respectively. CH_{4} and N_{2} increase the maximum point by 4.8% and 4.9% at 355 K, respectively. N_{2} does not change the maximum value but displaces it toward higher pressures and CH_{4} increases it about 5.8% at 395 K.
Fig. 12 Precipitation of asphaltene upon injection of 10 mole % of different gases at 355 K and 395 K into oils “A” and “B”. 
5 Conclusion
The knowledge of circumstances under which asphaltene starts to precipitate is important to prevent numerous problems associated with this phenomenon. The onset and bubble point pressures for the crude oil under study were modeled using PCSAFT EoS. The results of PCSAFT EoS correlate accurately with the measured onset pressure and bubble pressures taken from the literature. Furthermore, the fractions of precipitated asphaltene from the oil phase due to the injection of different types of gas at various temperatures were modeled. The following conclusions can be drawn from the results presented in this study:

No general rule for the effect of the injection of different types of gases into oil was seen in this work. Thus, a detailed evaluation of the oil characteristics is crucial prior to gas injection.

CO_{2} injection shows a crossover temperature under which CO_{2} increases crude oil solubility parameters and over which CO_{2} reduces the solubility of asphaltene. For temperatures below the crossover temperature, by increasing the mole percent of CO_{2}, asphaltene precipitation decreases.

CO_{2} may reduce the size of the dropout curve or move it toward the higher pressures.

Injection of CO_{2} into oil “B” has a different influence on the variation of upper onset pressure at different temperatures. It decreased and then increased the upper onset pressure at 395 K. However, a monotonic decrease was seen for the upper onset pressure by CO_{2} injection at 355 K.

CH_{4} and N_{2} expand the dropout curve by raising the upper onset point. CH_{4} increases the maximum point of the dropout curve for both oils at two different temperatures. N_{2} raises the maximum point of oil “A” by approximately 57% at 395 K, while it had no effect on the maximum point of oil “B”.

CH_{4} has widened the dropout curve by increasing the upper onset pressure and raised up the maximum point of the curve in all cases.

The higher the temperature, the lower asphaltene precipitation would be expected.

The effect of nitrogen injection on asphaltene precipitation is higher than other gases examined.
Acknowledgments
The authors are grateful to Dr. M. J. Amani for his technical help over the course of this study.
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All Tables
All Figures
Fig. 1 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressures for oil “A” prior to gas injection. 

In the text 
Fig. 2 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressures for oil “B” prior to gas injection. 

In the text 
Fig. 3 Comparison of the PCSAFT model and experimental data [44] for predicting bubble point and asphaltene onset pressure upon the injection of N_{2} at 420 K for oil “A”. 

In the text 
Fig. 4 Sensitivity analysis for asphaltene parameters on APE of crude oil “A”. (a): m, (b): σ, and (c): ε/k. 

In the text 
Fig. 5 The amount of asphaltene precipitation for oil “A” upon injection of various mole fractions of CO_{2} at (a) T = 355 K and (b) T = 395 K. 

In the text 
Fig. 6 Effect of CO_{2} on the APE for crude oil “A”. 

In the text 
Fig. 7 The amount of asphaltene precipitation for oil “B” upon injection of various mole fractions of CO_{2} at (a) T = 355 K and (b) T = 395 K. 

In the text 
Fig. 8 Effect of CO_{2} on the upper onset curve of oil “B” at 395 K and 355 K. 

In the text 
Fig. 9 The amount of asphaltene precipitation upon injection of various mole fractions of CH_{4} into oils “A” and “B” at T = 355 K. 

In the text 
Fig. 10 The amount of asphaltene precipitation upon the injection of various mole fractions of N_{2} into oils “A” and “B” at T = 355 K. 

In the text 
Fig. 11 The amount of asphaltene precipitation upon injection of 10 mole % of CH_{4} and N_{2} into oils “A” and “B” at different temperatures. 

In the text 
Fig. 12 Precipitation of asphaltene upon injection of 10 mole % of different gases at 355 K and 395 K into oils “A” and “B”. 

In the text 