Asphaltene precipitation in live crude oil during natural depletion: Experimental investigation and modeling

Asphaltene precipitation in live crude oil during natural depletion: Experimental investigation and modeling

Fluid Phase Equilibria 336 (2012) 63–70 Contents lists available at SciVerse ScienceDirect Fluid Phase Equilibria journal homepage: www.elsevier.com...

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Fluid Phase Equilibria 336 (2012) 63–70

Contents lists available at SciVerse ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Asphaltene precipitation in live crude oil during natural depletion: Experimental investigation and modeling Shahin Kord 1 , Shahab Ayatollahi ∗ Enhanced Oil Recovery (EOR) Research Center, School of Chemical and Petroleum Engineering, Shiraz University, P.O. Box 7134851154, Shiraz, Iran

a r t i c l e

i n f o

Article history: Received 18 January 2012 Received in revised form 18 April 2012 Accepted 10 May 2012 Available online 23 August 2012 Keywords: Asphaltene precipitation Deposition Scaling equation Solubility Solid model

a b s t r a c t The complicated nature of asphaltene molecules besides the unknown mechanism of phase separation of asphaltene-containing systems as well as lack of a suitable characterization parameter has questioned the generality of the available thermodynamic models. The scaling equation developed by Rassamdana et al. [10,13] and its generalized form presented by Hu et al. [20] proved existence of a general relationship to model the asphaltene precipitation envelope and the onset. However, it works only for dead oil systems; here it has been tried to extend this technique for live oil fluids at reservoir condition. In this study, three types of experiments were conducted on five live reservoir fluid samples. The samples were collected from a giant Iranian oil field to measure the amount of precipitated asphaltene for a wide range of temperature and pressure. The results of this study developed a new live oil scaling equation and successfully applied to predict a new real data-set. The predictions of the model were compared with the two widely used thermodynamic methods of single component solid and modified Flory–Huggins (FH) models. The results show that the phase stability and the regions where asphaltene precipitates from the live crude oil were predicted using this new scaling equation with an acceptable accuracy. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Almost in all stages of oil production and transportation, the petroleum industry suffers from separation of a heavy organic matter called “asphaltene.” Asphaltenes refer to the fraction of crude oil insoluble in excess normal alkanes such as n-pentane or nheptane, but soluble in benzene or toluene at room temperature; compared to resins which are the fraction of crude oil insoluble in liquid propane but soluble in n-pentane at ambient conditions [1–3]. Considering a sample of oil, it always has been desired to know “when,” “where,” “how much,” and “under what conditions” asphaltene precipitates as a solid phase out of the solution [4,5]. Crude oil is commonly divided into four chemically distinct fractions: saturates, aromatics, asphaltenes, and resins [6]. More or less, all crude oils contain the asphaltene fraction, so the question is “why do some of them with small fraction, face asphaltene separation during production while others do not?”

∗ Corresponding author. Present address: Sharif University of Technology, Iran. Tel.: +98 711 6474602; fax: +98 711 6473575. E-mail addresses: [email protected] (S. Kord), [email protected], [email protected] (S. Ayatollahi). 1 Tel.: +98 711 6474602. 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.05.028

One of the fundamental difficulties encountered in describing the phase behavior of asphaltene-containing systems is lack of a suitable characterization parameter [7]. Besides, the state of the asphaltene particles in the petroleum is doubtful. Depending on the asphaltene polarity and presence of other compounds (paraffins, aromatics, resins, etc.) in the crude oil, asphaltene particles are believed to be dissolved partly in the crude and partly in stericcolloidal and/or micellar forms [8,9]. Being certain about each of these states depends on the reversibility of the process of asphaltene separation from the solution. In the case of “solution theory,” molecular thermodynamics can be used, and in this category the most prevalent thermodynamic approach to describing asphaltene solubility has been the application of the solubility parameter or the concept of cohesion energy density [7]. The more the difference between the solubility parameter of the solvent and the asphaltene is, the more asphaltene precipitation forms. Therefore, this difference may be defined as the precipitation potential of a system. The precipitation potential of an aromatic solvent is close to zero and therefore, it can fully dissolve more asphaltene species [10]. A cycloparaffin with the same number of carbon atoms as a normal alkane can dissolve more asphaltene species, since the difference between the solubility parameter of the asphaltene and that of a cycloparaffin is less than that between the asphaltene and the normal alkane [10].

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Table 1 Composition and condition of crude oil samples (#1–5). Component

Crude oil samples 1

H2 S CO2 N2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7 C8 C9 C10 C11 C12 + Total Sample depth (mss) Reservoir temperature (◦ C) Bubble point pressure (MPa) API gravity stock tank oil Live oil molecular weight C12+ MW SG

2

3

4

(Test crude #5)

1.39 5.18 0.88 22.57 6.94 5.91 0.98 2.97 0.93 1.03 3.07 4.06 4.14 3.69 3.45 2.11 30.7

0.16 1.55 0.45 22.9 7.64 5.35 1.16 2.74 0.93 1.12 4.27 4.29 3.6 3.31 2.95 2.72 34.86

1.72 3.68 0.19 24.27 7.42 5.39 0.93 2.71 0.9 1.04 3.21 4.62 3.62 3.3 2.18 2.52 32.3

0.43 2.45 0.22 25.82 7.92 5.62 1 2.85 1 1.17 1.31 6.6 4.59 4.26 3.32 2.92 28.52

2.04 4.36 0.22 22.21 6.84 5.11 0.84 2.48 0.81 0.95 0.92 6.36 4.36 2.62 3.16 2.33 34.39

100 4139.1 123.89 12.72 24.46 138

100 3339.34 104.44 11.09 20.75 165

100 3754.24 123.89 13.10 19.85 158

100 3266.14 104.44 11.84 22.71 160

100 3706.85 121.11 13.13 20.93 143

326 0.9355

370 0.9599

On the other hand, some theories support the irreversibility of asphaltene precipitation process [11] as it demonstrates that it is impossible to completely re-dissolve the asphaltene precipitated during titration. Besides, some independent tests [10,12] support the idea that the asphaltene precipitation process is at least “partially” reversible. Besides the reversible and irreversible models, other approaches have been employed to study the asphaltene precipitation from petroleum fluids such as the scaling equations [12–17]. Rassamdana et al. [18] presented a scaling equation based on ideas of Park and Mansoori [19] who found asphaltene precipitation to some extent similar to aggregation/gelation phenomena. This simple model was capable of successfully predicting asphaltene titration experiments at standard conditions. Hu et al. [20,21] checked the scaling equation against the precipitation data available in the literature. They also examined the universality of exponents Z and Z , the main coefficients used in the scaling equation. It was concluded that Z = −2 is a universal constant regardless of oil composition and the type of the solvent, and the optimum value of Z varies between 0.1 and 0.5. In Iran, some major oil fields such as Ahwaz, Mansuri, Ab-Taymur, and Kupal have the asphaltene problem. Since treating the deposited asphaltene is too expensive and in some cases impossible (i.e., formation damage), in the current situation, mitigation and prevention of asphaltene precipitation and deposition is the main strategy proposed by the industry experts. Therefore, having an accurate model for predicting the amount of asphaltene precipitation during pressure, temperature, or composition changes seems essential. As large asphaltene molecules resemble the polymers in molecular structure and distribution as well as in polarity distribution, two well-known thermodynamic models of single component solid and modified Flory–Huggins (FH) are incorporated. The results show that the phase stability and also the regions where asphaltene precipitates from petroleum fluids cannot be predicted accurately by these models. The main objective of this work is to develop a scaling equation which, on one hand does not require the complicated and local calculations of the thermodynamic models, and on the other hand, leads to the expected results by a simple but highly precise

378 0.9652

420 0.9437

310 0.9637

approach for a wide range of pressure and temperature. To achieve this, in the first step, as described in Section 2, three types of tests were performed on some Iranian crude oil samples for wide pressure and temperature ranges; similar works can rarely be found in the literature for live oils. The validity of the model proposed here for predicting the amount of asphaltene precipitating from a crude oil was checked against the model developed by Hirschberg [22]. Besides, in Section 3.2, this model along with its modified form is compared with the single-component solid model. In Section 4.1, through our experimental study, a powerful scaling equation is obtained which can accurately predict asphaltene precipitation for wide ranges of pressure and temperature. Finally, in a comparative study, the results of the proposed model are checked against the well-known thermodynamic models. 2. Experimental work In order to mimic the reservoir conditions and check the possibility of fluid grading in the reservoir, five different regions were selected and the reservoir fluid samples were taken by downhole fluid sampling technique. All the experiments were performed on the live oil taken under the reservoir temperature and pressure. Three types of experiments (complete PVT experiments, SARA analysis, and asphaltene precipitation) were performed on the five different crude oil samples to find their composition, molecular weight, SARA fraction, PVT data, and the potential of asphaltene precipitation at different pressures (Table 1). 2.1. SARA analysis and asphaltene content determination SARA test is conventionally used for crude oil characterization. On this basis, the oil is characterized for saturates (S), aromatics (A), resins (R), and asphaltene (A), as described by the Institute of Petroleum [23]. The amount of asphaltene which precipitates from a crude oil under atmospheric conditions is usually considered as the crude asphaltene content. This value strongly depends on the type of the solvent used for precipitation. To have a reference

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Table 2 SARA analysis (wt%). Crude oil number Test Saturated Aromatic Resin Asphaltene Total

1 42.68 40.69 7.63 9 100

2 43.67 52.09 0.49 3.75 100

3 36.77 46.72 6.12 10.39 100

4 38.99 50.59 6.17 4.25 100

5 46.12 37.24 7.57 9.07 100

Fig. 1. Schematic of experimental setup utilized for precipitation tests.

point for future comparisons, n-heptane is used as precipitant for all crude samples. In our study, standard methods of IP-143 and ASTM D-3279 were used to measure the asphaltene content of the crude samples. Asphaltene content is in the range of 3.75–10.39 wt% for a single reservoir fluid under study; this may be a sign of fluid grading in the reservoir. The results of SARA analysis are presented in Table 2.

a result, the filtration process was very close to an isobaric process. Filtered oil was flashed in a separator and the asphaltene content of the residual oil was measured using the standard IP procedure. The difference between the asphaltene content of the original and filtered oils at each pressure determines the weight percent of the precipitated asphaltene (Fig. 2). 3. Theoretical consideration

2.2. Experimental setup for asphaltene precipitation tests under HPHT The schematic diagram of the experimental high pressure-high temperature (HPHT) test setup is shown in Fig. 1. Mercury pump was used to inject the fluid into the cell and to control the pressure. The main part of the system was a mercury-free, visual JEFRI equilibrium cell. An air bath was incorporated to control the cell temperature. The designed cell can properly work in the temperature range of −30 to 200 ◦ C and under the maximum pressure of 82.74 MPa. Moreover, the cell was equipped with an electrical shaker for mixture agitation holding 500 cm3 of liquid. A high pressure high temperature separator is used to measure the properties of the gas collected after reaching the equilibrium under reservoir conditions.

3.1. Flory–Huggins (FH) theory As large asphaltene molecules are similar to the polymers in molecular structure and polarity distribution, in this work, the well-known theory of polymers — Flory–Huggins (FH) theory is incorporated and the results are compared with the proposed scaling equation. We incorporated a mono-disperse model which brings the complex nature of asphaltene-containing systems through one pseudo-component with average properties (molar volume and solubility parameter) representing the whole system [3]. The most doubtful assumption of this model is reversibility which allows the use of polymeric solution models for performing phase equilibrium calculations.

2.3. Procedure The crude samples were continuously heated and agitated for three days to ensure their homogeneity. A known volume of oil was then injected into the cell under single-phase conditions at reservoir pressure. The equilibrium cell was thoroughly maintained at the reservoir temperature by setting the air bath temperature. The sample was allowed to reach equilibrium overnight. In order to accelerate the equilibrium process, an electrical stirrer was used to agitate the sample. A high pressure high temperature filtration test was conducted to quantify the amount of asphaltene that may precipitate at a given pressure. At each point, a high pressure filtration process was conducted with two steel sheets, one of thickness of 5 ␮m and the other of thickness of 0.5 ␮m. During the filtration process, it was important that the sample remain single phase as it passes through the filter manifold, where high pressure helium was used to maintain a back-pressure on the downstream of the filter. As

Fig. 2. Asphaltene precipitation envelope during natural depletion for crude #1–5.

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Technically speaking, two equilibrium states are considered in the system; vapor/liquid equilibrium (VLE) of the total reservoir fluid and liquid/liquid equilibrium (LLE) between the liquid oil and the pseudo liquid asphaltene phases [3]. The VLE of the reservoir fluid is modeled first to obtain the composition and fluid properties of the liquid phase. In the LLE segment of the model, the oil is considered to consist of two liquid phases; an oil-rich phase that acts as the solvent, and an asphaltene-rich phase that behaves as a polymer [8]. The original form of the model first proposed by Hirschberg et al. [22] was incorporated by many investigators [19,22,25–27,29] and soon after, many modifications and extensions were deduced from it. Mohammadi and Richon [24] considered a distribution of asphaltene and nonasphaltene components in the oil and precipitated phases and he showed that Hirschberg et al. [22] model is a specific case of their model. Based on the modified FH model proposed by Mohammadi et al. [24], the volume fraction of asphaltene in equilibrium with the petroleum mixture can be calculated from the solution of the following two equations. These equations were derived by combining the liquid–liquid equilibrium relationship and the activity coefficients of asphaltene and maltene (based on the Flory–Huggins polymer theory).



ln

oil m

Asph

m

 ln

aoil

Asph a

 

+ 1−

+ 1−



va Asph Asph 2 oil oil 2 (m − m ) + ((m ) − (m ) ) = 0 vm (2)

vm [(ım − ıa )2 + 2lam ıa ım ] RT

Value

Solubility parameter (MPa)0.5 Molar volume (m3 /kg mol) Molecular weight (g/mol) L1,2

18.7 0.7 600 0.01

Table 4 Scaling Model Parameters. Condition

Matching parameters

P > Pb P < Pb

(3)

where ı stands for the solubility parameter and subscripts m and a indicate maltene and asphaltene respectively; lam represents the binary interaction parameter. An appropriate value for the binary interaction parameter (lam = 0.01) has been used for FH-based models [22]. Perhaps, this formulation is the most general form of FH theory which is presented by more details in Flory [30] work. Two parameters are essential in the performance of this model; the molar volume and the solubility parameter of the asphaltene components [7]. This model has been applied to calculate the pressure and temperature dependencies of asphaltene solubility. 3.2. Solid model Single-component solid model is the simplest model for the precipitated asphaltene. In this model, which was originally tried by Gupta [31] and Thomas et al. [32], the precipitated asphaltene is represented as a pure solid while the oil and gas phases are modeled with a cubic equation of state [33]. In the most recent form of this model presented by Nghiem and Coombe [34], the heaviest component splits into two components; a non-precipitating component and a precipitating component. They considered the two components identical in critical properties and acentric factors but their interaction coefficients with the light components are different [34]. It was assumed that the precipitating component has larger interaction coefficients with the light components. Larger interaction coefficients correspond to greater “incompatibility” between components and favor the formation of the asphalt phase [34]. For

Z

Z

A

B

2 0.85

0.2 0.35

−0.096 0.02357

−0.0629 −0.004

a given temperature T and pressure P and assuming that the solid is incompressible, the fugacity of the solid phase is: ln fs = ln fs∗ +



where m , a , vm , and va are the volume fraction of maltene, volume fraction of asphaltene, molar volume of maltene, and molar volume of asphaltene respectively;  stands for the interaction parameter between asphaltene and maltene and is assumed to be independent of concentration. It is defined as: =

Parameter

2 vm Asph Asph 2 (aoil − a ) + ((aoil ) − (a ) ) = 0 va

(1)

 

Table 3 Matching parameters used by models.

+

Cps Vs (P1 − P0 ) + RT0 R[1 − T0 /T1 + ln(T0 /T1 )] Hf

(5)

R(1/T1 − 1/T0 )

where fs is the fugacity at pressure P1 and temperature T1 , fs∗ is the fugacity at pressure P0 and temperature T0 , Vs is the molar volume of the solid phase, R is the universal gas constant, Cps is the heat capacity of the solid phase, and Hf is the enthalpy of the solid phase. A robust three-phase flash calculation was incorporated to calculate the amount of each component in each phase [33]. 3.3. Prediction based on the thermodynamic models The objective of this section is to show the capability of the previously discussed thermodynamic models for estimating asphaltene precipitation in five crude oil samples. Details of calculation can be found in the literature [24]. Generally there are four parameters to be matched with experimental data — the solubility parameter, ı, the asphaltene molar volume, Va , the binary interaction parameter, lam , and the asphaltene molecular weight, MWa . To check the prediction ability of the models, one set of matching parameters –– as presented in Table 3 –– was used for comparison. To find these values, all three models were tuned by experimental data of crude oil number 2 and the best match was achieved by choosing the aforementioned model parameters as those of Table 3. If these model parameters are to be representative of crude oil samples, they should be capable of estimating the precipitation for other samples too. The reservoir fluid properties and its compositions are presented in Tables 4 and 5, respectively. Figs. 3–7 show the comparison among the behavior of traditional FH model [22], modified FH model [24], single component solid model [32], and measured experimental data (Fig. 2). From these figures, it is clear that the model cannot reliably predict the asphaltene content of oil

Table 5 Relative error (%) of different models for prediction of test crude #5 precipitation data. Pressure (MPa)

FH model

MFH model

Solid model

Scaling model

31.03 24.13 17.24 10.34 6.89 5.52

43.39 16.12 8.35 22.79 12.57 8.39

58.39 40.86 24.14 14.97 25.93 29.89

3.02 2.61 2.53 2.19 1.76 2.19

0.08 0.45 0.67 0.28 0.10 0.82

RE (%) =

W

Exp −WCal

WExp



× 100.

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Fig. 3. Soluble asphaltene envelope estimated by different models vs. experimental data for crude oil sample number 1, under reservoir temperature of 123.89 ◦ C.

Fig. 4. Soluble asphaltene envelope estimated by different models vs. experimental data for crude oil sample number 2, under reservoir temperature of 104.44 ◦ C.

for crude oil sample number 4. Our investigation shows that this shortcoming can be attributed to weaknesses associated with the proposed critical properties of C12+ . It should be noted that both models can perfectly tune the experimental data for each specific fluid sample but using the matching parameters for the predictions of the other samples are also verified. Therefore, more reliable results would be expected by changing the critical properties of this

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Fig. 6. Soluble asphaltene envelope estimated by different models vs. experimental data for crude oil sample number 4, under reservoir temperature of 104.44 ◦ C.

Fig. 7. Soluble asphaltene envelope estimated by different models vs. experimental data for crude oil sample number 5, under reservoir temperature of 121 ◦ C.

component. Results of this comparative study may be summarized as: 1. In comparison with FH-based models, single component solid model estimates the amount of precipitation more accurately and needs only one matching parameter (i.e., asphaltene molar volume).

Fig. 5. Soluble asphaltene envelope estimated by different models vs. experimental data for crude oil sample number 3, under reservoir temperature of 123.89 ◦ C.

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2. FH-based models are more powerful in matching experimental data but are weak in the prediction parts. This would indicate that increasing the number of matching parameters does not always lead to the better results. 3. For estimating precipitation of a specific sample on different pressures, FH-based models work better. Figs. 3–7 clearly show the deviation of the solid model prediction for the pressures less than saturation pressure. 4. Proposed scaling equation It is believed that the formation of large asphaltene molecules is to some extent similar to aggregation and gelation phenomena [18] which possess universal properties, independent of many microscopic properties of their structure. This idea leads to the development of some scaling equations which are very powerful and surprisingly general and predictive. Rassamdana et al. [10,13] argue that conventional thermodynamic models are not able to predict the experiment results accurately. Therefore, they presented a scaling equation based on the idea of Park and Mansoori [19] who found asphaltene precipitation to some extent similar to aggregation/gelation phenomena. This simple model was able to predict asphaltene titration experiments successfully at standard conditions. A three-parameter scaling equation is expressed in terms of X and Y through a third-order polynomial function [19]: Y = A0 + A1 X + A2 X 2 + A3 X 3 where R X= Z M

(X ≥ XC ) (6)

W Y = Z R

where (Ai , i = 1–4) are the scaling coefficients, R is the ratio of the volume of the injected solvent to the weight of the crude oil, M is the molecular weight of the solvent, and W is the weight percent of precipitated asphaltene. It was mentioned that for Z = −2 and Z = 0.25, all data points would collapse onto a single thirdorder polynomial curve. By a simple modification on X and Y, the above equation is extended for the case of temperature variation [19]. Hu et al. [20] checked the predictive capability of the scaling equation by comparison with the literature precipitation data. They also examined the universality of exponents Z and Z . It was concluded that Z = −2 is a universal constant regardless of oil composition and the type of solvent and that the optimum value of Z varies between 0.1 and 0.5. In the case of live oil, the mechanism of asphaltene deposition would be completely different. We believe that there is a turning point which can be seen in case temperature or solvent are involved in asphaltene precipitation. Passing this point, the mechanism of precipitation and state of asphaltene in the mixture change from soluble state to colloidal state. That is why the previously proposed scaling models predict only one wing of the precipitation envelope. To take into account the effect of pressure, five important parameters that influence the asphaltene precipitation were combined and two new scaling parameters were defined as: X=

(P − Pb /Pb ) × GORZ ,  TZ

Y=

W × Wc

 P − P −Z  Pb

b

(7)

where P is the pressure, Pb is the bubble point pressure, GOR is the gas-oil ratio, T is the temperature, W is the amount of asphaltene precipitation, and Wc is the asphaltene content of crude oil. Z, Z , and Z are the constants which need to be correlated by the experimental data. Four sets of experimental data discussed previously in part 2 (crude #1–4) were used to find the coefficients of the developed model. In this work, all experiments were performed at constant temperature, so Z does not need to be matched

Fig. 8. Collapse of the live oil asphaltene precipitation data onto a single scaling curve for pressures above saturation pressure.

anymore. The experimental data were rescaled based on the newly defined parameters X and Y and plotted vs. each other. Choosing the scaling model parameters as presented in Table 4, all the experimental data shown in Fig. 2 can be collapsed onto a single curve. Figs. 8 and 9 clearly demonstrate a scaling relationship for which no physical explanation is available up to the present. It is found that the asphaltene precipitation exhibits exponential growth above the bubble point and logarithmic behavior under saturation pressure. The scaling equation can be accurately presented by: P < Pb ,

Y = A Ln(X) + B

P > Pb ,

Y = A Exp(B × X)

(8)

Since the data can be collapsed onto a single curve, the universal scaling curve or its approximation by Eq. (8) can be used to predict asphaltene precipitation of other crudes for a wide range of pressure including above-bubble-point pressures. 4.1. Predictions based on the scaling equation The proposed model was used to predict the behavior of asphaltene precipitation. Crude number 5 was selected as a reference case to check the capability of different models in comparison with the scaling equation. It is worth to mention that the scaling equation developed based on the crude numbers 1–4 and the test results of crude number 5 were not included in the procedure leading to the scaling equation. The results presented in Fig. 11 reveal the agreement found between the experimental data and the model results. The average deviation error of the predicted values from experimental data is calculated and shown in Table 5. From Table 5 it can be seen that the predicted amount of precipitation for various pressures at 121 ◦ C agrees well with the experimental data measured in this work. The results of this study show that the phase stability as well as the regions where asphaltene precipitates from petroleum fluids are well predicted (Fig. 10). 4.2. Comparison with the thermodynamic models Fig. 11 compares the results of single component solid model, scaling model developed in this work, and the experimental data (Table 1). As can be seen, the solid model is not capable to reproduce the observed behavior of the real process for pressures below saturation pressure. For undersaturated mixtures, results are reasonably good. However, the newly developed scaling model produces encouraging results. This also shows that the use of the gelatin/aggregation concept may be in better agreement with real nature of asphaltene state in the mixture. The average deviation

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Fig. 9. Collapse of the live oil asphaltene precipitation data onto a single scaling curve for pressures below saturation pressure.

Fig. 10. Prediction of asphaltene precipitation envelope by scaling equation in comparison with test crude number five experimental data.

Fig. 11. Prediction of soluble asphaltene envelope by scaling equation in comparison with solid model and experimental data of test crude number five.

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error of the predictions compared to the experimental data is calculated and shown in Table 5. The difference between scaling equation predictions and the experimental data is not more than 1%, comparable to the accuracy of the tests, whereas the predictions of the thermodynamic model are generally not in good agreement with the experimental results. 5. Conclusions In this work, it was shown that the traditional asphaltene models may not be helpful for prediction of the amount of asphaltene precipitation at high pressures and temperatures (reservoir conditions). FH polymer theory and also single component solid model assume either the precipitated phase consists of asphaltene only or consists of asphaltene and non-asphaltene components and the oil phase is free of asphaltene. In comparison with FH-based models, single component solid model estimates the amount of precipitation more accurately and requires less matching parameters. It was shown that increasing the number of matching parameters does not always lead to better results because FH based models are more powerful in matching experimental data but are weak in their predictions while these models possess more matching parameters. In summary, the following conclusions can be drawn: 1. For estimating precipitation of a specific sample on different pressures, FH-based models work better because once matching parameters for one crude sample were obtained, its asphaltene precipitation would be predicted accurately. 2. Solid model predictions for pressures less than saturation pressure are not reliable. Considering the aforementioned weaknesses of the thermodynamic model, based on experimental data, a two-parameter scaling equation was then introduced which predicts the amount and onset of asphaltene precipitation for live crude samples at reservoir conditions. It was found that model parameters Z and Z are 0.2 are 2, respectively. The proposed model was used for prediction of precipitation behavior of a new crude sample with relative error of no more than 1%, comparable to the accuracy of the experimental data, whereas the predictions of the thermodynamic model are generally not in good agreement with the data. Future investigation should be performed to examine the universality of exponents Z and Z . List of symbols

Ai L1,2 MW R V W X Y Z, Z , Z A, B RE

coefficients of the scaling equation, Eq. (6) binary interaction parameter in Flory–Huggins [30] theory molar mass (g/mol) dilution ratio (ml/g or g/g) molar volume (m3 kg mol) weight (g) function defined by Eqs. (6) or (7) function defined by Eqs. (6) or (7) constants constant relative error

Greek letters ı solubility parameter (MPa0.5 )

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