High-Pressure Modeling of Asphaltene Precipitation during Oil

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High-pressure modeling of asphaltene precipitation during oil depletion based on the solid model Victor Bouzas Regueira, Renan Oliveira Soares, Anderson Souza, Gloria Meyberg Nunes Costa, and Sílvio Alexandre Beisl Vieira de Melo Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b00996 • Publication Date (Web): 12 Jul 2017 Downloaded from http://pubs.acs.org on July 13, 2017

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High-pressure modeling of asphaltene precipitation during oil depletion based on the solid model Victor B. Regueira, Renan O. Soares, Anderson D. Souza, Gloria M.N. Costa, Silvio A.B. Vieira de Melo * Programa de Engenharia Industrial, Escola Politécnica, Universidade Federal da Bahia, Rua Aristides Novis, 2, 6º andar, Federação, Salvador, Bahia, CEP 40210-630, Brasil; tel. +55 71 32389802, fax: + 55 71 32839800, e-mail: [email protected]. * To whom correspondence should be addressed.

ABSTRACT: Asphaltene precipitation is a complex and serious problem in all sectors of the oil industry because it has a severe and detrimental impact on oil production. Thus, it is crucial to investigate under which conditions asphaltenes precipitate in order to prevent or mitigate the effects. Several approaches have been reported in the literature regarding the modeling of asphaltene precipitation during oil production. The simplest one is the single-component solid model in which the precipitated asphaltene is considered a pure solid and the oil and gas phases are described by a cubic equation of state (EOS). These are the basic assumptions of the Nghiem and Coombe’s model. In this paper, based on this model, we make numerous improvements and simplifications such as reducing the number of parameters to be estimated and considering that the number of asphaltene fractions can vary according to the oil characteristics. The characterization method is performed using the exponential distribution and only the binary interaction parameter is fitted to the experimental oil saturation pressure data. The reference pressure is calculated according to de Boer’s method instead of only extrapolating precipitation

*

Corresponding author: [email protected] Tel. +55-71-32839802 Fax +55-71-32839800

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depletion experimental data. Furthermore, the solid molar volume is predicted using two correlations from literature, expressed as a function of the molecular weight of the asphaltene. The developed model is capable of calculating the amount of precipitated asphaltene as a function of pressure. Our results indicate that the proposed approach is quite accurate even having a smaller number of parameters to be estimated compared to the original model.

Keywords: asphaltene precipitation, solid model, equation of state, characterization, high pressure, oil depletion. 1. INTRODUCTION Asphaltenes are a class of molecules composed of condensed aromatic rings with alkane chains. Their structure and molecular weight remain a challenge and a subject of intense investigation. These components are the heaviest and most polarizable in the oil1, almost insoluble in low molecular weight alkanes, such as n-pentane and n-heptane, and soluble in benzene and toluene at room temperature1,2. Problems caused by asphaltene precipitation are very common resulting in major losses for the oil industry3. Therefore, a thorough understanding of the thermodynamic behavior of asphaltenes at operational conditions is critical for the oil extraction and production processes. However, a complete experimental thermodynamic study is not feasible due to the vast amount of data points required at reservoir temperature and pressure and the high cost experimental data determination. Hence, thermodynamic modeling is as an excellent alternative. Many models have been developed to predict the amount of asphaltene precipitated with a limited number of experimental data for a wide range of conditions. Forte and Taylor4 did an extensive review


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about models to describe asphaltene precipitation and divided them into two major groups: lattice fluid theory and equation of state. The lattice fluid theory is based on polymeric models to describe the asphaltene precipitation, usually combining Flory5 and Huggins6 models and the Scatchard-Hildebrand7 regular solution theory. The application of this theory is usually based on a pseudo-binary approximation, in which the mixture is comprised of two pseudo-components: the solvent (oil) and the polymer (asphaltene). The system is characterized by the solubility parameter and molar volume of these components. One of the first applications of the Flory-Huggins-Hildebrand model to calculate the amount of asphaltene precipitated from the liquid state was carried out by Hirschberg et al.8. Wang and Buckley9 used a correlation with the refractive index of non-polar species to estimate the solubility parameter of oil, reducing the uncertainty of this model. Akbarzadeh et al.10 considered the liquid-liquid equilibrium and the regular solution theory to model asphaltene precipitation. In addition, these authors used mole fraction, molar volume and solubility parameter for each component, calculated the equilibrium using the SARA (saturates, aromatics, resins and asphaltene) analysis and used the gamma molar mass distribution to characterize the asphaltene fraction. Tharanivasan et al.11 developed, tested and applied a compositional characterization method to pressure induced asphaltene precipitation, based on gas chromatography analysis and the SARA composition, using an adapted regular solution approach. Silva et al.12 analysed several variables affecting asphaltene precipitation by normal pressure depletion using the Hirschberg8 model and experimental data from literature. They found that this model could be improved with modifications in the oil characterization and in the oil and the asphaltene solubility parameter calculation. A disadvantage of using models based on


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the regular solution theory is the fact that the solubility parameters of asphaltene and other oil components are not easily obtained. The second group of models used to describe asphaltene precipitation is composed of equations of state (EOS), which provide simplicity and versatility. Forte and Taylor4 classified the equations of state in cubic EOS, cubic plus association EOS and statistical associating fluid theory EOS. There are a wide number of studies that report the use of cubic equations of state to model phase behavior of asphaltenes. The Peng-Robinson cubic EOS13 was used by Kohse et al.14 assuming that the asphaltene fraction contained 12 pseudo-components and the heaviest one was further divided into a precipitating and a non-precipitating component, which was constituted mostly of asphaltenes and modeled as a pure solid phase. In a similar way, Behar et al.15 characterized the oil into components and pseudo-components, but the Peng-Robinson EOS was integrated to an industrial reservoir simulator to determine the amount of asphaltene precipitated at different operating conditions. Nghiem et al.16 considered the heaviest fraction of oil composed of non-precipitating components and asphaltenes. The precipitating part was treated as a pure solid phase, named the asphaltene solid model (ASM) and the Peng-Robinson EOS was used to describe the vapor and oil phase behavior. The asphaltene solid model was also adopted by Jamaluddin et al.17 and Tavakkoli et al.2. Panuganti et al.18 argued the prediction capacity of the asphaltene solid model based on a cubic EOS, such as Soave-Redlich-Kwong (SRK), in comparison to more sophisticated model using Statistical Associating Fluid Theory (SAFT) EOS. This approach is based on the thermodynamic perturbation theory of Wertheim et al.19 to take into account the possibility of the non-spherical nature of the molecules, likewise its association with directional interactions, which is characteristic of hydrogen bounds (not taken into account


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by the cubic EOS). The most popular version of SAFT models is known as Perturbed Chain form of the Statistical Associating Fluid Theory (PC-SAFT) equation20. Vargas et al.21 provided some insight into the effect of pressure, temperature and composition on asphaltene phase behavior using the PC-SAFT EOS to explain several field observations related to asphaltene precipitation. In addition, Panuganti et al.22 presented a detailed procedure to characterize crude oil and to plot the asphaltene phase envelope, using the PC-SAFT equation of state and Punnapala and Vargas23 presented an enhanced PC-SAFT characterization method that was applied to various reservoir fluids from three different fields in the Middle East region. However, the use of SAFT EOS with a limited amount of experimental data is burdensome due to the substantial number of parameters to be estimated. For this reason, the predictive capabilities of PC-SAFT EOS models are somewhat limited and are not studied in this work. It is important to say that the performance of the solid-liquid equilibrium model to describe asphaltene precipitation, which is also used in asphaltene deposition studies, is widely reported in literature24–35. This paper claims that based on minimum experimental data the cubic EOS is the best option to describe asphaltene precipitation. By modifying the solid model originally proposed by Nghiem and Coombe16,36, we introduced the following new features: •

There is no specified number of heavy oil components that represents the asphaltenes, unlike the Nghiem and Coombe16,36 model which considers C31+ a constant limit. In the present work, this number is flexible and depends on the oil characteristics and the pressure at which asphaltene precipitation occurs.

•

There is no residue partition into two fractions (precipitated and non-precipitated).

•

Peneloux’s correction37 is not needed to describe the liquid phase behavior, reducing the number of parameters to be estimated.


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•

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The pressure reference, defined according to the method mentioned by Nghiem and Coombe16,36, is checked with de Boer’s diagram38, ensuring that it is reasonable.

•

The estimation of only one parameter (kij) is needed to adjust the model, in comparison to 4 parameters in the Nghiem and Coombe16,36 model.

The other characteristics of our modifications to simplify the solid model are presented throughout the following sections of this work. The results show that this model performs adequately when applied to asphaltene precipitation in primary depletion reservoir conditions above the saturation point.

2. THERMODYNAMIC MODELING The solid-liquid equilibrium (SLE) could be expressed as a function of the fugacity of the heaviest components in the oil for both phases, where the precipitated asphaltene is considered as 𝑙𝑙 a pure solid phase36. This model is represented in Equations 1 and 2, where 𝑓𝑓𝑛𝑛𝑛𝑛 and 𝑓𝑓 𝑠𝑠 ∗ are the

fugacity of asphaltene in the liquid phase at pressure P and the fugacity of asphaltene in the solid phase at the reference pressure P* respectively. The parameter R is the universal gas constant, T is the temperature and Vs is the molar volume of pure asphaltene in the solid phase, assumed as independent of pressure. 𝑙𝑙𝑙𝑙𝑓𝑓𝑛𝑛𝑙𝑙𝑛𝑛 = 𝑙𝑙𝑙𝑙𝑓𝑓 𝑠𝑠

ln 𝑓𝑓𝑛𝑛𝑙𝑙𝑛𝑛 = 𝑙𝑙𝑙𝑙𝑓𝑓 𝑠𝑠 ∗ +

(1) 𝑉𝑉𝑆𝑆 (𝑃𝑃 − 𝑃𝑃 ∗ ) 𝑅𝑅𝑅𝑅

(2)

The reference pressure (P*) is the pressure above the upper asphaltene precipitation envelope,

obtained by extrapolating the depletion datapoints to the pressure at which asphaltene does not precipitate36. This behavior was further confirmed using de Boer´s graphic method38, checking if the reference pressure is located in the graphical region named “no problems”.


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Note that the fugacity is calculated without the Peneloux’s correction parameter37, unlike the original model of Nghiem and Coombe36. With this new approach, the volume shift parameter does not need to be calculated, which reduces the number of parameters to be estimated with experimental data. Nghiem and Coombe16,36 reported that the volume shift parameter is used to compensate the systematic error in the molar volume of pure asphaltene in the solid phase (𝑉𝑉𝑆𝑆 ) calculations. However, if a good correlation for the 𝑉𝑉𝑆𝑆 estimation is used, the volume shift

correction is not required, decreasing the number of parameters to be estimated in the model. Therefore, two different models were used to determine the solid molar volume Vs. The first one

is based on Derakhshan and Shariati method39, where Vs is calculated from the specific mass (𝜌𝜌𝑎𝑎𝑆𝑆 ), in kg/m³, and the molecular weight (MWa), in g/gmol, of asphaltene, given by Equations 3 and 4.

𝑉𝑉𝑠𝑠 =

𝜌𝜌𝑎𝑎𝑆𝑆� 𝑀𝑀𝑀𝑀𝑎𝑎

(3)

𝜌𝜌𝑎𝑎𝑆𝑆 = 836.93317 + 0.01446𝑀𝑀𝑀𝑀𝑖𝑖 −

15685.6 𝑀𝑀𝑀𝑀𝑎𝑎

(4)

The second model, proposed by Yarranton et al.40, provides a relationship of the solid molar volume, in cm3/mol, as a function of asphaltene molecular weight (MWa), expressed by Equation 5. 𝑉𝑉s = 1.493𝑀𝑀𝑀𝑀𝑎𝑎 0.9361

(5)

In order to calculate the fugacity, we use the Soave-Redlich-Kwong (SRK) equation of state41,

expressed by Equation 6, where T is the temperature, P is the pressure, V is the molar volume and R is the universal gas constant.


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𝑃𝑃 =

𝑅𝑅𝑅𝑅 𝑎𝑎(𝑇𝑇) − 𝑉𝑉 − 𝑏𝑏 𝑉𝑉(𝑉𝑉 + 𝑏𝑏)

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(6)

Mixture parameters a and b are calculated using classical mixing rules with 𝑧𝑧𝑖𝑖 as the molar

fraction, as given by Equations 7 and 8, where the pure parameters ai and bi are calculated from

the critical properties and the acentric factor of each components (Tc, Pc and ω). The interaction parameter 𝑘𝑘𝑖𝑖𝑖𝑖 of the heaviest pseudocomponent and the methane is adjusted through the bubble

point calculation of the oil.

The rest of the binary interaction parameters, which are not

estimated, are considered constant and extracted from Pedersen et al.3. Unlike Nghiem and Coombe's model, this paper does not use a correlation to determine the binary interaction parameter using critical volume of the components involved in this binary. 𝑁𝑁

𝑁𝑁

𝑎𝑎 = � � 𝑧𝑧𝑖𝑖 𝑧𝑧𝑗𝑗 �𝑎𝑎𝑖𝑖 𝑎𝑎𝑗𝑗 � 𝑖𝑖=1 𝑗𝑗=1

0.5

(1 − 𝑘𝑘𝑖𝑖𝑖𝑖 )

𝑁𝑁

𝑏𝑏 = � 𝑧𝑧𝑖𝑖 . 𝑏𝑏𝑖𝑖

(7)

(8)

𝑖𝑖=1

The characterization of the oil plus fraction was made using Pedersen et al.3 method. It consists of splitting the C7+ residue into single carbon number components with defined molecular weights and densities, followed by calculating its critical properties and acentric factors through correlations and finally the method lumps them again to a defined number of pseudocomponents. Pedersen et al.3 proposed a method using the linear relationship between the carbon number (Cn) and its molar fraction (zn), for components from C6 and beyond, expressed in Equation 9. 𝐶𝐶𝑛𝑛 = 𝐴𝐴 + 𝐵𝐵 𝑙𝑙𝑙𝑙(𝑧𝑧𝑛𝑛 )

(9)


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Coefficients A and B are determined by fitting the carbon number to the molar fractions. Similarly, it is possible to calculate the density of the extended fractions (ρn) and their molecular weights MWn, given by Equations 10 and 11. ρn = C + D ln(Cn )

(10)

𝑀𝑀𝑀𝑀𝑛𝑛 = 14𝐶𝐶𝑛𝑛 − 4

(11)

Besides this, the method correlates the critical temperature Tci (K) and the critical pressure Pci

(atm) of the extended fractions from their molecular weight MWi (g/gmol) and density ρi (g/cm³) value using Equations 12 and 13. 𝑇𝑇𝑐𝑐𝑐𝑐 = 𝑐𝑐1 𝜌𝜌𝑖𝑖 + 𝑐𝑐2 𝑙𝑙𝑙𝑙(𝑀𝑀𝑀𝑀𝑖𝑖 ) + 𝑐𝑐3 𝑀𝑀𝑀𝑀𝑖𝑖 + 𝑙𝑙𝑙𝑙(𝑃𝑃𝑐𝑐𝑐𝑐 ) = 𝑑𝑑1 + 𝑑𝑑2 𝜌𝜌𝑖𝑖 𝑑𝑑5 +

𝑐𝑐4 𝑀𝑀𝑀𝑀𝑖𝑖

𝑑𝑑3 𝑑𝑑4 + 𝑀𝑀𝑀𝑀𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖 2

(12)

(13)

In addition, the acentric factor was calculated by Equation 15, where the parameter m is calculated using the molecular weight and the component density of each extending fraction using Equation 14. 𝑚𝑚𝑖𝑖 = 𝑒𝑒1 + 𝑒𝑒2 𝑀𝑀𝑀𝑀𝑖𝑖 + 𝑒𝑒3 𝜌𝜌𝑖𝑖 + 𝑒𝑒4 𝑀𝑀𝑀𝑀𝑖𝑖 2 𝑚𝑚𝑖𝑖 = 0.480 + 1.574ω𝑖𝑖 − 0.176ω2𝑖𝑖

(14)

(15)

The coefficients c1 to c4, d1 to d5, and e1 to e4 were experimentally determined from the PVT equilibrium data and can be found in Pedersen et al.3. Using this characterization, the oil plus fraction can be extended to more components and the properties of the oil heaviest components can be obtained.


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3. RESULTS AND DISCUSSION The main differences between the method used in the present work and the one proposed by Ngheim and Coombe36 are listed on Table 1. Note that Ngheim and Coombe´s method requires 4 parameters to be estimated, while this method needs only 1 parameter. This was because the Peneloux correction (volume shift parameter) was not needed, most of the binary interaction parameters were taken from the literature (only one parameter was estimated) and we considered that distinct asphaltene fractions are precipitated.

Table 1. Comparison between the original Ngheim and Coombe’s proposition36 and the modifications proposed in the present work. Ngheim and Coombe36

Present work

Range of analysis

P < Psat and P > Psat

P > Psat

Phase equilibrium

Solid-liquid-vapor

Solid-liquid

Asphaltenes are partially precipitated (C31A+ and C31B+)

Distinct asphaltenes fractions are precipitated

Li et al.42

Pedersen et al.3

with Peneloux correction37

without Peneloux correction37

Peng Robinson

Soave- Redlich- Kwong

Arbitrarily defined

Derakshan and Shariati39 and Yarranton et al.40

Extrapolation of deposition depletion data

Extrapolation of deposition depletion data and checked with de Boer et al.38 plot.

4 parameters

1 parameter

Non-measured

Quantified by percentage

Comparison items

Fractions precipitated Characterization model Fugacity calculation Equation of state Vs calculation

Reference pressure Estimated parameters Errors


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In the present study, four oils were selected from the literature and their composition and properties, such as saturation pressure (Psat) are displayed in Table 2.

Table 2. Composition and properties of the selected oils. Oil O1

Oil O2

Oil O3

Oil O4

Bahrami et al.43

Moradi et al.44

Moradi et al.44

Nakhli et al.45

Component

Composition (mole %)

N2

0.39

0.06

0.21

1.08

CO2

1.74

2.45

5.14

4.64

H2S

0.00

0.59

2.70

7.28

C1

20.55

38.65

22.00

43.15

C2

7.31

6.66

7.10

7.16

C3

5.34

5.33

5.34

4.23

i-C4

1.00

1.01

0.99

1.08

n-C4

3.65

2.92

2.78

2.72

i-C5

3.10

1.24

1.12

1.46

n-C5

4.75

1.51

1.41

2.1

C6

5.48

4.67

5.55

2.91

C7+

46.69

34.92

45.66

22.19

370

492

418

331

ρ of C12+ at 288.71 K

0.9769

0.9569

0.976

0.909

Treservoir (K)

369.25

358.15

397.04

386

Psat at Treservoir (atm)

97.51

186.92

117.17

235.65

°API

20.32

24

20

33.6

MW of C12+


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Oil depletion data are shown in Table 3, indicating the reservoir temperature and pressures and the corresponding total amount of precipitated asphaltenes in mass fraction along with the saturation pressures and the reference pressure (P*) of each oil.

Table 3. Experimental weight fraction of asphaltenes as a function of pressure.

Oil O3 (397.04 K)

Oil O2 (358.15 K)

Oil O1 (369.25 K)

Oil

Oil O4 (386 K)

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Label

Pressure (atm)

P* P1 P2 P3 Psat P* P1 P2 P3 Psat P* P1 P2 P3 Psat P* P1 P2 P3 Psat -

313.01 299.33 204.19 105.5 97.51 69.38 276.34 232.58 218.97 198.56 186.92 150.79 69.07 353.84 341.66 239.25 137.18 117.17 89.48 69.07 48.65 416.48 307.83 270.23 242.03 235.65 176.24 103.39

Precipitated asphaltenes (%wt) 0.27 0.93 1.55 1.08 1.03 1.16 1.25 0.94 0.34 1.07 1.99 2.54 1.86 1.38 0.93 0.86 0.9 0.92 0.86 0.73


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For a better comprehension of the data, the pressure was sorted in descending order (P1, P2 and P3), as can be seen in Figure 1, showing that the precipitation data trend is similar to the behavior described in the literature36. In other words, as the pressure is reduced from P1 to P3 the amount of precipitated asphaltenes increases. Its maximum is reached near the oil saturation pressure (Psat). On the other hand, with the continuous pressure decrease, the amount of precipitated asphaltene starts to decrease, indicating the resolubilization thereof. It can also be seen that the amount of asphaltene precipitated as a function of pressure reduction can vary from oil to oil, indicating a possible relationship with its molar composition2. Furthermore, regarding the composition detailed in Table 3, it is important to highlight that the oils used in the present work have a relatively small precipitated asphaltene mass fraction, varying from 0.27 to 2.54%, which requires a highly accurate method to detail the composition of the residue. It is important to note that the only oil used in Nghiem and Coombe’s work has a percentage of precipitated asphaltene higher than 10%. The oils evaluated in this work have much lower amounts of precipitated asphaltenes. Therefore, it is understandable that Nghiem and Coombe’s model present some difficulties in parameter adjustment, because it has one only one parameter with a larger sensitivity in relation to the amount of asphaltenes. As shown in Table 1, the only parameter to be estimated in our simplified method is the binary interaction parameter between the heaviest pseudo component and methane. This parameter is obtained by minimizing the average error between the calculated and experimental values of the saturation pressure at the reservoir temperature. Values estimated for the binary interaction parameter are shown in Table 4 for each of the oils. It is worth noting that the adjustment of this binary interaction parameter must be performed before the extension of the C7+ residue. It is not advisable to perform this parameter estimation after the characterization because it would require


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the estimation of many interaction parameters what would make the method unfeasible. Moreover, all possible important interactions between the heaviest and the lightest components are taken into account in the bubble pressure. Note that the binary interaction parameter is actually a setting parameter, whose physical meaning is quite complex. This complexity becomes even greater when it comes to describing the phase behavior involving reservoir fluids, where the detailed composition is not accurately known. 4,0 3,5 Precipitate (% wt)

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3,0 2,5 2,0 1,5 1,0 0,5 0,0 0

50

100

150

200 P (atm)

250

300

350

400

Figure 1. Experimental data of asphaltene precipitation during depletion for Oil O143, O244, O344 and O445 (■ = Oil O1, ▲ = Oil O2, ● = Oil O3, × = Oil O4).

Table 4 shows the values of the adjustable parameters, which represent only an individual contribution to Equation 7. These values can be positive or negative, but the absolute value is not much higher than one as it represents component deviations from the mean geometric deviation.


14

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Energy & Fuels

Table 4. Binary interaction parameter estimated based on the saturation pressure calculation. Oil

kij

O1

0.42

O2

-1.67

O3

-0.52

O4

1.020

The next step is the oil characterization. The use of Pedersen’s method described by Equations 9 to 15 enables the extension/splitting of the C7+ fraction into 50, 60, 70 or even 80 components. This number can be established with the necessary precision for asphaltene precipitation, i.e., a smaller amount requires a more highly detailed composition. In fact the number of components that fill the description of the asphaltene fraction cannot be pre-established and for this reason, a detailed extension of the oil is required. Initially, we consider that the characterization with 50 components is sufficient. If the experimental value of precipitated asphaltene is not reached, another attempt must be made increasing the number of components to 60 and so on. The flexible number of components to represent the asphaltenes, resulting from the characterization procedure, is the major difference between this paper and that by Nghiem and Coombe, which assigns the residue at C31 +. Once the desired number of components to split the residue is defined, the molar composition, the critical temperature, the critical pressure, the acentric factor and the molecular weight of each of these fractions can be determined for each of the oils at each experimental pressure. After the oil characterization, the next step is the calculation of the representative fraction of asphaltenes, assuming they correspond to the heaviest components of the oil1. This is accomplished by adding the mass fraction of the pseudo-components at each pressure in order to


15

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Page 16 of 28

reach a value as close as possible to the experimental data and then group them. The reason for this grouping is the fact that the model considers only one pure solid pseudo component as the asphaltene fraction. The same detailed procedure was followed for the other three oils. This method requires the representative components of asphaltene, the critical temperature Tc, the critical pressure Pc and the acentric factor ω (Equations 9,10 and 11), its molecular weight Mw and molar fraction (Equations 12-15), depletion data (Figure 1) and the reference pressure P* of each oil. The algorithm for these calculations is presented in Figure 2 below. Table 5 shows the required number of fractions for the breakdown of the oil plus fraction for each of the oils at each experimental pressure. Note that the same number of fractions can occur at different pressure levels and can vary. The results of this model, expressed as the asphaltene representative fraction at each experimental pressure, according to the established nomenclature (P1, P2 and P3), are shown in Table 6. Two types of error were calculated: “% errorwt” and “%error”. The first one refers to the oil characterization (determination of asphaltene mass fraction) and compares experimental (% wtexp) and calculated (%wtcal) values of mass fraction by Equation 16. This error expresses the capability of the fraction selected to represent the amount of asphaltene in the oil and indicates how close the residue composition is to the experimental value of the amount of precipitated asphaltene. As can be seen from the characterization, Equations 9 to 11, there is conceptual coherence in the values of the molar fractions and their molecular weights. It is important to highlight this given the experimental uncertainties and limitations of the characterization method, which make it impossible that the sum of mass fractions matches the asphaltene mass fraction


16

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Energy & Fuels

exactly (which corresponds to zero %errorcal), where the theoretical error is given by Equation 16. %𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑤𝑤𝑤𝑤 = �

%𝑤𝑤𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒 − %𝑤𝑤𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐 � . 100 %𝑤𝑤𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒

(16)

Figure 2. Algorithm of the modified Nghiem and Coombe’s model36.


17

Energy & Fuels

Table 5. Number of fractions required for each oil residue at the experimental pressure.

Oil O3 (397.04 K)

Oil O2 (358.15K)

Oil O1 (369.25 K)

Oil

Oil O4 (386 K)

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Page 18 of 28

Label

Pressure (atm)

Number of fractions

P1

299.33

50

P2

204.19

60

P3

105.5

80

P1

232.58

70

P2

218.97

70

P3

198.56

70

P1

341.66

70

P2

239.25

70

P3

137.18

70

P1

307.83

60

P2

270.23

50

P3

242.03

70

The results presented in Table 6 indicate that the asphaltene representative component varied from C32+ to C50+, and its molecular weight (MW asp) varied between 511.53 and 776.63 g/gmol. Although these molecular weight results do not match the observations reported by Mansoori46, who considered between 1000 and 11000 g/gmol, it does satisfy the proposition of Pedersen et al.3, who stated that most of the asphaltene is constituted of a fraction between C50 and C100 and molecular weight between 700 and 1400 g/gmol. This demonstrates the complexity of determining the exact molecular structure and properties of asphaltenes47.


18

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Table 6. Calculated and experimental mass fractions of precipitated asphaltene.

P

%error

Asphaltene fraction

Mwasp

O1

C49+

696.00

0.27

0.26

3.70

1.71

1.23

O2

C33+

511.53

1.03

0.95

7.74

5.27

3.85

O3

C49+

760.55

1.07

1.07

0.00

0.75

0.54

O4

C49+

738.31

0.86

0.85

1.02

9.20

9.20

O1

C49+

736.00

0.93

0.91

2.15

6.09

2.76

O2

C32+

497.54

1.16

1.17

0.49

6.87

5.05

O3

C44+

696.62

1.99

2.02

1.51

12.70

9.49

O4

C45+

655.83

0.91

0.90

0.11

15.94

11.89

O1

C46+

727.00

1.55

1.55

0.00

17.15

12.27

O2

C32+

497.54

1.25

1.17

6.74

9.10

6.76

O3

C42+

670.34

2.54

2.58

1.57

17.28

11.77

O4

C50+

776.63

0.92

0.93

0.86

18.38

13.93

Oil

P1

P2

P3

%wtexp %wtcal %errorwt Derakhshan Yarranton

After determining all the fractions that comprise the asphaltene, the next step represented in 𝑙𝑙 Figure 2, is the calculation of the asphaltene fugacity in the liquid phase (𝑓𝑓𝑛𝑛𝑛𝑛 ) at the

experimental pressure and reservoir temperature and the asphaltene fugacity in the solid phase

(𝑓𝑓 𝑠𝑠 ∗ ) at the reference pressure and reservoir temperature using the SRK equation of state.

According to the Nghiem and Coombe’s model, asphaltene is considered a pure component. For this reason, the EOS parameters for the fugacity calculation of asphaltene are needed and must be the same as the representative pseudocomponent. Equations 17 to 19 are used to calculate the critical temperature Tca, the critical pressure Pca and acentric factor wa of asphaltene. This sum


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Page 20 of 28

must be extended to all fractions for which the total calculated mass fraction is closest to the experimental value of the mass fraction of asphaltene. Note that the values of the critical properties and acentric factors of all fractions are calculated during the characterization process, by Equations 9 to 15.

∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖 𝑇𝑇𝑐𝑐𝑐𝑐 = ∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖

(17)

∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖 . 𝑤𝑤𝑖𝑖 𝑤𝑤𝑎𝑎 = ∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖

(19)

𝑇𝑇𝑐𝑐𝑐𝑐

∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖 𝑃𝑃𝑐𝑐𝑐𝑐 𝑃𝑃𝑐𝑐𝑐𝑐 = ∑𝑛𝑛𝑖𝑖=𝑚𝑚 𝑧𝑧𝑖𝑖 𝑀𝑀𝑀𝑀𝑖𝑖

(18)

In Table 6 the second error (%error) comes from the application of the model, which compares 𝑙𝑙 the calculated values of asphaltene fugacity of the liquid phase (𝑓𝑓𝑛𝑛𝑛𝑛 ) with the asphaltene fugacity

of the solid phase (𝑓𝑓 𝑠𝑠 ). It is important to highlight that the calculation of the asphaltene fugacity

in the liquid phase can be accomplished without Peneloux’s correction factor, unlike Nghiem and Coombe’s procedure36. This simplifies the model and consequently reduces the number of parameters to be estimated. One can also notice an inverse relationship between the pressure and the application error (% error) for each oil: as the pressure is reduced, from P1 to P3, the asphaltene precipitated mass fraction error increases with both the Yarranton40 and Derakhshan and Shariati39 methods used to calculate the solid molar volume. The reason for this increase in (%error) is supposed to be due to its experimental nature because as the pressure gets closer to saturation, the pressure experimental data become less accurate. This must also account for the steep rise in the number


20

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Energy & Fuels

of errors for Oil O1 (1.23, 2.28 and 12.27 % at P1, P2 and P3, respectively), as in this case P3 is very close to Psat. However, it can be seen that this inverse relationship between the deviation of the model and the pressure reduction is not applicable to the error obtained in the oil characterization (% errocar). The comparison of the errors obtained for oils O3 and O4 using both methods for the calculation of the molar volume revealed that the inverse relationship between pressure and “%error” is not related to the reference pressure (P*) used. Oil O3 has a bigger difference between P* and P3 than oil O4, but in Oil O3 the error is smaller (11.77 %) than that for Oil O4 (13.93 %). This shows that the molar volume of the component as well as the pressure is more relevant for the determination of the asphaltene fugacity at solid state, expressed by Equation 2. Table 6 shows that for all pressure values, the method of calculation of asphaltene molar volume proposed by Yarranton et al.40 provides smaller errors than the one proposed by Derakshan and Shariati39. Therefore, it can be stated that the molar volume of asphaltene is best estimated using the molecular mass instead of its specific mass. It is widely known that there is a relationship between the presence of certain components in the oil and the possibility of asphaltene precipitation. For this purpose, a preliminary assessment was conducted between the oil composition and average errors of precipitated asphaltene quantities for each of the oils at various pressure levels. From the comparison of the average percentage errors of Yarranton’s method40 with the ratio between molar fraction of CO2 and C12+ for each oil (Table 7), it can be concluded that as this ratio grows, the precision of the determination of the precipitated amount of asphaltene falls. A possible explanation for this relationship is related to the higher impact of the CO2 on the fugacity of asphaltenes at higher concentrations, not taken in account by the model.


21

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Page 22 of 28

Table 7. Oil composition and the respective average percent error of the proposed method.

O1

𝐶𝐶𝐶𝐶2 � +� 𝐶𝐶12 0.05

5.42

O2

0.13

5.22

O3

0.17

7.27

O4

0.41

11.67

Oil

% erroravg

As highlighted before, asphaltene precipitation is dictated by the difference between the asphaltene fugacity in the liquid phase and the asphaltene fugacity in the solid phase. Therefore precipitation occurs when (ln fasp,L – ln fasp,S) ≥ 0. A slightly different way of evaluating the performance of this model is to analyze the trend in the difference between the asphaltene fugacity in the liquid and solid phase, which represents the equilibrium distance and indicates how in fact the estimated value of precipitated asphaltene reflects the actual amount in the equilibrium. Figure 3 along Equation 20 illustrates a comparison between this equilibrium distance calculated using Yarranton’s method and Derakhshan and Shariati’s method. The greatest difference between the fugacities occurs at pressure P3. This pressure is the closest to the saturation pressure (Psat) at which the maximum asphaltene precipitation occurs. As the pressure rises, the difference between the fugacities falls and likewise the amount of precipitated asphaltene, until the pressure reaches the resolubilization of asphaltene. A comparison between the methods indicates that this trend is sharpened when the molar volume is calculated using the Derakshan and Shariati39 method. The same behavior can be seen for all oils and was previously reported by Ngheim and Coombe36.


22

Page 23 of 28

∆ ln 𝑓𝑓 = ln 𝑓𝑓𝑎𝑎𝑎𝑎𝑎𝑎,𝐿𝐿 − ln 𝑓𝑓𝑎𝑎𝑎𝑎𝑎𝑎,𝑆𝑆

(20)

4,0

4,0

3,5

3,5

3,0

3,0

2,5

2,5 Δln f

Δln f

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2,0

2,0

1,5

1,5

1,0

1,0

0,5

0,5

0,0

0,0 0

100

200 P (atm)

300

a) Yarranton’s method

400

0

100

200 P (atm)

300

400

b) Derakhshan and Shariatis’ method

Figure 3. Comparison between the fugacity calculated using Yarranton’s method and Derakhshan and Shariati’s method for four oils (■ = Oil O1, ▲ = Oil O2, ● = Oil O3, × = Oil O4).

CONCLUSION In the present work, we improved Nghiem and Coombe’s model to calculate the amount of precipitated asphaltene. For the calculation of the reference pressure (P*), it is not necessary to use a large number of pressure experimental data versus the quantity of precipitated asphaltene because the de Boer´s graph assists in identifying the correct pressure with few data points. In addition, it is not necessary to estimate the solid molar volume because correlations available in the literature can provide good results. The method proposed in the present work, based on the pure solid-state model, provides accurate results for the prediction of asphaltene precipitation


23

Energy & Fuels

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Page 24 of 28

with a reduced number of parameters. Moreover, Yarranton’s method, which is used to estimate the solid molar volume as a function of the molecular weight, is more precise than Derakhshan and Shariati’s one. Finally, the molar fraction ratio of CO2 and C7+ of each oil seems to affect this analysis because the higher this ratio, the lower the precision of the method. ACKNOWLEDGEMENTS The authors acknowledge the support of ANP – Agência Nacional de Petróleo, Gás Natural e Biocombustíveis and Petrogal Brasil S.A., related to the grant from R&D investment rule.

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High-Pressure Modeling of Asphaltene Precipitation during Oil

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