Modeling of precipitation considering multi-component form of Asphaltene using a solid solution framework

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Modeling of precipitation considering multi-component form of Asphaltene using a solid solution framework Yasaman Hosseinzadeh Dehaghani, Hossein Ahmadinezhad, Farzaneh Feyzi, Mehdi Assareh

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Thermodynamics Research Laboratory, School of Chemical, Petroleum and Gas, Iran University of Science and Technology, Tehran 16846-13114, Iran

ARTICLE INFO

ABSTRACT

Keywords: Asphaltene precipitation Solid solution UNIQUAC PR PC-SAFT

Many investigations have focused on determining the precipitation conditions for Asphaltene content in reservoir fluids. In addition, there are experimental observations in reservoir fluids titration, using different normal alkanes, proving multi-component form for Asphaltene in crude oil. In this work, the thermodynamic modeling approach of Hosseinzadeh Dehaghani et al. (2018) is extended through replacing the multi-solid approach with a solid-solution approach, which is closer to the real nature of Asphaltene solid phase in estimation of phase behavior and precipitation conditions. Therefore, after characterization of Asphaltene content into a few sub-components, solid-solution framework was considered to model the solid phase. To do this, the UNIQUAC activity coefficient model was used to describe solid phase non-idealities. The liquid and high-pressure vapor phase non-idealities were modeled using both Peng-Robinson (PR) and perturbed chain statistical associating fluid theory (PC-SAFT) equations of state (EOSs). The results obtained from modeling of bubble point pressure, onset pressure and crude oil titration with n-pentane were compared with experimental data of two oil samples from literature. The analysis of the results shows that the multi-component modeling of Asphaltene content provides a higher accuracy in comparison to single component modeling. For multi-component analysis, the highest and lowest “mean absolute percentage errors” in calculation of precipitation amount for the first oil sample were 10.26 and 1.59, for PR + UNIQUAC and PC-SAFT + UNIQUAC, respectively; while values for the second oil sample were 4.15 and 1.02, for PR + UNIQUAC and PC-SAFT + UNIQUAC, respectively.

1. Introduction

1.1. Thermodynamic modeling

Asphaltene precipitation and deposition during production, refining and transportation of oil are among the most problematic issues of petroleum industry. Reservoir fluids are composed of saturated and aromatic hydrocarbons with a range of small to medium molecular weights. Asphaltene is a part of crude oil which is not soluble in normal alkanes, such as n-pentane and n-heptane, but is soluble in aromatics, such as benzene and toluene, at ambient temperature [2]. Asphaltenes are polar molecules and are the heaviest part of crude oil. They are also molecules with various molecular weights and complex molecular structures [3–5]. Factors contributing to the formation of Asphaltene in reservoirs are changes in pressure, temperature and oil composition. In addition, the amount and the type of injected gas in an enhanced oil recovery (EOR) process can affect Asphaltene stability. These factors can disrupt the chemical equilibrium of a reservoir resulting in precipitation phenomena [6]. Crude oil blending during transportation in pipelines may also disrupt oil composition and lead to Asphaltene precipitation.

In order to calculate Asphaltene precipitation onset and quantity, several models have been presented in recent years. Thermodynamic modeling of this phenomenon can be performed based on two general categories, the theory of solubility and the colloidal theory. In the theory of solubility, Asphaltene molecules are assumed to be soluble in crude oil and the precipitation process takes place when the solubility is less than a pre-defined value [7]. Models based on organized solution theory, proposed by Flory [8], Huggins [9] and Scott and Magat [10] are considered in this group. These models were originally presented to describe thermodynamic behavior of polymer solutions and were later developed to model the solubility of Asphaltenes in crude oil. Flory and Huggins [8,9] developed an independent equation for Gibbs free energy of polymer solutions using assumptions of the organized solution theory. They assumed that a polymer molecule is in the form of a flexible chain of segments and the size of each segment equals the size of the solvent molecule. They developed an equation that can be used for homogeneous polymer chains in a simple uniform solvent. Scott and Magat [10] developed the

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Corresponding author. E-mail address: [email protected] (M. Assareh).

https://doi.org/10.1016/j.fuel.2019.116766 Received 16 October 2018; Received in revised form 22 November 2019; Accepted 26 November 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Yasaman Hosseinzadeh Dehaghani, et al., Fuel, https://doi.org/10.1016/j.fuel.2019.116766

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Nomenclature

a res a hc a disp µires Ki wt K kg mol kmol cal m3 gr

EOS SARA PR PC-SAFT

Equation of state Saturates, Aromatics, Resins and Asphaltenes Peng- Robinson Perturbed chain form of the statistical associating fluid theory SAFT-VR Statistical associating fluid theory for potentials of variable attractive range MAPE Mean absolute percentage errors n-alkane Normal alkane fi Fugacity Ns Number of solid layers Number of components Nc n Number of moles P Pressure T Temperature Mole fraction of liquid x il x iv Mole fraction of vapor x is Mole fraction of solid Fugacity coefficient i Activity coefficient i R Gas universal constant v Molar volume Cp Heat capacity of fusion Hf Normal melting-point enthalpy of fusion MW Molecular weight ω Acentric factor r&q Structural molecular parameters Binary interaction parameters of UNIQUAC model ij σ Temperature independent segment diameter m Number of segments per chain ε Depth of potential k Boltzmann constant

Residual Helmholtz free energy Hard chain contribution to residual Helmholtz free energy Dispersion contribution to residual Helmholtz free energy Chemical potential Equilibrium ratio Amount of precipitated Asphaltene Kelvin Kilogram Mole Kilomole Calorie Cubic meters Gram

Subscripts

i j ij c f R b onset

Component Phase Cross parameter Property at the critical point Property at the normal melting-point Resin Bubble Onset of Asphaltene precipitation

Superscripts

s l v res hc disp

Solid Liquid Vapor Residual Hard chain Dispersion

1.2. Asphaltene multi-component nature

Huggins theory for polymer mixtures with variable chain lengths. The models based on Flory [8] and Huggins [9] assumed that Asphaltenes have homogeneous structures with no molecular weight distribution. In contrast, the models based on Scott and Magat [10] assumed an inhomogeneous structure for Asphaltenes. In the case of colloidal theory, Asphaltenes are assumed to be colloidal particles in which the absorbed resins on their surface stabilize them [11]. Precipitation can take place if resins detach colloids and therefore physical separation occurs. Micellization thermodynamic model is another example of colloidal theory for Asphaltene precipitation [12]. Over recent years, various research groups have focused on prediction of onset pressure and amount of precipitated Asphaltene in crude oils using models based on equations of state (EOSs). It has been widely acknowledged by various investigations that the perturbed chain form of the statistical associating fluid theory (PC-SAFT) EOS, proposed by Gross and Sadowski [13], results in better accuracy in predicting the phase behavior of complex mixtures, such as Asphaltenes. Panuganti et al. [14] presented a procedure to characterize crude oil and calculate Asphaltene phase envelope by PC-SAFT EOS. According to their results, the proposed procedure could model Asphaltene phase behavior better than a procedure using a cubic EOS. Punnapala and Vargas [15] presented an improved PC-SAFT characterization methodology for various reservoir fluids from three different fields in the Middle East. Most recently, the capabilities of PC-SAFT and Cubic-Plus-Association (CPA) EOSs to calculate Asphaltene onset pressure and phase envelope have been investigated by Nascimento et al. [16]. They concluded that PC-SAFT EOS with the association term is more accurate than CPA EOS. Similar results have been obtained in other recent studies that confirm the accuracy of the PC-SAFT EOS for Asphaltene thermodynamic modeling [17,18].

The molecular weight and structure of Asphaltene has been uncertain and controversial for decades. The results of different measurement methods for molecular weight of Asphaltenes vary more than one order of magnitude [5,19]. In a number of studies, a small molecular weight of Asphaltenes has been measured (about 750) using molecular diffusion methods [5,20–22] as well as mass spectrometry methods [23–25]. For ideal structures with much larger molecular weights, many chemical functions can be considered in a single molecule such as different alkane chains, various aromatics and sulfides. The varieties of Asphaltene molecules are large: some with nitrogen, some with sulfur, some with large ring systems, some with small ring systems, and some with metals [5]. Therefore, resolving the debate on the multi-component nature of Asphaltene is essential to progress in various fields of the oil industry. Titration of oil systems containing Asphaltene by normal hydrocarbon solutions is an indication of the presence of Asphaltenes with different nature. Therefore, insight into behavior of poly-disperse nature of Asphaltenes is important in precipitation modeling. Addition of light normal alkanes to crude oil causes instability, and finally precipitation of Asphaltene. Depending on the precipitating solvent and contact time duration, the amount and type of Asphaltene can be different. Ting et al. [26] showed that assuming single or multiple molecular weights for Asphaltenes, changes the phase behavior of Asphaltenes considerably. Their study was mainly focused on investigating the role of Asphaltene poly-disperse nature in oil mixtures. Modeling of Asphaltene poly-disperse nature in real crude oil systems was presented by Victorov and Smirnova [27]. In their work, the effect of molecular shape of resin on size distribution was considered. The relationship between shape and elastic constants of the 2

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resin shell of the aggregates were also presented. Precipitation curves for different real crude oil compositions were obtained and structural properties of aggregates were estimated. They reported an acceptable match between their model and available data in literature. Wang and Buckley [28] performed a number of experiments to investigate the effect of dilution ratio on several fractions of Asphaltenes. Tavakkoli et al. [29] modeled poly-disperse Asphaltene precipitation onset, and the amount of precipitation from crude oils diluted by solvent using PC-SAFT EOS for a wide range of crude oil densities. They also compared the results obtained from mono-disperse and poly-disperse modeling. They claimed that by assuming Asphaltene with multiple molecular weights and multi pseudo-components, the phase behavior and the amount of precipitated Asphaltene were more accurate compared to the results obtained by modeling of Asphaltene with a constant molecular weight (mono-disperse Asphaltene). Zúñiga-Hinojosa et al. [30] studied the modeling of Asphaltene precipitation process obtained by the addition of a n-alkane to seven bitumen mixtures and heavy oils under various temperature and pressure conditions using the PC-SAFT EOS. In their work, Asphaltenes were divided into sub-fractions with different densities and molar masses based on a gamma distribution function. They achieved good agreement between experimental data and predicted values calculated by PC-SAFT EOS. In poly-disperse Asphaltene modeling approaches, Asphaltene is assumed to have a non-uniform and non-homogeneous structure. Most of the investigations on Asphaltene modeling have assumed single component Asphaltene (mono-disperse Asphaltene). In addition, in poly-disperse modeling, Asphaltene splitting into several pseudo-components does not have a clear physical basis and it only increases model flexibility in the fitting process. Thus, by considering poly-disperse nature for Asphaltenes with pseudo-components, and according to dilution experiments, the precipitation model was improved in the work of Hosseinzadeh Dehaghani et al. [1]. Considering the solid phase, there are generally two approaches for calculation of precipitation amount. The first approach is the solid solution in which the solid phase is considered as a homogeneous solution similar to liquid solutions. This model was initially introduced by Won [31] and was used later by Pedersen et al. [32] and Schou Pedersen et al. [33] for determining wax precipitation of oil samples obtained from North Sea. The second approach is the multi-solid model developed by Lira Galeana et al. [34] in which a multi-layer solid phases is considered. Each layer is indicative of a pure component (or pseudocomponent) as a solid that cannot be dissolved in other solid layers.

solid phase acts as a homogeneous solution similar to liquid phase. Equilibrium conditions are assumed for vapor, liquid and solid phases and equality of fugacity criteria is applied for each component i.

fiv = fil = fis , i = Nc

fiv = fil , i = 1, 2,

Ns + 1,

, Nc

(1)

, Nc

(2)

Ns

In these relations, fi is the fugacity of component i and superscripts v , l and s represent the vapor, liquid and solid phases, respectively. The total number of components indicated by Nc . Ns , is the number of components precipitating in the solid phase. By considering φ-φ approach for vapor and liquid phases and activity coefficient for modeling non-idealities of the solid phase, one can write:

x iv

v i P

= x il

l iP

= x is

s s0 i fi

(3)

where x i represents the mole fraction of component i , P is the pressure, φ is fugacity coefficient and γ is activity coefficient. Superscript 0, represents the standard state conditions of pure component in solid phase. According to Eq. (3), solid phase fugacity of pure-component i is required to calculate solid phase fugacity for this component in the solid mixture [36]. Eq. (4) is used to calculate the fugacity ratio of purecomponent solid to pure-component liquid.

ln

fs fl

(pure, i)

Hf , i

=

RT

(1

T /Tf , i) +

1 R

Tf , i T

Cp, i T

dT

1 R

Tf , i

Cp, i dT + T

1 RT

P

(vis

vil ) dP

(4)

Pf

where Hf , i is the enthalpy of fusion at normal melting-point and Cp, i indicates heat capacity of fusion for component i. T and Tf , i are system temperature and normal melting-point temperature, respectively. The liquid molar volume (v l ) and the fugacity of pure liquid Asphaltene ( f l ) are calculated using an EOS. In addition, the following correlation developed by Won [31], is used to estimate the normal melting point temperature:

Tf , i /K = 374.5 + 0.02617MWis

2017/ MWis

(5) (v s )

It is assumed that the value of the solid molar volume minus liquid molar volume (v l ) is independent of temperature. Lira Galeana et al. [34] proposed an expression for the enthalpy of fusion as following (temperature is in Kelvin).

1.3. Contributions of this investigation In the previous work of Hosseinzadeh Dehaghani et al. [1], a multi-solid model was used, thus Asphaltene was split into a number of pseudo-components. Fitting of the parameters of PR and PC-SAFT EOSs was performed based on bubble point pressure, precipitation onset pressure and Asphaltene precipitation amount (due to titration of dead oil by n-pentane solvent at atmospheric conditions). Modeling of multi-component Asphaltene resulted in an acceptable match with the experimental data of two Mexican crude oil samples. Although the solid-solution model needs more adjustable parameters in comparison to multi-solid model, Asphaltene behavior follows solid-solution behavior during precipitation from a physical point of view. Consequently, in order to obtain more accurate estimates of Asphaltene precipitation, the solid-solution model is used in this work. For the liquidvapor modeling, PR [35] and PC-SAFT of Gross and Sadowski [13] are used. This work is organized as follows. Initially, solid-solution approach is introduced. Later, properties of the oil samples and their characterization method are presented. Finally, modeling results are discussed considering single component and multi-component, for calculations of bubble point pressure, onset pressure and precipitation amount.

Hf , i /Jmol

1

= 0.22089MWis Tf , i

(6)

MWi is the molecular weight of the Asphaltene’s “i”th sub-component. Schou Pedersen et al. [33] suggested a correlation for calculation of heat capacity of fusion ( Cp ),

Cp, i /Jmol 1K

1

= 1.2698MWis

1.9406 × 10 3MWis

(7)

In this research, fugacity coefficients of liquid and vapor phases are obtained from EOS models and fugacity of the components in solid phase is obtained from UNIQUAC activity coefficient model [37]. Liquid and vapor fugacity coefficients are calculated using PR and PCSAFT EOSs. PR, which is a common industrial EOS with reasonable simplicity and a wide range of successful implementations. PC-SAFT is an equation of state based on the statistical thermodynamics. 3. PC-SAFT In this equation, a basic relationship has been presented based on residual Helmholtz free energy that includes hard chain and dispersion contributions. This EOS can accurately estimate phase behavior of fluids with high molecular weight e.g. gigantic Asphaltene molecules.

2. Solid-solution approach Solid-solution approach assumes that Asphaltene is a single-solid phase which is formed from different hydrocarbon components and the 3

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4. Properties of crude oil samples

Table 1 Compositions and characteristics of the crude oil samples [38]. C1

Y3

Reservoir temperature/K Reservoir pressure/bar

393 552

410 427

Component

mole %

mole %

CO2 H2S N2 C1 C2 C3 IC4 NC4 IC5 NC5 C6 C7+ MW C7+ density C7+/kg m−3

1.57 5.39 0.91 24.02 10.09 9.58 1.83 4.83 2.27 2.74 4.77 32.00 334.66 882.20

1.59 1.44 0.47 32.22 12.42 10.29 2.03 4.87 2.22 2.71 4.12 25.62 284.36 804.80

Dead oil samples obtained from surface facilities of two problematic Mexican oil wells, named as C1 and Y3 were used to calculate bubble point pressure, onset pressure and amount of precipitated Asphaltene due to addition of solvents. These oil samples and separated Asphaltene/resin fractions and their characteristics are reported by Buenrostro‐Gonzalez et al. [38]. These samples were directly taken from the bottom hole sampling operation and kept at constant pressure until the start of the experiments. Table 1 indicates compositions and characteristics of oil samples measured by high temperature gas chromatography (HTGC). Table 2 shows general characterization of these oil samples. The molecular weights of resins were taken from literature [39,40]. For the Asphaltene molecular weight (using gel-permeation chromatography) the values are from the reports of Buenrostro-Gonzalez et al. [41]. A series of titration experiments with n-alkanes were performed to determine the precipitation amount for the stock tank oil samples and the effect of change in composition on Asphaltene precipitation. These experiments were similar to those performed by Kokal et al. [42]. As a first step, to remove any suspended compound, the dead oil samples are filtered using a 0.45µm Teflon membrane. Afterward, a volume of n-alkane corresponding to the specific ratio of titration fluid is added to a maximum of 5 g of oil in an appropriate flask. After 10 min of ultrasonic shaking, the mixture is left overnight. Then by using a vacuum system with the same filtration membrane, the solution of n-alkane and deasphalted oil is filtered. The flask and the filtration membrane are washed with a small amount of the corresponding n-alkane to remove any residual oil. In the next step, the membrane was dried with a precipitated material in a vacuum oven with a pressure of 0.1 bar and 333 K for 6 h. Finally weight of the membrane was measured to determine the mass of precipitated Asphaltenes, according to Buenrostro-Gonzalez et al. [41]. In the work of Hosseinzadeh Dehaghani et al. [1], a complete description of oil samples and description of the experiments has been reported.

Table 2 Results of SARA analysis [38–41].

Oil C1 Oil Y3 Asphaltene (C1 and Y3) Resin (C1 and Y3)

MW gr mol−1

Asphaltenes wt%

Resins wt%

Aromatics wt%

Saturates wt%

238.1 220.2 3066 800

3.80 3.25

12.66 10.88

28.89 30.73

54.67 55.14

One of the advantages of the SAFT family EOSs is that their parameters have physical meaning. PC-SAFT without association contribution contains three parameters including, molecular diameter of each segment (σ), number of segments in each molecule (m), and segmentsegment dispersion interaction energy (ε/k). Usually, these parameters are estimated based on experimental data for pure components. Determination of the values of these parameters is discussed in the next sections. The reduced residual Helmholtz free energy of a non-associating fluid in PC-SAFT EOS is presented by the following equation:

5. Reservoir fluid characterization According to a relation presented by Pedersen et al. [32], C7+ was split into C7 to C12+. Then, C12+ was split into “Saturates + Aromatics”, Asphaltene and resin pseudo-components regarding to saturates, aromatics, resins and Asphaltenes (SARA) analysis data as it is presented in Table 2. “Saturates + Aromatics” pseudo-component indicates normal alkanes (normal paraffins), iso-paraffins, cycloalkanes (naphthenics), benzene derivatives and poly-nuclear aromatics. Live oil composition after characterization is shown in Table 3. In Table 4, the values of precipitated Asphaltene weight percent by different normal alkanes (n-C5, n-C7 and n-C9) in different experimental conditions for the two oil samples (C1 and Y3) are presented. For a given value of dilution ratio, the amount of precipitated Asphaltene decreases with increasing carbon number of diluting normal alkane. In the next step, Riazi and Al-Sahhaf [43] relations were used as initial estimates for critical properties and acentric factor of “Saturates + Aromatics” pseudo-components. Initial estimates of these parameters for resin and Asphaltene pseudo-components were obtained using correlations presented by Avaullee et al. [44]. For “Saturates + Aromatics” and resin, PC-SAFT parameters were determined by equations developed by Assareh et al. [45]. Primary estimation of PCSAFT parameters for Asphaltene components were calculated using relationships presented by Gonzalez et al. [46]. The PC-SAFT parameters for pure components were obtained from the data reported by Gross and Sadowski [13]. All the above-mentioned correlations are presented in Appendix A. Moreover, a complete discussion on characterization process and relationships used in this research, has been reported in the work of Hosseinzadeh Dehaghani et al. [1].

(8)

a res = a hc + a disp

In this relation, a is the Helmholtz free energy and the superscripts res , hc , disp express residual, hard chain and dispersion contributions, respectively. The compressibility factor (Z ) is presented as. (9)

Z = 1 + Z hc + Z disp

Eq. (10) can be used to calculate liquid-vapor equilibrium ratio.

Ki =

l i v i

(10)

The following thermodynamic relation exists between chemical potential and fugacity coefficient.

ln

i

=

µires (T , v ) RT

lnZ

(11)

Chemical potential for each component is calculated Eq. (12):

µires (T , v ) RT

= a res + (Z

1) +

a res xi

Nc

xj T , v, xk xi

j=1

a res xj

T , v, xk xj

(12) Gross and Sadowski [13] have described the important terms and derivatives that are required for determination of the fugacity coefficients. 4

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Table 3 C1 and Y3 live oil compositions after characterization. Component

C1 Mole fraction

Y3 Mole fraction

CO2 H2S N2 C1 C2 C3 IC4 NC4 IC5 NC5 C6 C7 C8 C9 C10 C11 Saturates + Aromatics

0.0157 0.0539 0.0091 0.2402 0.1009 0.0958 0.0183 0.0483 0.0227 0.0274 0.0477 0.0037 0.0040 0.0043 0.0046 0.0049 0.2796

0.0159 0.0144 0.0047 0.3222 0.1242 0.1029 0.0203 0.0487 0.0222 0.0271 0.0412 0.0085 0.0093 0.0101 0.0111 0.0121 0.1939

Resins Asphaltenes

0.0176 0.0014

0.0104 0.0008

MW/gr mol−1 44.01 34.00 28.01 16.04 30.07 44.10 58.12 58.12 72.15 72.15 84.00 100.20 114.23 128.25 142.28 156.31 C1:307.68 Y3:285.61 800 3066

Fig. 2. (Upper plot) Bubble point pressure calculations for C1 oil sample. (Lower plot) Bubble point pressure calculations for Y3 oil samples. Single component Asphaltene modeling, experimental data from Buenrostro‐Gonzalez et al. [38].

Table 4 Weight percent of the precipitated Asphaltene of the oil samples after addition of n-alkane [38]. C1

6. Modeling results considering mono-disperse Asphaltene

Y3

Solvent Ratio cm3 n-alkane/gr oil

n-C5

n-C7

n-C9

Solvent Ratio cm3 n-alkane/gr oil

n-C5

n-C7

n-C9

2 3 4 10 30 50

1.71 2.31 2.52 3.54 3.69 3.81

1.36 1.74 1.85 2.35 2.95 3.08

1.19 1.41 1.67 2.00 2.54 2.60

2 4 10 50

1.89 2.72 3.00 3.25

1.82 2.29 2.38 2.71

1.35 2.06 2.19 2.30

In this method, single-component Asphaltene was assumed in which Asphaltene precipitates in the form of a pure solid. Calculations of bubble point pressure, onset pressure and amount of precipitated Asphaltene due to dead oil titration experiments were done using npentane as the titrant. Parameter regression (optimization) method and obtained results are discussed in the following sub-sections. 6.1. Parameters optimization In order to have more accurate estimates, in each calculation step

Table 5 Values of the fitted parameters in single component Asphaltene modeling.

Sample

C1 C1 Y3 Y3

Component

C12+ Saturates + Aromatics Asphaltenes C12+ Saturates + Aromatics Asphaltenes

PR Parameters

PC-SAFT Parameters

Adjusted parameters Tc/K

Pc/bar

ω

Vs/m3 mol−1

m

σ/A

ε/k/K

Vs/m3 mol−1

909.74 1572.16 718.68 1308.17

13.17 17.55 14.80 15.71

1.31 2.13 1.50 1.97

0.000511

11.35 21.67 14.32 20.03

3.98 4.11 4.03 4.22

329.23 430.88 310.11 451.41

0.000900

0.000518

Fig. 1. Summary of the optimization (fitting) process in the mono-disperse Asphaltene phase behavior modeling. 5

0.000900

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Table 6 Mean absolute percentage error for calculations of bubble point pressure, onset pressure and weight percent of the precipitated Asphaltene for C1 and Y3 oil samples in mono-disperse and poly-disperse Asphaltene modeling. Type of calculation

Type of crude oil C1 Pb

Buenrostro‐Gonzalez et al. [38] PR EOS- mono-disperse Asphaltene PR EOS- poly-disperse Asphaltene (Multisolid) [1] PR EOS- poly-disperse Asphaltene (Solidsolution) PC-SAFT EOS- mono-disperse Asphaltene PC-SAFT EOS- poly-disperse Asphaltene (Multi-solid) [1] PC-SAFT EOS- poly-disperse Asphaltene (Solid-solution)

Y3 Pb

C1 Y3 C1 Ponset Ponset wt%

Y3 wt%

4.53 1.40 4.58 3.82 3.45 0.90 3.82 3.45 1.65

7.01 3.27 2.89

7.40 6.90 10.26 4.14 4.43 3.53

3.82 3.45 0.54

2.63

2.37

2.78

2.73 1.06 0.43 2.65 1.04 0.59

1.82 1.07

3.16 1.73

3.31 1.08

2.65 1.04 0.41

0.98

1.59

1.02

Fig. 4. (Upper plot) Onset pressure calculations for C1 oil sample. (Lower plot) onset pressure calculations for Y3 oil sample. Single component Asphaltene modeling, experimental data: Buenrostro‐Gonzalez et al. [38].

Fig. 5. (Upper plot) Calculations of the precipitated Asphaltene weight percent due to injection of n-pentane solvent to C1 oil sample. (Lower plot) Calculations of the precipitated Asphaltene weight percent due to injection of n-pentane solvent to Y3 oil sample. single component Asphaltene modeling, experimental data: Buenrostro‐Gonzalez et al. [38].

Table 7 Molecular weights of the Asphaltene sub-components. MW/gr mol−1

MW-C5-7 MW-C7-9 MW-C9+

Fig. 3. Flow Diagram for onset pressure calculation. 6

Type of crude oil C1

Y3

2860.918 3090.326 3124.301

2860.918 3090.326 3114.000

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6.2. Calculation of Pb, Ponset and precipitated Asphaltene

Table 8 The UNIFAC model parameters for Asphaltene monomer. r

q

MW/gr mol−1

28.640

21.052

670

Bubble point pressure at different temperatures were calculated using PR and PC-SAFT EOS models and were compared with experimental data and modeling results of Buenrostro‐Gonzalez et al. [38]. Fig. 2 indicates the results of bubble point pressure calculation for two samples, C1 and Y3. Buenrostro‐Gonzalez et al. [38] used PR EOS with volume shift parameters to determine bubble point pressure. Mean absolute percentage error (MAPE) values for the two C1 and Y3 oil samples were calculated in accordance with Eq.13. These values are reported in Table 6.

Table 9 The UNIQUAC model size parameters for the Asphaltene sub-components of C1 and Y3 oil samples. Sub-component

Parameter

C5 7 C7 9 C9 +

r

q

122.00 132.00 132.46

89.68 97.05 98.10

MAPE =

11

12 13

21

22 23 31 32 33

Oil sample C1

Y3

1.0000 0.8518 1.4838 1.0133 1.0000 0.9930 1.2030 2.7989 1.0000

1.0000 0.5764 1.5365 0.0073 1.0000 1.9832 1.6593 1.5378 1.0000

|Experimental Calculated| |Experimental|

100

(13)

In the above equation, n, is the number of calculated points. As the table shows, PC-SAFT EOS has resulted in a small MAPE compared to PR EOS for the two oil samples. This may be due to the ability of the PC-SAFT EOS in estimating phase behavior of fluids with high molecular weights. Onset pressures were also calculated in different temperatures using PR and PCSAFT EOSs and were compared with experimental data and the data reported by Buenrostro‐Gonzalez et al. [38]. The flow diagram of onset pressure calculation is presented in Fig. 3. In Fig. 4, calculations for onset pressure using the two EOSs are shown for the oil samples. Buenrostro‐Gonzalez et al. [38] used SAFT-VR EOS for the calculations of Asphaltene onset pressure. Comparing values of MAPE in Table 6 for the oil samples, it is implied that a lower MAPE value has been calculated with PC-SAFT EOS for the onset pressure estimation. In the next step, the amount of precipitated Asphaltene caused by addition of n-pentane solvent was determined using PR and PC-SAFT EOSs. The results are shown in Fig. 5. Comparison was made with experimental data and the results obtained by Buenrostro‐Gonzalez et al. [38]. According to Table 6, it can be implied that a lower MAPE is obtained using PC-SAFT EOS for calculation of precipitated Asphaltene amount.

Table 10 Fitted binary interaction parameters of UNIQUAC model for C1 and Y3 oil samples. Interaction parameter*

1 n

* 1: C5-7 sub-component; 2: C7-9 sub-component; 3: C9+ sub-component.

including bubble point pressure, onset pressure and precipitation amount, a set of parameters were fitted using a genetic algorithm. A group of parameters were chosen for fitting process in each step of calculations. The selection was in a way that, there were lower sensitivities toward those parameters in the next step of regression. EOS parameters for “Saturates + Aromatics” pseudo-components were fitted as the first step in bubble point pressure calculations. Then, for calculations of onset pressure, molar volume of Asphaltene was fitted. Finally, the parameters of the EOSs for Asphaltene pseudo-components were fitted in the Asphaltene precipitation calculations step. Fitted parameters in one step were fixed in the next step and calculations were repeated using a set of all fitted parameters. Table 5 shows the final values for fitted parameters of PR and PC-SAFT EOSs for C1 and Y3 crude oil samples in mono-disperse Asphaltene modeling. In order to reduce the number of optimization parameters, all the binary interaction parameters between Asphaltene and other components were considered zero. In addition, binary interaction parameters between the other components were also considered as zero [7]. A summary of the optimization process in the mono-disperse Asphaltene phase behavior modeling is presented in Fig. 1.

7. Poly-disperse Asphaltene modeling results Ting et al. [26] showed that phase behavior of poly-disperse Asphaltene is different that of mono-disperse Asphaltene. In this step, Asphaltene was broken into three sub-components and it was assumed that precipitation has been taken place in the solid-solution form. Like the previous step, determination of bubble point pressure, onset pressure and amount of Asphaltene precipitation due to titration of dead oil by n-pentane solvent were considered. 7.1. Splitting Asphaltene pseudo-component into three Sub-components Based on the experimental data from oil titration with different normal alkanes reported in Table 4, Asphaltene was split into three subcomponents. Therefore, when n-pentane, n-heptane and n-decane were used as precipitators, Asphaltene was considered in modeling as n-C5-7, n-C7-9 and n-C9+ sub-components, with respect to these dilatants. Asphaltene pseudo-component n-C9+ indicates Asphaltene which is not soluble in n-nonane; Asphaltene pseudo-component n-C7-9 represents,

Table 11 The fitted parameters while Asphaltene is broken into three sub-components. PR Parameters

PC-SAFT Parameters

Sample

Adjusted parameters Component

Tc/K

Pc/bar

ω

Vs/m3 mol−1

m

σ/A

ε/k/K

Vs/m3 mol−1

C1 C1 C1 Y3 Y3 Y3

Asph-C5-7 Asph-C7-9 Asph-C9+ Asph-C5-7 Asph-C7-9 Asph-C9+

1686.91 1686.91 1686.91 1625.70 1625.70 1625.70

14.03 14.03 14.03 17.89 17.89 17.89

2.07 2.07 2.07 1.76 1.76 1.76

0.00066 0.00066 0.00066 0.00052 0.00052 0.00052

24.90 37.66 39.42 27.84 29.93 35.74

4.31 4.31 4.31 4.16 4.16 4.16

285.65 297.31 382.18 370.10 370.45 371.22

0.001263 0.001263 0.001263 0.001344 0.001344 0.001344

7

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Fig. 6. Summary of the optimization (fitting) process in the poly-disperse Asphaltene phase behavior modeling.

Fig. 8. (Upper plot) Onset pressure calculations for C1 oil sample (Lower plot) Onset pressure calculations for Y3 oil sample. Asphaltene was split into three sub-components. Experimental data: Buenrostro‐Gonzalez et al. [38].

Fig. 7. (Upper plot) Bubble point pressure calculations for C1 oil sample. (Lower plot) Bubble point pressure calculations for Y3 oil samples. Asphaltene was split into three sub-components. Experimental data: Buenrostro‐Gonzalez et al. [38].

parameters which were fitted in one step were left unchanged in the next step and finally, calculations were repeated with a set of the fitted parameters. As Eq. (14) shows, optimization of molecular weights of two Asphaltene sub-components that can be used in the calculation of molecular weight of the third sub-component. Molecular weights of Asphaltene subcomponents obtained by PR EOS are reported in Table 7.

Asphaltenes which are not soluble in n-heptane, but soluble in nnonane. Asphaltene pseudo-component n-C5-7 shows Asphaltenes which are not soluble in n-pentane but soluble in n-heptane. Amount of each Asphaltene sub-component is equal to the ratio of the amount of precipitated Asphaltene from the specific sub-component to the total precipitated Asphaltene.

MWtot = wtot

7.2. Parameters optimization

n i=1

1 wi /MWi

(14)

In Eq. (14), MWtot is the Asphaltene molecular weight before breaking; wtot is the amount of total precipitated Asphaltene; MWi is the molecular weight of the Asphaltene’s “i”th sub-component and wi is the weight percent of precipitated Asphaltene due to addition of the “i”th solvent. In order to obtain the parameters of the UNIQUAC activity coefficient model, a monomer Asphaltene structure was assumed [47,48]. The details are presented in Appendix B. Then, the parameters of the UNIQUAC activity coefficient model were estimated depending on extended equations [49]. For the structure shown in Appendix B, the UNIFAC model parameters for Asphaltene monomer are shown in Table 8. Asphaltenes were assumed to be macromolecular aggregates that are formed from mono-disperse Asphaltene monomers. Using the

Calculations of bubble point pressure, onset pressure and precipitation amount due to addition of n-pentane solvent were repeated after breaking Asphaltene into three sub-components. The parameters used in mono-disperse Asphaltene modeling, were also used in bubble point pressure calculation. Asphaltene molar volume was fitted for calculation of onset pressure. For Asphaltene precipitation calculations, it was assumed that Asphaltenes have been precipitated in the form of solid solution. The UNIQUAC activity coefficient model was used in poly-disperse modeling. Parameters of the EOS for three sub-components and their molecular weights were fitted for calculation of the precipitation amount. The 8

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Fig. 9. The Flow Diagram for calculation of Asphaltene precipitation amount.

ratio of molecular weights of Asphaltene sub-components (values in Table 7 obtained from regression using PR EOS) to molecular weight of Asphaltene monomer, the parameters of UNIQUAC model were calculated for each Asphaltene sub-component. In this way, it was assumed that each Asphaltene sub-component is formed from several Asphaltene monomers. This number equals the ratio of the sub-component molecular weight to the molecular weight of Asphaltene monomer. The parameters of UNIQUAC model for Asphaltene sub-components are presented in Table 9. Binary interaction parameters of the UNIQUAC model were fitted. These values are reported in Table 10. Based on the work of Nghiem et al. [50], critical properties and acentric factors of the three Asphaltene sub-components were considered to be the same in optimizing PR EOS parameters. Therefore, only the three

PR EOS parameters (Tc, Pc and for three Asphaltene sub-components) were fitted. Meanwhile, Tavakkoli et al. [29] reported the same values for parameters of all sub-components, when rounded to two decimals. Therefore, for three components, and Asphaltene modeling using PCSAFT, the same parameter σ was considered and was adjusted for all the sub-components. In addition, m and ε/k were adjusted for each of the sub-components. As in previous section, all the binary interaction parameters (interactions between Asphaltene sub-components and other components) in the EOSs were assumed to be zero. Table 11 indicates final values of the optimization parameters using PR and PCSAFT EOSs for C1 and Y3 oil samples in poly-disperse Asphaltene phase behavior modeling. A summary of the fitting process in the poly-disperse Asphaltene phase behavior modeling is presented in Fig. 6. 9

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were used for liquid-vapor equilibrium and Asphaltene phase description, respectively. Therefore, we may conclude that considering nonideal solid phase solution using the UNIQUAC activity coefficient model has improved the accuracy of the results. However, the effect of the PCSAFT in description of the liquid-vapor equilibrium and appropriate estimation of its parameters should not be neglected. It is necessary to mention that, MAPE values for the solid solution model are lower than the Multi-solid model (work of Hosseinzadeh Dehaghani et al. [1]) in all stages of the calculations, as it is shown in Table 6. 8. Conclusion A multi-component form for Asphaltene has been assumed in this work to investigate Asphaltene precipitation. According to the presented results the following conclusions can be drawn:

• In this work, a method was developed for characterization and de-

•

Fig. 10. (Upper plot) Calculations of the precipitated Asphaltene weight percent due to injection of n-pentane solvent to C1 oil sample. (Lower plot) Calculations of the precipitated Asphaltene weight percent due to injection of npentane solvent to Y3 oil sample. Asphaltene was split into three sub-components. Experimental data: Buenrostro‐Gonzalez et al. [38].

•

7.3. Calculation of Pb, Ponset and precipitated Asphaltene Using PR and PC-SAFT EOSs, bubble point pressure was determined at different temperatures and the results were compared to the experimental data and the calculated results of Buenrostro‐Gonzalez et al. [38]. Fig. 7 indicates the results of bubble point pressure modeling using the two EOSs considered in this work for C1 and Y3 oil samples. Comparing Figs. 2 and 7, no considerable difference is observed between the determined values for bubble point pressure with poly-disperse Asphaltene assumption in comparison to mono-disperse model. This may be due to the method of calculations for bubble point pressure. Repeating liquid-vapor equilibrium calculations with multi-component Asphaltene, does not change the obtained results considerably. Reported MAPE values, presented in Table 6, confirm this conclusion. The PC-SAFT and PR EOSs were used in order to calculate onset pressures at different temperatures. Fig. 8 indicates the subsequent calculations using the two EOSs for the two oil samples. In this figure, the results are compared with the experimental data and also with the modeling results reported by Buenrostro‐Gonzalez et al. [38]. According to Table 6, it can be deduced that the results of onset pressure calculations are better assuming poly-disperse Asphaltene than monodisperse Asphaltenes. In the next step, the amount of Asphaltene precipitation caused by addition of n-pentane solvent was determined using PR and PC-SAFT EOSs. In this step, Asphaltene was broken into three sub-components and it was assumed that it would precipitate in solid-solution form. The flow diagram for the calculation of Asphaltene precipitation amount is presented in Fig. 9. In Fig. 10, the results of modeling Asphaltene precipitation due to addition of n-pentane solvent for the oil samples using the two mentioned EOSs are presented. As Table 6 shows, the results of PC-SAFT EOS for calculations of Asphaltene precipitation amount indicates a lower MAPE compared to those obtained using PR EOS. Considering this table, the best results were obtained when PC-SAFT EOS and UNIQUAC activity coefficient models

• •

termination of the parameters of “Saturates + Aromatics” pseudocomponent, resin and three Asphaltene sub-components, based on dilution data. This method leads to improvements in crude oil sample characterization and estimation accuracy of the EOS parameters. Calculation of the amount of precipitated Asphaltene was performed with main emphasis on the solid phase method. Asphaltene was split into three sub-components, considering that Asphaltene would precipitate in the solid-solution form, based on the precipitating solvent. With this method improvements in the results were observed, especially for determination of the precipitated Asphaltene amount. Good consistency was observed between modeling results and the experimental data when the UNIFAC method was used for calculating the parameters of Asphaltene required for UNIQUAC activity coefficients. Generally, best results were obtained for the studied samples, when PC-SAFT EOS and solid-solution model were used for description of liquid-vapor equilibrium and Asphaltene phase. Modeling results indicated improvements when a solid-solution method was used instead of a multi-solid one (compared to the work of Hosseinzadeh Dehaghani et al. [1]). However, it should also be mentioned that due to the higher number of optimization (regression) parameters, more complicated implementation and higher uncertainty are expected for solid-solution modeling. Future effort could focus on reduction of the number of adjustable parameters used in this method.

Author contributions This scientific manuscript has been extracted from two master theses. Yasaman Hosseinzadeh Dehaghani and Hossein Ahmadinezhad are graduated master students. They have done the data gathering and model programming. Farzaneh Feyzi and Mehdi Assareh are the supervisors of the master theses. They have proposed the modeling approach and supervise/help its implementation. The corresponding author (Mehdi Assareh) is responsible for ensuring that the descriptions are accurate and agreed by all authors. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A The correlations for calculation of critical properties and acentric factors of different pseudo-components were as follows: 10

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“Saturates + Aromatics” pseudo-component: For this pseudo-component, the correlations provided by Riazi and Al-Sahhaf [43] were used for primary estimation because they rely only on molecular weight and still provides good accuracy. This relationship is as follows:

=

exp(a

(A-1)

bMW c )

where θ is the critical property such as Tc and is the limiting value for that property as MW . Different properties of n-alkanes, n-alkylcyclopentanes and n-alkylbenzenes (e.g. Tc, Pc and ) and also constants in Eq. (2) (a, b, c and ) are given in Ref. [43]. Resin and Asphaltene pseudo-component: There are no simple and precise relationships for these components. However, these components include a variety of poly-nuclear aromatics. Avaullee et al. [44] presented the following correlations to estimate the critical properties and acentric factor of Asphaltenes and resins. (A-2)

Tc / K = 77.856MW 0.4708

Pc / bar = 1891.4MW

(A-3)

0.7975

= cf {0.5837 ln(MW )

(A-4)

2.5389}

here, MW is the molecular weight of the component in g⁄mol and cf is the correction factor. While resins and Asphaltenes are both poly-nuclear aromatics, there are minor structural differences between these components. These differences were calculated with a different correction factor for each component. The cf values for resins and Asphaltenes are reported in Ref. [44]. The correlations for PC-SAFT EOS parameters of different pseudo-components were as follows: “Saturates + Aromatics” and Resin pseudo-components: The parameters of PC-SAFT EOS for “Saturates + Aromatics” and resin pseudo-components were also determined from the correlations (A-5) to (A-7) developed by Assareh et al. [45] for each oil fraction. These relationships are functions of molecular weight (MW) and specific gravity (S).

m = 33.58 + 0.08816MW m. m.

3

k

=

90.75S

75.14 + 2.848 MW + 231.7 S

= 3372 + 11.24 MW

8955 S

(A-5)

0.07727MW . S + 61.01S 2 1.288 MW . S

186.9

(A-6)

S2

5.925 MW . S + 6136 S 2

(A-7)

Asphaltene pseudo-component: The correlations proposed by Gonzalez et al. [46] have been used for initial estimation of PC-SAFT EOS parameters for Asphaltene pseudo-component ((A-8) to (A-10)).

m = (1

(A-8)

)(0.0223 MW + 0.751) + (0.0101 MW + 1.7296)

(A) = (1

/ k (K ) = (1

)(4.1377

(38.1483)/ MW ) +

)(0.00436MW + 283.93) +

(4.6169

508

(A-9)

(93.98)/ MW )

234100 (MW )1.5

(A-10)

where is aromaticity parameter of the Asphaltene. The parameter of aromaticity used in these correlations determines the Asphaltene pseudocomponent tendency to behave as a poly-nuclear aromatic ( = 1) or as a benzene derivative component ( = 0). Appendix B Based on Mullins et al. [51], initially a monomer Asphaltene structure was considered. This structure is shown in Fig. B1. Then, by using UNIFAC method [47,48], r and q parameters for the UNIQUAC activity coefficient model were estimated depending on Eqs. (B-1) and (B-2). UNIFAC method is based on the concept that a liquid mixture could be considered as a solution of structural units in which molecules are made from these units. These structural units are called sub-groups [49].

vk(i) Rk

ri =

(B-1)

k

Fig. B1. The hypothetical structure of the monomer Asphaltene [51].

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vk(i) Qk

qi =

(B-2)

k

In Eqs. (B-1) and (B-2), k indicates each sub-group. Rk and Qk are relative volume and relative area, respectively. Index “i” represents each type. vk(i) is the number of sub-groups of kind “k” in a molecule of type “i”. Properties of sub-groups, Rk and Qk were used from the available data in the literature. Sub-groups which form Asphaltene are reported in Table B1. Table B1 Parameters of UNIFAC method [52]. Subgroup

Rk

Qk

AC (aromatic carbon) ACH CH3 CH2 CH ACCH2 Pyrrole CH2S

0.3652 0.5313 0.9011 0.6744 0.4469 1.0396 2.5734 1.3863

0.1200 0.4000 0.8480 0.5400 0.2280 0.6600 1.8240 1.0600

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