A novel method to predict the risk of asphaltene precipitation due to CO2 displacement in oil reservoirs

A novel method to predict the risk of asphaltene precipitation due to CO2 displacement in oil reservoirs

Accepted Manuscript A novel method to predict the risk of asphaltene precipitation due to CO2 displacement in oil reservoirs Luisa L.O. Setaro, Verôni...

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Accepted Manuscript A novel method to predict the risk of asphaltene precipitation due to CO2 displacement in oil reservoirs Luisa L.O. Setaro, Verônica J. Pereira, Gloria M.N. Costa, Silvio A.B. Vieira de Melo PII:

S0920-4105(19)30138-X

DOI:

https://doi.org/10.1016/j.petrol.2019.02.011

Reference:

PETROL 5768

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 17 July 2018 Revised Date:

31 January 2019

Accepted Date: 4 February 2019

Please cite this article as: Setaro, L.L.O., Pereira, Verô.J., Costa, G.M.N., Vieira de Melo, S.A.B., A novel method to predict the risk of asphaltene precipitation due to CO2 displacement in oil reservoirs, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/j.petrol.2019.02.011. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT A NOVEL METHOD TO PREDICT THE RISK OF ASPHALTENE PRECIPITATION DUE TO CO2 DISPLACEMENT IN OIL RESERVOIRS Luisa L.O. Setaro1, Verônica J. Pereira1, Gloria M.N. Costa1 Silvio A.B. Vieira de Melo1,2* 1

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Programa de Engenharia Industrial, Escola Politécnica, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, 6º. andar, Federação, 40210-630, Salvador, Bahia, Brazil. 2 Centro Interdisciplinar em Energia e Ambiente, Campus Universitário da Federação/Ondina, Universidade Federal da Bahia, 40170-115, Salvador, Bahia, Brazil.

* To whom correspondence should be addressed: [email protected] Abstract

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A new fully predictive method was developed to calculate the risk of asphaltene precipitation in oil reservoirs based on a modification of the Asphaltene Instability Trend (ASIST) method. For prediction of asphaltene precipitation by oil depletion, this new method simplifies the ASIST method in order to use a minimum number of experimental data. As a novelty, prediction of asphaltene precipitation by CO2 displacement using a modification of the ASIST method is introduced. Both modifications were validated for a large number of oils from the literature. Results show that with both modifications this new method provides better results than previous ones to predict the risk of asphaltene precipitation in oils by depletion and unprecedented good results to evaluate potential asphaltene precipitation in oil reservoirs due to CO2 displacement with requirement of few experimental data. The proposed method may be used in the oil and gas industry to predict the risk of asphaltene precipitation by depletion or by CO2 displacement. Keywords: asphaltene precipitation, ASIST method, oil stability, solubility parameter, CO2 injection

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1. Introduction

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Evaluation of the risk of asphaltene precipitation in oil reservoirs and production facilities is always necessary to avoid falls in productivity. Asphaltene precipitation can occur due to changes in temperature, pressure and composition, for instance, during oil depletion or CO2 displacement. Among the problems caused by asphaltene precipitation, some of the most

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found are clogging the wellbores and other expensive equipments used in oil recovery as well as changing reservoir wettability, which may increase the oil production cost. CO2 displacement is a widely used enhanced oil recovery method due especially to the changes in the oil system and to the CO2 sequestration. In the latter case, asphaltene precipitation is more likely to increase as the amount of CO2 injected increases. In the literature, several methods

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have been reported to predict the risk of asphaltene precipitation, but none of them are widely accepted (Branco et al., 2001; Cho et al., 2019; Hirschberg et al., 1984; Mohebbinia et al.,

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2017; Moradi et al., 2012; Solaimany-Nazar and Zonnouri, 2011; Zahedi et al, 2009; Zanganeh et al., 2015). Moreover, most require a large amount of experimental data, which often cannot be easily measured as high-cost specific equipment and quite time-consuming experimental runs are needed. Therefore, an alternative way to predict the risk of asphaltene precipitation is the use of screening methods because usually few input data are needed and

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SARA analysis can be used in most cases.

The screening method proposed by de Boer et al. (1995) takes into account the density of the oil as well as the difference between the initial pressure and the bubble pressure, and allows the graphic prediction of the risk of asphaltene precipitation. A different approach was

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introduced by Yen et al. (2001), who considers the system a colloidal mixture formed of the constituents of SARA analysis: saturates, aromatics, resins and asphaltenes. Ashoori et al.

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(2016) studied the impact of each fraction of SARA analysis on Yen’s method. They stated that Yen’s method provides a good prediction of the risk of asphaltene precipitation for heavy oils, particularly, those oils with a high amount of saturates tend to face more problems of asphaltene precipitation.

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Jamaluddin’s method, in contrast, requires only the weight fractions of asphaltene and resins from SARA analysis (Jamaluddin et al., 2002). In another method, proposed by Bahrami et al. (2015), a relationship between the ratios of saturates to aromatics and asphaltenes to resins is needed. More recently, Pereira et al. (2017) carried out an extensive

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comparative study of all these four methods for a data bank of 172 oils built from the literature. They also proposed two new methods based on the improvement of de Boer’s and Jamaluddin’s ones. In the first, de Boers’s method was modified taking in account only experimental oil stability data in order to use input data which is easier to find than in its original form. In the second, a simplification of Jamaluddin’s method was proposed and

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provided better results.

Another approach to predict the onset of asphaltene precipitation by oil depletion was

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proposed by Wang et al. (2006) and named the Asphaltene Instability Trend (ASIST) method. Although it is theoretically well grounded, it requires several input data: the formation volume factor (FVF) at the bubble point and at 1 atm, the gas to oil ratio (GOR) at the bubble point, the onset solubility parameter (measured from n-C7 titration) and the temperature at n-C7 titration. These data are not usually easily determined. To overcome this

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and extend its use, we propose a new method to predict the risk of asphaltene precipitation for oil depletion, based on a simplification of the ASIST method, which is particularly useful when these input data are not available. Table 1 shows technical details and observations on

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some methods to predict the risk of asphaltene precipitation.

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ACCEPTED MANUSCRIPT Table 1. Comparison of methods that predict the risk of asphaltene precipitation. Method

Technique

Observations

de Boer et al. (1995)

First screening tool proposed to identify the risk of asphaltene precipitation Based on thermodynamics Needs density of the oil, bubble point pressure and initial pressure Based on the colloidal instability index, the mixture is a colloid Requires all four fractions of SARA analysis Based on asphaltene and resins weight percent Needs asphaltenes and resins fractions obtained through SARA analysis

Experimental data may be difficult to find/measure

Vargas et al. (2009)

Bahrami et al. (2015) Sulaimon and Govindasamy (2015)

Pereira et al. (2017) 1

Pereira et al. (2017) 2

Modification on Jamaluddin’s method, therefore the theories are similar Asphaltene and resins fractions from SARA analysis are needed Modification on de Boer’s method, similar theories Requires asphaltene and resins fractions from SARA analysis, bubble point pressure and initial pressure Created a simulation tool to predict the risk of asphaltene precipitation based on de Boer and Wang’s methods Specific gravity, API gravity, onset solubility parameter and its temperature, oil flow rate, flowing bottomhole pressure, GOR, reservoir pressure and temperature, wellhead temperature, tubing ID, well inclination angle, well depth, tubing roughness are the variables needed Based on Wang’s method, similar theories Completely predictive, does not need experimental data difficult to find/measure Based on Wang’s method, similar theories Proposal to use Wang’s method for oils with CO2 displacement Only one among the methods that considers CO2 injection Completely predictive, does not need experimental data difficult to find/measure

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Al-Safran (2018)

This paper 1 (ASIST by depletion) This paper 2 (ASIST by CO2 injection)

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Based on the difference between the solubility parameters of the solute and the solvent Proposed a curve between solubility parameters, cohesive energy, pressure and composition along the bubble point pressure and onset of asphaltene precipitation Considers resins peptizing agents Requires all four fractions of SARA Proposed a new approach of Yen’s method: instead of requiring SARA analysis data, it uses the molecular weight of the lumped components

Showed good results

Pereira et al. (2017) analyzed four screening techniques and found out this method was the least reliable Experimental data required may make it difficult to use Requires data difficult to find

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Wang et al. (2006)

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Jamaluddin et al. (2002)

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Yen et al. (2001)

Showed good results They tested it with four different oils and the results were satisfactory when compared to Yen’s method Provided better results than Jamaluddin’s method

Good results and the required data makes it easier to use than de Boer’s method

Experimental data required may be difficult to find/calculate

Easier to use than Wang’s method because of the need of less experimental data as input Showed good results

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Although the ASIST method requires many experimental data, it is widely used in the industry on its original form to evaluate the preliminary risk of asphaltene precipitation. In the literature, there are also some modifications of this method available regardless none of them similar to the modifications proposed in this work. For instance, Dolati et al. (2015)

reservoir conditions using routine PVT experimental data.

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extended the ASIST method to predict the onset pressure of asphaltene precipitation on

The ASIST method has been tested with a number of oils in the literature and has proven to be a good method to predict the risk of asphaltene precipitation (Creek et al., 2009).

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In some reservoirs, it was possible to adjust field work using the ASIST method to predict the risk of asphaltene precipitation. This method accurately predicted asphaltene instability

reservoirs (Whitfield, 2015).

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during early stages of production and during the injection of inhibitors on two different

We consider relevant investigating the onset of asphaltene precipitation based on the difference between solubility parameters as it is a simple and efficient method. The ASIST method, based on the difference between solubility parameters, is an established method although it needs longstanding experimental data. For these reasons, we found out a good

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opportunity to simplify this method and extend its application to CO2 injection. The purpose of the present work is precisely to avoid the use of experimental and/or field data, procedures that may be expensive and longstanding. Two modifications were done to simplify the ASIST method to calculate the risk of asphaltene precipitation by depletion.

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The first considers that the onset solubility parameter and the temperature at n-C7 titration are fixed at the average values calculated using experimental data of 27 oils as proposed by

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Wang et al. (2006). The second approach assumes that both the formation volume factors (FVF) and the gas to oil ratio (GOR) can be calculated by equations of state (EOS) instead of experimental values. For this calculation, Pedersen’s characterization was used with the Péneloux volume correction (Pedersen et al., 2015; Péneloux et al., 1982).

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In the present work, the risk of asphaltene precipitation was evaluated using a totally predictive approach not only by oil depletion but also due to CO2 displacement. As the addition of CO2 alters the oil composition and reservoir conditions, it may cause asphaltene precipitation. Therefore, it is necessary to know the amount of CO2 that can be injected

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before asphaltene starts to precipitate. However, there is no reliable and accurate screening method to predict the potential asphaltene precipitation due to CO2 injection reported in the literature. As a result of the improvements in the modified ASIST method to predict the risk of asphaltene precipitation by depletion, a new method is proposed to calculate the risk of asphaltene precipitation due to CO2 displacement. This novel method is based on a

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modification that consists of the calculation of the solubility parameter of CO2 using an EOS, and Pedersen’s characterization to calculate FVF and GOR with the Péneloux volume

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correction (Pedersen et al., 2015; Péneloux et al., 1982). In this case, only the recombined oil bubble point pressure at the desired CO2 molar fraction is required as input data. The modifications proposed in this study for the ASIST method were first validated with 27 oils with experimental data available, provided by Wang et al. (2006). The results of the solubility parameter, used to calculate the risk of asphaltene precipitation in live oil, were

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compared for two cases: solubility parameter calculated with the experimental data and solubility parameter obtained from the average values of this parameter. Ten different oils from the literature with data of asphaltene precipitation were used to validate the modified ASIST method for the case of oil depletion and the results were good. Other ten oils were

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used to validate the case of CO2 displacement. We also compared this new method with the modified Jamaluddin’s method for the case of oil depletion. The comparison for CO2

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displacement was not possible because Jamaluddin’s method is not applicable.

2.Materials and methods

2.1 Evaluation of the risk of asphaltene precipitation by oil depletion The ASIST method describes the risk of asphaltene precipitation based on the asphaltene instability, which indicates that precipitation can occur. This screening method is based on the linear extrapolation of the onset solubility parameter and the square root of the partial molar volume of a precipitant for a series of n-paraffins (Creek et al., 2009; Whitfield, 2015). As reported by Wang et al. (2006), the ASIST method proved to be more accurate than de Boer’s method to predict the risk of asphaltene precipitation.

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The Single Point ASIST method, proposed by Wang et al. (2006), is a simplification of the original ASIST method that calculates the risk of asphaltene precipitation through Eqs 1 to 6: 1/ 2 δ instabilit y , Pb = δ onset , nC 7 − 0.0128(Tres − Tmeas ) − 0.146 (v 1nC/ 27 − vlight , Pb )

δ live−oil ,Pb =

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1.3297 x10 5 ( FVFPb − FVFo ) GORPb

(2)

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vlight , Pb =

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2 v1nC/ 27 = 4.01x10−5 Tres + 4.60 x10−3 Tres + 11.97)

(1)

 GORPb 1 1   + 3.91x10−4 δ STO + 2.9041 − Rlight FVFPb FVFPb  FVFPb 

Rlight = −15.9

xC1−C 3 + 23 xC1−C 6

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δ STO = − 0 .078 API + 20 .426

(3)

(4)

(5)

(6)

(MPa1/2); δonset,

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where δinstability,Pb is the solubility parameter of asphaltene instability potential in live oil nC7

is the solubility parameter at the beginning of the precipitation of the

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stock-tank oil (STO) obtained with titration of n-C7 (MPa1/ 2); Tres is the reservoir temperature (ºC); Tmeas is the titration temperature with n-C7 (ºC); νnC7 is the molar volume of n-C7 (cm3/mol); νlight,Pb is the molar volume of the light ends at the bubble point (cm3/mol); FVFPb is the formation volume factor in bubble pressure (rb/stb); FVFo is the formation volume factor at 1 atm (rb/stb); GORPb is the gas-oil ratio at bubble pressure (scf/stb); δlive-oil,Pb is the solubility parameter of live oil at bubble pressure (MPa1/2); δSTO is the solubility parameter for STO under standard conditions (1 atm, 15.56 ºC) (MPa1/2); Rlight is the molar refraction of the light ends (cm3/mol); API is the API gravity at 1 atm and 15.56 °C; XC1-C3 is the mole fraction of C1-C3; XC1-C6 is the mole fraction of C1-C6. The light ends of oil are usually the sum of the molar fractions of the lightest components of the oil, such as the gases (the first

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carbon molar fractions). The heavy ends are the heaviest oil components, usually the sum of the last carbon molar fractions. According to this method, the risk of asphaltene precipitation is predicted by the following comparison:

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if δlive-oil,Pb > δinstability,Pb, there is no risk of asphaltene precipitation (the oil is referred to as stable);

if δlive-oil,Pb < δinstability,Pb, the asphaltene precipitation is expected (the oil is referred to

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as unstable).

The ASIST method is based on the difference between the solubility parameters of the solvent and the solute. The greater this difference is, the higher the risk of asphaltene

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precipitation. To use ASIST method, many experimental input data are required, which are difficult to obtain due to the cost and/or to the demand of time to perform such experiments. Wang et al. (2006) present data on the temperature at which titration with n-C7 is carried out (Tmeas) and the solubility parameter obtained at the beginning of precipitation in titration with n-C7 (δonset,nC7) for 27 different oils. Because this titration is often difficult and costly to perform, as the first simplification we suggest using the average values of these two input

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variables for these 27 oils: Tmeas = 59.58 ºC and δonset,nC7 = 16.27 MPa1/ 2. Thus, in the absence of titration with n-C7 experimental data, this method can be applied with these average values. Therefore, the aim of this work is to speed up the calculation of the risk of

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asphaltene precipitation using less experimental data than those proposed by Wang et al. (2006). These data allow finding the mean values of the solubility parameters of the solvent

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and the solute, keeping the principle of the difference between these solubility parameters. The second simplification consists of the calculation of both FVF and GOR values

using an EOS, instead of experimental values. Therefore, Pedersen’s characterization, with the Soave-Redlich-Kwong (SRK) equation of state (EOS) and the Péneloux volume correction were used (Pedersen et al., 2015; Péneloux et al., 1982; Soave, 1972). The SRK EOS is a simple equation of state that needs few input data, easily reaches convergence in calculation of phase equilibrium and has showed itself very efficient in countless works involving asphaltene precipitation. For this reason, it was chosen in the present work to calculate FVF and GOR values. Thus, there is a reduction in the number of experimental data required, avoiding the need to perform costly and time-consuming experiments. Experimental

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determination of each FVF data requires about five days if the PVT cell is used (total of ten working days in order to obtain FVF values at 1 atm and at the bubble pressure) and GOR measurement needs around 75 hours plus the time required to obtain the volume of oil production in the field in one day.

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Pedersen’s characterization is used to expand the C7+ fraction into as many pseudocomponents (fractions) as necessary. Eq 7 allows the calculation of the carbon number of the fractions as a function of the molar fraction if parameters "a" and "b" are known. Eq 8 expresses the relationship between the molecular weight and the carbon number of the

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fractions. Eq 9 expresses the density as a function of the number of carbons in these fractions.

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C N = a + b ln( x N )

MW = 14 C N − 4

ρ N = c + d ln( C N )

(7)

(8)

(9)

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where CN is the carbon number; xN is the molar fraction; MW is the molecular weight and ρN is the density of the carbon fraction.

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Prior to the use of SRK EOS with the Péneloux volume correction, it is necessary to calculate the critical properties and the acentric factor for each fraction in the mixture using the characterization method proposed by Pedersen expressed in Eqs 10 to 12 (Pedersen et al.,

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2015; Péneloux et al., 1982; Soave, 1972).

TC = d1 SG + d 2 ln(MW ) + d 3 MW + d 4

ln( PC ) = d 5 + d 6 SG +

d7

MW

+

d8

(10) MW

(11) MW 2

w = d 9 + d10 MW + d11SG + d12 MW 2

(12)

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where Tc is the critical temperature; SG is the density; Pc is the critical pressure; w is the acentric factor for each fraction and d1 to d12 are specific constants to SRK EOS proposed by Pedersen method. The global constants d1 through d12 presented in Eqs 10 to 12 are valid for

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each EOS and can be found in Pedersen et al. (2015).

The modifications proposed in this study for the ASIST method were validated using a 27-oil databank with experimental data available (Wang et al., 2006). The results of the solubility parameter to calculate the risk of asphaltene instability in live oil were compared for two cases: when there is experimental data and without experimental data, when the

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average parameters should be used. Further validation was carried out using ten other oils with asphaltene precipitation data used in the modified ASIST method proposed in this work,

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providing quite good results. With experimental values provided by Wang et al. (2006), it is possible to calculate the solubility parameter for the risk of asphaltene instability in live oil (using equation 1).

2.2 Evaluation of the risk of asphaltene precipitation by CO2 displacement

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When CO2 is injected into oil reservoirs, the risk of asphaltene precipitation is evaluated through the calculation of the solubility parameter of live oil at bubble pressure using Eqs 4 to 6. In this case Eqs 1 to 3 are not used because the solvent is just CO2, i.e. the

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solvent n-C7 is not needed. With CO2 as the solvent, its solubility parameter is needed instead of the solubility parameter of asphaltene instability potential in live oil. An important point to highlight is that the bubble pressure is the experimental bubble pressure of the recombined oil

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with the injected amount of CO2. Giddings et al. (1968) presented an equation to calculate the solubility parameter of CO2, as given by Eq 13.

 ρr    ρ  r (liq ) 

(13)

δ g = 0.326(Pc )0.5 

where

is the solubility parameter of CO2 (cal/cm3)0.5; Pc is the critical pressure (psia);

the reduced density, defined as

( is the density and

is the critical density);

is is

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the reduced density of liquid at its normal boiling point (a constant equal to 2.66). CO2 density is obtained using Reynolds equation.

For oils with an amount of CO2 lower than 40 %, the risk of asphaltene precipitation is

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predicted by the following comparison: If δlive-oil,Pb > δg, there is no risk of asphaltene precipitation (the oil is referred to as stable).

If δlive-oil,Pb < δg, the asphaltene precipitation is expected (the oil is referred to as

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unstable).

In the present work, we observed that for oils with CO2 molar fraction higher than 40

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% the results were not so good. Eqs. (14) to (16) were used to correct the solubility parameter and they were obtained by trial and error in comparison with experimental data. Another relevant fact is that if we examine experimental data in the literature, most oils show that the amount of CO2 injected before asphaltene starts to precipitate is often above 40 %. That is, it does not matter the oil composition neither the system temperature. Further, for most reservoirs, 40 % is the amount of CO2 injected at which the destabilization

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of phase equilibria starts, i.e., the onset of asphaltene precipitation. The following experimental studies indicate that the amount of CO2 injected at which asphaltene precipitation starts is quite often above 40%: Takahashi et al. (2003), Vafaie-Sefti and

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Mousavi-Dehghani (2006), Moghadasi et al. (2006), Nakhli et al. (2011), Adyani et al. (2011), Novosad and Costain (1990), Yang et al. (1999), Hu et al. (2004), Srivastava and Huang (1997). In these references, out of 9 oils, 6 show asphaltene precipitation when CO2

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injection is between 40 % and 50 %; two of them show asphaltene precipitation above 50 % of CO2 injection and only one shows precipitation under 40 % of CO2 injection. Therefore, in order to achieve a more accurate result, an additional adjustment is required when asphaltene precipitation is more likely to start: for injections of CO2 above 40 %.

α=

δ live − oil , Pb δg

(14)

(15)

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α x C1−C 3 x C1−C 6 (16)

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δ g* = β .δ g

where δlive-oil,Pb is the solubility parameter of live oil at bubble pressure (MPa1/2);

is the

solubility parameter of CO2 (MPa1/2); α is the first correction parameter; XC1-C3 is the mole

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fraction of C1-C3; XC1-C6 is the mole fraction of C1-C6; β is the second correction parameter is the corrected value for the solubility parameter of CO2.

and

predicted by the following comparison: if δlive-oil,Pb >

, there is no risk of asphaltene precipitation (the oil is referred to as

stable); if δlive-oil,Pb <

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For oils with a CO2 content higher than 40 %, the risk of asphaltene precipitation is

, the asphaltene precipitation is expected (the oil is referred to as

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unstable).

3. Results and Discussion

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3.1 The risk of asphaltene precipitation by oil depletion Wang’s experimental data of solubility parameter of the unstable asphaltene in live oil

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varied from 16.41 to 27.91 MPa1/2. Using the mean values of δonset,nC7 (16.27 MPa1/2) and Tmeas (59.58 ºC) as input data to calculate the solubility parameter of the unstable asphaltene in live oil (δinstability,Pb) instead of the 27 experimental data measured in the titration (Wang et al., 2006) the values varied from 15.39 to 27.27 MPa1/2. The maximum, mean and minimum deviations were 5.47 %, 2.09 % and 0.03 %, respectively. The mean standard deviation of the solubility parameter of the unstable asphaltene was ±0.35 MPa1/2, therefore, this approach provides acceptable results. In Figure 1, a comparison is made between the results of the solubility parameter of the unstable asphaltene in live oil (required in order to use ASIST method) calculated using two approaches. The first one using the experimental data of Tmeas and δonset,nC7 shown by

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Wang et al. (2006) and the second one using the mean values of the 27 experimental data employed in the first approach. The main difference between these approaches is that in the second one both solubility parameters are constant. The use of SRK-EOS with Pedersen’s characterization to calculate the gas-oil ratio

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and the formation volume factors (at 1 atm and at the bubble pressure), as well as the mean values of the onset solubility parameter and the temperature at n-C7 titration, makes the method proposed in the present work completely predictive and easier to use than the ASIST method (Pedersen, 2015). This is because fewer input data are required (only the reservoir

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temperature, composition, bubble pressure and API). This new method was validated for ten oils with experimental data on asphaltene precipitation (unstable oils) available in the literature. Unlike Wang et al. (2006), where no data regarding the oil stability is provided, in

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the present study only oils previously known as unstable were considered to validate this new

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method. This ensures that the prediction can be compared to the experimental data.

Figure 1. Comparison between solubility parameter values for asphaltene instability in live oil (δinstability,Pb) calculated using the experimental data of Tmeas and δonset,nC7 or using their mean values. Using Pedersen’s characterization in the software SPECS® (Separation and Phase Equilibrium Calculations, Technical University of Denmark), this new method was tested for ten unstable oils in which asphaltene precipitation by depletion occurs. It is very difficult to validate the proposed method using stable oils, i.e., in conditions where there is no asphaltene precipitation, because the pressure should be lower than the inferior limit of the asphaltene

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precipitation envelope (APE) to consider the oil as stable. Generally, the lower limit of the APE is not experimentally determined because the main interest is to know the higher limit of the APE, that is, throughout the process of depletion, which is the maximum pressure where precipitation starts. The composition of the oils and SARA analysis (when available) are

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shown in Table 2. Prior to use the SRK EOS, it is necessary to estimate the binary interaction parameter (kij) between the lightest and heaviest components, using bubble pressure experimental data (Soave, 1972). The fit of kij is only required for the lightest (C1) and heaviest (C7+)

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components because it expresses the biggest difference in the molecular mass and structure. Therefore, this should not be zero. The results are shown in Table 3, including the bubble

Deviation(%) = 100.

Pb ,exp − Pb ,cal Pb ,exp

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pressure relative deviation (%) between the experimental and calculated data, given by Eq 17.

(17)

Table 2. Composition and SARA analysis of the ten unstable oils (oils O1 to O10). O3

0.21 5.14 2.70 22.00 7.10 5.34 0.99 2.78 1.12 1.41 5.55 45.66 30.10 42.10 13.36 13.75

0.39 1.74 0.00 20.55 7.31 5.34 1.00 3.65 3.10 4.75 5.48 46.69 24.80 45.60 16.80 12.80

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0.06 2.45 0.59 38.65 6.66 5.33 1.01 2.92 1.24 1.51 4.67 34.92 65.46 19.44 6.40 8.70

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Component N2 CO2 H2S C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7+ Saturates Aromatics Resins Asphaltenes

O2

O4

O5

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O1

0.49 11.37 3.22 27.36 9.41 6.70 0.81 3.17 1.22 1.98 2.49 31.79 57.40 30.80 10.40 1.40

O6

O7

Composition (%) 0.48 0.91 0.47 0.92 1.57 1.59 0.00 5.39 1.44 43.43 24.02 32.22 11.02 10.09 12.42 6.55 9.58 10.29 0.79 1.83 2.03 3.70 4.83 4.87 1.28 2.27 2.22 2.25 2.74 2.71 2.70 4.77 4.12 26.88 32.00 25.62 68.30 54.67 55.14 11.60 28.89 30.73 18.80 12.66 10.88 1.30 3.08 3.25

O8

O9

O10

0.16 1.78 1.63 21.34 9.51 8.13 1.20 4.85 1.93 0.00 2.85 42.43 ---------

0.17 2.04 1.75 16.47 8.66 8.21 1.35 4.84 1.87 0.01 3.15 46.30 47.98 44.42 6.29 1.32

0.80 0.05 0.00 51.02 8.09 6.02 1.14 2.83 1.58 1.63 2.67 24.17 65.60 16.30 13.50 4.60

---: data not provided. References: O1 and O2: Moradi et al. (2012); O3: Bahrami et al. (2015); O4: Gonzalez et al. (2008); O5: Mohammadi et al. (2012); O6 and O7: Buenrosto-Gonzalez et al. (2004); O8 and O9: Yonebayashi et al. (2009); O10: Jamaluddin et al. (2001).

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Table 3. Binary interaction parameter of SRK EOS, experimental and calculated bubble pressure (Pb) at reservoir temperature (Tres), and bubble pressure deviation for oils O1 to O10. Tres (K)

Pb,exp (MPa)

kij

Pb,cal (MPa)

Deviation (%)

O1 O2 O3 O4 O5 O6 O7 O8 O9 O10

358.15 397.04 369.25 419.82 389.15 393.00 410.00 388.71 391.48 355.15

18.94 11.87 9.88 20.99 22.68 17.10 20.27 10.60 8.50 29.38

-0.113 -0.213 -0.146 -0.117 -0.231 -0.023 -0.034 -0.231 -0.246 -0.080

18.94 11.88 9.88 21.00 22.69 17.07 20.26 10.61 8.51 29.89

0.020 0.062 0.061 0.026 0.041 0.153 0.074 0.048 0.061 1.743

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Oil

Using the kij values of Table 3, the FVF value was calculated for oil depletion at the bubble pressure and at 1 atm to be used in Eqs 3 and 4. GOR value was obtained through a flash calculation at the bubble pressure and reservoir temperature and the liquid volume to vapor volume ratio was calculated to be used in Eqs 3 and 4. The results are shown in Table

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4.

Table 4. FVF and GOR results using Pedersen’s characterization (Pedersen et al., 2015) for oils O1 to O10. FVF (1 atm) (rb/stb)

FVF (Pb) (rb/stb)

GOR (Pb) (scf/stb)

O1 O2 O3 O4 O5 O6 O7 O8 O9 O10

1.0228 1.0394 1.0281 1.0666 1.0485 1.0367 1.0551 1.0562 1.0587 1.0197

1.3541 1.3007 1.281 1.6512 2.2900 1.4707 1.7471 1.5545 1.5136 1.4699

7.08 4.57 4.12 5.64 5.89 6.42 6.10 3.54 2.93 9.11

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Oil

Table 5 shows the values of the solubility parameters calculated using the FVF and GOR values of Table 4. The differences between the solubility parameters indicate that

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asphaltene precipitation occurs and these results match the experimental observation reported in the literature. Therefore, it can be concluded that the use of the average values of the two parameters as input data combined with the use of EOS, Pedersen’s characterization and Péneloux volume correction, are adequate for these oils (Pedersen et al., 2015; Péneloux et

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al., 1982).

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Table 5. Solubility parameter using Pedersen’s characterization (Pedersen et al., 2015) to predict the risk of asphaltene precipitation by oil depletion (for oils O1 to O10). Asphaltene δlive-oil,Pb δinst,Pb Oil 0.5 0.5 precipiation (MPa ) (MPa ) O1 14.48 25.61 Yes O2 15.19 26.26 Yes O3 15.36 27.14 Yes O4 12.02 30.32 Yes O5 9.24 38.09 Yes O6 13.15 27.44 Yes O7 10.86 31.26 Yes O8 12.39 33.63 Yes O9 12.65 34.63 Yes O10 13.15 25.98 Yes

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From the simplification of the ASIST method, the new method proposed here becomes completely predictive and does not need five experimental input data (named FVF at 1 atm, FVF at the bubble point, GOR at the bubble point, the solubility parameter obtained at the beginning of precipitation in titration with n-C7 and the temperature at which titration

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with n-C7 is carried out). Thus, it is easier to use this method because the required input data can be considered constant or calculated using an EOS.

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The new method proposed here was further evaluated by comparison with Pereira’s method to predict the risk of asphaltene precipitation by oil depletion (Pereira et al., 2017). Pereira et al. (2017) performed an extensive evaluation of four well-known screening methods used to predict the risk of asphaltene precipitation by depletion, using over 140 different oils to test and compare them. They also proposed two modified methods; the one shown in Figure 2 in the present work is a modification of the method of Jamaluddin et al. (2002). In their study, Pereira et al. (2017) observed that Jamaluddin’s method would be more accurate. Therefore, a modification was proposed by Pereira et al. (2017), which is compared to the ASIST method in the present work. The results using Pereira et al.’s method are shown in Figure 2, where two regions can be seen: a stable one under the straight line and

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an unstable one above it. The risk of asphaltene precipitation increases as the percentage of resins decreases. The data required by Pereira’s method are the fractions of asphaltenes and resins, both obtained through SARA analysis. Tests with the same nine unstable oils (except for oil O8, for which there is no SARA analysis available) report only one different

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prediction by both methods, as shown in Table 6.

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Figure 2. Results of Pereira et al.’s method for the 9 unstable oils (Pereira et al., 2017).

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Table 6. Results for 10 unstable oils tested. Method O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Proposed method P P P P P P P P P P Pereira et al. Not P P P P N P P P P (2017) tested “P” is for asphaltene precipitation predicted and “N” is for no asphaltene precipitation predicted. The result wrongly predicted by Pereira et al. (2017) for oil O5 may be due to its high

resin content and low asphaltene content. On the other hand, the new method proposed in the present work can correctly predict the asphaltene precipitation for all these ten oils, including oil O5.

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ACCEPTED MANUSCRIPT 3.2 The risk of asphaltene precipitation by CO2 displacement

This new method was developed to predict the risk of asphaltene precipitation due to CO2 injection, based on a modification of the ASIST method, and validated for ten oils. Table 7 shows the recombined composition values of these oils obtained from the literature, where

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the following experimental data were also available: the amount of CO2 injected, the bubble pressure of the recombined oil with the amount of CO2 injected, and if asphaltene precipitates or not.

Table 7. Composition of the recombined oils used for CO2 displacement.

-----

0.95 1.23 0.30 4.46 2.97 4.72 0.80 1.91 1.26 2.18 0.00 79.22

Composition (%) 0.95 0.11 0.11 0.11 0.69 1.18 1.12 0.86 0.00 0.00 0.00 0.00 23.93 36.54 36.57 36.66 0.76 5.57 5.57 5.59 3.24 6.62 6.63 6.64 0.64 1.67 1.67 1.67 2.69 2.89 2.89 2.90 0.52 1.43 1.43 1.43 1.05 1.29 1.29 1.29 0.70 2.53 2.53 2.54 64.84 40.17 40.19 40.30

332.15 336.15 339.00 16

16

O15

O16

O17

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O14

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0.11 2.06 1.15 1.32 0.00 0.12 36.55 7.45 5.57 4.20 6.62 7.80 1.67 1.57 2.89 4.94 1.43 2.00 1.29 2.56 2.53 0.00 40.18 65.98

O13

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Component N2 CO2 H2S C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7+ CO2 injection temperature (K) CO2 injection pressure (MPa)

O12

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O11

20

---

---

---

---

---

---

O18

O19

O20

2.06 1.10 0.12 7.46 4.20 7.82 1.57 4.95 2.00 2.57 0.00 66.13

0.96 0.74 0.30 4.48 2.99 4.74 0.81 1.92 1.27 2.19 0.00 79.61

0.96 0.36 0.00 24.01 0.76 3.25 0.64 2.69 0.52 1.06 0.70 65.05

336.15 332.15

339.00

16

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---: data not provided. References: O11, O15, O16 and O17: Adyani et al. (2011); O12, O13, O18 and O19: Srivastava and Huang (1997); O14 and O20: Hu et al. (2004).

Table 8 shows the experimental data of the content of CO2 in the recombined oil at the

asphaltene onset precipitation (AOP), the content of CO2 for an unstable oil condition (higher than AOP) as well as the content of CO2 for a stable oil condition (lower than AOP). Some of the ten oils shown in Table 7 have the same original oil composition. For instance, oils O11, O15, O16 and O17 have the same original oil composition but the amount of CO2 added in each case is different. This alters the oil composition, properties and may also change the stability (it depends on the amount of CO2 injected). Therefore, each of them was treated as a different oil. The same was done for oils O12 and O18; oils O13 and O19;

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and oils O14 and O20. Oils 11 to 16 are considered unstable oils due to the amount of CO2 injected shown in Table 8 and Oils 17 to 20 are considered stable oils with the amount of CO2 injected shown in Table 8. In Table 8, the oils with the same CO2 content at the AOP have the same original oil composition.

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Table 8. The experimental data of content of CO2 in oils O11 to O20: at AOP, for an unstable oil condition and for a stable oil condition. Content of CO2 for Content of CO2 for CO2 content at an unstable oil stable oil condition Oil AOP (mol %) condition (mol %) (mol %) O11 50.0 70.0 O12 44.5 58.6 O13 53.5 65.3 O14 51.3 53.0 O15 50.0 80.0 O16 50.0 60.0 O17 50.0 40.0 O18 44.5 36.6 O19 53.5 16.4 O20 51.3 20.0

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First, CO2 injection in a proportion greater than the asphaltene onset precipitation is analyzed, ensuring that the oil is unstable. As mentioned for the calculation of the risk of asphaltene precipitation by oil depletion, prior to the use of SRK EOS it is necessary to estimate the binary interaction parameter (kij) between the lightest (CO2) and heaviest (C7+)

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component using bubble pressure experimental data. Table 9 shows the kij values, the comparison between the experimental and the calculated bubble pressure and the reservoir

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temperature. In this case, the bubble pressure is at the point of CO2 injection, which means it is the bubble pressure of the mixture CO2 + recombined oil. For oil O14 neither the specific gravity nor the API gravity data are available in the

literature. However, this property is needed in Eq 5. Therefore, in order to obtain the API values of this oil, the SPECS software was used to calculate the specific gravity (SG). First the binary interaction parameter kij was estimated considering the interaction between the C7+ fraction and CO2, with the minimization of the bubble pressure deviation as the objective function. The following step consists of a calculation of a two-phase flash to obtain the SG value. The API gravity was calculated using Eq 18.

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API =

(18)

141.5 − 131.5 SG

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where API is the API gravity and SG is the specific gravity. Table 9. Binary interaction parameter (kij) of SRK EOS, experimental and calculated bubble pressure (Pb) at reservoir temperature (Tres), and bubble pressure deviation for oils O11 to O16. Tres (K)

Pb,exp (MPa)

kij

Pb,cal (MPa)

O11 O12 O13 O14 O15 O16

368.71 336.15 332.15 339.00 368.71 368.71

23.67 14.00 12.80 21.16 31.41 22.70

1.043 0.689 0.558 1.175 1.191 1.011

23.67 14.02 12.81 21.47 31.39 22.70

Deviation (%)

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Oil

0.000 0.163 0.044 1.447 0.073 0.119

The following step is the calculation of FVF (at bubble point and at 1 atm) and GOR

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(at bubble point pressure) values, using Pedersen’s characterization, as shown in Table 10.

Table 10. FVF and GOR results using Pedersen’s characterization for oils O11 to O16. FVF (Pb) (rb/stb)

GOR (Pb) (scf/stb)

1.0565 1.0150 1.0139 1.0405 1.0565 1.0565

1.5460 1.1138 1.0864 1.1948 1.5174 1.5498

6.46 8.21 5.98 7.77 8.01 6.21

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O11 O12 O13 O14 O15 O16

FVF (1 atm) (rb/stb)

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Oil

The solubility parameter values of CO2 were calculated using the critical properties obtained from the SPECS software: Pc is 72.87 atm and ρc is 468.19 kg/m3. Using the temperature and pressure of the CO2 injection provided for most oils (O12, O13, O14, O18, O19, O20), the density of CO2 was calculated. For the other oils (O11, O15, O16 and O17), a

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flash calculation of the pure component (CO2) at reservoir temperature and at the bubble pressure of the recombined oil was performed to obtain the density values using SRK EOS. Table 11 shows the values of the solubility parameters calculated using the FVF and GOR values of Table 10. The differences between the solubility parameters indicate that

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asphaltene precipitation occurs and these results match the experimental observation reported in the literature. Therefore, it is possible to conclude that the use of the average values of the two parameters as input data combined with the use of SRK EOS, Pedersen’s characterization and Peneloux volume correction are adequate for these oils. It is also possible to conclude that the use of Eqs 4, 5, 6, 13, 14, 15 and 16 for oils with CO2 displacement is satisfactory.

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Table 11 also demonstrates that a correction of the solubility parameter of CO2 is needed because oils O11 to O16 have higher than 40 % CO2 molar fraction. If these

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corrections had not been made, these six oils would have all been wrongly predicted as stable.

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Table 11. Oils with CO2 displacement (O11 to O16): solubility parameter of CO2 using Pedersen’s characterization to predict the risk of asphaltene precipitation. Asphaltene δlive-oil,Pb Oil δg (MPa0.5) δg* (MPa0.5) precipiation (MPa0.5) O11 12.16 9.22 14.61 Yes O12 16.50 11.30 25.90 Yes O13 16.98 10.67 25.57 Yes O14 14.41 12.01 17.29 Yes O15 12.34 11.43 14.83 Yes O16 12.14 8.60 14.59 Yes

For the oils O17 to O20 the amounts of CO2 injected are below the onset of

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asphaltene precipitation. Thus, these oils are referred to as stable. As previously stated, this evaluation begins with determining the value of the binary interaction parameter kij using the difference between the experimental and calculated values of the bubble pressure as the objective function. The results obtained are shown in Table 12. For these oils, the bubble pressure is for the recombined oil with the desired amount of CO2 injected, and the kij between CO2 and C7+ components.

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Table 12. Binary interaction parameter of SRK EOS, experimental and calculated bubble pressure (Pb) at reservoir temperature (Tres), and bubble pressure deviation for oils O17 to O20. Tres (K)

Pb,exp (MPa)

kij

Pb,cal (MPa)

Deviation (%)

O17 O18 O19 O20

368.71 336.15 332.15 339.00

20.96 9.20 4.60 9.60

1.014 0.644 0.320 0.800

20.96 9.20 4.65 9.62

0.020 0.014 1.123 0.309

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Oil

For oil O20, the previously procedure described to calculate the API value (similar to

are available in the literature.

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oil O14, using Eq 18) was necessary because neither the specific gravity nor the API gravity

The next step is to calculate FVF and GOR values, using Pedersen’s characterization, for oils O17 to O20 as shown in Table 13.

Table 13. FVF and GOR results using Pedersen’s characterization for oils O17 to O20. FVF (1 atm) (rb/stb)

O17 O18 O19 O20

1.0565 1.0150 1.0139 1.0405

FVF (Pb) (rb/stb)

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Oil

5.78 5.49 1.92 3.069

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1.5549 1.1173 1.0758 1.2207

GOR (Pb) (scf/stb)

The values of FVF and GOR shown in Table 13 are used in Eqs 4 to 6 to calculate

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δlive-oil,Pb and Eq 13 is used to calculate the solubility parameter of CO2. Table 14 shows the results for oils O17 to O20 (with CO2 displacement, named stable). As the amounts of CO2 injected are lower than 40 % CO2 molar fraction in these four cases, it is not necessary to use the correction of the solubility parameter of CO2. Table 14 shows satisfactory results for asphaltene precipitation prediction because the δlive-oil,Pb value is higher than δg, meaning the oil with that amount of CO2 injected (previously given in Table 8) is stable.

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Table 14. Oils with CO2 displacement (O17 to O20): solubility parameter of CO2 using Pedersen’s characterization to predict the risk of asphaltene precipitation. Asphaltene δlive-oil,Pb Oil δg (MPa0.5) 0.5 precipiation (MPa ) O17 12.11 8.54 No O18 16.44 10.67 No O19 17.09 11.30 No O20 14.14 12.03 No

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4. Conclusions

In this work, a new method was developed to calculate the risk of asphaltene precipitation in oil reservoirs. It is based on a simplification of the ASIST method in order to require a

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minimum number of experimental data. The average values of the solubility parameter obtained through the titration with n-C7 at the titration temperature resulted in fewer deviations than those obtained by the original ASIST method. The validation of these two values was done using 27 oils with experimental data. These respective results were compared with the average parameters proposed in this work. Furthermore, the calculation of

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FVF and GOR using Pedersen’s characterization showed good results for the other ten unstable oils tested, previously known that asphaltene precipitation occurs, and calculated results correctly predicted the precipitation of asphaltene. Thus, the goal to develop a completely predictive method to calculate the risk of asphaltene precipitation due to oil

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depletion was achieved. In addition, for all the oils tested, the assumptions made in this work proved to be correct as the modified ASIST method provided accurate results for all cases.

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Tests with the new method to calculate the risk of asphaltene precipitation due to CO2 displacement also showed satisfactory results. If the amount of injected CO2 is greater than 40 %, it is necessary to use a correction on the solubility parameter of CO2. Otherwise, the solubility parameter of CO2 alone is sufficient to provide a good prediction. Therefore, we conclude that, in comparison with the ASIST method proposed by

Wang et al. (2006), the method introduced in the present work is easier to use and more predictive: there is no need of costly experimental data. The huge unprecedented novelty of the proposed method is the use of the modified ASIST method for oils with CO2 displacement, a worldwide EOR technique. Moreover, the results were very good and satisfactory for both cases analyzed in this paper: the risk of asphaltene precipitation either by

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depletion or due to CO2 displacement. Therefore, the new method proposed in this work may be useful in the industry once it is faster to obtain the results and its outcome is quite reliable.

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Acknowledgments

The authors acknowledge the support by ANP – Agência Nacional de Petróleo, Gás

investment rule. Nomenclature and list of abbreviations

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Asphaltene onset precipitation Asphaltene precipitation envelope API gravity at 1 atm and 15.56 °C Asphaltene Instability Trend method Carbon number Carbon dioxide Lightest component on oil Heaviest component on oil Specific constants to SRK EOS proposed by Pedersen method Equation of state Formation volume factor Formation volume factor at 1 atm (rb/stb) Formation volume factor in bubble pressure (rb/stb) Gas to oil ratio Gas-oil ratio at bubble pressure (scf/stb) Binary interaction parameter Molecular weight n-heptane Calculated bubble pressure Experimental bubble pressure Critical pressure Pressure, volume, temperature cell Molar refraction of the light ends (cm3/mol) Saturates, aromatics, resins and asphaltene analysis Specific gravity Separation and Phase Equilibrium Calculations, Technical University of Denmark Soave-Redlich-Kwong Stock-tank oil Critical temperature Titration temperature with n-C7 (ºC) Reservoir temperature (ºC)

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AOP APE API ASIST CN CO2 C1 C7 + d1 to d12 EOS FVF FVFo FVFPb GOR GORPb kij MW n-C7 Pb,cal Pb,exp Pc PVT cell Rlight SARA analysis SG SPECS®

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Nomenclature and list of abbreviations

SRK STO Tc Tmeas Tres

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Natural e Biocombustíveis and by Petrogal Brasil S.A., related to the grant from R&D

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Acentric factor for each fraction Mole fraction of C1-C3 Mole fraction of C1-C6 Molar fraction

Greek Letters

νlight,Pb νnC7

References

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ρ ρc ρN ρr ρr(liq)

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δSTO

First correction parameter Second correction parameter Solubility parameter of CO2 (MPa1/2) Corrected value for the solubility parameter of CO2 Solubility parameter of asphaltene instability potential in live oil (MPa1/2) Solubility parameter of live oil at bubble pressure (MPa1/2) Solubility parameter at the beginning of the precipitation of the stock-tank oil obtained with titration of n-C7 (MPa1/ 2) Solubility parameter for STO under standard conditions (1 atm, 15.56 ºC) (MPa1/2) Density Critical density Density of the carbon fraction Reduced density Reduced density of liquid at its normal boiling point (a constant equal to 2.66) Molar volume of the light ends at the bubble point (cm3/mol) Molar volume of n-C7 (cm3/mol)

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α β δg δg* δinstability,Pb δlive-oil,Pb δonset, nC7

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Takahashi, S., Hayashi, Y., Takahashi, S., Yazawa, N., Sarma, H., 2003. Characteristics and impact of asphaltene precipitation during CO2 injection in sandstone and carbonate cores: an investigative analysis through laboratory tests and compositional simulation. In: SPE International Improved Oil Recovery Conference in Asia Pacific, 20-21 October, Kuala Lumpur, Malaysia. https://doi.org/10.2118/84895-MS.

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ACCEPTED MANUSCRIPT Highlights • A new method developed to calculate the risk of asphaltene precipitation in oil reservoirs.

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• The method simplifies the ASIST method in order to require a minimum number of experimental data.

• Results show better prediction of asphaltene precipitation by oil depletion than

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with the ASIST method.

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• Results validate the unprecedented prediction of asphaltene precipitation by CO2

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displacement using only the recombined oil bubble point pressure as input data.