Modeling of Asphaltene Precipitation in Calculation of Minimum

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Modeling of Asphaltene Precipitation in Calculation of Minimum Miscibility Pressure Ali Kariman Moghaddam, and Amir Hossein Saeedi Dehaghani Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 06 Jun 2017 Downloaded from http://pubs.acs.org on June 9, 2017

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Modeling of Asphaltene Precipitation in Calculation of Minimum Miscibility Pressure Ali Kariman Moghaddam † and Amir Hossein Saeedi Dehaghani †Department

∗, ‡

of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

‡Department

of Petroleum Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran

E-mail: [email protected]

Phone: +98 21 82883350. Fax: +98 21 82883350

Abstract An algorithm has been developed to investigate the eect of Asphaltene precipitation on calculation of minimum miscibility pressure (MMP) which is one of the key design parameters of any gas injection projects. In fact, this algorithm is the extension of procedure suggested by Jaubert et al. in 1998 for prediction of MMP whatever displacement mechanism. The VLE calculation and then LLE calculation are required to be taken account in order to estimate the amount of Asphaltene precipitation. The association equation of state (AEOS) has been applied to determine the phase behavior of Asphaltene. The algorithm has been used for the MMP prediction of Weyburn reservoir oil in which the precipitation of Asphaltene has been reported. The results show good agreement with those experimental data obtained by slim tube, and improved by 7.6% and 5.3% on average compared to Jaubert's algorithm and Ahmadi's approach, respectively. 1


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Introduction One of the most eective methods of enhance oil recovery is gas injection. A key parameter of this process is the determination of Minimum Miscibility Pressure (MMP), in which, at this pressure, the local displacement eciency becomes approximately 100%; thus, high cost of processing or unfavorable oil production can be taken place as a result of inaccurate prediction for MMPs. 1 The experimental methods of MMP determination are slim tube, 2 contact experiment, 3 rising bubble apparent 4 and vanishing interfacial tension (VIT), 5 and among these methods, slim tube results are more reliable so that it encompasses the interaction of ow in porous media and phase behavior of gas injection. 68 In the recent works, the novel criteria with the rising bubble apparatus and the slim tube test has been suggested and gured out to be more accurate and objective for the determination of MMPs. 9,10 Beside the mentioned methods, there are other experiments that can measure MMPs with good accuracy, such as oil swelling/extraction technique and microuidics-based approach. 1114 Nevertheless, researchers prefer to apply computational methods based on Equation of State (EOS) since experimental methods are time consuming and expensive. Three primary approaches used for the computational prediction of MMPs may be organized as: slim tube compositional simulation, the Method of Characteristics (MOC) and Multiple Mixing Cell (MMC) method. As matter of fact, slim tube compositional simulation approach is the duplication of slim tube experiment in which the ow of gases through porous media is simulated, and the MMP can be estimated by coming across the point that the recovery factor curve versus pressure is bent. 15 The main deciency of slim tube compositional simulation is the dispersion of numerical errors that may have inuence on the results of MMP estimation. 16 Furthermore, this approach is more time consuming compared to others. The MOC approach has been developed based on an analytical solution for the displacement of oil and gas. 17 According to the MOC technique, for Nc number of components, the Nc − 1 number of key tie-lines can be evolved so that MMP is the pressure at which one of these key tie-lines turn into critical (or its length becomes zero). 18,19 The 2



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major drawback of the MOC approach is its complication; consequently, it is feasible that the calculation converges to the wrong key tie-line, as pointed out by Yuan and Johns. 20 Moreover, MOC-based algorithms have a potential problem with negative ash calculation as indicated by Ahmadi et al., and the prediction of MMPs under bifurcation conditions is arisen with a huge error. 21 The MMC (or cell-to-cell) method presumes virtual PVT-cells lled by oil or gas, which may be a single cell or multiple cells, and the phase equilibrium calculations are carried out in them. The single cell method is based on the simplifying assumption that the oil tie-line or gas tie-line controls miscibility through repeated contacts between oil and gas in a forward or backward manner. The criterion for MMP is the pressure at which the converged tie line becomes the critical tie line. 22,23 The main disadvantage of a single cell model is its inability to estimate MMP when condensing/vaporizing drive controls the miscibility displacement. 24 Multiple-cell mixing cells consist of a series of PVT cells ranging from 5 to 500 cells wherein oil and gas are mixed, and the phase equilibrium calculation is performed. There are a variety of published multiple-cell mixing-cells methods; however, the authors have considered mainly two approaches to calculate the MMP. In the rst approach, slim tube simulation essentially is simplied in which only phase equilibrium calculation is carried out and solving the ow equation is ignored. The series of PVT cells that are connected and are initially lled with oil. The specic volume of gas is injected into the rst cell at a trial pressure and, assuming accomplished mixing, the P/T ash routine calculation is performed. Then the uid fractions of the cell are moved to the next cell and mixed with the uid in the next cell. The uid fractions moving from cell to cell can be the excess volume or determined by the fractional ow function for gas-oil two-phase ow. The process transacts in the series of cells until some specied volume of gas is injected (typically 1.2 times the total volume). Afterward the oil recovery factor is calculated and the procedure is repeated for several pressures. 2527 In the second approach, the calculations begin with two cells lled with injection gas and

3


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the reservoir oil. Additional cell-to-cell contacts between resulting equilibrium compositions are performed based on the fact that the equilibrium gas moves ahead of the equilibrium liquid phase. Number of contacts go up through applying negative ash calculation until all key tie-lines develop and converge to specic tolerances. In each pressure, the minimum tie line length is stored and the MMP is the pressure at which the minimum tie line length becomes critical (or its length becomes zero). 28,29 Moreover, the recent version of this approach considers the three-hydrocarbon-phase oil displacement by CO2 that is involved at low temperature. 30 All the previous models for the MMP calculation have not taken into account the effect of Aphaltene precipitation on their results. On the other hand, Asphaltene occulation and deposition during natural depletion and miscible/immiscible gas injection is a common problem that might take place in enhance oil recovery projects. 31 During the experimental measurement of MMP by slim tube, the observation of asphaltene deposition has been reported, and if the problem is not resolved, the slim tube can become completely plugged and inoperative. 32,33 Prediction of the phase behavior and the precipitation amount of Asphaltene is very delicate and tough because of its complicated structure and properties. 34,35 Through the past decades, several thermodynamics models have been introduced and developed in order to predict Asphaltene phase behavior upon changes in pressure, temperature and oil reservoir composition. The detailed reviews of these models have been come out within the literature. 36,37 In the recent years, a number of models have been developed based on the association uid theory, such as AEOS, CPA and SAFT which could estimate the amount of Asphaltene with a good accuracy. 3843 In this study, a new algorithm has been proposed for the prediction of minimum miscibility pressure, which is taken into account the Asphaltene precipitation through the calculation. In fact, this algorithm is the expansion of MMC method introduced by Jaubert et al, in which to predict the amount of Asphaltene precipitation the association equation of state (AEOS) has been used. Also, the results of this model are obtained for

4



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the Weyburn reservoir oil and MMP estimations are compared with the experimental data of slim tube and rising bubble apparatus.

The proposed algorithm The multiple mixing cell technique introduced in this paper and described below is similar to the one developed by Jaubert et al. in 1998. 25 Herein, the multiple mixing cell calculation is used in order to compute rst the recovery factors (RF1.2 ) and then the MMP; however, the amount of the Asphaltene precipitation is estimated in each cell and is eliminated for the calculation of next injection. This assumption is based on the experimental observations of the colloidal behavior of asphaltene suspensions which indicates that asphaltene precipitation is not reversible or less likely to be reversible. 4446 The model simulates a number of cells equal in volume and lled with the reservoir oil in a series as shown in Figure 1. The temperature and the pressure are the same in each cell, and the volume is kept constant; then a specied amount of gas is injected into the rst cell. It is assumed that perfect mixing takes place and thermodynamic phase equilibrium is reached. VLE calculation (or P/T ash) is performed and the overall equilibrium composition of vapor (y) and liquid (x) is obtained using any Equation of State. Afterward the liquid-liquid equilibrium (LLE) calculation is done on the resulting equilibrium liquid (x), if it is formed, to estimate the amount of Asphaltene precipitation as shown in Figure 2. The association equation of state (AEOS) has been utilized in the LLE calculation because of the association nature of Asphaltene. The ne detail of AEOS used for this paper has been described in the next section. The calculated amount of Asphaltene is remained in cell 1 and ignored for the subsequent injections. The total volume, which might be composed of Asphaltene, liquid and vapor phase, is estimated and the excess volume is transferred to cell 2. If the total volume of the cell is less than the assumed cell volume, the procedure is ceased and the subsequent injection is done. In a second step, the same procedure is applied for cell 2 and the excess volume of cell 2 is

5


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transferred to cell 3. This procedure goes on until production is obtained from the last cell; then the subsequent injection into cell 1 can take place. The following steps summarize the procedure used in the proposed model for the MMP estimation:

Figure 1: The schematic of Multiple Mixing Cell Method. 25

Figure 2: The owchart represnting the calculation in each cell

1. Choose a pressure below minimum miscibility pressure. All the calculation is performed at this pressure and reservoir temperature. Jaubert and co-workers have proposed the procedure to choose the proper pressure, and the same procedure can be used here. 25 2. The amount of gas to be injected is 1.2P V of total cells lled with oil (for instance 50 6



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cells). The volume of gas is 0.33% volume of a cell in each injection. Therefore, 180 numbers of gas injection must be done in order that total amount of 1.2P V is to be injected for 50 cells. 3. It is assumed that phase equilibrium is established in each cell and for any injection. The VLE calculation is performed to estimate the amount of vapor and liquid. The LLE calculation is done on resulting liquid phase to obtain the amount of Asphaltene and unprecipitated liquid phase. The amount of Asphaltene precipitation remains in the cell whenever it is observed. 4. The amount of excess volume is injected into the next cell. First gas phase is transferred to the next cell and if the liquid phase presents, the unprecipitated liquid phase is transferred. 5. This procedure from step 2 to 4 are repeated until 1.2P V of the gas is injected, and 1.2 the recovery factor (RF50 ) is stored.

6. The step 2 to 5 for the 100 and 200 number of cells are repeated; then the values of 1.2 1.2 ) are recorded. and RF200 recovery factor for 100 and 200 cells (RF100

√ 7. The Plot of RFN1.2 versus 1/ N is obtained, where N is the number of cells. Re1.2 ) can be estimated through linear covery factor at an innite number of cells (RF∞

extrapolation as shown by Jaubert et al. 8. The higher pressure is chosen and the procedure from step 1 to 7 are repeated. Af1.2 terward the value of RF∞ versus pressure is plotted. The MMP is estimated through

exponential extrapolating the curve till RF = 97% is obtained. The Asphaltene precipitation might be accumulated in each cell for any injection, and the uid injected into the specic cell is mixed with unprecipitated liquid and/or vapor phase as shown in Figure 3. Note that the results of the proposed algorithm are the same as the one introduced by Jaubert et al, when Asphaltene precipitation is not formed in any stages. 7


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Figure 3: The asphaltene precipitation is remained in each cell and will not be mixed with the uid of excess volume of the previous cell. The uid of excess volume is mixed with the unprecipitated phase of next cell.

Association Equation of State (AEOS) The association model explains the nonideality of the system as a result of a chemical reaction between associated species. Based on this theory, thermodynamic properties of associating compounds and their mixtures are assumed to be determined by chemical equilibrium between associated species and physical interactions between all species present in a solution. Lambert showed that for an associating uid the second virial coecient B is separable into the two physical and chemical so that the compressibility factor can be expressed as: 47

Z = Z (ph) + Z (ch) − 1

(1)

The physical part of compressibility factor can be obtained by cubic equations of state such as PR and SRK; however, several expressions have been suggested for the chemical part of the Z-factor. 4850 In this study SRK is used as the physical part, and the expression based on nite linear association of associative monomers, developed by Dehaghani et al., is applied as the chemical contribution of compressibility factor. 5153 The chemical expression for mixtures is written as:

8



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n

Z (ch) =

X nT = n0 (ci + i=1

ci x i Pn RT

1 P0 v

j=1 Kij xj )

+

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n X

xk

(2)

k=1

In the above equation n0 is the analytical (without the association) number of the moles of the mixture, nT is the total number of the moles of the mixture (with the association). kii , kij denotes chemical association constant related to similar and dissimilar component, and ci is an additional parameter implicitly representing association length, which depends on the chemical nature of the components. P 0 is the standard pressure of 1 bar. In Equation 2, the second right term represents the sum of mole fractions of non-associated components. 52,53 In this work, it is assumed that Asphaltene is the only associative component; therefore, the Equation 2 take simple form as:

Z (ch) =

cA +

cA x A 1 RT KAA xA P0 v

(3)

+ 1 − xA

The value of the total fugacity coecient is obtained by the following equations:

ph ch ch ln(φi Z) = ln(φph i Z ) + ln(φi Z )

1 ph ln(φph i Z ) = RT

Z

1 ch ln(φch i Z ) = RT

Z

V

∞

V

∞

RT − V

RT − V

∂P ph ∂ni

∂P ch ∂ni

(4)

! dV

(5)

dV

(6)

T,V,ni

!

T,V,ni

ch It should be emphasized that the values of ln(φch i Z ) for non-associative components are

equal to zero. 48

Results and discussion In this study, three oil and gas samples were investigated from Weyburn reservoir in Saskatchewan, 9


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Canada. The detailed experimental data of Asphaltene precipitation and CO2 miscible ooding is available in the literatures. 5456 Table 1 presents the overall composition and the properties for the reservoir uid and gas injections. Table 1: The overall composition of the reservoir oil and the injection gases for the Weburn reservoir. 56 Component

N2 CO2 H2 S C1 C2 C3 i − C4 C4 i − C5 C5 C6+ M wC6+ = 205 AP IOil = 29.6

Oil (A2) 0.96 0.58 0.3 4.49 2.99 4.75 0.81 1.92 1.27 2.19 79.74

Gas 1 (Pure CO2 ) 0 100 0 0 0 0 0 0 0 0 0

Gas 2 (Impure CO2 ) 0 90.1 0 9.9 0 0 0 0 0 0 0

Gas 3 (Impure CO2 ) 5.1 89.8 0 5.1 0 0 0 0 0 0 0

Whitson's splitting and lumping method was used for hexane plus fraction in order to obtain six pseudo-components and their properties. 57 In this work, the heaviest pseudocomponent (P S − 6) was assumed as Asphaltene that can precipitate.The critical properties of pseudo-components and Asphaltene were computed using Lee-Kesler correlation given in Table 2. The stability analysis was done through the following equation in order to identify the occurrence of asphaltene precipitation:

S fi (T, P, Zi ) − fi,P ure ≥ 0

(7)

S In the above equation, Zi is the mole fraction of component i, fi,P ure is fugacity of

component i in pure situation, fi (T, P, Zi ) is fugacity of component i with feed composition

Zi and the superscript S indicates the precipitated phase. The values of fugacities in pure and mixture situation were obtained; As a result, the occurrence of asphaltene precipitation 10



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is feasible at temperature and the range of pressure for this study due to the accomplishment of stability condition for the sixth pseudo-component. Table 2: Physical and critical properties of components and pseudo-components Component

N2 H2 S CO2 C1 C2 C3 iC4 nC4 iC5 nC5 PS − 1 PS − 2 PS − 3 PS − 4 PS − 5 P S − 6(Asphaltene)

Mole Fraction % 0.95 0.30 0.56 4.44 2.96 4.70 0.80 1.90 1.26 2.17 25.69 19.02 15.56 12.15 5.58 1.74

Molecular Weight

Critical Temperature (K) 126.20 373.60 304.70 190.60 305.43 369.80 408.10 419.50 460.40 465.90 573.11 674.78 769.84 880.92 1016.70 1195.80

28.01 34.08 44.01 16.04 30.07 44.10 58.12 58.12 72.15 72.15 101.25 153.02 216.12 309.05 450.95 689.82

Critical Pressure (MPa) 3.44 9.06 7.48 4.67 4.95 4.30 3.70 3.80 3.43 3.40 3.45 2.56 1.94 1.39 0.91 0.51

Acentric Factor 0.04 0.10 0.23 0.01 0.10 0.15 0.18 0.20 0.23 0.24 0.32 0.48 0.68 0.94 1.26 1.63

The derived association equation of state has two adjustable parameters related to Asphaltene properties including association constant ( KAA ) and association length ( cA ) as can be seen in Equation 3. Furthermore, the values of the interaction parameter ( kij ) between Asphaltene and other components require to be adjusted so that the Chueh and Prausnitz model is applied which is written as: 58 1

"

1

2vc6i vc6j

kij = 1 −

1

#θ

1

(8)

vc3i + vc3j These three parameters, denoted as KAA , cA and θ, were adjusted using Asphaltene precipitation data that are available for dierent pure and impure CO2 concentration as shown in Figure 4 and 5. The uid was used for the adjustment of impure CO2 injection is denoted as W2 in Srivastava et al.'s work for Weyburn reservoir. The detailed overall 11


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composition and physical properties of uid W2 are presented elsewhere. 55

Figure 4: Tuning of AEOS parameters by Asphaltene precipitation data of pure CO2 injection into Weyburn resevoir oil. Experimental data are from Srivastava et al. study. 55

Figure 5: Tuning of AEOS parameters by Asphaltene precipitation data of impure CO2 in W2 uid of Weyburn reservoir. The impure CO2 contains 2.68 mole% N2 +2.87 mole% CH4 + 94.45 mole% CO2 . Experimental data are from Srivastava et al. study. 55 The adjusted values of the parameters are indicated in Table 3 and used to estimate MMPs of pure and impure CO2 injection. The values of binary interaction parameters between other components are obtained from literatures in order to utilize in mixing rule. 59 It would be possible to use the binary interaction parameters (BIPS) calculated by the PPR78 model which is an accurate group-contribution method to estimate temperature-dependent

kij . 60,61 As mentioned before, the new proposed algorithm has been applied in order to compute the MMP for three systems of oil and gas injection. Also, the MMPs for these systems 12



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Table 3: The values of the adjusted parameters using for prediction of asphaltene precipitation Parameter

cA KAA θ

Adjusted Value for pure CO2 injection 2.7 × 10−4 2.3 × 10−4 0.77

Adjusted Value for impure CO2 injection 3.2 × 10−4 2.4 × 10−4 0.85

were calculated and compared with the previous algorithm proposed by Jaubert et al and Ahmadi's MMC method. In the rst case, the oil reservoir was displaced by pure Carbon √ Dioxide. The plot of RF1.2 , which is a linear function of 1/ N , for several pressures are indicated in Figure 6, and are obtained from two dierent algorithms. In this gure, the dashed lines and the solid lines represent the results obtained by applying the proposed algorithm and the one suggested by Jaubert et al., respectively. We carried out the calculation up to 200 numbers of cells instead of 500 cells in order to reduce the run time of computation. The ∞ exponential variation of RF1.2 versus pressure obtained through two algorithms is indicated

in Figure 7. As can be seen, for a specic pressure, the proposed model estimates the lower value of recovery factor in comparison with Jaubert et al.'s one which leads to predict the higher value of MMP.

√ Figure 6: The plot of RF1.2 versus 1/ N . The dashed and solid lines were obtained from the new proposed and Jauber et al.'s algorithm, respectively. The Recovery Factor is volumetric and dened as RF N =

Va , Vb

where the Va is the cu-

mulative oil volume produced from the last cell at tube conditions converted to surface 13


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∞ Figure 7: The plot of RF1.2 versus pressure and exponential extrapolation for the injection of Gas 1.

conditions (150 C, 1atm), and Vb is the total initial oil volume (at tube conditions) introduced in N cells and converted to surface conditions, as well described by Jaubert et al. 25 This recovery factor is related to all fractions; therefore, we have surveyed the overall mole fraction of the produced liquid for the injection of the rst system as depicted in Figure 8.The dashed line representing the mole fraction of PS-6, assumed as Asphaltene fraction, produced at each step of the injection. As can be seen, the produced Asphaltene fraction remains constant, up to 170 steps of the injection, and then begins to decrease; by contrast, other pseudo-components fractions increase. The decline of the PS-6 is related to increase in CO2 concentrate and Asphaltene deposition occurred in the last cell. It indicates that signicant amount of Asphaltene fraction is produced during the gas injection, but as the precipitation starts to occur, the amount of the produced Asphaltene fraction declines at a rapid rate. To investigate the amount of Asphaltene precipitation through the procedure, the plot of accumulated Asphaltene, in each cell at the end of 1.2 PV gas injection, has been shown in Figure 9. This gure was obtained at 11.5 MPa that is near below MMP for the 50 number of cells. As one can see, the accumulation of Asphaltene is further at the inlet cells, and this is because of fresh CO2 injected in these cells. It can be concluded that the blockage of slim tube might be occurred at the place near the entrance injection. Figure 10 and 11 demonstrate the results of MMP calculations for the displacement of 14



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Figure 8: Overall mole fraction of the produced liquid in each step of the injection at 10.8 MPa for 50 cells.

Figure 9: The ratio of total volume of accumulated Asphaltene to the cell volume at 11.5 MPa in 50 cells at the end of injection for Oil and Gas 1 the reservoir oil by contaminated Carbon Dioxide as introduced in Table 1. Dong et al. stated that three uids of A1, A2 and A3 were used in their study, which their compositions are very similar and is represented in Table 1. They reported that the API of uid A3 is 28.6 so that the re-characterization of the plus-fraction has been done for this uid, available in supporting information, in order to use for the injection of third gas. 56 The values of MMP calculated using the proposed are compared to those estimated by the Juabert's algorithm and Ahmadi's multiple mixing cells method. In Ahmadi's approach, the minimum tie line lengths are obtained following 100 numbers of contacts and extrapolated to an innite number of cells by (1/N )m with m = 0.2, and the same fraction plus characterization and SRK EOS are used. The plot of minimum tie line length versus pressure for each case are provided in supporting information, Figure S1 through S3. Table 4 represents the 15


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results of MMP estimation using the proposed and two aforementioned algorithms. As one can see, the results of the new proposed algorithm show better agreement with experimental data of the slim tube apparatus for the Weyburn reservoir oil.

∞ versus pressure and exponential extrapolation for the injection Figure 10: The plot of RF1.2 of Gas 2.

∞ Figure 11: The plot of RF1.2 versus pressure and exponential extrapolation for the injection of Gas 3.

The accuracy of MMP prediction depends on many factors, for instance type of EOS, characterization of undened cut and mixing rules as pointed out by researchers. 6264 However, the noticeable dierence between the results of experimental data and predicted MMP chiey is related to Asphaltene precipitation in this study. As mentioned previously, the precipitation of Asphaltene can be occurred during CO2 ooding and accumulation of precipitations might plug pore throats and pore body in porous medium. Moreover, Asphaltene precipitation might alter the wettability of the reservoir matrix and consequently aect the 16



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Table 4: The results of the proposed algorithm and comparsion with experimental data. Experimental Data (MPa) 56

Predicted MMP(MPa) Solvent

The proposed algorithm 12.82

Jaubert et al.'s algorithm 12.42

Ahmadi's Approach 13.49

Slim Tube

Impure CO2 (Gas 2)

15.91

14.94

15.79

17.5

Impure CO2 (Gas 3)

19.28

16.26

17.16

21.2

Pure CO2 (Gas 1)

12.8

ood performance 65 which are not considered in our modelling. In similar work, Mohebeenia et al. have simulated the asphaltene precipitation during gas injection using PC-SAFT EOS and brought up the aforementioned phenomena. 66 They have not considered the association term in PC-SAFT EOS and assumed that Van der Waals forces dominate the interactions between the molecules in Asphaltene mixtures. Although the association term adds two more parameters and more complexity in the calculations, it should be considered because of the association nature of Asphaltene molecules. Along the same line, they have conducted the prole of the damaged area and the reduction of well productivity index by asphaltene deposition. An analogous simulation might be applied for the estimation of MMP, but the problem with SAFT and PC-SAFT is that the parameters are tuned to the vapor pressure curve, not the critical point which is vital for MMP estimation. Furthermore, an iterative procedure for nding the density roots and phase equilibrium calculation is time-consuming when the PC-SAFT is used. 67

Conclusion In this study, a new algorithm has been proposed for the prediction of minimum miscibility pressure (MMP) in which the precipitation of Asphaltene has been considered. The proposed algorithm is similar to the one suggested by Jaubert et al. in 1998. In this algorithm, both 17


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the vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE) calculations have been utilized, and the association equation of state (AEOS) has been applied in order to predict the amount of Asphaltene precipitation. The results of MMP calculation have been obtained for the Weyburn reservoir oil in which the precipitation of Asphaltene has been reported, and compared to the experimental data of slim tube. The results show that the proposed algorithm has a good agreement with the experimental data in comparison with the previous MMC algorithms.

Acknowledgement The authors are grateful to Ali Nasseri Pouryazdi at the Department of Mechanical Engineering of Sharif University for preparing this paper.

Supporting Information Available • Table S1: The physical and critical properties of components for A3 • Figure S1. Minimum tieline length versus pressure and its extrapolation to zero length to obtain MMP using Ahmadi's approach and SRK EOS for System Oil /Gas 1

• Figure S2. Minimum tieline length versus pressure and its extrapolation to zero length to obtain MMP using Ahmadi's approach and SRK EOS for System Oil /Gas 2

• Figure S3. Minimum tieline length versus pressure and its extrapolation to zero length to obtain MMP using Ahmadi's approach and SRK EOS for System Oil (A3)/Gas 3

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Modeling of Asphaltene Precipitation in Calculation of Minimum

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