Determination of CO2 Minimum Miscibility Pressure from Measured


4 were used as adjustable parameters to tune the SRK EOS(10) and thus determined once the calculated density of the original crude oil best matched it...
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Ind. Eng. Chem. Res. 2008, 47, 8918–8925

Determination of CO2 Minimum Miscibility Pressure from Measured and Predicted Equilibrium Interfacial Tensions Morteza Nobakht,† Samane Moghadam,† and Yongan Gu*,‡ Fekete Associates Inc., Calgary, Alberta T2P 0M2, Canada, and Petroleum Technology Research Centre (PTRC), Faculty of Engineering, UniVersity of Regina, Regina, Saskatchewan S4S 0A2, Canada

Accurate determination of the minimum miscibility pressure (MMP) of a crude oil-CO2 system at the actual reservoir temperature is required in order to determine whether CO2 flooding is immiscible or miscible under the actual reservoir pressure. The objective of this study is to determine the MMPs of a crude oil-CO2 system from its measured and predicted equilibrium interfacial tension (IFT) versus equilibrium pressure data at a constant temperature. In the experiment, first, the CO2 solubilities in the crude oil are measured under four different equilibrium pressures. Second, the equilibrium IFTs of the crude oil-CO2 system are measured at 12 different equilibrium pressures and a constant temperature of T ) 27 °C by applying the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case. The detailed experimental results show that the CO2 solubility in the crude oil is increased almost linearly with the equilibrium pressure. It is also found that the measured crude oil-CO2 equilibrium IFT is reduced almost linearly with the equilibrium pressure as long as it is lower than a threshold pressure. The measured equilibrium IFT versus equilibrium pressure data are used to determine the MMP of the crude oil-CO2 system by applying the so-called vanishing interfacial tension (VIT) technique. In addition, the equilibrium IFT versus equilibrium pressure data of the crude oil-CO2 system are predicted by using the parachor model and linear gradient theory (LGT) model, respectively. The predicted equilibrium IFT data from each model are also used to determine the MMP of the same crude oil-CO2 system. Comparison of the MMPs determined from the two equilibrium IFT prediction models and that determined from the measured equilibrium IFTs shows that the LGT model is suitable for determining the MMP of the crude oil-CO2 system. 1. Introduction One of the foremost technical issues in the design process of a CO2 flooding project is to determine the minimum miscibility pressure (MMP) between a crude oil and CO2.1,2 The MMP of a crude oil-CO2 system is defined as the minimum pressure under which CO2 can achieve multicontact miscibility with the crude oil.2 If the actual reservoir pressure is lower than the MMP between the crude oil and CO2, the CO2 flooding is classified as an immiscible solvent injection. Otherwise, the CO2 flooding is considered to be a miscible displacement. In the latter case, the displacement becomes more efficient and accordingly the oil recovery is higher. Therefore, accurate determination of the MMP of a given crude oil-CO2 system at the actual reservoir temperature is required to predict and evaluate the performance of the CO2 flooding project. Among the existing experimental methods for determining the MMP, the slim-tube method is the most commonly used technique for measuring the MMP between a crude oil and CO2. It has become a standard method to measure the MMP in the petroleum industry.3 In this method, CO2 is injected into an extremely long (5-120 ft) slim tube at different injection pressures and the actual reservoir temperature to recover the oil from the slim tube. The measured oil recovery is then plotted versus the injection pressure. The MMP is determined as the pressure under which the measured oil recovery versus injection pressure curve shows a sudden change in slope.4 Another experimental method to measure the MMP between a crude oil and CO2 is by using the so-called rising bubble apparatus (RBA). * To whom correspondence should be addressed. Tel.: (306) 5854630. Fax: (306) 585-4855. E-mail: [email protected] † Fekete Associates Inc. ‡ University of Regina.

The RBA method is recognized as an inexpensive and fast alternative to the slim-tube method for determining the MMP.5 In the RBA method, a small CO2 bubble is injected into a thin transparent column of the crude oil inside the RBA at a different pressure each time. The MMP is then inferred from the observed rising CO2 bubble size-pressure dependence.2,5 The MMP is assumed to be reached when the rising CO2 bubble ultimately disappears in the oil column under a certain pressure. The RBA method is much cheaper and faster and requires much smaller amounts of crude oil and CO2, in comparison with the slimtube method.3,5 Recently, a new experimental approach, named the vanishing interfacial tension (VIT) technique, has been developed and utilized to determine the miscibility conditions of different crude oil-CO2 systems.6-8 The VIT technique is based on the concept that the interfacial tension (IFT) between a crude oil and CO2 becomes zero when they are miscible. In the experiment, the equilibrium IFTs between the crude oil and CO2 are measured at different equilibrium pressures and the actual reservoir temperature. Therefore, the MMP is determined by linearly extrapolating the measured equilibrium IFT versus equilibrium pressure data to zero equilibrium IFT. In this paper, the MMP between a crude oil and CO2 is determined from the predicted crude oil-CO2 equilibrium IFT versus equilibrium pressure data at T ) 27 °C by using the parachor model and the linear gradient theory (LGT) model, respectively. More specifically, in the experiment, the CO2 solubilities in the crude oil and the equilibrium IFTs of the crude oil-CO2 system are measured at different equilibrium pressures and T ) 27 °C. Then a commercial phase behavior simulation module with the Soave-Redlich-Kwong equation of state (SRK EOS) is applied to predict the vapor-liquid equilibrium (VLE) between the crude oil and CO2 phases at each equilibrium

10.1021/ie800358g CCC: $40.75  2008 American Chemical Society Published on Web 10/28/2008

Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8919 Table 1. Compositional Analysis Result of the Weyburn Crude Oil carbon no.

wt %

carbon no.

wt %

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15

0.00 0.00 0.00 0.00 0.00 0.00 3.20 4.68 7.79 6.53 4.63 4.17 4.20 4.05 4.08

C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30+

3.92 3.75 4.33 3.42 2.45 2.55 1.55 1.87 1.69 1.57 1.60 1.49 1.48 1.43 23.57

pressure and temperature. Such calculated VLE versus equilibrium pressure data are then used to predict the crude oil-CO2 equilibrium IFTs by applying the parachor model and LGT model, respectively. Furthermore, the predicted equilibrium IFTs from each model are used to determine the MMP of the crude oil-CO2 system by applying the VIT technique. Finally, the MMPs determined from these two equilibrium IFT prediction models are compared with that determined from the measured equilibrium IFT versus equilibrium pressure data of the same crude oil-CO2 system. 2. Experimental Section 2.1. Materials. A light crude oil sample was collected from the Weyburn oil field in Saskatchewan, Canada. The density and viscosity of the cleaned crude oil sample were measured to be Foil ) 901.0 kg/m3 and µoil ) 16.6 mPa · s at atmospheric pressure and T ) 27 °C, respectively. The asphaltene content of the crude oil was measured to be wasp ) 5.7 wt % (n-pentane insoluble) by using the standard method ASTM D2007 and 0.2 µm polytetrafluoroethylene (PTFE) syringe filters (Target, National Scientific, U.S.A.). The compositional analysis result of this dead crude oil was obtained by using the simulated distillation method and is given in Table 1. It can be seen from this table that there are no hydrocarbon components under C7 and that heavy hydrocarbon components of C30+ are found to be 23.57 wt %. The purity of carbon dioxide (Praxair, Canada) was 99.99%. The densities of CO2 at different pressures and T ) 27 °C were calculated by using the CMG Winprop module (Version 2006.11, Computer Modelling Group Limited, Canada) with the Peng-Robinson equation of state.9 2.2. Solubility Measurement. Figure 1 shows the schematic diagram of the experimental apparatus for measuring the CO2 solubility in the crude oil. The apparatus mainly consisted of a see-through-windowed high-pressure cell (IFT-10, Temco, U.S.A.) and a programmable syringe pump (100DX, ISCO Inc., U.S.A.). The constant temperature during the solubility measurement was maintained by wrapping the pressure cell with a heating tape (HT95504x1, Electrothermal, U.S.A.), which was connected to a temperature controller (Standard-89000-00, ColeParmer, Canada). The pressure inside the pressure cell was measured by using a digital pressure gauge (DTG-6000, 3D Instruments, U.S.A.). The temperature of the pressure cell was set at T ) 27 °C prior to each solubility measurement. The pressure cell was then pressurized with CO2 to a prespecified pressure, and its pressure was allowed to stabilize for 1 h. After the pressure inside the pressure cell reached its stable value, the initial CO2 pressure P0, temperature T0, and volume V0 were recorded. Next, a crude

Figure 1. Schematic of the experimental apparatus used to measure CO2 solubility in the crude oil.

oil sample of Voil ) 4.1 cm3 (i.e., 10% of the pressure cell volume) was injected into the pressure cell at an extremely low volume injection rate of 0.005 cm3/min by using the programmable syringe pump. Formation of pendant oil drops at such an extremely slow injection rate greatly accelerated the CO2 dissolution into the crude oil by creating large oil-CO2 contact area. Finally, after the crude oil-CO2 system reached the equilibrium state, as indicated by constant cell pressure within the measurement accuracy of 0.034 MPa for over 12 h, the equilibrium CO2 pressure Pe, temperature Te (Te ≈ T0), and volume Ve were noted. In this study, the solubility was defined as the ratio of the mass of the dissolved CO2 to that of the original crude oil sample used (i.e., g of CO2/100 g of oil). By applying the mass balance equation and the equation of state for a real gas, the CO2 solubility in the crude oil sample χ was determined from the following equation: χ)

MCO2

[

]

PeVe P0V0 × 100 FoilVoil Z0RT0 ZeRTe

(1)

where MCO2 is the molecular weight of CO2, Foil is the density of the original crude oil sample, Z0 and Ze are the compressibility Z-factors9 of CO2 at the initial state (P0, T0) and at the equilibrium state (Pe, Te), respectively, and R is the universal gas constant. 2.3. IFT Measurement. Figure 2 shows the schematic diagram of the experimental setup for measuring the equilibrium IFT between the crude oil and CO2 by applying the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case. The major component of this experimental setup was a see-through-windowed high-pressure cell (IFT-10, Temco, U.S.A.). A stainless steel syringe needle was installed at the top of the pressure cell and used to form a pendant oil drop. The crude oil was introduced from a crude oil sample cylinder (DBR, Canada) to the syringe needle by using the programmable syringe pump. A light source and a glass diffuser were used to provide uniform illumination for the pendant oil drop. A microscope camera (MZ6, Leica, Germany) was used to capture the sequential digital images of the dynamic pendant oil drop inside the pressure cell at different times. The high-pressure cell was positioned horizontally between the light source and the microscope camera. The entire ADSA system and the highpressure cell were placed on a vibration-free table (RS4000, Newport, U.S.A.). The digital image of the dynamic pendant oil drop at any time was acquired by using a digital frame grabber (Ultra II, Coreco Imaging, Canada) and stored in a DELL desktop computer.

8920 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008

Figure 2. Schematic of the experimental setup for measuring the dynamic and equilibrium IFTs between the crude oil and CO2 by applying the ADSA technique for the pendant drop case.

The pressure cell was first filled with CO2 at a prespecified pressure and a constant temperature. After the pressure and temperature inside the pressure cell reached their stable values, the crude oil was introduced from the crude oil sample cylinder to the pressure cell to form a pendant oil drop at the tip of the syringe needle. Once a well-shaped pendant oil drop was formed, the sequential digital images of the dynamic pendant oil drop were acquired and automatically stored in the computer as tagged image file format (TIFF) files. Then the ADSA program for the pendant drop case was executed to determine the dynamic and equilibrium IFTs of the pendant oil drop. The IFT measurement was repeated for at least three different pendant oil drops to ensure satisfactory repeatability at each prespecified pressure and constant temperature. In this study, the crude oil-CO2 dynamic and equilibrium IFTs were measured at a constant temperature of T ) 27 °C and 12 different equilibrium pressures, ranging from 2.4 to 11.0 MPa. It is worthwhile to point out that only the measured equilibrium IFTs for the crude oil-CO2 system at different equilibrium pressures are of interest and will be presented in this paper. 3. EOS Modeling In phase behavior studies, the vapor-liquid equilibrium (VLE) of the reservoir fluids under the actual reservoir conditions is usually predicted by using an equation of state (EOS). The required input data for the EOS modeling are the critical pressure (Pc), critical temperature (Tc), and Pitzer acentric factor (ω) for each component of the fluids. Because a crude oil has an extremely complicated composition and contains an extremely large number of chemical compounds, in practice, it is often represented by a series of pseudocomponents, each of which is treated as a single component with definite values of Pc, Tc, and ω. In this study, with the compositional analysis result given in Table 1, the original crude oil was roughly divided into the following four pseudocomponents: component no. 1 (C7-C15), component no. 2 (C16-C22), component no. 3 (C23-C29), and component no. 4 (C30+). Some important properties of the four pseudocomponents were determined by using the CMG Winprop module. More

specifically, the molecular weight M, specific gravity γ, Pc, Tc, and ω for each of components no. 1, no. 2, and no. 3 were calculated directly from the CMG Winprop library for hydrocarbon components. The molecular weight M and specific gravity γ of component no. 4 were used as adjustable parameters to tune the SRK EOS10 and thus determined once the calculated density of the original crude oil best matched its measured value.11 In tuning the SRK EOS, the so-called binary interaction coefficients for all the hydrocarbon pairs, δij, i, j ) 1, 2, 3, 4, i < j, were set to be zero.12 Once the molecular weight M and specific gravity γ of component no. 4 were determined, its critical properties (i.e., Pc and Tc) and Pitzer acentric factor (ω) were calculated by using the Twu13 correlation, and the Edmister and Lee14 correlation, respectively. These properties of the four pseudocomponents are listed in Table 2, which are needed to model the VLE of the crude oil-CO2 system and predict the CO2 solubility in the crude oil under each equilibrium pressure. With the determined molecular weights and known weight or mole percentages of the four pseudocomponents, the apparent molecular weight of the original crude oil is found to be Moil ) 216.54 g/mol. In order to predict the CO2 solubilities in the crude oil at different equilibrium pressures and T ) 27 °C, CO2 was considered as component no. 5 in the crude oil-CO2 system, in addition to the above-mentioned four pseudocomponents for the original crude oil. With the above-calculated Pc, Tc, and ω values for the four pseudocomponents and those for component no. 5 (CO2), two-phase flash calculations were performed at each equilibrium pressure and T ) 27 °C to determine the quantities and compositions of the liquid and gas phases and predict the CO2 solubility in the crude oil. It should be noted that the binary interaction coefficients for all the hydrocarbon pairs, δij, i, j ) 1, 2, 3, 4, i < j, were assumed to be zero.12 The binary interaction coefficients for each of the four pseudocomponents with component no. 5 (CO2), δi5, i ) 1, 2, 3, 4, were used as adjustable parameters and thus determined once the predicted CO2 solubilities in the crude oil at different equilibrium pressures best matched the measured solubility data. Such

Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8921 Table 2. Some Important Properties of the Four Pseudocomponents of the Original Crude Oil Calculated by Using the CMG Winprop Module with the SRK EOS pseudocomponent no. 1 (C7-C15)

no. 2 (C16-C22)

no. 3 (C23-C29)

no. 4 (C30+)

43.33 138.57 0.786 67.71 2.432 627.78 0.448 0.0290

21.97 253.77 0.858 18.75 1.531 763.77 0.765 0.1485

11.13 344.44 0.891 7.00 1.153 838.19 0.983 0.1499

23.57 780.21 1.351 6.54 1.556 1299.98 1.357 0.1701

weight percentage (wt %) molecular weight M (g/mol) specific gravity γ ) Fo/Fw mole percentage (mol %) critical pressure Pc (MPa) critical temperature Tc (K) Pitzer acentric factor ω binary interaction coefficient δi5 with CO2

determined binary interaction coefficients, δi5, i ) 1, 2, 3, 4, are given in Table 2.

between the parachor and the molecular weight of each crude cut and proposed the following empirical correlation: p ) -11.4 + 3.23M - 0.0022M2

4. Equilibrium IFT Prediction Models In the past, several theoretical models have been proposed to predict the equilibrium IFT between a liquid and a fluid that are immiscible. Among the best IFT prediction models reported in the literature are the parachor model, 15-21 the gradient theory (GT) model,22 and the linear gradient theory (LGT) model.23,24 In this study, the parachor and LGT models are chosen to predict the equilibrium IFT versus equilibrium pressure data of the crude oil-CO2 system at T ) 27 °C. 4.1. Parachor Model. The parachor model is the most commonly used model in the petroleum industry for predicting the equilibrium IFT between a liquid and an immiscible fluid. In the literature, Macleod15 and Sudgen16 related the surface tension of a pure component to the molar density difference between its bulk liquid and vapor phases by σ ) [p(FL - FV)]4

(2)

where σ is the surface tension in mJ/m2; FL and FV are the molar densities of the bulk liquid and vapor phases in mol/cm3, respectively; and p is known as the parachor. It is worthwhile to emphasize that the parachor is a property of a pure component, generally independent of the pressure and temperature.19,25 The above relation was later extended to a multicomponent mixture by Weinaug and Katz:17

(

r

γeq ) FL

r

∑xp -F ∑yp V

i i

i)1

i i

i)1

)

4

p ) 176.05005 - 7472.9807Vc - 0.87458088Tc + 1560.4793H + 19.309439H2 + 0.05013801H3 -

where M is the molecular weight of each crude cut. Furthermore, Ahmed26 correlated the parachor of a hydrocarbon mixture with its molecular weight M by p ) -4.614873 + 2.558855M + (3.4004065 × 10-4)M2 + 3767.396 (6) M Finally, Fanchi21 showed that the parachor of a normal alkane (n-CnH2n+2) has a linear relation with its molecular weight M: p ) 10 + 2.92M (7) 4.2. Linear Gradient Theory (LGT) Model. In the linear gradient theory (LGT), a planar interface is assumed between the bulk liquid and vapor phases. In addition, it is also assumed that the molar density of each component at the VLE state is linearly distributed across the liquid-vapor interface.23,24 Therefore, with known respective molar densities of each component in the bulk liquid and vapor phases, its molar density across the interface can be easily determined by using the linear distribution assumption. Unlike the GT, the LGT does not require solving a set of differential and algebraic equations to determine the molar density distribution of each component across the interface.22 Similar to the GT,22 the LGT calculates the equilibrium IFT γeq between the bulk liquid and vapor phases by using

(3)

In this equation, γeq is the equilibrium IFT between the bulk liquid and vapor phases of the multicomponent mixture; xi and yi are the respective mole percentages of the ith component in the bulk liquid and vapor phases, i ) 1, 2,..., r; r is the number of components in the mixture; and pi is the parachor of the ith component. Fanchi18 proposed the following correlation for calculating the parachor of a hydrocarbon mixture:

γeq )



F1L

F1V

√2c[P + ω(F)] dF1

∆F1 ) {max |FiL - FiV|;

(9)

Here, Fi and Fi are the molar densities of the ith component in the bulk liquid and vapor phases, respectively, i ) 1, 2,..., r. The influence parameter c in eq 8 can be calculated by applying the following mixing rule:23,24 r

Here, Vc is the molar specific critical volume in L/mol and Tc is the critical temperature in K. In addition, Firoozabadi et al.19 calculated the parachors of several crude cuts of various crude oils from their surface tensions. They found a quadratic relation

i ) 1, 2, ..., r}

V

where H ) Vc5⁄6Tc0.25

(8)

where c is the influence parameter, P is the equilibrium pressure, ω(F) is the grand canonical free energy density, and F1 represents the integral variable. As proposed by Zuo and Stenby,23,24 the subscript “1” denotes a component that has a maximum molar density difference between its bulk liquid and vapor phases at the VLE state:

L

25.691718 H (4)

(5)

c)

r

∑∑zzc

i j ij

(10)

i)1 j)1

where zi is the mole percentage of the ith component in the mixture, i ) 1, 2,..., r. The relation between the influence parameters of two pure components, cii and cjj, and their “crossterm” influence parameter cij is approximated as23,24

8922 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008

cij ) √ciicjj ;

i, j ) 1, 2, ..., r

(11)

Furthermore, a formula for estimating the influence parameter of an inorganic gas or hydrocarbon was derived by Zuo and Stenby23,24 on the basis of the SRK EOS: cii aibi2/3

) (1.403 × 10-16)Ai(1 - Tr,i)Bi ;

i ) 1, 2, ..., r (12)

Here, ai and bi are the SRK EOS constants of the ith component; Tr,i is its reduced temperature by its critical temperature; Ai and Bi are constant and can be calculated from the following equations, respectively:23,24 Ai ) 0.28367 - 0.05164ωi

(13)

Bi ) -0.81594 + 1.06810ωi - 1.11470ωi

2

(14)

where ωi is the Pitzer acentric factor of the ith component. The grand canonical free energy density, ω(F), is defined as r

ω(F) ) f(F) -

∑Fµ

(15)

i i

i)1

Here, f(F) is the Helmholtz free energy density of a homogeneous mixture with the molar density F, Fi is the molar density of the ith component in the mixture, and µi is its molar chemical potential in the bulk liquid or vapor phase at the VLE state. Both f(F) and µi can be directly derived from a given EOS by using the following respective relations:27

[

f(F) ) FRT



F

0

(

)

]

r



P 1 1 - dF + Fi ln Fi 2 F F RTF i)1

µi )

[ ] ∂f(F) ∂Fi

(16) (17)

T,V,Fj(j*i)

For the SRK EOS used in this study, f(F) and µi can be derived and are given by r

f(F) ) -FRT ln(1 - bF) -



aF ( ln 1 + bF) + RT Fi ln Fi b i)1 (18)

µi ) -RT ln

(

)

abiF FRTbi 1 - bF + Fi 1 - bF b(1 + bF)

[

r

]

abi ln(1 + bF) 2 zj√aiaj(1 - δij) + RT (19) b b j)1



In eqs 18 and 19, R is the universal gas constant; T is the absolute temperature; a and b are the SRK EOS constants of the mixture; and δij are the binary interaction coefficients between the ith and jth components, i, j ) 1, 2,..., r. The numerical procedure for predicting the equilibrium IFT of a crude oil-CO2 system by using the LGT model is summarized as follows: (1) The VLE is modeled by using the SRK EOS to calculate the molar densities and mole percentages of each component in the bulk liquid and vapor phases. (2) The calculated VLE results are then used to determine the integral variable F1 from eq 9. (3) The molar chemical potential of each component in the bulk liquid or vapor phase at the VLE state is calculated from eq 19. (4) The liquid-vapor interface is subdivided into a number of equal intervals in this study. The composition of the crude oil-CO2 mixture in each interval is then calculated by applying

Figure 3. Comparison of measured and calculated CO2 solubilities in the Weyburn crude oil at different equilibrium pressures and T ) 27 °C.

the linear molar density distribution assumption for each component across the interface at the VLE state. (5) Based on the calculated composition of the crude oil-CO2 mixture in each interval, the influence parameter, Helmholtz free energy density and grand canonical free energy density are calculated from eqs 10, 18, and 15, respectively. (6) Finally, the equilibrium IFT of the crude oil-CO2 system under an equilibrium pressure is predicted from eq 8 by using the trapezoidal numerical integration method. 5. Results and Discussion 5.1. CO2 Solubility Data. In this study, the CO2 solubilities in the crude oil were measured at four different equilibrium pressures and T ) 27 °C. The measured CO2 solubility in the crude oil versus equilibrium pressure data (solid symbols) at T ) 27 °C are shown in Figure 3. It is seen from this figure that the measured CO2 solubility in the crude oil sample increases almost linearly with the equilibrium pressure. A linear regression (solid line) of the measured solubility data was undertaken, and the linear correlation is also given in Figure 3. The large correlation coefficient of R2 ) 0.994 indicates excellent linearity between the measured solubility and the equilibrium pressure for the crude oil-CO2 system in the equilibrium pressure range 2.4-6.0 MPa. The CO2 solubilities in the crude oil at different equilibrium pressures were also calculated by using the CMG Winprop module with the SRK EOS and are shown in Figure 3. It is found that the calculated CO2 solubility data (dashed line) agree fairly well with the measured data in the equilibrium pressure range tested. 5.2. Measured Equilibrium IFTs. In the IFT measurement, it was found that, at each equilibrium pressure tested in this study, the measured dynamic IFT of the crude oil-CO2 system ultimately reached a minimum value after at most 30 min, which is referred to as the equilibrium IFT. The average value of the equilibrium IFTs of three repeated IFT measurements at the same equilibrium pressure and temperature is reported in this paper. The measured equilibrium IFTs between the crude oil and CO2 at 12 different equilibrium pressures and T ) 27 °C are plotted in Figure 4. It is found from this figure that the measured equilibrium IFT is reduced almost linearly with the equilibrium pressure as long as it is lower than a threshold pressure (i.e., 7.2 MPa). In this case, the equilibrium IFT reduction with the equilibrium pressure is attributed to the increased solubility or dissolution of CO2 in the crude oil at an increased equilibrium pressure.28

Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8923

Figure 4. Measured equilibrium IFTs of Weyburn crude oil-CO2 system at different equilibrium pressures and T ) 27 °C.

Figure 5. Comparison of predicted (lines) and measured (symbols) equilibrium IFTs of the Weyburn crude oil-CO2 system at different equilibrium pressures and T ) 27 °C.

In addition, Figure 4 shows that once the equilibrium pressure is equal to and higher than the threshold pressure (i.e., 7.2 MPa), a slightly reduced equilibrium IFT of as low as 1-2 mJ/m2 is achieved. In the dynamic IFT measurement, it was also observed that, at equilibrium pressures equal to or higher than 6.6 MPa, some light components were extracted from the pendant oil drop to CO2 phase at the beginning.29 Hence, at P g 6.6 MPa, some light components of the original crude oil were quickly extracted and the final pendant oil drop formed at the tip of the syringe needle was mainly composed of the heavy components of the original crude oil. These leftover heavy components made the measured equilibrium IFT between the remaining crude oil and CO2 marginally reduced with the equilibrium pressure at P g 7.2 MPa. With the measured data (symbols) in Figure 4, the measured equilibrium IFT γeq (mJ/m2) is correlated to the equilibrium pressure P (MPa) by applying the linear regression in the following two pressure ranges, respectively: γeq ) -3.356P + 26.34

(2.4 MPa e P e 7.2 MPa, R2 ) 0.994) (20)

γeq ) -0.232P + 3.69

(7.2 MPa e P e 11.0 MPa, R2 ) 0.999) (21)

5.3. Predicted Equilibrium IFTs from the Parachor Model. In this study, four different correlations, i.e., eqs 4, 5, 6, and 7, were used to calculate the parachors of the four pseudocomponents of the original crude oil. Such calculated parachors are then used to predict the equilibrium IFTs of the crude oil-CO2 system at different equilibrium pressures and T ) 27 °C by applying the parachor model. The parachor of CO2 (i.e., component no. 5 in the crude oil-CO2 system) used in this study was 78 (mJ/m2)0.25/(mol/cm3), which was obtained from the CMG Winprop library for nonhydrocarbon components. Table 3 summarizes the measured and predicted equilibrium IFTs at seven different equilibrium pressures and T ) 27 °C. It is worthwhile to point out that the equilibrium IFTs between the crude oil and CO2 are predicted in the equilibrium pressure range of 2.4-6.0 MPa only, in which the measured CO2 solubility data in the crude oil are available. In this study, the average relative error (ARE) between the predicted and measured equilibrium IFTs of the crude oil-CO2 system at seven different equilibrium pressures is used as a statistical measure to compare the four correlations for calculating the parachors of the four pseudocomponents. It is seen from Table 3 that the equilibrium IFTs predicted by using the parachor model with the parachors calculated from eq 5 have the smallest ARE among the four correlations. Therefore, Firoozabadi et al.19 provide the best correlation for modeling the crude oil-CO2 equilibrium IFT in the equilibrium pressure range 2.4-6.0 MPa and at a constant temperature of 27 °C in this study. This is because this correlation was based on the parachors of several crude cuts of various crude oils determined from their surface tensions, whereas the other three correlations were obtained from the parachors of normal alkanes (n-CnH2n+2). It is also found from Table 3 that, based on the ARE values, eq 4 is the worst correlation. This is due to the large error in determination of the molar specific critical volume Vc for the C7+ fraction of the crude oil, as indicated by Ali.30 It is worthwhile to note that, in the parachor model, the parachor correlations are determined from the measured surface tensions of several pure components or crude cuts. In addition, it is assumed that the parachor of a component in a mixture remains the same as that of a pure component.31 This assumption means that although there exist strong mutual interactions among various components in a mixture,32 they are not considered. Furthermore, all the correlations used to calculate the parachors of the four pseudocomponents of the original crude oil, except for eq 5, are obtained from the measured surface tensions of normal alkanes. However, different types of hydrocarbons other than normal alkanes are present in the C7+ fraction of the crude oil, whose parachors cannot be accurately calculated from the correlations developed for normal alkanes only. These are the major reasons why the parachor model is generally unsuitable for predicting the equilibrium IFT of the crude oil-CO2 system tested in this study. 5.4. Predicted Equilibrium IFTs from the LGT Model. The equilibrium IFTs predicted by using the LGT model at seven different equilibrium pressures and T ) 27 °C are also given in Table 3. It is noted from this table that the ARE of the equilibrium IFTs predicted from the LGT model is much smaller than those of the equilibrium IFTs predicted from the parachor model with any correlations. The LGT model provides the best predicted equilibrium IFTs between the crude oil and CO2 at the equilibrium pressures and temperature tested in this study. More precisely, the predicted equilibrium IFTs from the LGT model are always slightly higher than the measured data in the equilibrium pressure range 2.4-6.0 MPa. This is probably due

8924 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 Table 3. Comparison of the Predicted Equilibrium IFTs between the Crude Oil and CO2 from the Parachor and LGT Models and the Measured IFTs at Seven Different Equilibrium Pressures and 27 °C equilibrium pressure (MPa) measured or predicted IFT (mJ/m2)

2.4

3.5

4.2

4.6

5.0

5.5

6.0

ARE (%)

in this study Fanchi18 (eq 4) Firoozabadi et al.19 (eq 5) Ahmed26 (eq 6) Fanchi21 (eq 7) LGT model23,24 (eq 8)

17.61 30.37 10.78 18.67 25.07 20.48

14.66 26.86 9.43 16.47 22.14 16.28

12.65 24.53 8.48 14.99 20.20 13.56

11.35 23.26 7.94 14.18 19.13 12.47

9.98 21.90 7.35 13.31 17.97 10.91

7.93 20.25 6.60 12.23 16.57 9.14

6.08 18.79 5.86 11.26 15.31 6.91

119.8 26.3 33.5 80.3 11.6

to the combining rule in eq 11 for calculating the “cross-term” influence parameter cij from those for two pure components, cii and cjj. In principle, the combining rule33 tends to overestimate the influence parameter cij and thus the equilibrium IFT γeq from eq 8 by using the LGT model. 5.5. Comparison of MMPs. In this section, the equilibrium IFT versus equilibrium pressure data predicted from the parachor and LGT models are used to determine the MMPs of the crude oil-CO2 system at T ) 27 °C by applying the VIT technique, respectively. Such determined MMPs are then compared with the MMP determined from the measured crude oil-CO2 equilibrium IFT versus equilibrium pressure data. Hence, the suitability of these two equilibrium IFT prediction models for determining the MMP of the crude oil-CO2 system can be assessed. The detailed equilibrium IFTs of the crude oil-CO2 system predicted from the parachor and LGT models are given in Table 3. The predicted equilibrium IFTs γeq (mJ/m2) from each IFT model can be correlated to the equilibrium pressure P (MPa) in the equilibrium pressure range 2.4 MPa e P e 6.0 MPa: γeq ) -3.242P + 38.16

(R2 ) 0.999, for the parachor model with eq 4) (22)

γeq ) -1.371P + 14.17

(R2 ) 0.998, for the parachor model with eq 5) (23)

γeq ) -2.073P + 23.69

(R2 ) 0.999, for the parachor model with eq 6) (24)

γeq ) -2.731P + 31.66

(R2 ) 0.999, for the parachor model with eq 7) (25)

γeq ) -3.701P + 29.32

(R2 ) 0.999,

for the LGT model with eq 8) (26) The five linear correlations eqs 22-26 (lines) are plotted in Figure 5. The measured equilibrium IFTs (symbols) in the equilibrium pressure range 2.4-7.2 MPa are also shown in this figure for comparison purposes. Figure 5 shows that, in general, all the predicted equilibrium IFTs by using the parachor model, except for those predicted from eq 5, are always significantly higher than the measured data at 2.4 MPa e P e 6.0 MPa. In addition, the predicted equilibrium IFT versus equilibrium pressure data from each correlation for the parachor model or from the LGT model can be used to determine the MMP of the crude oil-CO2 system by applying the VIT technique. For the parachor model, only the equilibrium IFTs best predicted by using eq 5 are used to determine the MMP. Thus the linear correlations given in eqs 23 and 26 are extrapolated to zero equilibrium IFT (dotted lines) in Figure 5 to determine the MMPs of the crude oil-CO2 system, respectively. Such determined MMPs of the crude oil-CO2 system are found to be 10.34 MPa for the parachor model with the best correlation

in eq 5, and 7.92 MPa for the LGT model. On the other hand, the measured equilibrium IFT is correlated to the equilibrium pressure at 2.4 MPa e P e 7.2 MPa and this correlation is given in eq 20. The MMP of the crude oil-CO2 system is determined from the measured equilibrium IFTs and found to be 7.85 MPa by applying the VIT technique. The comparison of the MMPs determined from the predicted and measured equilibrium IFTs shows that the LGT model is suitable for determining the MMP of the crude oil-CO2 system tested in this study. Nevertheless, the parachor model with the best correlation for calculating the parachors overestimates the MMP by approximately 32%. 6. Conclusions In this paper, the CO2 solubilities in a crude oil and the equilibrium IFTs of the crude oil-CO2 system are measured under different equilibrium pressures and at 27 °C. The detailed experimental results show that the CO2 solubility in the crude oil is increased almost linearly but the crude oil-CO2 equilibrium IFT is reduced almost linearly with the equilibrium pressure. In addition, both the parachor model and the LGT model are applied to predict the equilibrium IFTs of the crude oil-CO2 system at different equilibrium pressures and 27 °C. The comparison of the predicted equilibrium IFTs from the parachor model and the measured data shows that, in general, the parachor model poorly predicts the equilibrium IFTs between the crude oil and CO2 in the equilibrium pressure range tested. On the other hand, the predicted equilibrium IFTs from the LGT model are in excellent agreement with the measured data. Furthermore, it is found that, by extrapolating the predicted equilibrium IFT versus equilibrium pressure linear correlation to zero equilibrium IFT, the MMP of the crude oil-CO2 system determined from the predicted equilibrium IFTs by using the LGT model agrees well with that determined from the measured equilibrium IFTs. However, the parachor model always significantly overestimates the MMP of the crude oil-CO2 system. Acknowledgment The authors wish to acknowledge a discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and an innovation fund from the Petroleum Technology Research Centre (PTRC) at the University of Regina to Y.G. Literature Cited (1) Bon, J.; Sarma, H. K.; Theophilos, A. M. An Investigation of Minimum Miscibility Pressure for CO2-Rich Injection Gases with PentanePlus Fractions. Presented at the SPE Pacific Improved Oil Recovery Conference, Kuala Lumpur, Malaysia, Dec 5-6, 2005; Paper SPE 97536. (2) Dong, M.; Huang, S.; Dyer, S. B.; Mourits, F. M. A Comparison of CO2 Minimum Miscibility Pressure Determinations for Weyburn Crude Oil. J. Pet. Sci. Eng. 2001, 31, 13–22.

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ReceiVed for reView March 4, 2008 ReVised manuscript receiVed September 12, 2008 Accepted September 18, 2008 IE800358G