Modeling the Saturation Pressure of Systems Containing Crude Oils

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Modeling the Saturation Pressure of Systems Containing Crude Oils and CO2 Using the SRK Equation of State Verônica J. Pereira,† Victor B. Regueira,† Gloria M. N. Costa,*,† and Silvio A. B. Vieira de Melo†,‡ †

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Programa de Engenharia Industrial, Escola Politécnica, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, Federaçaõ , 40210-630 Salvador, Bahia, Brazil ‡ Centro Interdisciplinar em Energia e Ambiente, Campus Universitário da Federaçaõ /Ondina, Universidade Federal da Bahia, 40170-115, Salvador, Bahia Brazil S Supporting Information *

ABSTRACT: This work investigates the saturation pressure of crude oil−CO2 mixtures and how the oil plus-fraction characterization methods affect it. Different distribution functions were tested to split the plus-fraction as well as correlations to calculate the critical parameters and the acentric factor. The Soave−Redlich−Kwong (SRK) equation of state was used to calculate the saturation pressure of the crude oil and its mixtures with pure and impure CO2. The results were compared with experimental data and reveal that the effect of the characterization methods on the modeling of the saturation pressure of reservoir fluids is strong mainly for CO2 molar fraction values higher than 50%.

1. INTRODUCTION Miscible gas injection is a useful option for enhanced oil recovery (EOR) in a mature oil reservoir because it improves the displacement efficiency of the oil and consequently increases the recuperation factor. Carbon dioxide is the most common miscible gas injected for enhanced oil recovery (EOR) processes. It has a lower minimum miscibility pressure (MMP) than other gases, such as nitrogen,1,2 and its injection improves the displacement efficiency and consequently increases the oil recuperation factor. However, the supply of CO2 usually contains other components, such as N2, H2S, and CH4, which have a strong effect on the phase behavior of CO2 mixtures and its capacity to recover oil.3−5 Knowledge of phase behavior for CO2−oil mixtures is crucial to the design and operation of EOR and surface processes.6 For instance, an accurate description of the phase diagram enables the easy identification of the phase boundaries.7 As a result, it is possible to know if the system remains miscible with the gas, which is required for a more efficient residual oil displacement and recovery process. Moreover, CO2 injection has a significant effect on asphaltene precipitation, and the proper thermodynamic modeling can aid in accurate predictions of the asphaltene onset precipitation curve (AOP).8,9 For models that describe the asphaltene precipitation through regular solution theory, as cubic and noncubic equations of state, parameter estimation requires experimental data of the saturation pressure and AOP to calculate the AOP for a wide range of gas−oil mixture compositions. Therefore, if the model does not provide a good description of the saturation pressure, then the AOP calculation is also impaired.10,11 Figure 1 shows an example of a diagram for the saturation pressure versus CO2 mole fraction in which there is only one © XXXX American Chemical Society

Figure 1. Oliveira et al.’s method9 based on the saturation pressure curve and the CO2 MMP versus CO2 molar fraction.

Special Issue: Latin America Received: November 14, 2018 Accepted: February 27, 2019

A

DOI: 10.1021/acs.jced.8b01077 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Splitting Distributions Evaluated in This Work distribution 33

exponential

Mi and xi

SGi

Mi = A + B ln xi ÄÅ ÅÅ ÅÅ (M − η)α − 1 exp − Å F(M ) = ÅÅÅÅ ÅÅ β α Γ(α) ÅÅ ÅÅÇ

(

gamma34

35

generalized

M−η β

)

ÑÉÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑÖ

SGi = C + D ln(Mi)

SGi = 0.2855 + Cf (Mi − 66)0.13

ÉÑ B 1 ÄÅ Ñ ÅÅ A ÅÅ gm jijj 1 zyzzÑÑÑ gm Å MWi = MW0 + MW0ÅÅ lnjj zzÑÑÑ ÅÅ Bgm j 1 − xi zÑÑ ÅÇ {ÑÖ k

ÉÑ B1 ÄÅ Ñ ÅÅ A Å gs ijjj 1 yzzzÑÑÑ gs SGi = SG0 + SG0ÅÅÅÅ lnjj zzÑÑÑ ÅÅ Bgs j 1 − x wi zÑÑ ÅÇ {ÑÖ k

readjustment of many oil properties to match the experimental data, several authors have raised concerns regarding indiscriminate EOS parameter readjustment. Therefore, the tuning method should be used cautiously with a critical analysis of the data; otherwise, it may end up negatively affecting the prediction of other properties.23 In this work, we proposed a framework for using the characterization and tuning methods in a more accurate manner.24,25 While some noncubic EOSs have a good capacity to describe the effect of specific intermolecular forces, the use of CEOS still predominates in industry,26 meeting the needs for reservoir fluid calculations. Moreover, in recent work, Varzandeh et al.27 showed that the CEOS approach with a volume translation and proper characterization can accurately predict the saturation pressure and density for a large database of reservoir fluids when compared to the PC-SAFT EOS. There is no study to date that shows a fair comparison of both approaches using the same number of estimated parameters and under the same conditions. Even some works, which focus on more recent thermodynamic approaches,28 suggest the need to improve the characterization methods18,29−31 as a result of the great uncertainty in the oil heavy-fraction properties and given the limitations of experimental characterization methods nowadays. Many applications use only the most common characterization methods without investigating their effects on the phase behavior description. They are usually easily available in commercial simulators and are not always the most appropriate. The objective of this article is to calculate crude oil saturation curves with pure and impure CO2 and investigate the effects of the oil characterization methods on this calculation. Furthermore, a tailored parameter estimation method is proposed to better use the experimental data and ensure an accurate calculation of the saturation curve for crude oil−CO2 mixtures in a wide range of compositions.

liquid phase on the left side of the saturation curve. On the right side of the saturation curve, there may be two (LL or LV) or three (LLV) phases in equilibrium depending on the pressure and CO2 mole fraction. Thus, asphaltene onset precipitation does not occur at pressures or CO2 mole fractions on the left side of the saturation pressure diagram. On the basis of this fact, Oliveira et al.9 proposed a method to predict the amount of injected CO2 that promotes asphaltene precipitation based on the saturation pressure curve of CO2−crude oil mixtures and CO2 MMP. According to this approach, the CO2 mole fraction that causes the onset of asphaltene precipitation corresponds to the point where the MMP line crosses the saturation pressure curve, indicated by letter B in Figure 1. Therefore, a good description of the saturation curve allows an accurate prediction of the onset of asphaltene precipitation by gas injection. Reservoir fluids are composed of hydrocarbon fractions of high complexity and diversity, and it is difficult to identify all heavy components by experimental analysis.12 Phase equilibrium calculations involving reservoir fluids require parameters for each component of the mixture, which are not easily available for the heaviest compounds, requiring a proper plus-fraction characterization to determine the input parameter values of the equation of state (EOS).13,14 An adequate characterization method should have a low computational cost, reduce the loss of information in the system description, and increase the EOS accuracy. This constitutes a fundamental step in the thermodynamic modeling of reservoir fluids. Aladwani and Riazi15 along with Kumar and Okuno16 emphasize the importance of the characterization methods for the prediction of properties by EOS and concluded that an inaccurate characterization could lead to a bad phase behavior prediction. The work of Abrishami et al.17 has already shown that the critical properties of heavy components greatly affect the simulation results of gas injection processes. Moreover, Hosseinifar and colleagues18 showed that the phase behavior and volumetric behavior results predicted by both the PC-SAFT model and cubic EOS (CEOS) strongly depend on the method that is used to estimate the properties of the heaviest fractions. However, there is no in-depth report in the literature about the effects of the characterization methods on the description of the saturation pressure curve after miscible gas injection. Besides the oil characterization, estimating the EOS binary interaction parameters is a common practice in modeling the saturation pressure of reservoir fluids.19−21 The binary interaction parameters of methane and heavy oil components along with the properties of pseudocomponents are recommended to be further adjusted22 with experimental data because of their experimental uncertainty and empirical correlation dependency. Although some process simulators suggest the

2. THERMODYNAMIC MODELING 2.1. Equation of State. In this work, the Soave−Redlich− Kwong (SRK) CEOS,32 expressed in eqs 1−3, was used to predict the saturation pressure, where P is the pressure, T is the temperature, R is the universal constant of gases, v is the molar volume, a is the temperature-dependent energy interaction parameter, and b is the covolume parameter. P=

a(T ) RT − v−b v(v + b)

(1)

Parameters a and b can be determined by the following van der Waals mixing rules B


Journal of Chemical & Engineering Data n

a=

Article

n

Table 2. Empirical Correlations for Estimating the Properties of the Pseudocomponents

∑ ∑ xixj(aiaj)0.5 (1 − kij) i

j

(2)

n

b=

∑ xibi i

(3)

where n is the number of components, xi and xj are the molar fractions of components i and j, kij is the binary interaction parameter between components i and j, and ai and bi are the pure component parameters obtained from the critical temperature (Tci), critical pressure (Pci) and acentric factor (ωi) . 2.2. Characterization Methods. Oil characterization is carried out following a three-step procedure to obtain the equation-of-state parameters from easily measured plus-fraction properties, such as the molecular weight (MW), specific gravity (SG), and boiling point (Tb): (a) The first step is called splitting, which consists of expanding the C7+ fraction based on grouped properties (MWC7+ or SGC7+) for a determined distribution. The exponential,33 gamma,34 and generalized distributions35 used in the present study are shown in Table 1. Although the parameters and shape of the gamma and generalized distributions can be adjusted using data beyond the C7+ fraction, if these data are not available then we follow the procedures given by the authors. These methods largely affect the phase behavior calculations due to MW and SG calculations. Thus, to evaluate all oils with the same base of comparison we decided to use C7+ data.

name and source

output properties

properties needed

Kesler−Lee (1976)37 API (1997)38 Riazi−Daubert (1987)39 Twu (1984)40 Cavett (1962)41 Winn (2014)42 Pedersen (2015)33 Lee−Kesler (1975)43 Kesler−Lee (1976)37 Edmister (1958)44 Korsten (1988)45 Soreide (1989)46 API (1997)38

Tc and Pc Tc and Pc Tc and Pc Tc and Pc Tc and Pc Tc and Pc Tc, Pc, and ω ω ω ω ω Tb Tb

SG and Tb SG and Tb MW and SG SG and Tb SG and Tb SG and MW SG and MW Tb, Tc, and Pc Tb, Tc, and Pc Tb, Tc, and Pc Tb, Tc, and Pc SG and MW SG and MW

the Pedersen correlation, as stated in the guidelines of Pedersen and colleagues,33 being lumping after the correlation step. 2.3. Parameter Estimation Methods. In this work, the initial values of the binary interaction parameters (kij) for the SRK EOS were obtained from the literature for predictive calculations.34 Usually, every kij is zero, except for the nonzero values shown in Table 3. Later, only the kij values between methane and the heavier pseudocomponents were further adjusted. Table 3. Initial Nonzero Binary Interaction Parameters

(b) The second step is a lumping procedure to reduce the number of components through grouping them in pseudocomponents and reduce the computational effort without reducing the accuracy of the predictions. To calculate the saturation pressure, the number of components does not have significant impact on computational time consumption. However, for reservoir simulation, this step is critical because of the complexity of the problem, and the literature recommends seven components at most.36 Nevertheless, it is not a critical step in this work because the computational time consumption is negligible in calculating the saturation pressure. First, the plus fraction was grouped into five pseudocomponents based only on the equality of mass fractions, and the other lighter components were left ungrouped.33

C1 C2 C3 to C7+

N2

CO2

0.02 0.06 0.08

0.12 0.15 0.15

Likewise, an adjustment of the pseudocomponent properties can be performed because they stem from empirical correlations and not measured values.34 However, much care should be taken to avoid making the calculation physically unfeasible and indicating a false phase separation prediction.33 Later on in this work, a new method is proposed to readjust the binary interaction parameter and the critical temperature to improve the oil phase behavior modeling after CO2 injection. 2.4. Experimental Data. The crude oil saturation pressure (Psat) is available at a given temperature (Tmes) for different molar fractions of CO2 in oil. The exceptions are oils O3 and O4, which have saturation curves for two different gases, G1−G2 and G3−G4, respectively, given in Table 4. Literature data were used to assess the effect of the characterization methods on modeling the saturation pressure of crude oil−CO2 mixtures. The composition and properties such as specific gravity (SG) and molar weight (MW) of nine selected oils are shown in Table 5. The uncertainty in the experimental data is not reported in the original papers.

(c) The third step is the use of empirical correlations to estimate the critical properties and the acentric factor of these pseudocomponents. There are several correlations in the literature, but only the most common and efficient were selected, which are shown in Table 2. It is worth noting that the Pedersen characterization that is referred to uses only the exponential distribution and Pedersen’s correlation, exactly as given by Pedersen et al.33 The other correlations use different combinations of the gamma and generalized distributions.

Table 4. Composition of Gases Injected into oil O3 (G1 and G2) and O4 (G3 and G4)

The Soreide46 correlation is always used after the gamma distribution to estimate the Tb distribution and SG distribution because of the limitations of this splitting technique. Also, the Lee−Kesler correlation43 is used only when Tb/Tc > 0.8, while for lower values the Kesler−Lee correlation37 is used for the acentric factor. The exponential distribution is used only with

N2 CO2 C1 C

G1

G2

G3

G4

0.2 95.0 4.8

Composition (%) 9.7 0.1 85.3 95.0 5.0 4.9

9.7 85.8 4.6



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Table 5. Composition and Properties of the Crude Oils

N2 CO2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 MWoil (kg·kmol−1) MWCn+ (kg·kmol−1) SGCn+ Tmes (K) Psat at Tmes (MPa)

[47]

[48]

[49]

[50]

[51]

[52]

[53]

[53]

[54]

O1

O2a

O3a

O4a

O5

O6

O7

O8

O9

0.96 0.16 24.06 0.76 3.26 0.64 2.70 0.52 1.06 0.70 0.58 1.86 2.30 0.82 59.62 (+)

0.96 0.03 3.87 2.51 4.63 1.24 3.88 2.30 2.82 0.00 77.65 (+)

0.11 0.45 25.40 1.09 2.76 1.04 2.32 1.28 1.75 1.71 62.09 (+)

0.34 0.25 4.07 3.11 4.88 2.09 3.58 2.45 3.07 5.51 70.67 (+)

0.39 1.74 20.55 7.31 5.34 1.00 3.65 3.10 4.75 5.48 3.23 1.32 2.27 2.19 1.81 35.87 (+)

1.38 6.88 27.42 5.64 5.78 1.88 3.38 2.65 3.67 5.06 36.24 (+)

279.5 442.0 0.922 339 7.4

211.5 259.0 0.902 338 2.2

209.9 319.7 0.889 328 7.6

176.9 227.9 0.861 344 2.6

167.7 370.0 0.977 369 9.9

113.4 247.0 0.887 326 12.7

0.12 1.86 31.69 6.19 5.75 1.34 3.38 1.51 2.09 3.25 3.76 3.95 3.58 3.35 2.76 2.37 2.30 2.38 2.13 1.93 1.68 1.47 1.35 9.82 (+) 111.0 403.8 0.909 386 15.5

0.10 2.74 32.86 6.68 6.47 1.59 4.06 1.81 2.53 3.60 3.94 4.15 3.74 3.35 2.70 2.20 1.98 1.64 1.50 1.23 1.06 0.95 0.90 8.24 (+) 100.2 424.5 0.916 398 16.2

0.22 0.44 40.28 4.83 5.73 1.54 2.76 1.54 1.44 2.59 5.42 7.81 4.57 4.01 2.71 2.05 2.17 1.92 2.35 1.36 1.00 1.11 0.45 1.70 (+) 76.6 335.0 0.860 369 15.9

a

Saturation curve points obtained using the experimental curve given in the original paper.

combination. The Pedersen characterization provided excellent results for oils O6 to O9. This makes sense given that these oils are lighter and more similar to the oils used in the development of the Pedersen correlation (North Sea oils). For crude oil O4, the saturation pressure results were very bad for all characterization methods, possibly caused by the fact that it has the lowest amount of methane. In general, it can be seen that a change in the characterization methods could lead to a wide range of results for the saturation pressure predictions. Moreover, to evaluate the impact of the number of pseudocomponents representing the heavy fraction, some characterization methods were fixed and the effect of changing the number of pseudcomponents to between one and five was evaluated. The average relative deviation (ARD) is presented in Figure 2 for all oils. It is possible to see that the effect is much less significant than changing the correlations or the splitting method. For the Pedersen correlation, the impact is more significant, but using three to five pseudocomponents is enough to achieve satisfactory results. 3.2. Effect of Characterization Methods on CO 2 Injection Processes. It is crucial to correctly model the saturation curve because the consequences of inaccuracy in the calculation of phase behavior for real applications are relevant. For instance, in a gas−EOR process, it is important to know if the system remains miscible with the gas to optimize the operation. If the predicted saturation curve is above the experimental saturation curve, then the recovery process is suboptimal and more gas has to be injected to improve the

However, as reported in the literature, the experimental errors in the molecular weight and the specific gravity of the plus fraction are about 5−10 and 5%, respectively.33

3. RESULTS AND DISCUSSION 3.1. Crude Oil Saturation Pressure. The saturation pressure is essential to understanding the reservoir fluid behavior because it is an indication of the phases present at a given temperature. An analysis was carried out that changed the characterization methods to predict the crude oil saturation pressure, using the kij values found in the literature. Considering only variations in the correlations and splitting techniques presented here, there are more than 50 different ways to characterize the oil. For this reason, some techniques were fixed at certain steps to analyze the effect of each characterization step separately. Initially, the number of pseudocomponents for the heavy fraction was fixed at five, an accepted number used in the literature. The absolute value of the relative deviation (RD) for the crude oil saturation pressure, defined as the absolute deviation divided by the magnitude of the experimental value, is shown in Table 6 for all oils. In Table 6, it can be seen that the calculated deviations are in the 0 to 60% range depending on the oil characteristics and the characterization method applied. By analyzing the results for oils O1, O2, O3, and O5, it was found that the lowest deviation was associated with the gamma distribution and the overall deviation was around 10%. However, for oil O1, the Twu correlation was the best, but for oil O3, it was the Cavett and Lee−Kesler D



Article

Table 6. Relative Deviation (% RD) of Each Characterization Method (Distribution and Correlations for Tc, Pc, and ω) for Each Oil and the Average for All Oils Regarding the Crude Oil Saturation Pressure at Tmes characterization methods distribution gamma

correlation (Tc, Pc) Winn

Kesler−Lee

API method

Twu

Cavett

generalized

Winn

Kesler−Lee

API method

Twu

Cavett

exponential

relative deviation (%) correlation (ω)

O1

O2

O3

O4

O5

O6

O7

O8

O9

ave

Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Lee−Kesler Edmister Korsten Pedersen

7.4 6.9 10.7 5.7 8.2 5.1 4.5 10.6 8.0 0.9 2.1 1.1 10.7 35.9 42.3 43.5 43.4 43.5 42.5 42.8 42.5 28.9 29.3 28.8 37.4 37.9 37.3 61.3 60.7 61.2 40.5

3.9 5.7 3.4 9.5 11.7 9.6 13.5 17.0 15.4 5.6 7.4 5.4 1.1 5.7 9.2 4.0 5.5 3.3 9.5 11.5 9.4 12.7 16.1 14.5 5.1 6.5 4.5 1.9 9.0 12.5 14.9

4.1 4.8 2.0 14.0 16.0 13.6 14.8 19.0 16.9 10.3 12.7 10.3 0.9 19.0 24.0 4.2 4.5 1.6 14.9 16.5 14.1 14.5 18.1 16.0 10.2 12.2 9.8 3.9 24.9 30.0 19.4

32.8 33.5 32.3 36.5 37.6 36.5 38.3 40.4 39.5 35.7 36.9 35.9 30.5 24.6 22.7 32.7 33.3 32.1 36.4 37.4 36.3 38.7 40.1 39.2 35.6 36.6 35.6 29.7 23.5 21.6 25.1

1.7 4.0 1.5 5.9 8.5 6.1 9.5 13.3 11.6 2.1 0.4 2.8 1.2 2.1 5.4 7.6 7.9 7.7 7.3 7.5 7.3 13.1 13.1 13.1 10.0 10.0 10.0 0.9 0.3 0.8 21.6

7.2 8.8 6.5 12.5 14.7 12.5 16.4 20.0 18.4 10.2 12.1 10.2 3.3 5.5 9.4 7.1 8.6 6.3 12.3 14.3 12.2 16.9 19.2 17.7 9.7 11.3 9.4 0.9 7.8 11.7 8.6

12.6 13.6 11.9 17.6 19.3 17.6 20.2 23.1 21.8 16.9 18.8 17.3 9.4 0.4 2.4 11.5 11.9 11.5 11.3 11.6 11.3 16.4 16.5 16.4 13.5 13.6 13.5 2.1 3.0 2.3 5.5

6.7 7.7 5.9 11.7 13.5 11.7 14.1 17.4 16.0 10.9 12.8 11.3 2.1 5.6 8.6 9.9 10.3 9.9 9.7 10.0 9.7 14.2 14.3 14.2 11.4 11.6 11.4 1.1 2.1 1.3 0.5

2.1 3.4 2.4 3.9 5.2 4.2 9.6 10.4 9.8 6.9 7.9 7.1 5.9 7.2 9.0 5.0 5.9 5.1 5.4 6.2 5.5 10.5 10.9 10.4 6.8 7.3 6.8 8.4 6.4 7.9 2.7

8.7 9.8 8.5 13.0 14.9 13.0 15.7 19.0 17.5 11.0 12.3 11.3 7.2 11.8 14.8 13.9 14.6 13.4 16.6 17.5 16.5 18.4 19.7 18.9 15.5 16.3 15.4 12.2 15.3 16.6 15.4

precipitation conditions, using the minimum miscibility pressure (MMP) of CO2.9 For these reasons, the same evaluation was done with gas injection to predict the mixture saturation pressure for different gas concentrations. This kind of analysis of characterization methods applied to the mixture saturation curve has never before been reported in the literature and is extremely important because an accurate description of the oil−gas phase diagram enables the easy identification of the phase boundaries and increases the efficiency of EOR processes. Five characterization methods, which provided different RDs in Table 6, were selected to be compared for the prediction of the whole mixture saturation curve. The results are presented in Figure 3 for oils O1 and O7 and reveal that the methods that provided the best result for the saturation pressure of crude oil (no gas addded) were not always able to correctly describe the whole curve for higher molar fractions of CO2. It was also seen that different characterization methods generate a wide range of saturation curves, depending on the method applied, changing the slope and the beginning of the curve. Subsequently, parameter kij between the pseudocomponents and methane was readjusted. The results are shown in Figure 4, and it can be seen that the correct adjustment of the saturation pressure of the crude oil without CO2 injection does not guarantee that the rest of the curve will be well described. The variability due to the characterization still has a considerable

Figure 2. Average relative deviation calculated by varying the number of pseudocomponents for the oils.

recovery while retaining the same miscibility. Alternatively, if the predicted saturation curve is below the experimental saturation curve, then the planned gas injection can be excessive and the gas becomes immiscible in the system. In addition, the effects are not restricted to reservoir processes because pipeline flow could also be affected. Maintaining a single-phase flow in pipelines is recommended, mainly because the biphasic flow pressure drop is much greater and much more complicated to estimate than the monophasic one. If the phase boundaries are not properly identified, then a second phase could appear, impairing the transport processes. A proper description of the saturation pressure curve is useful even in the identification of asphaltene E



Article

Figure 3. Effect of each characterization method for oils O1 and O7 saturation curves without parameter estimation.

Figure 4. Effect of each characterization for each oil saturation curve kij of the pseudocomponents with methane readjusted.

Figure 5. Complementary effects on the oil O1 saturation curve after exchanging Tc and kij of the pseudocomponents with methane for gamma|Cavett| Lee−Kesler characterization.

that of the experimental curve. Therefore, as the injected gas composition increases, the curve behavior becomes increasingly dependent on the characterization method, and the accuracy of the classic kij adjustment decreases. Significant changes in the slope of the curve are associated with the characterization methods, which indirectly affect the pseudocomponent properties through Tc, Pc, and ω. Thus, in addition to the kij adjustment between methane and the pseudocomponents, which affects only the CEOS attractive parameter (a), a modification of the critical temperature (Tc), which affects both the attractive and covolume parameters (a and b), is required to improve the saturation curve description. For this reason, the effects of changing these properties were analyzed. Figure 5 shows the effect of changing kij between

effect. It is important to note that for higher concentrations of CO2 the existence of multiple phases can often occur. An accurate description of the saturation curve can help to detect this; otherwise, it could impair the whole gas injection and the EOR processes. However, the kij between methane and heavy fraction adjustment is enough for small fractions of the injected gas because it makes the starting points of the calculated saturation pressure curves match the experimental value. The results and ARD for each oil can be found in Appendix A. It is important to say that readjusting kij can change the initial point but not the slope and the shape of the saturation curve, as seen before and after the adjustment. In other words, changing methane-heavy fractions kij only shifts the curve vertically and cannot match the whole curve because its slope is different from F



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Figure 6. Effects of the characterization methods on the saturation curve prediction if the proposed method is used for readjusting parameters MTc and kij.

Table 7. Changes in ARD (%) for the Saturation Curve with the Proposed Method of Parameter Readjusting kij readjusting

no readjusting O1 O2 O3−G1 O3−G2 O4−G3 O4−G4 O5 O6 O7 O8 O9

proposed readjusting

max

min

ave

max

min

ave

max

min

ave

105.7 71.1 21.7 34.6 24.7 22.1 32.5 122.8 39.1 27.6 13.4

11.4 7.9 5.8 1.7 11.3 0.0 16.2 39.2 15.4 9.1 5.9

37.9 33.2 13.7 14.5 17.2 13.6 24.8 88.6 26.0 15.8 9.7

71.0 63.2 18.0 17.7 31.1 18.2 31.6 112.0 41.8 27.2 14.1

11.0 6.9 0.5 1.7 9.7 0.0 9.9 49.9 7.2 2.8 2.1

26.4 30.5 10.4 7.6 20.8 10.5 21.6 84.2 24.7 15.1 6.8

10.4 2.5 0.4 1.5 3.4 12.3 9.4 13.9 5.7 3.1 2.5

4.5 2.0 0.4 1.3 2.8 0.0 4.2 10.9 4.0 2.3 1.9

8.9 2.2 0.4 1.4 3.1 9.0 7.0 12.7 4.5 2.6 2.2

the crude oil and P2 is another saturation pressure for a higher molar gas fraction mixed with the oil (e.g., saturation pressure of a mixture of 60% CO2 and 40% oil). However, care should be taken to adjust the critical temperature, avoiding the calculation of physically false phase separations.31 The adjustment based on the pseudocomponent critical temperatures is understandable because this is obtained from empirical correlations and is not measured. There are similar procedures for this method in the literature, but they were not applied in gas injection to overcome the variability in the characterization methods.

methane and pseudocomponents as well as the effect of Tc on the saturation curve for oil O1. It is clear how the adjustment of kij of the pseudocomponents with methane causes a vertical translation in the saturation curve, and the modification of Tc changes the slope of the curve. The effects of Pc and ω are similar but are not as strong on the slope and require considerable changes in the properties. By combining the adjustments to kij and Tc, an excellent fit can be obtained for the saturation curve. The two effects are complementary because the first (kij) has a significant effect on the beginning of the curve and the second (Tc) has a great impact on the final slope of the saturation curve. For this reason, an efficient framework for readjusting the model parameters is proposed by adjusting the kij of the pseudocomponents with methane and the critical temperature multiplier of each pseudocomponent based on the crude oil saturation pressure and another saturation pressure for a higher molar fraction of CO2. Therefore, the method of readjusting parameters proposed here consists of adjusting the critical temperature of the pseudocomponents through a multiplier (Mtc), according to eq 4, where N is the number of pseudocomponents representing the heavy fraction, Tc,i is the critical temperature of each pseudocomponent, and Tc,in is the adjusted critical temperature. Tc,n i = (Tc, i)(M t c), i = 1, 2, ..., N

sat 2 sat 2 E = (P1sat − P1,exp ) + (P2sat − P2,exp )

(5)

The results are illustrated in Figure 6 (for oils O1 and O7) and are excellent for all oils because there is a reduction in the variability due to the characterization methods, which ensures that all curves fit the experimental data. Further results can be seen in the Supporting Information. The changes in ARD for all characterization methods can be found in Table 7, where the results of the largest deviation (max), smallest deviation (min), and average deviations of all the different characterization methods can be found. Notice that in general the proposed method results in smaller deviations for all characterization methods than the adjustment of kij. The advantage of using the proposed method is made clear here, and it ensures a good prediction of the saturation curve in all cases, regardless of the characterization method. Only one additional experimental data point of saturation pressure, for high CO2 concentration, is used,

(4)

The adjustment is made on the basis of the minimization of the error (E), given by eq 5, where P1 is the saturation pressure of G



Article

ω x kij

acentric factor molar fraction binary interaction parameter between components i and j Tb boiling point SG specific gravity RD relative deviation ARD average relative deviation

but better results can be achieved if there is more data. Using only the minimum data highlights the usefulness of the method even in cases of data shortage.

4. CONCLUSIONS This article investigates the effects of oil heavy-end characterization methods on simulation of the high-pressure phase behavior of systems containing crude oils and pure or impure CO2. The adjustment of a binary interaction parameter is not enough to model the whole saturation curve correctly. It was seen that it is able to obtain good results mainly at low concentrations, close to the range where the model was adjusted. On the other hand, the effect of different characterization methods is significant at higher CO2 concentrations, and a new method to readjust parameter kij is proposed. This new method provided good results using as input experimental data only for the crude oil and one more saturation pressure data point for the oil−gas mixture to adjust the binary interaction parameter and the critical temperature of the pseudocomponents. The results were clearly better than those obtained when only the binary interaction parameter is fitted, and the method ensures a good prediction of the saturation curve in every case, independent of the characterization method. Therefore, this work provides valuable information and useful guidelines for applying characterization methods to model CO2−oil saturation curves using cubic equations of state.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01077. Results of CO2 injection processes (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Gloria M. N. Costa: 0000-0002-1689-0090 Silvio A. B. Vieira de Melo: 0000-0002-8617-3724 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support of ANP − Agência ́ Nacional de Petróleo, Gás Natural e Biocombustiveis and Petrogal Brasil S.A., related to grant number 19102-3 from the R&D investment rule.

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NOMENCLATURE EOR enhanced oil recovery MMP minimum miscibility pressure MW molecular weight EOS equation of state P pressure T temperature R universal constant of gases v molar volume a temperature-dependent interaction parameter b covolume parameter Tc critical temperature Pc critical pressure H



Article

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Modeling the Saturation Pressure of Systems Containing Crude Oils

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