Open access peer-reviewed chapter

Evaluation of Different Correlation Performance for the Calculation of the Critical Properties and Acentric Factor of Petroleum Heavy Fractions

By Dacid B. Lacerda, Rafael B. Scardini, André P. C. M. Vinhal, Adolfo P. Pires and Viatcheslav I. Priimenko

Submitted: August 9th 2017Reviewed: September 21st 2017Published: December 20th 2017

DOI: 10.5772/intechopen.71166

Downloaded: 445

Abstract

The characterization of petroleum fluids is fundamental for the calculation of their thermodynamic properties. Laboratory experiments are able to identify a limited number of pure components present in a sample. All remaining species, the so called “cut”, are characterized by its molecular weight and density. The thermodynamic calculations performed using cubic equations of state require the critical properties and the acentric factor, which are unknown for the petroleum “cut.” In this chapter, different correlations are used to calculate the critical properties and the acentric factor of the “cut” fraction. The performance of the correlations is evaluated through the comparison of a simulated pressure-volume-temperature (PVT) experiment using an equation of state and experimental data of two reservoir fluids.

Keywords

  • correlations of critical properties
  • petroleum heavy fractions
  • PVT experiments
  • thermodynamics
  • phase equilibrium

1. Introduction

Petroleum is a complex mixture of several chemical components, mainly hydrocarbons. In addition to the hydrocarbons, it may also contain some inorganic contaminants such as carbon dioxide (CO2), nitrogen (N2) and hydrogen sulfide (H2S).

The physical properties of reservoir fluids are related to the concentration of their components. Some properties such as bubble point pressure, oil formation volume factor, solubility ratio, oil density, gas formation volume factor and gas specific gravity are of particular interest in black oil reservoir engineering studies. These properties are generally obtained in laboratory using reservoir fluids samples. These experiments seek to replicate the isothermal recovery path of an oil field.

Pressure-volume-temperature (PVT) experiments are carried out in liquid mixtures of hydrocarbons and during the pressure reduction steps, dissolved gas is released. There are two types of experiments that simulate the constant temperature depletion of a reservoir fluid, “flash” and “differential”. In a “flash” experiment, the overall composition of the system is kept constant, whereas in a “differential” experiment the gas phase is removed from the system at each pressure step.

These experiments can be simulated using equations of state in order to evaluate different recovery schemes without carrying out one experiment for each possible scenario, especially in the cases of enhanced oil recovery techniques. The correct identification of the species and their concentrations is fundamental for the success of the simulation. However, in any laboratory test, the heavy fraction of the oil, the so-called “cut,” is characterized by its molecular weight and density. In order to simulate the experiment, correlations are necessary to calculate the critical properties and the acentric factor of the “cut” from its molecular weight and density. In this chapter, different correlations are used to determine the critical properties and acentric factor of the heavy fraction of two reservoir fluids, the PVT experiments of these fluids are simulated using an equation of state and the results are compared with laboratory data.

2. Methodology

Cubic equations of state are widely used to describe the volumetric properties of pure substances and mixtures in the petroleum industry. Furthermore, these models can be used for equilibrium calculations and to estimate PVT properties, such as bubble point pressure, oil formation volume factor, solubility ratio, oil specific weight, gas formation volume factor and gas density.

The input parameters of the most used equations of state are the acentric factor, ω, critical temperature, Tc, and critical pressure, Pc, of the mixture components. These parameters are tabulated for a large number of chemical compounds, but for the heavy fractions of petroleum fluids, they are determined from correlations. Most correlations are functions of density, γ, molecular mass, M, and/or normal boiling temperature, Tb, of the fractions [1].

Edmister [2] proposed a correlation to estimate the acentric factor of pure liquids and petroleum fractions. This correlation is given by:

ω=3logPc14.77TcTb11E1

Cavett [3] presented equations to estimate the critical temperature and pressure of hydrocarbon fractions. These correlations are a function of the normal boiling point and the API gravity:

Tc=a0+a1Tb+a2Tb2+a3APITb+a4Tb3+a5APITb2+a6API2Tb2E2
log(Pc)=b0+b1(Tb)+b2(Tb)2+b3(API)(Tb)+b4(Tb)3+b5(API)(Tb)2+b6(API)2(Tb)+b7(API)2(Tb)2E3

Tb: normal boiling temperature [°F].

The coefficients of Eqs. (2) and (3) are shown in Table 1.

iaibi
0768.07121000002.82904060
11.71336930000.94120109 × 10−3
2−0.0010834003−0.30474749 × 10−5
3−0.0089212579−0.20876110 × 10−4
40.3889058400 × 10−60.15184103 × 10−8
50.5309492000 × 10−50.11047899 × 10−7
60.3271160000 × 10−7−0.48271599 × 10−7
70.13949619 × 10−9

Table 1.

Coefficients of Cavett [3] correlation.

Kesler and Lee [4] developed correlations for critical temperature and pressure, molecular weight and acentric factor of oil fractions. These expressions are given by:

ln(Pc)=8.36340.0566γ(0.24244+2.2898γ+0.11857γ2)103Tb+(1.4685+3.648γ+0.47227γ2)107Tb2(0.42019+1.6977γ2)1010Tb3E4
Tc=341.7+811.1γ+0.4244+0.1174γTb+0.46693.26238γ105TbE5
ω=7.904+0.1352Kw0.007465Kw2+8.359Tbr+1.4080.01063Kw1Tbr,E6

for Tbr > 0.8, and

ω=lnPc14.75.92714+6.09648Tbr+1.28862lnTbr0.169347Tbr615.251815.6875Tbr13.4721lnTbr+0.43577Tbr6,E7

for Tbr ≤ 0.8.

In Eq. (6), Kw is the Watson characterization factor, given by:

Kw=Tb13γE8

Standing [5] developed the following correlations based on experimental data:

Tc=608+364logM71.2+2450logM3800logγE9
Pc=1188431logM61.1+2319852logM53.7γ0.8E10

Riazi and Daubert [6] proposed a simple two-parameter equation to calculate the physical properties of pure components and mixtures of hydrocarbons:

θ=aTbbγcE11

where θ is the property (Tc, Pc, vc or M), vc is the critical volume (ft3/lb) and a to c are constants for the correlation of each property.

Table 2 shows the coefficients of Eq. (11) and the errors in the estimative of each property.

θabcAverage deviation (%)Max deviation (%)
M−4.56730 × 10−52.19620−1.01642.611.8
Tc24.278700.588480.35961.310.6
Pc−3.12281 × 109−2.312502.32013.1−9.3
Vc−7.52140 × 10−30.28960−0.76662.3−9.1

Table 2.

Coefficients of Riazi and Daubert [6] correlation.

Sim and Daubert [13] determined expressions to calculate the critical pressure and critical temperature of petroleum “cuts,” given by:

Pc=3.48242×109Tb2.3177γ2.4853E12
Tc=exp3.99347Tb0.08615γ0.04614E13

Twu [7] proposed a set of correlations, based on the perturbation-expansion theory with normal paraffins as the reference state, to determine the critical properties of heavy fractions of hydrocarbons. The method is based on the selection of a normal paraffin with normal boiling temperature, TbPi, identical to the normal boiling temperature of the Cn+ fraction. Once the normal paraffin is chosen, the heavy fraction critical properties are calculated through the following steps:

1. Calculate the critical properties of the normal paraffin

TcPi=TbC++A1+A2TbC++A3TbC+2+A4TbC+3+A5A6TbC+13E14
PcPi=A1+A21TbC+TcPi0.5+A31TbC+TcPi+A41TbC+TcPi2+A51TbC+TcPi4E15
γPi=A1+A21TbC+TcPi+A31TbC+TcPi3+A41TbC+TcPi12E16
vcPi=1A1+A21TbC+TcPi+A31TbC+TcPi3+A41TbC+TcPi148E17

The constants of the Eqs. (14)(17) are shown in Table 3.

PropertyA1A2A3A4A5A6
TcPi0.53322720.191017 × 10–30.779681 × 10−7−0.284376 × 10−100.959468 × 10−20.01
PcPi3.838541.1962934.888836.1952104.193
γPi0.843593−0.128624−3.36159−13749.5
vcPi−0.4198690.5058391.564369481.7

Table 3.

Constants used in the calculation of the critical properties of the normal paraffin [7].

2. Calculate the heavy petroleum fraction properties from the equations

TcCn+=TcPi1+2fTi12fTiE18
fTi=exp5γpiγCn+1A1TbCn+0.5+A2+A3TbCn+0.5exp5γpiγCn+1E19
vcCn+=vcPi=1+2fvi12fvi2E20
fvi=exp4γpi2γCn+21A1TbCn+0.5+A2+A3TbCn+0.5exp4γpi2γCn+21E21
PcCn+=PcPivcPivcCn+1+2fPi12fPi2E22
fPi={exp[0.5(γpiγCn+)]1}[(A1+A2TbCn+0.5+A3TbCn+)+(A4+A5TbCn+0.5+A6TbCn+){exp[0.5(γpiγCn+)]1}]E23

where TcPi is the critical temperature of the normal paraffin (°R), TcC+ is the critical temperature of the heavy petroleum fraction (°R), PcPi is the critical pressure of the normal paraffin (psia), PcC+ is the critical pressure of the heavy oil fraction (psia), γPi is the density of the normal paraffin, γC+ is the density of the heavy petroleum fraction, vcPi is the critical volume of the normal paraffin (ft3/lbmol) and vcC+ is the critical volume of the heavy oil fraction (ft3/lbmol).

Constants utilized in Eqs. (18)(23) are presented in Table 4.

PropertyA1A2A3A4A5A6
fTi−0.3624560.0398285−0.948125
fvi0.466590−0.1824213.01721
fPi2.53262−46.19553−0.00127885−11.4277252.140.00230535

Table 4.

Constants used in the calculation of the critical properties of the heavy oil fraction Cn+ [7].

Riazi and Daubert [8] developed a general correlation given by the following expression:

θ=aθ1bθ2cexpdθ1+eθ2+fθ1θ2E24

In Eq. (24), θ1 and θ2 are two parameters accounting for the molecular forces and molecular size of a component. It was found that (Tb, γ) and (M, γ) are appropriate sets of input parameters for the correlation. Based on these results, two expressions were proposed:

θ=aTbbγcexpdTb++fTbγE25
θ=aMbγcexpdM++fMγE26

Tables 5 and 6 present the coefficients for Eqs. (25) and (26).

θabcdef
M581.96−0.974766.512740.0005430769.533840.00111056
Tc10.64430.810670.53691−0.000517470−0.544440.00035995
Pc6162000−0.48444.0846−0.00472500−4.80140.0031939
Vc0.00062330.7506−1.2028−0.00146790−0.264040.001095

Table 5.

Coefficients of Riazi and Daubert [8] correlation as a function of Tb and γ.

θabcdef
Tc544.40.29981.0555−0.000134780−0.61641
Pc45203−0.80631.6015−0.000180780−0.3084
Vc0.012060.20378−1.3036−0.002657000.52870.0026012
Tb6.778570.401673−1.582620.003774092.984036−0.00425288

Table 6.

Coefficients of Riazi and Daubert [8] correlation as a function of M and γ.

The coefficients were adjusted to experimental data of 38 pure hydrocarbons with carbon number in the range of 1–20, including paraffins, olefins, naphthenes and aromatics with molecular weight between 70 and 300, and boiling point in the range of 80–650°F.

Magoulas and Tassios [9] correlated the critical properties of heavy fractions through the following expressions:

Tc=1247.4+0.792M+1971γ27000M+707.4E27
lnPc=0.019010.0048442M+0.13239γ+227M1.1663γ+1.2702lnME28
ω=0.64235+0.00014667M+0.021876γ4.559M+0.21669lnME29

Riazi and Alsahhaf [10] developed a correlation for the acentric factor:

ω=0.3exp6.252+3.64457M0.1E30

Sancet [11] proposed correlations for Pc and Tc as a function of the molecular weight of the heavy oil fractions:

Pc=82.82+653exp0.007427ME31
Tc=778.5+383.5lnM4.075E32

From the aforementioned correlations, 22 sets were created and used to calculate the critical properties and acentric factor of the heavy fraction of two reservoir fluids (Table 7). These sets were evaluated by comparing the experimental data and simulated PVT analysis of these fluids. The PVT experiment was simulated using the Peng-Robinson equation of state [12]:

P=RTvbavv+b+bvbE33

where R is the universal gas constant, T is the temperature and v is the molar volume.

SetPc and TcωSetPc and Tcω
1Cavett [3]Riazi and Alsahhaf [10]12Twu [7]Riazi and Alsahhaf [10]
2Cavett [3]Edmister [2]13Twu [7]Edmister [2]
3Standing [5]Riazi and Alsahhaf [10]14Riazi and Daubert [8]Riazi and Alsahhaf [10]
4Standing [5]Edmister [2]15Riazi and Daubert [8]Edmister [2]
5Kesler and Lee [4]Kesler and Lee [4]16Riazi and Daubert [8]Riazi and Alsahhaf [10]
6Kesler and Lee [4]Riazi and Alsahhaf [10]17Riazi and Daubert [8]Edmister [2]
7Kesler and Lee [4]Edmister [2]18Magoulas and Tassious [9]Magoulas and Tassious [9]
8Riazi and Daubert [6]Riazi and Alsahhaf [10]19Magoulas and Tassious [9]Riazi and Alsahhaf [10]
9Riazi and Daubert [6]Edmister [2]20Magoulas and Tassious [9]Edmister [2]
10Sim and Daubert [13]Riazi and Alsahhaf [10]21Sancet [12]Riazi and Alsahhaf [10]
11Sim and Daubert [13]Edmister [2]22Sancet [12]Edmister [2]

Table 7.

Sets used to characterize the properties of heavy oil fractions.

3. Results

In order to choose the most appropriate correlation for the calculation of the critical properties of heavy fractions of a reservoir fluid, 22 sets of correlations were used in the estimative of properties of the “cut” of fluids A and B [14]. The compositions of the fluids A and B are presented in Tables 8 and 9, respectively.

ComponentMole fraction (%)ComponentMole fraction (%)ComponentMole fraction (%)
N20.390nC52.150C131.590
CO20.300C62.790C141220
C140.200C74.280C151.250
C27.610C84.310C161.000
C37.950C93.080C170.990
iC41.190C102.470C180.920
nC44.080C111.910C190.600
iC51.390C121.690C20+6.640

Table 8.

Fluid A composition [14].

ComponentMole fraction (%)ComponentMole fraction (%)ComponentMole fraction (%)
H2S0.383iC51.937C120.02285
N20.450nC52.505C132.364
CO22.070C63.351C151.752
C126.576C74.311C161.589
C27.894C84.133C171.492
C36.730C90.03051C181.263
iC41.485C100.02033C190.812
nC43.899C110.02635C20+12.962

Table 9.

Fluid B composition [14].

Fluid A contains approximately 40% of methane and 6% of hydrocarbons with 20 or more carbons, while fluid B contains 13% of heavy fractions and 27% of methane.

The PVT experiments were simulated using the Peng-Robinson equation of state. The results were compared with the experimental data, and the total relative deviations are shown in Tables 10 and 11.

SetAverage Bo (%)Average Rs (%)Average ρo (%)Average Bg (%)Average Zg (%)Average γg (%)Average Pb (%)Total deviation (%)
11.985.646.002.332.551.7411.0731.31
22.759.697.872.042.081.0422.4347.91
35.2115.6023.081.721.141.4038.5886.74
47.3615.8918.632.532.791.718.8357.73
52.066.886.482.252.421.5414.9036.51
62.016.086.132.292.481.5312.6133.13
72.428.427.202.132.221.2319.2742.88
85.9711.2815.582.082.090.4016.9854.38
95.129.5815.812.182.220.7418.3754.04
101.157.332.482.672.982.366.9025.88
111.739.083.532.312.481.6913.8434.67
121.963.953.642.522.791.457.3223.61
132.259.065.482.192.311.3118.8841.48
142.674.244.692.422.630.838.5426.01
152.849.837.231.891.770.5923.7547.91
165.7514.7123.211.841.650.8629.2377.24
176.9621.1527.121.181.321.3625.0084.08
183.2011.828.441.881.781.1027.9756.20
191.756.045.572.402.642.2411.9032.54
202.558.996.992.042.101.0920.7744.52
214.5313.0020.591.911.730.7930.8573.39
224.6313.4920.851.831.640.7332.2975.46

Table 10.

Deviations between measured and calculated properties for fluid A.

SetAverage Bo (%)Average Rs (%)Average ρo (%)Average Zg (%)Average Pb (%)Total deviation (%)
10.5610.875.172.650.5619.80
21.738.507.183.1417.8638.41
33.5226.8528.743.6038.09100.80
43.4129.2227.193.2928.3291.42
51.308.003.602.745.4421.07
60.599.162.822.603.5418.70
71.807.394.282.9211.6127.99
84.4228.1119.983.2311.9967.73
93.6426.3120.313.1815.2568.69
100.5310.684.322.586.3524.47
112.215.791.542.837.6320.00
120.977.902.042.5021.1634.57
132.954.920.812.767.6119.04
140.818.781.612.7116.2730.18
153.516.762.183.2717.5633.28
164.2431.3128.493.3127.6995.04
174.6925.4432.523.4049.36115.40
182.179.2510.623.0924.9350.05
190.8212.167.852.602.5725.99
201.959.8410.623.1925.1050.71
213.0226.6726.453.4332.5392.10
223.1626.6326.783.4834.5094.55

Table 11.

Deviations between measured and calculated properties for fluid B.

The best correlation for fluids A and B is chosen based on the sum of the average deviation for each property (Tables 10 and 11). For fluid A, the correlation of Twu [7] led to the best results in terms of the critical properties while for the fluid B it was the correlation of Kesler and Lee [4]. For both fluids, the correlation of Riazi and Alsahhaf [10] was chosen to calculate the acentric factor (Table 12).

FluidSetPc and Tcω
Fluid A12Twu [7]Riazi and Alsahhaf [10]
Fluid B6Kesler and Lee [4]Riazi and Alsahhaf [10]

Table 12.

Best correlations for the critical properties and the acentric factor.

Figures 16 compare the experimental and calculated PVT data of fluid A using the Peng-Robinson equation of state with the critical pressure and temperature calculated from the correlation of Twu [7] and the acentric factor calculated from the Riazi and Alsahhaf [10] correlation. It is possible to note the excellent agreement between the experimental and simulated data. Figures 710 show the same results for fluid B, with similar performance.

Figure 1.

Fluid A—oil formation-volume-factor.

Figure 2.

Fluid A—solubility ratio.

Figure 3.

Fluid A—oil density.

Figure 4.

Fluid A—gas formation-volume-factor.

Figure 5.

Fluid A—gas compressibility factor.

Figure 6.

Fluid A—gas specific gravity.

Figure 7.

Fluid B—oil formation-volume-factor.

Figure 8.

Fluid B—solubility ratio.

Figure 9.

Fluid B—oil density.

Figure 10.

Fluid B—gas compressibility factor.

4. Conclusions

Overall, 22 sets of correlations to calculate the critical properties and acentric factors of heavy oil fractions were tested in order to simulate a PVT experiment of two reservoir fluids. The results obtained from the simulation were compared with experimental laboratory PVT data. The Twu [7] correlation showed the best performance for one case, while the Kesler and Lee [4] correlation led to better results for the other fluid. In both cases, the Riazi and Alsahhaf [10] correlation was used to calculate the acentric factor. These results show the importance of evaluating the correlations for each reservoir fluid since no model for the critical properties and acentric factor calculations can be applied in any case.

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Dacid B. Lacerda, Rafael B. Scardini, André P. C. M. Vinhal, Adolfo P. Pires and Viatcheslav I. Priimenko (December 20th 2017). Evaluation of Different Correlation Performance for the Calculation of the Critical Properties and Acentric Factor of Petroleum Heavy Fractions, Recent Insights in Petroleum Science and Engineering, Mansoor Zoveidavianpoor, IntechOpen, DOI: 10.5772/intechopen.71166. Available from:

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