Experiments and Modeling of Volumetric Properties and Phase

Article pubs.acs.org/IECR

Experiments and Modeling of Volumetric Properties and Phase Behavior for Condensate Gas under Ultra-High-Pressure Conditions Chang-Yu Sun,* Huang Liu, Ke-Le Yan, Qing-Lan Ma, Bei Liu, and Guang-Jin Chen* State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China

Xiang-Jiao Xiao and Hai-Ying Wang Research Institute of Exploration and Development, PetroChina Tarim Oilfield Company, Korla 841000, China

Xi-Tan Zheng and Shi Li Research Institute of Petroleum Exploration and Development, PetroChina, Beijing 100083, China S Supporting Information *

ABSTRACT: Four reservoir samples under ultra-high-pressure and high-temperature conditions were collected from condensate gas fields in China. Constant-composition expansion tests were performed to determine the phase behavior and volumetric properties of reservoir fluid using an ultra-high-pressure fluid PVT test system. The compressibility factor and dewpoint pressure were obtained at four temperatures for four samples. The range of pressure was from 22.03 to 118.89 MPa. For the samples studied, the experimental results showed that the dew-point pressure decreased with increasing temperature and the compressibility factors increased with increasing pressure but decreased with increasing temperature at a given high reduced pressure. A thermodynamic model based on an equation of state was developed to describe the volumetric properties and phase behavior of the condensate gas under ultra-high-pressure conditions. The calculated results are in good accordance with the experimental data, which is important for the development of condensate gas reservoirs in ultra-high-pressure environments.

1. INTRODUCTION Although most producing oil and gas fields exhibit pressures lower than 50 MPa and temperatures lower than 423 K, oil and gas fields have been found under more severe conditions in several regions as a result of improvements in drilling techniques.1 These kinds of complex reservoirs are called ultra-high-pressure gas reservoirs with high pressures (generally higher than 100 MPa) and high temperatures. For instance, several condensate gas reservoirs at temperatures as high as 463 K and pressures above 110 MPa have been found in the North Sea.1 Ultra-high-pressure gas reservoirs were also discovered in the Gulf of Mexico, Japan, and Australia. In the Tarim region of China, ultra-high-pressure gas reservoirs/condensate gas reservoirs were also discovered with buried at great depths with high reservoir pressures and temperatures. Condensate gas is considered to be a very complex reservoir fluid because of its high gas/oil ratio. Knowledge of the phase behavior of condensate gas systems is important for predicting reservoir performance and future processing needs.2 Two of the most important factors to be evaluated by engineers in planning the development of a condensate gas reservoir are the fluid compressibility factor, which determines its volumetric behavior, and the dew-point pressure of the original fluid, which determines the retrograde dew-point curve below which heavier components form a liquid phase.3−6 For reservoirs under high pressure and high temperature, it becomes a very interesting challenge not only to sample fluids and perform © 2012 American Chemical Society

PVT experiments, but also to predict the phase behavior using typical thermodynamic models.5 Three types of methods are used to determine dew-point pressures and volumetric behavior: experimental determination, empirical correlations (with some accuracy limitations), and thermodynamic models mostly based on equations of state. As examples of experimental studies, Ungerer et al.1 studied the phase behavior of four synthetic gas condensates at 298−426 K and pressures up to 60 MPa. Guo et al.7 measured the compressibility factors of three natural gas samples in the ranges of 322.5−413.4 K and 20.1−95.9 MPa. Gozalpour et al.8 measured the densities and viscosities of two North Sea-based gas condensates at temperature up to 423 K and pressures up to 140 MPa. They also measured the vapor−liquid equilibrium data of condensate gas at five temperatures in the range of 278.2−383.2 K and pressures of 10.45−41.47 MPa.9 Only a small number of experiences with reservoirs where the pressure and temperature of formation can reach up 110 MPa have been reported in the open literature.10,11 As examples of empirical correlations, Standing and Katz12 developed a chart according to the theory of corresponding states for the compressibility factor. Since their work, more than 20 correlations have become available for calculating the Received: Revised: Accepted: Published: 6916

November 9, 2011 April 24, 2012 April 27, 2012 May 8, 2012 dx.doi.org/10.1021/ie2025757 | Ind. Eng. Chem. Res. 2012, 51, 6916−6925

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic diagram of the ultra-high-pressure fluid PVT system.

compressibility factor, including those of Papay,13 Hall and Yarborogh,14 Brill and Beggs,15 Dranchuk et al.,16 Dranchuk and Abou-Kassem,17 Porshakov et al.,18 and Heidaryan et al.19 Many researchers, such as Kurata and Katz,20 Eilerts and Smith,21 Olds et al.,22,23 Reamer and Sage,24 Nemeth and Kennedy,25 Carlson and Cawston,26 Potsch and Braeuer,27 Marruffo et al.,28 Humoud and Al-Marhoun,29 and Elsharkawy,3 have correlated the dew-point pressures of condensate gas reservoirs with gas/oil ratio, temperature, composition, boiling point, oil gravity, or characteristics of the heptanes-plus (C7+) fraction. Such correlations are limited to the complexity and range of condensate gas parameters used. To overcome the limitations of empirical correlations, thermodynamic models such as equations of state are used extensively in the petroleum industry to study the volumetric and phase behavior of petroleum reservoir fluids. However, such an approach can deteriorate for phase-behavior modeling of complex hydrocarbons, such as volatile oils and condensate gas, especially in the retrograde region.6,30 Choosing a suitable equation of state (EOS)5,31−36 is important. In addition, it is necessary to fit some parameters to predict the thermodynamic behavior of condensate gas for thermodynamic models.37 The following tuning methods have been employed to improve EOS capabilities for predicting the phase behavior of condensate gas: splitting and characterization of the C7+ fraction,38−44 adjustment of the methane interaction coefficient,45−47 adjustment or regression of the EOS parameters,48 adjustment of the critical properties,39,49 adjustment of the molecular weight of the heavy fraction,50 and volume translation.51−53 As an alternative to EOS methods, Elsharkawy and Foda2 developed a neural network model capable of predicting the dew-point pressure and simulating the depletion performance of condensate gas reservoirs. Nowroozi et al.54 proposed a fuzzy neural system to estimate dew-point pressures. Shokir6 applied genetic programming with an orthogonal least-squares algorithm to generate a dew-point-pressure prediction model represented by tree structures. In addition, Monte Carlo simulations have also been used to predict the thermodynamic properties of condensate gases.4,55,56 Although many correlations and models for describing the phase behavior of condensate gas exist, their suitable application range generally requires a reduced pressure of less than 15, as high errors occur when they are applied at reduced pressures higher than 15 in view that the lack of corresponding experimental data under ultra-high-pressure conditions for this type of condensate gas reservoirs. Therefore, in this work, the compressibility factors and dew-point pressures of four condensate gas samples at high pressure and temperature were measured. A thermodynamic model based on an EOS was

developed to describe the volumetric properties and phase behavior of condensate gas under ultra-high-pressure conditions. The obtained results could be of importance for the development of condensate gas reservoirs under ultra-highpressure environments.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. Four groups of condensate gas fluids from China gas reservoirs were sampled using the separator sampling method. The separator gas composition was analyzed with a HP6890 gas chromatograph. The gas chromatograph was calibrated by injecting standard gases in advance, and its minimum detection limit was found to be 200 ppmv. Each gas sample was measured at least three times, and the average value was used as the composition of the gas mixture. The separator oil was flashed, the tank gas was analyzed with the HP6890 instrument, and the tank oil was analyzed with an HP5890A gas chromatograph. The compositions of the separator oil and in situ reservoir fluids were then obtained by recombining the oil and gas according to the gas/oil ratio. The compositions of the separator gas, separator oil, and reservoir fluid; the gas/oil ratio; and the molecular weight and relative densities of the C11+ fraction for four groups of condensate gas samples are listed in Table S1 in the Supporting Information. The reservoir fluids were then prepared in the laboratory by recombining the separator oil with the separator gas according to the gas/oil ratio data based on a standard analytical method for condensate gas properties (Chinese standard SY/T 55432002). An ultra-high-pressure fluid PVT system was used for preparation of the reservoir fluid. To check the reliability of the prepared reservoir fluid samples, a sample was pressed to a single phase at the corresponding reservoir temperature, and a flash test was performed. Only when the compositions of the fluid recombined from the flashed gas and flashed oil were in agreement with those of the reservoir fluid could the sample prepared be used for the subsequent phase behavior measurements. 2.2. Constant-Composition Expansion Test. An ultrahigh-pressure fluid PVT system manufactured by Sanchez Technologies Co., Viarmes, France, was used to carry out phase behavior measurements on the condensate gas in this work. A schematic diagram of the experimental device is shown in Figure 1. The maximum operating pressure was up to 150 MPa, and the operating temperature was within the range from room temperature to 473 K. The accuracies of pressure and temperature measurements were ±0.01 MPa and ±0.1 K, respectively. The maximum working volume of the cell was 240 mL. 6917

dx.doi.org/10.1021/ie2025757 | Ind. Eng. Chem. Res. 2012, 51, 6916−6925


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The experimental measurements were processed by loading reservoir fluid into the condensate gas PVT cell. A constantcomposition expansion (CCE) test was performed to determine the compressibility factor, dew-point pressure, and liquid dropout behavior of the fluid. Thereafter, the dew point was determined from a dew-point detection system. The pressure was dropped in steps, and the liquid volume was recorded at each pressure stage after the experimental pressure had decreased below the dew-point pressure. For each group of sample, volumetric properties, liquid dropout curves at constant mass, and dew-point pressures at the reservoir temperature and three other temperatures below reservoir conditions were measured. 2.3. Experimental Results. In this work, similar experimental phenomena for the CCE test were observed through the windows of the PVT device for condensate gas fluid sampled from China gas fields. Sample 1, at a reservoir temperature of 407.2 K, is described here as an example to introduce the phenomena observed during the CCE test. The prepared sample was pressurized to 106.30 MPa at a reservoir temperature of 407.2 K. The reservoir fluid was a single phase that was transparent and pale yellow in color. As the CCE test proceeded and the pressure dropped, the color of the reservoir fluid also changed gradually from pale yellow to pale red. When the pressure was decreased to below 45 MPa, which is close to the dew point under reservoir conditions, the fluid began to fog up, and the fog thickened with decreasing pressure. The convective phenomena of the thick fog could also be observed by the naked eye, because of differences in the density of the fluid at different heights of the PVT cell and the adjustment of the fluid to maintain an equilibrium state. With a continuous drop in pressure, a tiny liquid drop precipitated, and the corresponding pressure was then assumed to be the dewpoint pressure of the reservoir fluid. In this group of experiments, the dew-point pressure was determined to be 40.2 MPa at a reservoir temperature of 407.2 K after repetitive measurements. Below the dew-point pressure, many tiny anomalous particles were observed to fall in the PVT cell with a further decrease of the pressure, whereas some of them adhered to the cell wall and others accumulated on the bottom of the cell and formed an unflowing liquid interface. The amount and size of the particles and the small liquid drop adhered to the cell wall also increased with decreasing pressure and then slid down and fell to the bottom of the cell after they attained a certain size. These phenomena continued until a new gas−liquid equilibrium was reached at the current pressure. For sample 1, CCE tests were performed at 313.2, 343.2, 373.2, and 407.2 K to determine the phase behavior at different temperatures from the stratum zone to the wellhead. Experimental phenomena similar to that occurring at 407.2 K were observed at the three other temperatures. Similarly, the constant-composition expansion tests for the other three samples, namely, samples 2−4, were also performed at four temperatures. The compressibility factors at different pressures above the dew-point pressure at four temperatures for samples 1−4 are listed in Tables S2−S5, respectively, of theSupporting Information. The four compressibility charts for the four samples at different reduced temperatures and reduced pressures are presented in Figures 2−5, where the calculation of the critical properties of the condensate gas will be introduced in a later section of this article. It was found that, in the single-phase zone, the compressibility factor increased with increasing pressure. Higher compressibility factor values

Figure 2. Compressibility chart at different reduced temperatures and reduced pressures for sample 1.



were obtained at lower temperatures for a given high reduced pressure. The variations of the retrograded liquid amount with pressure at four temperatures for samples 1−3 are shown in Figures 6−8, respectively. It was found that, in the initial stage, the retrograded liquid amount was not obvious. It increased with decreasing pressure and reached a maximum at the maximum retrograded pressure. After that, the retrograded liquid amount decreased with a continuous decrease of the pressure. The maximum retrograded liquid amounts for sample 1 at 313.2, 343.2, 373.2, and 407.2 K were 1.79%, 0.99%, 0.69%, and 0.52% at the corresponding maximum retrograded pressures of 17.47, 17.33, 16.07, and 17.13 MPa, respectively. 6918



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Figure 8. Variation of the retrograded liquid percent of sample 3 with pressure during constant-composition expansion experiments at four different temperatures.


maximum retrograded liquid amount at stratum conditions was only 0.033% at a pressure of 17.04 MPa. The retrograded liquid amount for sample 4, with a gas/oil ratio of 112193 m3/m3, was very small and could not even be measured accurately. Table 1 lists the dew-point pressures at four temperatures for the four groups of condensate gas samples. It can be seen that, Table 1. Experimental Dew-Point Pressures (DPPs) for Samples 1−4 at Different Temperatures T (K)

DPP (MPa)

T (K)

sample 1 313.2 343.2 373.2 407.2


46.13 42.09 41.02 40.20

313.2 343.2 373.2 411.1

29.95 29.20 27.68 24.65

323.2 353.2 383.2 418.6

sample 3 303.2 333.2 363.2 397.4

DPP (MPa) sample 2 46.55 43.84 42.18 40.99 sample 4 28.88 24.07 23.44 22.03

for each group of samples, the dew-point pressure decreased with increasing temperature. For samples 3 and 4, which had higher gas/oil ratios, lower dew-point pressure values were obtained than for samples 1 and 2.

3. THERMODYNAMIC MODEL Phase equilibrium and volumetric properties of condensate gas in the pressure and temperature range encountered during production operations are expected to be well-predicted. For this purpose, cubic equations of state are generally used to describe vapor−liquid equilibria of these fluids. However, these equations of states do not generally lead to good predictions under all PVT conditions.57 In particular, for condensate gas fluids, the calculated PVT properties do not match the experimental data.53,58 As reviewed in the Introduction, many tuning methods have been applied to improve EOS capabilities for describing the thermodynamic behavior of condensate gas. In this work, a thermodynamic model was used to describe the vapor−liquid equilibria and PVT properties for condensate gas under high-pressure and high-temperature conditions by introducing suitable methods for plus-fraction splitting and characterization of pseudocomponents. A transition function wais also introduced to improve the description of the


The maximum retrograded liquid amount increased with decreasing temperature, meaning that more retrograded liquid will precipitate during condensate gas exploitation from the bottom of the well to the ground. A comparison of Figures 6−8 shows that the retrograded liquid amount decreased to a large extent with increasing gas/oil ratio. For sample 2, with a gas/oil ratio of 10683 m3/m3, the maximum retrograded liquid amount at stratum conditions was 0.48% at a pressure of 18.08 MPa. However, for sample 3, with a gas/oil ratio of 96424 m3/m3, the 6919



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volumetric properties of condensate gas throughout the entire pressure range. 3.1. Development of the Model. A suitable equation of state is important for describing the phase behavior of condensate gas. In this work, the Soave−Redlich−Kwong (SRK) EOS31 was used, which is given by p=

a(T ) RT − v−b v(v + b)

a(T ) = 0.42747

b = 0.08664

R2Tc 2 α(Tr) Pc

RTc Pc

(1)

(2)

(3)

Tr )]2

m = 0.480 + 1.574ω − 0.176ω 2

(4) (5)

van der Waals-type single-fluid mixing rules for EOS parameters a and b were used a=

∑ ∑ xixj(aiaj)0.5 (1 − kij) i

j

(6)

n

b=

∑ xibi i=1

(7)

(13)

Pr 2 Tr

(14)

where β(T r ,P r ) is the transition function; Z 0 is the compressibility factor before the introduction of the transition function; and C1, C2, and C3, are the transition function parameters, which are 0.94134, 0.19822 × 10−2, and 0.34748 × 10−4, respectively, determined from the measured PVT data. The critical temperature and critical pressure of condensate gas were calculated by the following expressions according to the critical properties of the definite components and pseudocomponents

(8)

(9)

where, in this case, j refers to components other than CO2 and CH4 in the condensate gas sample. For ωj values larger than 0.35, the values of kCO2−j were set equal to 0.105. The methods of plus-fraction splitting and pseudocomponent characterization are also important for describing the phase behavior of condensate gas. In this work, because the C11+ component makes up only a small fraction of the total mixture, the extended analysis from C7 to C11+ was first lumped into a new pseudocomponent (i.e., C7+). Afterward, a suitable plus-fraction splitting method for the C7+ fraction was chosen to improve the capacity of the EOS under high-pressure and high-temperature conditions. Here, the following formula proposed by Ahmed et al.59 was used to split the C7+ fraction ⎛ MW(n + 1) + − MWn + ⎞ ⎟⎟ zn = zn +⎜⎜ ⎝ MW(n + 1) + − MWn ⎠

(12)

β(Tr , Pr) = C1 + C2Pr + C3

where j refers to components other than methane in the condensate gas sample. For kij between CO2 and other components (except CH4), the following correlation was used k CO2 − j = 0.12443 + 0.083828ωj − 0.093302ωj 2

MWn + = MWC7+ + S(n − 7)

Z = Z0β(Tr , Pr)

The binary interaction parameters between components i and j, kij, were considered to be equal to zero for hydrocarbon− hydrocarbon interactions, except for those between methane or CO2 and other components. For interactions between CH4 and other components, the interaction parameters were calculated by the following correlations k CH4 − j = 0.0575(ωj 0.5 − ωCH4 0.5)

(11)

where n is the single carbon number, which is greater than or equal to 7. For n = 7 or 8, S is 15.5; for n > 8, S is 17.0. For a given plus fraction, constraint equations were used to ensure that the distributions of mole fractions, molecular weights, and densities were consistent with the measured data for the plus fraction. The number of components and C7+ fractions in the final distribution might be too large. To reduce the overall number of components, a common procedure of lumping several components into a pseudocomponent, as described by Pedersen et al.,60 such that the weight fractions of all groups are approximately equal was used. In this work, 10 hydrocarbon groups were used to represent the hydrocarbon part of a reservoir fluid. The method proposed by Kesler and Lee61 was used to evaluate the critical properties and acentric factors for pseudocomponents. It is known that the main role of an EOS is to reproduce the PVT data accurately, whereas the correct vapor−liquid equilibrium (VLE) description can be achieved by devising an integration path.62 The calculations of PVT properties and VLE behavior using an EOS are relatively independent.63 Volume translation methods51−53 have been used to improve the description of the volume of the liquid phase by the equation of state. Similarly, in this work, a transition function was introduced to improve the description of the compressibility factor throughout the entire pressure range, without modifying the description of vapor−liquid equilibrium, that is

The form of α(Tr) in the original SRK EOS was employed for the whole Tr range α(Tr) = [1 + m(1 −

zn + = z(n − 1) + − z(n − 1)

Pc =

∑ xiPci

Tc =

∑ xiTci

(15)

n i=1

(16)

3.2. Comparison with Different α Functions in the Attractive Term. In view that the modification of the attraction term of an equation of state will favor the description of the phase behavior of condensate gas, the SRK EOS31 and two other models proposed by Twu et al.64 and Souahi et al.65 that are based on the modification of the α function of the attractive term of the Redlich−Kwong equation of state66 were used to examine the influence of the EOS form. Table 2 lists the corresponding results of calculating the dew-point pressure for sample 1. The absolute average deviations (AADs) for four temperatures were 11.02%, 4.44%, and 4.06% for the SRK EOS and the modifications by Twu et al.64 and Souahi et al.,65 respectively. The plus-fraction splitting method and the

(10)

where 6920



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calculating the dew-point pressure for sample 2 are listed in Table 4. The absolute average deviations at four temperatures were 2.44%, 16.86%, 17.15%, 14.76%, 19.19%, and 18.33%, respectively, for the six combination methods. It was found that the model developed in this work, in which the SRK EOS was combined with the plus-fraction splitting method proposed by Ahmed et al.59 and the pseudocomponent characterization method proposed by Kesler and Lee,61 provided the best results for describing the phase behavior of condensate gas under highpressure and high-temperature conditions. 3.4. Prediction of Dew-Point Pressure for Four Samples. Table 5 lists the dew-point pressures predicted

Table 2. Comparison of Dew-Point-Pressure Calculation Results for Sample 1 with Different α Functions in the Attractive Terms of Three Equations of State RDa (%) T (K)

DPP (MPa)

SRK

Twu et al.64

Souahi et al.65

46.13 42.09 41.02 40.20

−11.67 −6.34 −9.32 −16.74 11.02

0.65 3.45 −2.01 −11.68 4.44

0.96 7.38 4.62 −3.29 4.06

313.2 343.2 373.2 407.2 AADa (%) a

RD = relative deviation, AAD = absolute average deviation. The same definitions of RD and AAD apply to Tables 4−6

Table 5. Comparison of Experimental and Calculated DewPoint Pressures

pseudocomponent characterization method used by these three models are the same and can be referred to as the methods of Whitson38 and Kesler and Lee,61 respectively. The binary interaction parameters kij between CH4 and other components and between CO2 and other components were set according to eqs 8 and 9, respectively. Other interactions between hydrocarbons were set to zero. It was found that the modification of the α function of the attractive term improved the description of the phase behavior of condensate gas under high-pressure and high-temperature conditions. Therefore, in the subsequent discussion, the results calculated with the models of Twu et al.64 and Souahi et al.65 are also listed for comparison. 3.3. Comparison with Different Characterization Methods. To examine the influence of the plus-fraction splitting and pseudocomponent characterization methods on describing the phase behavior of condensate gas, the three plusfraction splitting methods proposed by Ahmed et al.,59 Pederson et al.,67 and Whitson38 and the two characterization methods proposed by Kesler and Lee61 and Pederson et al.67 were investigated with the SRK EOS. The combinations of methods are listed in Table 3. The corresponding results of

RD (%) T (K)

Table 3. Methods of Plus-Fraction Splitting and Characterizationa

a

overall method

method for plus-fraction splitting

method for pseudocomponent characterization

this work method 2 method 3 method 4 method 5 method 6

Ahmed et al.59 Ahmed et al.59 Pederson et al.67 Pederson et al.67 Whitson38 Whitson38

Kesler and Lee61 Pederson et al.67 Kesler and Lee61 Pederson et al.67 Kesler and Lee61 Pederson et al.67

DPP (MPa)

313.2 343.2 373.2 407.2 AAD (%)

46.13 42.09 41.02 40.20

313.2 343.2 373.2 411.1 AAD (%)

46.55 43.84 42.18 40.99

303.2 333.2 363.2 397.4 AAD (%)

29.95 29.20 27.68 24.65

323.2 353.2 383.2 418.6 AAD (%)

28.88 24.07 23.44 22.03

this work sample −2.94 3.95 2.09 −3.88 3.22 sample 0.01 3.46 2.77 −3.54 2.44 sample 1.87 −1.90 −8.30 −14.66 6.68 sample 3.59 14.43 1.59 −20.77 10.10

AAD (%) for four samples

5.61

Twu et al.64

Souahi et al.65

0.65 3.45 −2.00 −11.68 4.45

0.96 7.38 4.62 −3.29 4.06

2.99 2.85 −0.78 −10.48 4.27

3.33 6.95 6.21 −1.19 4.42

13.47 6.27 −2.67 −16.39 9.69

12.92 8.87 2.20 −9.90 8.47

0.049 3.96 10.96 −50.07 16.26

1.43 7.94 −11.09 −50.07 17.63

1

2

3

4

8.67

8.65

using the model developed in this work for four samples at different temperatures. For comparison, the results calculated using two other models (those of Twu et al.64 and Souahi et al.65) based on the modification of the α function of the

Used with the SRK EOS.

Table 4. Comparison of Dew-Point-Pressure Calculation Results for Sample 2 Using Different Methods of Plus-Fraction Splitting and Characterization RD (%) T (K) 313.2 343.2 373.2 411.1 AAD (%)

DPP (MPa)

this work

method 2

method 3

method 4

method 5

method 6

46.55 43.84 42.18 40.99

0.01 3.46 2.77 −3.54 2.44

30.40 21.40 11.40 −4.25 16.86

−16.85 −13.82 −15.18 −22.73 17.15

−6.45 −9.11 −15.20 −28.27 14.76

−18.50 −15.67 −17.29 −25.31 19.19

−10.82 −12.72 −18.42 −31.39 18.33

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three models for sample 1 at four temperatures are shown in Figures 9−12, which clearly demonstrate the beneficial effect of

attractive term of the Redlich−Kwong equation of state are also included because of their high accuracy. As shown in Table 5, for sample 1, the predicted precisions were 3.22%, 4.45%, and 4.06% for this work and the models of Twu et al.64 and Souahi et al.,65 respectively. For sample 2, the corresponding predicted precisions were 2.44%, 4.27%, and 4.42%. It was thus found that the model developed in this work can be successfully used to describe the phase equilibrium of condensate gas at the low gas/oil ratio of about 10000 m3/m3. However, the errors increased with increasing gas/oil ratio. The predicted precisions for sample 3 were 6.68%, 9.69%, and 8.47% for this work and the models of Twu et al.64 and Souahi et al.,65 respectively. The corresponding predicted precisions for sample 4 were 10.10%, 16.26%, and 17.63%. For samples 3 and 4, the gas/oil ratio was about 100000 m3/m3, or about 10 times that for samples 1 and 2. The concentration of C11+ in condensate gas is low, and the measurement deviation for the C11+ composition is relatively high. Because the measured value of the dew-point pressure is sensitive to the C11+ content, the experimental data at higher gas/oil ratios have higher experimental deviations, which results in higher deviations of dew-point pressure predictions. Compared with those of the Twu et al.64 and Souahi et al.65 models, the predictive capabilities of the model developed in this work were always higher for the four groups of samples investigated. 3.5. Prediction of Compressibility Factor for Four Samples. Table 6 lists the compressibility factor values for four

Figure 9. Experimental and calculated compressibility factors of sample 1 at 313.2 K.

Table 6. Comparison of Experimental and Calculated Compressibility Factors AAD (%) T (K)

this work

Twu et al.64

Souahi et al.65

sample 1 313.2 343.2 373.2 407.2

2.07 1.59 1.06 0.69

3.20 3.63 4.18 4.62

3.69 4.58 5.01 5.54

313.2 343.2 373.2 411.1

0.54 1.53 1.76 1.71

2.85 4.05 4.37 4.32

2.83 4.47 5.11 5.74

303.2 333.2 363.2 397.4

0.89 1.16 1.60 1.95

3.38 3.45 3.71 3.82

3.26 3.63 4.22 4.72

323.2 353.2 383.2 418.6

2.05 1.54 2.15 1.15

2.28 1.93 1.28 1.84

2.75 2.23 2.72 3.51

total AAD (%)

1.46

3.31

4.00


sample 2

sample 3

sample 4


introducing the transition function for describing the compressibility factor. In addition, it can be seen that similar precisions for the four samples were obtained for the description of the compressibility factor, whereas the precision for the description of the dew-point pressure is related to the gas/oil ratio and the composition of plus fraction. It can also be seen that, compared with the calculation of the dew-point pressure, the calculation of the compressibility factor is significantly less sensitive to the characterization of the petroleum fraction.

samples at different temperatures predicted by the model developed in this work and by the models proposed by Twu et al.64 and Souahi et al.65 It was found that the total absolute average deviation was only about 1.46% using the model developed in this work. In comparison, the absolute average deviations were 3.31% and 4.00% using the models of Twu et al.64 and Souahi et al.,65 respectively. The comparisons of the 6922



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equations of state. The model developed in this work favors the description of the phase behavior and volumetric properties of condensate gas under high-pressure and high-temperature conditions.

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ASSOCIATED CONTENT

S Supporting Information *

Properties of reservoir fluid for four groups of condensate gas samples (Table S1) and compressibility factors at different pressures and four temperatures for four samples (Tables S2− S5). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +86 10 89732126. E-mail: [email protected] (C.-Y.S.), [email protected] (G.-J.C.).

In addition, the liquid drop-out amount was also predicted using the model developed in this work. Figure 13 shows the

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support received from PetroChina Tarim Oilfield Company; the National Natural Science Foundation of China (Nos. 20925623, U1162205, 21076225); and the Science Foundation of China University of Petroleum, Beijing (LLYJ2011-63), is gratefully acknowledged.

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REFERENCES

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Figure 13. Model-predicted results for the condensate liquid amount of sample 1.

results predicted for sample 1. It was found that the calculated retrograde liquid amount was approximatively in agreement with the experimental data, although a certain deviation still existed. One reason for the deviation is that the amount of retrograde liquid is very low for condensate gas at such high gas/oil ratios as used in this work, which could result in a relatively large measurement error.

4. CONCLUSIONS Volumetric properties, liquid drop-out curves at constant mass, and dew-point pressures of four groups of condensate gas fluid from China natural gas reservoirs at the reservoir temperature and three other temperatures below reservoir conditions were measured using an ultra-high-pressure fluid PVT system. A model based on the original SRK equation of state was presented in this study to describe the vapor−liquid equilibria and PVT properties of condensate gas under high-pressure and high-temperature conditions by introducing suitable plusfraction splitting and pseudocomponent characterization methods. A transition function was also introduced to improve the prediction of volumetric properties of condensate gas throughout the entire pressure range. The accuracies of the proposed model were verified by comparison with other 6923



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Experiments and Modeling of Volumetric Properties and Phase

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