Gas condensate initially exists in gas phase in a reservoir when the reservoir pressure is above the dew-point pressure (DPP). When the reservoir pressure drops below the DPP, liquid oil starts to drop out, forming a condensate ring around the wellbore which would block the flow of natural gas and thus lead to the reduction of gas effective permeability. When the reservoir pressure drops below the DPP, the gas productivity will decrease rapidly^[1]. Moreover, a substantial amount of condensate remains in the reservoir, and is difficult to recover. Calculating the DPP accurately is particularly important for the development of gas-condensate reservoirs.

DPP can be measured most accurately by constant composition expansion experiments. But the experiment takes money and time; the effect of the experiment also depends on whether there is a large enough sample, and human error is hard to eliminate when recombining separator oil and gas samples. Therefore, it is necessary to find a simple and accurate method for DPP calculation.

Some mathematical methods have been previously proposed for predicting DPP when reliable samples are unavailable, or when performing pressure-volume-temperature (PVT) experiments is difficult^[1-2] . In general, they include two kinds: equations of state (EOS) and empirical correlations. Many studies on using different EOS to characterize fluid behavior in condensate gas reservoirs have been conducted^[3,4,5,6,7]. Of these methods, the EOS proposed by Soave^[3], and Peng and Robinson^[5] are regarded as the most reliable for calculating the properties of reservoir fluids^[8-9] . However, the predictions of EOS are not unique because the EOS schemes splitting fractions, and characterization methods of fractions, and binary interaction coefficients that used in the prediction may be different^[1]. Empirical correlations are an alternative approach for DPP calculation. However, the application of an empirical correlation is limited to the range of data used in its development. Of the two types of empirical correlations, one depends on the composition and properties of the heptane-plus fraction, and the other depends on production data. In the well-known first type of correlation, DPP is expressed as a function of composition and reservoir temperature^[1,10-15]. In the second type of empirical correlations, DPP is expressed as a function of production data and reservoir temperature^{[16,17,18,19,20]} .

In this study, the accuracy and applicable scope of previously published methods for DPP calculation have been evaluated, a new correlation for the estimation of DPP of gas-condensate reservoirs has been established and compared with the correlations and EOS published before.

A large amount of data was collected from various sources, and a large data bank was built. On this basis, the EOSs and correlations published before were evaluated, and a new mathematical correlation was developed to improve DPP estimation in the absence of reliable samples or when experimental work cannot be performed.

The DPPs of six gas condensate samples were measured using the automated mercury-free PVT cell fluid evaluation analyzer (VINCI) at the Petroleum Fluid Research Center, Kuwait University. Of them, some were taken from well bottom, and the others from surface separators. The DPP, initial composition, and gas/oil ratio of the samples taken from well bottom were measured by the constant composition expansion test (also known as constant mass depletion (CMD)) and the flash vaporization method. The oil and gas samples taken from separators were recombined based on the initial gas/oil ratio, and the composition was checked against the samples taken from well bottom. The CMD test was performed using the Macro Software, in which each sample was put at the reservoir temperature first; secondly, the pressure was adjusted to the initial reservoir pressure; thirdly, the pressure was reduced further until retrograde condensed liquid came up, and then the DPP was measured. A gas chromatograph (Agilent 7890B) was used to test the compositions of the separator gas and oil samples that were to be recombined based on the field gas/oil ratio, and the reservoir fluid composition was calculated. Table 1 shows the tested composition, relative molecular weight, and relative density of C₇₊ wellbore fluid, and the DPP of the wellbore fluid.

In this study, most of the data were collected from existing literatures. A total of 925 samples were gathered from previous research (579 samples from Nemeth and Kennedy^[13] and 340 unpublished samples from Elsharkawy^[1]). In addition, six samples were measured by us at the Kuwait University Research Center. The collected data were screened to remove repeated and defective samples. During the screening process, the sum of the mole fractions (which should be 1.0), relative molecular weight, C₇₊ mole fraction, and C₁ mole fraction were checked.

There is no universal agreement on the identification of gas condensate. McCain^[21], Danesh^[22], Lake and Holstein^[23], Beggs^[24], and Ahmed^[25] each put forward their own identification criterion, as shown in Tables 2 and 3.

It can be seen from Table 2 that the identification criteria proposed by different researchers have significant differences in GOR and relative density. According to the identification method proposed by Lake and Holstein^[23] based on composition and molecular weight (Table 3), the identification criteria in Table 2 could wrongly take other reservoir fluids as gas condensate. It is important to note that most of the published literatures have no GOR and relative density data.

First, the repeated samples were removed. Then, the samples for which the sum of the mole fractions was not equal to one ($\sum$Zi$\ne$1) were eliminated. These abnormal samples could be the result of reporting errors during the measurement of composition or typing errors in the published studies.

According to Table 3, typical gas-condensate has a relative molecular weight from 23 to 40. The phase envelopes of all the samples were plotted with PVTi software. It is found that the samples with relative molecular weight of more than 40 show features of volatile oil, so they were eliminated. Then the envelops of samples with relative molecular weight of less than 40 were checked one by one. It was found that some samples with molecular weight ranging from 35 to 40 had features of gas condensate, while others had features of volatile oil. Therefore, for the samples with relative molecular weight of 23-40, the samples with phase envelop showing volatile oil features were screened out too. The samples with a molecular weight of less than 23 were checked with the same method. The screening process of samples according to relative molecular weight and phase envelop are shown in Table 4 and Fig. 1.

After filtering based on the relative molecular weight, the samples were screened based on the mole fraction of C₇₊. According to Table 3, gas condensate has mole fraction of C₇₊ from 1% to 6%, whereas volatile oil has mole fraction from 10% to 30%. However, Table 2 shows that the gas condensate samples have C₇₊ mole fractions below 12.5% in general, and as high as 15% in exceptional cases. Samples with a mole fraction of C₇₊ greater than 11% were rejected because their phase envelopes show volatile oil features. Among the samples with a mole fraction of C₇₊ ranging from 6% to 11%, some show behavior of gas condensate, and some show behavior of volatile oil. When the mole fraction of C₇₊ is more than 1%; most of the samples show the behavior of gas condensate. Only a few samples show the behavior of wet gas. For example, sample 9 has C₇₊ mole fraction of 0.4% and falls within the wet-gas region at the given reservoir temperature. In contrast, even with zero C₇₊ mole fraction, sample 10 has phase envelope of gas condensate features. Examples of the screening process are shown in Table 5 and Fig. 2.

Finally, the samples were screened according to the mole fraction of C₁. Gas samples generally have high C₁ content; therefore, the phase envelopes of samples with a C₁ mole fraction of greater than 90% were examined by using PVTi. For example, sample 11 has mole fractions of C₁ and C₇₊ of 94.5% and 1.6%, respectively (Table 6). The reservoir temperature of the sample is 104 °C, higher the critical condensation temperature (49 °C). Phase envelope of the sample exhibits wet-gas features (Fig. 3). Phase envelop of Sample 7 also shows characteristics of wet gas. Samples with a low mole fraction of C₁ can also exhibit gas condensate behavior. For example, sample 10, even though with C₁ content of 58% and C₇₊ content of 0%, still show features of gas condensate in phase envelop (Fig. 2c).

After screening with the above methods, the number of samples was reduced from 925 to 715. Statistical analysis was done on the 715 samples (Table 7). The results of sample screening show that the margins stated in Tables 2 and 3 are not necessarily accurate. Therefore, we recommend that the classification of reservoir fluids should not be based on production data such as GOR and relative density, nor on the mole fraction of heptane-plus, but should be based on the phase envelope of reservoir fluid.

The empirical correlations with compositional data as inputs and the uncorrected PR equation of state were evaluated in this study. This type of correlations commonly used include those proposed by Nemeth and Kennedy^[1], Elsharkawy^[11], Shokir^[13], and Godwin^[26]. Because all these correlations take heptane-plus components as one group, it is logical to compare the performance of these correlations with the uncorrected EOS.

The average absolute error (AAE), average relative error (ARE), root mean square error (RMSE), and R-squared (R²) parameters were used to statistically evaluate the above-mentioned correlations and the uncorrected Peng-Robinson EOS^[5], and the results are shown in Table 8. It can be seen from Table 8 that among all the correlations considered, the Nemeth and Kennedy correlation^[13] has the highest accuracy. This finding is not surprising because most of the data used in this study were used in the development of the Nemeth and Kennedy correlation. In general, the Nemeth-Kennedy correlation is applicable across the entire range of input parameters. However, it can underestimate the DPP of some samples with low mole fractions of intermediate components (C₂, C₃, C₄, and C₅). The low fractions of intermediate components are counterbalanced by high mole fractions of C₁ or nonhydrocarbons. Statistically, the Elsharkawy correlation^[1] shows the second-best accuracy and can give good predictions for most of the data range except for the samples with very high and very low C₁ mole fractions, and high nitrogen and hydrogen sulfide mole fractions. The Godwin correlation^[11] is the third-best in terms of accuracy. It underestimates the DPP of samples with a very low mole fraction of C₁ and no C₇₊. In addition, it yields DPP with large errors for samples with high mole fractions of non-hydrocarbons and/or intermediate components (accompanied with relatively low C₁ content). The Shokir correlation^[26] is the least accurate. A negative R² value means that its prediction results are not reliable and invalid. Our explanation for the high errors of the Shokir correlation is that it cannot predict the DPP of samples with no C₇₊ components. For such samples, the DPPs calculated by Shokir correlation are negative, which is physically impossible. In addition to these four correlations, the uncorrected Peng-Robinson EOS was also used to estimate the DPPs for the dataset with the PVTi software. In the solution of PR EOS, the splitting scheme used was lumped C₇₊; the relation between critical pressure and critical temperature, and the relation of deviation factor used were all Kesler-Lee correlation. Table 8 shows that Nemeth-Kennedy and Elsharkawy correlations have higher accuracy than Peng-Robinson EOS in estimating the DPPs of the samples considered in this study. Among the six statistical errors reported in Table 8, the average absolute error (AAE) is the most conclusive index to judge the accuracy of each method.

It has been stated previously that the DPP from EOS is not unique and depends on the number and division of pseudo- fractions. In this section, we show how the number and division of subfractions affect the DPP value calculated from EOS. The changing parameters considered in the analysis were the C₇₊ characterization correlation and splitting scheme (Table 9), while the binary interaction coefficients were kept constant. In each scheme, two cases of splitting C₁₂₊ and C₁₆₊ from C₇₊ fraction were considered (evaluated as two cases), and the PVTi software was used to run the three-parameter Peng-Robinson EOS with its built-in set of plus fraction characterization correlation considered. In sample 12, the mole fractions of C₁, C₂, C₃, C₄, C₅, C₆, C₇₊, N₂, CO₂ and H₂S are 81.3%, 4.8%, 2.3%, 1.7%, 1.3%, 1.4%, 4.3%, 1.9%, 1.1% and 0 respectively. This sample has a C₇₊ relative density of 0.74, C₇₊ relative molecular weight of 139.9, reservoir temperature of 54 °C, and DPP of 27.0 MPa.

A total of 126 possible combinations were obtained by changing these parameters, and thus 126 values of DPP were calculated (Fig. 4).

Fig. 4 shows the EOS has no unique solution. In this example, it has 126 results. The complexity further increases if the binary interaction coefficient changes. Moreover, fine-tuning a customized EOS for a certain sample is complex, time-consuming, and not necessarily accurate.

First, the published correlations were improved by refitting their coefficients. Next, a new correlation for DPP estimation was built.

The Nemeth and Kennedy, Elsharkawy, Shokir, and Godwin correlations have several constant coefficients. These coefficients were numerically derived based on the data used for developing each correlation. Our data bank was utilized to modify the four correlations by updating their coefficients and minimizing error.

Table 10 shows the accuracy of the correlations before and after modification. The Nemeth and Kennedy correlation shows the minimum improvement after modifying the coefficients. This is because most of the samples collected for this study are those used when Nemeth and Kennedy correlation is developed^[13]. The modified Elsharkawy correlation has a small improvement after modification, because the rest of the data used in this study are the unpublished data provided by Elsharkawy, whereas Shokir and Godwin correlations have noticeable improvements in accuracy after modification.

First, the input and output parameters were analyzed to find out the relationships between them and the possibility of grouping these parameters. Table 11 shows the correlation coefficients between DPP and other parameters. It can be seen from the table that the DPP decreases as the mole fraction of intermediate components increases, but is in positive correlation with mole fraction, relative molecular weight, and relative density of C₇₊. Compared with other variables, the non-hydrocarbon has less effect on DPP. These observations are in good agreement with the findings of Elsharkawy^[1] and Shokir et al.^[26]. The correlation between DPP and mole fraction of C₁ in Table 11 is also consistent with the Shokir correlation.

According to Table 11, mole fractions of C₂-C₆ are in negative correlation with DPP, so they are taken as a group. The correlations shown in Table 11 were translated into a mathematical formula, Equation (1), which is a linear equation and can be solved by multiple linear regression.

The initial equation was adjusted by changing the grouped components and/or adding new parameters. After evaluating several regression scenarios and testing many possible combinations, the final correlation was obtained and is expressed as Equation (2).

where

$I_{1}=B_{1}+B_{2}(1.8T+32)$

$I_{2}=B_{3}F_{C_{1}}+B_{4}(F_{C_{2}}+F_{C_{3}})+B_{5}F_{C_{4}}+B_{6}(F_{C_{5}}+F_{C_{6}})$

$I_{3}=B_{7}F_{CO_{2}}+B_{8}F_{H_{2}S}+B_{9}F_{N_{2}}$

$I_{4}=B_{10}(\gamma_{C_{7+}}M_{C_{7+}})+B_{11}(F_{C_{7+}}\gamma_{C_{7+}}M_{C_{7+}})+B_{12}\frac{M_{C{7+}}}{\gamma_{C{7+}}+0.00001}+B_{13}\lgroup\frac{M_{C{7+}}}{\gamma_{C{7+}}+0.00001}\rgroup$

$I_{5}=B_{14}\frac{F_{C_{1}}}{F_{C_{7+}}+0.00001}+B_{15}\frac{F_{C_{1}}}{I_{2}-B_{3}F_{C_{1}}}+B_{16}\frac{M_{C_{7+}}}{F_{C_{2}}+F_{C_{3}}+F_{C_{4}}+F_{C_{5}}}$

It can be seen from Fig. 5 that the error tends to decrease with the increase of total molecular weight, except some scattering abnormal points. Samples with a relative molecular weight less than 25 and higher than 30 have errors of high dispersion.

The correlation can be improved if the data set is divided into three groups based on the total molecular weight: the first with relative molecular weight below 25, the second between 25 and 30, and the third greater than 30. It can be seen from Table 12 and Fig. 6 that after regrouping, the new correlation improves significantly in accuracy, with AAE reducing from 10.03% to 7.58%, RMSE dropping from 705 to 588, and R² increasing from 0.81 to 0.87. After regrouping, the correlation is the same as equation 2 in structure, only the coefficients were refitted (Table 13).

The statistical parameters of the four published correlations in Table 10 were compared with the statistical parameters of the new correlation after regrouping of the dataset in Table 12, and the results show that the new correlation has the highest accuracy. By making cross plots of the experimental and calculated DPPs (Fig. 7), we also found that the DPP values calculated with the new correlation match best with the experimental DPP values. Because the new correlation divides the dataset into three groups based on the total molecular weight, it is necessary to compare its performance with the published correlations by each group of the dataset. It can be seen from Table 14, for the first group (MWt < 25 lb./lb.-mole), the new correlation resulted in the lowest AAE and highest R². For the second group (25 lb./lb.-mole < MWt < 30 lb./lb.-mole), the new correlation resulted in the lowest AAE (7.2%), while the Nemeth and Kennedy correlation resulted in the highest R² (0.89). Finally, for the third group (MWt > 30 lb./lb.-mole), results from the new correlation had the lowest AAE and highest R².

After statistical evaluation, the sensitivity of the published correlations and the new proposed correlation to parameters such as temperature, methane mole fraction, heptane-plus mole fraction, and molecular weight of heptane plus were analyzed.

5.2.1. Sensitivity to temperature

For the dataset in the study, many samples were experimentally tested at several temperatures. The correlations and the untuned Peng-Robinson EOS were applied to these samples, and the predicted trends of DPP vs. temperature were compared with those of experimental data. Two samples (samples 13 and 14) were selected to illustrate temperature sensitivity of the correlations. Table 15 shows the compositions of these two samples.

On a typical gas condensate phase envelope, the DPP increases with temperature until the cricondenbar value is reached, then it starts decreasing. Fig. 8 shows the tested DPP and the DPP calculated with the untuned PR EOS both have a clear decreasing trend as the temperature increases. The DPP values calculated by the new correlation show a slight decrease. The DPP values calculated by Nemeth and Kennedy, Elsharkawy, and Shokir correlations show a slight increase as the temperature increases. The DPP values calculated by Godwin correlation show a relatively sharp increase with the increase in temperature. Therefore, all the correlations fail to capture the actual variation trend of DPP with temperature.

Fig. 9 show that as temperature increases, the DPP tested by experiment and DPP calculated by untuned PR EOS increase to a maximum value (the temperature at the cricondenbar) and then start to decrease. All the correlations are unable to capture the actual trend of DPP with temperature. Therefore, we do not recommend the use of any DPP correlation to construct the phase envelope for a gas condensate reservoir.

Both Figs. 8 and 9 show that the DPP calculated by the new correlation has a slight decrease trend as temperature increases, which is what we expected, because the temperature is negatively correlated with the DPP for some samples, as shown by Equation (2) and Table 13 (B₂ is negative). Although the decreasing trend in the figures is minor, the new correlation is the only one to reflect it.

5.2.2. Sensitivity to mole fractions of C₁ and C₇₊

No experimental data in the dataset shows the sensitivity of DPP to variations of the C₁ and C₇₊ mole fractions. In this study, several synthetic samples were generated by changing the C₁/C₇₊ mole ratio of an original sample. Sample 15 was selected to analyze sensitivity of the correlations to methane and heptane-plus mole fractions. The compositions of the original sample (sample 15) and the synthetic samples (sample 15a, 15b and 15c) are shown in Table 16. Only the original sample has one experimental DPP; therefore, the variation trend of DPP with C₁ and C₇₊ mole fractions predicted by the EOS was taken as a reference. The PVTi software was used to generate phase envelopes for the samples in Table 16. The dew point lines of these samples are shown in Fig. 10. It can be seen the reservoir temperature line intersects with the dew point lines of all samples; and with the increase of C₁ and C₇₊ mole fractions, the phase envelops contract and move toward left.

Fig. 11 shows the DPP calculated by PR EOS decreases with the increase of C₁/C₇₊ mole ratio. The Nemeth and Kennedy, Shokir, and Godwin correlations, as well as the new correlation, capture this trend, whereas the Elsharkawy correlation results in an opposite trend.

5.2.3. Sensitivity to C₇₊ molecular weight

The sensitivity of the DPP predicted by the correlations to the molecular weight of C₇₊ was analyzed by varying the C₇₊ molecular weight of Sample 15 and generating 5 synthetic samples (with no change in composition). Fig. 12 shows the dew-point lines of the samples. According to this figure, as MW_C7+ increases, the phase envelope becomes flatter and shifts toward the right.

Fig. 13 shows that the DPP values calculated by the four correlations, the new correlation and the PR EOS tend to increase with the increase of molecular weight of C₇₊.

Gas condensate samples measured experimentally and collected from literatures were screened rigidly to remove the defective and unreliable ones. It is found during the screening that the industrial standards for identifying gas condensate reservoirs based on relative molecular weight and heptane plus content are not accurate. Four previously published empirical correlations, the Nemeth and Kennedy, Elsharkawy, Shokir, and Godwin correlations, as well as the untuned Peng-Robinson EOS, were applied to the filtered dataset to test their accuracy. The results show that the Nemeth and Kennedy correlation is the most accurate, followed by the Elsharkawy and Godwin correlations.

The Shokir correlation has the lowest accuracy because it cannot be used to samples with no C₇₊ components. DPP calculated by EOS is not unique and not necessarily accurate. The four previous correlations were modified, and a new correlation was worked out based on the data bank collected. The new correlation is better than the former four correlations according to statistics.

The sensitivity analysis results show that the PR EOS can reflect the variation trend of DPP with reservoir temperature, while all correlations cannot. The PR EOS, and Nemeth and Kennedy, Shokir, and Godwin correlations can reflect the decrease trend of DPP with the increase of C₁/C₇₊, while the Elsharkawy correlation cannot. The PR EOS and all the correlations can reflect the increase trend of DPP with the increase of C₇₊ relative molecular weight.

Finally, a new correlation was presented based on the large data bank. The new correlation yields an AAE of 7.5% and a correlation coefficient of 0.87, which is statistically superior to all other published correlations. Moreover, the new correlation successfully captured the physical trends in DPP when the temperature, C₁/C₇₊, and molecular weight of the heptane plus fraction were varied.

A₁—A₁₀, B₁—B₁₆—coefficient;

F_C1—F_C6—mole fractions of C₁—C₆ , %;

F_C7+—mole fraction of C₇₊, %;

F_CO2—mole fraction of CO₂, %;

F_H2S—mole fraction of H₂S, %;

F_N2—mole fraction of N₂, %;

M_C7+—relative molecular weight of C₇₊;

p_d—dew point pressure, MPa;

T—temperature, °C;

γ_C7+—relative density of C₇₊.