Assessment of Empirical Pressure–Volume–Temperature Correlations in Gas Condensate Reservoir Fluids: Case Studies

Abstract

Measurement and modeling of fluid properties and phase behavior of gas condensate reservoir fluids are challenging tasks. Many researchers proposed various empirical correlations based on either simple measurable field or laboratory data (e.g., gas-to-condensate ratio (GCR), compositions, and plus fraction characteristics) to estimate other PVT (pressure–volume–temperature) properties. In this study, several empirical correlations for estimating gas condensate fluid properties have been selected to be evaluated against available field data gathered from Iranian gas condensate fields. Experimental data from 30 lean gas condensate samples taken from nine gas condensate fields in the south of Iran were collected to examine the reliability of the empirical correlations. A wide range of field data were used for the evaluation: reservoir temperatures of 343.7–385.9 K, gas molecular weights of 17.40–21.13 g/mol, dew point pressures of 21.37–35.64 MPa, gas compressibility factors of 0.84–1.06 at dew point pressure, maximum retrograde condensates of (MRC) 0.09–2.91%, and GCRs of 5964–110,012.6 m³/m³. The estimated empirical correlations were compared to the measured field data, and the accuracy of the correlations was evaluated via error analysis. The parameters included in the assessment of empirical correlations were C₇₊ mole%, gas molecular weight, MRC, GCR, dew point pressure, and gas compressibility factor at dew point pressure. The results indicate that correlations of parameters with dew point pressure and with MRC have minimum and maximum errors, respectively. In cases where the GCR is high, correlations with C₇₊ mole% were not suitable for assessment. Also, estimation of gas compressibility factors at dew point pressure based on empirical correlations is not recommended.

Appendix

Nemeth and Kennedy (1967)

Nemeth and Kennedy (1967) suggested a correlation between dew point pressure of fluid (Pa) and its composition, reservoir temperature (K), and characteristics of the C₇₊ fraction including molecular weight and specific gravity.

$$\begin{aligned} \ln \left( {14.7 \times 10^{ - 4} {P}_{\text{d}} } \right) & = {A}_{1} \left( {{X}_{{{\text{C}}_{2} }} + {X}_{{{\text{CO}}_{2} }} + {X}_{{{\text{H}}_{2} {\text{S}}}} + {X}_{{{\text{C}}_{6} }} + 2\left( {{X}_{{{\text{C}}_{3} }} + {X}_{{{\text{C}}_{4} }} } \right) + {X}_{{{\text{C}}_{5} }} + 0.4{X}_{{{\text{C}}_{1} }} + 0.2{X}_{{{\text{N}}_{2} }} } \right) \\ & \quad +\, {A}_{2} \gamma_{{{\text{C}}_{7 + } }} + {A}_{3} \left( {\frac{{{X}_{{{\text{C}}_{1} }} }}{{{X}_{{{\text{C}}_{7 + } }} + 0.002}}} \right) + {A}_{4} ({\text{T*}}1.8 - 459.67) + {A}_{5} \left( {{X}_{{{\text{C}}_{7 + } }} {\text{MW}}_{{{\text{C}}_{7 + } }} } \right) \\ & \quad +\, {A}_{6} \left( {{X}_{{{\text{C}}_{7 + } }} {\text{MW}}_{{{\text{C}}_{7 + } }} } \right)^{2} + {A}_{7} \left( {{X}_{{{\text{C}}_{7 + } }} {\text{MW}}_{{{\text{C}}_{7 + } }} } \right)^{3} + {A}_{8} \left( {\frac{{{\text{MW}}_{{{\text{C}}_{7 + } }} }}{{\gamma_{{{\text{C}}_{7 + } }} + 0.0001}}} \right) \\ & \quad +\, {A}_{9} \left( {\frac{{{\text{MW}}_{{{\text{C}}_{7 + } }} }}{{\gamma_{{{\text{C}}_{7 + } }} + 0.0001}}} \right)^{2} + {A}_{10} \left( {\frac{{{\text{MW}}_{{{\text{C}}_{7 + } }} }}{{\gamma_{{{\text{C}}_{7 + } }} + 0.0001}}} \right)^{3} + {A}_{11} \\ \end{aligned}$$

(A.1)

$$\begin{aligned} A_{1} & = - 2.0623054\quad A_{2} = 6.6259728\quad A_{3} = - 4.4670559 \times 10^{ - 3} \quad A_{4} = 1.0448346 \times 10^{ - 4} \\ A_{5} & = 3.2673714 \times 10^{ - 2} \quad A_{6} = - 3.6453277 \times 10^{ - 3} \quad A_{7} = 7.4299951 \times 10^{ - 5} \quad A_{8} = - 1.1381195 \times 10^{ - 1} \\ A_{9} & = 6.2476497 \times 10^{ - 4} \quad A_{10} = - 1.0716866 \times 10^{ - 6} \quad A_{11} = 1.0746622 \times 10 \\ \end{aligned}$$

Elsharkawy (2001)

Elsharkawy (2001) developed a simple, accurate, and reliable empirical model to calculate the dew point pressures (Pa) for condensate gas systems as a function of available gas analysis and reservoir temperature (K).

$$\begin{aligned} 0.000147 * {P}_{\text{d}} & = {A}_{0} + {A}_{1} ({T*}1.8 - 459.67) + {A}_{2} {X}_{{{\text{H}}2{\text{S}}}} + {A}_{{3 {X}_{{{\text{CO}}2}} }} \\ & \quad + {A}_{4} {X}_{{{\text{N}}2}} + {A}_{5} {X}_{{{\text{C}}1}} + {A}_{6} {X}_{{{\text{C}}2}} + {A}_{7} {X}_{{{\text{C}}3}} + {A}_{8} {X}_{{{\text{C}}4}} + {A}_{9} {X}_{{{\text{C}}5}} + {A}_{10} {X}_{{{\text{C}}6}} \\ & \quad + {A}_{11} {X}_{{{\text{C}}_{7 + } }} + {A}_{12} {\text{MW}}_{{{\text{C}}_{7 + } }} + {A}_{13} \gamma_{{{\text{C}}_{7 + } }} {A}_{14} {X}_{{{\text{C}}_{7 + } }} {\text{MW}}_{{{\text{C}}_{7 + } }} + {A}_{15} \left( {\frac{{{\text{MW}}_{{{\text{C}}_{7 + } }} }}{{\gamma_{{{\text{C}}_{7 + } }} }}} \right) \\ & \quad + {A}_{16} \left( {\frac{{{X}_{{{\text{C}}_{7 + } }} {\text{MW}}_{{{\text{C}}_{7 + } }} }}{{\gamma_{{{\text{C}}_{7 + } }} }}} \right) + {A}_{17} \left( {\frac{{{X}_{{{\text{C}}_{7 + } }} }}{{{X}_{{{\text{C}}1}} + {X}_{{{\text{C}}2}} }}} \right) + {A}_{18} \left( {\frac{{{X}_{{{\text{C}}_{7 + } }} }}{{{X}_{{{\text{C}}2}} + {X}_{{{\text{C}}3}} + {X}_{{{\text{C}}4}} + {X}_{{{\text{C}}5}} + {X}_{{{\text{C}}6}} }}} \right) \\ \end{aligned}$$

(A.2)

$\begin{aligned} & A_{0} = 4268.85\quad A_{1} = 0.094056\quad A_{2} = - 7157.87\quad A_{3} = - 4540.58\quad A_{4} = - 4663.55\quad A_{5} = - 1357.56 \\ & A_{6} = - 7776.10\quad A_{7} = - 9967.99\quad A_{8} = - 4257.10\quad A_{9} = - 1417.1\quad A_{10} = 691.5298\quad A_{11} = 40660.36 \\ & A_{12} = 205.26\quad A_{13} = - 7260.32\quad A_{14} = - 352.413\quad A_{15} = - 114.519\quad A_{16} = 8.133\quad A_{17} = 94.916 \\ & A_{18} = 238.252 \\ \end{aligned}$

Ovalle et al. (2007)

Ovalle et al. (2007) proposed a power function correlation to estimate composition of the C₇₊ mole fraction of original reservoir gas using GCR (m³/m³). This correlation has been developed based on 862 condensate gas samples with AARE (absolute average relative error) of 6.23%.

$${\text{C}}_{7 + } {\text{mole}}\;{\text{\% }} = \left( {\frac{\text{GCR}}{64137.6}} \right)^{ - 0.86391}$$

(A.3)

Shokir (2008)

Shokir (2008) proposed a dew point pressure (Pa) prediction model as a function of reservoir fluid composition in terms of mole fraction of C₁ through C₇₊, N₂, CO₂, and H₂S, MW_C7+, and reservoir temperature (K).

$$1.47 \times 10^{ - 4} P_{\text{d}} = B_{1} + B_{2} + B_{3} + B_{4}$$

(A.4)

$$\begin{aligned} {B}_{1} & = 201.875481\left( {{X}_{{{\text{C}}_{7 + } }} \left( {\left( {\left( {1.8 * {T} - 459.67} \right)} \right.} \right.} \right.\left. {\left( {\left( {\left( {{X}_{{{\text{C}}_{3} }} - \left( {{X}_{{{\text{H}}_{2} {\text{S}}}} - {X}_{{{\text{CO}}_{2} }} } \right)} \right) - \left( {{X}_{{{\text{C}}_{6} }} - \left( {{X}_{{{\text{CO}}_{2} }} - {X}_{{{\text{C}}_{4} }} } \right)} \right)} \right) - {X}_{{{\text{C}}_{2} }} } \right)} \right) \\ & \quad - \left( {\left( {{X}_{{{\text{C}}_{4} }} \left( {\left( {\left( {{X}_{{{\text{CO}}_{2} }} - {X}_{{{\text{C}}_{4} }} } \right) - \left. {\left( {{\text{MW}}_{{{\text{C}}_{7 + } }} - {X}_{{{\text{N}}_{2} }} } \right)} \right)} \right.} \right.} \right.} \right. - \left. {\left. {\left( {{\text{MW}}_{{{\text{C}}_{7 + } }}^{2} {X}_{{{\text{C}}_{5} }} } \right)} \right)} \right) - {X}_{{{\text{C}}_{7 + } }} \\ & \quad - \left( {{X}_{{{\text{H}}_{2} {\text{S}}}} - \left( {\left( {{X}_{{{\text{N}}_{2} }} \left. {\left( {(1.8 * {T} - 459.67)\left( {{X}_{{{\text{C}}_{1} }}^{2} - {X}_{{{\text{C}}_{7 + } }} } \right)} \right)} \right)} \right.} \right.} \right. \\ & \quad \left. {\left. {\left. {\left. { -\, \left( {{\text{MW}}_{{{\text{C}}_{7 + } }} - \left( {{X}_{{{\text{C}}_{2} }} - {X}_{{{\text{H}}_{2} {\text{S}}}} } \right)} \right)} \right)} \right)} \right)} \right) + 38456.87953{X}_{{{\text{C}}5}} \\ \end{aligned}$$

(A.5)

$$\begin{aligned} {B}_{2} & = 0.000007\left( {\left( {(1.8 * {T} - 459.67)} \right.\left( {\left( {\left( {\left( {{X}_{{{\text{CO}}_{2} }} - {\text{MW}}_{{{\text{C}}_{7 + } }} } \right) - {X}_{{{\text{C}}_{7 + } }} } \right)\left( {\left( {(1.8 * {T} - 459.67) - {\text{MW}}_{{{\text{C}}_{7 + } }} } \right)} \right.} \right.} \right.} \right. \\ & \quad \left. {\left. { - \left( {{X}_{{{\text{CO}}_{2} }} - {T}} \right)} \right)} \right) - \left. {\left. {\left( {\left( {{X}_{{{\text{H}}_{2} {\text{S}}}} - (1.8 * {T} - 459.67)} \right)\left( {\left( {{\text{MW}}_{{{\text{C}}_{7 + } }} - {X}_{{{\text{C}}_{3} }} } \right){\text{MW}}_{{{\text{C}}_{7 + } }} } \right)} \right)} \right)} \right){X}_{{{\text{N}}_{2} }} \\ & \quad + 225500.9399{X}_{{{\text{C}}_{6} }} \\ \end{aligned}$$

(A.6)

$$\begin{aligned} {B}_{3} & = 120586.9719\left( {{X}_{{{\text{C}}_{1} }} \left( {\left( {\left( {\left( {{X}_{{{\text{H}}_{2} {\text{S}}}} {X}_{{{\text{C}}_{3} }} } \right) - \left( {{X}_{{{\text{C}}_{5} }} - {X}_{{{\text{C}}_{7 + } }} } \right)} \right){X}_{{{\text{H}}_{2} {\text{S}}}} } \right)} \right.} \right. \\ & \quad - \left. {\left. {\left( {\left( {\left( {{X}_{{{\text{C}}_{7 + } }} - {X}_{{{\text{C}}_{1} }} } \right)\left( {{X}_{{{\text{C}}_{7 + } }} - {X}_{{{\text{C}}_{6} }} } \right)} \right) - \left( {{X}_{{{\text{H}}_{2} {\text{S}}}} {X}_{{{\text{N}}_{2} }}^{2} } \right)} \right)} \right)} \right) + 72.6908{\text{MW}}_{{{\text{C}}_{7 + } }} \\ \end{aligned}$$

(A.7)

$$\begin{aligned} {B}_{4} & = - 1962.40851\left( {{X}_{{{\text{C}}_5}} \left( {{\text{MW}}_{{{\text{C}}_{7 + } }} - {X}_{{{\text{C}}_1}}^{2} } \right)} \right) \\ & \quad - 253385.67764\left( {\left( {{X}_{{{\text{C}}_{7 + } }} \left( {\left( {{X}_{{{\text{CO}}_2}} {X}_{{{\text{C}}_3}} } \right) - \left( {{X}_{{{\text{C}}_4}} - {X}_{{{\text{C}}_{7 + } }} } \right)} \right)} \right)\left( {{X}_{{{\text{CO}}_2}} \left( {{X}_{{{\text{C}}_3}} \left( {{X}_{{{\text{C}}_3}} - {\text{MW}}_{{{\text{C}}_{7 + } }} } \right)} \right)} \right)} \right) \\ & \quad - 13358.59271{X}_{{{\text{C}}_4}} + 4676.933602{X}_{{{\text{C}}_2}} - 6567.9 \\ \end{aligned}$$

(A.8)

In Eqs. A.4–A.8, X_i is the mole fraction of ith component.

Al-Dhamen and Al-Marhoun (2011)

Al-Dhamen and Al-Marhoun (2011) presented correlations to calculate the dew point pressure (Pa) as functions of reservoir temperature (K), condensate specific gravity (γ_cond), gas specific gravity (γ_g), and GCR (m³/m³). The data used for developing the models are obtained from CCE experiments from Middle East fields.

$$\ln \left( {1.47 \times 10^{ - 4} P_{\text{d}} } \right) = a_{1} + a_{2} \ln \left[ {\frac{{5.615*{\text{GCR}} \times \gamma_{\text{g}} }}{{\gamma_{7 + } }}} \right] + a_{3} \ln \left( {1.8*T} \right) + a_{4} \gamma_{\text{g}} + \frac{{a_{5} }}{{\gamma_{{{\text{cond}} .}} }} + a_{6} {\text{e}}^{{a_{7} + a_{8} \ln \left( {5.615*{\text{GCR}}} \right)}}$$

(A.9)

$$\begin{aligned} a_{1} & = 18.6012\quad a_{2} = - 0.1520\quad a_{3} = - 0.1674\quad a_{4} = 0.0685\quad a_{5} = - 5.8982\quad a_{6} = - 0.0559 \\ a_{7} & = 8.4960\quad a_{8} = - 0.7466 \\ \end{aligned}$$

$${P}_{\text{d}} = {\text{e}}^{{{c}_{1} {F}\left( {{P}_{\text{d}} } \right)^{3} + {c}_{2} {F}\left( {{P}_{\text{d}} } \right)^{2} + {c}_{3} {F}\left( {{P}_{\text{d}} } \right) + {c}_{4} }}$$

(A.10)

$$F\left( {P_{\text{d}} } \right) = \ln [F\left( T \right) + F\left( {\text{GCR}} \right) + F\left( {\gamma_{\text{g}} } \right) + F\left( {\gamma_{\text{cond}} } \right) + 1$$

(A.11)

$$F\left( T \right) = p_{1} (1.8*T)^{3} + p_{2} (1.8*T)^{2} + p_{3} (1.8*T) + p_{4}$$

(A.12)

$$F\left( {\text{GCR}} \right) = r_{1} \ln \left( {5.615*{\text{GCR}}} \right) + r_{2}$$

(A.13)

$$F\left( {\gamma_{\text{g}} } \right) = q_{1} \gamma_{\text{g}}^{2} + q_{2} \gamma_{\text{g}} + q_{3}$$

(A.14)

$$F\left( {\gamma_{{{\text{cond}} .}} } \right) = s_{1} \gamma_{{{\text{cond}} .}}^{3} + s_{2} \gamma_{{{\text{cond}} .}}^{2} + s_{3} \gamma_{{{\text{cond}} .}} + s_{4}$$

(A.15)

$$\begin{aligned} & c_{1} = 49.1377\quad c_{2} = - 336.5699\quad c_{3} = 770.0995\quad c_{4} = - 580.0322 \\ & p_{1} = - 0.35014 \times 10^{ - 6} \quad p_{2} = 0.18048 \times 10^{ - 3} \quad p_{3} = - 0.32315 \times 10^{ - 1} \quad p_{4} = 1.2058 \\ & r_{1} = - 0.3990\quad r_{2} = 5.1377\quad q_{1} = - 23.8741\quad q_{2} = 36.9448 \\ & q_{3} = - 12.0398\quad s_{1} = - 30120.78\quad s_{2} = 69559\quad s_{3} = - 53484.21 \\ & s_{4} = 13689.39 \\ \end{aligned}$$

Paredes et al. (2012)

Paredes et al. (2012) proposed two correlations for estimating MRC based on gas molecular weight and GCR (m³/m³).

$${\text{MRC}} = A + B\left( {{\text{MW}}_{\text{g}} } \right) + C({\text{GCR}})$$

(A.16)

$$A = - 32.34\quad B = 1.541\quad C = 0.0001045$$

$${\text{MRC}} = {A} + {B}\left( {\text{GCR}} \right) + {C}\left( {{\text{MW}}_{\text{g}} } \right) + {D}\left( {{\text{GCR}}^{2} } \right) + {E}\left( {{\text{GCR}} \times {\text{MW}}_{\text{g}} } \right) + {F}({\text{MW}}_{\text{g}}^{2} )$$

(A.17)

$$\begin{aligned} & A = - 59.5\quad B = 0.01278\quad C = 3.232\quad D = - 0.0000002124 \\ & E = - 0.0005257\quad F = - 0.02092 \\ \end{aligned}$$

Paredes et al. (2012) recommended using Eq. A.16 because it presented less variability with respect to the measured data.

Dindoruk (2012)

Dindoruk (2012) developed a correlation for estimation of condensate-to-gas ratio. Here, condensate-to-gas ratio (m³/10⁶m³) is estimated based on gas molecular weight value with a fourth-degree equation.

$${\text{CGR}} = 5.615(7.5537 \times 10^{ - 5} {\text{MW}}_{\text{g}}^{4} - 9.5072 \times 10^{ - 3} {\text{MW}}_{\text{g}}^{3} + 4.9304 \times 10^{ - 1} {\text{MW}}_{\text{g}}^{2} - 2.5463{\text{MW}}_{\text{g}} - 60)$$

(A.18)

Paredes et al. (2014)

Paredes et al. (2014) proposed below set of correlations for estimating C₇₊ mole%, gas molecular weight, MRC, dew point pressure (Pa), and gas compressibility factor in dew point pressure. These correlations were obtained from the analysis of more than 100 PVT studies mainly from Mexico and other regions of Latin America.

$${\text{C}}_{7 + } {\text{mole}}\;{\text{\% }} = 2258.31297446475 \times {\text{GCR}}^{ - 0.816117090683706}$$

(A.19)

$${\text{MW}}_{\text{g}} = 687.1830018707650 \times {\text{GCR}}^{ - 0.42937078961255}$$

(A.20)

$${\text{MRC}}\;{\text{\% }} = 2.921696607928510 \times {\text{C}}_{7 + } {\text{mole}}\;{\text{\% }} - 2.64046698519896$$

(A.21)

$$\begin{aligned} {\text{e}}^{Z} & = \left[ { - 89.543548 + \left( {34.620795 \times \ln \left( {{\text{MW}}_{\text{g}} } \right)} \right) + \left( {29.186098 \times \ln \left( {{\text{C}}_{7 + } {\text{mole}}\;{\text{\% }}} \right)} \right)} \right. \\ & \quad \left. { +\, \left( { - 16.777186 \times \ln \left( {{\text{MW}}_{\text{g}} } \right) \times \ln \left( {{\text{C}}_{7 + } {\text{mole}}\;{\text{\% }}} \right)} \right) + \left( {7.2393271 \times \ln \left( {{\text{MW}}_{\text{g}} } \right) \times \ln \left( {{\text{MW}}_{\text{g}} } \right)} \right)} \right] \\ & \quad \times { \ln }({\text{C}}_{7 + } {\text{mole}}\;{\text{\% }}) \\ \end{aligned}$$

(A.22)

$$\ln \left( {1.02 \times 10^{ - 5} P_{\text{d}} } \right) = - 0.27522065593 \times \left( {{\text{e}}^{Z} } \right)^{2} + 2.121956466266 \times {\text{e}}^{Z} + 2.129009818$$

(A.23)

In Eqs. A.19 and A.20, C₇₊mole% and gas molecular weight are computed based on GCR. In Eqs. A.19 and A.20, GCR is in m³/m³. In Eq. A.21, MRC is a function of C₇₊mole%. Equation A.22 gives gas compressibility factor in dew point pressure based on C₇₊mole% and gas molecular weight. Finally, in Eq. A.23 dew point pressure in Pa is obtained using gas compressibility factor.

This set of correlations (A.19–A.23) has been evaluated both successively and independently. For example in continuous form, calculated C₇₊mole% from Eq. A.19 has been used for estimating MRC in Eq. A.21. In independent form, the actual values of any quantity have been taken from PVT reports and the correlation has been evaluated.

Starling (1973)

A modification of the Benedict–Webb–Rubin EOS as proposed by Starling (1973) with 11 parameters has been developed to predict the compressibility factor of reservoir fluids (Danesh 1998).

$$\begin{aligned} Z & = 1 + \left( {A_{1} + \frac{{A_{2} }}{{T_{r} }} + \frac{{A_{3} }}{{T_{r}^{3} }} + \frac{{A_{4} }}{{T_{r}^{4} }} + \frac{{A_{5} }}{{T_{r}^{5} }}} \right)\rho_{r} + \left( {A_{6} + \frac{{A_{7} }}{{T_{r} }} + \frac{{A_{8} }}{{T_{r}^{2} }}} \right)\rho_{r}^{2} - A_{9} \left( {\frac{{A_{7} }}{{T_{r} }} + \frac{{A_{8} }}{{T_{r}^{2} }}} \right)\rho_{r}^{5} \\ & \quad + A_{10} (1 + A_{11} \rho_{r}^{2} )\left( {\frac{{\rho_{r}^{2} }}{{T_{r}^{3} }}} \right){\text{e}}^{{( - A_{11} \rho_{r}^{2} )}} \\ \end{aligned}$$

(A.24)

$$\begin{aligned} & A_{1} = 0.3265\quad A_{2} = - 1.0700\quad A_{3} = - 0.5339\quad A_{4} = 0.01569\quad A_{5} = - 0.05165\quad A_{6} = 0.5475 \\ & A_{7} = - 0.7367\quad A_{8} = 0.1844\quad A_{9} = 0.1056\quad A_{10} = 0.6134\quad A_{11} = 0.7210 \\ \end{aligned}$$

$$\rho_{\text{r}} = 0.27\left[ {\frac{{P_{\text{r}} }}{{ZT_{\text{r}} }}} \right]$$

(A.25)

Here, P_r and T_r are reduced pressure and temperature, respectively.