Correlations for Volumetric Properties

Molar Split Approximation

Given $y_{i}$ at reservoir conditions and assume that $y_{n+}$ goes to the liquid phase and $y_{n-}$ goes to the vapor phase at surface conditions.

Derivation

Given the definition of the gas FVF and the real gas law, the definition of the gas FVF can be re-written as

$\begin{equation}\label{eq:step1} B_{gd}(p) = \frac{Z(p)\frac{nRT}{p}}{Z(p_{sc})\frac{n_{sc}RT_{sc}}{p_{sc}}} \end{equation}$

From the molar material balance and the assumption that $y_{n+}$ goes to the liquid phase at surface conditions and the fact that the Z-factor at surface conditions is equal to 1 yields

$\begin{equation}\label{eq:step2} n_{sc} = n\cdot (1-y_{n+}) \end{equation}$

Inserting equation \eqref{eq:step2} in equation \eqref{eq:step1} and re-arranging the fraction yields

$\begin{equation}\label{eq:step3} B_{gd}(p) = \frac{p_{sc}}{T_{sc}}\frac{Z(p)T}{p}\frac{1}{(1-y_{n+})} \end{equation}$

Method

The approximation for the dry gas FVF using the real gas law becomes

$\begin{equation}\label{Bgd_split} B_{gd}(p) = \frac{p_{sc}}{T_{sc}}\frac{Z(p)T}{p}\frac{1}{(1-y_{n+})} \end{equation}$

where the Z-factor can be calculated by an EOS or by correlation.

Example

Given a mixture

$y_i=[0.57116,0.04317,0.00416,0.01561,0.07881,0.13290,0.15417]$

Assume that $C_{5+}$ goes to the liquid phase at surface conditions then $y_{5+}=0.36589$. The ratio of the dry and wet gas FVF then becomes

$\begin{equation}\label{example_split} \frac{B_{gd}(p)}{B_{gw}(p)} = \frac{1-0.36589}{1} = 0.634... \end{equation}$

which indicates a widely different value of for the shrinkage of the gas!

Cragoe Correlation

Note

The units used in this correlation are field units, i.e. pressure: (psia), temperature: (R), OGR: (STB/scf) and FVF: (ft3/scf).

Method

$\begin{equation}\label{Bgd_cragoe} B_{gd}(p) = \frac{p_{sc}}{T_{sc}}\frac{Z(p)T}{p}[1+C_{\bar{o}g}r_s] \end{equation}$

where

$\begin{equation}\label{cragoe_factor} C_{\bar{o}g} = 133000\frac{\gamma_{\bar{o}g}}{MW_{\bar{o}g}} \end{equation}$

and

$\begin{equation}\label{cragoe_MW} MW_{\bar{o}g} = \frac{6084}{\gamma_{API}-5.9} \end{equation}$

In equation \eqref{cragoe_MW} $\gamma_{API}$ is the API gravity of the surface oil.

Standing Oil FVF and GOR Correlations

In 1947 Standing published correlations for both oil FVF (for both saturated and undersaturated conditions), solution GOR and a bubble-point correlation¹. The correlations were based on 105 different data-points for 22 different hydrocarbon systems. In the following sub-sections the oil FVF and solution GOR correlations are given.

Note

The units used in this correlation are temperature: (F), pressure: (psia), solution GOR: (scf/STB).

Oil FVF (Saturated)

$\begin{equation}\label{eq:standing_Bo_sat} B_o = 0.972 + 1.44\cdot 10^{-4} [R_s(\frac{\gamma_g}{\gamma_o})^{1/2}+1.25T]^{1.175} \end{equation}$

where $\gamma_o$ and $\gamma_g$ are the surface gas and oil specific gravities.

Oil FVF (Underaturated)

$\begin{equation}\label{eq:standing_Bo_und_sat} B_o(p) = B_{ob} \exp{\{ -c_o(p-p_{bp}) \}} \end{equation}$

where $c_o$ is the oil compressibility, $p_b$ is the bubble-point pressure and $B_{ob}$ is the oil FVF at the bubble-point pressure. The oil compressibility can be calculated by correlation or measured values.

Typically the bubble-point is calculated by correlation. Standing provides a correlation for the bubble-point given by re-arranging equation \eqref{eq:standing_GOR} given by

$\begin{equation}\label{eq:standing_BP} p_{bp} = 18.2[(\frac{R_s}{\gamma_g})^{0.83}\cdot 10^{0.00091T-0.0125\gamma_{API}} - 1.4] \end{equation}$

where $\gamma_{API}$ is the surface oil API gravity.

Solution GOR

$\begin{equation}\label{eq:standing_GOR} R_s = [(\frac{p_{bp}}{18.2}+1.4)\cdot\frac{10^{0.0125\gamma_{API}}}{10^{0.00091T}}]^{\frac{1}{0.83}}\cdot \gamma_g \end{equation}$

where $\gamma_{API}$ is the surface oil API gravity and $\gamma_g$ is the gas gravity specific gravities.

M.B. Standing. A pressure-volume-temperature correlation for mixtures of california oils and gases. In Drilling and Production Practice, paper API–47–275. American Petroleum Institute, 1947. ↩