Volumetric Properties

whitson comment

Note from Markus Hays Nielsen: The notation used for associated surface volumes and rates (e.g. $V_{\bar{g}o}$) defines the surface volume type and from which reservoir phase it comes from - e.g. $V_{\bar{g}o}$ is the surface gas (denoted by $\bar{g}$) from the reservoir oil phase (denoted by $o$)).

The reason why the petroleum industry has adapted a whole field of study into the volumetric behavior of hydrocarbon fluids is in some ways an accident of history. If the petroleum industry had applied mass or molar flow instead of volume, many of the ideas of volumetric behavior would be simplified. With this disclaimer, the following sections will describe some of the most important volumetric properties used to relate surface and reservoir volumes.

Formation Volume Factor

The formation volume factor (FVF) relates reservoir volumes of gas and oil with the corresponding surface volumes of gas and oil. The FVF is the inverse of the sometimes more natural shrinkage factor - i.e. how much the reservoir volume shrinks when brought to the surface.

Oil FVF

$\begin{equation}\label{Bo} B_o(p) = \frac{V_o(p)}{V_{\bar{o}o}} \end{equation}$

Gas FVF

The gas FVF ($B_{g}$) is given by

$\begin{equation}\label{Bg} B_{g}(p) = \frac{V_g(p)}{V_{\bar{g}g}} \end{equation}$

However, when calculating the gas FVF, some books or articles tend to neglect the contribution of the oil condensing from the gas ($V_{\bar{o}g}$). This "fake" gas FVF gives is referred to as the "wet" gas FVF because it contains more liquids than it should. When calculating the gas FVF by the use of the real gas law, the dry gas FVF can be estimated by correlations like the Cragoe correlation¹ or by a first order approximation of the molar split.

Surface Volume Ratios (GOR|OGR)

Solution GOR|OGR

The formal definition of the solution gas-oil ratio (GOR - $R_s$) and oil-gas ratio (OGR - $r_s$) are given below

$\begin{equation}\label{Rs} R_s(p) = \frac{V_{\bar{g}o}}{V_{\bar{o}o}} \end{equation}$

$\begin{equation}\label{rs} r_s(p) = \frac{V_{\bar{o}g}}{V_{\bar{g}g}} \end{equation}$

Producing GOR|OGR

The formal definition of the producing gas-oil ratio (GOR - $R_p$) and oil-gas ratio (OGR - $r_p$) are given below

$\begin{equation}\label{Rp} R_s(p) = \frac{V_{\bar{g}o} + V_{\bar{g}g}}{V_{\bar{o}o} + V_{\bar{o}g}} \end{equation}$

$\begin{equation}\label{rp} r_s(p) = \frac{V_{\bar{o}g} + V_{\bar{o}o}}{V_{\bar{g}g} + V_{\bar{g}o}} \end{equation}$

Correlations

Note

Main article is: 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. 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.

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).

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

where

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

C.S. Cragoe. Thermodynamic properties of petroleum products. Bureau of Standards, US Department of Commerce, pages 22, 1929. ↩