# 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

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

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

### Method

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

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

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

where

and

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)

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

### Oil FVF (Underaturated)

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

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

### Solution GOR

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

1. 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.