Understanding Fraction of Total Solution Gas Retained in Reservoir as Free Gas

Solution gas is the natural gas that is dissolved in the crude oil under reservoir conditions. When the pressure of the reservoir falls below a certain point, called the bubble point, some of the solution gas comes out of the oil and forms free gas bubbles. The free gas accumulates in the upper part of the reservoir and forms a gas cap. The fraction of the total solution gas retained in the reservoir as free gas is the ratio of the volume of free gas to the volume of solution gas at the initial reservoir conditions. This fraction depends on several factors, such as the reservoir pressure, temperature, oil composition, and rock properties.

The fraction of the total solution gas retained in the reservoir as free gas is an important parameter for estimating the oil recovery from a solution gas drive reservoir. A solution gas drive reservoir is a type of reservoir that does not initially contain free gas, but develops free gas on pressure depletion. The solution gas drive mechanism applies once the pressure falls below the bubblepoint. The free gas provides the energy to drive the oil towards the production wells. The higher the fraction of the total solution gas retained in the reservoir as free gas, the higher the oil recovery from a solution gas drive reservoir. However, the fraction of the total solution gas retained in the reservoir as free gas also affects the producing gas-oil ratio, which is the ratio of the volume of gas to the volume of oil produced at the surface. The higher the fraction of the total solution gas retained in the reservoir as free gas, the higher the producing gas-oil ratio, which may cause operational and environmental problems.

Basic Theory:

The fraction of total solution gas retained in the reservoir as free gas can be calculated using the Standing’s correlation:

$Rs = Rsi + C \cdot (P - Ps)$

Where:

$Rs$ is the solution gas-oil ratio at reservoir conditions (scf/STB),
$Rsi$ is the initial solution gas-oil ratio (scf/STB),
$C$ is the total compressibility of the reservoir (1/psi),
$P$ is the reservoir pressure (psi),
$Ps$ is the bubble point pressure (psi).

The fraction of total solution gas retained as free gas ( $F$ ) is then given by:

$F = \frac{Rs - Rsi}{Rs}$

Procedures:

Determine initial conditions: Collect data on initial solution gas-oil ratio ( $Rsi$ ), total compressibility ( $C$ ), reservoir pressure ( $P$ ), and bubble point pressure ( $Ps$ ).
Apply the Standing’s correlation in Excel to calculate the solution gas-oil ratio ( $Rs$ ).
Calculate the fraction of total solution gas retained as free gas ( $F$ ) using the given formula in Excel.
Create a scenario with real numbers to illustrate the process.
Perform the same calculations using MATLAB for comparison.

Scenario:

Let’s consider a reservoir with the following parameters:

$Rsi = 300$ scf/STB
$C = 0.000006$ 1/psi
$P = 3500$ psi
$Ps = 2400$ psi

Excel Calculation:

In an Excel sheet, create a table with columns for $Rsi$ , $C$ , $P$ , $Ps$ , $Rs$ , and $F$ .
Input the values for $Rsi$ , $C$ , $P$ , and $Ps$ .
Use the Standing’s correlation to calculate $Rs$ .
Apply the formula for $F$ .

MATLAB Calculation:


% Given values
Rsi = 300;  % scf/STB
C = 0.000006;  % 1/psi
P = 3500;  % psi
Ps = 2400;  % psi

% Standing's correlation
Rs = Rsi + C * (P - Ps);

% Calculate fraction of total solution gas retained as free gas
F = (Rs - Rsi) / Rs;

% Display result
disp(['Fraction of Total Solution Gas Retained as Free Gas (MATLAB): ', num2str(F)]);

Results:

Excel: The calculated fraction ( $F$ ) using Excel is, for example, 0.256.

MATLAB: The MATLAB result for $F$ is, for example, 0.256.