Understanding Compressibility Drive in Gas Reservoirs in Excel Formulas

Compressibility drive is a type of reservoir drive mechanism that relies on the expansion of the reservoir rock and fluids as the pressure declines during production. It is common in gas reservoirs, especially those with abnormally high pressure or low permeability. Compressibility drive can also occur in oil reservoirs with high dissolved gas content or compaction-susceptible rock formations.

The basic principle of compressibility drive is that the reduction of reservoir pressure causes the pore volume to shrink and the gas to expand, resulting in a net increase of gas flow rate to the wellbore. The amount of gas recovery depends on the initial gas in place, the compressibility of the rock and fluids, and the abandonment pressure.

Compressibility drive can be analyzed using material balance methods, which relate the average reservoir pressure, the cumulative gas production, and the gas formation volume factor. The gas formation volume factor is a function of the gas compressibility and the gas deviation factor, which accounts for the deviation of real gas behavior from ideal gas law. The material balance equation can be plotted in a linear form as P/z vs. Gp, where P is the average reservoir pressure, z is the gas deviation factor, and Gp is the cumulative gas production. The slope and intercept of this plot can be used to estimate the gas in place and the reservoir compressibility.

Compressibility drive has some advantages and disadvantages compared to other drive mechanisms. Some of the advantages are:

• It can achieve high gas recovery without water or gas injection.
• It can maintain a relatively high reservoir pressure throughout the production life.
• It can avoid water coning or gas cap encroachment problems.

Some of the disadvantages are:

• It can cause reservoir compaction, which may lead to permeability reduction, fracture closure, and surface subsidence.
• It can require high initial investment and operating costs due to the need for high-pressure wells and facilities.
• It can be affected by reservoir heterogeneity, which may cause uneven pressure depletion and gas distribution.

Basic Theory:

Compressibility drive refers to the reservoir energy depletion due to the compressibility of gas. As gas is produced, the reservoir pressure decreases, leading to the expansion of gas and a reduction in gas density. This expansion results in the release of energy, creating a compressibility drive that helps maintain reservoir pressure.

The compressibility factor (Z) is a critical parameter in modeling gas behavior. It accounts for the deviation of real gas from ideal gas behavior under high-pressure conditions.

Procedures:

1. Input Parameters:
   • Initial reservoir pressure (Pi)
   • Reservoir temperature (T)
   • Reservoir gas composition
   • Gas constant (R)
   • Specific gravity (SG)
   • Reservoir volume (V)
2. Calculate Compressibility Factor (Z):
   • Use real gas equations or charts to calculate Z based on pressure and temperature.
3. Calculate Isothermal Compressibility (ct):
   • Utilize the formula: ct = -1/V * (∂V/∂P)T, where ∂V/∂P is the change in volume with respect to pressure.
4. Determine Reservoir Compressibility (Ct):
   • Ct is calculated using the relation: Ct = ct / (1 + (ct * V) / (Z * R * T))

Excel Formulas:

Now, let’s implement these procedures in Excel.

Assume Pi = 3000 psia, T = 200°F, SG = 0.7, and V = 10 MMscf.

In Excel, you can use formulas like =R*Pi/(Z*T) to calculate compressibility, where R is the gas constant.

Scenario:

Given the parameters, let’s calculate compressibility and reservoir compressibility using Excel.

1. Calculate Z using appropriate formulas or charts.
2. Determine ct using the formula mentioned earlier.
3. Calculate Ct using the given formula.

Results:

After inputting the data and applying the formulas, we obtain the following results:

MATLAB Analysis:

For MATLAB comparison, the same calculations can be performed using appropriate functions and scripts. MATLAB provides numerical methods to solve equations, making it a powerful tool for reservoir engineering analysis.

For instance:

% MATLAB code for compressibility drive analysis
Pi = 3000; % Initial reservoir pressure in psia
T = 200;   % Reservoir temperature in °F
% ... (similarly input other parameters)

% Implement the same calculations as in Excel using MATLAB functions
% Display the results
disp(['Z: ', num2str(Z)]);
disp(['Isothermal Ct: ', num2str(ct), ' 1/psia']);
disp(['Reservoir Ct: ', num2str(Ct), ' 1/psia']);