Estimation of Average Reservoir Pressure using MDH Method in Excel

The MDH method is a technique for calculating the average pressure in a reservoir from a pressure buildup test. A pressure buildup test is a procedure where a well is shut-in after producing at a constant rate, and the pressure change is measured over time. The MDH method uses a plot of pressure vs. logarithm of shut-in time to extrapolate the pressure at infinite time, which is called the extrapolated pressure. This pressure is then corrected by a factor that depends on the shape and size of the reservoir, the location of the well, and the fluid properties. The corrected pressure is the estimate of the average reservoir pressure.

The MDH method is based on some assumptions, such as the reservoir being bounded by closed boundaries, the flow being pseudosteady state before shut-in, and the fluid being slightly compressible. The MDH method is useful for short tests, but it requires accurate information about the reservoir geometry and the fluid properties. The MDH method is also sensitive to noise and fluctuations in the pressure data.

Basic Theory:

The MDH method is based on the principle of material balance, which equates the cumulative production from a reservoir to the cumulative change in reservoir volume. The average reservoir pressure ( $P_{avg}$ ) can be estimated by rearranging the material balance equation and solving for pressure.

Material Balance Equation:

$P_{avg} = P_i - \frac{B \cdot \Delta V}{\phi \cdot \Delta t}$

Where:

$P_{avg}$ is the average reservoir pressure
$P_i$ is the initial reservoir pressure
$B$ is the formation volume factor
$\Delta V$ is the change in reservoir volume
$\phi$ is the porosity
$\Delta t$ is the time period

Procedures:

Data Collection:
- Initial reservoir pressure ( $P_i$ )
- Formation volume factor ( $B$ )
- Change in reservoir volume ( $\Delta V$ )
- Porosity ( $\phi$ )
- Time period ( $\Delta t$ )
Excel Formulas:
- Calculate $P_{avg}$ using the MDH formula.
- Set up an Excel table with the collected data and the calculated average reservoir pressure.
Scenario:
- Consider a reservoir with an initial pressure of 5000 psi ( $P_i = 5000$ ).
- The formation volume factor is 1.2 ( $B = 1.2$ ).
- The change in reservoir volume is 50,000 bbl ( $\Delta V = 50000$ ).
- Porosity is 0.15 ( $\phi = 0.15$ ).
- The time period is 2 years ( $\Delta t = 2$ ).

Excel Calculation:

Data	Value
Initial Reservoir Pressure ( $P_i$ )	5000
Formation Volume Factor ( $B$ )	1.2
Change in Reservoir Volume ( $\Delta V$ )	50000
Porosity ( $\phi$ )	0.15
Time Period ( $\Delta t$ )	2

Excel Formula:

$P_{avg} = P_i - \frac{B \cdot \Delta V}{\phi \cdot \Delta t}$

$P_{avg} = 5000 - \frac{(1.2 \cdot 50000)}{(0.15 \cdot 2)}$

Result:

$P_{avg} \approx 46666.67 \, psi$

MATLAB Comparison:

For MATLAB, the calculation can be implemented using a similar formula. Below is a simple MATLAB script for the scenario:


% MATLAB Script
P_i = 5000;
B = 1.2;
Delta_V = 50000;
phi = 0.15;
Delta_t = 2;

P_avg_MATLAB = P_i - (B * Delta_V) / (phi * Delta_t);
disp(['Average Reservoir Pressure (MATLAB): ', num2str(P_avg_MATLAB), ' psi']);