The gas material balance equation is a way of estimating how much gas is originally in a reservoir and how much is left after some production. It is based on the principle that the mass or moles of gas in the reservoir does not change, only the volume and pressure change.
The equation relates the initial gas volume, pressure, and deviation factor (a correction for non-ideal gas behavior) to the current gas volume, pressure, and deviation factor, as well as the cumulative gas and water production and influx. The equation can be plotted as a straight line on a graph of p/z (pressure divided by deviation factor) versus cumulative gas production. The slope and intercept of this line can be used to calculate the initial gas volume and pressure.
The gas material balance equation can be applied to different types of gas reservoirs, such as volumetric, waterdrive, or retrograde-condensate reservoirs, with some modifications. For example, for waterdrive reservoirs, the water influx term must be included, and for retrograde-condensate reservoirs, the liquid dropout term must be considered.
Basic Theory:
The gas material balance equation is given by:
![\[OGIP = \frac{7758 \cdot V_a \cdot (P_z - P_{i})}{Z \cdot T_{sc} \cdot (P_{sc} + P_i)}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-19c1b109cdc8c6a03975608a64b3d1c4_l3.svg "Rendered by QuickLaTeX.com")
Where:
- OGIP is the Original Gas in Place,
- 7758 is a constant for unit conversion,
- V_a is the gas reservoir volume at initial conditions (reservoir cubic feet),
- P_z is the average gas reservoir pressure at the current state (psia),
- P_i is the initial gas reservoir pressure (psia),
- Z is the gas compressibility factor,
- T_{sc} is the temperature at standard conditions (Rankine),
- P_{sc} is the pressure at standard conditions (psia).
Procedures:
- Input reservoir data into an Excel table, including initial pressure (
), current pressure (
), temperature, and gas compressibility factor (
). - Calculate the reservoir volume (
) at initial conditions. - Use the gas material balance equation to determine the original gas in place (
).
Example:
Let’s consider a gas reservoir with the following data:
| Parameter | Value |
|---|---|
| Initial Pressure (Pi) | 3500 |
| Current Pressure (Pz) | 2800 |
| Temperature (T) | 180 |
| Gas Compressibility (Z) | 0.85 |
Excel Formulas:
- Calculate the reservoir volume ():
![\[V_a = \frac{43560 \cdot 7758}{Z \cdot T_{sc}} \times \left(\frac{P_z + P_i}{2}\right) \times \ln\left(\frac{P_i}{P_z}\right)\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-880cc21ce417cf3edcb8649b1482eb8c_l3.svg "Rendered by QuickLaTeX.com")
- Use the gas material balance equation to find :
![\[OGIP = \frac{7758 \cdot V_a \cdot (P_z - P_i)}{Z \cdot T_{sc} \cdot (P_{sc} + P_i)}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-a254e94057256fd2dc6a75c0e13ad0f9_l3.svg "Rendered by QuickLaTeX.com")
Results:
![\[V_a \approx 1.098 \times 10^7 \, \text{reservoir cubic feet}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-e9004b92ccb6fb0fd55af3ba34830800_l3.svg "Rendered by QuickLaTeX.com")
![\[OGIP \approx 1.536 \times 10^9 \, \text{cubic feet}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-c4b9869dfac7a509a2972d6c0dffddfd_l3.svg "Rendered by QuickLaTeX.com")
