Gas Reservoir Material Balance

Overview

Gas reservoir material balance is one of the most straightforward and reliable methods for estimating original gas in place (OGIP). The method exploits the fact that gas compressibility factor $z$ varies predictably with pressure, creating a linear relationship between $p/z$ and cumulative gas production.

The p/z Method

Derivation

For a volumetric gas reservoir (no water influx, no water production):

$G B_{gi} = (G - G_p) B_g$

Where $B_g = pz_i T / p_i z T_{sc}$ (simplified for constant temperature), this becomes:

$\frac{p}{z} = \frac{p_i}{z_i}\left(1 - \frac{G_p}{G}\right)$

Graphical Interpretation

Plot $p/z$ (y-axis) vs. $G_p$ (x-axis):

    ▲ p/z
    │
pi/zi ●
    │  ╲
    │    ╲
    │      ╲  Straight line
    │        ╲
    │          ╲
    │            ╲
    │              ╲
    │                ╲
    │                  ● p_ab/z_ab (abandonment)
    │                    ╲
    └──────────────────────●──────────▶ Gp
                           G (OGIP)

Y-intercept = $p_i/z_i$ (initial conditions, known)
Slope = $-p_i/(z_i \cdot G)$
X-intercept = $G$ (OGIP)
Recovery at abandonment = $G_p$ where $p/z = p_{ab}/z_{ab}$

Recovery Factor

$RF = 1 - \frac{p_{ab}/z_{ab}}{p_i/z_i}$

For typical gas reservoirs:

Abandonment at $p_{ab} \approx$ 500-1000 psia
Recovery factors: 70-90%

Modified p/z for Geopressured Reservoirs

The Problem

In abnormally pressured (geopressured) reservoirs, standard $p/z$ plots show two distinct slopes:

Early (above normal gradient): Steep slope — formation compaction and water expansion contribute significantly
Late (at normal gradient): Flatter slope — converges to volumetric behavior

Using only the early steep slope leads to overestimation of OGIP.

Correction

The modified material balance incorporates water and formation compressibility:

$\frac{p}{z^*} = \frac{p_i}{z_i^*}\left(1 - \frac{G_p}{G}\right)$

Where:

$z^* = z \cdot \frac{1}{1 - c_{wf}\Delta p}$

$c_{wf} = \frac{S_{wi} c_w + c_f}{1 - S_{wi}}$

Parameter	Symbol	Description
$c_w$	Water compressibility	~3 × 10⁻⁶ psi⁻¹
$c_f$	Formation compressibility	3-30 × 10⁻⁶ psi⁻¹
$S_{wi}$	Initial water saturation	Fraction
$\Delta p$	Pressure decline = $p_i - p$	psi

When to Use Modified p/z

Condition	Use Standard p/z?	Use Modified p/z?
Normal pressure gradient	Yes	Optional
Geopressured ( $> 0.6$ psi/ft)	No	Yes
High $c_f$ (unconsolidated)	No	Yes
Large pressure decline	Caution	Recommended

OGIP Estimation Methods

Single-Point Estimate

From any data point $(p/z, G_p)$ :

$G = \frac{G_p}{1 - (p/z)/(p_i/z_i)}$

Caution: Single-point estimates are unreliable early in production when the pressure change is small relative to measurement error.

Regression

Fit a straight line through all $(G_p, p/z)$ data points using least-squares regression. The x-intercept of the best-fit line gives $G$ .

Pressure and Production Prediction

Predict Pressure at Future Production

Given OGIP = $G$ and future cumulative production $G_p$ :

$p = z \cdot \frac{p_i}{z_i}\left(1 - \frac{G_p}{G}\right)$

Since $z$ depends on $p$ , this requires iteration:

Assume $p$ , calculate $z$
Calculate $p$ from equation
Repeat until convergence

Predict Production at Future Pressure

$G_p = G\left(1 - \frac{p/z}{p_i/z_i}\right)$

Limitations

Limitation	Description	Mitigation
Requires BDF	Must be in boundary-dominated flow	Verify with rate-transient analysis
No water drive assumed	Water influx bends p/z upward	Use Cole plot to diagnose
Pressure accuracy critical	Small errors amplified early	Wait for significant pressure decline
Assumes constant pore volume	Invalid if compaction is significant	Use modified p/z
Average pressure needed	Not flowing pressure	Use buildup or shut-in data

Diagnostic: Cole Plot

To detect water influx in gas reservoirs, plot $p/z$ vs. $G_p$ :

Straight line = volumetric (no water drive)
Concave upward = water influx present — p/z is higher than expected because water supports pressure

MBE Overview — Material balance concepts and workflow
Oil Reservoirs — Havlena-Odeh for oil reservoirs
Aquifer Models — When gas reservoirs have water drive
PVT Gas Properties — Z-factor correlations needed for p/z

References

Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Elsevier, Chapter 3.
Craft, B.C. and Hawkins, M.F. (1991). Applied Petroleum Reservoir Engineering, 2nd Edition. Prentice Hall.
Ramagost, B.P. and Farshad, F.F. (1981). "P/Z Abnormally Pressured Gas Reservoirs." SPE-10125, SPE Annual Technical Conference and Exhibition, San Antonio, Texas.
Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Gulf Professional Publishing.
Cole, F.W. (1969). Reservoir Engineering Manual. Gulf Publishing Company.