This article will demonstrate a material balance equation in a natural water drive mechanism. A full material balance equation is shown below:

**Assumptions**

- Reservoir pressure above the bubble point (Pb). Above a bubble point, Rs = Rsi.
- No water injection
- No gas injection
- No gas cap
- Neglect formation and connate water compressibility (Cf and Cw have little effect for a gas cap drive mechanism.)

The material balance shown in Figure 2 can be simplified like this:

This can be described in a simple equation (Havlena + Odeh (1963)) like this:

# F = N Eo + We

# F/Eo = N + We/Eo

Where;

F = Net fluid production

N = Oil in place

Eo = oil expansion term

We = water influx

The plot is constructed between F/Eo and (We/Eo).

The interception point on Y-Axis is oil in place (N). If the plot is not a straight line, it indicates that the size of the aquifer is either too small or too big (Figure 3).

**Nomenclatures**

N = oil initially in place (STOIIP) in reservoir (stb)

Np = cumulative oil production (stb)

Boi = oil volume factor at initial reservoir pressure (rb/stb)

Bo = oil volume factor at current reservoir pressure (rb/stb)

Rsi = solution GOR at initial reservoir pressure (scf/stb)

Rs = solution GOR at current reservoir pressure (scf/stb)

Rp = cumulative produced gas oil ratio (scf/stb)

G = gas volume initially in place (GIIP) in reservoir (scf)

m = ratio of initial gas cap volume to initial oil volume (rb/rb)

Bgi = gas volume factor at initial reservoir pressure (rb/scf)

Bg = gas volume factor at current reservoir pressure (rb/scf)

Swc = connate water saturation (fraction or %)

Cw = water compressibility (1/psi)

Cf = formation (rock) compressibility (1/psi)

Wp = cumulative water production (stb)

We= cumulative water influx from aquifer (rb)

Bw = water volume factor at initial reservoir pressure (rb/stb)

Wi = cumulative water injection (stb)

Gi = cumulative gas injection (scf)

Gp = cumulative gas production (scf)

Eg = gas expansion term (rb/stb)

Eo = oil expansion term (rb/stb)

Efw = formation and connate water expansion term (rb/stb)

**References**