Material balance equation can be applied for any drive mechanism and this article demonstrates how to apply the material balance equation in a solution drive mechanism. For a solution drive mechanism, there are 2 cases. The first case is when reservoir pressure is above a bubble point and the second case is when reservoir pressure is below a bubble point.

**Solution Gas above Bubble Point**

Start with a full material balance equation.

**Assumptions**

- No water production
- No water injection
- No gas injection
- No gas cap
- No water influx

**Fact**

Rs = Rsi

Cancel out parameters to match with solution gas assumptions.

The material balance will be like this:

Oil Compressibility is the equation below;

Co = (Bo – Boi) ÷ (Boi ×ΔP)

**Solution Gas below Bubble Point**

**Assumptions**

- No water production
- No water injection
- No gas injection
- No gas cap
- No water influx

Cancel out parameters to match with solution gas assumptions.

The material balance will be like this:

The equation can be simplified (Havlena + Odeh (1963)) in this form.

F = N (Eo + Efw)

Where;

F= Net fluid production

N = Oil in place

For this form, a graphical method can be used to verify oil in place (N) as shown in Figure 4.

If the plot shows a straight line, the slope is oil in place (N). However, if the slope is not a straight line, it indicates that oil in place is either too big or too small.

**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**