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.
Figure 1 – 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.
Figure 2 – Cancel out some parameters
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.
Figure 3 – Cancel some parameters
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.
Figure 4 – Graphical plot for a solution gas drive
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