This article will demonstrate a material balance equation in a natural water drive mechanism. A full material balance equation is shown below:
Figure 1 – Full Material Balance Equation
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.)
Figure 2 – Material Balance Equation with Assumption for a Natural Water 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).
Figure 3 – Graphic Solution for Natural Water Drive Mechanism
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
