Material balance is a mathematic way to express mass conservation in a reservoir and a simple key principle is “what reservoir is produced must be replaced by other mass.”
Volume Produced = Volume Replaced
Volume Produced comes from Gas Production, Oil Production, and Water Production.
Volume Replaced comes from volume expansion, water in flux and water/gas injection.
Figure 1 shows the relationship of the material balance.
Let’s take a look at each component of equation.
Gas Production (rb) = Np (Rp – Rs) Bg
Oil Production (rb) = Np Bo
Water Production (rb) = Wp Bw
Total Production = Np [Bo + (Rp – Rs) Bg ] + Wp Bw
Oil expansion consists of two parts. The first one is only oil expansion and the second one is solution gas expansion that happens when reservoir pressure is below a bubble point.
Oil expansion (rb) = N (Bo – Boi)
Solution gas expansion (rb) = N (Rsi – Rs) Bg
Total oil expansion (rb) = N [ (Bo – Boi) + (Rsi – Rs) Bg ]
Rock and Connate Water Expansion
Rock expansion (rb) = Vp ×Cf ×ΔP
Connate water expansion (rb) = Vp ×Swc× Cw ×ΔP
Total rock and connate water expansion (rb) = Vp ×(Cf + Swc× Cw)× ΔP
Pore Volume (Vp) = [ N× (1 + m) ×Boi ]÷ (1 – Swc)
Initial Gas Cap Expansion
Initial gas cap volume (rb) = m ×N ×Boi
Current gas cap volume (rb) = m ×N ×Boi ×(Bg ÷ Bgi)
Gas cap expansion (rb) = Current gas cap volume – Initial gas cap volume
Gas cap expansion (rb) = m ×N ×Boi ×[(Bg ÷ Bgi)-1]
Oil expansion term (Eo)
Eo = (Bo – Boi) + (Rsi – Rs) ×Bg
Rock and connate water expansion term (Ef,w)
Gas cap expansion term (Eg)
Eg = Boi ×[(Bg ÷ Bgi)-1]
With all expansion terms, total expansion can be mathematically expressed like this:
Total expansion (rb) = N (Eo + Efw + m Eg)
Aquifer Influx and Injection
Aquifer influx volume (rb) = We
Water injection volume (rb) = Wi×Bw
Gas injection volume (rb) = Gi×Bg
All relationships can be put in a material balance equation based on the following concept:
The equation above is simplified by using an expansion term.
The equation above can be rearranged like this:
Simplify a term like this:
F = N×Et + We
F = Net fluid production (Volume Produced – Volume Injection)
N = Oil in place
Et = Total expansion term (oil, water, gas cap and rock)
We = water influx
This simplified equation was presented by Havlena + Odeh (1963). With this equation form, graphical plots can be easily made and material balance evaluation is donemore easily and accurately.
The graphic can be drawn based on #1 form. The line should be a horizontal line and an intersection at y-axis is N (oil in place). Deviation from the horizontal line indicates adding or losing enery (Figure 2).
This is the form of a simplified material balance equation.
A slope of the curve is 1 and the intersection on the y-axis is N. Deviation from the straight line indicates extra energy in or energy out (Figure 3).
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)
Abhijit Y. Dandekar, 2013. Petroleum Reservoir Rock and Fluid Properties, Second Edition. 2 Edition. CRC Press.
L.P. Dake, 1983. Fundamentals of Reservoir Engineering, Volume 8 (Developments in Petroleum Science). New impression Edition. Elsevier Science.
Tarek Ahmed PhD PE, 2011. Advanced Reservoir Management and Engineering, Second Edition. 2 Edition. Gulf Professional Publishing.