This document discusses material balance equations used to relate fluid movement and production from a reservoir to the amount of fluids contained. It provides an equation that accounts for: 1) remaining oil, 2) free gas remaining, 3) change in gas cap volume, and 4) net water influx. The equation is based on conservation of mass as production causes pore volume contraction and fluid expansion/contraction. Applications of the material balance equation include calculating stock tank oil originally in place and gas originally in place.

1. Shell Special Intensive Training Programme
8 BASIC MATERIAL BALANCE EQUATIONS
Material balance is a technique that relates the movement into and removal from the
reservoir of fluids to the amount of fluids contained in the reservoir The method
relates fluid production to reservoir pressure and cumulative fluid produced It is
based on the principle of conservation of mass.
Original Volume occupied by fluids = Present volume occupied + Contraction in
pore space
For a given production from pressure pi to p,
Original oil m place (N. Boi ) = Remaining oil(N-Np)Bo
+
Free Gas Remaining[ NRsi –(N-Np)Rs - Gps ]Bg
+
Change in gas cap volume[(G-Gpc )Bg – GBgi ]
+
Net water influx [We – Wp ]Bw
N.Boi = (N-Np )Bo + [NRsi -(N-Np)Rs – Gps]Bg + [(G-Gpc )Bg – GBgi ] + [We – Wp] Bw
N =Stock tank oil originally in place, barrels
Np= Stock tank oil produced, stb
Rsi = Gas in solution at original pressure, SCF/stb
Boi = Formation volume factor for oil at original pressure
Rs =Gas in solution at stock tank conditions, SCF/stb
G =Stock tank gas originally in place
Gp = Gas produced
Bg = Gas formation volume factor at stock tank conditions
Page 1 of 3 ©Univation

2. Shell Special Intensive Training Programme
Bgi = Gas Formation volume factor at original reservoir pressure
We = Cumulative gross water influx into reservoir
Wp = Cumulative water produced, barrels
The above equation has been based on the fact that if there is fluid production , the
following changes will take place:
1. The pore volume will became smaller
2. Existing connate water will expand
3. Oil if under-saturated will expand
4. If reservoir pressure is less or equal to bubble point pressure, oil will shrink as
gas comes out of solution
5. Free gas will expand if present
6. Water may flow into reservoir from aquifer
From the above, if reservoir pressure is above bubble point, Gp = Np.Rs
G=0
If no water influx, We = 0 and WP = 0 if connate water is immobile
Alternatively,
Total Reservoir size = Original oil zone size + Original gas zone size
= NBoi +mNBoi
m = ratio of gas cap size to oil zone size.
Remaining Liquid = Remaining oil zone size + Net water influx
=(N-NP)Bo + (We –Wp)Bw
Free Gas remaining = Total reservoir space - Remaining liquid volume
=(NBoi + mNBoi) - [(N-Np)Bo +(We – Wp )Bw ]]
SCF of Free Gas remaining= (NBoi + mNBoi) - [(N-Np)Bo +(We – Wp )Bw ]]/Bg
Page 2 of 3 ©Univation

3. Shell Special Intensive Training Programme
Remaining gas in solution = (N-Np)Rs .
Bt = Boi = Bo + (Rsi – Rs )Bg
8.1 Applications of Material Balance Equation
1. STOIIP - Stock Tank Oil originally in Place
STOIIP=N=
oi
wi
B
S
V
)1( −
φ
V = Reservoir volume = Ah
In field units
STOIIP =
oi
wi
B
SAh )1(7758 −φ
A= Areal extent of reservoir, acres
h = pay thickness, ft
7758= conversion factor, bbls per acre-ft
Sw = connate water saturation
Ultimate Recovery= STOIIP x RF
RF = Recovery Factor
2. Gas Originally in Place
GOIIP= 7758Ahφ (1-Swi )
8.2 Gas Reservoir Material Balance
g
g
gi B
G
V
B
G
+=
G = Reservoir gas space, barrels
Bgi = Gas volume factor, bbIs /SCF at initial reservoir conditions
Bs = Gas volume factor at standard conditions
Vg = Cumulative gas produced
Page 3 of 3 ©Univation