I.3
Gas Reservoirs with Water Influx and Water and Rock Compressibilities
 C + C w S wi 
G (B g - B gi ) + GB gi  f
 ∆ pt + W e = G p B g + W p B w
 1 - S wi 
Let:
Cf
Cˆ e =
+ C w S wi
1 - S wi
Dividing all through by Bg and rearranging yields:
 B
 W - W p Bw
G 1 - gi (1 - Cˆ e ∆ pt ) + e
= Gp
Bg
 Bg

Substituting for Bg = C z/p yields:


p/z
(1 - Cˆ e ∆ pt ) + W e - W p Bw = G p
G 1 Bg
 pi / z i

Rearranging in a straight line form yields:
p
(1 - Cˆ e ∆ pt )= pi - pi
z
zi zi G


 G p - W e W p Bw 


Bg


Which suggests plotting (Gp - (We - Wp Bw)/Bg) on the x-axis versus p/z(1-Ce∆pt) on the
y-axis and drawing the best fit line through the set of points. The slope of the best fit line
would be -pi/(zi G) and the y-intercept would be pi/zi.
1
EPS-441: Petroleum Development Geology
Material Balance Calculations for a Gas Reservoir with Water Influx
and Water and Rock Compressibilities: p/z plot
Semester:
Homework #:
Name:
SS#:
Given the following reservoir and rock properties:
Water compressibility, Cw = 3 x 10-6
Formation compressibility, Cf = 4 x 10-6
Areal extent, A = 8870 acres
Formation thickness, h = 32.5 ft
Porosity, φ = 30.8 %
Initial water saturation, Swi = 42.5 %
Gas deviation factor at standard conditions, zb = 1.0
Performance History
Time
years
Gp
MMM SCF
p
psia
z
Bg
bbl/SCF
0
2
4
6
8
10
12
14
16
18
20
0
2.305
20.257
49.719
80.134
105.930
135.350
157.110
178.300
192.089
205.744
2333
2321
2203
2028
1854
1711
1531
1418
1306
1227
1153
0.882
0.883
0.884
0.888
0.894
0.899
0.907
0.912
0.921
0.922
0.928
0.001,172
0.001,180
0.001,244
0.001,358
0.001,496
0.001,630
0.001,820
0.001,995
0.002,187
0.002,330
0.002,495
1)
Estimate the initial gas in place by the MB calculation with water
water and rock compressibilities
2)
Discuss the results
2
influx and
Solution:
A) Prepare the following table:
p/z
We, bbl
GpBg - G(Bg-Bgi)
Gp - We/Bg
p/z(1-Ce∆pt)
2645.12
2628.54
2492.08
2283.78
2073.83
1903.23
1687.98
1554.82
1418.02
1330.80
1242.46
0.00E+00
1.62E+04
8.66E+05
4.66E+06
1.04E+07
1.79E+07
2.73E+07
3.53E+07
4.69E+07
5.62E+07
6.62E+07
0.00E+00
2.29E+09
1.96E+10
4.63E+10
7.32E+10
9.50E+10
1.20E+11
1.39E+11
1.57E+11
1.68E+11
1.79E+11
2645.12
2628.25
2489.11
2277.39
2064.71
1892.37
1675.56
1541.77
1404.66
1317.30
1229.01
Plot (Gp - We/Bg) on the x-axis versus p/z(1-Ce∆pt) on the y-axis and draw the best-fit
line through the set of points, see Fig. 5. The best-fit equation is: p/z = -7.92292x109
(Gp-We/Bg) + 2643.94; i.e Gp-We/Bg = (2643.94 - p/z)/7.92292. Thus setting p/z = 0 in
the best-fit equation yields the value of G to be 333.7 MMM SCF.
D) Discussion of results:
The amount of water influx was calculated on the assumption that the volumetric
calculation of the gas in place is valid. However, a more elaborate technique for water
influx calculation should be used. Such techniques will be covered in the "Water Influx"
chapter.
3
Fig. 5: p/z(1-Ce∆pt) plot versus Gp - We/Bg
4
I.4
Abnormally High-Pressure Gas Reservoirs
In abnormally high-pressure gas reservoirs, Cf is a strong function of pressure.
Thus we set:
n
n
j=0
j=0
(
Cˆ e ∆ pt = ∑ Cˆ ej ∆ p j = ∑ Cˆ ej p j+1 - p j
)
Therefore the equation is written as follows:
n
pi

p
 1 - ∑ Cˆ ej ∆ p j  =

z  j=0

zi
-
pi 
G p
zi G 
Which is in the form:
y = b + mx
Where:
ppi  Wn - W p B w 
bxy =
=  Gp1-- ∑e Cˆ ej ∆
p j 


zzi  j=0 B g
pi
m= zi G
5
-
We
-W
Bg
p
B w 



I.5 Abnormally High-Pressure Gas Reservoirs with Dissolved Gas in Water
(Fetkovitch Method)
For high-pressure gas reservoirs with dissolved gas in water, Fetkovitch et al.
expressed the material balance equation as follows:



p
(1 - C e ∆ pt )= pi - pi / zi  (G p - G I +W p Rsw ) -  W e +W I Bw - W p Bw 
z
G 
zi
Bg


Where:
Ce =
C f + C tw S wi + M (C f + C tw )
1 - S wi
Cf =
1  V pi - V p  1  φ i - φ 

= 

V pi  pi - p  φ i  pi - p 
C tw =
1  Btw - Btwi 


Btwi  pi - p 
Btw = B w + (R swi - R sw ) B g
"M" is defined as the associated water volume ratio. The associated water and
pore volumes external to the net pay include Non-Net Pay (NNP) such as interbedded
shales and dirty sands plus external water volume found in AQuifers. This volume is
expressed as a ratio relative to the pore volume of the net-pay reservoir; i.e.
M = M NNP + M AQ
M NNP =
V P NNP h NNP hGROSS - h RES
=
=
h RES
V P RES h RES
M AQ =
V P AQ
V P RES
≈ (r e2 )
6
I.6 Abnormally High-Pressure Gas Reservoirs with Dissolved Gas in Water
(Kazemi's Method)
7
I.7 Graphical Technique for the Abnormally High-Pressure Gas Reservoirs (A
Non-p/z Form of the Gas Material Balance)
8
I.8 Wet Gas Reservoirs
In wet gas reservoirs, the stock tank barrels of the Liquid condensate produced
must be accounted for in the cumulative gas production. This is done as follows:
(G p )eff = G p + (G Lc K Lc )
Where:
(Gp)eff = Effective cumulative gas produced, SCF
Gp = Cumulative gas produced, SCF
GLc = Cumulative liquid condensate produced, STB
KLc = Liquid condensate conversion factor, SCF/STB, which is given by:
K Lc = 132,790
SG Lc
MW Lc
SGLc = Specific gravity of the liquid condensate which is given by:
SG Lc =
141.5
131.5 + ° API
MWLc = Molecular weight of the liquid condensate which is given by:
MW Lc =
5954
° API - 8.8
Therefore the effective gas production would be given by:
° API - 8.8 
 G Lc
 131.5 + ° API 
(G p )eff = G p + 3155.8255 
9