A Semianalytical p/z Technique for the Analysis of
Abnormally Pressured Gas Reservoirs
Ronald Gunawan Gan,VICO Indonesia
andT. A. Blasingame,
Texas A&M University
SPE 71514
ObjectiveTo present a new technique that can beused to :
Calculate gas-in-place for an abnor-mally pressured gas reservoir using only average reservoir pressure and cumulative production data.
Calculate pore volume compressibi-lity as a function of reservoir pressure.
Presentation Outline
Introduction
Overview of Existing Methods
New Method
Field Examples
Conclusions
Introduction
p/z schematic for a normally-pressured volumetric gas reservoir
G
p/z
Gp
G
G
z
p
z
p p
i
i 1
Introduction p/z schematic for an abnormally-pressured gas reservoir
p/z
Gp G
G
G
z
ppp
z
p p
i
ii 1)(1
Gapp
Introduction
Reasons for the non-linear p/z behavior:
Rock and water compressibility effects — "rock collapse theory" (Hawkins, 1969)
Shale water influx (Bourgoyne, 1989)
Existing Methods
Methods based on presumed knowledge of system compressibility:
Hammerlindl (Constant Compressibility), 1971
Ramagost & Farshad (Constant Comp.), 1981
Yale et al. (Variable Compressibility), 1993
G
G
z
p
S
ccSp
z
p p
i
i
w
fww 1)1(
)(1
Methods based on presumed knowledge of system compressibility (continued)
Fetkovich, Reese, and Whitson - 1991
- Derived General Material Balance Eq.
- Define cumulative effective compressibility,
wi
ftwftwwie S
pcpcMpcpcSpc
1
)]()([)()()(
- ce represents the cumulative change in hydrocarbon PV caused by compressi- bility effects (and water influx).
Methods which do not require a prior knowledge of system compressibility
Roach - 1981 - very sensitive to initial pressure.- method sometimes doesn’t exhibit a negative intercept (which is not possible).
Bernard - 1985 - using Least Squares approach. - very sensitive to data scatter.
Ambastha - 1991: Type Curve Approach - non-uniqueness problems.
New Method
Develops 2 new plotting functions:
1. )/)/(/(versus)( iiie zpzpppc
2. /GGzpzp pii versus)/)/(/(
Requires production data only (p and Gp)
Satisfies both "rock collapse" and "shale water influx" theories
New Method Uses general material balance equation (proposed by Fetkovich, et al.)
G
G
z
pppc
z
p p
i
iie 1)(1
Rearranging, we obtain
G
G
zp
zpppc pii
ie 1/
/1)(
New Method
Calculate the ce(pi-p) function for each p/z versus Gp trend
ce(pi-p) = ???
ce(pi-p) = ???
Gp
p/z
G Gapp
New Method For early time data (1st straight line) :
G
G
G
Gppc app
zp
zp
app
zp
zpie
i
i
i
i
)/(
1
)/(
11)(
For late time data (2nd straight line) :
G
Gppc pA
zpzpie
ii
A1
11)(
)/()/(
where: A is the inflection point
New Method
Plot of log ce(pi-p) versus (p/z)/(pi/zi):
(p/z)/(pi/zi)
h
l og
ce(
pi-p
) G/Gapp=0.7
G/Gapp=0.6
G/Gapp=0.8
inflection point
Plot of log ce(pi-p) versus (p/z)/(pi/zi) :
(p/z)/(pi/zi)
h
l og
ce(
pi-p
)
inflection point
New Method
New Method
/GGzpzp pii versus)/)/(/(
Gp/G
h
(p/z
)/(p
i/zi)
0 1
1
Infl. Point: GpA/G, (p/z)A /( pi /zi )
G
G
G
G1
/zp
p/z p
appii
G
G
GGzp
zp
/zp
p/z p
pAii
A
ii )/1)(/(
)/(
New Method
/GGzpzp pii versus)/)/(/(
Gp/G
h
(p/z
)/(p
i/zi)
0 1
1
G/Gapp=1
G/Gapp= 0.8
G/Gapp=0.6
Inflection point
New Method
/GGzpzp pii versus)/)/(/(
Gp/G
h
(p/z
)/(p
i/zi)
0 1
1Inflection point
G/Gapp=0.8
New Method
/GGzpzp pii versus)/)/(/(
Dynamic Type Curve Matching.
Automatic Matching using SOLVER m(Excel function for non-linear regression).
New Method
Data required for analysis: Fluid property data
Initial Reservoir p and T
p and Gp data
New Method
Computer program: Visual Basic Application in MS Excel
Easy to use - especially for analysis
Only requires MS Excel
Data Analysis Sheet
Example 1: G is too low
Example 1: G is too high
Example 1: Correct G
Example 2: Long transition period
Example 3: Early time data
Example 4: Synthetic Dry Gas Case
Example 4: Backcalculated cf
Procedure to calculate cf vs. p from production data:
1. Get )( pce from type curve matching
3. Calculate cf (p):
jfnif pcppcn
jj
1)(
wi
ftwftwwie S
pcpcMpcpcSpc
1
)]()([)()()(
2. Use the following equation to calculate )( pc f :
Example 4: Backcalculated cf
Conclusions We have developed a straightforward approach for analyzing p/z versus Gp
behavior for abnormally pressured gas reservoirs — the approach considers that two straight-lines must be ob- served on the p/z plot.
The proposed method determines gas-in-place without using system compressibility data. Only p, Gp, and fluid property data are required.
Conclusions (continued)
Our approach of using ce(pi-p) versus (p/z)/(pi /zi) and (p/z)/(pi /zi) versus Gp/G as dynamic type curve matching func- tions has been shown to work extreme- ly well. Using our new method, it is possible to calculate rock compressibility as a func- tion of pressure from p and Gp data
Conclusions (continued)
The "dynamic type curve matching technique" used for calculating gas-in-place from production data is more representative (and more stable) than the non-linear optimization method provided by SOLVER.
A Semianalytical p/z Technique for the Analysis of
Abnormally Pressured Gas Reservoirs
Ronald Gunawan Gan,VICO Indonesia
andT. A. Blasingame,
Texas A&M University
SPE 71514
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