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