A Semianalytical p / z Technique for the Analysis of Abnormally Pressured Gas Reservoirs

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

GG

zp

zp p

i

i 1

Introduction p/z schematic for an abnormally-pressured gas reservoir

p/z

Gp G

GG

zppp

zp 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

GG

zp

SccSp

zp 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.)

GG

zpppc

zp p

i

iie 1)(1

Rearranging, we obtain

GG

zpzpppc 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) :

GG

GG

ppc app

zp

zp

app

zp

zpie

i

i

i

i

)/(1

)/(11)(

For late time data (2nd straight line) :

GG

ppc pA

zpzpie

iiA

111)()/(

)/(

where: A is the inflection point

New Method

Plot of log ce(pi-p) versus (p/z)/(pi/zi):

(p/z)/(pi/zi)

h

log

c e(p

i-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

log

c e(p

i-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 )

GG

GG1

/zpp/z p

appii

GG

GGzpzp

/zpp/z p

pAii

A

ii )/1)(/()/(

New Method /GGzpzp pii versus)/)/(/(

Gp/G

h

(p/z

)/(p i

/zi)

0 1

1

G/Gapp=1G/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