texas a&m university lecture 05: gas material · pdf filepete 613 (2005a) slide —3...

PETE 613(2005A)

Slide — 1Gas MaterialBalance

T.A. Blasingame, Texas A&M U.Department of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected]

Petroleum Engineering 613Natural Gas Engineering

Texas A&M University

Lecture 05:Gas Material Balance

PETE 613(2005A)


Material Balance

"Accounting" Concept of Material Balance:Require all inflows/outflows/generations.(Average) reservoir pressure profile is REQUIRED.Require rock, fluid, and rock-fluid properties (at some scale).

Oil Material Balance:Less common than gas material balance (pressure required).

Gas Material Balance:Volumetric dry gas reservoir (p/z versus Gp (straight-line)).Abnormally-pressured gas reservoirs (various techniques).Waterdrive/water influx cases (always problematic) (i.e., we

don't know the influx, so we use a model).Material Balance yields RESERVOIR VOLUME!

PETE 613(2005A)


General Concept of Material Balance...

From: Petroleum Reservoir Engineering— Amyx, Bass, and Whiting (1960).

a. Initial reservoir conditions. b. Conditions after producing Np STB of oil,and Gp SCF of gas, and Wp STB of water.

Material Balance: Key IssuesMust have accurate production measurements (oil, water, gas).Estimates of average reservoir pressure (from pressure tests).Suites of PVT data (oil, gas, water).Reservoir properties: saturations, formation compressibility, etc.

Material Balance of a Petroleum Reservoir

PETE 613(2005A)


Average Reservoir Pressure

From: Engineering Features of the Schuler Field andUnit Operation — Kaveler (SPE-AIME, 1944).

Average Reservoir Pressure: Key IssuesMust "average" pressures over volume or area (approximation).Pressure tests must be representative (pavg extrapolation valid).Can average using cumulative production (surrogate for volume).

Average Reservoir Pressure for Material Balance

PETE 613(2005A)


General Gas Material Balance:

"Dry Gas" Material Balance: (no reservoir liquids )

ewinjpg

swpinjpi

i

i

i

ie

WBWWB

RWGGGz

pzp

pppczp

)(1

615.51

))((1

p

i

i GGz

pzp 1

1

Gas Material Balance Case (1/3)

PETE 613(2005A)



"Abnormal Pressure" Material Balance: (cf=f(p))

"Quadratic Cumulative" Approximation:

ewinjpg

swpinjpi

i

i

i

ie

WBWWB

RWGGGz

pzp

pppczp

)(1

615.51

))((1

G

G

pppczp

zp p

iei

i 1))((1

1

)(

)1(1

)( fwpR

pAQ

pR

pNNPfwwi

wie cc

V

V

V

VccS

Spc


2)

1(1 pp

i

i GG

GGz

pzp

PETE 613(2005A)



"Water Influx" Material Balance:

"Cubic Cumulative" Approximation: (Current Research)

ewinjpg

swpinjpi

i

i

i

ie

WBWWB

RWGGGz

pzp

pppczp

)(1

615.51

))((1


1

1

1//

G

G

giGBwBeW

zp piizp

32)()(11

GpG

GpG

GpG

zp

zp

i

i

PETE 613(2005A)


"Dry Gas" Material Balance: Normally Pressured Reservoir ExampleVolumetric reservoir — no external energy (gas expansion only).p/z versus Gp yields unique straight-line trend.Linear extrapolation yield gas-in-place (G).

Volumetric Gas Material Balance

PETE 613(2005A)


"Dry Gas" Material Balance: Abnormally Pressured Reservoir ExampleVolumetric reservoir — no water influx or leakage.p/z versus Gp yields unique quadratic trend (from approximated MBE).Quadratic extrapolation yield gas-in-place (G).

Gas MBE Abnormally-Pressured Reservoir

PETE 613(2005A)


a. Gas Material Balance Plot: p/z vs. Gp — simulatedperformance. Note effect of aquifer permeability onfield performance.

b. Gas Material Balance Plot: p/z vs. Gp — simulatedperformance. Note effect of displacementefficiency (Ep).

Gas Material Balance: Water Drive Gas ReservoirPressure (hence p/z) is maintained during production via communication

with an unsteady-state aquifer (this study).From: Unsteady-State Performance of Water Drive Gas Reservoirs, Agarwal

(Texas A&M Ph.D., 1967).

Gas MBE "Water Influx" Case

PETE 613(2005A)


Simulated Performance: Agarwal Dissertation (1967)Recovery is a function of production rate, Ep, and kaquifer.p/z vs. Gp performance appears to be cubic (i.e., f(Gp

3)).

Concept: p/z vs. Gp — Water Influx Case

PETE 613(2005A)


T.A. Blasingame, Texas A&M U.Department of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected]



Lecture 05:Gas Material Balance

(End of Lecture)

PETE 613(2005A)


A Quadratic Cumulative Production Modelfor the Material Balance of

Abnormally-Pressured Gas Reservoirs

F.E. GonzalezM.S. Thesis (2003)

Department of Petroleum EngineeringTexas A&M University

College Station, TX 77843-3116



PETE 613(2005A)


Executive Summary — "p/z-Gp2" Relation (1/4)

The rigorous relation for the material balance of a drygas reservoir system is given by Fetkovich, et al. as:

)(61551

))((1

ewinjwpg

swpinj WBWBWB.

RWGpGGiz

ip

izip

pippeczp

Eliminating the water influx, water production/injection,and gas injection terms; defining Gp=ce(p)(pi-p) andassuming that Gp<1, then rearranging gives the follow-ing result:

2)

1(1 pp

i

i GG

GGz

pzp

PETE 613(2005A)


Simulated Dry Gas Reservoir Case — Abnormal Pressure:Volumetric, dry gas reservoir — with cf(p) (from Fetkovich).Note extrapolation to the "apparent" gas-in-place (previous approaches).Note comparison of data and the new "Quadratic Cumulative Production" model.


PETE 613(2005A)


Anderson L Reservoir Case — Abnormal Pressure:South Texas (USA) gas reservoir with abnormal pressure.Benchmark literature case.Note performance of the new "Quadratic Cumulative Production" model.


PETE 613(2005A)


Presentation Outline

Executive SummaryObjectives and RationaleRigorous technique for abnormal pressure analysis.

Development of the p/z-Gp2 model

Derivation from the rigorous material balance.Validation — Field ExamplesCase 1 — Dry gas simulation (cf(p) from Fetkovich).Case 3 — Anderson L (South Texas, USA).

Demonstration (MS Excel — Anderson L case)SummaryRecommendations for Future Work

PETE 613(2005A)


Objectives and RationaleObjectives:Develop a rigorous functional form (i.e., a model) for

the p/z vs. Gp behavior demonstrated by a typicalabnormally pressured gas reservoir.

Develop a sequence of plotting functions for theanalysis of p/z—Gp data (multiple plots).

Provide an exhaustive validation of this new modelusing field data.

Rationale: The analysis of p/z—Gp data for abnorm-ally pressured gas reservoirs has evolved from empi-rical models and idealized assumptions (e.g., cf(p)=constant). We would like to establish a rigorous ap-proach — one where any approximation is based onthe observation of some characteristic behavior, notsimply a mathematical/graphical convenience.

PETE 613(2005A)


Development of the p/z-Gp2 model

Concept:Use the rigorous material balance relation given by

Fetkovich, et al. for the case of a reservoir wherecf(p) is NOT presumed constant.

Use some observed limiting behavior to construct asemi-analytical relation for p/z—Gp behavior.

Implementation:Develop and apply a series of data plotting functions

which clearly exhibit unique behavior relative to thep/z—Gp data.

Use a "multiplot" approach which is based on thedynamic updating of the model solution on eachdata plot.

Develop a "dimensionless" type curve approach thatcan be used to validate the model and estimate G.

PETE 613(2005A)


p/z-Cumulative Model: (1/3)The rigorous relation for the material balance of a drygas reservoir system is given by Fetkovich, et al. as:

)(61551

))((1

ewinjwpg

swpinj WBWBWB.

RWGpGGiz

ip

izip

pippeczp

Eliminating the water influx, water production/injection,and gas injection terms, then rearranging gives thefollowing definition:

)])(([where1)1(

// pippecG

G

G

Gzp

pp

p

iizp

PETE 613(2005A)


Considering the condition where:

p/z-Cumulative Model: (2/3)

Then we can use a geometric series to represent the Dterm in the governing material balance. The appropriategeometric series is given by:

1 pD G

1)1(3111 2 x...xxxx/

1)1(1)1(

1

ppp

GGG

or, for our problem, we have:

2)

1(1 pp

i

i GG

GGz

pzp

Substituting this result into the material balance relation,we obtain:

PETE 613(2005A)


p/z-Cumulative Model: (3/3)

A more convenient form of the p/z-cumulative model is:

We note that these parameters presume that is con-stant. Presuming that is linear with Gp, we can derivethe following form:

i

izp

G)

1(

i

izp

G

32)()1

( pi

ip

i

ip

i

i

i

i Gzp

Gb

Gzp

bGa

Gzp

aGz

pzp

pbGawhere

Obviously, one of our objectives will be the study of thebehavior of vs. Gp (based on a prescribed value of G).

2pp

i

i GGzp

zp

PETE 613(2005A)


Simulated Dry Gas Reservoir Case — Abnormal Pressure:A linear trend of vs. Gp is reasonable and should yield an accurate model.is approximated by a constant value within the trend.A physical definition of is elusive —Gp=ce(p)(pi-p) implies that has units of

1/volume, which suggests is a scaling variable for G.

-Gp Performance (Case 1) (1/2)

a. Case 1: Simulated Performance Case — Plot ofversus Gp (requires an estimate of gas-in-place). Note the apparent linear trend of thedata. Recall that Gp=ce(pp-p).

b. Case 1: Simulated Performance Case — Plot ofp/z versus Gp. The constant and linear trendsmatch well with the data — essentially a con-firmation of both models.

PETE 613(2005A)


Anderson L Reservoir Case — Abnormal Pressure:Field data will exhibit some scatter, method is relatively tolerant of data scatter.Constant approximation is based on the "best fit" of several data functions.The linear approximation for is reasonable (should favor later data).

-Gp Performance (Case 3) (2/2)

a. Case 3: Anderson L Reservoir Case (SouthTexas, USA) — Plot of versus Gp (requires anestimate of gas-in-place). Some data scatterexists, but a linear trend is evident (recall thatGp=ce(p )(pi-p)).

b. Case 3: Anderson L Reservoir Case (SouthTexas, USA) — Plot of p/z versus Gp. Bothmodels are in strong agreement.

PETE 613(2005A)


Validation of the p/z-Gp2 model: Orientation

Methodology:All analyses are "dynamically" linked in a spread-

sheet program (MS Excel). Therefore, all analysesare consistent — should note that some functions/plots perform better than others — but the modelresults are the same for every analysis plot.

Validation: Illustrative Analysesp/z-Gp

2 plotting functions — based on the proposedmaterial balance model.

-Gp performance plots — used to calibrate analysis.Gan analysis — presumes 2-straight line trends on a

p/z-Gp plot for an abnormally pressured reservoir.pD-GpD type curve approach — use p/z-Gp

2 materialbalance model to develop type curve solution — thisapproach is most useful for data validation.

PETE 613(2005A)


p/z-Gp2 Plotting Functions: Case 1 (1/5)

a. b. c. ppp

pGdGzp

G

Gvs.)/Δ(

0

1 pp

GzpG

vs.)/Δ(1

d. e.ppp

pGdGzp

G

Gvs.

2)/Δ(

0

1 ppp

pGdGzp

G

Gzp vs.)/Δ(

0

1)/Δ( f. pp

p

ppGdGzp

G

Gzp

Gvs.)/Δ(

0

1)/Δ(

1

pGzp

izip

zp vs.)/Δ(

PETE 613(2005A)


-Gp Plotting Functions: Case 1 (2/5)

a. Case 1: Simulated Performance Case — Plot ofce(p)(pi-p) versus Gp (requires estimate of G).

b. Case 1: Simulated Performance Case — Plot of1/ce(p)(pi-p) versus Gp (requires estimate of G).

c. Case 1: Simulated Performance Case — Plot of versus Gp (requires estimate of G).

d. Case 1: Simulated Performance Case — Plot of versus Gp/G (requires estimate of G).

PETE 613(2005A)


Simulated Dry Gas Reservoir Case — Abnormal Pressure:Summary p/z—Gp plot for =constant and =linear cases.Good comparison of trends, =linear trend appears slightly conservative as it

emerges from data trend — but both solutions appear to yield same G estimate.


PETE 613(2005A)


Gan-Blasingame Analysis (2001): Case 1 (4/5)

a. Case 1: Simulated Performance Case — Gan Plot 1ce(p)(pi-p) versus (p/z)/(pi/zi) (requires est. of G).

b. Case 1: Simulated Performance Case — Gan Plot 2(p/z)/(pi /zi ) versus (Gp/G) (requires est. of G).

c. Case 1: Simulated Performance Case — Gan Plot 3(p/z) versus Gp (results plot).

Gan-Blasingame Analysis:Approach considers the "match"

of the ce(p)(pi-p) — (p/z)/(pi/zi)data and "type curves."

Assumes that both abnormaland normal pressure p/z trendsexist.

Straight-line extrapolation of the"normal" p/z trend used for G.

PETE 613(2005A)


pD-GpD Type Curve Approach: Case 1 (5/5)

a. pD-GpD Type curve solution based on the p/z-Gp2

model. pD= [(pi/zi)-(p/z)]/(pi/zi) and GpD=Gp/G —both pD and pDi functions are plotted.

b. Case 1: Simulated Performance Case — Typecurve analysis of (p/z)-Gp data, this case is"force matched" to the same results as all of theother plotting functions.

PETE 613(2005A)


p/z-Gp2 Plotting Fcns: Case 3 (Anderson L) (1/5)

a. b. c. ppp

pGdGzp

G

Gvs.)/Δ(

0

1 pp

GzpG

vs.)/Δ(1

d. e.ppp

pGdGzp

G

Gvs.

2)/Δ(

0

1 ppp

pGdGzp

G

Gzp vs.)/Δ(

0

1)/Δ( f. pp

p

ppGdGzp

G

Gzp

Gvs.)/Δ(

0

1)/Δ(

1

pGzp

izip

zp vs.)/Δ(

PETE 613(2005A)



a. Case 3: Anderson L (South Texas) — Plot ofce(p)(pi-p) versus Gp (requires estimate of G).

b. Case 3: Anderson L (South Texas) — Plot of1/ce(p)(pi-p) versus Gp (requires estimate of G).

c. Case 3: Anderson L (South Texas) — Plot of versus Gp (requires estimate of G).

d. Case 3: Anderson L (South Texas) — Plot of versus Gp/G (requires estimate of G).

PETE 613(2005A)


Case 3 — Anderson L Reservoir (South Texas (USA))Summary p/z—Gp plot for =constant and =linear cases.Good comparison of trends, =constant and =linear cases in good agreement.Data trend is very consistent.


PETE 613(2005A)


Gan-Blasingame Analysis (2001): Case 3 (4/5)

a. Case 3: Anderson L Reservoir — Gan Plot 1 ce(p)(pi-p)versus (p/z)/(pi/zi) (requires est. of G).

b. Case 3: Anderson L Reservoir — Gan Plot 2 (p/z)/(pi /zi )versus (Gp/G) (requires est. of G).

c. Case 3: Anderson L Reservoir — Gan Plot 3 (p/z)versus Gp (results plot).

Gan-Blasingame Analysis:We note an excellent "match" of

the ce(p)(pi-p) — (p/z)/(pi/zi) dataand the "type curves."

Both the abnormal and normalpressure p/z trends appear ac-curate and consistent.

Straight-line extrapolation of the"normal" p/z trend used for G.

PETE 613(2005A)


Case 3 — Anderson L Reservoir (South Texas (USA))pD-GpD type curve solution matched using field data.Note the "tail" in the pD trend for small values of GpD (common field data event)."Force matched" to the same results as each of the other plotting functions.

pD-GpD Type Curve Approach: Case 3 (5/5)

PETE 613(2005A)


Example Analysis Using MS Excel: Case 3

Case 3 — Anderson L (South Texas (USA))Literature standard case.A 3-well reservoir, delimited by faults.Good quality data.Evidence of overpressure from static pressure tests.

Analysis: (Implemented using MS Excel)p/z-Gp

2 plotting functions.-Gp performance plots.Gan analysis (2-straight line trends on a p/z-Gp plot).pD-GpD type curve approach.

PETE 613(2005A)


Summary: (1/3)

Developed a new p/z-Gp2 material balance model for

the analysis of abnormally pressured gas reservoirs:

The -function is presumed (based on graphicalcomparisons) to be either constant, or approximatelylinear with Gp. For the =constant case, we have:

where:

2)

1(1 pp

i

i GG

GGz

pzp

))((1

pippecGp

2pp

i

i GGzp

zp

i

izp

G)

1(

i

izp

G

PETE 613(2005A)


Summary: (2/3)

Base relation: p/z-Gp2 form of the gas material balance

a. Plotting Function 1:(quadratic)

b. Plotting Function 2:(linear)

c. Plotting Function 3:(quadratic)

ppp

pGdGzp

G

Gvs.)/Δ(

0

1

pp

GzpG

vs.)/Δ(1

pGzp

izip

zp vs.)/Δ(

pp

p

pGdGzp

G

Gvs.

2)/Δ(

0

1

ppp

pGdGzp

G

Gzp vs.)/Δ(

0

1)/Δ(

ppp

ppGdGzp

G

Gzp

Gvs.)/Δ(

0

1)/Δ(

1

2pp

i

i GGzp

zp

i

izp

G)

1(

i

izp

G

d. Plotting Function 4 :(linear)

e. Plotting Function 5 :(quadratic)

f. Plotting Function 6:(linear)

PETE 613(2005A)


Summary: (3/3)

The plotting functions developed in this work havebeen validated as tools for the analysis reservoirperformance data from abnormally pressured gasreservoirs. Although the straight-line functions (PF2,PF4, and PF6) could be used independently, but werecommend a combined/simultaneous analysis.The -Gp plots are useful for checking data con-

sistency and for guiding the selection of the -value.These plots represent a vivid and dynamic visualbalance of all of the other analyses.The Gan analysis sequence is also useful for orient-

ing the overall analysis — particularly the ce(p)(pi-p)versus (p/z)/(pi/zi) plot.The pD-GpD type curve is useful for orientation —

particularly for estimating the or (D ) value.

PETE 613(2005A)


Recommendations for Future Work:

Consider the extension of this methodology forcases of external drive energy (e.g., water influx, gasinjection, etc.).Continue the validation of this approach by applying

the methodology to additional field cases.Implementation into a stand alone software.

PETE 613(2005A)


A Quadratic Cumulative Production Modelfor the Material Balance of

Abnormally-Pressured Gas Reservoirs(End of Presentation)

F.E. GonzalezM.S. Thesis (2003)

Department of Petroleum EngineeringTexas A&M University

College Station, TX 77843-3116



texas a&m university lecture 05: gas material · pdf filepete 613 (2005a) slide —3...

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