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)
Slide — 2Gas MaterialBalance
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)
Slide — 3Gas MaterialBalance
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)
Slide — 4Gas MaterialBalance
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)
Slide — 5Gas MaterialBalance
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)
Slide — 6Gas MaterialBalance
General Gas Material Balance:
"Abnormal Pressure" Material Balance: (cf=f(p))
"Quadratic Cumulative" Approximation:
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swpinjpi
i
i
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WBWWB
RWGGGz
pzp
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)(1
615.51
))((1
G
G
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zp p
iei
i 1))((1
1
)(
)1(1
)( fwpR
pAQ
pR
pNNPfwwi
wie cc
V
V
V
VccS
Spc
Gas Material Balance Case (2/3)
2)
1(1 pp
i
i GG
GGz
pzp
PETE 613(2005A)
Slide — 7Gas MaterialBalance
General Gas Material Balance:
"Water Influx" Material Balance:
"Cubic Cumulative" Approximation: (Current Research)
ewinjpg
swpinjpi
i
i
i
ie
WBWWB
RWGGGz
pzp
pppczp
)(1
615.51
))((1
Gas Material Balance Case (3/3)
1
1
1//
G
G
giGBwBeW
zp piizp
32)()(11
GpG
GpG
GpG
zp
zp
i
i
PETE 613(2005A)
Slide — 8Gas MaterialBalance
"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)
Slide — 9Gas MaterialBalance
"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)
Slide — 10Gas MaterialBalance
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)
Slide — 11Gas MaterialBalance
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)
Slide — 12Gas 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
(End of Lecture)
PETE 613(2005A)
Slide — 13Gas MaterialBalance
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
Petroleum Engineering 613Natural Gas Engineering
Texas A&M University
PETE 613(2005A)
Slide — 14Gas MaterialBalance
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)
Slide — 15Gas MaterialBalance
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.
Executive Summary — "p/z-Gp2" Relation (2/4)
PETE 613(2005A)
Slide — 16Gas MaterialBalance
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.
Executive Summary — "p/z-Gp2" Relation (3/4)
PETE 613(2005A)
Slide — 17Gas MaterialBalance
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)
Slide — 18Gas MaterialBalance
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)
Slide — 19Gas MaterialBalance
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)
Slide — 20Gas MaterialBalance
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)
Slide — 21Gas MaterialBalance
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)
Slide — 22Gas MaterialBalance
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)
Slide — 23Gas MaterialBalance
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)
Slide — 24Gas MaterialBalance
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)
Slide — 25Gas MaterialBalance
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)
Slide — 26Gas MaterialBalance
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)
Slide — 27Gas MaterialBalance
-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)
Slide — 28Gas MaterialBalance
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.
-Gp Plotting Functions: Case 1 (3/5)
PETE 613(2005A)
Slide — 29Gas MaterialBalance
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)
Slide — 30Gas MaterialBalance
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)
Slide — 31Gas MaterialBalance
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)
Slide — 32Gas MaterialBalance
-Gp Plotting Functions: Case 3 (2/5)
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)
Slide — 33Gas MaterialBalance
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.
-Gp Plotting Functions: Case 3 (3/5)
PETE 613(2005A)
Slide — 34Gas MaterialBalance
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)
Slide — 35Gas MaterialBalance
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)
Slide — 36Gas MaterialBalance
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)
Slide — 37Gas MaterialBalance
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)
Slide — 38Gas MaterialBalance
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)
Slide — 39Gas MaterialBalance
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)
Slide — 40Gas MaterialBalance
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)
Slide — 41Gas MaterialBalance
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
Petroleum Engineering 613Natural Gas Engineering
Texas A&M University