well performance analysis — low to ultra-low permeability

Presentation at SPE Mid-Continent Section02 April 2009 — Tulsa, OK

Well Performance Analysis — Low to Ultra-Low Permeability ReservoirsT.A. Blasingame and D. Ilk (02 April 2009) Sl

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Presentation at SPE Mid-Continent Section 02 April 2009 — Tulsa, OK

Dilhan ILK Tom BLASINGAMEPetroleum Engineering Petroleum EngineeringTexas A&M University Texas A&M UniversityCollege Station, TX 77843-3116 (USA) College Station, TX 77843-3116 (USA)+1.979.571.8158 [email protected] [email protected]

Well Performance Analysis —Low to Ultra-Low Permeability

Reservoirs



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Topics:●Introduction/Biographies●Abstract●Orientation — Production Data Analysis and Diagnostics●SPE 114947: Generalized PA for Tight Gas/Shale Gas●SPE 116731: Rate-Time Relation — Tight Gas/Shale Gas●SPE 119897: Production Analysis for Shale Gas●Shale Gas Analysis — Future View ●Blasingame: Current Interests/Projects





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Tom Blasingame:● Professor, Department of Petroleum Engineering, Texas A&M U.● Teaching and Research in Reservoir Engineering since 1984.● Professional Interests:—Petrophysics—Phase Behavior—Reservoir Engineering—Reservoir Models

Dilhan Ilk:● Graduate Assistant, Department of Petroleum Engineering, Texas A&M U.● Ph.D. Student at Texas A&M University since 2006.● Research in Reservoir Engineering since 2003.● Professional Interests:—Well Test and Production Data Analysis—Deconvolution/Inverse Problems—Reservoir Engineering—Modeling Tight/Shale Gas Reservoir Systems

Introductions/Bios:



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●Orientation Production Data Analysis and Diagnostics: (Blasingame)—Assembly of historical and current PA methods.

●SPE 114947: (Ilk)—Demonstrative examples for implementing this workflow.—Integrated diagnostics and analysis of production data ("Dashboards").

●SPE 116731: (Ilk)—New rate-time relation for tight gas/shale gas performance.—"Self-limiting" formulation — should yield constrained extrapolations.—Applications to field data are quite convincing.

●SPE 119897: (Blasingame)—Model for a horizontal well with multiple hydraulic fractures.—Diagnostics remain very difficult.

●Shale Gas Analysis — Future View (Blasingame)—Vertical wells (elliptical flow).—Horizontal wells (compound linear flow). —Diagnostic issues (horizontal well with multiple hydraulic fractures).

Abstract of the Presentation:



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Orientation —Production Data Analysis

and Diagnostics





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Decline Analysis — Arps Relations: Base Relations

Case Rate-Time Relation Cumulative-Time Relation

]exp[ tDqq igig −=

)/1()(1 bi

gig

tbD

qq

+=

)(1 tDq

qi

gig +=

Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

]]exp[[1 tDDq

G ii

gip −−=

])(1[1 )(1

)/1(1 bi

i

gip tbD

Dbq

G −+−−

=

)ln(1 tDDq

G ii

gip +=

Loss Ratio:

Loss Ratio Derivative:

]exp[ /

1 tDqqdtdq

qD igig

g

g −=→−≡

)/1()(1

/ bi

gig

g

g

tbD

qq

dtdqq

dtdb

+=→

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≡

Trans., AIME (1945) 160, 228-247.Analysis of Decline CurvesJ.J. Arps

Question(s):●How were the Arps' rate relations derived?

The BASIS for the Arps' relations — i.e., the behavior of the D- and b- parameters, is derived from OBSERVATIONS. These are empirical results.



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x

yPressure

MonitoringPoint No. 1

PressureMonitoringPoint No. 2

HydraulicFracture

Wellbore

X

X

x

y

x

yPressure

MonitoringPoint No. 1

PressureMonitoringPoint No. 2

HydraulicFracture

Wellbore

X

X

Numerical Model Considers:●Reservoir Layering.●kv/kh ratio.●Fracture Length, xf.●Fracture Conductivity, FcD.Analysis/Validation Approach:●Fit q(t) with Arps' hyperbolic relation.●Compare reserves to model at 30 years.

Decline Analysis: Tight Gas SystemsSPE 109625 (2007)Estimating Reserves in Tight Gas Sands at HP/HT Reservoir Conditions: Use and Misuse of an Arps Decline Curve MethodologyJ.A. Rushing, A.D. Perego, R.B. Sullivan, Anadarko Petroleum, and T.A. Blasingame, Texas A&M U.



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Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

⎥⎦

⎤⎢⎣

⎡

−≡⎥

⎦

⎤⎢⎣

⎡−= −

i

gibpgig Db

qG

GG

qq)(1

1 )1(1

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= pgii

gig GqDqq exp

Case Plotting Function

pGgq versus

⎥⎥⎦

⎤

⎢⎢⎣

⎡−GpG

gq 1log versus)log(

pGgq versus)log(

⎥⎥⎦

⎤

⎢⎢⎣

⎡≡−=

i

giDq

GpGiDgiqgq

Decline Analysis: EUR Plots (Arps' relations)SPE 98042 (2005)A Production-Based Method for Direct Estimation of Gas-in-Place and ReservesT.A. Blasingame, Texas A&M U. andJ.A. Rushing, Anadarko Petroleum.

Question(s):●Graphical extrapolations of EUR? Family of "EUR

plots" derived from the Arps' exponential and hyperbolic relations. Hyperbolic "EUR plot" requires a modular computing environment (e.g., a spreadsheet), as multiple variables are established simultaneously.



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⎥⎥⎦

⎤

⎢⎢⎣

⎡≡−=

i

giDq

GpGiDgiqgq⎥⎦

⎤⎢⎣

⎡

−≡⎥

⎦

⎤⎢⎣

⎡−= −

i

gibpgig Db

qG

GG

qq)(1

1 )1(1

Hyperbolic Decline: (0<b<1) Exponential Decline: (b=0)

a. "Hyperbolic Plot:" (log-log format) —Provides a straight-line for ALL cases.

b. "Hyperbolic Plot:" (Cartesian format) —Provides a straight-line ONLY for b=0 case.

Decline Analysis: Blasingame-Rushing EUR PlotSPE 98042 (2005)A Production-Based Method for Direct Estimation of Gas-in-Place and ReservesT.A. Blasingame, Texas A&M U. andJ.A. Rushing, Anadarko Petroleum.

Question(s):● Is there a distinctly unique mechanism for

establishing the validity of the hyperbolic relation? Yes, the "hyperbolic" decline "type curve" plot yields straight-line trends.



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Theory:●pi < 6000 psia.●pwf = constant.

Rate-Cumulative Result:

Gzpzp

qD

GGD

GDqq

ii

wfwf

gii

pi

pigig

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎥⎦

⎤⎢⎣

⎡−

=

+−=

2

2

//

1

2

where21

) (gas 1

eq.) flow ( 22

MBEGG

zp

zp

PSSzp

zpCq

p

ii

wf

wfg

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥⎦

⎤⎢⎣⎡=

Buba Gas Reserves Estimation Plot:

a. The "Buba" method utilizes only rate-time data (cumulative is cal-culated) in order to create a series of semi-analytical plotting functions for the estimation of gas reserves.

b. The "Buba" approach is based on the Ansah et al result for a semi-analyti-cal gas flow solution.

Decline Analysis: Buba Rate-Cumulative RelationM.S Thesis, Texas A&M University, College Station, TX (2003)Direct Estimation of Gas Reserves Using Production DataI.M. Buba, Texas A&M U.

Question(s):● Is there a semi-rigorous mechanism for correlating

qg and Gp? Yes, the "Buba" relation and associated plots provide a unique extrapolation of gas-in-place.



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Theory:●Palacio and Blasingame [1993]●Mattar and McNeil [1997]●Agarwal et al [1999]

Advantages:●Straightforward and intuitive.●Shut-in pressures NOT required.●Direct estimation of contacted

gas-in-place.

Limitations:●Boundary-dominated flow

regime must exist.

"Flowing Material Balance" Plot:

a. The "Flowing Material Balance" (Normalized Rate-Cumula-tive Function Plot) formulation is derived using the solution for the diffusivity equation during boundary-dominated flow regime. This formulation provides a direct estimate of the contacted gas-in-place using time, flowing wellbore pres-sure, and flowrate data.

Decline Analysis: "Flowing Material Balance" PlotJCPT (June 1997), 52-55.The 'Flowing' Gas Material BalanceL. Mattar and R. McNeil, Fekete Associates

Question(s):●What is the "Flowing Material Balance" plot? In

simple terms, pwf(t) data are "converted" to pavg(t)data using the pseudosteady-state flow equation, then plotted as a straight-line extrapolation function and "solved" for gas-in-place.



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Transient Stems: (left)Numerical or analytical model (pwf = constant).q(t) is concave up.

Depletion Stems: (right)q(t) is concave down.b=0: pwf = con.b=1: qo = con. (qo/Δp).b>1: transient flow or external drive energy.λ: numerical gas flow solutions (λ =f(pwf/(pi)).

Reservoir Properties:k — y-axis match.G — x&y-axis matches.s — reD match.

a. Original format Fetkovich-Carter type curve — most important observation is that 0<b<1. For cases where b>1; either transient flow OR external energy is being added to the reservoir system.

swwa

wae

gigi

wfiDd

wae

wewtigi

Dd

err

rrB.

ppkhtqq

rr

rrrc

kt.t

−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡

−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

21ln 2141

)( )(

21ln 1

21

1 006330 22

μ

φμ

Variables for the Carter Decline Type Curve

Decline Analysis: Fetkovich-Carter Type CurveSPEJ (October 1985) 719-728.Type Curves for Finite Radial and Linear Gas Flow Systems: Constant Terminal Pressure CaseR.D. Carter, Amoco Production

JPT (June 1980) 1065-1077.Decline Curve Analysis Using Type CurvesM.J. Fetkovich, Phillips Petroleum



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response at early times, very strong evidence of closed system at late times.

a. Raw (daily) rate and pressure data — bottomhole pressures are calculated, note the effect of liquid loading.

(1/4) )(

⎥⎥⎦

⎤

⎢⎢⎣

⎡≈

⎥⎥⎦

⎤

⎢⎢⎣

⎡Δ

g

ppss,g

transg qG

m̂qpm

(1) )(

⎥⎥⎦

⎤

⎢⎢⎣

⎡≈

⎥⎥⎦

⎤

⎢⎢⎣

⎡Δ

g

ppss,g

bdfg qG

m̂qpm

Boundary-DominatedFlow

TransientFlow

Question(s):●Can the well-reservoir model be inferred

from such data? Yes.● Is diagnosis sufficient? No, we must also

be able to model/history match data with a model (complete process).

Decline Analysis: Palacio Material Balance Time

? )(1 )/1( bi

gig

tbD

qq

+=

SPE 25909 (1993)Decline Curve Analysis Using Type Curves —Analysis of Gas Well Production DataJ.C. Palacio and T. Blasingame, Texas A&M U.



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Production AnalysisDiagnostics

(SPE 114947)





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●The following plots are used for data diagnostics and analyses:■History Plot — Flowrate and pressure data versus time.■Diagnostic Plot — Pressure versus flowrate.■Flow. Mat. Bal. Plot — Time, pressure, flowrate■Cartesian Plot — Empirical rate-cumulative.■Cartesian Plot — Semi-analytical rate-cumulative plot.■Hyperbolic Plot — Hyperbolic model plot.■Log-log Plot — Material balance time.■Model Match Plot — Complete model match.■Summary Plot — Model validation plot (history match).

●Integrated Diagnostics/Analysis of Production Data:■Objective is to ensure that the production data are correlated.■What diagnostic/analysis tools are most appropriate for tight gas

(and/or shale gas) reservoirs?■Use the "dashboard" approach to improve the function of production

analysis by improved diagnostics and with sound reservoir models.

Integrated Diagnostics and PA: SPE 114947 (2008)Integrating Multiple Production Analysis Techniques To Assess Tight Gas Sand Reserves: Defining a New Paradigm for Industry Best Practices.D. Ilk, et al Texas A&M U.

Question(s):●Why do we need a comprehensive suite of

diagnostics for production analysis? More information/presentation ensures that we obtain the maximum diagnostic value from the data.



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SPE 114947: East TX Gas Well (Dashboard)



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SPE 114947: Dashboard — Large WF Tight Gas Well



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New Rate Model for Tight Gas and Shale Gas Performance

(SPE 116731)





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SPE 116731: Inadequacy of Arps' Rate RelationsASSUMPTION: The Arps decline para-

meter, b, defines the decline behavior...

REALITY: Difficult to identify the correct b-parameter during the early decline period —greatly impacts reserve estimates.

b. (Log-log plot) Production forecast of a tight gas well.a. (Semilog plot) Production forecast of a tight gas well.

SPE 116731 (2008)Exponential vs. Hyperbolic Decline in Tight Gas Sands — Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves.D. Ilk, Texas A&M U., J.A. Rushing and A.D. Perego, Anadarko Petroleum, and T.A. Blasingame, Texas A&M U.



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●Rate Function Definitions:– Loss Ratio:

– Derivative of Loss Ratio:

– Exponential and Hyperbolic Rate Relations:

●Cause and Effect:– Hyperbolic relation is mis-applied to transient data.– What is the "characteristic behavior" of the D and

b-parameters? Evaluate continuously using data.

or /

1⎥⎦

⎤⎢⎣

⎡−≡−≡dQdqD

dtdqq

D

⎥⎦

⎤⎢⎣

⎡⎥⎦⎤

⎢⎣⎡≡⎥

⎦

⎤⎢⎣

⎡−≡⎥⎦

⎤⎢⎣⎡≡

DdQdqb

dtdqq

dtd

Ddtdb 1or

/1

)/1(][1 con or ; ]exp[ con b

i

iii

tbD

qqbtDqqD

+=→=−=→=

SPE 116731: Definitions of Rate Functions

(Exponential Decline) (Hyperbolic Decline)



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[ ]Bni AtDtDnD

dtdq

qD −

∞−−

∞ +≈+≈−≡ ˆ1 )1(

●Observed Behavior of the "Decline" Parameter [D(t)]:

●Solving for Flowrate [q(t)] Using the D(t) Relation:

] ˆ exp[ ˆ nii tDtDqq −−= ∞

●Solving for the "Hyperbolic" Parameter [b(t)]:

nn

i

i ttDDn

nDnb −

−∞+

−= 2)1( ] ˆ[

)1(ˆ

SPE 116731: "Power-Law Exponential" Rate Result



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CIPC 2008-109 (2008)Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls.D. Ilk, Texas A&M U., J.A. Rushing, Anadarko Petroleum, and T.A. Blasingame, Texas A&M U.

CIPC 2008-109: q-D-b Plot — W. Virginia Gas Well A



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CIPC 2008-109: q-D-b Plot — ETx Gas Well CIPC 2008-109 (2008)Estimating Reserves Using the Arps Hyperbolic Rate-Time Relation — Theory, Practice and Pitfalls.D. Ilk, Texas A&M U., J.A. Rushing, Anadarko Petroleum, and T.A. Blasingame, Texas A&M U.



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●Discussion: Small "Waterfrac" Gas Well■ Liquid loading effects are obvious in the latter portion of the flowrate data.■ The onset of the boundary-dominated flow regime is observed.■ We observe a very good match of the flowrate data using D∞=0.

SPE 116731: q-D-b Plot — Small WF Tight Gas Well



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●Discussion: Large "Waterfrac" Gas Well■ Erratic rate behavior caused by liquid loading is seen at late times.■ Outstanding matches of the computed D- and b-parameters with the

power-law exponential model are observed.

SPE 116731: q-D-b Plot — Large WF Tight Gas Well



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●Discussion: Hybrid "Waterfrac" Gas Well■ Severe liquid loading is observed at late times.■ The computed D- and b-parameters reflect the effects of liquid loading.■ Good matches of the computed D- and b-parameters .

SPE 116731: q-D-b Plot — Hybrid WF Tight Gas Well



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Production Analysis and Fore-casting of Shale Gas Reservoirs:

Case History-Based Approach(SPE 119897)





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Base Simulation Modelfor Horizontal Well with Multiple Hydraulic Fractures

Top View HorizontalWell

MultipleVertical

Fractures

SPE 119897: Schematic Model for Simulation



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●Discussion: Horizontal Wells with Transverse Fractures■ Very high resolution simulation case.■ Very good D-parameter and good b-parameter computed from results.■ Excellent rate match using the new model (all regimes).

SPE 119897: q-D-b Plot — Numerical SimulationFinite-Acting

Reservoir Case



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●Discussion: Horizontal Wells with Transverse Fractures■ Very high resolution simulation case.■ Transient D- and b-parameters at late times (quasi-radial flow).■ Impossible to predict reserves.

SPE 119897: q-D-b Plot — Numerical SimulationInfinite-Acting

Reservoir Case



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●Discussion: Barnett Shale Gas Well 1■ Monthly data from PUBLIC records.■ Fair D-parameter and fair/weak b-parameter computed from data.■ Excellent rate match using the new model (transient and BDF).

SPE 119897: q-D-b Plot — Barnett Shale Gas Well 1



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●Discussion: Barnett Shale Gas Well 3■ Monthly data from PUBLIC records.■ Good D-parameter and good/fair b-parameter computed from data.■ Excellent overall rate match with the new model (all transient flow?).




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●Discussion: Barnett Shale Gas Well 5■ Monthly data from PUBLIC records.■ Good D-parameter and good b-parameter computed from data.■ Excellent rate match using the new model (transient and BDF).




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Shale Gas Analysis— Future View





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b. Elliptical flow type curve solution — high fracture conductivity case.

a. Elliptical flow type curve solution — low fracture conductivity case.

Vertical TG/SG Wells: Elliptical Flow Domination

c. Elliptical boundary configurations (finite con-ductivity fracture case [Amini, et al (2007)].

SPE 106308 (2007)Evaluation of the Elliptical Flow Period forHydraulically-Fractured Wells in Tight GasSands — Theoretical Aspects and PracticalConsiderationsS. Amini, D. Ilk, and T. A. Blasingame,SPE, Texas A&M U.



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a. Pressure profile at 0 year (0 hr).

b. Pressure profile at 1 year (8768 hr).

c. Pressure profile at 5.59 years (49,010 hr).

d. Pressure profile at 9.26 years (81,200 hr).

e. Pressure profile at 18.44 years (161,700 hr).

f. Pressure profile at 44.10 years (386,600 hr).

Results Generated Using:Ecrin Product Suite, Kappa Engineering, Sophia-Antipolis, France (2008).

Vertical TG/SG Wells: Elliptical Flow Domination



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a. Rate performance behavior for a horizontal well with 4 trans-verse fractures — infinite-acting reservoir (analog to van Kruysdijk and Dullaert work). Fine-scale numerical model .

Horizontal TG/SG Wells: Compound Linear Flow

c. Schematic diagram for the "compound linear flow" concept [van Kruysdijk and Dullaert (1989)].

Presented at the 2nd European Conference on the Mathematics of Oil Recovery, Cambridge, England (1989).A Boundary Element Solution of the Transient Pressure Response of Multiply Fractured Horizontal WellsC.P.J.W. van Kruysdijk and G.M. Dullaert, Shell

b. Specialized derivative plot (ref: van Kruysdijk and Dullaert) for a horizontal well with 4 transverse fractures — infinite- and finite-acting reservoir cases. Fine-scale numerical model .



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Horizontal TG/SG Wells: Diagnostics?Q1.Compound Linear Flow Domination? (transient flow)A1. Possibilities for estimating reservoir properties:

a. Just give up — impossible to resolve anything. (default)b. "Lump" k, xf, and Lwell into a "parameter." ("mechanistic model")c. Develop testing practices to estimate properties. (maybe…)d. Other model concepts (e.g., propagating ellipse). (very tedious)

Q2.Estimating Reserves?A2. Issues:

a. Extremely long transition to boundary-dominated flow. (reality)b. Hyperbolic rate relation will overestimate reserves. (as always)c. Power-law/exponential rate relation? (more validation)

Q3.Role of simulation/modeling?A3. In the short-term, simulation/modeling is the primary

tool at our disposal — the analogy of using a hammer in place of a screwdriver comes to mind… (sometimes effective, but always a sub-optimal solution — particu-larly in the hands of children).



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BlasingameCurrent Projects/Interests





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Current Work: Blasingame●Projects: Status■ Characteristic Permeability Relations (closed)■ Simple Rate-Time Models for Shale Gas Systems (active)■ Diagnostics and Simplified Production Analysis (active)■ (Ana/Num) Models for Shale Gas Performance (active)■ IPR for Solution Gas-Drive Systems (active)

●Concepts: Status■ Production Mechanisms for Shale Gas Systems (start-up)■ Petrophysical Properties of Shales (2009+)■ Price Modeling and Predictions (2009+)■ Solutions for Horizontal Wells with Multiple Fractures (start-up)

●Focus Priority■ Simple Rate-Time Models for Shale Gas Systems very high■ (Ana/Num) Models for Shale Gas Performance very high■ Rigorous Production Analysis for Shale Gas Systems high■ Correlation/Quality Control for Data Analysis high■ Petrophysical Properties of Shales/Tight Gas Sands medium



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Students: Blasingame●Boulis: Extended Hyperbolic Models for Rate-Time Analysis (M.S./active)●Carballo: TBA (Gas Reservoir Eng.?) (Ph.D. coursework — DL)●Currie: Simple Rate-Time Models for Shale Gas Systems (M.S./active)●Freeman: Numerical Models for Shale Gas Well Performance (M.S./active)●Froboese: Empirical/Analytical Decline Curve Analysis (M.S./inactive — DL)● Ilk: Production Analysis — Tight Gas Systems (Ph.D./active)● Jam: Analytical Models for Shale Gas Well Performance (M.S./active)● Johnson: Simplified Production Analysis for Gas Wells (B.S./active)●Kelly: TBA (Behavior of CO2 Injection Systems?) (M.S./inactive — DL)●Mendel: PTA/PA for Heavy Oil Production Systems (B.S./active)●Nass: IPR For Solution Gas-Drive Reservoirs (M.S./active — DL)●Olsen: TBA (Reserves? Price Predictions?) (M.S./coursework — DL)●Westler: TBA (Production Analysis?) (M.S./coursework — DL)

well performance analysis — low to ultra-low permeability

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