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Slide — 1/54T.A. Blasingame Performance-Based Reservoir Characterization — State-of-the-Technology

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SPE FOUNDATIONThe Society gratefully acknowledges

those companies that support the programby allowing their professionals

to participate as Lecturers.

And special thanks to The American Institute of Mining, Metallurgical,and Petroleum Engineers (AIME) for their contribution to the program.

Society of Petroleum EngineersDistinguished Lecturer 2005-06 Lecture Season



Performance-Based ReservoirCharacterization – State-of-the-Technology

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

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected] materials located at:

link → http://pumpjack.tamu.edu/~t-blasingame/folder → z_SPE_DL


Prelude: Performance-Based Reservoir CharacterizationQ. What is "Performance-Based Reservoir Characterization?"A. In the context of this lecture, "Performance-Based Reservoir Charac-

terization" is the diagnosis, analysis, and interpretation of production data taken from an individual well — and the integration of the results of this analysis with other forms of data (e.g., petrophysical data, re-sults of well test analysis, geological data, etc.).

Discussion: PreludeProduction analysis (PA) versus pressure transient analysis (PTA)? (same)Weakness of PA? (data quality/quantity)Strength of PA? (continuous monitoring, PTA becomes a subset of PA)

Diagnosis/Interpretation:Generally pretty good, mostly an issue of pro-duction data quality.Analysis:Modern tools for pro-duction data analysis are excellent — analytical, semi-analytical, and numerical modelling are essentially without flaw.Integration:Evolving — major issues are data quality and the scale(s) of the results.


Guidelines: Performance-Based Reservoir CharacterizationsREVIEW production data for consistency (allocations, accuracy, etc.).REVIEW well history, particularly recompletions/stimulations.GATHER/CORRELATE petrophysical data (core, logs, etc.).PERFORM simplified analysis of production data (Arps, EUR, etc.).

REVIEW measured rate/pressures (quality check).PERFORM model-based analysis of production (and well test) data.

INTEGRATE results at different scales (without reservoir simulation).

Prelude: Guidelines for Production Analysis


Darcy's Law:

Oil Material Balance Eq.: (p>pb)

Oil Diffusivity Eq.: (p>pb)

Oil Pseudosteady-State Flow Eq.: (p>pb)

Primer: Reservoir Engineering

Discussion: Primer — Reservoir EngineeringDiffusivity equation? (mass continuity (balance) + Darcy's Law)Oil pseudosteady-state equation? (material balance + diffusivity equation)Implications? (origin of virtually all reservoir engineering relations)

Q. What do I need to know for reservoir engineering ... ?A. All you need is ... Darcy's law and material balance.

poio

ti N

BB

Ncpp 1−=

owA

oowf qs

r

ACekh

Bpp 214ln

21 141.2

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

γμ

⎥⎦⎤

⎢⎣⎡

∂∂

−=rpr

Bkh

.q

μ21411)(

tp

kc

rp

rr

p t∂∂

=∂∂

+∂

∂ φμ0002637.0

112

2


Orientation: PA TheoryQ. What is the theory to represent boundary-dominated flow behavior?A. Combine material balance and pseudosteady-state flow equations.

Discussion: Orientation — PA Theory"Production Analysis Relation" implies? (plot: log[(pi-pwf)/qo] vs. log[Np/qo])Use of "log-log" plot (i.e., log[(pi-pwf)/qo] vs. log[Np/qo])? (diagnosis/analysis)Does material balance time work? (yes — very robust formulation)

The quantity Np/qo (or Gp/qg) is known as "ma-terial balance time" — is rigorous for boundary-dominated flow, and is a very good approxima-tion for transient flow.

Oil Material Balance Eq. (MBE): (p>pb)

Oil Pseudosteady-State Flow Eq. (PFE): (p>pb)

Production Analysis Relation:

oio

tpss,oppss,oi B

BNc

mNmpp 1 where =−=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡=+= s

r

ACekh

BbqbppwA

oopss,oopss,owf 2

14ln 21 141.2 where

γμ

o

ppss,opss,o

o

wfiqN

mbq

pp+=

− )((Oil — analytical form)

g

ppss,gpss,g

g

wfiqG

m̂b̂q

pmpm+=

− )()((Gas — approximate form)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡= ∫ dp

zpp

ppm

gbase μ21)(


Orientation: Production Analysis (PA)

Discussion: Orientation — Production Analysis (PA)What are the major issues? (pressure and rate data quality/quantity)What are the benefits? (est. reservoir properties/volume, rate prediction)Where are the tools? (commercial vendor products)

Production Analysis (PA) is analogous to raising children — it is problematic — every case is unique (and poten-tially very frustrating). BUT, the PA experience is also potentially very rewarding ... you always learn something in the process.


Orientation: Production Analysis (PA) DataQ. What is Production Analysis (PA)?A. Combined analysis of rate and flowing bottomhole pressure data.

Discussion: Orientation — Production Analysis (PA) DataPA is a passive technology — can it yield high resolution results? (yes)What is/are the key data issue(s)? (q and pwf data accurate and correlated)Erratic q and pwf data — how to analyze? (boundary-dominated flow theory)

Rate Data:Flowrates are measured on a per-well basis for most gas wells — oil flowrates are often al-located (this is a major issue).Pressure Data:Measured bottomhole pressure data are es-sentially non-existent —surface pressure data are often available for gas wells, flowing (sur-face) pressure data for oil wells are rare at best.


Orientation: PA Data Analysis Example (Gas)Q. Does material balance time work? (prove with an example)A. Typical low productivity gas well example (mid-Continent US).

Discussion: Orientation — PA Data Analysis Example (Gas)What are the limitations of this approach? (poor rate data, poor sampling)What is the "best" data frequency? (minimum preferred frequency = daily)What is the effect of pressure? (pressure data critical — but in practice ...)

Transient Behavior:Appears to reflect be-havior of a vertical well with a finite-conducti-vity vertical fracture.

BDF/PSS Behavior:Clear indication of (approximate) material balance behavior.

Material balance behav-ior is independent of reservoir shape!

(1) )(

⎥⎥⎦

⎤

⎢⎢⎣

⎡≈

⎥⎥⎦

⎤

⎢⎢⎣

⎡Δ

g

ppss,g

bdfg qG

m̂q

pm

(1/4) )(

⎥⎥⎦

⎤

⎢⎢⎣

⎡≈

⎥⎥⎦

⎤

⎢⎢⎣

⎡Δ

g

ppss,g

transg qG

m̂q

pm


Orientation: PA ObjectivesQ. What are the objectives of Production Analysis (PA)?A. Estimate reservoir properties and volume, and predict performance.

Discussion: Orientation — PA ObjectivesIn THEORY — any differences in PA and PTA? (none, could use same tools)In PRACTICE — differences in PA and PTA? (PTA data is higher resolution)In FUTURE — what will happen with PA and PTA? (applications will merge)

Transient Radial Behavior: (PTA/PA) Pseudosteady-State Behavior: (PA)

r(t)

[ ] [ ] )ln(

)ln()(

cr,trns

cr,trnscr,trnswfi

mptd

dpdtdt'p

tmbppp

=Δ=Δ=Δ

+=−=Δ

[ ] [ ] tmptd

dpdtdt'p

tmbppp

cr,pss

cr,psscr,psswfi

=Δ=Δ=Δ

+=−=Δ

)ln(

)(

Common Characteristics:Constant rate (q).Constant reservoir properties.Constant fluid properties.

Differences:Volume ONLY from pseudo-steady-state data.Reservoir properties ONLY from transient flow data.

re

0=⎥⎦⎤

⎢⎣⎡

erdrdp

(closed outerboundary)

(infinite-actingradial flow behavior)

...) , ( ...) ( s,kfb,kfm cr,trnscr,trns == ...) , ( ...) ( s,kfb,Nfm cr,psscr,pss ==


Orientation: PA Data RequirementsQ. What are the data requirements for Production Analysis (PA)?A. Rate and pressure data, reservoir and fluid properties, well history.

Discussion: Orientation — PA Data RequirementsIssues with pressure? (measured infrequently at surface)Issues with rate? (gas → usually good, oil → problematic, water → poor)Issues with well completion? (review history, keep completion simple)

Required Data:Good pressure data!Consistent rate!Well history.Fluid properties.

Issues:Effect of well comple-tion (see example).Conversion of ptf →pwf (will remain a major issue, consider pwf measurement).Always review well history prior to per-forming PA.


History: Production Analysis (PA)

Discussion: History — Production Analysis (PA)PA up to 1970? (estimate reserves, maximum rate, and future rates)PA 1970-1990? (estimate reservoir properties — simple models [pwf=con])PA 1990-2000? (estimate reservoir properties — general q and pwf profiles)PA 2000-? (interactive diagnosis, analysis-by-modelling, and forecasting)

Past:Estimate reserves.Simple rate forecasts.Simple estimates of reservoir properties.

Present:Full variable-rate/vari-able pressure capabil-ity — analysis and modelling (rigorous).Robust analysis methods and very good software.

Future:Measured pwf data.Larger data volumes.Will still need tools for poor (i.e., field) qual-ity data.


This relationship is rigor-ous for low pressure gas reservoirs (it can be deriv-ed from the p2-form of the gas diffusivity equation (n=1) for laminar flow).

Q. What is "deliverability" analysis, and why did it evolve?A. Analysis of rate-pressure data, evolved to estimate maximum rate.

History: Production Analysis (PA) — q(pwf)

Discussion: History — Production Analysis (PA) — q(pwf)Purpose of a q(pwf) relation? (maximum rate, inflow performance)Typical applications? ("deliverability" tests, darcy/non-darcy flow)Limitations? (rate a function of pressure (not time), laminar flow)

—Fr

om: R

awlin

s, E

. L. a

nd M

. A. S

chel

lhar

dt: B

ackp

ress

ure

Dat

a on

Nat

ural

Gas

Wel

ls a

nd T

heir

App

licat

ion

To

Prod

uctio

n Pr

actic

es, M

onog

raph

7, U

.S. B

urea

u of

Min

es,

Was

hing

ton,

DC

, (19

36).

Well Deliverability:The original purpose of well performance analysis was to quan-tify well deliverability.The empirically de-rived "deliverability" equation is given by:

nwfg ppCq )( 22 −=

a. Wellbore Diagram: Ancient,but still accurate.

b. "Deliverability" Plot: (pav2-pwf

2)versus qg (log-log format) —used to estimate qg(pwf=0) (an indicator of well performance and recovery).


Q. What is "rate-time" analysis, and what was its original purpose?A. Analysis of rate-time data (graphically), originally used for taxation.

Discussion: History — Production Analysis (PA) — q(t) (Case 1)Theory for q(t)=qiexp(-Dit)? (... log(qo) vs. t straight-line data confirms model)Theory for q(t)=qi/[(1+bDit)(1/b)]? (... other plots would be required to confirm)Theory for "Averaged and Extrapolated" trend given by Cutler? (unknown)

Concept:Create an extrapolation of the rate-time profile to yield "estimated ultimate recovery" (EUR) (i.e., to provide a reserves esti-mate).Limitation(s):Early rate-time models had no direct basis in theory — but ironically, these models have been proven in modern times, and are regularly used as standards for re-serves estimation (i.e., the exponential and hyperbolic rate-time relations).

History: Production Analysis (PA) — q(t) (Case 1)—

From

: Cut

ler,

W.W

., Jr

.: Es

timat

ion

of U

nder

grou

nd O

il R

eser

ves

by O

il-W

ell P

rodu

ctio

n C

urve

s, D

epar

tmen

t of t

he

Inte

rior,

U.S

. Bur

eau

Of M

ines

Bul

letin

228

(192

4).


Q. "Non-exponential" q(t) behavior — is it real?A. See calibrated analysis using exponential and hyperbolic models.

History: Production Analysis (PA) — q(t) (Case 2)—

From

: Cut

ler,

W.W

., Jr

.: Es

timat

ion

of U

nder

grou

nd O

il R

eser

ves

by O

il-W

ell P

rodu

ctio

n C

urve

s, D

epar

tmen

t of t

he

Inte

rior,

U.S

. Bur

eau

Of M

ines

Bul

letin

228

(192

4).

Discussion: History — Production Analysis (PA) — q(t) (Case 2)q(t) behavior? ("higher" resolution than qo(Np))qo(Np) behavior? ("confirms" q(t) behavior — also extrapolate Np(qo→0))Issue 1?(exponential and hyperbolic relations show early linear qo vs. log(t))Issue 2? (in concept — apply to single well; in practice — field/pool data)

a. "Rate-Time" Plot: qo versus t (or qg versus t) — hyperbolic behavior dominant, note that "early" exponential is required.

b. "Rate-Cumulative" Plot: qo versus Np (or qgversus Gp) — apparent hyperbolic behavior, analysis calibrated with q(t) data.


Oil Material Balance Eq. (MBE): (p>pb)

Oil Pseudosteady-State Flow Eq. (PFE): (p>pb)

Steps:1. Differentiate oil MBE and oil PFE with respect to time.2. Assume: pwf = constant [i.e., d(pwf)/dt = 0].3. Equate results → 1st order o.d.e.4. Separate/integrate.5. Exponentiate result — final form:

Q. Can the "exponential" rate-time relation (q(t)=qiexp(-Dit)) be derived?A. Yes, see steps below — slightly compressible liquid, pwf=constant.

Discussion: History — Production Analysis (PA) — q(t)=qiexp(-Dit)Is the q(t)=qiexp(-Dit) relation rigorous? (oil (p>pb) — yes, gas — ?)Other formulations? (rate-cumulative: q(t)=qi – DiNp)Applications? (estimate reserves (Np,max = Np(q→0)), q(t) predicton)

The q(t)=qiexp(-Dit) form is correct for boundary-dominated flow behavior — slightly compressible liquid, pwf=constant. oi

ot

pss,oppss,oi BB

NcmNmpp 1 where =−=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡=+= s

r

ACekh

BbqbppwA

oopss,oopss,owf 2

14ln 21 141.2 where

γμ

History: Production Analysis (PA) — q(t)=qiexp(-Dit)

⎥⎥⎦

⎤

⎢⎢⎣

⎡=−=

pss,o

pss,oiii b

mDtDqq )exp(


Discussion: History — Production Analysis (PA) — q(t)Is the q(t)=qiexp(-Dit) model supported by theory? (yes — liquid; pwf=con)Is the q(t)=qi/[(1+bDit)^(1/b)] model supported by theory? ("not exactly")Issues? (exponential = conservative; hyperbolic = liberal → use caution)

—Fr

om: F

etko

vich

, M.J

.: "D

eclin

e C

urve

Ana

lysi

s U

sing

Typ

e C

urve

s,"

JPT

(Jun

e 19

80) 1

065-

1077

.History: Production Analysis (PA) — q(t)Q. "Rate-Time" Plot: qo versus t (or qg versus t)? (original purpose?)A. Base "performance" plot for PA. (originally used for taxation...)

Theory: (exp model)Assume slightly com-pressible liquid, pwf= constant — use oil MBE and oil PSS FE to yield: (p<pb)

Theory: (hyp model)APPROXIMATE deriva-tion using oil MBE (p<pb), and oil PSS FE (also p<pb):

)exp( tDqq ii −=

)1()(1 b/i

itbD

qq+

=


Q. What is an Estimated Ultimate Recovery (or EUR) plot?A. Plot q(t) vs. Np, extrapolate to zero rate using a straight line ((EUR)exp).

Discussion: History — Production Analysis (PA) — (EUR)expIs the estimated ultimate recovery (EUR)exp supported by theory? (yes)Is the (EUR)exp conservative or liberal? ((EUR)exp is always conservative)Other issues? (use of other EUR models (e.g., hyperbolic) requires caution)

History: Production Analysis (PA) — (EUR)exp—

From

: Fet

kovi

ch, M

.J.:

"Dec

line

Cur

ve A

naly

sis

Usi

ng T

ype

Cur

ves,

" JP

T(J

une

1980

) 106

5-10

77.

Theory: (exp model)The q(t)=qiexp(-Dit) model (i.e., slightly com-pressible liquid, pwf= constant) is integrated to yield:

Application: (EUR)expPlot q(t) versus Np, ex-trapolate trend using a straight-line model to Np(q=0) — this gives estimated ultimate re-covery (EUR)exp.

pii NDqq −=


Q. Origin and purpose of the EUR versus qo,1yr correlation?A. Potential value as a correlation, but must quantify theory (N, k, s, etc).

Discussion: History — Production Analysis (PA) — EUR vs. qo,1yrOrigin? (1919 — production data correlation (>85 years old)!)Theory? (Constant pwf (liquid) boundary-dominated flow conditions)Rationale? (Correlate reserves versus production (or reservoir properties))

"Ancient" Technique:The proposed correla-tion of EUR vs. qo,1yr was used to estimate oil re-serves from initial pro-duction performance data.Modern Application:Approach is based in theory — EUR = f[k, s, xf, ... and contacted fluidsin-place (i.e., N or G)].Could be used as a "re-servoir characterization" tool to classify well per-formance.

History: Production Analysis (PA) — EUR vs. qo,1yr—

From

: Man

ual f

or T

he O

il an

d G

as In

dust

ry U

nder

The

R

even

ue A

ct o

f 191

8, T

reas

ury

Dep

artm

ent —

Uni

ted

Stat

es

Inte

rnal

Rev

enue

Ser

vice

(191

9).


Arps' observations:b=0 — Reservoir is highly undersaturated (p>pb).b=0 — Gravity drainage and no free surface.b=0.5 — Gravity drainage with free surface.b=0.667 — Soln. gas-drive reservoir ( vs. Np → linear).b=0.333 — Soln. gas-drive reservoir ( vs. Np → linear).

Q. Theory for Arps' relations?A. Arps derived the exponential and hyperbolic relations from loss ratio.

Discussion: History — Production Analysis (PA) — Arps"Theory" for the Arps' relations? (loss ratio (exp) and its derivative (hyp))Validity of the Arps' observations? (only qualitative (except for p>pb case))Graphical analysis using the hyperbolic relation? (only using Fetkovich TC)

History: Production Analysis (PA) — Arps—

From

: Arp

s, J

.J: "

Ana

lysi

s of

Dec

line

Cur

ves,

" Tr

ans.

, AIM

E (1

945)

160

, 228

-247

.

Case Rate Relation Cumulative Relation )exp( tDqq ii −=

)1()(1 b/i

itbD

qq+

=

)(1 tDqq

ii

+=

Exponential: (b=0)

Hyperbolic: (0<b<1)

Harmonic: (b=1)

)]exp([1 tDDqN i

ii

p −−=

[ ] )1(1)(11 )(1

b/i

ii

p tbDDb

qN −+−−

=

)ln(1 tDDqN i

ii

p +=

p2

p

Loss Ratio:

Loss Ratio Derivative:dtdq

qD

a/

1−≡≡

[ ] ⎥⎦

⎤⎢⎣

⎡−≡⎥⎦

⎤⎢⎣⎡≡≡

dtdqq

dtd

Ddtda

dtdb

/1

Theory???

Theory???


Q. What is the "Fetkovich" Decline Type Curve, and how is it used?A. A composite of analytical (pwf=con) and empirical (Arps) solutions —

used as a "type curve" (data overlay) to estimate reservoir properties.

Discussion: History — Production Analysis (PA) — FetkovichAn original purpose of the Fetkovich TC? (graphical solution of Arps Eqs.)Use of "transient" stems? (estimate reservoir properties — k and s)Use of "depletion" stems? (estimate reservoir volume, predict rate)

History: Production Analysis (PA) — Fetkovich—

From

: Fet

kovi

ch, M

.J.:

"Dec

line

Cur

ve A

naly

sis

Usi

ng T

ype

Cur

ves,

" JP

T(J

une

1980

) 106

5-10

77.

Transient Stems: (left)Infinite-acting radial flow model (pwf = con).q(t) is concave up.

Depletion Stems: (right)Bounded circular re-servoir (pwf = con).q(t) is concave down.b=0: pwf = con.b=1: qo = con. (qo/Δp).b>1: transient flow or external drive energy.

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

swwa

wae

wfiDd

wae

wewt

Dd

err

rrB.

ppkhtqq

rr

rrrc

kt.t

−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡

−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

21ln 2141

)( )(

21ln 1

21

1 006330 22

μ

φμ

Variables for the Fetkovich Decline Type Curve


Q. What is the "Carter" Decline Type Curve, and how is it used?A. A numerically-generated gas rate solution (pwf=con) — used as a

"type curve" (data overlay) to estimate reservoir properties.

Discussion: History — Production Analysis (PA) — CarterGenisis of the Carter TC? ("correction" of Fetkovich gas flow solutions)Use of "transient" stems? (estimate reservoir properties — k and s)Use of "depletion" stems? (estimate reservoir volume, predict rate)

History: Production Analysis (PA) — Carter—

From

: Car

ter,

R.D

.: "T

ype

Cur

ves

for F

inite

Rad

ial a

nd

linea

r Gas

Flo

w S

yste

ms:

Con

stan

t Ter

min

al P

ress

ure

Cas

e,"

SPE

J(O

ctob

er 1

985)

719

-728

.

Transient Stems: (left)Numerical flow model (pwf = con).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 cases (λ =f(pwf/(pi)).

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

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


Modern PA: OrientationVariable Rate/Pressure:

Material balance time (equi-valent constant rate time function).Derived by applying the superposition formulation to the pseudosteady-state solution.

Auxiliary Plotting Functions:Time-averaged rate func-tion (rate integral function).Derivative, integral, and in-tegral-derivative functions.

Semi-Analytical Solutions:Ansah, et al gas solutions/ Buba method.Advanced methods for hyperbolic rate analysis.

Adv. Decline Type Curves:"Palacio" type curve."Doublet" type curve.Cumulative production TC.

"Modern production analysis (PA) is a mature and functional process — but we have to recognize that these methods may make us overconfident in our abilities to diagnose, interpret, and analyze a particular field data case."

Blasingame

Discussion: Modern PA — OrientationMajor advances in PA? (variable q/variable pwf analysis methods)

(auxiliary plotting functions to improve analysis)(semi-analytical solutions — advances from the Arps' relations)


Modern PA: Material Balance Time (Theory)Q. Concept of material balance time?A. Constant-rate equivalent function (variable-rate → constant rate case).

Discussion: Modern PA — Material Balance Time (Theory)Value of material balance time? ("deconvolution" → constant rate response)Δp/qo versus Np/qo (pressure drop form)? (PTA analog (constant rate case))qo/Δp versus Np/qo (rate decline form)? (decline curve analysis format)

Pressure Drop Form:

tmbq

ppss,opss,o

o+=

Δ

Flowrate Form:

tmbpq

pss,opss,oo

+=

Δ1

(intercept)

oio

tpss,o B

BNc

m 1 =

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡= s

r

ACekh

BbwA

oopss,o 2

14ln 21 141.2

γμ

(slope)

(material balance time)o

pqN

t =


Modern PA: Material Balance Time (Application)Q. Application of material balance time?A. Requires pressure and rate histories (accurate rates essential).

Discussion: Modern PA — Material Balance Time (Application)Effectiveness on raw data? (note example — excellent correlation)Δp/qo versus Np/qo data? (transient flow — ?, BDFB — yes!)qo/Δp versus Np/qo (rate decline form)? (transient flow — ?, BDFB — yes!)

Theory:Material balance time and the general boun-dary-dominated flow relation:

Application:Plot Δp/qo versus Np/qoand qo/Δp versus Np/qoto correct for rate ef-fects — and to establish boundary-dominated flow behavior (BDFB).

o

pqN

t =

tmbq

ppss,opss,o

o+=

Δ

tmbpq

pss,opss,oo

+=

Δ1

]/[ pqo Δ

]/[ oqpΔ

]/ [ op qNt =


Normalized Pressure Drop:"Pressure Derivative"

"Pressure Integral"

"Pressure Integral-Derivative"

Normalized Flowrate:"Rate Derivative"

"Rate Integral"

"Rate Integral-Derivative"

Modern PA: Auxiliary Plotting Functions (Theory)Q. What are the "auxiliary" plotting functions for PA?A. Time (or material balance time)-averaged pressure drop and flowrate

functions — "integral" and "integral-derivative" forms are used.

Discussion: Modern PA — Auxiliary Plotting Functions (Theory)Theory for auxiliary plotting functions? (just calculus ...)Purpose of auxiliary plotting functions? (more resolution for PA data)Advice? (use BOTH pressure drop and flowrate functions (separate plots))

tdq

pt

tqp

oio⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ

ioido qp

tddt

qp

tdp

qt

tpq o

i

o⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ i

o

id

op

qtd

dtp

q

⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ p

qtd

dtp

q o

d

o

Theory:The auxiliary func-tions (specifically the integral and integral derivative functions)are designed to pro-vide "smooth" data functions – which should improve inter-pretation and analy-sis.

⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ

odo qp

tddt

qp

Application:"Pressure drop" functions → "Nor-malized PI" plot .Flowrate" functions → "Blasingame" plot .


Modern PA: Auxiliary Plotting Fcns (Application 1)Q. Application 1 — What is the "Normalized PI" plot?A. Pressure drop auxiliary functions versus material balance time.

Discussion: Modern PA — Aux. Plotting Fcns ("Normalized PI" plot)Δp/qo functions versus Np/qo? (PTA form: transient flow — ?, BDFB — yes!)Validity of (Δp/qo)d function? (exceptional case — downhole pressure data)(Δp/qo)i and (Δp/qo)id functions? (smooth and representative)

Theory:(Δp/qo) fcns versus Np/qo:

Application:Analysis approach same as PTA — look for char-acteristic behavior.

o

pqN

t =

tdq

pt

tqp

oio⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ ∫01

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ

ioido qp

tddt

qp

⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ

odo qp

tddt

qp

]/ [ op qNt =

]/[ oqpΔ

ioqp ]/[Δ

doqp ]/[Δ

idoqp ]/[Δ


Modern PA: Auxiliary Plotting Fcns (Application 2)Q. Application 2 — What is the "Blasingame" plot?A. Rate auxiliary functions versus material balance time.

Discussion: Modern PA — Auxiliary Plotting Fcns ("Blasingame" plot)qo/Δp versus Np/qo? (rate decline form: transient flow — ?, BDFB — yes!)Validity of (qo/Δp)d function? ((again) good — downhole pressure data)(qo/Δp)i and (qo/Δp)id functions? (well-behaved and representative)

Theory:(qo/Δp) fcns versus Np/qo:

Application:Transient flow behavior is complex, but transition and BDFB unique.

o

pqN

t =

tdp

qt

tpq o

i

o⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ i

o

id

op

qtd

dtp

q

⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ p

qtd

dtp

q o

d

o

]/ [ op qNt =

]/[ pqo Δ

io pq ]/[ Δ

do pq ]/[ Δ

ido pq ]/[ Δ


Modern PA: Ansah, et al Gas Solution/Buba MethodQ. What is the Ansah, et al gas solution/Buba method?A. A gas-specific solution for qg(Gp).

Discussion: Modern PA — Ansah, et al Gas Solution/Buba MethodValidity of the Ansah, et al gas solution? (general criteria: pi < 6000 psia)Application of the Buba method? (assortment of plotting functions)Advantages? (rigorous solution for gas flow cases (pwf = constant))

Theory:

Rate-Cumulative Result:

Gzpzp

qD

GGDGDqq

ii

wfwf

gii

pi

pigig

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎥⎦

⎤⎢⎣

⎡−

=

+−=

2

2

//

1

2

where21

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥⎦

⎤⎢⎣⎡=

GG

zp

zp

zp

zpCq

p

ii

wf

wfg

1

22


Modern PA: Hyperbolic EUR Methods (Type Curves)Q. Straight-line or characteristic behavior for Arps hyperbolic relation?A. Rate-cumulative ratios used to define "type curve" behavior.

Discussion: Modern PA — Hyperbolic EUR Methods (Type Curves)Example gas case from Fetkovich (SPE 13169)? ("typical" gas case)log[(qg/qgi)] versus log[1-(Gp/G)]? (straight-line characteristic behavior)Cartesian (qg/qgi) versus (Gp/G)? (note that 0.4<b<0.5)


Liquid: (pwf = constant)

Gas: (pwf = constant)

Hyperbolic:

Harmonic:

Modern PA: EUR Methods (Schematic Behavior)Q. Collection of modern EUR methods?A. Comparison of methods illustrates behavior.

Discussion: Modern PA — EUR MethodsLiquid (oil) flow behavior? (straight-line rate-cumulative behavior)Gas flow behavior? (rigorous) (rate-quadratic cumulative behavior)General hyperbolic relation? (straight-line log[qg] versus log[1-(Gp/G)])

⎥⎥⎦

⎤

⎢⎢⎣

⎡≡−=

i

giDq

GpGiDgiqgq

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−≡

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= −

i

gi

bpgig

Dbq

G

GG

qq

)(1

1 )1(1

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= p

gii

gig GqDqq exp

Gzpzp

qD

GGDGDqq

ii

wfwf

gii

pi

pigig

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎥⎦

⎤⎢⎣

⎡−

=

+−=

2

2

//

1

2

21


Auxiliary functions:Rate integral:

Rate integral-derivative:

dtqt

tq oi,o

0

1∫=

[ ] i,oid,o qdtdtq =

Modern PA: Palacio Type Curve (Constant pwf case)Q. Enhancement of the functions on the original Fetkovich type curve?A. "Palacio" type curve uses auxiliary rate functions (better resolution).

Discussion: Modern PA — Palacio Type Curve (Constant pwf case)Auxiliary functions: Rate integral, integral derivative. (smoothness/detail)Rate integral: qo,i = (1/t) Int(qo, 0, t). (time-averaged rate function)Rate integral derivative: qo,id = t |d/dt[qo,i]|. (derivative-like rate function)


Auxiliary functions:Material Balance Time:

Rate integral:

Rate integral-derivative:

tdp

qt

tpq o

i

o⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ i

o

id

op

qtd

dtp

q

dtqt

qt o

o 0

1 ∫=

Discussion: Modern PA — Doublet Type Curve (constant rate eq.)Material Balance Time: tmb = (1/q) Int(qo, 0, t). (material bal. "deconvolution")Auxiliary Functions: Defined using qo and Δp. (accounts for qo and Δp = f(t))Validity: Variable-rate/variable pressure drop cases. (rigorous for pss flow)

Modern PA: Doublet Type Curve (Constant Rate Eq.)Q. Type curve solution for variable-rate/variable pressure case?A. "Doublet" type curve uses material balance time function.


Modern PA: Rate-Cumulative Type CurvesQ. Rate-cumulative type curves ... how can these help?A. "Gross" comparison of rate-cumulative behavior.

Discussion: Modern PA — Rate-Cumulative Type CurvesValue? (probably most value as a screening tool)Pitfalls? (VERY difficult to distinguish individual trends → hyperbolic)Implementation? (recommend use as a validation tool with Arps' analysis)


Modern PA: Normalized PI PlotQ. What is the "Normalized PI" plot (and how is it used)?A. This is pressure transient analysis (PTA) analog analysis plot.

Discussion: Modern PA — Normalized productivity index (PI) plotHow is the Normalized PI plot used? (diagnose characteristic flow regimes)Transient flow behavior? (radial flow, fractured wells, horizontal wells ... )Boundary-dominated flow behavior? (unique "unit-slope" behavior)

Plotting Functions:(Δp/qo)id versus Np/qo:(Pressure Integral-Derivative)

o

pqN

t = tdq

pt

tqp

oio⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ=⎥

⎦

⎤⎢⎣

⎡Δ

ioido qp

tddt

qp

Orientation:(0) IARF → k(1/4) Fin. Con. → FcD(1/2) Inf. Con. → xf(1/2) Horizontal → Lh(1) BDF → N


Modern PA: "Blasingame" PlotQ. What is the "Blasingame" plot (and how is it used)?A. This is the decline curve analysis plot (i.e., modern Fetkovich plot).

Discussion: Modern PA — "Blasingame" plotHow is the "Blasingame" plot used? (diagnose characteristic flow regimes)TF behavior? (fractured wells, horizontal wells ... IARF not unique (k,s tied))BDF behavior? (unique transition from TF, unique "unit-slope" at late times)

Plotting Functions:(qo/Δp)id versus Np/qo:(Rate Integral-Derivative)

o

pqN

t = tdp

qt

tpq o

i

o⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ ∫0

1

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡Δ

=⎥⎦

⎤⎢⎣

⎡Δ i

o

id

op

qtd

dtp

q

Orientation:(?) IARF → k+s(-1/4) Fin. Con. → FcD(-1/2) Inf. Con. → xf(?) Horizontal → ?(-1) BDF → N


∑ −−==

−n

jj,DDcp,Dj,wfi ttqpp

Bkh

.q

11)( )(

21411

μ

∑ −−−==

−−n

jj,DDcr,sDjji ttpqq

khB.pp

111 )( )(2141 μ

Variable-rate case:

Variable pressure drop case:

Approach:Assemble time-pressure-rate (TPR) data.Perform quality control (particularly on pressure data).Establish initial reservoir model using normalized PI/Blasingame plots. Generate: rate data + model → pwf(t); pressure data + model → q(t)Generate: FORECAST of production and/or pressure performance.

Modern PA: Analysis-by-ModellingQ. What is "Analysis-by-Modelling?"A. Interactive (dynamic) analysis using a specified reservoir model.

Discussion: Modern PA — "Analysis-by-ModellingIssues? (superposition is rigorous — q and pwf data must be accurate)Typical case? (pressure data quality is less-than-optimal → interpretation)Unexpected benefit(s)? (modelling validates/disputes q and pwf data quality)

Issues:These superposition relations are rigorous — i.e., for EXACT in-puts, we will obtain EXACT results.The superposition rela-tions must be modified for the gas case — OR, the gas (or multiphase)case(s) can be gen-erated NUMERICALLY.

Constant Rate Solution

Constant Pressure Solution


Modern PA: Analysis-by-Modelling (Oil Case) (1/3)

Discussion: Modern PA — Oil CaseOrigin of data? (DAILY data: rate → surface, pressure → downhole gauge)Likelihood of a successful analysis? (VERY HIGH)Rate decline at late times? (damage, gas-blocking, ?)

Points to Consider:DAILY data (pressure is measured continuous-ly, with a single value reported per day).Rates appear to be ac-curate and well-corre-lated with pressure.



Discussion: Modern PA — "Normalized PI" and "Blasingame" plotsTransient flow data? (Transition regime is apparent, NOT transient flow)Boundary-dominated flow? (very strong agreement — all data functions)Influence of late-time effect? (damage?) (not significant compared to BDF)

a. "Normalized PI" Plot: (Δp/qo) functions versus Np/qo — extraordinary agreement between data and reservoir model.

b. "Blasingame" Plot: (qo/Δp) functions versus Np/qo — excellent data-model performance (note that even derivative function is valid).

Q. Behavior of "normalized PI" and "Blasingame" plots for this case?A. Both plots perform EXTREMELY well → driven by data quality.



Discussion: Modern PA — Final model/data matchRate match? (EXCELLENT — near perfect match until late times)Pressure match? (virtually perfect)Accounting for "damage?" (use PTA, or "cheat" → use variable skin effect)

Q. Performance of final model match? (i.e., rate and pressure functions)A. Extraordinary agreement of model and data — again, data quality ...

Comment:Excellent data quality yields results similar to pressure transient analysis (PTA).This case strong ad-vocates continuous rate and pressure measurement — the data are worth the cost.Downhole pressure measurement must be considered if the eco-nomics support the implementation.There is no substitute for vigilance in data acquisition.


Modern PA: Analysis-by-Modelling (Gas Case) (1/4)

Discussion: Modern PA — Gas CaseOrigin of data? (DAILY data: rate → surface, pressure → surface)Likelihood of a successful analysis? (high to very high, data well-correlated)Integration of PTA data? (designed for production, modelling for shut-ins)

Points to Consider:Using both PA and PTA can yield compliment-ary analyses.Accurate rate and pres-sure data are required.

Q. Analysis-by-modelling for gas cases?A. Same general procedure, must use pseudopressure/pseudotime, or

numerical (or semi-analytical) gas solutions.



Discussion: Modern PA — "Normalized PI" and "Blasingame" plotsTransient flow data? (confirms fractured well behavior, moderate FcD)Boundary-dominated flow?("convergence" (Blasingame plot) confirms BDF)What is required to achieve similar results? (accurate q and pwf data)

a. "Normalized PI" Plot: (Δpp/qg) functions versus Gp/qg — excellent agreement in data and model functions.

b. "Blasingame" Plot: (qg/Δpp) functions versus Gp/qg — excellent agreement — note that the qDd functions converge (confirms BDF).

Q. Behavior of "normalized PI" and "Blasingame" plots for this case?A. Both plots perform EXTREMELY well → driven by data quality.



Discussion: Modern PA — PA model/data matchRate match? (EXCELLENT — near perfect match until late times)Pressure match? (virtually perfect — including shut-ins)Accounting for "damage?" (use PTA, or "cheat" → use variable skin effect)

Q. How well can a gas case be modeled?A. Depends on the data — can be excellent...

Comment:Modelling captures individual shut-ins, for both rate and pressure data.Such performance REQUIRES very accurate rate and pressure data.This case is an ex-ception (low per-meability reservoir permits use of daily data). High per-meability reservoirs require continuous rate and pressure measurements.



Discussion: Modern PA — PTA model/data matchPTA match? (VERY GOOD — note that production pwf data also matched)Comparison of PA and PTA results? (minor differences, due to data quality)etc.? (note that pressure history is matched for PTA (entire history))

Q. Analysis of individual pressure transient tests?A. Should be straightforward — vigilance in data acquisition is required.

Comment:Excellent match on log-log plot (pressure drop funct-ions) and very good match of the entire production pressure history.Daily rate and pressure data are sufficient for this low permeability reservoir case.


Summary: Production Analysis (PA)PA Present:

Strong roots in theory.Very good software tools in the market.Fair to good data acqui-sition practices.

PA Future:Improved data acquisition systems, particularly permanent bottomhole pressure measurement.Integration of analytical/ numerical tools — numeri-cal models may govern the future of production data analysis."Event" analysis (PTA) will fade and "continuous" data analysis will dominate.

"The future looks familiar ... We should be able to perform continuous reservoir monitoring using production analysis (PA). The theory and tools are well-established — the trick is vigilant data acquisition and quality control"

Blasingame

Discussion: Summary — Production Analysis (PA)PA Theory? (variable q/variable pwf analysis methods proven)PA Tools? (software products are robust and easy to use)PA Future? (better data acquisition, numerical models, continuous analysis)


Discussion: Summary — Production Analysis (PA) — IssuesPressure data are critical! (ptf → pwf conversion hard to model/correlate)Consistent rate measurements! (rates frequency/accuracy is an issue)Review the well history! (note that several completion changes can occur)

Summary: Production Analysis (PA) — IssuesQ. Major issues for PA?A. Rate data, pressure data, and well completion history.

Pressure:Measure consistently.Check for relevance (i.e., is the pressure measured in the cor-rect location?).Pressure conversions to bottomhole condi-tions are always ap-proximate (at best).

Flowrates:Daily rates are best (as a practical minimum).Be sure to check rates for accuracy.


Discussion: Summary — Production Analysis (PA) — AnalysisInterpretation of production data should be obvious. (if complex, beware)DATA should provide analysis. (do not impose an analysis)Keep the reservoir/well model simple as possible. (simple = appropriate)

Summary: Production Analysis (PA) — AnalysisQ. Analysis approach for PA?A. Not like PTA — in PA data quality determines "analyzability" of data.

Interpretation:Boundary-dominated flow data should "self-interpret."Transient flow data should also "self-inter-pret" — however, a major issue is the quantity (i.e., frequen-cy) of transient flow data.

Modelling:Simple is always best.Do not use approxi-mations in modelling (if at all possible).


Discussion: Summary — Production Analysis (PA) — PressuresReality: All pressure data are suspect. (scrutinize ALL pressure data)Fantasy: Pressure at bottomhole conditions. (ptf → pwf conversion issue)Future: pwf (bottomhole measurements) common. (rate becomes issue)

Summary: Production Analysis (PA) — PressuresQ. Pitfalls of pressure data as these relate to PA?A. Put simply – pressure data (quality/quantity) remain weakest link.

Due Diligence:Correlate pwf versus q — this should give some indication of "correlation."No correlation ≈ no analysis/interpretation.

Advice:Pressure is the weak link — but ... try to perform an analysis regardless, at least validate that pressure data are relevant or not.Reconstruct a pwf(t)profile by any reason-able means.


Discussion: Summary — Production Analysis (PA) — FlowratesReality: Rates are generally better than pressures. (allocations are an issue)Fantasy: Rates measured at high frequency. (rate-pressure mismatch)Future: Downhole flowrate measurement. (continuous monitoring/analysis)

Summary: Production Analysis (PA) — FlowratesQ. Pitfalls of flowrate data as these relate to PA?A. Flowrate data — beware of allocations/frequency of measurements.

Due Diligence:Allocated flowrates always have issues.

Advice:Flowrate data are generally better than pressure data — you should be able to obtain an analysis.


Current Assessment: Production Analysis (PA)

"Technology ... is a queer thing. It brings you great gifts in one hand, and it stabs you in the back with the other."

C.P. Snow (1905-1980)

Discussion: Current Assessment — Production Analysis (PA)Analysis? (Very good tools for PA and PTA (incremental improvements))Modelling? (Analytical modelling is sufficient, numerical modelling evolving)Data Issues? (Improvement in data handling (good/bad data, large volumes))Data Acquisition? (Lack of innovation in testing/monitoring methodologies)Integration? (Breakthrough to integrate PA/PTA results with other data)


Challenges:Technical — data acquisition/management.Operational— "reservoir management" (use of the data).

Current Assessment: PA Reality Check—

From

: Sim

ulat

or P

aram

eter

Ass

ignm

ent a

nd th

e Pr

oble

m

of S

calin

g in

Res

ervo

ir En

gine

erin

g—

Hal

ders

on (1

986)

.

Q. What is the "reality check" with regard to PA?A. It is just time-pressure-rate data, do not expect a miracle.

Discussion: Current Assessment — PA Reality CheckReservoir scale issues? (petrophysical data, PTA, PA, seismic data, etc.)Results from PTA/PA? ("reservoir-scale" flow character)Key to success? (high precision/frequency reservoir performance data)

Reservoir Engineering Model●Works 95+ percent of the time...●Why? Pressure and volume

averaging of reservoir properties.●When does it not work? High

contrast in reservoir properties.

Actual Reservoir Model●Complex geology.●Complex fluid behavior.●Poor lateral (and vertical) continuity.


— From: Simulator Parameter Assignment andthe Problem of Scaling in ReservoirEngineering — Halderson (1986).

— From: How Heterogeneity AffectsOil Recovery — Weber (1986).

— Crossplot: ko (PA and PTA) vs. klog mean— Santa Barbara Field (Venezuela)..

Discussion: Current Assessment — Future Work in PTA/PAAdditional reservoir/well models. (elliptical flow, moving boundary, ...)Full incorporation of PVT character. (volatile oil, gas condensate, ...)Reservoir scaling for PTA/PA. (scaling of petrophysical data?)Handling poor quality rate/pressure data. (major issue at present)Continuously measured pwf data. (this is coming ... high frequency rates?)Multiple well analysis (integration). (analytical (material balance) or models)Coupling of analysis/interpretation (3D/3P models). (over-determined case)

Current Assessment: Future Work in PTA/PAQ. What are the prospects for PTA/PA?A. Most important issue is data quality/frequency → characterization.



Performance-Based Reservoir Characterization –State-of-the-TechnologyEnd of Presentation

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

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected] materials located at:

link → http://pumpjack.tamu.edu/~t-blasingame/folder → z_SPE_DL


SPE DISTINGUISHED LECTURER SERIESis funded principally

through a grant of the

SPE FOUNDATIONThe Society gratefully acknowledges

those companies that support the programby allowing their professionals

to participate as Lecturers.

And special thanks to The American Institute of Mining, Metallurgical,and Petroleum Engineers (AIME) for their contribution to the program.



Selected References: Production Data Analysis

(Appendix)

References — Production Data Analysis:1. Lewis, J.O., and Beal, C.H.: "Some New Methods for Estimating the Future Production of Oil Wells," Trans. AIME (1918) 59, 492-525.2. Manual for The Oil and Gas Industry Under The Revenue Act of 1918, Treasury Department — United States Internal Revenue Service (1919).3. Cutler, W.W., Jr.: Estimation of Underground Oil Reserves by Oil-Well Production Curves, Department of the Interior, U.S. Bureau Of Mines Bulletin 228 (1924).4. Roeser, H.M.: "Determining the Constants of Oil-Production Decline Curves," Trans AIME (1925) 71, 1315-1321.5. Larkey, C.S.: "Mathematical Determination of Production Decline Curves," Trans AIME (1925) 71, 1322-23.6. Johnson, R.H. and Bollens, A.L.: "The Loss Ratio Method of Extrapolating Oil Well Decline Curves," Trans. AIME (1927) 77, 771.7. Lindsly, B.E., and Berwald, W.B.: Effect of Vacuum on Oil Wells, U.S. Department of Commerce, Bureau of Mines, Bulletin 322 (1930).8. Allen, R.E.: "Control of California Oil Curtailment," Trans AIME (1931) 92, 47-66.9. Rawlins, E. L. and M. A. Schellhardt: Backpressure Data on Natural Gas Wells and Their Application To Production Practices, Monograph 7, U.S. Bureau of Mines, Washington, DC, (1936).

10. Arps J.J.: "Analysis of Decline Curves," Trans. AIME (1945) 160, 228-247. 11. Gurley, J.: "A Productivity and Economic Projection Method — Ohio Clinton Sand Gas Wells," JPT (Nov. 1963) 1183-1188.12. Slider, H.C.: "A Simplified Method of Hyperbolic Decline Curve Analysis," JPT (Mar. 1968) 235-236.13. Stewart, P.R.: "Low-Permeability Gas Well Performance at Constant Pressure," JPT (Sept. 1970) 1149-1156.14. Gentry, R.W.: "Decline-Curve Analysis," JPT (Jan. 1972) 38-41.15. Gringarten, A.C.: "Reservoir Limits Testing for Fractured Wells," paper SPE 7452 presented at the 1978 SPE Annual Technical Conference and Exhibition, Houston, TX., 1-3 October 1978.16. Fetkovich, M.J.: "Decline Curve Analysis Using Type Curves," JPT (March 1980) 1065-1077. 17. Nind, T.E.W.: Principles of Oil Well Production, McGraw-Hill Book Company, 2nd Ed., 1981, 31-44. 18. Carter, R.D.: "Type Curves for Finite Radial and linear Gas Flow Systems: Constant Terminal Pressure Case," SPEJ (October 1985) 719-728.19. Fraim, M.L., Lee, W.J., and Gatens, J.M., III: "Advanced Decline Curve Analysis Using Normalized-Time and Type Curves for Vertically Fractured Wells," paper SPE 15524 presented at the 1986

SPE Annual Technical Conference and Exhibition, New Orleans, LA, 05-08 October 1986.20. Fetkovich, M.J., Vienot, M.E., Bradley and M.D., Kiesow, U.G.: "Decline Curve Analysis Using Type Curves – Case Histories," SPEFE (Dec. 1987) 637-656.21. McCray, T.L.: Reservoir Analysis Using Production Decline Data and Adjusted Time, M.S. Thesis, Texas A&M U., College Station, TX (1990).22. Palacio, J.C. and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves — Analysis of Gas Well Production Data," paper SPE 25909 presented at the 1993 Joint Rocky Mountain

Regional/Low Permeability Reservoirs Symposium, Denver, CO, 26-28 April 1993.23. Doublet, L.E., Pande, P.K., McCollum, T.J., and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves — Analysis of Oil Well Production Data Using Material Balance Time: Application

to Field Cases," paper SPE 28688 presented at the 1994 Petroleum Conference and Exhibition of Mexico held in Veracruz, Mexico, 10-13 October 1994.24. Shih, M.-Y. and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves: Horizontal Wells," paper SPE 29572 presented at the 1995 Joint Rocky Mountain Regional/Low Permeability

Reservoirs Symposium, Denver, CO, 20-22 March, 1995.25. Doublet, L.E. and Blasingame, T.A.: "Evaluation of Injection Well Performance Using Decline Type Curves," paper SPE 35205 presented at the 1996 SPE Permian Basin Oil and Gas Recovery

Conference, Midland, TX, 27-29 March 1996.26. Crafton, J. W.: "Oil and Gas Well Evaluation Using the Reciprocal Productivity Index Method," paper SPE 37409 presented at the 1997 SPE Production Operations Symposium, held in Oklahoma

City, Oklahoma, 09-11 March 1997.27. Agarwal, R.G., Gardner, D.C., Kleinsteiber, S.W., and Fussell, D.D.: "Analyzing Well Production Data Using Combined Type Curve and Decline Curve Analysis Concepts," paper SPE 49222

prepared for presentation at the 1998 SPE ATCE, New Orleans, LA, 27-30 September 1998.28. Marhaendrajana, T. and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves — Evaluation of Well Performance Behavior in a Multiwell Reservoir System," paper SPE 71514 presented

at the 2001 Annual SPE Technical Conference and Exhibition, New Orleans, 30 September-03 October 2001.29. Araya, A. and Ozkan, E.: "An Account of Decline-Type-Curve Analysis of Vertical, Fractured, and Horizontal Well Production Data," paper SPE 77690 presented at the SPE Annual Technical

Conference and Exhibition held in San Antonio, Texas, 29 September-02 October 2002.30. Pratikno, H., Rushing, J.A., and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves: Fractured Wells," paper SPE 84287 presented at the 2003 Annual SPE Technical Conference and

Exhibition, Denver, CO., 05-08 October 2003.31. Mattar, L. and Anderson, D.: "A Systematic and Comprehensive Methodology for Advanced Analysis of Production Data," paper SPE 84472 presented at the SPE Annual Technical Conference

and Exhibition held in Denver, Colorado, U.S.A., 05-08 October 2003.32. Anderson, D. and Mattar, L.: "Practical Diagnostics Using Production Data and Flowing Pressures," paper SPE 89939 presented at the SPE Annual Technical Conference and Exhibition held in

Houston, Texas, U.S.A., 26-29 September 2004.33. Fuentes-Cruz, G., Camacho-Velázquez, R., and Vásquez-Cruz, M. : "Pressure Transient and Decline Curve Behaviors for Partially Penetrating Wells Completed in Naturally Fractured-Vuggy

Reservoirs, paper SPE 92116 presented at the 2004 SPE International Petroleum Conference in Mexico, Puebla, Mexico, 08-09 November 2004.


Selected Vendors: PA Software

(Appendix)

Vendor A: FeketeProduct: RTAContact: Ed Ferguson ([email protected])web: www.fekete.com

Vendor B: Kappa EngineeringProduct: TopazeContact: Kevin Siggery ([email protected])web: www.kappaeng.com

Vendor C: Weatherford/eProduction SolutionsProduct: PanSystemContact: Carol Marini ([email protected])web: www.ep-solutions.com


Simple Rules for Life:Righty-tighty — lefty-loosey solves most problems in life.You can learn a lot from a Chihuahua (no fear, all love).Don't mow the grass until the city tells you to.Leadership is not defined by vision, strength, integrity, or courage — JUST PASSION.If you have to herd cats, then be a rat.If you have to hold yourself out as an example, then make sure to be a bad one (Mark Twain).

Important Rules for Life:Always work harder than those you work for.Never own anything that eats while you sleep.Never own anything that needs repainting.

Rules for Life: Blasingame

"An empty stomach is not a good political advisor — moral — know your convictions, but take care of yourself as well"

Mahatma Gandhi (+ Blasingame)

(Appendix)


Mathematics:(for reservoir engineering)

1.Cheat (approximate, trun-cate, etc.). (except for material balance)

2.Take the Derivative.3.Take the Integral.4.Take the Laplace Transform.5.Go back to Rule 1 (Cheat).

Favorite Numbers: 0, 1, ∞.

(What else do we need?)

Rules for Mathematics: Blasingame

(Appendix)

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