Petroleum Engineering 613
Natural Gas Engineering
Texas A&M University
Lecture 08:
Well Testing —
Historical Perspectives
T.A. Blasingame, Texas A&M U.
Department of Petroleum Engineering
Texas A&M University
College Station, TX 77843-3116
+1.979.845.2292 — t-blasingame@tamu.edu
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 1
Well Testing — Historical Perspectives
Origin of the "Deliverability" (or Backpressure) Relation
 Empirical.
 Used to assess "open flow" potential of gas wells.
 Does not provide a "time-dependent" behavior.
Multi-Rate Testing
 Historically, VERY popular — still used quite often,
especially on new wells to estimate deliverability and
"non-Darcy" flow effects.
 Keep it simple — a "4-point" test is appropriate.
 Isochronal testing is very difficult to implement.
Pressure Transient Analysis
 Expected Results: Pressure Transient Analysis (PTA).
 Example Data Sets: PTA and Production data.
 Basic Plots: Lee Text Example 2.2 (Pressure Buildup).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 2
Origin of the "Deliverability" Relation
Well Testing — Historical Perspectives
Origin of the "Deliverability"
(or Backpressure) Relation
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 3
History of the "Deliverability" Equation
Gas Well Deliverability:
 The original well deliverability
relation was completely empirical (derived from observations),
and is given as:
qg  C( p2  p2 )n
wf
 This relationship is rigorous (i.e.,
it can be derived) for low pressure gas reservoirs, (n=1 for laminar flow).
 From: Back-Pressure Data on NaturalGas Wells and Their Application to
Production Practices — Rawlins and
Schellhardt (USBM Monograph, 1935).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 4
Multi-Rate Testing
Well Testing — Historical Perspectives
Multi-Rate Testing
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 5
Deliverability Testing: Basics
a. "Standard" 4-point test deliverability test — note
that the rates increase (to protect the reservoir).
c. Modified "Isochronal" test sequence — note that
each "buildup" is not required to achieve pi.
b. "Isochronal" test sequence — note that each
"buildup" is required to achieve pi.
d. Governing equations for "deliverability" test
analysis/interpretation.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 6
Deliverability Testing: Orientation
a. Basic "pressure-squared" relation
that is presumed to describe gas
flow — analogous form can be
derived from steady-state flow theory
(Darcy's law).
PETE 613
(2005A)
b.Traditional "deliverability" plot —
probably derived from empirical
plotting of data.
Well Testing —
Historical Perspectives
Slide — 7
Deliverability Testing: Orientation
a."Rate-squared" (or velocitysquared) formulation — analogous
form can be derived from steadystate flow theory (Forchheimer
Eq.).
PETE 613
(2005A)
b. Modified "deliverability" plot —
note that bqsc2 must be known (...
need alternative approach).
Well Testing —
Historical Perspectives
Slide — 8
Origin of the "Deliverability" Relation
Well Testing — Historical Perspectives
Expected Results:
Pressure Transient Analysis (PTA)
Production Analysis (PA)
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 9
Expected Results from PTA
 Expected Results of Pressure Transient Analysis (PTA):
— "Conventional" PTA: Use of semilog and other specialized plots to
estimate reservoir properties from a particular "flow regime" (i.e., a flow
regime is a characteristic behavior derived from an analytical solution —
e.g., the constant pressure derivative function for infinite-acting radial
flow (IARF)). Examples of other specialized plots: square-root and fourthroot of time plots for fractured wells.
— "Model-based" analyses: Using analytical/numerical reservoir models to
perform simultaneous analysis/modelling procedures. Provides estimates
of dynamic formation properties: (i.e., model parameters)
 Radial Flow: k, S, CD
 Fractured Wells: k, xf, FCD, CfD
 Horizontal Wells: kr, kr/kv, hwell, (effective length) zw (position), ChD
 Dual porosity reservoir properties: w, l
 Data Requirements/Assessment/Review:
— Typically involves very accurate measurements of bottomhole pressures
(this is a priority).
— Rate history is most often the weakest link — must perform "due
diligence" and obtain the best possible rate history.
— Should use downhole shut-in device to minimize wellbore storage.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 10
Expected Results from PA
 Expected Results of Production Analysis (PA):
— "Conventional" decline curve analysis: (Arps, etc.) — empirical relations
used to provide estimates of recovery and forecasts of future
performance.
— "Model-based" analyses: Using analytical/numerical reservoir models to
perform simultaneous analysis/modelling procedures. Provides
estimates of dynamic formation properties (k, S, xf, dual porosity
properties, etc.)
— "Model-based" forecasting: A direct extension of model-based analysis
— generation of a time-dependent pressure and/or rate forecast.
 Data Requirements/Assessment/Review:
— Are production data available?
(BOTH rates and PRESSURES!)
— Is the well completion history available?
(review for issues)
— PVT and static reservoir properties?
(must be assessed/included)
— Is the production "analyzable?"
(can major issues be resolved?)
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 11
PTA and PA Data Quality and Data Artifacts
Well Testing — Historical Perspectives
Reservoir Performance Analysis:
PTA and PA Data Quality and Data Artifacts
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 12
Production Data: Example 1
Sewell Ranch Well No. 1 — Barnett Field (NorthTexas)
2000
Gas Flowrate
Wellbore Pressure
1800
1600
1.E+03
1400
1200
1.E+02
1000
800
600
1.E+01
Surface Pressure, psig
Gas Production Rate, MSCFD
1.E+04
400
200
1.E+00
0
500
0
1000 1500 2000 2500 3000 3500 4000
Producing Time, days
 Production Example 1: Sewell Ranch No. 1 (North Texas (US))
 Rate and pressure data affected by water loading.
 Late-time data affected by line pressure (other wells in flow system).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 13
Production Data: Example 2
UPR22 Gas Well — Mid-Continent (US)
2000
Gas Flowrate
Wellbore Pressure
1800
1600
1.E+03
1400
1200
1.E+02
1000
800
600
1.E+01
Calculated BHP, psia
Gas Production Rate, MSCFD
1.E+04
400
200
1.E+00
0
250
500
750
1000
1250
0
1500
Producing Time, days
 Production Example 2: UPR22 Gas Well (Mid-Continent (US))
 Rate and pressure data affected by fluid loading.
 Seasonal cycles in demand/production.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 14
Pressure Transient Data: Example 1
Bourdet Example (SPE 12777) (Dt Format)
Bourdet Example (SPE 12777) (Dt e Format)
1.E+04
1.E+04
Pressure Drop
Pressure Drop Derivative
Pressure Drop
Pressure Drop Derivative
1.E+03
D p and D p' , psi
D p and D p' , psi
1.E+03
1.E+02
1.E+01
1.E+00
1.E-03
1.E+02
1.E+01
1.E-02
1.E-01
1.E+00
Dt , hr
1.E+01
1.E+02
1.E+00
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
Dt e , hr
a. No Rate History: (Dt format) Pressure drop and
pressure drop derivative versus shut-in time
(Bourdet (SPE 12777)).
b.Rate History: (Dte format) Pressure drop and
pressure drop derivative versus Agarwal
superposition time (Bourdet (SPE 12777)).
 Pressure Transient Example 1: Bourdet (SPE 12777)
 Production history effects are obvious.
 Interpretation should consider "no rate" and "rate" history cases.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 15
Pressure Transient Data: Example 2
DaPrat Example (Well Mach 3X, SPE 13054) (Dt Format)
1.E+04
D p and D p' , psi
1.E+03
1.E+02
1.E+01
1.E+00
1.E-02
Pressure Drop
Pressure Drop Derivative (L=0.2)
Pressure Drop Derivative (L=0.3)
Pressure Drop Derivative (L=0.4)
Simulated Pressure Drop
Simulated Pressure Drop Derivative
1.E-01
1.E+00
1.E+01
Dt , hr
1.E+02
1.E+03
 Pressure Transient Example 2: DaPrat (SPE 13054)
 Dual porosity/naturally fractured reservoir (PSS interporosity flow).
 Illustrates the sensitivity of the pressure derivative function.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 16
Data Artifacts: Example 1
Womack Hill Well No. 1633 — Womack Hill Field (Alabama)
1800
Conversion to
Jet Pump
Acid
Stimulation
Recompletion
Initial
Depletion
(no pressure
support )
1.E+03
Oil Flowrate
Wellbore Pressure
1600
1400
1200
1000
800
1.E+02
600
400
p wf assumed constant
200
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
1.E+01
Estimated BHFP Pressure, psia
2000
Prorated
Production
Oil Production Rate, STBD
1.E+04
Producing Time, days
 Data Artifacts Example 1: Womack Hill Field (Alabama (US))
 Note the various events (value of annotated production records).
 No pressure data (typical).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 17
Data Artifacts: Example 2
Well Told 3 — Colombia (South America)
1.E+04
2500
2000
1750
1500
1.E+03
1250
1000
750
500
Est. BHF Pressure, psia
p wf not synchronous
with rate profile
2250
Pump
Change
Oil Production Rate, STBD
Oil Flowrate
Wellbore Pressure
250
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0
1.E+02
Producing Time, days
 Data Artifacts Example 2: Told Well 3 (Colombia)
 pwf NOT synchronous with qo (pwf from fluid levels).
 Note that effect of pump change is captured by pwf and qo.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 18
Data Artifacts: Example 3
Gas Well (Poor Early Time Data) — (Canada)
3500
Gas Flowrate
Wellbore Pressure
2500
2000
1500
1.E+03
p wf variations not
1000
synchronized with q g
Calc. BHF Pressure, psia
3000
1.E+04
qo and pwf
increasing
Gas Production Rate, MSCFD
1.E+05
500
600
550
500
450
400
350
300
250
200
150
100
50
0
0
1.E+02
Producing Time, days
 Data Artifacts Example 3: Canada Gas Well
 pwf NOT synchronous with qg at early/intermediate times.
 Dispersion in pwf at middle times not reflected in the qg function.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 19
Data Artifacts: Example 4
Gas Well with Evolving Condensate — (Southeast TX (US))
7000
Flow up Annulus
Gas Production Rate, MSCFD
Gas Flowrate
Wellbore Pressure
Flow up Casing
1.E+04
6500
6000
5500
5000
4500
4000
Flow up Tubing
3500
3000
2500
1.E+03
2000
1500
1000
500
600
550
500
450
400
350
300
250
200
150
100
50
0
0
1.E+02
Surface Pressure, psig
1.E+05
Producing Time, days
 Data Artifacts Example 4: Southeast TX Gas Well (US)
 Multiple completion changes.
 Issues related to pressure profile — measure bottomhole pressure?
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 20
Data Artifacts: Example 5
Sanger Gas Well Case (South Texas (US))
Sanger Gas Well Case (South Texas (US))
5000
Pressure
1.E+04
4500
Pressure Drop
Pressure Drop Derivative
4000
D p and D p' , psi
pwf , psia
3500
3000
2500
2000
1500
1.E+03
1.E+02
1.E+01
1000
500
0
1.E-03
1.E+00
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E-02
1.E+03
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Dt , hr
Dt , hr
a. Semilog Plot: (Dt format) Pressure versus shutin time (South Texas Gas Well (US)) — Packer
leak (most likely cause).
b.Log-log Plot: (Dt format) Pressure drop and
pressure drop derivative versus shut-in time
time (South Texas Gas Well (US)) — Packer
leak (most likely cause).
 Data Artifacts Example 5: South Texas Gas Well (US)
 Gas well with anomalous pressure "jump" — packer leak?
 No "reservoir" mechanism (other than injection) could produce feature.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 21
Data Artifacts: Example 6
Dunn Prefracture Pressure Buildup (Condensate Banking)
(Mid-Continent (US))
Pseudopressure Drop, D pp and D pp' , psi
1.E+04
Pressure Drop
Pressure Drop Derivative
1.E+03
1.E+02
1.E+01
1.E+00
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
Shut-In Pseudotime, Dt a , hr
 Data Artifacts Example 6: Mid-Continent Gas Well (US)
 Changing wellbore storage and condensate banking (very high skin).
 Interpretation depends on understanding of reservoir and fluids.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 22
Well Test Analysis — Basic Plots
Well Testing — Historical Perspectives
Well Test Analysis — Basic Plots
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 23
Well Test Analysis: Basic Plots (Lee Text Example)
a. Log-log "preliminary analysis"
plot — wellbore storage and
radial flow (Cs, k).
b. Cartesian "early-time" plot —
used to analyze wellbore
storage (p0, Cs).
c. Cartesian "Arps" plot — used
to estimate average reservoir
pressure.
d. Semilog "middle-time" plot —
used to analyze radial flow
behavior (k, s).
e. Horner "middle-time" plot —
used to analyze radial flow
behavior (k, s, p*).
f. Log-log "summary" plot —
summary of all analysis (Cs, k,
s, A, etc).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 24
Basic Plots: "Preliminary" Log-log Plot
 Basic Plots: "Preliminary" Log-Log Plot
 Pressure drop function does not give much resolution.
 Pressure drop derivative function shows wellbore storage/radial flow.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 25
Basic Plots: Early Cartesian Plot
 Basic Plots: Early Cartesian Plot
 Used to estimate wellbore storage coefficient (slope of trend).
 Pressure at start of the test estimated from extrapolation.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 26
Basic Plots: Late Cartesian Plot (PBU)
 Basic Plots: Late Cartesian Plot (Pressure Buildup)
 NOT a universally valid plot (ONLY valid for very late times).
 Average reservoir pressure estimated from extrapolation.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 27
Basic Plots: Semilog Plot (MDH)
 Basic Plots: Semilog Plot (Miller-Dyes-Hutchinson)
 NOT corrected for rate history.
 Can be difficult to interpret (semilog straight line needs orientation).
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 28
Basic Plots: Horner Semilog Plot
 Basic Plots: Horner Semilog Plot
 CORRECTED for rate history.
 Used to estimate permeability, skin factor, average reservoir pressure.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 29
Basic Plots: "Summary" Log-log Plot
 Basic Plots: "Summary" Log-Log Plot
 Used to show simulated reservoir response (based on analysis).
 Multiple data functions used to orient analysis/interpretation.
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 30
Module 4: Well Test Analysis — Work Relations
 Given data — Lee text (1st edition),
Example 2.2.
PETE 613
(2005A)
 Working relations — Lee text (1st
edition), Example 2.2).
Well Testing —
Historical Perspectives
Slide — 31
Petroleum Engineering 613
Natural Gas Engineering
Texas A&M University
Lecture 08:
Well Testing —
Historical Perspectives
(End of Lecture)
T.A. Blasingame, Texas A&M U.
Department of Petroleum Engineering
Texas A&M University
College Station, TX 77843-3116
+1.979.845.2292 — t-blasingame@tamu.edu
PETE 613
(2005A)
Well Testing —
Historical Perspectives
Slide — 32