Everything You Always Wanted to Know About Well Test Analysis but Were Afraid to Ask

Everything you always wanted to know about well test analysis but were afraid to ask

Alain C. Gringarten Imperial College London Content

• WTA: what, why, how

• Challenges

• Milestones

• Other applications

• Conclusion: a very powerful tool - use it or lose it

2/44 What is well test analysis (WTA)? • It is the extraction of information from pressure and rate data measured in a producing well

10000 6000 q BUILD UP 9000 PIPELINE 8000 ) 5000 7000

6000 (psia) (STB/D p WELL 4000 5000 q 4000

DRAWDOWN 3000 Pressure Pressure 3000 Rate Oil RESERVOIR 2000 1000

p 2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Time from the start of production (hrs)

3/44 Pressure History Why do we do well test analysis?

• To obtain information on the well • Permeability • Well damage or stimulation (skin effect)

• To obtain information on the reservoir • Fluid • Average reservoir pressure • Reservoir heterogeneities • Reservoir hydraulic connectivity • Distances to boundaries 4/44 How do we do well test analysis?

• We select a period at constant rate (usually, a build up)

6000 10000 FP4 FP76 8000 5000

6000

4000

3000 2000 Pressure (psia) Oil Rate (STB/D)

2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Time from the start of production (hrs) • We plot some function of pressure vs. some function of time • We try to identify flow regimes (radial, linear, spherical,…) • We include these flow regimes into an interpretation model which can reproduce the pressure given the rate (or vice-versa) • We verify that the interpretation model is consistent with all other information (geology, seismic, cores, logs, completion, etc…). 5/44 WTA: the Good

• WTA allows to assess well condition and to estimate reservoir parameters

• Over the last 50 years, new WTA techniques have been developed which give more and better results, and more confidence in those results

• Nowadays, WTA potential contribution to reservoir knowledge has never been greater

• Only WTA provides reservoir hydraulic connectivity

• Well test analysis is the technique of choice in arbitrations

6/44 WTA: the Bad • Interest and knowledge in WTA seems to be fading • One reason may be that the latest new techniques (deconvolution) are perceived as too complex • This fear of complexity is compounded by WTA being often taught, wrongly, as “basic” and “advanced” which is mistaken for “practical (for everybody)” and “esoteric (for experts only)” • Reservoir engineers tend to believe they know how to interpret well tests as a side benefit of knowing how to do simulation • The Big Crew Change: WTA experts educated by Ramey at Texas A&M and Stanford, or trained in Flopetrol/Schlumberger during the heyday of WTA have retired or are about to retire, with no systematic replacements 7/44 WTA: the Ugly • Buttonology instead of domain expertise: engineers often believe software will do the interpretation for them

• Resistance to changes: commercial software vendors are often forced by their clients to include techniques which are obsolete or have been proven wrong over 40 years ago

• Pressure from operators: Regular well testing is no longer mandatory in many oil provinces

• Short term focus: In Unconventionals, data acquisition in general (and well testing) is considered unnecessary cost

• Economic constraints: Formal WTA teams have disappeared

in many oil companies following the latest oil price drop 8/44 The challenge

“Partially, we (the experts) are to be blamed for the decline of the importance of testing.

The SPE testing literature is so much polluted that it is difficult to find relevant papers.

Many interpretations (80%) even in published papers are incorrect.

And MDT has replaced the Testing fluid sampling.”

Expert in WTA, personal communication 9/44 The challenge

“The picture actually looks very gloomy. It is not because inexperienced hands ask the same questions about the same old problems as 30 years ago, but because they get the same answers as 30 years ago, even though our industry has advanced tremendously and gotten much better answers and solutions, but this knowledge that resides in repositories and in the heads of the experienced and knowledgeable older experts is not being transmitted effectively.”

The Big Crew Change: Knowledge Loss or Management of Change? Robert Mathes http://oilpro.com/post/22284/big-crew-change-knowledge-loss-management-change 10/44 Publication inflation

800 1960 2012 Well Test papers SPE 700 Well Test papers OnePetro 600 Rig Count U.S./20 500 Rig Count Total World/40 Oil price, 2015 $ /Bbl 400

300 1972 200

100 Number of publications “welltesting” with publications of Number 0 1927 1941 1968 1995 2023 1954 1982 2009

11/44 Publication inflation & WTA undersold

104 PowerPoint 47002012 (13 years) Word SPE membership/25 103 265 (9 months) 400 (13 months)

SPE membership/50 102 WT/Total SPE (19%) SPE Total 10%30 (1 month)

Number of publications of Number 10 7% DL % WTA (~7%)

SPE Well Test 1 1941 1995 1954 1927 1982 1968 2009 2023

12/44 Well test interpretation milestones

1960 Interpretation methods Hardware/Completion Mathematical tools DEVELOPERS GROUNDWATER IOC UNIVERSITIES SERVICE ??????? UNIVERSITIES Straight Type Derivatives Single well lines Curve Deconvolution Analysis IKVF Electronic Horizontal Multiple-fraced Multiwell gauges wells horizontal wells Deconvolution MHF MDT Permanent gauges Laplace transform Stehfest Green’s functions 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2005 2015

http://www.spe.org/industry/history/oral_archives.php 13/44 Straight line methods

IOC Shell, Horner Analysis - Flow Period 4 Gulf Oil Corp, 5100 ARCO… 5000

Straight 4900

Line 4800 p*= 5000 psia Methods 4700

4600 k = 485mD Horner 4500 S = 102 MDH MBH Pressure (psia) 4400

4300 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 Superposition Function (STB/D) 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2005 2015 Year

Horner, D. R.: "Pressure Build-ups in Wells", Proc., Third World Pet. Cong., E. J. Brill, Leiden (1951) II, 503-521. 14/44 Straight line methods

IOC Shell, Horner Analysis - Flow Period 76 Gulf Oil Corp, 5100 ARCO… 5000

Straight 4900

Line 4800 FP 4 Methods 4700

Horner 4600 p*= 4953 psia p*= 5000 psia

4500 MDH MBH Pressure (psia) k = 1060 mD k = 485 mD 4400 S = 232 S = 102 4300 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 Superposition Function (STB/D) 15 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2005 2015 Year

15/44 Log-log pressure analysis

GROUNDWATER IOC UNIVERSITIES Theis (1935) , Shell, Texas A&M, Stanford Jacob (1947), Gulf Oil Corp, Henry J. Ramey, et al. Hantush (>1947) ARCO… 5100 8000 Straight Type 5000 7000 Line Curve 4900 6000 Dp 5000 Methods Analysis 4800 4000 4700 Horner 3000 4600 Dt 2000 Pressure Pressure (psia) FP3 FP4 (STB/D) Rate Oil MDH MBH 4500 1000

4400 0 25 26 27 28 Production time (hrs) 19 years 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2005 2015 Year

Ramey, H. J., Jr.: "Short-Time Well Test Data Interpretation in The Presence of Skin Effect and Wellbore Storage," J. Pet. Tech. ( Jan., 1970) 97. 16/44 Pressure log-log plot

1000 FP4 p(psi) D FP76

100

INTERPRETATION MODEL Radial flow ?

10 Wellbore storage and Skin Homogeneous behaviour Infinite reservoir

1 0.0001 0.001 0.01 0.1 1 10 100 1000

Elapsed time Dt (hrs) Rate NormalisedChangeRate Pressure

17/44 Wellbore storage and skin type curves

104 2 D

10 50 500 250 100 3 5,000 2,500 1,000 25,000 10,000 50,000 500,000 250,000 100,000 cp ft cp md ft psi ft md

103 , C 10 m kh / kh 5.6146 5.6146 t, MINUTES t, ‘’’’’’’’’’’’’’’’’’ D 102

10-1

SHUT-IN TIME,SHUT-IN 10 Dimensionless Pressure,Dimensionless p H. J. Ramey, Jr (1970)

-2 McKinley (Exxon) 1971 10 102 103 104 105 106 107 108 1 10-4 10-3 10-2 10-1 1 10 102 5.6146 Dp C ft3 day Dimensionless time, t PRESSURE BUILDUP GROUP , D qB RBbl

1 qB 24C p t -1 D Same interpretation model D 10 = D D t C D p Different type curves Earlougher and Kersch (Marathon) 1974 10-2 Different results 103 104 105 106 1 t kh Dt md.ft hr D = , . 0.000295 CD m C cp bbl/psi Type curve analysis

GROUNDWATER IOC UNIVERSITIES SERVICE Theis (1935) , Shell, Texas A&M, Stanford Flopetrol Jacob (1947), Gulf Oil Corp, Henry J. Ramey, et al. Schlumberger Hantush (>1947) ARCO…

Straight Type TC with Line Curve Independent Methods Analysis parameters 102 2S

D C e Approximate start of semi-log radial flow D10 30 Horner p 1015

106

10 103 102 MDH MBH 5 1 Approximate 0.5 end of 10-1 10-2

wellbore 10-3 storage 1

19 years 9 years 1979

Dimensionless Dimensionless pressure, 10-1 10-1 1 10 102 103 104 105

Dimensionless time, tD /CD 1935 1940 1945 1950 1955 1960 1965 1970 1975 1979 1985 1990 2010 1995 2000 2005 2015 Year

19/44 SPE 8205, Gringarten, A. C. et al.: "A Comparison between Different Skin and Wellbore Storage Type-Curves for Early-Time Transient Analysis” Pressure type curve matching

Elapsed time Dt (hrs) 102 10-3 10-2 10-1 1 10 102 103 103 p(psi) Approximate start of semi-log radial flow 10103030 D D

p FP4 FP76 1015

106 10 103 102 102 5 Approximate 1 0.5 end of 10-1 wellbore 10-2 storage 10-3 2S 1 CD e 10 k = 175 mD C = 0.01 Bbl/psi Dimensionless Dimensionlesspressure, S = 32 ? -1 10 1 10-1 1 10 102 103 104 105

Dimensionless time, tD /CD NormalisedChangeRate Pressure

20/44 Methodology (workflow)

GROUNDWATER IOC UNIVERSITIES SERVICE Theis (1935) , Shell, Texas A&M, Stanford Flopetrol Jacob (1947), Gulf Oil Corp, Henry J. Ramey, et al. Schlumberger Hantush (>1947) ARCO…

Straight Type Methodology Line Curve Methods Analysis TC with Horner Independent parameters MDH MBH

19 years 11 years 1935 1940 1945 1950 1955 1960 1965 1970 1975 1981 1985 1990 2010 1995 2000 2005 2015 Year

21/44 Methodology (workflow)

IDENTIFICATION VERIFICATION

DATA

EARLY TIMES MIDDLE TIMES LATE TIMES

Wellbore Storage Homogeneous Specified Rate NO Skin Fractures Heterogeneous Specified Pressure COMPARE CONSISTENT? Partial Penetration -2-Porosity WITH -2-Permeability Horizontal Well Leaky Boundary DATA -Composite YES

CONSISTENT NEAR WELLBORE RESERVOIR BOUNDARY WELL TEST EFFECTS BEHAVIOUR EFFECTS INTERPRETATION MODEL

CALCULATE WELL TEST INTERPRETATION MODEL MODEL BEHAVIOUR ANOTHER YES MODEL?

SPE 102079 Gringarten ATCE San Antonio Sept 2006 END 22/44 Verification: wellbore storage and skin model

Log-Log Match - Flow Period 76 Simulation (Constant Skin) - Flow Period 76 1000 5100 5000 4900

4800 100 4700 4600 4500 10 k = 175 mD 4400 4300 C = 0.01 Bbl/psi 4200 4100 1 S = 32 Pressure (psia) 4000 3900 Pressure Pressure Change (psi) 3800 0.1 3700 0.0001 0.001 0.01 0.1 1 10 100 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Elapsed time (hrs) Production time (hrs)

Horner Match - Flow Period 76 5100 5010 4400

5000 5000

4900 4990 4300

4800 4980

4700 4970 4200 Pressure(psia) 4600 4960

4500 4950 4100 Pressure Pressure (psia)

4400 4940

4300 4930 4000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 Superposition Function (STB/D) 23/44 Pressure derivative

GROUNDWATER IOC UNIVERSITIES SERVICE Theis (1935) , Shell, Texas A&M, Stanford Flopetrol Jacob (1947), Gulf Oil Corp, Henry J. Ramey, et al. Schlumberger Hantush (>1947) ARCO…

Straight Type Methodology Line Curve Methods Analysis Derivatives = dDp / d ln Dt

Horner TC with MDH MBH Independent parameters

15 years 13 years 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1983 1995 2000 2005 2015 Year

Bourdet et al.: "A New Set of Type Curves Simplifies Well Test Analysis," World Oil ( May, 1983) 95-106. 24/44 Pressure derivative

No radial1000 flow FP4 FP76 PRESSURE

100

Wellbore storage 10 & skin model Radial flow FP4

1 DERIVATIVE FP76 Pressure ChangePressureDerivative(psi) and 0.1 0.0001 0.001 0.01 0.1 1 10 100 1000 Elapsed time Dt (hrs)

25/44 Pressure derivative

No radial1000 flow FP4 FP76

100

10 FP4

1 No radial flow FP76 Closed reservoir? Pressure ChangePressureDerivative(psi) and 0.1 0.0001 0.001 0.01 0.1 1 10 100 1000 Elapsed time Dt (hrs)

26/44 Verification: WB & S, limited entry, closed rectangular reservoir

Log-Log Match - Flow Period 76 Simulation (Constant Skin) - Flow Period 76 1000 5100 5000 4900

4800 100 4700 4600 4500 10 4400 FP4 4300 4200 4100 1 4000 Pressure Pressure (psia) 3900 Pressure Pressure Change (psi) FP76 3800 0.1 3700 0.0001 0.001 0.01 0.1 1 10 100 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Elapsed time (hrs) Production time (hrs)

Horner Match - Flow Period 76 5100 5010 4400

5000 5000

4900 4990 4300

4800 4980

4700 4970 4200 Pressure(psia) 4600 FP4 4960 4500 4950 4100 Pressure Pressure (psia) 4400 FP76 4940

4300 4930 4000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 Superposition Function (STB/D) 27/44 Verification: WB & S, limited entry, closed rectangular reservoir

Log-Log Match - Flow Period 76 Simulation (Constant Skin) - Flow Period 76 1000 5100 5000 4900

Typical field Parameter Analysis Design Difference uncertainty Initial pressure (pav)i 5000 psia 5000 0% ± 5 psia Horizontal permeability k(xy) 470 mD 500 -6% ± 20% Vertical permeability k(z) 0.54 mD 0.5 8% ± 20% Wellbore storage coefficient C 0.01 bbl/psi 0.01 0% ± 20% Penetration ratio hw/h 0.06 0.05 20% ± 20%± Wellbore skin effect S(w) 0.8 0 + 0.8 ± 0.5 7 Reservoir area A 6 107 ft2 6 10 0% ± 30%

28/44 Single well deconvolution

GROUNDWATER IOC UNIVERSITIES SERVICE ??????? Imperial College Theis (1935) , Shell, Texas A&M, Stanford Flopetrol Jacob (1947), Gulf Oil Corp, Henry J. Ramey, et al. Schlumberger Hantush (>1947) ARCO… SSI

Straight Type Methodology Line Curve Methods Analysis Derivatives

Horner Commercial Single well MDH MBH Software Deconvolution

19 years 13 years 19 years 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2002 2005 2015 Year

SPE 71574: von Schroeter, T., Hollaender, F., Gringarten, A.:"Deconvolution of Well Test Data as a Nonlinear Total Least Square Problem" 29/44 What is Deconvolution?

Deconvolution is data processing with an algorithm which converts pressures at variable rates:

6000 10000 72 hrs 168 hrs 8000 5000

6000

4000

3000 2000 Pressure (psia) Oil Rate (STB/D)

2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Time from the start of production (hrs) into a single drawdown at constant rate, with a duration equal to that of the test:

6000 10000 What is deconvolution?

Deconvolution converts pressures at variable rates: 8000 5000 2644 hrs 6000 10000 5000 8000 6000 6000 4000 4000 4000 3000 2000

Pressure(psia) 20000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 28000 Time from the start of production (hrs) Oil Rate (STB/D) 4000 into a single drawdown at constant rate, with a duration equal to the duration of the test: 3000 2000 Pressure (psia) Oil Rate (STB/D)

2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 30/44 Deconvolved derivative

103 No radial flow

FP4 FP76 PRESSURE

102 Deconvolved

Radial flow stabilisation FP4

1 DERIVATIVE FP76 > 1 log cycle Pressure ChangePressureDerivative(psi) and 10-1 10-4 10-3 10-2 10-1 1 10 102 103 104 Elapsed time Dt (hrs)

31/44 Correction of erroneous rates

5000 3 Gas well in UKCS Erroneous

4000 rates

3000

2000 2

Pressure (psia) Pressure 1000 FP 12 FP 39

0 Suspicious rates 1 Time-correctedTotal (MMscf/D) Rate

0 0 100 200 300 400 500 Elapsed time (hrs)

32/44 Correction of erroneous rates

5000 3 Given rates, time corrected 4000

3000

2000 FP 12 FP 39 2

Pressure (psia) Pressure 1000

1 Total(MMscf/D) Rate

0 500 Elapsed time (hrs)

33/44 Estimation of missing rates

6000 9000

8000 5000 7000

4000 6000

5000 3000 Iteration 321 Final No rates 4000

2000 3000 Pressure Pressure (psia) Oil Rate Oil (STB/D) 2000 1000 1000

0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Production time (hrs)

34/44 Example: Deepwater Horizon oil spill (Macondo)

DATA Sparse WHP Sampling MDT Assume a constant rate Apply deconvolution Apply deconvolution Deconvolved surface rates Calculate kh

Scale surface rates to kh

Calculate BHP Assume a constant rate Apply deconvolution

Deconvolved Bottomhole rates

Scale bottomhole rates to kh

CUMMULATIVE PRODUCTION

35/44 Example: Deepwater Horizon oil spill (Macondo)

5.00 Judge: 4.0 Spilled 4 Volume 3.26 (MMSTB) 2

L H L H L H L H L H L H L H 0 Blunt(MB) Hsieh (Sim) Hsieh Griffiths Griffiths (Sim) Hasan (Sim) Hasan Dykhuizen(Sim) Liu, Shah,Liu, Mannan, Pooladi-Darvish Pooladi-Darvish (Sim) Kelkar/Raghavan(MB) Gringarten(deconvolution) Compiled by K. Shah from http://www.sciencemag.org/news/2015/01/after-geoscientists-joust-judge-rules-bp-gulf-spill-totaled-319-million-barrels-oil 36/44 Multiwell deconvolution

Straight Type Methodology Multiwell Line Curve Deconvolution Methods Analysis Derivatives

Horner Commercial Single well MDH MBH Software Deconvolution

19 years 13 years 19 years 13+ years 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 2010 1995 2000 2005 2015 Year

37/33 Multiwell deconvolution: field example

• North Sea oilfield

N Six interfering producers

P15 P14

and two injectors. P13

P11 I12 P12 Testing group 2 I14 P10

SPE 174353 Thornton et al., Europec Madrid June 2015 38/44 Benefits of multiwell deconvolution • Conventional well test analysis impaired by short buildups • Single well deconvolution impaired by interference • Multiwell deconvolution yields the correct shape • Multiwell deconvolution provides interference between wells Interferences WELL P13 1.E+00 Single well deconvolution N Δp (psia) Δp 1.E-01 (psia) Δp

P15 P14 1.E-02

P13 Multiwell I12 deconvolution P11 1.E-03 I14 P12

Conventional well test 3 log cycles P10 analysis Time (hr) 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Slope ½ Increasing = channel Channel width 39/43 WTA Value = Identification + Verification

ANALYSIS METHOD IDENTIFICATION VERIFICATION

50’s Straight lines Poor None

70’s Pressure Type Curves Fair ( limited) Fair to Good

80’s Pressure Derivative Very Good Very Good

00’s Deconvolution Much better Same as derivative

10’s Multiwell deconvolution >> >> NEXT ? >>> >>> 40/44 Other application:WTA of blood pressure Deconvolved Deconvolved pressure and derivative

AORTA

41 Where we are

• Well test analysis has improved immensely since straight lines and pressure log-log analysis, and even derivative log-log analysis

• Methodology makes it repeatable and easy to learn

• Derivatives and deconvolution make well test analysis a reliable tool for reservoir characterization

42/44 But

• Understanding of WTA still required

• Derivatives must be calculated correctly

• Deconvolution requires prior interpretation

• WTA requires other knowledge (geology, etc…)

43/44 AND concepts proven wrong 30 years ago still used

• MDH instead of Horner

• Horner instead of superposition

• Horner equivalent production time

• Ramey’s one and ½ cycle rule

• Different start of radial flow in Drawdowns and Build ups

• Derivative plotted vs. Agarwal effective time

• Uniform flux vs. infinite conductivity solution

• etc…… 44/44