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Mini‐frac (DFIT)Analysis for Unconventional Reservoirs using F.A.S.T. WellTest™
Course Outline
• Introduction• What is a Mini‐frac Test?• Why Perform a Mini‐frac Test?
• Mini‐frac Test Overview
• Analysis• Pre‐Closure Analysis• Leak‐off Types• Nolte After‐Closure Analysis• Soliman/Craig After‐Closure Analysis• ACA Modeling
• Radial Flow Example
• Linear Flow Example
• Mini‐frac Test Design2Copyright © Fekete Associates Inc.
What is a Mini‐frac Test?
• A mini‐frac test is an injection/falloff diagnostic test performed without proppant before a main fracture stimulation treatment
• The intent is to break down the formation to create a short fracture during the injection period, and then to observe closure of the fracture system during the ensuing falloff period.
3Copyright © Fekete Associates Inc.
What is a Mini‐frac Test?
• The created fracture can cut through near‐wellbore damage, and provide bettercommunication between the wellbore and true formation.
• A mini‐frac test is capable of providing better results than a closed chamber test performedon a formation where fluid inflow is severely restricted by formation damage.
4Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
• Determine initial formation pressure (Pi) & effective permeability (k) to:– Assist production/pressure data analysis– Provide initial inputs for reservoir models– Assess stimulation effectiveness– Help quantify reserves
• Estimate fracture design parameters such as:– Fracture gradient– Closure pressure (minimum horizontal stress)– Leak‐off coefficients
5Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
For Shale/Tight Formations:
Effective Permeability (k) is very low• Matrix permeability of a few nanodarcies to a few microdarcies (when
natural fractures exist) render conventional tests impractical before stimulation
Horizontal Multi‐Frac Wells• Massive hydraulic fracture treatments• Multiple fracture stages• Multiple perforation clusters per fracture stage• Numerous fracture networks created• Difficult to quantify effective formation permeability and pressure after
stimulation6Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
Shut‐in Time Required to Estimate Pi & k (After Perforating)Based on Haynesville Shale Properties
Simulated Pressure Buildup After Perforating
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
11500
Pres
sure
(p
si(a
))
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Time (h)
1000Nanodarcies2Weeks
100Nanodarcies5Months
10Nanodarcies4Years!
Skin=+2
7Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
Simulated PITA Derivative After Perforating
1.0
101
102
103
104
105
106
107
2
4
2
4
2
4
2
4
2
4
2
4
2
4
Impu
lse
Der
ivat
ive
(
t a)2
d
/d(
t a)
((1
06p
si2/
cP)
hr)
10-1 1.0 101 102 103 104 1052 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
Pseudo-Time (h)
Shut‐in Time Required to Estimate Pi & k (After Perforating)Based on Haynesville Shale Properties
10Nanodarcies4Years!
100Nanodarcies5Months1000Nanodarcies
2Weeks
Skin=+2
8Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
Shut‐in Time Required to Estimate Pi & K (After Mini‐frac)Based on Haynesville Shale Properties
Simulated Pressure Falloff After Minifrac
10500
11000
11500
12000
12500
13000
13500
14000
14500
15000
15500
16000
Pres
sure
(p
si(a
))
0 100 200 300 400 500 600 700 800 900 1000
Time (h)
1000Nanodarcies1Day
100Nanodarcies2Weeks
10Nanodarcies5Months
Skin=‐2.5
9Copyright © Fekete Associates Inc.
Why Perform a Mini‐frac Test?
Simulated PITA Derivative After Minifrac
1.0
101
102
103
104
105
106
107
2
4
2
4
2
4
2
4
2
4
2
4
2
4
Impu
lse
Der
ivat
ive
(
t a)2
d
/d(
t a)
((1
06p
si2/
cP)
hr)
10-1 1.0 101 102 103 104 1052 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
Pseudo-Time (h)
Shut‐in Time Required to Estimate Pi & K (After Mini‐frac)Based on Haynesville Shale Properties
10Nanodarcies5Months
100Nanodarcies2Weeks
1000Nanodarcies1Day
Skin=‐2.5
10Copyright © Fekete Associates Inc.
Mini‐frac Test Overview
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Mini‐frac Analysis
Mini‐frac Test Analysis is conducted in two steps:
• Pre‐Closure Analysis (PCA)– Uses special derivatives and time functions (G‐Func on, √t)– Indentify leak‐off behaviour and closure pressure
• After‐Closure Analysis (ACA)– Similar workflow to traditional pressure transient analysis– Uses “impulse” solution to establish formation permeability (k)
and pressure (Pi)
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PCA: ParametersThe following parameters are determined from the Pre‐Closure Analysis (PCA):
• Fracture Closure Pressure (pc)pc = Minimum Horizontal Stress
• Instantaneous Shut‐In Pressure (ISIP)/Propagation PressureISIP = Final Bo omhole Injec on Pressure ˗ Fric on Component
• Fracture Gradient
Fracture Gradient = ISIP / Formation Depth
• Net Fracture Pressure (Δpnet)
Δpnet = ISIP – Closure Pressure
• Fluid Efficiency: the ratio of the stored volume within the fracture to the total fluid injected
13Copyright © Fekete Associates Inc.
PCA: G‐FunctionThe G‐function is a dimensionless time function relating shut‐in time (t) to totalpumping time (tp) at an assumed constant rate and are based on the followingequations:
Two limiting cases for the G‐function are shown here:
α = 1.0 is for low leak‐off
α = 0.5 is for high leak‐off
The value of g0 is the computed value of g at shut‐in.14Copyright © Fekete Associates Inc.
PCA: G‐Function Analysis
Fracture closure is identified as the point where the G‐Function derivative starts to deviate downward from the straight line
15Copyright © Fekete Associates Inc.
G-Function
0
100
200
300
400
500
600
700
800
900
1000
Sem
ilog
Deriv
ativ
e G
dp/
dG
(psi
(a))
0
10
20
30
40
50
60
70
80
90
100
110
120
First Derivative dp/dG
(psi(a))
6600
6700
6800
6900
7000
7100
7200
7300
7400
7500
7600
7700
7800
7900
8000
p (psi(a))
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52
G-function time
Semilog Derivativepdata
First Derivative
Inj. Volume 3.99 bblISIP 7930.1 psi(a)Ddatum 9650.000 ftFrac grad 0.822 psi/ft
Fracture Closure
Gc 21.014tc 159.76 minpc 7308.4 psi(a)
Fracture Closure
Gc 21.014tc 159.76 minpc 7308.4 psi(a)
Fracture Closure
Gc 21.014tc 159.76 minpc 7308.4 psi(a)
PCA: Leak‐Off TypesNormal Leak‐off: occurs when the fracture area is constant during shut‐in and the leak‐off occurs through a homogeneous rock matrix
The characteristic signatures of normal leak‐off are :1. A constant pressure derivative (dP/dG) during fracture closure.2. The G‐Function derivative (G dP/dG) lies on a straight line that passes through the
origin16Copyright © Fekete Associates Inc.
Normal Leakoff
GFunctionDerivative(Gdp/dG)
G‐Function(GTime)
• NormalLeakoff
PCA: Leak‐Off TypesTransverse Fracture Storage/Fracture Height Recession is indicated when the G‐Function derivative G dP/dG falls below a straight line that extrapolates through the normal leak‐off data, and exhibits a concave up trend
Two characteristics are visible on the G‐function curve:1. The G‐Function derivative G dP/dG lies below a straight line extrapolated through the normal
leak‐off data.2. The G‐Function derivative G dP/dG exhibits a concave up trend.3. The First Derivative dP/dG also exhibits a concave up trend.
TransverseFractureStorage/FractureHeightRecession
18Copyright © Fekete Associates Inc.
Fracture Height Recession
• Fracture penetrates impermeable zone
Fracture Height Recession
• Fracture penetrates impermeable zone
Transverse Storage
• Early Time – Secondary fractures open
Transverse Storage
• Late Time – Secondary fractures close
PCA: Leak‐Off TypesPressure Dependent Leak‐off (PDL): indicates the existence of secondary fractures intersecting the main fracture, and is identified by a characteristic “hump” in the G‐ Function derivative that lies above the straight line fit through the normal leak‐off data.
The characteristic signatures of pressure dependent leak‐off are:1. A characteristic large “hump” in the G‐Function derivative G dP/dG lies above the straight
line that passes through the origin..2. Subsequent to the hump, the pressure decline exhibits normal leak‐off.3. The portion of the normal leak‐off lies on a straight line passing through the origin.4. The end of the hump is identified as “fissure opening pressure”.
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Pressure Dependant Leak‐off• Early Time ‐ Extra leak‐off from microfractures at high
pressure/early time
Pressure Dependant Leak‐off• Late Time‐Microfractures close, normal leak‐off resumes
PCA: Leak‐Off TypesFracture Tip Extension occurs when a fracture continues to grow even after injection is stopped and the well is shut‐in. It is a phenomenon that occurs in very low permeability reservoirs, as the energy which normally would be released through leak‐off is transferred to the ends of the fracture.
The characteristic signatures of fracture tip extension are:1. The G‐Function derivative G dP/dG initially exhibits a large positive slope that continues to
decrease with shut‐in time, yielding a concave‐down curvature.2. Any straight line fit through the G‐Function derivative G dP/dG intersects the y‐axis above the
origin. 26Copyright © Fekete Associates Inc.
Fracture Tip Extension
• Fracture Tip Extension Provides Extra Leak‐Off
After‐Closure Analysis (ACA)• ACA is performed on falloff data collected after fracture closure• Similar workflow to traditional pressure transient analysis
• Traditional PTA founded on the “constant‐rate solution” • Main ACA techniques are founded on the “impulse solution” • The “constant‐rate solution” hinges on the flow rate prior to SI• The “impulse solution” hinges on a “defined volume”
28Copyright © Fekete Associates Inc.
After Closure – Linear Flow
PlanView
After Closure – Radial Flow
• Radial Flow in Horizontal Plane– If linear flow is observed before radial flow, can use fracture model
PlanView– VerticalModelwithFracture
3D
After Closure
• Radial Flow in Horizontal Plane– If only radial flow is observed, can be modelled as vertical with negative skin
VerticalModelConceptualModel
PlanView
After‐Closure Analysis (ACA)
• After‐Closure Analysis (ACA) is performed on falloff data collected after fracture closure.
• Similar workflow to traditional pressure transient analysis.• Traditional PTA founded on the “constant‐rate solution”; Mini‐Frac ACA
techniques are founded on the “impulse solution”.• The “constant‐rate solution” hinges on the flow rate prior to the analyzed
shut‐in period whereas the “impulse solution” hinges on a “defined volume”.• Impulse solutions are used because of the short injection period and assume
the entire injected volume is injected instantaneously. • There are two ACA techniques available in F.A.S.T. WellTest™ (Nolte and
Soliman/Craig).
32Copyright © Fekete Associates Inc.
Nolte ACA
• This after‐closure analysis method is based on the work of K.G. Nolte8, and expanded on by R.D. Barree4.
• Based on the solution of a constant pressure injection followed by a falloff.
• The impulse equations are obtained by approximating the injection duration as very small.
• Uses injected volume as the impulse volume and the falloff begins at fracture closure.
• Characteristic slopes of the semi‐log derivative when plotted on the log‐log derivative plot differ from traditional PTA:
• Impulse Linear flow has a slope of ‐1/2.• Impulse Radial flow has a slope of ‐1.
33Copyright © Fekete Associates Inc.
Nolte ACA
34Copyright © Fekete Associates Inc.
Derivative
101
102
103
104
2
3
5
23
5
23
5
p,
Sem
ilog
Der
ivat
ive
(F L
2 2 )d
p/
d(F L
2 2 )
(ps
i(a))
10-210-11.0 2345678923456789
FL2 2
pdataDerivativedata
Impulse Radial -1
k 0.0165 md
t 38.73 hp 6652.6 psi(a)
Impulse Linear -1/2
t 15.08 hp 6750.9 psi(a)
Soliman/Craig ACA
• This after‐closure analysis method is based on the combined works of M.Y. Soliman and D. Craig1.
• Soliman’s solution is based on a constant rate injection followed by a long falloff2.
• Soliman applied superposition in Laplace space to obtain a single equation and then took the late‐time approximation to obtain impulse equations (for bilinear, linear and radial flow).
• D. Craig developed an analytical model which accounts for fracture growth, leak‐off, closure and after‐closure3.
• The late‐time approximation of Craig’s model produced impulse equations that are consistent with Soliman's solutions.
• Uses injected volume as the impulse volume.• Characteristic slopes of the impulse derivative when plotted on the log‐log
derivative plot are identical to those of traditional PTA.• Soliman/Craig's solutions facilitate the use of analytical models in F.A.S.T.
WellTest™. 35Copyright © Fekete Associates Inc.
Soliman/Craig ACA
36Copyright © Fekete Associates Inc.
Derivative
1.0
101
102
103
104
2
46
2
4
23
5
2
4
Impu
lse
Der
ivat
ive
t (
tp +
t)
dp/d
t (p
si h
r)
10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
t (h)
Derivativedata
Radial 0
k 0.0165 md
t 12.98 hp 6777.5 psi(a)
Linear 1/2
Xf(sqrt(k)) 1.24 md1/2ftk 0.0165 mdXf 9.676 ftsXf -2.780
t 38.13 hp 6653.5 psi(a)
ACA ‐Modelling• Once the initial reservoir pressure (Pi) and permeability (k) are estimated, a model is
generated (Soliman/Craig)to confirm these estimates. Note that the existing model does not account for the change in storage that occurs while the induced fracture is closing, and the analysis is focused on the after‐closure data.
• This is especially critical when reservoir dominated (radial) flow is not achieved within a test period, or when data scatter aggravates the analysis.
37Copyright © Fekete Associates Inc.
Derivative
10-2
10-1
1.0
101
102
103
104
3
3
3
3
3
3
Impu
lse
Der
ivat
ive
(
t)2
dp/
d(
t)
(psi
hr)
10-3 10-2 10-1 1.0 101 102 1032 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6
t (h)
DerivativedataDerivativemodelExt. Derivativemodel
pi (syn) 6592.0psi(a)kh 0.6138md.fth 40.000ftk 0.0153md
s' -2.731sXf -2.738Xf 9.273ft
Mini‐frac Observations from Real Data
• An example of a Mini‐frac test conducted on a vertical well at a formation depth of 10,000 ft analyzed using F.A.S.T. WellTest™ is depicted in the following slides.
38Copyright © Fekete Associates Inc.
History
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
11500
Pres
sure
(psi
(a))
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
Liquid Rate (bbl/d)
1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58
Time (h)
qwater
pdata
Inj . Volume 16.35 bblISIP 9444.2 psi(a)Ddatum 10100.000 ftFrac grad 0.935 psi/ft
Formation Breakdown
pdata 10942.7 psi(a)
Stop Injection
t 0.31 hpdata 9557.0 psi(a)qw -1440.00 bbl/d
Estimated ISIP
pdata 9444.2 psi(a)
Start Injection
Mini‐frac Observations from Real Data
• The pre‐closure analysis using the semi‐log and first derivative corresponding to G‐function time is shown below:
• From this plot, fracture closure is identified within the initial 3‐hours of the falloff period
39Copyright © Fekete Associates Inc.
G-Function
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
Sem
ilog
Der
ivat
ive
G d
p/dG
(p
si(a
))
0
100
200
300
400
500
600
700
800
900
1000
First Derivative dp/dG
(psi(a))
5500
6000
6500
7000
7500
8000
8500
9000
9500
p (psi(a))
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
G-function time
Semilog Deriv ativ epdata
First Deriv ativ e
Inj . Volume 16.35 bblISIP 9444.2 psi(a)Ddatum 10100.000 ftFrac grad 0.935 psi/ft
Analysis 1
Fracture Closure
Gc 6.233tc 166.76 minpc 7217.0 psi(a)
Fracture Closure
Gc 6.233tc 166.76 minpc 7217.0 psi(a)
Fracture Closure
Gc 6.233tc 166.76 minpc 7217.0 psi(a)
Mini‐frac Observations from Real Data
• The Nolte ACA log‐log diagnostic plot is shown below:
• The semi‐log derivative, calculated with respect to closure time, exhibits a slope of ‐1 after 5.64 hours, suggesting that radial flow has developed.
• The fluctuations in the derivative slope can be attributed to gas‐entry that is not accounted for with the bottomhole pressure calculations.
40Copyright © Fekete Associates Inc.
Derivative
101
102
103
104
2
3
57
2
3
57
2
3
5
, Sem
ilog
Der
ivat
ive
(F L
2 2 )
d
/d(F
L2 2 )
(1
06ps
i2/c
P)
10-210-11.0 2345678923456789
FL2 2
dataDerivativedata
Impulse Radial -1k 1.8577e-03md
t 23.07hp 5604.5psi(a)rinv 21.976ft
t 5.64hp 6322.9psi(a)
Mini‐frac Observations from Real Data
• The falloff data plotted with the Nolte ACA radial time function FR2 is shown below:
41Copyright © Fekete Associates Inc.
Minifrac Radial (Nolte)
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
(106
psi2
/cP)
5200
5400
5600
5800
6000
6200
6400
6600
6800
7000
7200
7400
7600
p (psi(a))
0.000.040.080.120.160.200.240.280.320.360.400.440.480.520.560.600.64
FR1
data
Analysis 1kh 0.1115md.fth 60.000ftk 1.8577e-03mdp* 5363.9psi(a)
t 23.07hp 5604.5psi(a)rinv 21.976ft
Mini‐frac Observations from Real Data
• The log‐log plot of the derivative used in the Soliman/Craig impulse solution shows the match obtained with the model:
• The model suggests radial flow was not quite achieved during the test period, and would likely develop after ~50 hours of shut‐in.
• In this case, the transition to radial flow is sufficiently developed to yield reliable estimates of formation pressure and permeability.
42Copyright © Fekete Associates Inc.
Derivative
101
102
103
104
2
4
2
4
2
4
Impu
lse
Der
ivat
ive
t a
(tp
+
t a) d
/d
t a
((10
6 psi
2 /cP
) hr)
10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7
ta (h)
DerivativedataDerivativemodelExt. Derivativemodel
kh 0.1978md.fth 60.000ftk 3.2968e-03md
Xf 1.572ftsXf -0.963pi 5461.7psi(a)
ApproachingRadial Flow
t 23.07hRadialFlowΔt=50.0h
Mini‐Frac Test Design
• Short duration injection period, followed by extended falloff period.
• Water commonly used for injection.
• Optimum injection rate/duration:
• 1 – 2 bpm (1500 – 3000 bbld)
• 2 – 3 minute injection (after wellbore fill‐up)
• sufficient to breakdown formation, while minimizing fracture growth and closure time
• Falloff duration controlled by permeability (k) and rock properties:
• minimum 2 days for k > 0.001 md (1000 Nanodarcies)
• minimum 2 weeks for k < 0.001 md (1000 Nanodarcies)
43Copyright © Fekete Associates Inc.
References1. "New Method for Determination of Formation Permeability, Reservoir Pressure, and Fracture Properties from a Minifrac Test",
Soliman, M.Y., Craig D., Barko, K., Rahim Z., Ansah J., and Adams D., Paper ARMA/USRMS 05‐658, 2005
2. “Analysis of Buildup Tests With Short Producing Times”, M. Y. Soliman, SPE, Halliburton Services Research Center, Paper SPE 11083 August 1986.
3. “Application of a New Fracture‐Injection/Falloff Model Accounting for Propagating, Dilated, and Closing Hydraulic Fractures, D. P. Craig, Haliburton, and T. A. Blasingame, Texas A&M University, Paper SPE 100578, 2006.
4. “Holistic Fracture Diagnostics”, R. D. Barree, SPE, and V. L. Barree, Barree & Associates, and Craig, SPE, Halliburton, Paper SPE 107877, Presented at the Rocky Mountain Oil & Gas Technology Symposium held in Denver, Colorado, USA, 16‐18 April 2007.
5. “After‐ Closure Analysis of Fracture Calibration Tests”, Nolte, K.G., Maniere, J.L., and Owens, K.A., Paper SPE 38676, Presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5‐8 October, 1997.
6. "Background for After‐Closure Analysis of Fracture Calibration Tests", Nolte, K. G., Paper SPE 39407, Unsolicited companion paper to SPE 38676 July, 1997.
7. “Modified Fracture Pressure Decline Analysis Including Pressure‐Dependent Leakoff”, Castillo, J. L., Paper SPE 16417, presented at the SPE/DOE Low Permeability Reservoirs Joint Symposium, Denver, CO, May 18‐19, 1987.
8. “Determination of Fracture Parameters from Fracturing Pressure Decline", Nolte, K. G., Paper SPE 8341, Presented at the Annual Technical Conference and Exhibition, Las Vegas, NV, Sept. 23‐26, 1979.
9. "Use of PITA for Estimating Key Reservoir Parameters", N. M. Anisur Rahman, Mehran Pooladi‐Darvish, Martin S. Santo and Louis Mattar, Paper CIPC 2006 ‐ 172, presented at 7th Canadian International Petroleum Conference, Calgary, AB, June 13 ‐ 15, 2006.
10."Development of Equations and Procedure for Perforation Inflow Test Analysis (PITA)", N. M. Anisur Rahman, Mehran Pooladi‐Darvish and Louis Mattar, Paper SPE 95510, presented at 80th Annual Technical Conference and Exhibition of the SPE, Dallas, TX, October 9 ‐ 12, 2005.
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