Pre‐Frac Injection Tests
R.D. Barree
In this session …
• Discuss DFIT requirements and procedures
– Look at SRT Analysis
– Pressure loss at Perfs
– Near‐Wellbore Pressure Loss
– Look at Post Shut‐In Analysis
– discuss G‐function analysis in detail
•
•
•
•
Importance of correct determination of closure
Pore pressure and permeability
Efficiency and Leakoff
Discuss the effects of Variable Storage and Tip Extension
© 2009
Diagnostic Fracture Injection Test:
DFIT
Requirements:
• Data Acquisition
–
–
–
0.01‐0.1 psi resolution surface gauge
Record all rates and pressures at 1/sec sampling rate Injection schedule must be precisely recorded
• Use Newtonian, non‐
wall building fluid (water, oil, or N2).
Procedure:
• Bring rate to max
• Pump for 2‐5 minutes
• Rapid step‐down to get WHP at each rate
• Isolate wellhead
• Shut‐down for 90 minutes (minimum) or up to 48 hrs
© 2009
Pre‐Frac Injection/Falloff Tests
Why pre‐frac test?
• obtain specific data
– Characterize the reservoir and completion
• every pump‐in carries risk of damage
– testing procedure must be designed to minimize damage
Types:
• Step‐rate injections
– pipe and near‐well friction
– # of effective perfs open
– frac extension pressure
• Pressure falloff after shut‐in
– frac closure pressure
– fluid efficiency and leakoff coefficient
– fracture closure mechanism
© 2009
Application of Pre‐Frac Tests
• Calibration of logs:
– Total closure stress • Mechanical properties
• Tectonic strain and stress
• Net fracture extension pressure
– Frac width
– Height containment
– Created fracture length and width
• Leakoff
– Pad volume requirements
– Maximum sand concentration
• Overall design
– Expected pack concentration
– Final fracture conductivity
– Necessary frac length for optimum stimulation
If you’re going to do this,
you’d better do it right!
© 2009
Pre‐Frac Step‐Rate Injection Test
© 2009
Traditional Step Rate Test
(SRT) Analysis
© 2009
System Friction Analysis from SRT Data
• Step‐down data preferred
– pressure response to rate changes should be related to frictional components
• Requires accurate pipe friction estimate
• Additional rate‐dependent pressure drop caused by
– perforation
• Square of the rate
– near‐well flow restriction
• Square root of rate
© 2009
© 2009
Resolving Components of Friction
• Pipe friction
– Generally varies with rate^2 in turbulent flow
– Must know the pipe friction to separate it from BH and near‐well friction
• Perf friction
– Varies with rate^2
– Changes with sand injection
• CD change and perf rounding
• Diameter change and perf erosion
• Tortuosity
– Varies with rate^0.5 (or some other factor)
– Some restriction that dissipates with injection rate
© 2009
Pipe Friction Estimates
Water
Slick-water (FR)
20# Linear gel
40# gel
Gelled Oil
70Q N2 Foam
Data calculated for
2-7/8” tubing
© 2009
Perforation Restriction Causes Large Pressure Drop
• Correct number & size of perfs can be estimated
• Pressure drop should be at least 100‐200 psi more than the confining stress between zones
• Also depends on coefficient of discharge (CD)
– Jet perfs: 0.754; Bullets: 0.822
– higher value indicates more efficient perf
1.975q ρ f
2
Ppf =
2
D
2
p
C N d
4
p
; psi
© 2009
Tortuosity:
Near‐Wellbore Pressure Loss
• Stress halo around perf
• Flow around cement micro‐annulus
• Perforation interference
• Narrow fracture width
• Fracture turning and branching (multiples)
• Off‐vertical fractures
• Pulverized cement debris
• Charge debris
• Leakoff into drilling and perf induced fracs
© 2009
Current SRT Spreadsheet
© 2009
Post Shut‐In:
What is G‐function Analysis?
• Post shut‐in pressure decline analysis using dimensionless function
• Extends the analysis through use of the first derivative and semi‐log derivative of BHP (dP/dG and GdP/dG)
• Also uses the characteristic shapes of derivative curves to locate specific modes of pressure decline
• Extension to After‐Closure Analysis (ACA) to define reservoir linear and pseudo‐radial flow
© 2009
G‐function Analysis in
Pre‐Completion Decision Making
• Estimate pore pressure
– Is the zone depleted, normally pressured or over‐
pressured
– Impacts reserve estimates and cleanup
• Detection of natural fractures
– Significance to fracture placement
– Do they impact flow performance?
• Estimation of permeability
• Determine leakoff mechanism and magnitude
• Combine reservoir and fracture data to make realistic estimates of post‐frac rate
© 2009
Algebraic Definition of the G‐Function
G-function is a dimensionless function of shut-in
time normalized to pumping time:
G (ΔtD ) =
4
π
(g (ΔtD ) − g0 )
ΔtD = (t − t p ) t p
© 2009
G‐Function: Two limiting cases
•Low Leakoff, high efficiency
•Fracture area open varies approximately linear w/time
(α = 1.0 )
(
4
1.5
1.5
g (ΔtD ) = (1 + ΔtD ) − ΔtD
3
)
•High leakoff, low efficiency
•Fracture area varies w/ square‐root of time
(α = 0.5)
g (ΔtD ) = (1 + ΔtD )sin
−1
((1 + Δt
)
−0.5
D
) + Δt
0.5
D
© 2009
Falloff Analysis Methods
• Observed shut‐in pressure versus square‐
root of shut‐in time (Sqrt(t) Plot)
– Use of diagnostic derivatives on Sqrt(t) plot
• G‐Function and its diagnostic derivatives
• Log‐Log plot of pressure change after shut‐in versus time after shut‐in
After Closure analyses to define reservoir properties:
– Flow regime identification
– Horner analysis
– Talley‐Nolte method
© 2009
Evaluated Pressure Falloff Cases
1. Fracture extension after shut‐in
2. Constant leakoff in a well‐confined fracture with tip recession during closure
3. Pressure dependent leakoff
4. Pressure dependent leakoff and modulus 5. Leakoff with variable storage or fracture compliance (transverse storage)
© 2009
Ambiguous Closure Using Sqrt(t) Analysis
2
Which one is closure?
Pressure
3
1
4
6
5
Sqrt(Shut-in Time)
© 2009
Normal Leakoff G‐Function
© 2009
Derivatives
Pressure
Sqrt(t) Plot for Normal Leakoff
Time
© 2009
Log‐Log Plot for Normal Leakoff
4
3
BH ISIP = 9998 psi
1
Delta-Pressure and Derivative
2
1000 9
8
7
6
(m = 0.632)
5
4
3
2
(m = -1)
100 9
8
7
6
5
4
3
2
10
0.1
2
3
4
5
6
7 8 9
1
2
3
4
5
6
7 8 9
10
2
3
4
5
6
7 8 9
100
2
3
4
5
6
Time (0 = 8.15)
© 2009
7 8 9
1000
Summary of Characteristic Slopes on Log‐Log Plot
© 2009
Fracture and Reservoir Transient Flow Regimes
Fracture Linear Flow
(Tip-Extension, ½ slope)
Formation Linear Flow
(Before closure, ½ slope
After closure, -½ slope)
Bi-Linear Flow (Before closure, ¼ slope
After closure, -3/4 slope)
Pseudo-Radial Flow
(After closure, -1 slope)
© 2009
After‐Closure Flow Regime Plot
10000 9
8
7
6
5
ΔP vs. FL2
4
3
ΔP=(pw-pr)
Delta-Pressure and Derivative
2
1000 9
Start of Radial Flow
8
7
6
5
4
3
2
100 9
(m = 1)
8
7
6
FL2 dΔP/dFL2 vs. FL2
5
4
3
2
10
0.001
2
3
4
5
6
7
8
9
0.01
2
3
4
5
6
7
8
9
0.1
2
3
4
5
6
7
8
9
1
Square Linear Flow (FL^2)
© 2009
After‐Closure Analysis
⎡ Vi ⎤
= 251,000 ⎢
⎥
μ
⎣ M R tc ⎦
Pressure
kh
Vi: bbls
k: md
tc: min
MR: psi-1
h: ft
μ: cp
RESULTS:
Reservoir Pressure = 7475.68 psi
Transmissibility, kh/μ =298.94991 md*ft/cp
kh=7.94014 md*ft
Permeability, k = 0.0968
Start of Pseudo Radial Time = 2.15 hours
Radial flow time function
© 2009
Horner Analysis: Only Valid in Pseudo‐Radial Flow
9750
1
9500
9250
9000
kh
8750
μ
8500
=
162.6(1440 )q
mH
q: bpm
k: md
mH: psi-1
h: ft
μ: cp
8250
8000
(m = 14411)
7750
7500
7250
(Reservoir = 7476)
P*=7476 psi
kh/μ=298 md-ft/cp
kh=7.9 md-ft
k=0.097 md
2
1
3
Horner Time
© 2009
Permeability Estimation from G at Closure (Gc)
• Good estimate when after‐closure radial‐flow data not available
k=
0.0086μ 0.01 Pz
1.96
⎛ Gc E rp
⎞
φ ct ⎜
⎟
0.038 ⎠
⎝
Where:
k = effective perm, md
ct = total compressibility, 1/psi
μ = viscosity, cp
E = Young’s Modulus, MMpsi
Pz = process zone stress rp = leakoff height to gross frac
or net pressure
height ratio
φ = porosity, fraction
© 2009
Permeability Estimate from G‐at‐Closure ‐ Illustrated
Permeability, md
Estimated Permeability = 0.0974 md
Gc
© 2009
Computation of Efficiency and Leakoff Coefficient
• Efficiency is given by:
Gc
η=
2 + Gc
• Leak‐off is given by:
dP
2h
CL =
π rp E t p dG
These equations are only valid with no
pressure dependent behavior during closure.
© 2009
Typical PDL Behavior of G‐Function Derivatives
P vs. G
Derivatives
Pressure
Fracture Closure
GdP/dG vs. G
End PDL
dP/dG vs. G
© 2009
Log‐Log Plot for PDL Example
2
BH ISIP = 10000 psi
Pressure Difference and Derivative
10009
1
Linear Flow
ΔP vs. Δt
8
7
6
5
(m = -0.5)
4
3
Radial Flow
(m = 0.5)
2
1009
Fracture closure
8
7
(m = -1)
ΔtdΔP/dΔt vs. Δt
6
5
4
3
2
10
0.1
2
3
4
5
6 7 8 9
1
2
3
4
5
6 7 8 9
10
2
3
4
Time (0 = 9.133333)
5
6 7 8 9
100
2
3
4
© 2009
5
6 7 8 9
1000
Sqrt(t) Plot for PDL Example
10250
500
1
False Closure
10000
Fracture Closure
Pressure
9500
300
√tdP/d√t vs. √t
9250
200
9000
8750
8500
100
dP/d√t vs. √t
8250
00:20
1/24/2007
00:40
Time
01:00
01:20
01:40
© 2009
02:00
1/24/2007
0
Derivatives
9750
400
P vs. √t
Estimation of PDL Coefficient from Falloff Data
Leakoff coefficient can be estimated
from the ratio of dP/dG before and after fissure closure Cp
Co
⎛ dP ⎞
= ⎜
⎟
⎝ dG ⎠
P > P fo
⎛ dP ⎞
⎜
⎟
⎝ dG ⎠
P < P fo
or
⎛C ⎞
ln ⎜ p ⎟ = C d p Δ P
⎝ Co ⎠
Cdp
© 2009
Determination of PDL Coefficient 6
ln(Cp/Co)
5
Ln(Leakoff Ratio)
4
3
2
1
(PDL Coefficient = 0.0019)
0
(Fissure Opening Pressure = 9311)
-1
9300
9400
9500
9600
9700
9800
9900
Bottom Hole Pressure (psi)
10000
10100
10200
© 2009
10300
Natural Fracture System in Hard‐Rock
σΗmin
σΗmax
© 2009
Fissures Opened By Tensile Stress Field
df
Sh
(
)
⎤
1 ⎡ Pf − Sh
≤
xf 2 ⎢⎢
T + Sh )⎥⎥
(
⎣
⎦
2
df
SH
Typical leakoff volume:
0.05 ft3/ft2 each face
3” depth in 20% φ rock
10’ depth in 1/2% φ fractures
© 2009
Width of Fracture Zone for Various Half‐Lengths (Sh=5000 psi, Tn=1000 psi)
Fracture
Half-Length
© 2009
Estimated Efficiency with PDL
0.75*(ISIP-Pclosure)
Using best straight-line
extrapolation to closure:
Computed efficiency = 0.48
Actual efficiency (simulator) = 0.28
Using 75% rule:
Computed efficiency = 0.35
η=
Gc
2 + Gc
© 2009
Pressure
Derivatives
G‐Function Analysis for Leakoff with Variable Storage
© 2009
Pressure
Derivatives
Sqrt(t) Plot for Leakoff with Variable Storage
Time
© 2009
Delta-Pressure and Derivative
Variable Storage Signature on the Log‐Log Plot
© 2009
Fracture Height Recession and Transverse Storage
Leakoff through a thin permeable layer:
Decreasing storage relative to leakoff rate accelerates pressure decay
Expulsion of fluid from transverse fractures:
Maintains pressure in fracture until fissures close
© 2009
Pressure Derivative
Closure‐Time Correction for Variable Storage
© 2009
Permeability Estimate with Storage Correction
Mini-Frac Permeability = 0.0617 md
Data Input
rp
φ
ct
E
μ
Gc
Pz
0.85
0.08
6.00E-05
5
1
3
944.0
© 2009
V/V
-1
psi
Mpsi
cp
psi
Pressure
Derivatives
Tip‐Extension G‐Function Analysis
© 2009
Derivatives
Pressure
Sqrt(t) Plot for Tip‐Extension
© 2009
Delta-Pressure and Derivative
Log‐Log Plot for Tip‐Extension
© 2009
Potential Problems in Pressure Diagnostics
• Bad ISIP
– Extreme perf restriction
– Wellbore fluid expansion
• Zero surface pressure during falloff
– Falling fluid level
– Non‐zero sandface rate
– Partial vacuum above fluid column
• Gas entry to closed wellbore
– Phase segregation • Use of gelled (wall‐building) fluid
– Disruption of after‐closure pressure gradients
– Masking of reservoir flow capacity
© 2009
Example of Ambiguous ISIP Caused by Near‐Well Restriction
GohWin Pumping Diagnostic Analysis Toolkit
Job Data
Minifrac Events
Time
A
90000
Bottom Hole Pressure (kPa)
Slurry Rate (m³/min)
A
B
1
2
BHP
SR
1
Start
00:05:45
78547 0.990
2
Shut In
00:10:31
57469 0.000
3
Stop
04:37:46
45868 0.000
ISIP=80000
80000
B
1.2
1.0
70000
0.8
60000
0.6
(ISIP = 56975)
50000
0.4
40000
0.2
30000
00:00
3/20/2007
00:05
00:10
Time
00:15
© 2009
00:20
3/20/2007
0.0
BHP G‐function for Early ISIP Shows Apparent “PDL”
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - G Function
A
80000
Bottom Hole Pressure (kPa)
Smoothed Pressure (kPa)
1st Derivative (kPa)
G*dP/dG (kPa)
A
A
D
D
1
End of Test
Time
BHP
SP
20.29
45908
45907
DP
FE
25457 91.53
D
15000
1
75000
12500
70000
10000
65000
7500
60000
(20.05, 6681)
5000
55000
(m = 333.3)
2500
50000
45000
(0.002,
(Y
= 0) 0)
5
10
G(Time)
15
20
© 2009
0
Late ISIP G‐Function Suppresses “PDL Hump”
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - G Function
A
58000
Bottom Hole Pressure (kPa)
1st Derivative (kPa)
G*dP/dG (kPa)
Time
A
D
D
1
Closure
BHP
19.43 45928
SP
45924
DP
FE
11047 91.19
1
56000
D
20000
18000
16000
54000
14000
12000
52000
10000
50000
8000
6000
48000
(19.65, 5933
4000
46000
44000
(m = 302)
(0.002,
(Y
= 0) 0)
2
4
6
8
10
G(Time)
2000
12
14
16
© 2009
18
0
Early ISIP Log‐Log Plot Shows Increased Separation and Long Negative Derivative Slope
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - Log Log
Delta Bottom Hole Calc Pressure (kPa)
Delta Smoothed Pressure (kPa)
Smoothed Adaptive 1st Derivative (kPa/min)
Adaptive DTdDP/dDT (kPa)
A
3
A
A
B
A
BH ISIP = 71366 kPa
1
End of Test
Time DBHCP
DSP
264.72
25458 91.53
25457
FE
1
(3.255, 21772)
2
B
14000
12000
(m = 0.506)
10000 9
8
7
6
5
7x Separation
(0.29, 6408)
4
3
(Y = 3134)
(Y = 3734)
(m = 0.254)
(82.06, 2319)
2
1000 9
8000
(250.5, 3079)
6000
4000
8
7
6
5
4
10000
2000
(Y = 421.8)
3
0
2
100
0.1
2
3
4
5
6
7
8 9
1
2
3
4
5
6
7
8 9
10
Time (0 = 9.283333)
2
3
4
5
6
7
8 9
100
© 2009
2
-2000
Late ISIP Log‐Log Plot Gives Consistent Separation
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - Log Log
Delta Bottom Hole Calc Pressure (kPa)
Delta Smoothed Pressure (kPa)
Smoothed Adaptive 1st Derivative (kPa/min)
Adaptive DTdDP/dDT (kPa)
2
Time DBHCP DSP
1
Closure 260.51
11037
FE
11037 91.17
BH ISIP = 56975 kPa
1
10000 9
8
7
6
5
4
4x
(Y = 2956)
3
2
(41.34, 1853)
(254
(m = 0.25)
1000 9
8
7
6
5
4
3
(Y = 410.3)
2
100 9
8
7
6
5
4
3
2
10
0.1
2
3
4
5
6
7
8 9
1
2
3
4
5
6
7
8 9
10
Time (0 = 10.5)
2
3
4
5
6 7 8 9
© 2009
100
2
BHP Gauge Data with Falling Fluid Level
GohWin Pumping Diagnostic Analysis Toolkit
Job Data
Time
BH Gauge Pressure (psi)
Slurry Rate (bpm)
A
6500
1
A
B
2
BGP
SR
1
Start
10/2/2006 19:19:03
6393 6.100
2
Shut In 10/2/2006 19:35:34
4368 0.000
3
Stop
3027 0.000
10/2/2006 23:23:40
B
7
3
6000
6
5500
5
5000
4
4500
(ISIP = 4366)
3
4000
2
3500
1
3000
2500
19:00
10/2/2006
20:00
21:00
22:00
23:00
00:00
Time
10/3/2006
01:00
02:00© 2009 03:00
10/3/2006
0
Long‐Term Falloff with BHP Gauges and Falling Fluid Level GohWin Pumping Diagnostic Analysis Toolkit
Job Data
Minifrac Events
Time
BH Gauge Pressure (psi)
Slurry Rate (bpm)
A
6500
1
6000
A
B
Start
10/2/2006 19:19:03
6393
6.100
2
Shut In
10/2/2006 19:35:34
4368
0.000
3
Stop
10/2/2006 23:23:39
3027
0.000
B
7
3
2
6
5
5000
4
(ISIP = 4367)
3
4000
2
3500
1
3000
2500
SR
1
5500
4500
BGP
10/3/2006
10/4/2006
10/5/2006
Time
10/6/2006
© 2009
10/7/2006
0
Effect of Falling Fluid Level on G‐
Function Derivative Plot
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - G Function
A
4400
BH Gauge Pressure (psi)
Smoothed Adaptive 1st Derivative (psi)
Smoothed Adaptive G*dP/dG (psi)
Time
A
D
D
1
Closure
5.36
BGP
SP
3423
3439 913.5 73.99
1
FE
D
2000
1800
4200
4000
DP
1600
(7.373, 1558)
1400
3800
1200
3600
1000
3400
800
(m = 211.4)
3200
600
3000
400
2800
2600
200
(0.002,
(Y
= 0) 0)
10
20
30
G(Time)
40© 2009
0
Effect of Falling Fluid Level on Log‐Log Diagnostic Plot
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - Log Log
Time
Delta Bottom Hole Calc Pressure (psi)
Smoothed Adaptive 1st Derivative (psi/min)
Adaptive DTdDP/dDT (psi)
2
1
BH ISIP = 4352 psi
Closure
DBHCP DSP
123.46
929.1
FE
912.6 73.99
1
1000 9
(168.5, 1099)
8
7
6
5
(m = 0.912)
4
3
(32.69, 246.3)
2
100 9
8
7
6
5
4
3
2
10
0.1
2
3
4
5
6 7 8 9
1
2
3
4
5
6 7 8 9
10
2
3
4
5
6 7 8 9
100
Time (0 = 1175.566667)
2
3
4
5
6 7 8 9
© 2009
1000
2
3
4
5
6
Effect of Falling Fluid Level on ACA Log‐
Log Linear Plot
GohWin Pumping Diagnostic Analysis Toolkit
ACA - Log Log Linear
Results
Start of Pseudo Linear Time = 71.87 min
End of Pseudo Linear Time = 98.57 min
Start of Pseudo Radial Time = 110.06 hours
(p-pi) (psi)
Moving Avg Of Slope (psi)
10000 9
8
7
6
5
Analysis Events
SLF BGP Slope (p-pi)
4
3
3
Start of Pseudoradial Flow
0.01
2777
0.000
478.0
2
2
End of Pseudolinear Flow
0.32
3028
0.000
728.3
1
Start of Pseudolinear Flow
0.37
3093
0.000
793.1
1000 9
8
7
6
5
4
(m = 0.5)
3
(m = 1)
2
100 9
8
7
6
5
4
3
2
3
10
6
7
8
2
9
0.01
2
3
4
5
6
7
8
9
0.1
Square Linear Flow (FL^2)
2
3
1
4
© 2009
5
6
7
8
9
1
Effect of Falling Fluid Level on ACA Linear Flow Plot
GohWin Pumping Diagnostic Analysis Toolkit
ACA - Cartesian Pseudolinear
Analysis Events
LFTF BGP
BH Gauge Pressure (psi)
2
End of Pseudolinear Flow
0.56
3028
1
Start of Pseudolinear Flow
0.61
3093
3500
3400
3300
3200
3100
(m = 1297.8)
3000
2900
Results
2800
2
2700
0.0
0.1
0.2
0.3
0.4
0.5
1
0.6
Linear Flow Time Function
Reservoir Pressure = 2296.52 psi
Start of Pseudo Linear Time = 71.87 min
End of Pseudo Linear Time = 98.57 min
0.7
0.8
© 2009
0.9
1.0
Pressure Increase Caused by Gas Entry and Phase Segregation
A
Wellhead Pressure (psi)
6000
A Slurry Rate (bpm)
B
B
3.5
3.0
5000
2.5
4000
2.0
3000
1.5
2000
1.0
1000
0
22:00
3/22/2003
0.5
00:00
3/23/2003
02:00
04:00
06:00
08:00
Time
10:00
12:00
14:00© 200916:00
0.0
18:00
3/23/2003
Pressure Increase from Rising Gas Bubbles
P2 = P1 =
zNRT
V
Phead=0.45 psi/ft
P1 = Phead =
zNRT
V
© 2009
Early‐Time WHP G‐function Analysis
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - G Function
A
8500
Bottom Hole Calc Pressure (psi)
Smoothed Pressure (psi)
1st Derivative (psi)
G*dP/dG (psi)
A
A
D
D
Time BHCP
1
Closure
1.00
7192
SP
DP
FE
7202 1182 34.54
1
D
2000
1800
8000
1600
(1.316, 1600)
7500
1400
1200
7000
1000
6500
800
(m = 1218)
600
6000
400
5500
5000
200
(0.002,
(Y
= 0) 0)
1
2
3
G(Time)
4
5
© 2009 6
0
Effect of Gas Entry and Phase Segregation on G‐Function
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - G Function
Bottom Hole Calc Pressure (psi)
Smoothed Pressure (psi)
1st Derivative (psi)
G*dP/dG (psi)
A
8500
A
A
D
D
Time
1
Closure
1.00
BHCP
7192
SP
DP
FE
7212 1190 34.54
1
D
2000
1800
8000
1600
(1.316, 1600)
7500
1400
1200
7000
1000
6500
800
(m = 1218)
600
6000
400
5500
5000
200
(0.002,
(Y
= 0) 0)
5
10
15
G(Time)
20
© 200925
0
Effect of Gas Entry and Phase Segregation on Log‐Log Plot
GohWin Pumping Diagnostic Analysis Toolkit
Minifrac - Log Log
Delta Bottom Hole Calc Pressure (psi)
Delta Smoothed Pressure (psi)
1st Derivative (psi/min)
DTdDP/dDT (psi)
4
3
Time
1
BH ISIP = 8377 psi
DBHCP DSP
5.31
Closure
1185
FE
1175 34.54
1
2
1000 9
(11.41, 922.9)
8
7
6
5
(m = -0.5)
(77.1, 355)
4
3
2
100 9
(Y = 96.55)
8
7
6
5
4
3
2
10
0.1
2
3
4
5
6
7 8 9
1
2
3
4
5
6
7 8 9
10
2
Time (0 = 12.666667)
3
4
5
6
7 8 9
100
2
© 2009
3
4
5
6
7 8 9
1000
Effect of Gas Entry and Phase Segregation on ACA Log‐Log Plot
ACA - Log Log Linear
Analysis Events
SLF BHCP Slope (p-pi)
Slope (psi)
(p-pi) (psi)
3
Start of Pseudoradial Flow
2
0.14Linear
5617
1337
End of Pseudolinear
StartFlow
of Pseudo
Time 652.2
= 11.88 min
End
of
Pseudo
Linear
Time
=
28.70
min
6103 913.1 1823
Start of Pseudolinear Flow 0.27
Start of Pseudo Radial Time = 17.37 hours
1
0.01
5280
Results
297.5
999.9
10000 9
8
7
6
5
4
(m = 1)
3
2
1000 9
8
7
6
5
4
(m = 0.5)
3
2
100 9
8
7
6
5
4
3
2
10
0.001
3
2
3
4
5
2
6
7
8
9
0.01
2
3
4
5
6
7
8
Square Linear Flow (FL^2)
9
0.1
1
2
3
© 2009
4
5
6
7
8
9
1
Effect of Gas Entry and Phase Segregation on ACA Linear Plot
GohWin Pumping Diagnostic Analysis Toolkit
ACA - Cartesian Pseudolinear
Analysis Events
LFTF BHCP
Bottom Hole Calc Pressure (psi)
2
End of Pseudolinear Flow
0.38
5617
1
Start of Pseudolinear Flow
0.52
6103
7250
7000
6750
6500
6250
6000
(m = 3541.8)
5750
5500
Results
5250
5000
0.0
2
0.1
0.2
0.3
Reservoir Pressure = 4279.89 psi
Start of Pseudo Linear Time = 11.88 min
End of Pseudo Linear Time = 28.70 min
1
0.4
0.5
0.6
Linear Flow Time Function
0.7
0.8
© 2009
0.9
1.0
Effect of Gas Entry and Phase Segregation on ACA Radial Plot
GohWin Pumping Diagnostic Analysis Toolkit
ACA - Cartesian Pseudoradial
Analysis Events
RFTF BHCP
1
Bottom Hole Calc Pressure (psi)
Start of Pseudoradial Flow
0.01
5280
7250
7000
6750
6500
6250
6000
5750
5500
Results
(m = 5638.5)
5250
5000
Reservoir Pressure = 4894.94 psi
Transmissibility, kh/µ = 87.73613 md*ft/cp
kh = 2.07706 md*ft
Permeability, k = 0.0495 md
Start of Pseudo Radial Time = 17.37 hours
1
4750
0.0
0.2
0.4
0.6
0.8
1.0
Radial Flow Time Function
1.2
1.4 © 2009 1.6
1.8
Pressure Decay without Filter‐Cake: One‐Dimensional Transient Flow
Pfrac
Ppore
Distance from frac face
© 2009
Impact of Resistances in Series
ΔP3=L3/k3
10
K=100
+
ΔP2=L2/k2
+
ΔP1=L1/k1
2
K=1
= ΔPT
0.5
K=0.001
Kavg=Lt/(L1/k1+ L2/k2+ L3/k3)=0.025
© 2009
Frac Fluid Loss: Discontinuous Pressure Gradient with Filtercake
With filtercake pressure gradient is discontinuous
and far-field gradient is not related to leakoff rate
through reservoir permeability
Pfrac
Ppore
Distance from frac face
© 2009
Recall: Complete Stress Equation
Pc =
ν
(1 − ν )
[Pob − α v Pp ] + α h Pp + ε x E + σ t
• Pc = closure pressure, psi
• ν = Poisson’s Ratio
• Pob = Overburden
Pressure
• αv = vertical Biot’s
poroelastic constant
• αh = horizontal Biot’s
poroelastic constant
• Pp = Pore Pressure
• εx = regional horizontal
strain, microstrains
• E = Young’s Modulus,
million psi
• σt = regional horizontal
tectonic stress
© 2009
Estimation of Pore Pressure & Flow Capacity • Horner plot is only valid in pseudo‐radial flow
• Short‐term after‐closure data can be misleading
• In linear flow, ½ slope and 2x factor between DP and DP’ is diagnostic
• Pore pressure can be obtained from the linear flow period
• Reservoir kh can be determined when radial flow is identified
• Pore pressure is related to closure stress
© 2009
Conclusions:
• G‐function response in low perm, hard rock is definitive and relatively easily interpreted
• Closure pressure and leakoff mechanism can be defined
• Natural fractures and their stress state can be determined
• Closure pressure is related to reservoir pore pressure
• Correlations between Gc and production can be developed for clean fluid (acid and/or water) injection tests
• Extended falloff data can be used for pseudo radial flow analysis of perm
© 2009