Feketes Course Notes
Transcript of Feketes Course Notes
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Rate Transient AnalysisTheory/Software Course
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Introduction to Well Performance Analysis
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Traditional
- Production rate only
- Using historical trends to predict future
- Empirical (curve fitting)
- Based on analogy
- Deliverables:- Production forecast- Recoverable Reserves under current conditions
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Modern
- Rates AND Flowing Pressures
- Based on physics, not empirical
- Reservoir signal extraction and characterization
- Deliverables:- OGIP / OOIP and Reserves- Permeability and skin- Drainage area and shape- Production optimization screening- Infill potential
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Recommended Approach
- Use BOTH Traditional and Modern together
- Production Data Analysis should include a comparison of multiple methods
- No single method always works
- Production data is varied in frequency, quality and duration
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- Flow regime characterization over life of well
- Estimation of fluids-in-place
- Performance based recovery factor
- Able to analyze transient production data (early-time production, tight gas etc)
- Characterization of perm and skin
-Estimation of contacted drainage area
-Estimation of reservoir pressure
- Estimation of reserves when flowing pressure is unknown
- High resolution early-time characterization
- High resolution characterization of the near-wellbore
-Point-in-time characterization of wellbore skin
- Projection of recovery constrained by historical operating conditions
Welltest AnalysisModern Production Analysis
Empirical DeclineAnalysis
Modern Production Analysis - Integration of Knowledge
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Theory
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Traditional Decline Curves – J.J. Arps
- Graphical – Curve fitting exercise
- Empirical – No theoretical basis
- Implicitly assumes constant operating conditions
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The Exponential Decline Curve
2001 2002 2003 2004 2005 20060.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00Gas Rate, MMscfd
Rate vs TimeUnnamed Well
2001 2002 2003 2004 2005 200610-1
1.0
101
2
3
4
567
2
3
4
567
Gas
Rat
e, M
Msc
fd
Rate vs TimeUnnamed Well
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50
Gas Cum. Prod., Bscf
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Gas
Rat
e, M
Msc
fd
Rate vs. Cumulative Prod.Unnamed Well
tDi
ieqq −=
log log2.302
ii
D tq q= −i iq q D Q= −
2.302*iD Slope= iD Slope=
iSlopeD
q=
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The Hyperbolic Decline Curve
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60
Gas Cum. Prod., Bscf
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Gas
Rat
e, M
Msc
fd
Rate vs. Cumulative Prod.Unnamed Well
bi
i
tbDqq /1)1( +
=
( )D f t=
i bb
i
DD qq
=
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Hyperbolic Exponent “b”
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60
Gas Cum. Prod., Bscf
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Gas Rate, MMscfd
Rate vs. Cumulative Prod.Unnamed Well
0 . 0 0 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 . 4 0 0 .4 5 0 . 5 0 0 .5 5 0 . 6 0 0 .6 5 0 . 7 0 0 .7 5 0 .8 0 0 .8 5 0 .9 0 0 .9 5 1 . 0 0 1 .0 5
G a s C u m u l a t iv e , B s c f
0 .0 0
0 .2 0
0 .4 0
0 .6 0
0 .8 0
1 .0 0
1 .2 0
1 .4 0
1 .6 0
1 .8 0
2 .0 0
2 .2 0
2 .4 0
2 .6 0
2 .8 0
3 .0 0
3 .2 0
Gas
Rat
e, M
Msc
fd
R a te v s . C u m u la t iv e P r o d .N B U 9 2 1 - 2 2 G
Mild Hyperbolic – b ~ 0
Strong Hyperbolic – b ~ 1
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Analytical Solutions
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Definition of Compressibility
1 VcV p
∂= −
∂
V
pi
V
dVpi-dp
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Compressibility Defines Material Balance of a Closed Oil Reservoir (above bubble point)
1 p
i
pi
t
i pss p
NcN p p
Np pc N
p p m N
=−
= −
= −
Assumptions: 1. c is constant2. Bo is constant
V=N
ΔV = NpΔp = pi - p
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Illustration of Pseudo-Steady-State
Distance
pres
sure
pwf1
1p
rw re
1
2p
pwf2
2
3p
pwf3
3
timeConstant Rate q
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Steady-State Inflow Equation
Distance
pres
sure
rw re
p
pwf
141.2 3ln4
wf pss
epss
wa
p p qbB q rb
kh rμ
− =
⎛ ⎞= −⎜ ⎟⎝ ⎠
pi
Inflow (Darcy) pressure drop- Constant- Productivity Index
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The Two Most Important Equations in Modern Production Analysis
i pss pp p m N= −
wf pssp p qb= +
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Constant Pressure=
Production
Constant Rate=
Welltest
q
pwf
q
pwf
Operating Conditions - Simplified
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Constant Flowing Pressure Solution
- Required: q(t), Npmax and N for constant pwf
- Take derivative of both equations and solve for q
- Integrate to find Np(t), as t goes to infinity Npgoes to Npmax
( )max
( )pss
pss
m ti wf b
pss
i wfp i wf t
pss
p pq t ebp pN p p c N
m
−−=
−= = −
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Constant Flowing Pressure Solution – Relate back to Arps Exponential, Determine N
max
max
( ) ( )
i wfi
pss
pssi
pss
ip
i
t i wf t i wf i
p i
p pqb
mDb
qND
c p p c p p DNN q
−=
=
=
− −= =
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Constant Rate Solution
- Required: pwf(t), Npmax and N for constant rate
- Equate left side to right and solve for pi-pwf
- Set pwf = 0 to find Npmax
- Plot pi-pwf versus Np to get N
max
( )i wf pss p pss
i pssp
pss
p p t m N b qp b qN
m
− = +−
=
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Constant Rate – PSS Plot
Np
1m mpsscN
= =
i wfp p−
141.2 3ln 4
p ei wf
t wa
y mx bN B q rp pc N kh r
μ= +
⎛ ⎞− = + −⎜ ⎟⎝ ⎠
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- Normalize the PSS equation with q
- Invert the PSS equation
1 1( )
1
( ) 1
pss pi wf pss psspss
pss
pssi wf
pss
qm Np p t m t bb
q
q bmp p t tb
= =− ++
=− +
Constant Rate Solution – Relate back to Arps Harmonic
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Plot Constant p and Constant q together
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30 35 40 45
Constant rate q/Δp (Harmonic)
Constant pressure q/Δp (Exponential)
1
( ) 1
pss
pssi wf
pss
q bmp p t tb
=− +
( ) 1 pss
pss
m tb
i wf pss
q t ep p b
−=
−
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Transient Flow
- Early-time OR Low Permeability
- Flow that occurs while a pressure “pulse” is moving out into an infinite or semi-infinite acting reservoir
- Like the “fingerprint” of the reservoir- Contains information about reservoir properties (permeability, drainage shape)
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Boundary Dominated Flow
- Late-time flow behavior
- Typically dominates long-term production data
- Reservoir is in a state of pseudo-equilibrium –physics reduces to a mass balance
- Contains information about reservoir pore volume (OOIP and OGIP)
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Transient Flow
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Transient and Boundary Dominated Flow
2000
2200
2400
2600
2800
3000
3200
3400
3600ps
Cross Section
Plan View
Transient Well Performance = f(k, skin, time)
Boundary Dominated Well Performance =
f(Volume, PI)
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Radius (Region) of Investigation
2000
2200
2400
2600
2800
3000
3200
3400
3600ps
Cross Section
Plan View
948
948
inv
inv
ktrc
ktAc
φμπ
φμ
=
=
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Transient Equation
1( ) 141.2 1 0.0063ln 0.4045
2i wf
t
q khp p B kt s
cμ
φμ
=− ⎛ ⎞
+ +⎜ ⎟⎝ ⎠
Describes radial flow in an infinite acting reservoir
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q(t)’s compared
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25 30 35 40 45
Transient flow: compares to Arps “super hyperbolic” (b>1)
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0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30 35 40 45
Blending of Transient into Boundary Dominated Flow
Complete q(t) consists of:Transient q(t) from t=0 to tpss
Depletion equation from t = tpss and higher
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Comparison of qD with 1/pDCylindrical Reservoir with Vertical Well in Center
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14
tD
qD a
nd 1
/p
0.9
Constant Pressure Solution Exponential
Constant Rate SolutionHarmonic
Log-Log plot: Adds a new visual dynamic
Infinite Acting Boundary Dominated
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Type Curves
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Type Curve
- Dimensionless model for reservoir / well system
- Log-log plot
- Assumes constant operating conditions
- Valuable tool for interpretation of production and pressure data
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Type Curve Example - Fetkovich
10-1 1.0 1012 3 4 5 6 7 8 9 2 3 4 5 6 7 8 2 3 4 5 6 7 8
Time
10-2
10-1
1.0
2
3
4
567
9
2
3
4
567
Rat
e,
Fetkovich Typecurve Analysis
Exponential
Harmonic
qDd
tDd
DdtDd eq −=
11
DdDd
qt
=+
tDtqtqq
iDd
iDd
=
=)(
Hyperbolic
1/
1(1 )
Dd bDd
qbt
=+
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Plotting Fetkovich Type Curves- Example
Well 1 (exponential)
qi = 2.5 MMscfdDi = 10 % per year
Well 2 (exponential)
qi = 10 MMscfdDi = 20 % per year
Raw Data Plot
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0 5 10 15
Time (years)
Rat
e (M
Msc
fd)
Well 1Well 2
Dimensionless Plot
0.10
1.00
0.01 0.10 1.00 10.00
tDd
qDd Well 1
Well 2
Time (years)Well 1 Well 2 Well 1 Well 2 Well 1 Well 2
0 2.50 10.00 0.00 0.00 1.00 1.001 2.26 8.19 0.10 0.20 0.90 0.822 2.05 6.70 0.20 0.40 0.82 0.673 1.85 5.49 0.30 0.60 0.74 0.554 1.68 4.49 0.40 0.80 0.67 0.455 1.52 3.68 0.50 1.00 0.61 0.376 1.37 3.01 0.60 1.20 0.55 0.307 1.24 2.47 0.70 1.40 0.50 0.258 1.12 2.02 0.80 1.60 0.45 0.209 1.02 1.65 0.90 1.80 0.41 0.17
10 0.92 1.35 1.00 2.00 0.37 0.14
Rate (MMscfd) tDd qDd
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Fetkovich Typecurve Matching
In most cases, we don’t know what “qi” and “Di” are ahead of time. Thus, qi and Di are calculated based on the typecurve match (ie. The typecurve is superimposed on the data set
ttD
qtqq
Ddi
Ddi
=
=)(
Knowing qi and Di, EUR (expected ultimate recovery) can be calculated
1.0 1013 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2
Time
10-1
1.0
5
6
789
2
3
4
5
6
78
Rat
e,
Fetkovich Typecurve AnalysisNBU 921-22G
qDd
tDd
q
t
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Analytical Model Type Curve
10-4 10-3 10-2 10-1 1.0 1012 3 4 567 9 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 67
Time
10-2
10-1
1.0
101
2
34
6
9
2
34
6
9
2
34
6
9
2
34
6
Rat
e,
Fetkovich Typecurve Analysis
Boundary Dominated FlowExponential
Transient Flow
re/rwa = 10 re/rwa = 100 re/rwa = 10,000qDd
tDd
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Dimensionless Variable Definitions (Fetkovich)
2
2
141.2 1ln( ) 2
0.00634
1 1ln 12 2
eDd
i wf wa
waDd
e e
wa wa
q B rqkh p p r
ktctrt
r rr r
μ
φμ
⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎣ ⎦
=⎡ ⎤⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎢ ⎥⎣ ⎦
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Type Curve Matching (Fetkovich)
2
141.2 1ln( ) 2
0.00634 1 ln1 1ln 12 2
141.2 0.006342( )
e
i wf wa Dd match
wwa
t Dd wae e
wa wamatch
ei wf t Dd Dd matchmatch
B r qkh p p r q
k t rr sc t rr r
r r
B q trh p p c q t
μ
φμ
φ
⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎣ ⎦
⎛ ⎞= = ⎜ ⎟⎡ ⎤ ⎝ ⎠⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎢ ⎥⎣ ⎦
=−
The Fetkovich analytical typecurves can be used to calculate three paramters: permeability, skin and reservoir radius
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10-4 10-3 10-2 10-1 1.0 1012 3 4 5 678 2 3 4 5678 2 3 4 5678 2 3 4 5678 2 3 4 5678 2 3 4 5678
Time
10-3
10-2
10-1
1.0
101
2
34
68
2
34
68
2
34
68
2
34
68
Rat
e,
Fetkovich Typecurve Analysis10
Type Curve Matching - Example
Boundary Dominated FlowExponential
Transient Flow
tDd
reD = 50
qDd
q
t
k = f(q/qDd)
s = f(q/qDd * t/tDd, reD)re = f(q/qDd * t/tDd)
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What about Variable Rate / Variable Pressure Production?The Principle of Superposition
Superposition in Time:
1. Divide the production history into a series of constant rate periods2. The observed pressure response is a result of the additive effect of each rate
change in the history
Example: Two Rate History
q1
q2
Effect of (q2-q1)
t1
1 2 1 1( ) ( ) ( )i wfp p q f t q q f t t− = + − −q
pwf
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The Principle of Superposition - Continued
1 2 1 1( ) ( ) ( )i wfp p q f t q q f t t− = + − −Two Rate History
N - Rate History
1 11( ) ( )
N
i wf j j jj
p p q q f t t− −
=
− = − −∑f(t) is the Unit Step Response
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Superposition Time
Convert multiple rate history into an equivalent single rate history by re-plotting data points at their “superposed” times
11
1
( ) ( )N
i wf j jj
N Nj
p p q q f t tq q
−−
=
− −= −∑
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The Principle of Superposition – PSS Case
11
1
( ) ( )N
i wf j jj
N Nj
p p q q f t tq q
−−
=
− −= −∑
141.2 3( ) ln 4
i wf e
t wa
p p t B rf tq c N kh r
μ− ⎛ ⎞= = + −⎜ ⎟⎝ ⎠
11
1
1 ( ) 141.2 3( ) ln 4
1 141.2 3ln4
Ni wf j j e
jN t N waj
i wf p e
N t N wa
p p q q B rt tq c N q kh r
p p N B rq c N q kh r
μ
μ
−−
=
− − ⎛ ⎞= − + −⎜ ⎟⎝ ⎠
− ⎛ ⎞= + −⎜ ⎟⎝ ⎠
∑
Superposition Time: Material Balance Time
![Page 47: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/47.jpg)
Actual Rate Decline Equivalent Constant Rate
q
Q
actual time (t)
Q
Definition of Material Balance Time(Blasingame et al)
= Q/qmaterial balance time (tc)
![Page 48: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/48.jpg)
Features of Material Balance Time
-MBT is a superposition time function
- MBT converts VARIABLE RATE data into an EQUIVALENT CONSTANT RATE solution.
- MBT is RIGOROUS for the BOUNDARY DOMINATED flow regime
- MBT works very well for transient data also, but is only an approximation (errors can be up to 20% for linear flow)
![Page 49: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/49.jpg)
Comparison of qD (Material Balance Time Corrected) with 1/pDCylindrical Reservoir with Vertical Well in Center
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14
tD
qD a
nd 1
/p
0
0.2
0.4
0.6
0.8
1
1.2
Ratio
1/p
D to
q
Beginning of "semi-log" radial flow (tD=25)Ratio (qD to 1/pD) ~ 97%
0.97
Very early time radial flowRatio (qD to 1/pD) ~ 90%
Constant Pressure Solution qDCorrected to Harmonic
Constant Rate Solution 1/pDHarmonic
MBT Shifts Constant Pressure to Equivalent Constant Rate
![Page 50: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/50.jpg)
Corrections for Gas Reservoirs
![Page 51: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/51.jpg)
Corrections Required for Gas Reservoirs
• Gas properties vary with pressure– Formation Volume Factor– Compressibility– Viscosity
![Page 52: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/52.jpg)
Corrections Required for Gas Reservoirs
141.2 3ln 4
o ei wf
o wa
qt qB rp pc N kh r
μ ⎛ ⎞− = + −⎜ ⎟⎝ ⎠
Depletion TermDepends on compressibility
Reservoir FlowTerm: Depends on “B” and Viscosity
![Page 53: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/53.jpg)
Darcy’s Law Correction for Gas Reservoirs
Darcy’s Law states : qp ∝Δ
∫=p
pZ
pdpp0
2μ
Solution: Pseudo-Pressure
For Gas Flow, this is not true becauseviscosity (μ) and Z-factor (Z) vary with pressure
![Page 54: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/54.jpg)
Depletion Correction for Gas Reservoirs
Gas properties (compressiblity and viscosity) vary significantly with pressure
Gas Compressibility
0
0.002
0.004
0.006
0.008
0.01
0.012
0 1000 2000 3000 4000 5000 6000
Pressure (psi)
Com
pres
sibi
lity
(1/p
si)
pc g
1≈
![Page 55: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/55.jpg)
Solution: Pseudo-Time
( )
→
∫=
g
t
giga
cc
dtct
,
0
μμ
μ
Evaluated at average reservoir pressure
Not to be confused with welltest pseudo-time which evaluates properties at well flowing pressure
Depletion Correction for Gas Reservoirs: Pseudo-Time
![Page 56: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/56.jpg)
Boundary Dominated Flow Equation for Gas
⎟⎠⎞
⎜⎝⎛ −+=−=Δ
43ln*6417.1
)(2
wa
ea
iig
ipwfpip
rr
khTqeqt
GZcpppp
μ
Pseudo-pressure Pseudo-time
Constant Rate Case
Variable Rate Case
pssi
pap bqGG
qp
+=Δ α
Pseudo-Cumulative Production
![Page 57: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/57.jpg)
Overall time function -Material Balance Pseudo-time
( )∫∫
∫
==
=
t
g
igtaaca
tc
cqdt
qcqdt
qt
qdtq
t
00
0
1
1
μμ
![Page 58: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/58.jpg)
Overall material balance pseudo-time function (corrected for variable fluid saturations and formation expansion):
( )[ ]
0
ca)(1
)(
t
ift
it dtppcc
tqqct ∫ −−
=μ
μ
Where,
ggwwooft cscscscc +++= Evaluated at average reservoir pressure
Corrected Material Balance Pseudo-time
![Page 59: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/59.jpg)
Practice
- Traditional- Blasingame - Agarwal – Gardner and NPI - Flowing p/z analysis- Transient - Models and History Matcning
![Page 60: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/60.jpg)
Notes About Drive Mechanism and b Value (from Arps and Fetkovich)
b value Reservoir Drive Mechanism
0 Single phase liquid expansion (oil above bubble point)Single phase gas expansion at high pressureWater or gas breakthrough in an oil well
0.1 - 0.4 Solution gas drive
0.4 - 0.5 Single phase gas expansion
0.5 Effective edge water drive
0.5 - 1.0 Layered reservoirs
> 1 Transient (Tight Gas)
![Page 61: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/61.jpg)
Advantages of Traditional
- Easy and convenient
- No simplifying assumptions are required regarding the physics of fluid flow. Thus, can be used to model very complex systems
- Very “Real” indication of well performance
![Page 62: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/62.jpg)
Limitations of Traditional
- Implicitly assumes constant operating conditions
-Non-unique results, especially for tight gas (transient flow)
- Provides limited information about the reservoir
![Page 63: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/63.jpg)
Example 1: Decline Overpredicts Reserves
October November December January February March April2001 2002
4
Gas
Rat
e, M
Msc
fdRate vs TimeUnnamed Well
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50
Gas Cum. Prod., Bscf
0
1
2
3
4
Gas
Rat
e, M
Msc
fd
Rate vs. Cumulative Prod.Unnamed Well
EUR = 9.5 bcf
![Page 64: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/64.jpg)
Example 1 (cont’d)
Flowing Pressure and Rate vs Cumulative Production
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 1 2 3 4 5 6 7 8 9 10
Cumulative Production (bcf)
Rate
(MM
scfd
)
0
200
400
600
800
1000
1200
Flow
ing
Pres
sure
(psi
a)
True EUR does not exceed 4.5 bcf
Rates
Pressures
Forecast is not valid here
![Page 65: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/65.jpg)
Example 2: Decline Underpredicts Reserves
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20
Gas Cum. Prod., Bscf
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
Gas
Rat
e, M
Msc
fd
Rate vs. Cumulative Prod.Unnamed Well
EUR = 3.0 bcf
![Page 66: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/66.jpg)
Example 2 (cont’d)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Normalized Cumulative Production, Bscf
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0.065
0.070
0.075
0.080
0.085N
orm
aliz
ed R
ate,
MM
scfd
/(106
psi2 /
cP)Flowing Material BalanceUnnamed Well
Original Gas In Place
LegendDecline FMB
OGIP = 24 bcf
![Page 67: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/67.jpg)
Example 2 (cont’d)
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720
Time, days
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Gas
, MM
scfd
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
Pressure, psi
Data ChartUnnamed Well
LegendPressureActual Gas Data
Operating conditions: Low drawdownIncreasing back pressure
![Page 68: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/68.jpg)
Arps Production Forecast
0.01
0.1
1
10
Dec-00 May-06 Nov-11 May-17 Oct-22 Apr-28 Oct-33
Time
Gas
Rat
e (M
Msc
fd)
Economic Limit = 0.05 MMscfd
b = 0.25, EUR = 2.0 bcf
b = 0.50, EUR = 2.5 bcf
b = 0.80, EUR = 3.6 bcf
Example 3 – Illustration of Non-Uniqueness
![Page 69: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/69.jpg)
Blasingame Typecurve Analysis
Blasingame typecurves have identical format to those of Fetkovich. However, there are three important differences in presentation:
1. Models are based on constant RATE solution instead of constant pressure
2. Exponential and Hyperbolic stems are absent, only HARMONIC stem is plotted
3. Rate Integral and Rate Integral - Derivative typecurvesare used (simultaneous typecurve match)
Data plotted on Blasingame typecurves makes use of MODERN DECLINE ANALYSIS methods:
- NORMALIZED RATE (q/Δp)
- MATERIAL BALANCE TIME / PSEUDO TIME
![Page 70: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/70.jpg)
Blasingame Typecurve Analysis-Comparison to Fetkovich
log(qDd)
log(tDd)
log(q/Δp)
log(tca)
log(qDd)
log(tDd)
log(q)
log(t)
Fetkovich Blasingame
- Usage of q/Δp and tca allow boundary dominated flow to be represented by harmonic stem only, regardless of flowing conditions
- Blasingame harmonic stem offers an ANALYTICAL fluids-in-place solution
- Transient stems (not shown) are similar to Fetkovich
![Page 71: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/71.jpg)
Blasingame Typecurve Analysis- Definitions
Normalized Rate
Typecurves Data - Oil Data - Gas
⎥⎦
⎤⎢⎣
⎡−⎟
⎠⎞
⎜⎝⎛
Δ=
21ln2.141
wa
eDd r
rPkhqq βμ
Pq
Δ
pPq
Δ
( )dttqt
qDAt
Dd
DADdi ∫=
0
1 ∫ Δ
=⎟⎠⎞
⎜⎝⎛
Δ
ct
ci
dtP
qtP
q
0
1 ∫ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛
Δ
cat
pcaip
dtPq
tPq
0
1
DA
DdiDADdid dt
dqtq =
c
ic
id dtP
qdt
Pq
⎟⎠⎞
⎜⎝⎛
Δ=⎟
⎠⎞
⎜⎝⎛
Δ
ca
ipca
idp dt
Pqdt
Pq ⎟
⎟⎠
⎞⎜⎜⎝
⎛
Δ=⎟
⎟⎠
⎞⎜⎜⎝
⎛
Δ
Rate Integral
Rate Integral -Derivative
![Page 72: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/72.jpg)
actual rate
Q
actual time
Q
Concept of Rate Integral(Blasingame et al)
rate integral = Q/t
actual time
![Page 73: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/73.jpg)
Rate Integral: Like a Cumulative Average
t1
Average rate over time period“0 to t1”
q
Effective way to remove noise
Average rate over time period“0 to t2”
t2
![Page 74: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/74.jpg)
∫ Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛Δ
ct
ci
dtp
qtp
q
0
1
Rate Integral: Definition
![Page 75: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/75.jpg)
Typecurve Interpretation Aids: Integrals, Derivatives
Integral / Cumulative
Removing the scatter from noisy data sets
Dilutes the reservoir signal
Fetkovich, Blasingame, NPI
DerivativeAmplifying the reservoir signal embedded in production data
Amplifies noise - often unusable
Agarwal-Gardner, PTA
Integral-Derivative Maximizing the strengths of Integral and Derivative
Can still be noisy Blasingame, NPI
Used in AnalysisTypecurve Most Useful For Drawback
Other methods: Data filtering, Moving averages, Wavelet decomposition
![Page 76: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/76.jpg)
Rate Integral and Rate Integral Derivative(Blasingame et al)
Rate Integral
Rate (Normalized)
Rate Integral Derivative
![Page 77: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/77.jpg)
Blasingame Typecurve Analysis-Transient Calculations
Oil:
k is obtained from rearranging the definition of
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛=
21
rr
lnkh2.141
pqq
matchwa
eDd
βμΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
=21
rr
lnh2.141
qp
qk
matchwa
e
match
Dd
βμΔ
Solve for rwa from the definition of
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛=
21
rr
ln1rr
rc21
kt006328.0t
matchwa
e
2
matchwa
e2wat
cDd
φμ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
21
matchwarerln1
2
matchwarer
21
tc
k006328.0
matchDdtt
war c
φμ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
wa
w
rr
lns
![Page 78: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/78.jpg)
Blasingame Typecurve Analysis-Boundary Dominated Calculations- Oil
Oil-in-Place calculation is based on the harmonic stem of Fetkovich typecurves.
In Blasingame typecurve analysis, qDd and tDd are defined as follows:
( )( ) ciDd
iDd tDt
pqpqq =
ΔΔ
= and //
Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for oil in harmonic form:
11
1
and 1
1
+=
Δ+=
ct
DdDd
tNbc
bp
qt
q
From the above equations:
NbcD
bpq
tDp
q
pq
ti
ici
i 1 and , 1
ere wh 1
==⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Δ+Δ
=Δ
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
PSS equation for oil in harmonic form, using material balance time
Definition of Harmonic typecurve
![Page 79: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/79.jpg)
Blasingame Typecurve Analysis- Boundary Dominated Calculations- Oil (cont’d)
Oil-in-Place (N) is calculated as follows:
Rearranging the equation for Di:
bDcN
it
1=
Now, substitute the definitions of qDd and tDd back into the above equation:
( )
( )⎥⎦
⎤⎢⎣
⎡ Δ⎥⎦⎤
⎢⎣⎡=
⎥⎦
⎤⎢⎣
⎡Δ⎥⎦
⎤⎢⎣⎡
=DdDd
c
tDd
c
Ddt
qpq
tt
cpq
qttc
N /1
/
1
Y-axis “match-point”from typecurve analysis
X-axis “match-point from typecurve analysis
![Page 80: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/80.jpg)
Blasingame Typecurve Analysis- Boundary Dominated Calculations- Gas
Gas-in-Place calculation is similar to that of oil, with the additional complications of pseudo-time and pseudo-pressure.
In Blasingame typecurve analysis, qDd and tDd are defined as follows:
( )( ) caiDd
ip
pDd tDt
pqpqq =
ΔΔ
= and //
Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for gas in harmonic form:
( ) 12
1
and 1
1
+=
Δ+=
caiit
ipDdDd
tbGcZ
pb
pq
tq
μ
PSS equation for gas in harmonic form, using material balance pseudo-time
Definition of Harmonic typecurve
From the above equations:
( ) bGcZpD
bpq
tDp
q
pq
iit
ii
ipci
i
μ2 and , 1
ere wh
1==⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
Δ+Δ
=Δ
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
![Page 81: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/81.jpg)
Gas-in-Place (Gi) is calculated as follows:
Rearranging the equation for Di:
( )bcZDpG
iti
ii
μ2
=
Now, substitute the definitions of qDd and tDd back into the above equation:
Y-axis “match-point”from typecurve analysis
X-axis “match-point from typecurve analysis
Blasingame Typecurve Analysis- Boundary Dominated Calculations- Gas
( ) ( )( )
⎥⎦
⎤⎢⎣
⎡ Δ⎥⎦⎤
⎢⎣⎡=
Δ⎟⎠⎞
⎜⎝⎛
=
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛ Dd
p
Dd
ca
it
i
p
Ddit
ca
Dd
ii
qpq
tt
cZp
pqqcZ
tt
pG /2
)/(
2μ
μ
![Page 82: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/82.jpg)
Agarwal-Gardner Typecurve Analysis
Agarwal and Gardner have developed several different diagnostic methods, each based on modern decline analysis theory. The AG typecurves are all derived using the WELLTESTING definitions of dimensionless rate and time (as opposed to the Fetkovich definitions). The models are all based on the constant RATE solution. The methods they present are as follows:
1. Rate vs. Time typecurves (tD and tDA format)
2. Cumulative Production vs. Time typecurves (tD and tDAformat)
3. Rate vs. Cumulative Production typecurves (tDAformat)
- linear format- logarithmic format
![Page 83: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/83.jpg)
Agarwal-Gardner Typecurve Analysis
![Page 84: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/84.jpg)
Agarwal-Gardner - Rate vs. Time typecurves
Agarwal and Gardner Rate vs. Time typecurves are the same as conventional drawdown typecurves, but are inverted and plotted in tDA (time based on area) format.
qD vs tDA
The AG derivative plot is not a rate derivative (as per Blasingame). Rather, it is an INVERSE PRESSURE DERIVATIVE.
pD(der) = t(dpD/dt) qD(der) = t(dqD/dt)
1/pD(der) = ( t(dpD/dt) ) -1
![Page 85: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/85.jpg)
Agarwal-Gardner - Rate vs. Time typecurves
Comparison to Blasingame typecurves
Rate Integral-Derivative
Inv. Pressure Integral-Derivative
qDd and tDdplotting format
qD and tDAplotting fomat
![Page 86: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/86.jpg)
Agarwal-Gardner - Rate vs. Cumulative typecurves
Agarwal and Gardner Rate vs. Cumulative typecurves are different from conventional typecurves because they are plotted on LINEAR coordinates.
They are designed to analyze BOUNDARY DOMINATED data only. Thus, they do not yield estimates of permeability and skin, onlyfluid-in-place.
Plot: qD (1/pD) vs QDA
Where (for oil):
( )( )tpp
tqkh
Bqwfi
D −=
μ2.141
wfi
i
wfitDADDA pp
ppppNc
QtqQ−−
−==
ππ 21ely alternativor
)(21*
![Page 87: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/87.jpg)
Where (for gas):
Agarwal-Gardner - Rate vs. Cumulative typecurves
( )( )t
tqkh
Teqwfi
D ψψ −=
*6417.1
( ) wfi
i
wfiiit
caDADDA GZc
qttqQψψψψ
πψψμπ −−
−==
21ely alternativor
)(2
21*
![Page 88: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/88.jpg)
Agarwal-Gardner - Rate vs. Cumulative typecurves
qD vs QDA typecurves always converge to 1/2π (0.159)
![Page 89: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/89.jpg)
NPI (Normalized Pressure Integral)
NPI analysis plots a normalized PRESSURE rather than a normalized RATE. The analysis consists of three sets of typecurves:
1. Normalized pressure vs. tc (material balance time)
2. Pressure integral vs. tc
3. Pressure integral - derivative vs. tc
- Pressure integral methodology was developed by Tom Blasingame; originally used to interpret drawdown data with a lot of noise. (ie. conventional pressure derivative contains far too much scatter)
- NPI utilizes a PRESSRE that is normalized using the current RATE. It also utilizes the concepts of material balance time and pseudo-time.
![Page 90: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/90.jpg)
NPI (Normalized Pressure Integral): Definitions
Normalized Pressure
Typecurves Data - Oil Data - Gas
βμqPkhPD 2.141
Δ=
qPΔ
qPpΔ
( )DA
DDd td
dPP
ln=
( )cd tdqPd
qP
ln
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
( )
( )ca
p
i
p
tdqPd
qP
ln
Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
( )dttPt
PDAt
pDA
Di ∫=0
1∫
Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ ct
ci
dtqP
tqP
0
1∫
Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ catp
cai
p dtqP
tqP
0
1
DA
DiDADid dt
dPtP =
c
ic
id dtqPd
tqP ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
ca
i
pca
id
p
dtqP
dt
qP ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
Conventional Pressure Derivative
Pressure Integral
Pressure Integral -Derivative
![Page 91: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/91.jpg)
NPI (Normalized Pressure Integral): Diagnostics
Transient
Boundary Dominated
Integral - Derivative Typecurve
Normalized Pressure Typecruve
![Page 92: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/92.jpg)
NPI (Normalized Pressure Integral): Calculation of Parameters- Oil
Oil - Radial
βμqPkhPD 2.141
Δ= 2
00634.0
et
cDA rC
ktt
πφμ=
match
D
qP
Ph
k⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Δ=
βμ2.141
matchDA
c
te t
tC
kr ⎟⎟⎠
⎞⎜⎜⎝
⎛=
πφμ00634.0
matchwa
ewq
rre
rr
⎟⎟⎠
⎞⎜⎜⎝
⎛= ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
wa
w
rr
S ln
matchDA
c
match
D
t tt
qP
PSC
N ⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Δ⎟⎠⎞
⎜⎝⎛=
1000*615.52.14100634.0 0 (MBBIS)
![Page 93: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/93.jpg)
Gas – Radial
TqPkh
P pD 6417.1 Ε
Δ= 2
00634.0
etii
caDA rC
ktt
πφμ=
match
p
D
qP
Ph
Tk
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
ΔΕ
=6417.1
matchDA
ca
tiie t
tC
kr ⎟⎟⎠
⎞⎜⎜⎝
⎛=
πφμ00634.0
matchwa
e
ewa
rr
rr
⎟⎟⎠
⎞⎜⎜⎝
⎛= ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
wa
w
rrS ln
( )( ) 910*6417.100634.0
match
p
D
matchDA
ca
scitii
scig
qP
Ptt
PzcTPS
G
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
Δ⎟⎟⎠
⎞⎜⎜⎝
⎛Ε=
μ(bcf)
NPI (Normalized Pressure Integral): Calculation of Parameters- Gas
![Page 94: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/94.jpg)
pG
Measured at wellduring flow
Pressure loss due to flow in reservoir (Darcy’s Law) is constant with time
iG
i
i
zp
wf
wf
zp
- Mattar L., McNeil, R., "The 'Flowing' Gas Material Balance", JCPT, Volume 37 #2, 1998
Flowing p/z Method for Gas – Constant Rate
constant+⎟⎠⎞
⎜⎝⎛=
wfzp
zp
![Page 95: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/95.jpg)
pG
Measured at wellduring flow
i
i
zp
wf
wf
zp
Graphical Method Doesn’t Work!
iG ?
Graphical Flowing p/z Method for Gas –Variable Rate
![Page 96: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/96.jpg)
pG
Measured at wellduring flow
Pressure loss due to flow in reservoir is NOTconstant
iG
i
i
zp
wf
wf
zp
pss
wf
qbzp
zp
+⎟⎠⎞
⎜⎝⎛=
Unknown
Flowing p/z Method for Gas – Variable Rate
![Page 97: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/97.jpg)
Variable Rate p/z – Procedure (1)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
Cumulative Production, Bscf
0
50
100
150
200
250
300
350
400
450
500
550
Flowing Pressure, psi
Flowing Material BalanceUnnamed Well
Original Gas In Place
LegendStatic P/Z*
P/Z LineFlowing Pressure
Step 1: Estimate OGIP and plot a straight line from pi/zi to OGIP. Include flowing pressures (p/z)wfon plot
![Page 98: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/98.jpg)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
Cumulative Production, Bscf
0.00
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
3.60
4.00
4.40
Prod
uctiv
ity In
dex,
MM
scfd
/(106
psi2 /
cP)
0
50
100
150
200
250
300
350
400
450
500
550
Flowing Pressure, psi
Flowing Material BalanceUnnamed Well
Original Gas In Place
LegendStatic P/Z*
P/Z LineFlowing PressureProductivity Index
Variable Rate p/z – Procedure (2)
Step 2: Calculate bpss for each production point using the following formula:
Plot 1/bpss as a function of Gp
line wfpss
p pz z
bq
⎛ ⎞ ⎛ ⎞−⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
=
![Page 99: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/99.jpg)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
Cumulative Production, Bscf
0.00
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
3.60
4.00
4.40
Prod
uctiv
ity In
dex,
MM
scfd
/(106
psi2 /
cP)
0
50
100
150
200
250
300
350
400
450
500
550
Flowing Pressure, psi
Flowing Material BalanceUnnamed Well
Original Gas In Place
LegendStatic P/Z*
P/Z LineFlowing PressureProductivity Index
Variable Rate p/z – Procedure (3)
Step 3: 1/bpss should tend towards a flat line. Iterate on OGIP estimates until this happens
![Page 100: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/100.jpg)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
Cumulative Production, Bscf
0.00
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
3.60
4.00
4.40
Prod
uctiv
ity In
dex,
MM
scfd
/(106
psi2 /
cP)
0
50
100
150
200
250
300
350
400
450
500
550
P/Z*, Flow
ing Pressure, psi
Flowing Material BalanceUnnamed Well
Original Gas In Place
LegendStatic P/Z*
P/Z LineFlowing P/Z*
Flowing PressureProductivity Index
Variable Rate p/z – Procedure (4)
Step 4: Plot p/z points on the p/zline using the following formula:
“Fine tune” the OGIP estimate
pss
data wf
p p qbz z
⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
1/bpss
![Page 101: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/101.jpg)
Transient (tD format) Typecurves
Transient typecurves plot a normalized rate against material balance time (similar to other methods), but use a dimensionlesstime based on WELLBORE RADIUS (welltest definition of dimensionless time), rather than AREA. The analysis consists of two sets of typecurves:
1. Normalized rate vs. tc (material balance time)
2. Inverse pressure integral - derivative vs. tc
- Transient typecurves are designed for analyzing EARLY-TIME data to estimate PERMEABILITY and SKIN. They should not be used (on their own) for estimating fluid-in-place
- Because of the tD format, the typecurves blend together in the early-time and diverge during boundary dominated flow (opposite of tDA and tDd format typecurves)
![Page 102: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/102.jpg)
log(qDd)
log(tDd)log(tD)
log(qD)
Transient versus Boundary Scaling Formats
![Page 103: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/103.jpg)
Transient (tD format) Typecurves: Definitions
Normalized Rate
Typecurves Data - Oil Data - Gas
PkhqqD Δ
=βμ2.141
Pq
Δ pPq
Δ
( )1
0
1/1−
⎥⎥⎦
⎤
⎢⎢⎣
⎡= ∫ dttP
tP
DAt
pDA
Di
1
0
1−
⎥⎥⎦
⎤
⎢⎢⎣
⎡ Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ∫ct
ci
dtqP
tqPInv
1
0
1−
⎥⎥⎦
⎤
⎢⎢⎣
⎡ Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ∫cat
p
cai
p dtqP
tqP
Inv
1
/1−
⎥⎦
⎤⎢⎣
⎡=
DA
DiDADid dt
dPtP1−
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
c
ic
id dtqPd
tqPInv
1−
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ
ca
i
pca
id
p
dtqP
dt
qP
Inv
Inverse Pressure Integral
Inverse PresssureIntegral - Derivative
![Page 104: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/104.jpg)
Transient (tD format) Typecurves:Diagnostics (Radial Model)
Transient Transition to Boundary Dominated occurs at different points for different typecurves
Inverse Integral -Derivative Typecurve
Normalized Rate Typecurve
![Page 105: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/105.jpg)
Transient (tD format) Typecurves:Finite Conductivity Fracture Model
Increasing Fracture Conductivity (FCD stems)
Increasing Reservoir Size (xe/xf stems)
![Page 106: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/106.jpg)
Transient (tD format) Typecurves:Calculations (Radial Model)
O il W ells :
U s ing the de fin itio n o f q D ,
pe rm eab ility is ca lcu la ted as fo llo w s :
F rom the de fin ition o f tD ,
rw a is ca lcu la te d as fo llo w s :
S k in is ca lcu la ted as fo llo w s :
/ 2.141
matchDqpq
hBk ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ=
μ
/ 2.14100634.0 matchD
c
matchDtwa
tt
qpq
hB
cr ⎟
⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ⎟⎠⎞
⎜⎝⎛=
φ
)(
2.141wfi
Dppkh
qBq−
=μ
00634.0 2
wat
cD
rcktt
φμ=
ln w⎟⎠⎞
⎜⎝⎛=
warrs
Gas Wells:
For gas wells, qD is defined as follows:
The permeability is calculated from above, as follows:
From the definition of tD and k, rwa is calculated as follows
Skin is calculated as follows:
q6.4171p
RD
pkhTEq
Δ=
/6.4171
matchD
pR
qpq
hTEk ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ=
/6.417100634.0 matchD
p
matchD
caR
tiiwa
qpq
tt
hTE
cr ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛=
φμ
ln w⎟⎠⎞
⎜⎝⎛=
warrs
![Page 107: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/107.jpg)
Modeling and History Matching
Well / Reservoir Model
Well Pressure at Sandface
Production Volumes
Constraint (Input)
Signal (Output)
Well / Reservoir Model
Production Volumes
Well Pressure at Sandface
Constraint (Input)
Signal (Output)
1. Pressure Constrained System:
2. Rate Constrained System:
![Page 108: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/108.jpg)
Modeling and History Matching
Models - Horizontal Rectangular reservoir with a horizontal well located anywhere inside.
L
Models - Radial Rectangular reservoir with a vertical well located anywhere inside.
Models - Fracture Rectangular reservoir with a vertical infinite conductivity fracture located anywhere inside.
![Page 109: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/109.jpg)
A Systematic and Comprehensive Method for Analysis
![Page 110: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/110.jpg)
Modern Production Analysis Methodology
Diagnostics Interpretation andAnalysis
Modeling and History Matching
Forecasting
- Data Chart- Typecurves
- Analytical Models- Numerical Models
- Data Validation- Reservoir signal extraction
- Identifying dominant flow regimes- Estimating reservoir characteristics- Identifying important system parameters- Qualifying uncertainty
- Traditional- Fetkovich- Blasingame- AG / NPI- Flowing p/z- Transient
- Validating interpretation- Optimizing solution- Enabling additional flexibility and complexity
- Reserves- Optimization scenarios
![Page 111: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/111.jpg)
Practical Diagnostics
![Page 112: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/112.jpg)
• Qualitative investigation of data– Pre-analysis, pre-modeling– Must be quick and simple
What are diagnostics?
• A VITAL component of production data analysis (and reservoir engineering in general)
![Page 113: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/113.jpg)
Illustration- Typical Dataset
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Liqu
id R
ates
, bb
l/d
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
Gas
, M
Mcf
d
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Pressure , psi
Data ChartUnnamed Well
LegendPressureActual Gas Data
![Page 114: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/114.jpg)
“Face Value” Analysis of Data
OGIP = 90 bcf
![Page 115: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/115.jpg)
Go Back: Diagnostics
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Liqu
id R
ates
, bb
l/d
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
Gas
, M
Mcf
d
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Pressure , psi
Data ChartUnnamed Well
LegendPressureActual Gas Data
Data ChartUnnam ed Well
LegendPressureActual Gas Data
Pressures are not representative of bhdeliverability
![Page 116: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/116.jpg)
Correct Data Used
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
Liqu
id R
ates
, bb
l/d
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
Gas
, M
Mcf
d
4600
4800
5000
5200
5400
5600
5800
6000
6200
6400
6600
6800
7000
7200
7400
Pressure , psi
DataChartUnnamed Well
LegendPressureActual Gas DataOil ProductionWater Production
OGIP = 19 bcf
![Page 117: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/117.jpg)
Diagnostics using Typecurves
10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7
10-11
10-10
10-9
10-8
10-7
2358
2358
23
58
2358
2358
2
Blasingame Typecurve MatchRadial Model
qDd
tDd
Base Model:- Vertical Well in Center of Circle- Homogeneous, Single Layer
Transient (concave up) Boundary Dominated
(concave down)
![Page 118: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/118.jpg)
Material Balance Diagnostics
Diagnostics using Typecurves
10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7
10-11
10-10
10-9
10-8
10-7
2358
2358
23
58
2358
2358
2
Blasingame Typecurve MatchRadial Model
Leaky Reservoir (interference)
Reservoir With Pressure Support
Volumetric
qDd
tDd
Infinite Acting Pressure Support
Dual Depletion System
![Page 119: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/119.jpg)
Productivity Diagnostics
Diagnostics using Typecurves
10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7
10-11
10-10
10-9
10-8
10-7
2358
2358
23
58
2358
2358
2
Blasingame Typecurve MatchRadial Model
Well Cleaning Up
Liquid Loading
Increasing Damage (difficult to identify)
qDd
tDd
Productivity Shifts (workover, unreported tubing change)
![Page 120: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/120.jpg)
Transient Flow Diagnostics
Diagnostics using Typecurves
10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7
10-11
10-10
10-9
10-8
10-7
2358
2358
2358
2358
2358
2
Blasingame Typecurve MatchRadial Model
Transitionally Dominated Flow (eg: Channel or Naturally Fractured)
Fracture Linear Flow(Stimulated)
Radial Flow
DamagedqDd
tDd
![Page 121: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/121.jpg)
10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7
10-11
10-10
10-9
10-8
10-7
2358
2358
2358
2358
2358
2
Blasingame Typecurve MatchRadial Model
Δp in reservoir is too high-Tubing size too large ?- Initial pressure too high ?- Wellbore correlations underestimate pressure loss ?
Δp in reservoir is too low-Tubing size too small ?- Initial pressure too low ?- Wellbore correlations overestimate pressure loss ?
qDd
tDd
“Bad Data” Diagnostics
Diagnostics using Typecurves
![Page 122: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/122.jpg)
Selected Topics and Examples
![Page 123: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/123.jpg)
Tight Gas
![Page 124: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/124.jpg)
Industry Migration to Tight Gas Reservoirs
![Page 125: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/125.jpg)
Production Analysis – Tight Gas versus Conventional Gas
Analysis methods are no different from that of high permeability reservoirs
Transient effects tend to be more dominant – Establishing the region (volume) of influence is critical
Drainage shape becomes more important (Transitional effects)
Linear flow is more common
Layer effects are more common
![Page 126: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/126.jpg)
Tight Gas Type Curves
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
tDd
qDd
Tight Gas- Common Geometries
Linear flow dominated Limited, bounded
drainage area
Infinite acting reservoir
1/2
1
![Page 127: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/127.jpg)
Tight Gas Model 1
Extensive, continuous porous media; very low permeability
Pi = 2000 psi1800 psi
Pi = 1500 psi
![Page 128: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/128.jpg)
Tight Gas Type Curves
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
tDd
qDd
1/2
Infinite Acting System
![Page 129: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/129.jpg)
10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 678 2 3 4 5 6 78 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678
Material Balance Pseudo Time
10-2
10-1
1.0
101
102
2
3
57
2
3
57
2
34
6
9
2
3
57
2
34
6
2
Nor
mal
ized
Rat
e
Agarwal Gardner Rate vs Time Typecurve Analysis10
Example#1 – Infinite Acting System
10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678
Material Balance Pseudo Time
10-2
10-1
1.0
101
102
2
3
57
2
3
57
2
34
6
9
2
3
57
2
34
6
2
Nor
mal
ized
Rat
e
Agarwal Gardner Rate vs Time Typecurve Analysis10
k = 0.08 mdxf = 53 ft
OGIP = 10 bcf
k = 0.08 mdxf = 53 ft
Minimum OGIP = 2.6 bcf
![Page 130: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/130.jpg)
No flow continuity across reservoir- Well only drains a limited bounded volume
Tight Gas Model 2
Example: Lenticular Sands
![Page 131: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/131.jpg)
Tight Gas Type Curves
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
tDd
qDd
1/2
1- Limited or no flow continuity in reservoir - Very small drainage areas- Very large effective fracture lengths
Bounded Reservoir
Commonly observed in practice
![Page 132: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/132.jpg)
Example #2- Bounded Drainage Areas
0
1
2
3
4
5
6
7
8
9
10
0 100 200 300 400 500 600
xf (feet)
OG
IP (b
cf)
.
0
5
10
15
20
25
30
35
10 20 30 40 50 60 70 80 90 100 More
Drainage Area (acres)
Freq
uenc
y
0%
20%
40%
60%
80%
100%
120%
Frequency Cumulative %
10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78
Material Balance Pseudo Time
10-2
10-1
1.0
101
23
57
23
57
23
57
2
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisROBINSON 11-1 ALT
- West Louisiana gas field - 80 acre average spacing- All wells in boundary dominated flow
![Page 133: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/133.jpg)
Linear flow dominated system
Tight Gas Model 3
kx
ky
Example: Naturally fractured, tight reservoir
![Page 134: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/134.jpg)
Infinite Systems versus Linear Flow Systems
Establish permeability and xfindependently
Establish xf sqrt (k) product only
![Page 135: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/135.jpg)
Tight Gas Type Curves
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
tDd
qDd
1/2
- Channel and faulted reservoirs- Naturally fractured (anisotropic) reservoirs- Very large effective fracture lengths- Very difficult to uniquely interpret
Linear Flow Systems
Commonly observed in practice
![Page 136: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/136.jpg)
Example #3- Linear Flow System
101 102 1032 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8
10-8
10-7
5
79
2
3
45
7
2
3
45
Blasingame Typecurve MatchFracture Model
k = 1.1 mdxf = 511 ft
ye = 5,500 ftyw = 2,900 ft
ye
2xf
yw
![Page 137: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/137.jpg)
More Examples
![Page 138: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/138.jpg)
Example #3- Multiple Layers
10-1 1.03 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
Material Balance Pseudo Time
10-1
1.0
9
2
3
4
5
6
7
8
2
3
Nor
mal
ized
Rat
e
Blasingame Typecurve Analysis
1.0 101 102 103 1042 3 4 5 6 789 2 3 4 5 6 789 2 3 4 5 6 789 2 3 4 5 6 7810-10
10-9
10-8
2
34
68
2
345
7
Blasingame Typecurve MatchMulti Layer Model
Well
- Blasingame typecurve match, using Fracture Model- Pressure support indicated
- Three-Layer Model (one layer with very low permeability) used, late-time match improved
![Page 139: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/139.jpg)
10-3 10-2 10-1 1.06 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
Material Balance Pseudo Time
10-1
1.0
3
4
567
9
2
3
4
5
67
2
3
4
5
Nor
mal
ized
Rat
e
Agarwal Gardner Rate vs Time Typecurve AnalysisWell
Example #4- Shale Gas
- Multi-stage fractures, horizontal well- Analyzed as a vertical well in a circle
k = 0.02 mds = -4
OGIP = 4.5 bcf
![Page 140: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/140.jpg)
Tight Gas: Assessing Reserve Potential – Recovery Plots
Objectives
Determine incremental reserves that are added as the ROI expands into the reservoir (only relevant for infinite or semi-infinite systems)
To establish a practical range of Expected Ultimate Recovery
![Page 141: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/141.jpg)
Typical Recovery ProfileRecovery Curves for k = 1 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
1 md reservoir, unfractured(~10 bcf / section)
100% Recovery
![Page 142: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/142.jpg)
Typical Recovery ProfileRecovery Curves for k = 1 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- unlimited time
Actual EUR (qab = 0.05 MMscfd)
100% Recovery
1 md reservoir, unfractured(~10 bcf / section)
![Page 143: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/143.jpg)
Typical Recovery ProfileRecovery Curves for k = 1 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- 30 year EUR- unlimited time
30 Year Limited
Actual EUR (qab = 0.05 MMscfd)
100% Recovery
1 md reservoir, unfractured(~10 bcf / section)
![Page 144: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/144.jpg)
Typical Recovery ProfileRecovery Curves for k = 1 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- 30 year EUR- 20 year EUR- unlimited time
20 Year Limited30 Year Limited
Actual EUR (qab = 0.05 MMscfd)
100% Recovery
1 md reservoir, unfractured(~10 bcf / section)
![Page 145: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/145.jpg)
Tight Gas Recovery ProfileRecovery Curves for k = 0.02 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- unlimited time
0.02 md reservoir, fractured(~10 bcf / section)
Actual EUR (qab = 0.05 MMscfd)
![Page 146: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/146.jpg)
Tight Gas Recovery ProfileRecovery Curves for k = 0.02 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- 30 year EUR- unlimited time
30 Year
Actual EUR (qab = 0.05 MMscfd)
0.02 md reservoir, fractured(~10 bcf / section)
![Page 147: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/147.jpg)
Tight Gas Recovery ProfileRecovery Curves for k = 0.02 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- 30 year EUR- 20 year EUR- unlimited time
30 Year20 Year
Actual EUR (qab = 0.05 MMscfd)
0.02 md reservoir, fractured(~10 bcf / section)
![Page 148: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/148.jpg)
Tight Gas Recovery ProfileRecovery Curves for k = 0.02 md
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR
(bcf
)
EUR- 30 year EUR- 20 year EUR- unlimited time
30 Year
Max EUR (30 y) = 2 bcf
Actual EUR (qab = 0.05 MMscfd)
20 Year
0.02 md reservoir, fractured(~10 bcf / section)
![Page 149: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/149.jpg)
Example – South Texas, Deep Gas Well
1.0 101 102 1032 3 4 5 6 7 8 9 2 3 4 5 6 7 89 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8
10-9
10-8
7
9
2
3
45
7
2
3
AG Typecurve MatchFracture Model
Sqrt k X xf = 155Min OGIP = 4.2 bcf
![Page 150: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/150.jpg)
Example – South Texas, Deep Gas Well
Recovery Plot - Linear System
0
1
2
3
4
5
6
7
0 100 200 300 400 500 600
ROI (acres)
EUR
(bc
Minimum EUR = 3.5 bcf
Maximum EUR = 6.7 bcf
Recovery period = 30 yearssqrt k X xf = 155pi = 6971 psia
![Page 151: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/151.jpg)
Water Drive Models
![Page 152: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/152.jpg)
Water Drive (Aquifer) Models:
Models for reservoirs under the influence of active water encroachment can be categorized as follows:
1. Steady State Models (inaccurate for finite reservoir sizes)- Schilthuis
2. Pseudo Steady-State Models (geometry independent, time discretized)
- Fetkovich
3. Single Phase Transient Models (geometry dependent)- infinite aquifer (linear, radial or layer geometry)- finite aquifer (linear, radial or layer geometry)
4. Modified Transient Models - Moving saturation front approximations- Two phase flow approximations
![Page 153: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/153.jpg)
Water Drive (Aquifer) Models:Pseudo Steady-State Models
PSS models (such as that of Fetkovich) use a TRANSFER COEFFICIENT (similar to a well productivity index) to describe the PSS rate of water influx into the reservoir, in conjunction with a MATERIAL BALANCE model that predicts the decline in reservoir boundary pressure over time.
The Fetkovich model is generally used to determine reservoir fluid-in-place by history matching the CUMULATIVE PRODUCTION and AVERAGE RESERVOIR PRESSURE.
![Page 154: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/154.jpg)
Water Drive (Aquifer) Models:Pseudo Steady-State Models
Advantages:
- Geometry independent (applicable to aquifers of any shape, size or connectivity to the reservoir)- Works well for finite sized aquifers of medium to high mobility- Computationally efficient
Disadvantages:
- Does not provide a full time solution (transient effects are ignored)- Does not work well for infinite acting or very low mobility aquifers
![Page 155: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/155.jpg)
Water Drive (Aquifer) Models:Pseudo Steady-State Model- Equations
The Fetkovich water influx equation for a finite aquifer is:
( ) /1 ⎟⎠⎞⎜
⎝⎛ −= − iei
ii
eie
WtJpe-ppp
WW
The above equation applies to the water influx due to a constant pressure difference between aquifer and reservoir. In practice, the reservoir pressure “p” will be declining with time. Thus, the equation must be discretized as follows:
Initial encroachable water
Aquifer transfer coefficient
Reservoir boundary pressure
( ) /1 1 ⎟⎠⎞⎜
⎝⎛ −=Δ −
−
i
nn
eina
i
eie
WtJpep-pp
WW
The average aquifer pressure at the previous timestep (n-1) is evaluated explicitly, as follows:
1
1
11
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛Δ
−=∑
−
=−
ei
n
j
ej
iaW
Wpp n
(1)
![Page 156: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/156.jpg)
Water Drive (Aquifer) Models:Pseudo Steady-State Model- Equations
But there is another equation that relates the average reservoir pressure to the amount of water influx: the material balance equation for a gas reservoir under water drive.
1 1 -1
⎟⎠⎞
⎜⎝⎛ −⎟
⎠⎞
⎜⎝⎛ −=
i
ie
i
p
i
i
GBW
GG
zp
zp
Now, we have one equation with two unknowns (water influx “We” and reservoir boundary pressure “p”)
As with the water influx equation, the material balance equation can be discretized in time:
(2) 1 1 -1
⎟⎠⎞
⎜⎝⎛ −⎟
⎠⎞
⎜⎝⎛ −=⎟
⎠⎞
⎜⎝⎛
i
ie
i
p
i
i
n GBW
GG
zp
zp nn
Equations 1 and 2 are now solved simultaneously at each timestep, to obtain a discretizedreservoir pressure and water influx profile through time.
Cumulative Production
FVF at initial conditions
Gas-in-place
![Page 157: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/157.jpg)
Water Drive (Aquifer) Models:Transient Models
Transient models use the full solution to the hydraulic DIFFUSIVITY EQUATION to model rates and pressures.
The transient equations can be used to model either FINITE or INFINITE acting aquifers. There are a number of different transient models available for analyzing a reservoir under active water drive:
- Radial Composite (edge water drive)- Linear (edge water drive)- Layered (bottom water drive)
Advantages:
- Offers full continuous pressure solution in the reservoir- Includes early time effects
Disadvantages:
- Geometry dependent (only a disadvantage if aquifer properties are unknown)- Limited to assumption of single phase flow - Does not account for water influx
![Page 158: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/158.jpg)
Water Drive (Aquifer) Typecurves:Radial Composite Model
Blasingame, AG and NPI dimensionless formats can be used to plottypecurves for SINGLE PHASE production (oil or gas) from a reservoir under the influence of an EDGE WATER DRIVE. A typecurve match using this model can be used to predict
1. Reservoir fluid-in-place
2. Aquifer mobility
- These typecurves are designed to estimate fluid-in-place by detecting the shift in fluid mobility as the transient passes the reservoir boundaries, into the aquifer.
- Their usefulness is limited to single phase flow (ie: the transition from reservoir fluid to aquifer is assumed to be abrupt)
![Page 159: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/159.jpg)
Water Drive (Aquifer) Typecurves: DefinitionsModel Type: Radial Composite (two zones); outer zone is of infinite extent
Reservoir Aquifer
aq
res
res
aq
res
aq
kk
MMM
μμ
==Mobility Ratio (M):
![Page 160: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/160.jpg)
Water Drive (Aquifer) Typecurves: Diagnostics
Increasing Aquifer Mobility (M)
M=0 (Volumetric Depletion)
M=10 (Constant Pressure System (approx))
Decreasing reD value
![Page 161: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/161.jpg)
Water Drive (Aquifer) Typecurves: Diagnostics
M=10 (Constant Pressure System (approx))
M=0 (Volumetric Depletion)
Decreasing reD value
Increasing Aquifer Mobility (M)
![Page 162: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/162.jpg)
Water Drive (Aquifer) Models:Modified Transient Models
1. Moving aquifer front (reservoir boundary)
The radial composite model previously discussed can be enhanced to accommodate a shrinking reservoir boundary, caused by water influx. This is achieved by discretizingthe transient solution in time and using the PSS water influx equations to predict the advancement of the aquifer front. The solution still assumes single phase flow, but can now more accurately estimate the time to water breakthrough.
2. Two phase flow (after M. Abbaszadeh et al)
The previously discussed model can also be modified to accommodate a region of two-phase flow (located between the inner region - hydrocarbon phase and outer region - water phase). Thus, geometrically, the overall model is three zone composite. The pressure transient solution for the two-phase zone is calculated by superimposing the single phase pressure solution on a saturation profile determined using the Buckley-Leverettequations.
![Page 163: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/163.jpg)
Water Drive (Aquifer) Models: Example
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct2002 2003
0
2
4
6
8
10
12
14
16
18
20
22
Gas
, MM
scfd
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
Pressure, psi
Data ChartExample F
LegendPressureActual Gas Data
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
Material Balance Pseudo Time
10-2
10-1
1.0
101
2
3
456
8
2
3
456
8
2
3
456
8
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisExample F
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
Material Balance Pseudo Time
10-2
10-1
1.0
101
2
3
456
8
2
3
456
8
2
3
456
8
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisExample F
10-1 1.0 101 1022 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 2 3 4
Material Balance Pseudo Time
10-2
10-1
1.0
3
4
56
8
2
3
4
56
8
2
3
4
56
8
Nor
mal
ized
Rat
e, D
eriv
ativ
e
Agarwal Gardner Rate vs Time Typecurve AnalysisExample F
k = 8.5 mds = 0OGIP = 12 bcfM = 0.001
k = 3.1 mds = -4OGIP = 13.5 bcfIWIP = 47 MMbblPI (aq) = 0.59 bbl/d/psi
-Boundary dominated-Pressure support evident
-Gulf coast gas condensate reservoir
Transient Water DriveModel
PSS Water Drive Model
![Page 164: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/164.jpg)
Multiple Well Analysis
![Page 165: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/165.jpg)
1. Empirical- Group production decline plots
2. Material Balance Analysis- Shut-in data only
3. Reservoir Simulation
4. Semi-analytic production data analysis methods- Blasingame approach
Multi-well / Reservoir-based Analysis-Available Methods
![Page 166: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/166.jpg)
Multi-well Analysis- When is it required?
1. Situations where high efficiency is required- Scoping studies / A & D- Reserves auditing
2. Single well methods sometimes don’t apply- Interference effects evident in production / pressure data- Wells producing and shutting in at different times- Predictive tool for entire reservoir is required- Complex reservoir behavior in the presence of multiple wells (multi-phase flow, reservoir heterogeneities)
![Page 167: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/167.jpg)
Multi-well Analysis- When is it not required?
The vast majority of production data can be analyzed effectively without using multi-well methods
1. Single well reservoirs
2. Low permeability reservoirs- Pressure transients from different wells in reservoir do not interfere over the production life of the well
3. Cases where “outer boundary conditions” do not change too much over the production life of the well
- Wide range of reservoir types
![Page 168: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/168.jpg)
Identifying Interference
q
Q Q
Well A Well B
Rate is adjusted at Well A Response at Well B
![Page 169: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/169.jpg)
Correcting Interference Using Blasingame et al Method
A
BAtotce
qqt QQ Q +
⇒=
Define a “total material balance time” function
tce is used in place of tc to plot the data in the typecurve match
(for analyzing Well A)
![Page 170: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/170.jpg)
Multi-Well Analysis as a Typecurve Plot
log(q/Δp)
log(tc)
tce= (QB +QA)/qA
tcA tce
MBT is corrected for interference caused by production from
Well B
Analysis of Well A:
Also applies to Agarwal-Gardner, NPI and FMB
![Page 171: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/171.jpg)
Multi-Well Analysis- Example
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 20020.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
Oil
/ Wat
er R
ates
, bbl
/d
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
Gas
, MM
scfd
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
24000
26000
28000
30000
32000
34000
36000
Pressure, psi
Data ChartWell 1
LegendPressureActual Gas DataPool ProductionWater Production
-Three well system-“Staggered” on-stream dates-High permeability reservoir
Aggregate production of well group
Production history of well to be analyzed
![Page 172: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/172.jpg)
10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78
Material Balance Pseudo Time
10-2
10-1
1.0
101
2
3
45
7
2
3
45
7
2
3
45
7
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisWell 1
Multi-Well Analysis- Example
“Leaky reservoir” diagnostic
10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78
Material Balance Pseudo Time
10-2
10-1
1.0
101
2
3
45
7
2
3
45
7
2
3
45
7
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisWell 1
Corrected using multi-well modelTotal OGIP = 7 bcf
![Page 173: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/173.jpg)
0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60 6.00 6.40 6.80 7.20 7.60
Cumulative Production, Bscf
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
P/Z*, psi
Flowing Material BalanceWell 1
Original Gas In Place
LegendP/Z LineFlowing P/Z*
Multi-Well Analysis- Example
OGIP for subject well = 3.5 bcf
0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60 6.00 6.40 6.80 7.20 7.60 8.00
Cumulative Production, Bscf
0
200
400
600
800
1000
1200
1400
1600
1800
2000
P/Z*, psi
Flowing Material BalanceWell 1
Original Gas In Place
LegendP/Z LineFlowing P/Z*
Total OGIP = 7.0 bcf
![Page 174: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/174.jpg)
Overpressured Reservoirs
![Page 175: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/175.jpg)
1. Analysis methods are the same as normally pressured case
2. Additional parameters to be aware of• Formation compressibility• In-situ water compressibility• Compaction effects (pressure dependent permeability)
3. Two models available, depending on required complexity• p/z* model (accounts for constant cf, cw and co in
material balance equation• Full geomechanical model (accounts for cf(p) and k(p))
Overpressured Reservoirs
![Page 176: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/176.jpg)
Compresibilities of gas and rock
Compressibility vs. Pressure (Typical Gas Reservoir)
0.00E+00
5.00E-05
1.00E-04
1.50E-04
2.00E-04
2.50E-04
3.00E-04
0 2000 4000 6000 8000 10000 12000
Reservoir Pressure (psi)
Com
pres
sibi
lity
(1/p
si)
gas
formation
Formation energy is critical in this regionFormation energy may be influencial in this region
Formation energy is negligible in this region
![Page 177: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/177.jpg)
p/z* Model – Corrects Material Balance
( )ca
0
( ) 1 ( )
tt i
t f i
c q tt dtq c c p p
μμ ⎡ ⎤
⎢ ⎥⎣ ⎦
=− −∫
*
1 11 ( )
1
i
i
p
f i
p
p p Gzz c p p OGIP
p p Gzz OGIP
⎡ ⎤⎛ ⎞⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎜ ⎟⎡ ⎤ ⎢ ⎥⎝ ⎠ ⎣ ⎦⎢ ⎥⎣ ⎦
⎡ ⎤⎛ ⎞⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎣ ⎦
= −− −
= −Flowing MB
Typecurves
![Page 178: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/178.jpg)
Geomechanical Model – Corrects Well Productivity
⎟⎠⎞
⎜⎝⎛ −+=Δ
43ln*6417.1
)(2 **
wa
e
ia
iit
ip
rr
hkTqet
GZcqpp
μ
∫=Δpi
pwfip
zpdppk
kp
μ)(2*
∫=t
ti
ita
cdtk
kct
0
* )(μ
μ
where
In the standard pressure transient equations, permeability is usually considered to be constant. There are several situations where this may not be a valid assumption:
1. Compaction in overpressured reservoirs 2. Very low permeability reservoirs in general 3. Unconsolidated and/or fractured formations
One way to account for a variable permeability over time is to modify the definition of pseudo-pressure and pseudo-time.
Pressure dependent permeability included in pseudo-pressure and pseudo-time
![Page 179: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/179.jpg)
Overpressured Reservoirs - Example
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
Material Balance Pseudo Time
10-2
10-1
1.0
101
2
3
4
56
8
2
3
456
8
2
3
456
8
Nor
mal
ized
Rat
eBlasingame Typecurve Analysis
Gulf Coast, deep gas condensate reservoir
Boundary dominated flowOGIP = 17 bcf
![Page 180: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/180.jpg)
Overpressured Reservoirs - Example
June July August September October2003
0
10
20
30
40
50
60
70
80
Rat
e, M
Msc
fd
2000
4000
6000
8000
10000
12000
14000
16000
18000
Pressure, psi
History MatchRadial Model
218 Prod and Pressure Data
Good flowing pressure match,Poor shut-in pressure match
OGIP = 17 bcf
![Page 181: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/181.jpg)
June July August September October2003
0
10
20
30
40
50
60
70
80
Rat
e, M
Msc
fd
2000
4000
6000
8000
10000
12000
14000
16000
18000
Pressure, psi
History MatchRadial Model
218 Prod and Pressure Data
Overpressured Reservoirs - Example
Good flowing pressure match,Good shut-in pressure match
OGIP = 29 bcf
![Page 182: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/182.jpg)
Overpressured Reservoirs - Example
0 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000
Pressure, psi(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
k / k
i
k (p)k (p) Permeability
218 Prod and Pressure Data
LegendDefaultCustomInterpolation
Assumed permeability profile
![Page 183: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/183.jpg)
Horizontal Wells
![Page 184: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/184.jpg)
Horizontal Wells
Horizontal wells may be analyzed in any of three different ways, depending on
completion and petrophysical details:
1. As a vertical well,• if lateral length is small compared to drainage area
2. As a fractured well,• if the formation is very thin• if the vertical permeability is high• if the lateral is cased hole with single or multiple stage
fractures• to get an idea about the contributing lateral length
3. As a horizontal well (Blasingame model)• all others
![Page 185: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/185.jpg)
Horizontal Wells – Blasingame TypecurvesThe horizontal well typecurve matching procedure is based on a square shaped reservoir with uniform thickness (h). The well is assumed to penetrate the center of the pay zone. The procedure for matching horizontal wells is similar to that of vertical wells. However, for horizontal wells, there is more than one choice of model. Each model presents a suite of typecurves representing a different penetration ratio (L/2xe) and dimensionless wellbore radius (rwD). The definition of the penetration ratio is illustrated in the following diagram: The characteristic dimensionless parameter for each suite of horizontal typecurves is defined as follows:
hLLD β2
=
Where is the square root of the anisotropic ratio:
v
h
kk
=β
For an input value of “L”,
L
2xe
rwa h
Plan
Cross Section
L
Lrr wa
wD2
=
![Page 186: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/186.jpg)
Horizontal Wells – Example
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
Material Balance Pseudo Time
10-2
10-1
1.0
101
102
2
34
68
2
34
68
2
34
68
2
34
68
Nor
mal
ized
Rat
e
Blasingame Typecurve AnalysisUnnamed Well
L/2xe = 1rwD = 2e-3
Ld = 5Le = 1,968 ft
k (hz) = 0.18 mdk (v) = 0.011 mdOGIP = 1.1 bcf
![Page 187: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/187.jpg)
Oil Wells
![Page 188: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/188.jpg)
Oil Wells
Analysis methods are no different from that of gas reservoirs (in fact they are simpler) provided that the reservoir is above the bubble point
If below bubble point, a multi-phase capable model (Numerical) must be used
Include relative permeability effectsInclude variable oil and gas properties
![Page 189: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/189.jpg)
Oil Wells – Example
Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct2001 2002
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
Liqu
id R
ates
, bbl
/d
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
Gas
, MM
scfd
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
Pressure, psi
Data Chartexample7
LegendPressureActual Gas DataOil ProductionWater Production
- Pumping oil well- Assumed to be pumped off
Producing GOR ~ constant(indicates reservoir pressure is above bubble point
![Page 190: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/190.jpg)
Oil Wells – Example
Rs input from production data,Pbp and co calculated using Vasquez and Beggs
![Page 191: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/191.jpg)
Oil Wells – Example
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
Material Balance Time
10-2
10-1
1.0
101
2
3
456
8
2
3
456
8
2
3
456
8
Nor
mal
ized
Rat
eBlasingame Typecurve Analysisexample7
k = 1.4 mds = -3OOIP = 2.4 million bbls
![Page 192: Feketes Course Notes](https://reader034.fdocuments.us/reader034/viewer/2022042505/5525fcbe550346126f8b4b5b/html5/thumbnails/192.jpg)
Oil Wells – Example
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 20220
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
Oil
Rat
e, b
bl/d
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
Pressure, psi
Numerical Radial Model - Production Forecastexample7
LegendHistory Oil RateFlow PressSyn RateHistory Reservoir PressForecasted PressForecasted Reservoir PressForecasted Rate
240 month forecastEUR = 265 Mbbls