Conventional RTA Theory - Downloadable PDF

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Modern Production Data Analysis
Day 1 - Theory
1. Introduction to Well Performance Analysis
2. Arps – Theory
a) Exponential
b) Hyperbolic
c) Harmonic
3. Analytical Solutions
a) Transient versus Boundary Dominated
Flow
b) Boundary Dominated Flow
i. Material Balance Equation
ii. Pseudo Steady-State Concept
iii. Rate Equations
c) Transient Flow
i. Radius of Investigation Concept
ii. Transient Equation (Radial Flow)
4. Theory of Type Curves
a) Dimensionless variables
b) The log-log plot
c) Type Curve matching
5. Principle of Superposition
a) Superposition
b) Desuperposition
c) Material Balance Time
6. Gas Corrections
a) Pseudo-Pressure
b) Pseudo-Time

Modern Production Data Analysis
Day 2 - Practice
7. Arps – Practical Considerations
a) Guidelines
b) Advantages
c) Limitations
8. Analysis Using Type Curves
a) Fetkovich
b) Blasingame (Integrals)
c) AG and NPI (Derivatives)
d) Transient
e) Wattenbarger
9. Flowing Material Balance
10. Specialized
11. Modeling and History Matching
12. A Systematic and Comprehensive
Approach
13. Practical Diagnostics
a) Data validation
b) Pressure support
c) Interference
d) Liquid loading
e) Accumulating skin
damage
f) Transient flow regimes
14. Tutorials
15. Selected Topics and Examples

Introduction to Well
Performance Analysis

Traditional
- Production rate only
- Using historical trends to predict future
- Empirical (curve fitting)
- Based on analogy
- Deliverables:
- Production forecast
- Recoverable Reserves under current conditions

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

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

Modern Production Analysis -
Integration of Knowledge
Welltest Analysis
- High resolution
early-time
characterization
- High resolution
characterization
of the nearwellbore
-Point-in-time
characterization
of wellbore skin
- Characterization
of perm and skin
-Estimation of
contacted
drainage area
-Estimation of
reservoir
pressure
Modern Production Analysis
- Flow regime
characterization over
life of well
- Estimation of fluidsin-place
- Performance based
recovery factor
- Able to analyze
transient production
data (early-time
production, tight gas
etc)
- Projection
of recovery
constrained
by historical
operating
conditions
Empirical Decline
Analysis
- Estimation of
reserves when
flowing pressure
is unknown

Arps - Empirical

Traditional Decline Curves
– J.J. Arps
- Graphical – Curve fitting exercise
- Empirical – No theoretical basis
- Implicitly assumes constant operating conditions

Gas Rate, MMscfd
Gas Rate, MMscfd
Gas Rate, MMscfd
The Exponential Decline Curve
Unnamed Well
Rate vs Time
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
q
Dit
qie
Slope
Di
q
0.50
0.00
2001 2002 2003 2004 2005 2006
Unnamed Well
Rate vs Time
Unnamed Well
Rate vs. Cumulative Prod.
10 1 7
6
5
4
3
2
1.0
2
log qlog
q
Di
i
Dt i
2.302
2.302* Slope
4.50
4.00
3.50
3.00
2.50
q qiDQ
i
Di
Slope
7
2.00
6
5
4
1.50
3
1.00
0.50
10 -1
2001 2002 2003 2004 2005 2006
0.00
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

Gas Rate, MMscfd
The Hyperbolic Decline Curve
Unnamed Well
Rate vs. Cumulative Prod.
4.50
4.00
3.50
3.00
2.50
2.00
1.50
q
( 1
bD t)
Di
D
q
b
qi
i
q
1/
b
i
b
1.00
0.50
D
f () t
0.00
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

Gas Rate, MMscfd
Gas Rate, MMscfd
Hyperbolic Exponent “b”
Unnamed Well
Rate vs. Cumulative Prod.
4.50
4.00
3.50
3.00
Mild Hyperbolic – b ~ 0
2.50
2.00
1.50
1.00
0.50
0.00
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
NBU 921-22G
Rate vs. Cumulative Prod.
3.20
3.00
2.80
2.60
2.40
Strong Hyperbolic – b ~ 1
2.20
2.00
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
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
Gas Cumulative, Bscf

Analytical Solutions

Transient vs Boundary Dominated Flow

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)

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)

Boundary Dominated Flow

Definition of Compressibility
p i
p i -dp
dV
V
V
c
1
V
V
p

Compressibility Defines Material Balance of a
Closed Oil Reservoir (above bubble point)
Dp = p i - p
DV = N p
V=N
1 Np
c
N p
p pi
i
p
N
p
cN t
p p m N
i pss p
Note: only valid if c is constant

Single Phase Oil MB
pi
p
y
mx
p
i
p
m
pss
N
p
slope mpss
Np

pressure
Illustration of Pseudo-Steady-State
1
p1
2
3
p wf1
p wf2
p wf3
p2
p3
time
Constant Rate q
r w
Distance
r e

Flowing Material Balance
pi pwf
y mx b
p
i
p
wf
m
pss
N
p
b
slope mpss
b
Np

pressure
Steady-State Inflow Equation
p i
p
p wf
p p
b
pss
wf
f
qb
pss
( kh,
s,
area)
Inflow (Darcy) pressure drop- Constant-
Productivity Index
r w
Distance
r e

Flowing Material Balance
Variable Rate
p
i
p
q
wf
y mx
b
p
i
p
q
wf
mpssN
q
p
b
pss
slope mpss
bpss
Np
q

The Three Most Important Equations
in Modern Production Analysis
p pi mpssNp
p pwf
qbpss
p
i
p
wf
m
pss
N
p
qb
pss

Operating Conditions - Simplified
Constant Pressure
=
Production
Constant Rate
=
Welltest
q
q
p wf
p wf

Constant Rate Solution
Relate Back to Arps Harmonic
- Invert the PSS equation
q
1 1
p p () t mpssNp
b
m t b
pss
q
i wf pss pss
1
q bpss
pi
pwf
() t mpss
t 1
bpss

Constant Flowing Pressure Solution
- Required: q(t), N pmax and N for constant pwf
- Take derivative of both equations and solve for q
- Integrate to find Np(t), as t goes to infinity Np goes to
N pmax
mpss
pi
pwf
t
bpss
q()
t e
bpss
pi
pwf
max
Np pi pwf ctN
mpss

Constant Flowing Pressure Solution
Relate Back to Arps Exponential, Determine N
pi
pwf
qi
bpss
mpss
Di
b pss
qi
Np
max
Di
c ( p p ) c ( p p ) D
N
Np
max qi
t i wf t i wf i

Plot Constant p and Constant q together
1
0.9
0.8
0.7
0.6
Constant rate q/Dp (Harmonic)
q
pi
pwf
() t
1
bpss
mpss
t 1
bpss
0.5
0.4
0.3
Constant pressure q/Dp (Exponential)
0.2
0.1
qt ( ) 1
p p b
i wf pss
e
m
b
pss
pss
t
0
0 5 10 15 20 25 30 35 40 45

Transient Flow

Pressure, psi
Transient and Boundary Dominated Flow
3600
10
Numerical Radial Model
Cross Section Pressure Plot
3400
Cross Section
3200
3000
2800
2600
2400
2200
2000
Transient Well
Performance = f(k, skin,
time)
Boundary Dominated
Well Performance =
f(Volume, PI)
1800
1600
1400
1200
Plan View
1000
800
600
400
200
0
-4000 -3600 -3200 -2800 -2400 -2000 -1600 -1200 -800 -400 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000
Radii, ft

Pressure, psi
Radius (Region) of Investigation
10
Numerical Radial Model
Cross Section Pressure Plot
3600
3400
Cross Section
3200
3000
2800
r
inv
kt
948c
2600
2400
2200
A
inv
kt
948c
2000
1800
1600
1400
1200
1000
Plan View
800
600
400
200
0
-4000 -3600 -3200 -2800 -2400 -2000 -1600 -1200 -800 -400 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000
Radii, ft

Transient Equation
Describes radial flow in an infinite acting reservoir
q kh
1
( pi
pwf
) 141.2B 1 0.0063kt
ln 0.4045
2
c
t
s

q(t)’s compared
1.6
1.4
1.2
1
Transient flow: compares to Arps “super
hyperbolic” (b>1)
0.8
0.6
0.4
0.2
0
0 5 10 15 20 25 30 35 40 45

Type Curves

Blending of Transient into
Boundary Dominated Flow
3
2.5
Complete q(t) consists of:
Transient q(t) from t=0 to tpss
Depletion equation from t = tpss and higher
2
1.5
1
0.5
0
0 5 10 15 20 25 30 35 40 45

qD and 1/pD
Log-Log Plot: Adds a New
Visual Dynamic
Comparison of qD with 1/pD
Cylindrical Reservoir with Vertical Well in Center
1000
100
10
Infinite Acting
Boundary Dominated
Constant Rate Solution
Harmonic
0.9
1
0.1
0.01
0.001
Constant Pressure Solution Exponential
0.0001
0.00001
0.000001
0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14
tD

Type Curve
- Dimensionless model for reservoir / well system
- Log-log plot
- Assumes constant operating conditions
- Valuable tool for interpretation of production and
pressure data

Rate,
Type Curve Example - Fetkovich
Fetkovich Typecurve Analysis
1.0
7
6
5
4
3
2
q Dd
q
t
Dd
Dd
q(
t)
qi
Dit
Harmonic
q
Dd
1
1 t
Dd
10 -1
9
7
6
5
4
3
Exponential
tDd
qDd e
Hyperbolic
q
Dd
1
(1 btDd)
1/ b
2
10 -2
t Dd
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -1 1.0 10 1
Time

Rate (MMscfd)
qDd
Plotting Fetkovich Type Curves-
Example
Well 1 (exponential)
q i = 2.5 MMscfd
D i = 10 % per year
Well 2 (exponential)
q i = 10 MMscfd
D i = 20 % per year
Raw Data Plot
Time (years) Rate (MMscfd) tDd qDd
Well 1 Well 2 Well 1 Well 2 Well 1 Well 2
0 2.50 10.00 0.00 0.00 1.00 1.00
1 2.26 8.19 0.10 0.20 0.90 0.82
2 2.05 6.70 0.20 0.40 0.82 0.67
3 1.85 5.49 0.30 0.60 0.74 0.55
4 1.68 4.49 0.40 0.80 0.67 0.45
5 1.52 3.68 0.50 1.00 0.61 0.37
6 1.37 3.01 0.60 1.20 0.55 0.30
7 1.24 2.47 0.70 1.40 0.50 0.25
8 1.12 2.02 0.80 1.60 0.45 0.20
9 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
Dimensionless Plot
12.00
1.00
10.00
8.00
6.00
4.00
Well 1
Well 2
Well 1
Well 2
2.00
0.00
0 5 10 15
0.10
0.01 0.10 1.00 10.00
Time (years)
tDd

Rate,
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
NBU 921-22G
Fetkovich Typecurve Analysis
q
i
D
i
q(
t)
qDd
t
t
Dd
1.0
8
q
q Dd
7
6
5
4
3
2
10 -1
9
8
7
6
t
5
t Dd
3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2
1.0 10 1
Time
Knowing qi and Di, EUR (expected ultimate recovery) can be calculated

Rate,
Analytical Model Type Curve
Fetkovich Typecurve Analysis
10 1 2
6
4
3
2
1.0
9
6
4
3
Transient Flow
2
q Dd
10 -1
9
6
4
3
r e /r wa = 10 r e /r wa = 100 r e /r wa = 10,000
2
10 -2
9
6
4
3
Boundary Dominated Flow
Exponential
2 3 4 5 6 7 9 2 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 7
10 -4 10 -3 10 -2 10 -1 1.0 10 1
Time
t Dd

Modeling Skin using Apparent Wellbore
Radius
rwa (s)
ΔP(s)
r
wa
r
w
e
s
rwa(d)
ΔP(d)
rw
re

Dimensionless Variable Definitions
(Fetkovich)
q
Dd
141.2qB
re
1
ln
kh( pi pwf )
rwa
2
t
Dd
0.00634kt
2
ctrwa
2
e e
1 r 1 r
ln 1
2
rwa
2
rwa

Type Curve Matching (Fetkovich)
The Fetkovich analytical typecurves can be used to calculate three parameters:
permeability, skin and reservoir radius
141.2B re
1 q
k
ln
h( pi pwf )
rwa 2
qDd match
0.00634k 1
t rw
rwa
sln
2
ct 1 re
1 re
tDd rwa
ln 1
2
rwa
2
rwa
match
141.2B 0.00634 q t
re
2
h ( pi pwf ) ct qDd tDd match
match

Rate,
Type Curve Matching - Example
10
Fetkovich Typecurve Analysis
8
6
4
3
2
r eD = 50
k = f(q/q Dd )
s = f(q/q Dd * t/t Dd , r eD )
r e = f(q/q Dd * t/t Dd )
1.0
8
6
4
3
2
q
Transient Flow
10 -1
8
6
q Dd
4
3
10 1 2
10 -2
8
6
4
3
2
t
Boundary Dominated Flow
Exponential
10 -3
2 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 2 3 4 5 6 78
10 -4 10 -3 10 -2 10 -1 1.0 10 1
Time
t Dd

Superposition

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 periods
2. The observed pressure response is a result of the additive effect of each rate
change in the history
Example: Two Rate History
q
p wf
q 2
q 1
pi
pwf
q f t q q f t t
Effect of (q 2 -q 1 )
( ) ( ) ( )
t 1
1 2 1 1

The Principle of Superposition
Two Rate History
pi
pwf
q1 f ( t) ( q2 q1) f ( t t1)
N - Rate History
N
i wf ( j j 1) ( j 1)
p p q q f t t
j1
f(t) is the Unit Step Response

Superposition versus Desuperposition
Simple
- Unit step response f(t)
- Type Curve
- Superposition Time
Superposition
Complex
- Real rate and pressure
history
- Modeling (history
matching)
q
pwf
Desuperposition
q
pwf

Superposition Time
Convert multiple rate history into an equivalent single rate history by re-plotting
data points at their “superposed” times
p p q q
qN
qN
N
i wf ( j j 1)
j1
f t
( tj
1)

The Principle of Superposition –
PSS Case
p p q q
qN
qN
N
i wf ( j j 1)
j1
f t
( tj
1)
pi pwf t 141.2B
re
3
f( t) ln
q ctN kh rwa
4
N
pi pwf 1 ( qj qj 1) 141.2B
re
3
( t tj
1) ln
qN ctN j1
qN kh rwa
4
pi pwf 1 Np 141.2B
re
3
ln
qN ctN qN kh rwa
4
Superposition Time: Material Balance Time

Definition of Material Balance Time
(Blasingame et al)
Actual Rate Decline
Equivalent Constant Rate
q
Q
Q
actual
time (t)
material
balance
time (t c )
= Q/q

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)

qD and 1/pD
Ratio 1/pD to qD
MBT Shifts Constant Pressure to
Equivalent Constant Rate
Comparison of qD (Material Balance Time Corrected) with 1/pD
Cylindrical Reservoir with Vertical Well in Center
1000
100
10
1
Very early time radial flow
Ratio (qD to 1/pD) ~ 90%
Constant Rate Solution
1/p D
Harmonic
1.2
1
0.97
0.8
0.1
0.01
Beginning of "semi-log" radial flow (tD=25)
Ratio (qD to 1/pD) ~ 97%
0.6
0.001
0.4
0.0001
0.00001
Constant Pressure Solution q D
Corrected to Harmonic
0.2
0.000001
0
0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14
tD

Corrections for Gas Reservoirs

Corrections Required for Gas
Reservoirs
• Gas properties vary with pressure
– Formation Volume Factor
– Compressibility
– Viscosity

Corrections Required for Gas
Reservoirs
Depletion Term
Depends on
compressibility
Reservoir FlowTerm:
Depends on “B” and
Viscosity
p
i
qt 141.2qBo re
3
pwf
ln
coN kh rwa
4

Darcy’s Law Correction for Gas
Reservoirs
Darcy’s Law states :
Dp
q
For Gas Flow, this is not true because
viscosity () and Z-factor (Z) vary with pressure
Solution: Pseudo-Pressure
p
p
p
pdp
2
Z
0

Compressibility (1/psi)
Depletion Correction for Gas
Reservoirs
Gas properties (compressibility and viscosity) vary
significantly with pressure
Gas Compressibility
0.012
0.01
0.008
0.006
0.004
cg
1
p
0.002
0
0 1000 2000 3000 4000 5000 6000
Pressure (psi)

Depletion Correction for Gas
Reservoirs: Pseudo-Time
Solution: Pseudo-Time
t
a
,
c
g
c
g
i
t
0
dt
c
g
Evaluated at average reservoir
pressure
Not to be confused with welltest pseudo-time which evaluates properties
at well flowing pressure

Boundary Dominated Flow
Equation for Gas
Constant Rate Case
Pseudo-pressure
Pseudo-time
Dp
p
p
pi
p
pwf
2 pi
( cgZ
) iG
i
qt
a
1.417e6*
Tq
kh
ln
r
r
e
wa
3
4
Variable Rate Case
Dp
q
p
G
qGi
pa
b
pss
Pseudo-Cumulative Production

Overall time function - Material
Balance Pseudo-time
t
t
c
ca
1
q
1
q
t
0
ta
0
qdt
qdt
a
c
q
g
i
t
0
qdt
c
g

Improved Material Balance
Pseudo-time
Overall material balance pseudo-time function (corrected for
variable fluid saturations, water encroachment, in-situ fluids & formation expansion and
desorption):
t
t ct
i
q(
t)
ca
q
ct1
cf
( pi
0
p)
dt

Arps – Practical Consideration

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 pressure
Water 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)

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

Limitations of Traditional
- Implicitly assumes constant operating conditions
- Non-unique results, especially for tight gas (transient flow)
- Provides limited information about the reservoir

Gas Rate, MMscfd
Gas Rate, MMscfd
Example 1: Decline Overpredicts
Reserves
Unnamed Well
Rate vs Time
4
October November December January February March April
2001 2002
Unnamed Well
Rate vs. Cumulative Prod.
4
EUR = 9.5 bcf
3
2
1
0
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

Rate (MMscfd)
Flowing Pressure (psia)
Example 1 (cont’d)
Flowing Pressure and Rate vs Cumulative Production
5
4.5
4
3.5
3
2.5
2
1.5
Rates
Pressures
True EUR does not
exceed 4.5 bcf
Forecast is not
valid here
1200
1000
800
600
400
1
0.5
0
200
0
0 1 2 3 4 5 6 7 8 9 10
Cumulative Production (bcf)

Gas Rate, MMscfd
Example 2: Decline Underpredicts
Reserves
8.50
Unnamed Well
Rate vs. Cumulative Prod.
8.00
7.50
7.00
6.50
6.00
5.50
5.00
EUR = 3.0 bcf
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
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

Normalized Rate, MMscfd/(10 6 psi 2 /cP)
Example 2 (cont’d)
0.085
0.080
Unnamed Well
Flowing Material Balance
Legend
Decline FMB
0.075
0.070
0.065
0.060
0.055
0.050
OGIP = 24 bcf
0.045
0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.005
Original Gas In Place
0.000
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

Gas, MMscfd
Pressure, psi
Example 2 (cont’d)
Unnamed Well
Data Chart
18
17
Legend
Pressure
Actual Gas Data
1300
1200
16
15
1100
14
1000
13
12
900
11
10
9
8
Operating conditions: Low drawdown
Increasing back pressure
800
700
600
7
500
6
400
5
4
300
3
200
2
1
100
0
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
0
Time, days

Gas Rate (MMscfd)
Example 3 – Illustration of Non-
Uniqueness
Arps Production Forecast
10
1
0.1
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
0.01
Dec-00 May-06 Nov-11 May-17 Oct-22 Apr-28 Oct-33
Time

Analysis using Type Curves

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 typecurves are used
(simultaneous typecurve match)
Data plotted on Blasingame typecurves makes use of MODERN DECLINE ANALYSIS
methods:
- NORMALIZED RATE (q/Dp)
- MATERIAL BALANCE TIME / PSEUDO TIME

Blasingame Typecurve Analysis-
Comparison to Fetkovich
Fetkovich
Blasingame
log(q)
log(q/Dp)
log(q Dd )
log(q Dd )
log(t)
log(tca)
log(t Dd )
log(t Dd )
- Usage of q/Dp 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

Blasingame Typecurve Analysis-
Definitions
Normalized Rate
q
Dd
Typecurves Data - Oil Data - Gas
141.2q
re
1
q
q
ln
khDP
rwa
2
DP
DPp
Rate Integral
Rate Integral - Derivative
q
Ddi
1
t
DA
Ddid
t DA
0
q
q t
Dd
DA
t
dt
dq
dt
Ddi
DA
q
P
D
i
q
P
D
t c
1 q
dt
t D P
id
c
0
t
c
q
d
DP
dt
c
i
q
DP
q
DP
p
p
i
id
1
t
t
ca
ca
t ca
q
D P
0
ca
p
q
d
DP
dt
p
dt
i

Concept of Rate Integral
(Blasingame et al)
actual rate
rate
integral =
Q/t
Q
Q
actual
time
actual
time

Rate Integral: Like a Cumulative
Average
Average rate over time period
“0 to t 1 ”
Average rate over time period
“0 to t 2 ”
q
t 1
t 2
Effective way to remove noise

Rate Integral: Definition
q
Dp
i
1
t
c
t c
q
D p
0
dt

Typecurve Interpretation Aids:
Integrals, Derivatives
Typecurve Most Useful For Drawback
Used in Analysis
Integral /
Cumulative
Removing the scatter from
noisy data sets
Dilutes the reservoir
signal
Fetkovich,
Blasingame, NPI
Derivative
Amplifying 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
Other methods: Data filtering, Moving averages, Wavelet decomposition

Rate Integral and Rate Integral
Derivative (Blasingame et al)
Rate Integral
Rate (Normalized)
Rate Integral Derivative

Blasingame Typecurve Analysis-
Transient Calculations
Oil:
k is obtained from rearranging the definition of
2
1
r
r
ln
kh
141.2
p
q
q
match
wa
e
Dd
D
2
1
r
r
ln
h
141.2
q
p
q
k
match
wa
e
match
Dd
D
Solve for r wa from the definition of
2
1
r
r
ln
1
r
r
r
c
2
1
0.006328kt
t
match
wa
e
2
match
wa
e
2
wa
t
c
Dd
2
1
match
wa
r
e
r
ln
1
2
match
wa
r
e
r
2
1
t
c
0.006328k
match
Dd
t
t
wa
r
c
wa
w
r
r
ln
s

Blasingame Typecurve Analysis-
Boundary Dominated Calculations-Oil
Oil-in-Place calculation is based on the harmonic stem of Fetkovich typecurves.
In Blasingame typecurve analysis, q Dd and t Dd are defined as follows:
q
Dd
q
q
/
/
Dp
Dp
i
and
t
Dd
Dit
Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for oil in
harmonic form:
q
Dd
1
1
t
Dd
From the above equations:
Definition of Harmonic
typecurve
and
q
Dp
c
1
b
1
t
ctNb
c
1
PSS equation for oil in
harmonic form, using
material balance time
q
Dp
q
Dp
1
Dit
q
Dp
i
1
1
where
, and Di
c
b
i
ctNb

Blasingame Typecurve Analysis-
Boundary Dominated Calculations-Oil
Oil-in-Place (N) is calculated as follows:
Rearranging the equation for Di:
N
1
ctDib
Now, substitute the definitions of q Dd and t Dd back into the above equation:
N
t
ct
t
Dd
c
1
qDd
q
/ Dp
1
ct
t
t
c
Dd
q / Dp
qDd
X-axis “match-point from
typecurve analysis
Y-axis “match-point”
from typecurve analysis

Blasingame Typecurve Analysis- Boundary
Dominated Calculations- Gas
Gas-in-Place calculation is similar to that of oil, with the additional complications of pseudotime
and pseudo-pressure.
In Blasingame typecurve analysis, q Dd and t Dd are defined as follows:
q
Dd
q
q
/
/
Dp
Dp
p
i
p
and
t
Dd
Dit
Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for gas in
harmonic form:
q
Dd
1
1
t
Dd
From the above equations:
Definition of Harmonic
typecurve
and
q
Dp
p
ca
1
b
2 pi
t
Zct
Gib
i
ca
1
PSS equation for gas in
harmonic form, using
material balance pseudotime
q
Dp
q
Dp
i
1
Dit
c
where
q
Dp
p
i
1
b
,
and
D
i
2 p
ZctiG
ib
i

Blasingame Typecurve Analysis-
Boundary Dominated Calculations- Gas
Gas-in-Place (G i ) is calculated as follows:
Rearranging the equation for Di:
G
i
D
i
2 pi
Zctb
i
Now, substitute the definitions of q Dd and t Dd back into the above equation:
G
i
t
t
Dd
ca
2 p
Zct
i
i
qDd
( q / Dpp)
2 pi
Zct
i
t
t
ca
Dd
q / Dp
qDd
p
X-axis “match-point from
typecurve analysis
Y-axis “match-point”
from typecurve analysis

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 tDA
format)
3. Rate vs. Cumulative Production typecurves (tDA
format)
- linear format
- logarithmic format

Agarwal-Gardner Typecurve Analysis

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.
p D (der) = t(dp D /dt)
q D (der) = t(dq D /dt)
1/p D (der) = ( t(dp D /dt) ) -1

Agarwal-Gardner - Rate vs.
Time Typecurves
Comparison to Blasingame Typecurves
Rate Integral-
Derivative
Inv. Pressure
Integral-
Derivative
qDd and tDd
plotting format
qD and tDA
plotting fomat

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, only fluid-in-place.
Plot: qD (1/pD) vs QDA
Where (for oil):
q
D
141.2B
kh
p
i
t
q
p
wf
t
Q
DA
q
D
* t
DA
1
2
Q
or alternativ
ely
ctN(
pi
pwf
)
2
1
pi
p
p p
i
wf

Agarwal-Gardner - Rate vs.
Cumulative Typecurves
Where (for gas):
q
D
t
1.417e6*
T q
kh
i
wf
t
Q
DA
q
D
* t
DA
1
2
2qt
ca
or alternativ
ely
ctZ
iGi
(
i
wf
)
i
wf
1
2
i

Agarwal-Gardner - Rate vs.
Cumulative Typecurves
qD vs QDA typecurves
always converge to 1/2
0.159)

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 pseudotime.

NPI (Normalized Pressure Integral):
Definitions
Normalized Pressure
Conventional
Pressure Derivative
Pressure Integral
Pressure Integral -
Derivative
P
Di
Typecurves Data - Oil Data - Gas
khDP
DP
DP
P D
p
141. 2q
q
q
P
Dd
1
t
dPD
d ln t
DA
t DA
0
P t
Did
P
p
DA
DA
t
dt
dP
dt
Di
DA
DP
q
DP
q
i
DP
q
id
DP
d
q
d ln
d
t c
1
t
c
t c
D P
dt
q
0
t
c
c
DP
d
q
dt
i
DP
q
DP
q
DP
q
p
p
p
i
id
i
d DP
p
q
d ln t
1
t
t
ca
ca
ca
D P
q
tca
0
ca
p
DP
d
q
dt
p
dt
i

NPI (Normalized Pressure Integral):
Diagnostics
Transient
Normalized
Pressure
Typecruve
Integral - Derivative
Typecurve
Boundary
Dominated

NPI (Normalized Pressure Integral):
Calculation of Parameters- Oil
Oil - Radial
khDP
P D
141. 2q
0.00634kt
c
DA
2
C tre
t
141.2 PD
k
h DP
q
match
r
r
e
wq
0.00634k
t
C
t t
re
r
wa
r
e
match
c
DA
match
S
r
ln
r
w
wa
N
.00634 141.2S
PD
C
DP
t 5.615*1000
q
0 0
match
t
t
c
DA
match
(MBBIS)

NPI (Normalized Pressure Integral):
Calculation of Parameters- Gas
Gas – Radial
P
D
khDP
0.00634kt
p
ca
t
DA
2
1.4176Tq
iC
tire
1.4176T
PD
k
h DP
q
p
match
r
e
0.00634k
t
iC
ti t
ca
DA
match
r
wa
G
re
re
r
wa
match
r
S ln
r
0.006341.4176S
g
PT
i sc t P
9
c z P
i
ti
i
sc
t
ca
DA
w
wa
match
D
DP
q
p
match
*10
(bcf)

Transient (tD format) Typecurves
Transient typecurves plot a normalized rate against material balance time
(similar to other methods), but use a dimensionless time 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)

Transient versus Boundary
Scaling Formats
log(q D )
log(q Dd )
log(t D )
log(t Dd )

Transient (tD format) Typecurves:
Definitions
Normalized Rate
Inverse Pressure
Integral
1/ P
Di
Typecurves Data - Oil Data - Gas
141.2q
q
q
khDP
DP
DP
q D
t
1
DA
Pp
t
dt
tDA
0
1
DP
1
Inv
q i
tc
t
c
0
DP
dt
q
1
DP
Inv
q
p
p
1
t
i ca
t ca
0
DP
q
p
dt
1
Inverse Presssure
Integral - Derivative
1/ P
Did
t
DA
dP
dt
Di
DA
1
DP
Inv
q
id
t
c
DP
d
q i
dt
c
1
DP
Inv
q
p
id
t
ca
DP
d
q
dt
ca
p
i
1

Transient (tD format) Typecurves:
Diagnostics (Radial Model)
Transient
Inverse Integral -
Derivative
Typecurve
Transition to Boundary
Dominated occurs at
different points for
different typecurves
Normalized Rate
Typecurve

Transient (tD format) Typecurves:
Finite Conductivity Fracture Model
Increasing Fracture
Conductivity (FCD
stems)
Increasing
Reservoir Size
(xe/xf stems)

Transient (tD format) Typecurves:
Calculations (Radial Model)
Oil Wells:
Using the definition of q D ,
q
D
141.2qB
kh(
pi
pwf
)
permeability is calculated as follows:
Gas Wells:
For gas wells, q D is defined as follows:
q
D
1.417E6T
kh
R
q
Dp
p
141.2B
q/
Dp
k
h qD
From the definition of t D ,
match
The permeability is calculated from above, as follows:
1.417E6TR
q/
Dpp
k
h qD
match
t
D
0.00634kt
2
ctrwa
c
From the definition of t D and k, r wa is calculated as follows
r wa is calculated as follows:
r
wa
0.00634 141.2B
q/
Dp
ct
h qD
match
tc
tD
match
r
wa
0.00634 1.417E6T
icti
h
Skin is calculated as follows:
R
t
t
ca
D
match
q/
Dpp
qD
match
Skin is calculated as follows:
rw
s ln
rwa
s
rw
ln
rwa

Flowing Material Balance

Flowing p/z Method for Gas –
Constant Rate
p
z
p
zi
wf
wf
i
- Mattar L., McNeil, R., "The 'Flowing' Gas
Material Balance", JCPT, Volume 37 #2, 1998
Pressure loss due to flow
in reservoir (Darcy’s Law)
is constant with time
p
z
p
z
wf
constant
Measured at well
during flow
Gi
Gp

Graphical Flowing p/z Method
for Gas – Variable Rate
p
z
i
i
p
z
wf
wf
Graphical Method Doesn’t
Work!
G i ?
Measured at well
during flow
Gp

Flowing p/z Method for Gas –
Variable Rate
p
z
p
zi
wf
wf
i
Pressure loss due to flow
in reservoir is NOT
constant
p
z
p
z
wf
qb
pss
Unknown
Measured at well
during flow
Gi
Gp

Flowing Pressure, psi
Variable Rate p/z – Procedure (1)
Unnamed Well
Flowing Material Balance
Legend
Static P/Z *
P/Z Line
Flow ing Pressure
550
500
Step 1: Estimate OGIP and
plot a straight line from pi/zi
to OGIP. Include flowing
pressures (p/z)wf on plot
450
400
350
300
250
200
150
100
Original Gas In Place
50
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
0
Cumulative Production, Bscf

Productivity Index, MMscfd/(10 6 psi 2 /cP)
Flowing Pressure, psi
Variable Rate p/z – Procedure (2)
Unnamed Well
Flowing Material Balance
4.40
4.00
3.60
3.20
2.80
2.40
2.00
1.60
Legend
Static P/Z *
P/Z Line
Flow ing Pressure
Productivity Index
Step 2: Calculate bpss for
each production point using
the following formula:
b
pss
p p
z line
z
q
wf
550
500
450
400
350
300
250
200
1.20
0.80
Plot 1/bpss as a function of
Gp
150
100
0.40
Original Gas In Place
50
0.00
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
0
Cumulative Production, Bscf

Productivity Index, MMscfd/(10 6 psi 2 /cP)
Flowing Pressure, psi
Variable Rate p/z – Procedure (3)
Unnamed Well
Flowing Material Balance
4.40
4.00
3.60
3.20
2.80
Legend
Static P/Z *
P/Z Line
Flow ing Pressure
Productivity Index
Step 3: 1/bpss should tend
towards a flat line. Iterate on
OGIP estimates until this
happens
550
500
450
400
350
2.40
300
2.00
250
1.60
200
1.20
150
0.80
100
0.40
Original Gas In Place 50
0.00
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
0
Cumulative Production, Bscf

Productivity Index, MMscfd/(10 6 psi 2 /cP)
P/Z * , Flowing Pressure, psi
Variable Rate p/z – Procedure (4)
Unnamed Well
Flowing Material Balance
4.40
4.00
3.60
3.20
2.80
2.40
2.00
1.60
Legend
Static P/Z *
P/Z Line
Flow ing P/Z *
Step 4: Plot p/z points on the
p/z line using the following
formula:
p p
qb
z z
data
“Fine tune” the OGIP estimate
wf
Flow ing Pressure
Productivity Index
pss
550
500
450
400
350
300
250
200
1.20
150
0.80
100
0.40
1/b pss
Original Gas In Place 50
0.00
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
0
Cumulative Production, Bscf

Specialized

Modeling and History Matching

Modeling and History Matching
1. Pressure Constrained System:
Constraint (Input)
Well Pressure at Sandface
Well / Reservoir
Model
Signal (Output)
Production Volumes
2. Rate Constrained System:
Constraint (Input)
Production Volumes
Well / Reservoir
Model
Signal (Output)
Well Pressure at Sandface

Modeling and History Matching
Models - Radial
Rectangular reservoir with a vertical well located anywhere inside.
Models - Horizontal
Rectangular reservoir with a horizontal well located anywhere inside.
L
Models - Fracture
Rectangular reservoir with a vertical infinite conductivity fracture located anywhere inside.

A Systematic and Comprehensive
Method for Analysis

Modern Production Analysis
Methodology
Diagnostics
Interpretation and
Analysis
Modeling and
History Matching
Forecasting
- Data Validation
- Reservoir signal
extraction
- Identifying dominant
flow regimes
- Estimating reservoir
characteristics
- Identifying important
system parameters
- Qualifying
uncertainty
- Validating interpretation
- Optimizing solution
- Enabling additional
flexibility and complexity
- Reserves
- Optimization scenarios
- Data Chart
- Typecurves
- Traditional
- Fetkovich
- Blasingame
- AG / NPI
- Flowing p/z
- Transient
- Analytical Models
- Numerical Models

Practical Diagnostics

What are diagnostics?
• Qualitative investigation of data
– Pre-analysis, pre-modeling
– Must be quick and simple
• A VITAL component of production data
analysis (and reservoir engineering in
general)

Pressure , psi
Illustration- Typical Dataset
Unnamed Well
Data Chart
28
26
5.50
Legend
Pressure
Actual Gas Data
1600
1500
24
5.00
1400
22
20
18
4.50
4.00
1300
1200
1100
1000
16
3.50
900
Gas , MMcfd
Liquid Rates , bbl/d
14
12
10
8
6
4
2
0
3.00
2.50
2.00
1.50
1.00
0.50
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
Time, days
800
700
600
500
400
300
200
100
0

“Face Value” Analysis of Data
OGIP = 90 bcf

Pressure , psi
Go Back: Diagnostics
Unnamed Well
Data Chart
28
26
5.50
Legend
Pressure
Actual Gas Data
1600
1500
24
5.00
1400
22
20
4.50
1300
1200
18
4.00
1100
1000
Liquid Rates , bbl/d
16
3.50
Unnamed Well
Data Chart
900
14
3.00
Legend
Pressure
Actual Gas Data
800
Gas , MMcfd
12
700
10
2.50
600
8
6
4
2
2.00
1.50
1.00
Pressures are not
representative of
bh deliverability
500
400
300
200
100
0
0.50
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
Time, days
0

Liquid Rates , bbl/d
Gas , MMcfd
Pressure , psi
Correct Data Used
6.00
5.50
Unnamed Well
5.50
5.00
Data Chart
Legend
Pressure
Actual Gas Data
Oil Production
Water Production
7400
7200
7000
5.00
4.50
6800
4.50
6600
4.00
4.00
6400
3.50
3.50
6200
3.00
3.00
6000
2.50
2.00
2.50
2.00
5800
5600
5400
OGIP = 19 bcf
1.50
1.00
1.50
5200
5000
0.50
1.00
4800
0.00
0.50
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
Time, days
4600

Diagnostics using Typecurves
Radial Model
Blasingame Typecurve Match
2
8
5
3
2
qDd
10 -7
10 -8
8
5
3
2
10 -9
8
5
3
2
8
5
3
2
8
5
3
2
10 -10
10 -11
Transient
(concave up)
Base Model:
- Vertical Well in Center of Circle
- Homogeneous, Single Layer
Boundary Dominated
(concave down)
tDd
4 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 -1 1.0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Diagnostics using Typecurves
Material Balance Diagnostics
Radial Model
Blasingame Typecurve Match
2
10 -7 2
10 -8
qDd
8
5
3
2
8
5
3
2
Reservoir With
Pressure Support
10 -9
10 -10
8
5
3
2
8
5
3
2
10 -11
8
5
3
Leaky Reservoir
(interference)
tDd
4 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 -1 1.0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Diagnostics using Typecurves
Productivity Diagnostics
Radial Model
Blasingame Typecurve Match
2
8
5
3
2
Increasing Damage (difficult to identify)
qDd
10 -7 2
10 -8
10 -9
10 -10
8
5
3
2
8
5
3
2
8
5
3
2
Well Cleaning Up
Liquid Loading
Productivity Shifts
(workover,
unreported tubing
change)
10 -11
8
5
3
tDd
4 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 -1 1.0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Diagnostics using Typecurves
Transient Flow Diagnostics
Radial Model
Blasingame Typecurve Match
qDd
10 -8
10 -9
2
10 -7 2
8
5
3
2
8
5
3
2
8
5
Radial Flow
Damaged
Fracture Linear Flow
(Stimulated)
Transitionally
Dominated Flow (eg:
Channel or Naturally
Fractured)
3
2
10 -10
8
5
3
2
10 -11
8
5
3
tDd
4 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 -1 1.0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Diagnostics using Typecurves
“Bad Data” Diagnostics
Radial Model
Blasingame Typecurve Match
2
10 -7 2
qDd
10 -8
8
5
3
2
8
5
3
2
Dp in reservoir is too low
-Tubing size too small ?
- Initial pressure too low ?
- Wellbore correlations
overestimate pressure loss ?
10 -9
10 -10
8
5
3
2
8
5
3
2
Dp in reservoir is too high
-Tubing size too large ?
- Initial pressure too high ?
- Wellbore correlations
underestimate pressure loss ?
10 -11
8
5
3
tDd
4 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 -1 1.0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

Selected Topics and Examples

Tight Gas

Industry Migration to Tight Gas
Reservoirs

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

qDd
Tight Gas- Common Geometries
Tight Gas Type Curves
1.00E-05
Infinite acting reservoir
1.00E-06
1.00E-07
1/2
1.00E-08
1.00E-09
1
1.00E-10
Linear flow
dominated
Limited, bounded
drainage area
1.00E-11
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

Tight Gas Model 1
‣ Extensive, continuous porous media; very low
permeability
Pi = 2000 psi
1800 psi
Pi = 1500 psi

qDd
Infinite Acting System
Tight Gas Type Curves
1.00E-05
1.00E-06
1.00E-07
1/2
1.00E-08
1.00E-09
1.00E-10
1.00E-11
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

Normalized Rate
Normalized Rate
Example#1 – Infinite Acting System
10
Agarwal Gardner Rate vs Time Typecurve Analysis
10
Agarwal Gardner Rate vs Time Typecurve Analysis
2
2
6
6
4
4
3
3
2
2
10 1
10 1
7
7
5
5
3
3
2
2
1.0
9
1.0
9
6
6
4
3
4
3
2
2
10 -1
10 -1
7
5
7
5
3
3
2
2
10 2 2
10 -2
7
5
10 2 2
10 -2
7
5
3
3
2 3 4 5 6 7 8 2 3 4 5 6 78 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -5 10 -4 10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time
2 3 4 5 6 7 8 2 3 4 5 6 78 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -5 10 -4 10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time
k = 0.08 md
xf = 53 ft
OGIP = 10 bcf
k = 0.08 md
xf = 53 ft
Minimum OGIP = 2.6 bcf

Tight Gas Model 2
‣ No flow continuity across reservoir- Well only
drains a limited bounded volume
Example: Lenticular Sands

qDd
Bounded Reservoir
Tight Gas Type Curves
1.00E-05
1.00E-06
1.00E-07
1/2
1.00E-08
1.00E-09
1.00E-10
- Limited or no flow continuity in reservoir
- Very small drainage areas
- Very large effective fracture lengths
1
1.00E-11
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
Commonly observed in practice

OGIP (bcf) .
Frequency .
Normalized Rate
Example #2- Bounded Drainage
Areas
10
ROBINSON 11-1 ALT
2
Blasingame Typecurve Analysis
9
8
- West Louisiana gas field
- 80 acre average spacing
- All wells in boundary dominated flow
10 1 2
1.0
7
5
3
2
7
5
3
2
7
10 -1
7
5
3
6
10 -2
2 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
10 -3 10 -2 10 -1 1.0 10 1 10 2
5
Material Balance Pseudo Time
4
3
35
30
25
120%
100%
80%
20
2
15
60%
1
10
5
40%
20%
0
0 100 200 300 400 500 600
xf (feet)
0
10 20 30 40 50 60 70 80 90 100 More
Drainage Area (acres)
Frequency Cumulative %
0%

Tight Gas Model 3
‣ Linear flow dominated system
Example: Naturally fractured, tight reservoir
ky
kx

Infinite Systems versus Linear Flow
Systems
Establish
permeability and
xf independently
Establish xf sqrt
(k) product only

qDd
Linear Flow Systems
Tight Gas Type Curves
1.00E-05
1.00E-06
1.00E-07
1/2
1.00E-08
1.00E-09
1.00E-10
- Channel and faulted reservoirs
- Naturally fractured (anisotropic) reservoirs
- Very large effective fracture lengths
- Very difficult to uniquely interpret
1.00E-11
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
Commonly observed in practice

ye
yw
Example #3- Linear Flow System
Fracture Model
Blasingame Typecurve Match
5
4
3
2
k = 1.1 md
xf = 511 ft
ye = 5,500 ft
yw = 2,900 ft
10 -7 5
7
5
4
3
2
2xf
10 -8
9
7
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8
10 1 10 2 10 3

More Examples

Normalized Rate
Example #3- Multiple Layers
Blasingame Typecurve Analysis
3
Well
Multi Layer Model
Blasingame Typecurve Match
10 -8 2
1.0
2
7
5
4
3
8
7
2
6
5
4
3
2
10 -9
8
6
4
3
10 -1
9
3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
10 -1 1.0
Material Balance Pseudo Time
10 -10
2 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
1.0 10 1 10 2 10 3 10 4
- Blasingame typecurve match, using Fracture Model
- Pressure support indicated
- Three-Layer Model (one layer with very low
permeability) used, late-time match improved

Normalized Rate
Example #4- Shale Gas
Well
Agarwal Gardner Rate vs Time Typecurve Analysis
5
4
3
2
- Multi-stage fractures, horizontal well
- Analyzed as a vertical well in a circle
1.0
7
6
5
4
3
2
10 -1
9
7
6
5
4
3
k = 0.02 md
s = -4
OGIP = 4.5 bcf
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 9
10 -3 10 -2 10 -1 1.0
Material Balance Pseudo Time

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

EUR (bcf)
Typical Recovery Profile
Recovery Curves for k = 1 md
10
9
8
7
1 md reservoir, unfractured
(~10 bcf / section)
100% Recovery
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)

EUR (bcf)
Typical Recovery Profile
Recovery Curves for k = 1 md
10
9
8
7
1 md reservoir, unfractured
(~10 bcf / section)
100% Recovery
6
5
4
3
2
Actual EUR (qab = 0.05 MMscfd)
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- unlimited time

EUR (bcf)
Typical Recovery Profile
Recovery Curves for k = 1 md
10
9
8
7
1 md reservoir, unfractured
(~10 bcf / section)
100% Recovery
6
5
30 Year Limited
4
3
Actual EUR (qab = 0.05 MMscfd)
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- 30 year
EUR- unlimited time

EUR (bcf)
Typical Recovery Profile
Recovery Curves for k = 1 md
10
9
8
7
1 md reservoir, unfractured
(~10 bcf / section)
100% Recovery
6
5
30 Year Limited
4
3
2
20 Year Limited
Actual EUR (qab = 0.05 MMscfd)
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- 30 year EUR- 20 year EUR- unlimited time

EUR (bcf)
Tight Gas Recovery Profile
Recovery Curves for k = 0.02 md
10
9
8
7
6
0.02 md reservoir,
fractured
(~10 bcf / section)
Actual EUR (qab = 0.05 MMscfd)
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- unlimited time

EUR (bcf)
Tight Gas Recovery Profile
Recovery Curves for k = 0.02 md
10
9
8
7
6
0.02 md reservoir,
fractured
(~10 bcf / section)
Actual EUR (qab = 0.05 MMscfd)
5
4
30 Year
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- 30 year
EUR- unlimited time

EUR (bcf)
Tight Gas Recovery Profile
Recovery Curves for k = 0.02 md
10
9
8
7
0.02 md reservoir, fractured
(~10 bcf / section)
Actual EUR (qab = 0.05 MMscfd)
6
5
4
3
20 Year
30 Year
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- 30 year EUR- 20 year EUR- unlimited time

EUR (bcf)
Tight Gas Recovery Profile
Recovery Curves for k = 0.02 md
10
9
8
7
6
0.02 md reservoir,
fractured
(~10 bcf / section)
Actual EUR (qab = 0.05 MMscfd)
Max EUR (30 y) = 2 bcf
5
4
3
20 Year
30 Year
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Original Gas in Place (bcf)
EUR- 30 year EUR- 20 year EUR- unlimited time

Example – South Texas, Deep
Gas Well
Fracture Model
AG Typecurve Match
3
2
10 -8 7
7
5
4
3
Sqrt k X xf = 155
Min OGIP = 4.2 bcf
2
10 -9
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 2 3 4 5 6 7 8
1.0 10 1 10 2 10 3

EUR (bcf)
Example – South Texas, Deep
Gas Well
Recovery Plot - Linear System
7
6
Maximum EUR = 6.7 bcf
5
4
Minimum EUR = 3.5 bcf
Recovery period = 30 years
sqrt k X xf = 155
pi = 6971 psia
3
2
1
0
0 100 200 300 400 500 600
ROI (acres)

Water Drive Models

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

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 fluidin-place
by history matching the CUMULATIVE PRODUCTION and
AVERAGE RESERVOIR PRESSURE.

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

Water Drive (Aquifer) Models:
Pseudo Steady-State Model- Equations
The Fetkovich water influx equation for a finite aquifer is:
W
W
p
pi-p
/
1 Jpit
We
e
e
ei
i
i
Aquifer transfer coefficient
Initial encroachable water
Reservoir boundary pressure
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:
D W
e
n
W
p
ei
i
pa
- p
n
/
1
1
Jpit
Wei
n
e
The average aquifer pressure at the previous timestep (n-1) is evaluated explicitly, as follows:
(1)
n 1
DWej
j1
pa
n
pi
1
ei
1
W

Water Drive (Aquifer) Models:
Pseudo Steady-State Model- Equations
Now, we have one equation with two unknowns (water influx “W e ” and reservoir boundary
pressure “p”)
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.
p
z
pi
zi
G
1
G
p
i
WeB
1
Gi
i
-1
Cumulative Production
FVF at initial conditions
Gas-in-place
As with the water influx equation, the material balance equation can be discretized in time:
p
z
n
pi
zi
Gp
1
Gi
n
We
B
1
n
Gi
i
-1
(2)
Equations 1 and 2 are now solved simultaneously at each timestep, to obtain a discretized
reservoir pressure and water influx profile through time.

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

Water Drive (Aquifer) Typecurves:
Radial Composite Model
Blasingame, AG and NPI dimensionless formats can be used to plot
typecurves 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)

Water Drive (Aquifer) Typecurves:
Definitions
Model Type: Radial Composite (two zones);
outer zone is of infinite extent
Reservoir
Aquifer
Mobility Ratio (M):
M
M
M
aq
res
k
k
aq
res
res
aq

Water Drive (Aquifer) Typecurves:
Diagnostics
M=10 (Constant Pressure System
(approx))
Decreasing reD value
Increasing Aquifer Mobility
(M)
M=0 (Volumetric Depletion)

Water Drive (Aquifer) Typecurves:
Diagnostics
M=10 (Constant Pressure System
(approx))
Increasing Aquifer Mobility
(M)
Decreasing reD value
M=0 (Volumetric Depletion)

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 discretizing the 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-
Leverett equations.

Gas, MMscfd
Normalized Rate, Derivative
Pressure, psi
Normalized Rate
Normalized Rate
Water Drive (Aquifer) Models: Example
Example F
Data Chart
Example F
Blasingame Typecurve Analysis
22
14000
Legend
Pressure
Actual Gas Data 13000
8
6
5
20
12000
4
3
18
11000
2
16
10000
1.0
9000
8
14
8000
6
5
2
10 1 2
12
7000
4
3
10
6000
8
6
4
2
-Gulf coast gas
condensate reservoir
5000
4000
3000
2000
1000
10 -1
8
6
5
4
3
-Boundary dominated
-Pressure support evident
0
0
10 -2
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
2002 2003
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10-3 10-2 10-1 1.0 101 102
Material Balance Pseudo Time
Example F
Agarwal Gardner Rate vs Time Typecurve Analysis
Example F
Blasingame Typecurve Analysis
1.0
8
6
5
Transient Water Drive
Model
8
6
5
4
3
PSS Water Drive Model
4
2
3
2
1.0
8
10 -1
8
6
5
4
3
2
10 -2
8
6
5
4
k = 8.5 md
s = 0
OGIP = 12 bcf
M = 0.001
10 1 6
5
4
3
2
10 -1
8
6
5
4
3
2
k = 3.1 md
s = -4
OGIP = 13.5 bcf
IWIP = 47 MMbbl
PI (aq) = 0.59 bbl/d/psi
3
10 -2
2 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
10-1 1.0 101 102
Material Balance Pseudo Time
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10-3 10-2 10-1 1.0 101 102
Material Balance Pseudo Time

Multiple Well Analysis

Multi-well / Reservoir-based Analysis-
Available Methods
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 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)

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

Identifying Interference
Well A
Well B
Rate is adjusted at Well A
Response at Well B
q
Q
Q

Correcting Interference Using
Blasingame et al Method
Define a “total material balance time” function
t
ce
Q
q
tot
Q
A
Q
qA
B
(for analyzing Well A)
t ce is used in place of t c to plot the data in the typecurve match

Multi-Well Analysis as a
Typecurve Plot
Analysis of Well A:
log(q/Dp)
MBT is corrected for
interference caused
by production from
Well B
log(tc) t cA t ce
t ce = (Q B +Q A )/q A
Also applies to Agarwal-Gardner, NPI and FMB

Oil / Water Rates, bbl/d
Gas, MMscfd
Pressure, psi
Multi-Well Analysis- Example
Well 1
Data Chart
6.00
5.50
5.00
4.50
2.80
2.60
2.40
2.20
-Three well system
-“Staggered” on-stream dates
-High permeability reservoir
Legend
Pressure
Actual Gas Data
Pool Production
Water Production
36000
34000
32000
30000
28000
26000
4.00
3.50
2.00
1.80
1.60
Aggregate production of well group
24000
22000
20000
3.00
1.40
18000
16000
2.50
1.20
14000
2.00
1.00
12000
0.80
10000
1.50
0.60
8000
1.00
0.50
0.40
0.20
Production history of well to be analyzed
6000
4000
2000
0.00
0.00
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
0

Normalized Rate
Normalized Rate
Multi-Well Analysis- Example
Well 1
Blasingame Typecurve Analysis
10 1 2
7
5
4
3
2
Well 1
Blasingame Typecurve Analysis
10 1 2
1.0
7
5
4
3
2
7
5
4
3
2
10 -1
7
5
4
3
“Leaky reservoir” diagnostic
1.0
7
5
4
3
2
10 -2
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time
10 -1
7
5
4
3
Corrected using multi-well model
Total OGIP = 7 bcf
10 -2
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time

P/Z *, psi
P/Z *, psi
Multi-Well Analysis- Example
Well 1
Flowing Material Balance
Legend
P/Z Line
Flow ing P/Z *
1900
1800
1700
1600
OGIP for subject well = 3.5 bcf
1500
1400
1300
1200
1100
1000
900
800
Well 1
Flowing Material Balance
Legend
P/Z Line
Flow ing P/Z *
2000
1800
700
600
500
400
Total OGIP = 7.0 bcf
1600
1400
300
1200
Original Gas In Place
200
100
1000
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
800
600
400
Original Gas In Place
200
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
0
Cumulative Production, Bscf

Overpressured Reservoirs

Compressibility (1/psi)
Compresibilities of Gas and Rock
Compressibility vs. Pressure (Typical Gas Reservoir)
3.00E-04
gas
2.50E-04
2.00E-04
Formation
energy is
negligible in
this region
Formation
energy may
be influencial
in this region
Formation energy is critical in this region
1.50E-04
1.00E-04
5.00E-05
formation
0.00E+00
0 2000 4000 6000 8000 10000 12000
Reservoir Pressure (psi)

p/z* Model – Corrects Material
Balance
p 1
p
Gp
1
z 1 cf( pi
p)
z
i OGIP
*
p
p
Gp
1
z z
i OGIP
Flowing MB
t
ca
t
ct
i qt ()
q
ct 1 cf ( pi
p)
0
dt
Typecurves

Geomechanical Model – Corrects
Well Productivity
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.
Dp
*
p
where
qpi
( ctZ
) iG
2 *
ta
i
1.417e6*
Tq
ln
kih
r
r
e
wa
3
4
Dp
t
*
p
2
ki
pi
pwf
* ( ct)
i
a
i
k
k(
p)
pdp
z
t
0
kdt
c
t
Pressure dependent
permeability included in
pseudo-pressure and pseudotime

Normalized Rate
Overpressured Reservoirs -
Example
Blasingame Typecurve Analysis
8
6
5
4
Gulf Coast, deep gas condensate reservoir
3
2
10 1
1.0
8
6
5
4
2
3
2
10 -1
8
6
5
4
3
Boundary dominated flow
OGIP = 17 bcf
10 -2
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time

Rate, MMscfd
Pressure, psi
Overpressured Reservoirs -
Example
80
218 Prod and Pressure Data
Radial Model
History Match
18000
70
16000
60
14000
50
40
Good flowing pressure match,
Poor shut-in pressure match
OGIP = 17 bcf
12000
10000
30
8000
20
6000
10
4000
0
June July August September October
2003
2000

Rate, MMscfd
Pressure, psi
Overpressured Reservoirs -
Example
80
218 Prod and Pressure Data
Radial Model
History Match
18000
70
16000
60
50
40
Good flowing pressure match,
Good shut-in pressure match
OGIP = 29 bcf
14000
12000
10000
30
8000
20
6000
10
4000
0
June July August September October
2003
2000

k / ki
Overpressured Reservoirs -
Example
1.05
1.00
0.95
218 Prod and Pressure Data
Legend
Default
Custom
Interpolation
k (p) Permeability
k (p)
0.90
0.85
0.80
0.75
0.70
0.65
Assumed permeability profile
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000
Pressure, psi(a)

Horizontal Wells

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

Horizontal Wells – Blasingame
Typecurves
The 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:
Plan
Cross Section
L
h
L
r wa
2x e
The characteristic dimensionless parameter for each suite of horizontal typecurves is defined as follows:
2x e
2rwa
rwD
L
Where is the square root of the anisotropic ratio: For an input value of “L”,
L D
L
2
h
k
k
h
v

Normalized Rate
Horizontal Wells – Example
Unnamed Well
Blasingame Typecurve Analysis
8
10 2 6
4
3
2
10 1
8
6
2
L/2xe = 1
rwD = 2e-3
Ld = 5
Le = 1,968 ft
4
3
2
1.0
8
6
k (hz) = 0.18 md
k (v) = 0.011 md
OGIP = 1.1 bcf
4
3
2
10 -1
8
6
4
3
10 -2
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Pseudo Time

Oil Wells

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 effects
‣Include variable oil and gas properties

Liquid Rates, bbl/d
Gas, MMscfd
Pressure, psi
Oil Wells – Example
example7
Data Chart
190
180
170
160
150
140
130
0.11
0.10
0.09
0.08
- Pumping oil well
- Assumed to be pumped off
Producing GOR ~ constant
(indicates reservoir pressure is above
bubble point
Legend
Pressure
Actual Gas Data
Oil Production
Water Production
4000
3800
3600
3400
3200
3000
2800
2600
120
0.07
2400
110
100
0.06
2200
2000
90
80
0.05
1800
1600
70
0.04
1400
60
1200
50
0.03
1000
40
30
0.02
800
600
20
0.01
400
10
200
0
0.00
Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
0
2001 2002

Oil Wells – Example
Rs input from production data,
P bp and c o calculated using
Vasquez and Beggs

Normalized Rate
Oil Wells – Example
example7
Blasingame Typecurve Analysis
8
10 1 6
5
4
3
2
1.0
8
2
k = 1.4 md
s = -3
OOIP = 2.4 million
bbls
6
5
4
3
2
10 -1
8
6
5
4
3
10 -2
2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
10 -3 10 -2 10 -1 1.0 10 1 10 2
Material Balance Time

Oil Rate, bbl/d
Pressure, psi
Oil Wells – Example
example7
Numerical Radial Model - Production Forecast
300
4000
280
260
240
220
240 month forecast
EUR = 265 Mbbls
Legend
History Oil Rate
Flow Press
Syn Rate
History Reservoir Press
Forecasted Press
Forecasted Reservoir Press
Forecasted Rate
3800
3600
3400
3200
3000
2800
200
2600
180
2400
160
140
2200
2000
1800
120
1600
100
80
1400
1200
1000
60
800
40
20
600
400
200
0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
0