10/10/2011
Production Forecasting for
Unconventional Resources
Lecture 2-2
Basic Type Curve Analysis
Learning Objectives
You will be able to
 Explain value of dimensionless variables in type
curves
 Sketch basic Gringarten type curve and state inherent
assumptions
 Sketch basic derivative type curve
 State expected shapes on diagnostic plot for
volumetric, radial, linear, bilinear, and spherical flow
 Estimate formation properties from type curve
matches
 Identify flow regimes on log-log plots
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Type Curves




Powerful method for analyzing transient
pressure and rate data
Pre-plotted solutions to flow equations
for selected formations and conditions
Field data overlaid on type curve
Best-match provides qualitative and
quantitative descriptions of formation
and properties
Relevance of Type Curves in Production
Forecasting

Advanced decline curve analysis


Important method for forecasting future
production from unconventional (and
conventional) resources
Makes extensive use of type curves
(including derivative type curves)
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Dimensionless Variables
qB  948ct r 2 
p  pi  70.6
Ei 


kh
kt


2

 r  rD  r

 

 rw
rw 
kh pi  p 
1

  Ei  

141.2qB
2   0.0002637 kt  

4

2



kh pi  p 
pD 
   ct rw  
141.2qB
1  rD2 
p D   Ei 
2  4t D 
tD 
0.0002637 kt
ct rw2
Dimensionless Variables

Advantages



Solution can be expressed in terms of
single variable (tD) and parameter (rD)
Much simpler graphical or tabular
presentation of solution
Can include dimensionless skin factor (s)
and wellbore storage coefficient (CD)
CD 
0 .8936C
ct hrw2
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Gringarten Type Curves

Based on solution to radial diffusivity
equation





Vertical well, constant production rate
Infinite-acting, homogenous-acting reservoir
Single-phase, slightly compressible liquid
flowing
Infinitesimal skin factor (thin ‘membrane’) at
production face
Constant wellbore-storage coefficient
Gringarten Type Curve
CD e 2s=1060
100
pD
Similarities of
curves make
matching difficult
CDe 2s=0.01
100,000
0.01
tD/CD
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Derivative Type Curve

Eliminates ambiguity in Gringarten type curve
matching


‘Derivative’ of solution to radial diffusivity
equation on Gringarten type curve
Derivative is
p D
p
 t D D  t D pD
 ln t D
t D
or
 p
 p
t
 t  p
 ln t 
t
Pressure Derivative

Infinite-acting radial flow
70.6qB
p  
kh
Derivatives:
 p
 p
t

t
 ln t 
p 70.6qB
t

t
kh
  1688 c r 2 

t w 
 2s
ln

kt
 


In dimensionless terms,
p D  0.5lnt D   0.809  2 s 
Derivatives:
tD
p D
p D

t D  ln t D 
tD
p D
 0 .5
t D
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Pressure Derivative

Complete wellbore storage distortion
p 
qBt
24C
In dimensionless terms,
pD  t D / C D
Derivative:
p qBt
t

 p
t
24C
Derivative:
tD
p D
 t D / C D  pD
t D
Derivative Type Curve
100
Differences in curve
shapes make
matching easier
CDe2s=1060
CDe2s=1010
tDp´D
CDe2s=100
CDe2s=0.01
100,000
0.01
tD/CD
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Pressure + Derivative Type Curves
100
Combining curves
gives each stem
value two distinctive
shapes
pD
100,000
0.01
tD/CD
Using Type Curves
100
1,000
pD
p
1
teq
1,000
100,000
0.01
tD/CD
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Move Field Data Toward Horizontal
100
1,000
pD
p
1
Align data with
horizontal part of
teq type curves
1,000
100,000
0.01
tD/CD
Move Field Data Toward Horizontal
100
1,000
pD
Stop when data align
with horizontal
derivative
p
1
teq
1,000
100,000
0.01
tD/CD
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Move Field Data Toward Unit Slope
100
1,000
pD
p
Begin to move toward unit slope line
1
teq
1,000
100,000
0.01
tD/CD
Move Field Data Toward Unit Slope
100
1,000
pD
p
1
teq
1,000
100,000
0.01
tD/CD
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Move Field Data Toward Unit Slope
100
1,000
Stop when data align
with unit slope line
p
pD
1
teq
1,000
100,000
0.01
tD/CD
Interpret the Type Curve
Calculate CDe2s from
matching stem value
100
1,000
 C De 2s
Extrapolate
s  0.5 ln curve
 C
as necessary
D
p/pD k
pD
p

1
teq
teq/tD  CD




1,000
100,000
0.01
tD/CD
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10/10/2011
Calculate k From Pressure Match
k
k
141.2qB  pD 


h
 p  M .P .
141.2501.3250.609  10 


15
262


 14.5 md
Calculate CD From Time Match
0.0002637 k  t eq 


CD 

2
 ct rw  t D C D  M.P .
CD 
0.000263714.5
 0.0546 


2
5
1

0.1830.6091.76  10 0.25 
 1703
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Calculate s From CD e 2s
1  C D e 2 s 
s  ln
2  C D 
1  7  10 9 
s  ln
2  1703 
 7 .6
Type-Curve Plots for Variable Rate Production

‘Normalized rate,’
𝑝𝑖 −𝑝𝑤𝑓
𝑞
, and its time
derivative can be plotted and analyzed
on a log-log plot in many cases


Smoothly changing rates modeled best
Procedure valid even for constant BHP
production in many cases

1
Log-log plot of q (or ) vs. t appropriate
𝑞
for constant BHP pressure production since
∆𝑝 constant
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10/10/2011
Type Curves
Diagnostic Plots
Diagnostic Plot
Pressure change (p)
Pressure derivative (p )
Elapsed time (t ), hrs
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10/10/2011
Time Regions
Unit-slope
line
Near-wellbore effects
(wellbore storage) Horizontal derivative
Early-time
region
Middletime
region
Late-time
region
Elapsed time (t ), hrs
Volumetric Behavior
Reservoir acts like tank
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10/10/2011
Volumetric Behavior
Fluids from outside ‘recharge’
tank or reduce pressure at
uniform rates throughout
drainage area
Volumetric Behavior Examples

Wellbore storage



Pseudosteady-state flow



Dominates during early-time period
Fluid leaves or enters ‘tank’ during early
test time
Closed reservoir, constant-rate production
Pressure changes uniformly as fluid leaves
through well
Buildup test with recharge entering
reservoir
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10/10/2011
Volumetric Models

Wellbore storage
p 
 Pseudosteady-state flow
pi  pwf 

qBt
24C
0.0744qBt
c t hre2
141.2qB
kh
  re
ln
  rw
 3 
   s
 4


Volumetric Models

General form
p  mV t  bV
 Derivative of general form
 mV t  bV 
 p
t
t
t
t
 mV t
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10/10/2011
Derivative Plot
Pressure change during recharge
or pseudosteadystate flow
Pressure derivative
Pressure change during
wellbore storage
Elapsed time (t ), hrs
Radial Flow
Vertical, Unfractured Well
Wellbore
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10/10/2011
Radial Flow
Vertically Fractured Well
Wellbore
Fracture
Radial Flow
Horizontal Well
Late radial flow
Wellbore
Early radial flow
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10/10/2011
Radial Flow Models

Logarithmic approximation to Eisolution

162.6qB   kt 
p 
 3.23  0.869s 
log
2 

kh

c
r
 

t w 
 General form p  m log t   b
 Derivative
t
 p
m

t
2.303
Radial Flow Models
Pressure
Pressure derivative
Elapsed time (t ), hrs
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10/10/2011
Linear Flow
Hydraulically Fractured Well
Vertical wellbore
Fracture
Linear flow
Linear Flow
Vertical
wellbore
Channel Reservoir
Linear
flow
Channel (ancient
stream) reservoir
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Linear Flow
Horizontal Well
Wellbore
Early linear flow
Linear Flow
Late linear flow
Wellbore
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10/10/2011
Linear Flow



Occurs in channel reservoirs,
hydraulically fractured wells,
horizontal wells
With estimate of permeability,
provides data to estimate channel
width, fracture halflength
In horizontal wells, with known
productive well length open to flow,
enables permeability estimates
Linear Flow Models

Channel of width w
16.26qB  kt

p 
khw  ct




12
 Hydraulically fractured well, fracture
length 2Lf
12
4.064qB
p 
khL f
 kt

 ct





 c1 s 



 c2 s f 


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10/10/2011
Linear Flow Models

General form
p  m L t 1 2  b L
 Derivative
t
 p 1
 m Lt 1 2
t
2
Linear Flow Models
Pressure change in damaged-fractured
or horizontal well
Pressure change in
undamaged
fractured well
Pressure 1
derivative
2
Elapsed time (t ), hrs
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10/10/2011
Bilinear Flow
Bilinear Flow Model

 44.1qB   1
p  
 
h

  w f k f

12
 t 



c
k
t 

14

 c3 s f 


p  m B t 1 4  b B
 General form
 Derivative




t
 p 1
 mBt1 4
t
4
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10/10/2011
Bilinear Flow Models
Pressure in fractured,
damaged well
Pressure in fractured,
undamaged well
Pressure derivative
1
4
Elapsed time (t ), hrs
Spherical Flow
Vertical wellbore
Few perforations
open
Spherical flow
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10/10/2011
Spherical Flow
Vertical wellbore
Wireline
testing tools
Spherical flow
Spherical Flow Models
pwf  pi 
70.6qB
1 70.6qB
 ms

s
k s rs
k s rs
t
ks = (khkz1/2)2/3
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10/10/2011
Spherical Flow Model

General form
p   m s t 1 / 2  b s
 Derivative
 p 1
t
 m s t 1 / 2
t
2
Spherical Flow Model
Pressure
Pressure derivative
1
2
Elapsed time (t ), hrs
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10/10/2011
Flow Regimes on Diagnostic Plot
Wellbore
storage
Radial
flow
Spherical flow
Recharge?
Elapsed time (t ), hrs
Diagnostic Plot for Variable Rate Production

‘Normalized rate,’
𝑝𝑖 −𝑝𝑤𝑓
𝑞
, and its time
derivative can be plotted and analyzed
on the diagnostic plot in many cases


Smoothly changing rates modeled best
Procedure valid even for constant BHP
production in many cases

1
Log-log plot of q (or ) vs. t appropriate
𝑞
for constant BHP pressure production since
∆𝑝 constant
28
10/10/2011
Accomplishments
You can now
 Explain value of dimensionless variables in type
curves
 Sketch basic Gringarten type curve and state inherent
assumptions
 Sketch basic derivative type curve
 State expected shapes on diagnostic plot for
volumetric, radial, linear, bilinear, and spherical flow
 Estimate formation properties from type curve
matches
 Identify flow regimes on log-log plots
Production Forecasting for
Unconventional Resources
Lecture 2-2
Basic Type Curve Analysis
29