Status Presentation
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis
and Rate-Time Analysis
via Parametric Correlations —
Montney Shale Case Histories
Yohanes ASKABE
Department of Petroleum Engineering
Texas A&M University
College Station, TX 77843-3116 (USA)
yohanes.askabe@pe.tamu.edu
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 1/38
(Alt.) Rate-Decline Relations for
Unconventional Reservoirs and
Development of Parametric Correlations for
Estimation of Reservoir Properties
Outline:
● Objectives
● Introduction
● Rate-Time Models:
— PLE Model
— Logistic Growth Model (LGM)
— Duong Model
● Models performance analysis
● Modified rate decline models
● A Parametric correlation study
● Methodology:
— Analysis of time-rate model parameters
— Correlation of time-rate model parameters with reservoir/well
parameters
— Development of Parametric Correlations
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 2/38
● Conclusions and Recommendations
Objectives/ Problem Statement:
■ Ilk et al., (2011) have demonstrated that rate-time parameters can be
correlated with reservoir/well parameters using limited well data
from unconventional reservoirs.
■ Theoretical verification and analysis of large number of high quality
field data is necessary to test and verify the parametric correlations
that correlate reservoir/well parameters with time-rate model
parameters.
■ This study will provide the opportunity to investigate performance of
modern time-rate models in matching and forecasting rate-time data
from unconventional reservoirs. The models considered are:
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 3/38
— PLE Model
— Logistic Growth Model (LGM)
— Duong Model
Introduction
■ Modern time-rate models (PLE) have been shown to provide accurate
EUR estimates and forecast future production when bottomhole
flowing pressure (pwf) is constant.
■ Time-Rate model Constraints:
—Constant Bottomhole Pressure (pwf)
—Constant Completion Parameters (Well lateral length, xf....)
Time-Rate model parameters can be correlated with reservoir/well
parameters (k, kxf, EUR)
■ A diagnostic Approach
—Diagnostic Plots
—Data Driven matching process
'qdb' type
diagnostic plot—
discussed below
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 4/38
■
Governing Relations: Time-Rate Definitions
● Time-Rate Analysis: Base Definitions
■ Based on the "Loss Ratio" concept (Arps, 1945).
■ Loss Ratio:
1
D

qg
dq g / dt
■ Loss Ratio Derivative:
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 5/38

d 1 
d  qg
b





dt  D 
dt  dq g / dt 
● Approach
■ Continuous evaluation of D(t) and b(t) relations provide a
diagnostic method for matching time-rate data.
■ Diagnostic relations are used to derive empirical models.
Time-Rate Analysis: Power Law Exponential
●History:
■ SPE 116731 (Ilk et al., 2008)
■ Derived from data (D(t) and b(t))
■ Analogous to Stretched-Exponential, but derived independently
■ Has a terminal term for boundary-dominated flow (D∞)
●Governing Relations:
■ Rate-Time relation:
n
q ( t )  qˆ gi exp[  D  t  Dˆ i t ]
g
■ PLE Loss Ratio relation:
n 1
D ( t )  n Dˆ i t
 D
n
Dˆ i ( n  1) nt
b (t )  
n 2
( D t  Dˆ nt )

i
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 6/38
■ PLE Loss Ratio Derivative relation:
Time-Rate Analysis: Duong Model
●History:
■ SPE 137748 (Duong, 2011)
■ Based on extended linear/bilinear flow regime
■ Derived from transient behavior of unconventional-fractured
reservoirs
■ Relation extracted from straight line behavior of q/Gp vs. Time
(Log-Log) plot
●Governing Relations:
■ Duong Rate-Time relation:
q g ( t )  q gi t
m
 a

1 m
exp 
(t
 1) 
1  m

■ Duong Loss Ratio relation:
1
m
D ( t )  mt  at
■ Duong Loss Ratio Derivative relation:
b (t ) 
m
 at )
( at  mt )
m
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 7/38
m
mt ( t
Time-Rate Analysis: Logistic Growth Model (LGM)
●History
■ SPE 144790 (Clark et al., 2011)
■ Adopted from population growth models
■ Modified form of hyperbolic logistic growth models
●Governing Relations:
■ LGM Cumulative and Rate-Time relation:
Q g (t ) 
Kt
n
at
q g (t ) 
n
aKnt
( n 1 )
(a  t )
n
2
■ LGM Loss Ratio relation:
D (t ) 
a  an  (1  n ) t
n
t (a  t )
n
■ LGM Loss Ratio Derivative relation:
 a ( n  1)  2 a ( n  1) t  ( n  1) t
b (t ) 
2
n
( a  an  ( n  1) t )
n
2n
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 8/38
2
Theoretical Consideration: Time-rate analysis
● Well 1: k = 2000 nD
■
■
■
PLE Model
Transient
Transitional and
boundary-dominated
flow regimes.
●
■
■
LGM Model
Transient and
Transitional flow
regimes.
●
■
Duong Model
Transient flow
regimes.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 9/38
●
Theoretical Consideration: Time-rate analysis
● Well 1: k = 2000 nD
●
PLE
■
Excellent time-rate
data match.
■ Accurate estimate of
EUR is possible.
LGM and Duong Models
■ Excellent match
during Transient
flow regimes.
■ Lack boundary
conditions.
■ EUR is
overestimated.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 10/38
●
Theoretical Consideration: Time-rate analysis
● Well 2: k = 50 nD
PLE, LGM and Duong Models.
■
■
All models match transient flow-regimes very well.
In the absence of boundary-dominated flow, all models provide reliable
EUR estimate.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 11/38
●
Theoretical Consideration: Time-rate analysis
●Well 2: k = 50nD
● In the absence of
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 12/38
boundary-dominated
flow, PLE, LGM and
Duong Models can:
■ match transient flow
regimes very well and
■ provide good estimate
of EUR.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 13/40
●Modified Time-Rate Relations
Modified Time-Rate Models: Duong Model – (MODEL 1)
●Modified Duong Model
■With boundary parameter, DDNG
■Boundary-dominated flow can be modeled.
■ Derivation is based on loss-ratio definition. The modified form of
loss-ratio relation is given by:
D ( t )  D DNG 
m
 at  m
t
■ It is derived by assuming constant loss-ratio during boundarydominated flow regimes.
■ New time-rate relation can be derived from the loss-ratio relation.
It is given by:
q g ( t )  q 1t
m
 a
1 m
exp 
t
 1  D DNG
1  m



t

■ Cumulative production relation can not be derived.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 14/38
Numerical methods are necessary.
(Cont.) Modified Time-Rate Models: Duong Model - (MODEL 1)
●Modified Duong Model D
DNG
■The loss-ratio derivative is given by:
mt (  at  t )
m
b (t ) 
m
( at  t ( m  D DNG t ))
m
2
● Modified Duong Model
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 15/38
■ Boundary-dominated flows can be modeled.
■ EUR estimates are constrained.
■ Exponential decline characterizes boundary-dominated flow.
Modified Duong Model: 'qdb' type diagnostic plot. (MODEL 1)
Derived based on loss-ratio
derivation of Duong Model.
D (t ) 
m
t
●
 at
m
 D DNG
Added Constant
Modified Duong Model
■ Boundary-dominated flows
can be modeled.
■ EUR estimates are
constrained.
■ Exponential decline
characterizes boundarydominated flow.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 16/38
●
Modified Time-Rate Models: Duong Model - (MODEL 2)
●Modified Duong Model
■With boundary parameter DDNG
■Boundary-dominated flow can be modeled.
■Based on q/Gp Vs. time diagnostic plot.
■New q/Gp model-relation:
q
Gp
 at  m exp[  D DNG t ]
■New time-rate relation:
t
m

exp D DNG (1  t )  aD DNG
m 1
 [1  m , D DNG
]   [1  m , D DNG t ] 
■New Cumulative production relation:
G p (t ) 
q1
a

exp D DNG  aD DNG
m 1
 [1  m , D DNG
]   [1  m , D DNG t ] 


Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 17/38
q g (t ) 
q1
Modified Time-Rate Models: Duong Model - (MODEL 2)
●Cont. (Model parameters)
■The loss-ratio relation is given by:
D ( t )  D DNG 
m
t
 at  m exp[  D DNG t ]
■The loss-ratio derivative is given by:
at
m
 at ( m  D LGM t ) 
 exp[ D LGM t ]t ( m  D LGM t ) 
m
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 18/38
b (t ) 
exp[ D LGM t ]t m exp[ D LGM t ] mt
Modified Time-Rate Models: Duong Model – (MODEL 2)
● q/Gp vs. Time — Diagnostic Plot
● On log-log plot of q/Gp vs.
time:
■ Transient flow can be
characterized by a powerlaw relation, and
■ Boundary-dominated flow
can be characterized by an
exponential decline
relation.
■ q/Gp data can be matched
with the following relation:
Gp
 at  m exp[  D DNG t ]
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 19/38
q
Slide — 20/40
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Modified Time-Rate Models: Duong Model (Cont.)
Gp d  q
t

q dt  G p

m

●Modified Duong Model - (Model-2)
Gp d  q
t

q dt  G p

  m  D DNG t

Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 21/38
●Duong Model
Duong Model: Diagnostic Plot (Cont.)- Montney Shale Wells



vs. time Diagnostic Plot
● m – Duong parameter
describes rock-types,
stimulation practices and
fracture properties.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 22/38
Gp d  q
t

q dt  G p
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 23/38
Modified Time-Rate Models: Duong Model - (MODEL 2)
● Numerical Simulation Case, k=8µD.
● Model shows excellent data match for all flow regimes.
Modified Time-Rate Models: Models Comparison
●
●
Model Comparison
■ Duong Model
■ Model 1 and
■ Model 2
Modified Duong
Models provide a
better match
EUR is
constrained.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 24/38
●
Modified Time-Rate Models: Models Comparison
Numerical Simulation Case (k = 8 µD)
●
●
Model Comparison
■ Duong Model
■ Model 1 and
■ Model 2
Modified Duong Models
provide excellent match
to Transient, Transition
and boundary-dominated
flow regimes.
Duong Model can also
match observed early
time Skin and production
constraints.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 25/38
●
Modified Time-Rate Models: Logistic Growth Model (MODEL 3)
●Modified Logistic Growth Model
■With boundary parameter DLGM
■Boundary-dominated flow can be modeled.
■ Modified LGM time-rate relation: Assuming exponential decline
during boundary dominated flow regimes.
q g (t ) 
aKnt
( n 1 )
(a  t )
n
2
exp[  D LGM t ]
■Modified LGM Loss Ratio relation:
a (1  n  D LGM t )  t (1  n  D LGM t )
n
D (t ) 
t (a  t )
n
■Modified LGM Loss Ratio derivative relation:
2
b (t ) 
2
n
2n
( a (1  n  D LGM t )  t (1  n  D LGM t ))
n
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 26/38
 a ( n  1)  2 a ( n  1) t  ( n  1) t
Modified Logistic Growth Model: MODEL 3-qdb' type
diagnostic plot.
●
●
Modified Logistic Growth
Model:
■ Boundary-dominated
flows can be modeled
accurately
■ EUR estimates are
constrained.
■ Exponential decline
characterizes
boundary-dominated
flow.
Prior knowledge of gas in
place (K) is required.
Direct formulation of Gp is
not possible. Numerical
methods are necessary.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 27/38
●
Modified Logistic Growth Model: (MODEL 4)
● Using Diagnostic plot of [K/Qg – 1]
From LGM Model we
have
K
at

at
Q g (t )
K
n
t
 at
relation with modification for boundary
dominated flow regimes.
K
1
Q g (t )
Q g (t )

K
Q g (t )
plot of [K/Qgt – 1] versus time shows a
power-law relation for transient flow
regimes.
● Now, we can suggest the following
n
n
n
● The last relation suggests that a log-log
 1  at
n
 1  at
n
exp[  D LGM t ]  R
Where
K = Initial Gas in
Place.
R = Remaining
Gas Reserve at t∞.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 28/38
Q g (t ) 
Kt
n
vs. t or tmb
Modified Logistic Growth Model: (MODEL 4)
● Now, we can derive the associated modified relations.
K
Q g (t )
 1  at  n exp[  D LGM t ]  R
Kt exp[  D LGM t ]
n
Q g (t ) 
q g (t ) 
a  (1  R ) exp[ D LGM t ]t
a exp[ D LGM t ] Kt
n 1
n
( n  D LGM t )
R = Remaining Gas Reserve at
t∞


K
t
lim 
 1 
R

 Q g ( t )
a  (1  R ) exp[ D LGM t ]t n 2
● Cumulative Production [Gp(t)] relation can be derived for
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 29/38
Model 4.
Modified Logistic Growth Model: Diagnostic Plot
Corrected K/Q-1 Relation (MODEL 4)
● If K is known, we
can estimate
parameters a and n
from the transient
flow regime.
● .DLGM can be
modified based on
boundary
behaviors.
= 161
= 0.79
= 20,219,576.75
= 0.00029
= 0.157
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 30/38
a
n
K
Dlgm
R
Modified Logistic Growth Model: Comparison
(MODEL and MODEL 4)
● Modified LGM models
can match transient and
boundary-dominated
flow regimes better than
LGM model.
● EUR is constrained.
● MODEL 4 provides a
better match.
● Gp relation can be
derived for MODEL 4.
● Prior knowledge of gas
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 31/38
in place (K) is required.
Theoretical Consideration: Synthetic Case Examples
■ A horizontal well with multiple transverse fractures is modeled.
■ The model inputs are as follows:
Reservoir Properties:
Net pay thickness, h
Formation permeability, k
Wellbore Radius, rw
Formation
compressibility, cf
Porosity, 𝝓
Initial reservoir pressure, pi
Gas saturation, sg
Skin factor, s
Reservoir Temperature, Tr
= 39.624 m
= 0.25 µD - 5µD
= 0.10668 m
= 4.35E-7 kPa-1
=
=
=
=
=
0.09 (fraction)
34,473.8 kPa
1.0 (fraction)
0.01 (dimensionless)
100 °C
Fluid Properties:
Gas specific gravity, γg
= 0.6 (air=1)
Hydraulically Fractured Well Model Parameters:
Fracture half-length, xf
Number of Fractures
Horizontal well length, l
Horizontal well with multiple transverse
fractures
= 50 m
= 20
= 1,500 m
Transverse Fractures
●Synthetic Examples
■ 14 Models with permeability (k)
■
ranging from 0.25 µD - 5µD.
All other reservoir/well and
fluid parameters are identical.
Production parameters:
= 3447.4 kPa
= 10,598 days (30 Years)
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 32/38
Flowing pressure, pwf
Producing time, t
Parameter Analysis: PLE Time-Rate Model
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 33/38
● PLE model parameters are related to EUR estimates from PDA
Parameter Analysis: PLE Time-Rate Model
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 34/38
● PLE model parameters are related to permeability
Parameter Correlation: Permeability
A parametric correlation
that relates reservoir
permeability with ratetime model parameters
can be produced.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 35/38
■
Parameter Correlation: EUR
■
A parametric correlation
that relates EUR
estimates with rate-time
model parameters can be
produced.
The parametric
correlation may not be
unique.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 36/38
■
Field Data Example: Permeability
● Field data example: Montney Shale, (Brassey) Wells
■ Careful analysis of
pressure/production data
is necessary to accurately
estimate reservoir/well
parameters (k, EUR, xf).
■ Decline curve analysis is
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 37/38
then carried out to
estimate EUR.
Field Data Example: EUR
● Field data example: Montney Shale, (Brassey) Wells
EUR is normalized by
initial BHP (Pi), and
number of effective
fractures.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 38/38
■
Conclusion:
■ It is possible to integrate time-rate model parameters with
reservoir/well parameters using parametric correlations.
■ Parametric correlations solve the uncertainty regarding the number
of unknown parameters in model based production data analysis.
■ Modern rate decline models are successful at modeling different flow
regimes observed from unconventional reservoirs. In summary:
— PLE Model
› Transient, transition, and, boundary-dominated flow regimes are
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 39/38
successfully modeled.
— Logistic Growth Model (LGM)
› Transient, and transition flow regimes are successfully modeled.
— Duong Model
› Only transient flow regimes are matched.
› EUR is overestimated.
› Doesn’t conform to ‘qdb’ type diagnostic plot.
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 40/38
Extra Slides
Slide — 41/38
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 42/38
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 43/38
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Summary: Model Comparison
Model Relations
Power-law
exponential
n
q ( t )  qˆ gi exp[  D  t  Dˆ i t ]
g
Diagnostic Plots
n 1
D ( t )  n Dˆ i t
 D
Duong Model
q g ( t )  q gi t
m
qg
Gp
 a

1 m
exp 
(t
 1) 
1  m

Modified Duong
Model
Logistic Growth
Model (LGM)
q
Gp
q g (t ) 
q1
tm
 at  m
Recommendation
● Use diagnostic
relation
● Use diagnostic
relation
● Do not match
boundary flow
regimes.
 at  m exp[  D DNG t ]
 D DNG (1  t )  aD DNG m 1

exp 

  [1  m , D DNG ]   [1  m , D DNG t ] 
Modified LGM
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 44/38
Rate Decline
Models
Modified Logistic Growth Model: Corrected K/Q-1 Relation
● LGM K (Carrying
capacity) is equivalent
to Gas in Place
volumetric estimate.
● Gas in place estimate
should be available to
use this model
● K/Q(t)-1 vs. tmb
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 45/38
diagnostic plot can be
used.
n
q ( t )  qˆ gi exp[  D  t  Dˆ i t ]
g
q g ( t )  q gi t
aKnt
q g (t ) 
q g (t ) 
( n 1 )
n
q1
t
m
m
Duong
LGM
2
 a

1 m
exp 
t
 1  D DNG t  Modified Duong MODEL 1
1  m




exp D DNG (1  t )  aD DNG
m 1
 [1  m , D DNG ]   [1  m , D DNG t ] 
Modified Duong MODEL 2
aKnt
( n 1 )
(a  t )
n
2
exp[  D LGM t ]
Modified LGM MODEL 1
a exp[ D LGM t ] Kt n 1 ( n  D LGM t )
a  (1  R ) exp[
D LGM t ]t n 
2
Modified LGM MODEL 2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 46/40
q g (t ) 
 a

1 m
exp 
(t
 1) 
1  m

(a  t )
q g ( t )  q1t
q g (t ) 
m
PLE
n 1
D ( t )  n Dˆ i t
 D
n
Dˆ i ( n  1) nt
b (t )  
n 2
( D t  Dˆ nt )

D ( t )  mt
D (t ) 
1
 at
b (t ) 
n
n
D ( t )  D DNG 
t
m
t
mt ( t
m
 at )
( at  mt )
m
Duong
2
 a ( n  1)  2 a ( n  1 ) t  ( n  1) t
2
b (t ) 
t (a  t )
m
i
m
a  an  (1  n ) t
D ( t )  D DNG 
b (t ) 
m
PLE
2
( a  an  ( n  1) t )
n
mt (  at  t )
m
 at
m
n
b (t ) 
m
( at  t ( m  D DNG t ))
m
2
2n
LGM
2
Modified Duong
MODEL 1
 at  m exp[  D DNG t ]
exp[ D LGM t ]t m exp[ D LGM t ] mt m  at ( m  D LGM t ) 
at  exp[
D LGM t ]t m ( m  D LGM t ) 
2
Modified Duong
MODEL 2
a (1  n  D LGM t )  t (1  n  D LGM t )
n
t (a  t )
n
 a ( n  1)  2 a ( n  1) t  ( n  1) t
2
b (t ) 
2
n
2n
( a (1  n  D LGM t )  t (1  n  D LGM t ))
n
Modified LGM
MODEL 1
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 47/40
D (t ) 
Modified Time-Rate Models: Duong Model - (MODEL 2)
q g (t ) 
G p (t ) 
Gp
t
m
q1
a

exp D DNG (1  t )  aD DNG

exp D DNG  aD DNG
m 1
m 1
 [1  m , D DNG
 [1  m , D DNG
]   [1  m , D DNG t ] 
]   [1  m , D DNG t ] 


 at  m exp[  D DNG t ]
D ( t )  D DNG 
b (t ) 
m
t
 at  m exp[  D DNG t ]
exp[ D LGM t ]t m exp[ D LGM t ] mt m  at ( m  D LGM t ) 
at  exp[
D LGM t ]t m ( m  D LGM t ) 
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 48/38
q
q1
Power Law Exponential (PLE) Model
Loss Ratio Relation
n 1
D ( t )  n Dˆ i t
 D
Basis for PLE Model
Rate-Time Relation
n
q ( t )  qˆ gi exp[  D  t  Dˆ i t ]
g
Loss-Ratio Derivative
n
Dˆ i ( n  1) nt
b (t )  
n 2
( D t  Dˆ nt )
i
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 49/40

Duong Time-Rate Relation
q/Gp vs. Production Time Log-Log Plot
q
 at
m
Basis for Duong Model
Gp
Rate-Time Relation
q g ( t )  q 1t
m
 a

1 m
exp 
(t
 1) 
1  m

Cumulative-Time Relation
Gp 
 a

1 m
exp 
(t
 1) 
a
1  m

q1
Loss-Ratio
1
m
D ( t )  mt  at
Loss-Ratio Derivative
b (t ) 
m
 at )
( at  mt )
m
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 50/40
m
mt ( t
Logistic Growth Model (LGM)
K/Q(t) -1 vs. Production Time Log-Log Plot
K
n
 1  aˆ t
Basis for LGM
Q (t )
Rate-Time Relation
q g (t ) 
aˆ Knt
( n 1 )
( aˆ  t )
n
2
Cumulative-Time Relation
Gp 
Kt
n
n
aˆ  t
Loss-Ratio
D (t ) 
a  an  (1  n ) t
n
t (a  t )
n
Loss-Ratio Derivative
n 2
( aˆ  aˆ n  ( n  1) t )
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 51/40
b (t ) 
2
2
n
2n
 aˆ ( n  1)  2 aˆ ( n  1) t  ( n  1) t
Modified Duong Model (Model 1)
Loss Ratio Relation
D ( t )  D DNG  mt
1
 at
m
Basis for Modified Duong Model
Rate-Time Relation
q g ( t )  q1t
m
 a

1 m
exp 
t
 1  D DNG t 
1  m



Loss-Ratio Derivative
mt (  at  t )
b (t ) 
m
( at  t ( m  D DNG t ))
m
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 52/40
m
Modified Duong Model (Model 2)
q/Gp vs. Production Time Log-Log Plot
q
Gp
 at  m exp[  D DNG t ]
Basis for Modified Duong Model (Model 2)
Rate-Time Relation
q g (t ) 
q1
t
m

exp D DNG (1  t )  aD DNG
m 1
 [1  m , D DNG ]   [1  m , D DNG t ] 
Cumulative-Time Relation
G p (t ) 
q1
a

exp D DNG  aD DNG
m 1
 [1  m , D DNG ]   [1  m , D DNG t ] 
Loss-Ratio
D ( t )  D DNG 
m
t
 at  m exp[  D DNG t ]
Loss-Ratio Derivative
at  exp[
D LGM t ]t m ( m  D LGM t ) 
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 53/40
b (t ) 
exp[ D LGM t ]t m exp[ D LGM t ] mt m  at ( m  D LGM t ) 
Modified Logistic Growth Model (Model 1)
Loss Ratio Relation
D (t ) 
n
aˆ  aˆ n  (1  n ) t
t ( aˆ  t )
n
 D LGM
Basis for Modified Logistic Growth Model
(Model 1)
Rate-Time Relation
q g (t ) 
aˆ Knt
( n 1 )
( aˆ  t )
n
2
exp[  D LGM t ]
Loss-Ratio Derivative
( aˆ (1  n  D LGM t )  t (1  n  D LGM t ))
n
2
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 54/40
b (t ) 
2
2
n
2n
 aˆ ( n  1)  2 aˆ ( n  1) t  ( n  1) t
Modified Duong Model (Model 2)
K/Q(t) -1 vs. Production Time Log-Log Plot
K
Q g (t )
n
 1  aˆ t exp[  D LGM t ]  R
Basis for Modified LGM (Model 2)
Rate-Time Relation
q g (t ) 
aˆ exp[ D LGM t ] Kt
n 1
( n  D LGM t )
aˆ  (1  R ) exp[ D
LGM
t ]t

n 2
Cumulative-Time Relation
Kt exp[  D LGM t ]
n
Q g (t ) 
n
aˆ  (1  R ) exp[ D LGM t ]t
Loss-Ratio
1
D
 
qg
dq g / dt
b

d 1
d  qg




dt  D 
dt  dq g / dt 
Status Presentation — Yohanes ASKABE — Texas A&M University
College Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations
Montney Shale Case Histories
Slide — 55/40
Loss-Ratio Derivative