yohanes askabe department of petroleum engineering texas a&m university
DESCRIPTION
Status Presentation College Station, TX (USA) — 12 August 2012. Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations — Montney Shale Case Histories. - PowerPoint PPT PresentationTRANSCRIPT
Integration of Production Analysis and Rate-Time Analysis
via Parametric Correlations — Montney Shale Case Histories
Yohanes ASKABEDepartment of Petroleum Engineering
Texas A&M UniversityCollege Station, TX 77843-3116 (USA)
Status PresentationCollege Station, TX (USA) — 12 August 2012
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
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(Alt.) Rate-Decline Relations for Unconventional Reservoirs and
Development of Parametric Correlations for Estimation of Reservoir Properties
●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
●Conclusions and Recommendations
Outline:
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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■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:
— PLE Model— Logistic Growth Model (LGM)—Duong Model
Objectives/ Problem Statement:
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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■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
Introduction
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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'qdb' type diagnostic plot—discussed below
●Time-Rate Analysis: Base Definitions■Based on the "Loss Ratio" concept (Arps, 1945).■Loss Ratio:
■Loss Ratio Derivative:
●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.
dtdqq
D g
g
/1
dtdqq
dtd
Ddtdb
g
g
/1
Governing Relations: Time-Rate Definitions
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●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:
■PLE Loss Ratio relation:
■PLE Loss Ratio Derivative relation:
]ˆexp[ˆ)( nigi tDtDqtgq
DtDntD n
i1ˆ)(
2)ˆ()1(ˆ)(
ni
ni
ntDtDntnDtb
Time-Rate Analysis: Power Law Exponential
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●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:
■Duong Loss Ratio relation:
■Duong Loss Ratio Derivative relation:
)1(
1exp)( 1 mm
gig tmatqtq
matmttD 1)(
2)()()( m
mm
mtatattmttb
Time-Rate Analysis: Duong Model
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●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:
■LGM Loss Ratio relation:
■LGM Loss Ratio Derivative relation:
2
)1(
)()( n
n
g taaKnttq
)()1()( n
n
tattnanatD
2
222
))1(()1()1(2)1()( n
nn
tnanatntnanatb
Time-Rate Analysis: Logistic Growth Model (LGM)
n
n
g taKttQ
)(
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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● PLE Model■ Transient■ Transitional and■ boundary-dominated
flow regimes.
● LGM Model■ Transient and■ Transitional flow
regimes.
● Duong Model■ Transient flow
regimes.
●Well 1: k = 2000 nD
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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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 UniversityCollege Station, TX (USA) — 12 August 2012
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Theoretical Consideration: Time-rate analysis
● 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.
●Well 2: k = 50 nD
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Theoretical Consideration: Time-rate analysis
●Well 2: k = 50nD
● In the absence of 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 UniversityCollege Station, TX (USA) — 12 August 2012
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Theoretical Consideration: Time-rate analysis
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
●Modified Time-Rate Relations
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●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:
■It is derived by assuming constant loss-ratio during boundary-dominated flow regimes.■New time-rate relation can be derived from the loss-ratio relation.
It is given by:
■Cumulative production relation can not be derived. Numerical methods are necessary.
tDt
matqtq DNG
mmg 1
1exp)( 1
1
mDNG at
tmDtD )(
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 – (MODEL 1)
●Modified Duong Model ■The loss-ratio derivative is given by:
●Modified Duong Model ■ Boundary-dominated flows can be modeled.■ EUR estimates are constrained.■ Exponential decline characterizes boundary-dominated flow.
2))(()()(tDmtat
tatmttbDNG
m
mm
DNGD
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
(Cont.) Modified Time-Rate Models: Duong Model - (MODEL 1)
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Modified Duong Model: 'qdb' type diagnostic plot. (MODEL 1)
● Derived based on loss-ratio derivation of Duong Model.
● Modified Duong Model ■ Boundary-dominated flows
can be modeled.■ EUR estimates are
constrained.■ Exponential decline
characterizes boundary-dominated flow.
DNGm Dat
tmtD )(
Added Constant
●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:
■New time-rate relation:
■New Cumulative production relation:
],1[],1[)1(exp)( 11 tDmDmaDtDtqtq DNGDNG
mDNGDNGmg
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 - (MODEL 2)
]exp[ tDatGq
DNGm
p
],1[],1[exp)( 11 tDmDmaDDaqtG DNGDNG
mDNGDNGp
●Cont. (Model parameters)■The loss-ratio relation is given by:
■The loss-ratio derivative is given by:
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 - (MODEL 2)
]exp[)( tDattmDtD DNG
mDNG
2)(]exp[
)(]exp[]exp[)(tDmttDat
tDmatmttDttDtbLGM
mLGM
LGMm
LGMm
LGM
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 – (MODEL 2)● q/Gp vs. Time — Diagnostic Plot
● On log-log plot of q/Gp vs. time:■ Transient flow can be
characterized by a power-law relation, and
■ Boundary-dominated flow can be characterized by an exponential decline relation.
■ q/Gp data can be matched with the following relation:
]exp[ tDatGq
DNGm
p
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●Duong Model
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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.)
mGq
dtd
qGt
p
p
●Modified Duong Model - (Model-2)
tDmGq
dtd
qGt DNG
p
p
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Duong Model: Diagnostic Plot (Cont.)- Montney Shale Wells
p
p
Gq
dtd
qGt vs. time Diagnostic Plot
● m – Duong parameter describes rock-types, stimulation practices and fracture properties.
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 - (MODEL 2)● Numerical Simulation Case, k=8µD.● Model shows excellent data match for all flow regimes.
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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: Models Comparison
● Model Comparison■ Duong Model■ Model 1 and■ Model 2
● Modified Duong Models provide a better match
● EUR is constrained.
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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: Models ComparisonNumerical 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 UniversityCollege Station, TX (USA) — 12 August 2012
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●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.
■Modified LGM Loss Ratio relation:
■Modified LGM Loss Ratio derivative relation:
]exp[)(
)( 2
)1(
tDta
aKnttq LGMn
n
g
)()1()1()( n
LGMn
LGM
tattDnttDnatD
2
222
))1()1(()1()1(2)1()(tDnttDnatntnanatb
LGMn
LGM
nn
Modified Time-Rate Models: Logistic Growth Model (MODEL 3)
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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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 UniversityCollege Station, TX (USA) — 12 August 2012
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Modified Logistic Growth Model: (MODEL 4)
n
g
n
g
n
n
g
n
n
g
attQK
attQK
tta
tQK
taKttQ
1)(
1)(
)(
)(
● Using Diagnostic plot of [K/Qg – 1] vs. t or tmb
From LGM Model we have ● The last relation suggests that a log-log
plot of [K/Qgt – 1] versus time shows a power-law relation for transient flow regimes.
● Now, we can suggest the following relation with modification for boundary dominated flow regimes.
WhereK = Initial Gas in Place.R = Remaining Gas Reserve at t∞.
RtDattQK
LGMn
g
]exp[1)(
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Modified Logistic Growth Model: (MODEL 4)
● Now, we can derive the associated modified relations.
RtDattQK
LGMn
g
]exp[1)(
nLGM
LGMn
g ttDRatDKttQ]exp[)1(]exp[)(
21
]exp[)1()(]exp[)(
nLGM
LGMn
LGMg ttDRa
tDnKttDatq
R = Remaining Gas Reserve at t∞
RtQK t
g
1)(
lim
● Cumulative Production [Gp(t)] relation can be derived for Model 4.
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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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.
a = 161n = 0.79K = 20,219,576.75Dlgm = 0.00029R = 0.157
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Modified Logistic Growth Model: Comparison
● 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 in place (K) is required.
(MODEL and MODEL 4)
■A horizontal well with multiple transverse fractures is modeled.
Reservoir Properties: Net pay thickness, h = 39.624 m Formation permeability, k = 0.25 µD - 5µD Wellbore Radius, rw = 0.10668 m Formation compressibility, cf
= 4.35E-7 kPa-1
Porosity, 𝝓 = 0.09 (fraction) Initial reservoir pressure, pi = 34,473.8 kPa Gas saturation, sg = 1.0 (fraction) Skin factor, s = 0.01 (dimensionless) Reservoir Temperature, Tr = 100 °C
Fluid Properties: Gas specific gravity, γg = 0.6 (air=1)
Hydraulically Fractured Well Model Parameters: Fracture half-length, xf = 50 m Number of Fractures = 20 Horizontal well length, l = 1,500 mProduction parameters: Flowing pressure, pwf = 3447.4 kPa Producing time, t = 10,598 days (30 Years)
Theoretical Consideration: Synthetic Case Examples
■The model inputs are as follows:
Transverse Fractures
Horizontal well with multiple transversefractures
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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●Synthetic Examples■ 14 Models with permeability (k)
ranging from 0.25 µD - 5µD.■ All other reservoir/well and
fluid parameters are identical.
●PLE model parameters are related to EUR estimates from PDA
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Parameter Analysis: PLE Time-Rate Model
●PLE model parameters are related to permeability
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Parameter Analysis: PLE Time-Rate Model
■ A parametric correlation that relates reservoir permeability with rate-time model parameters can be produced.
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Parameter Correlation: Permeability
■ 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 UniversityCollege Station, TX (USA) — 12 August 2012
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Parameter Correlation: EUR
●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 then carried out to estimate EUR.
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Field Data Example: Permeability
■ EUR is normalized by initial BHP (Pi), and number of effective fractures.
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Field Data Example: EUR●Field data example: Montney Shale, (Brassey) Wells
■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
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 UniversityCollege Station, TX (USA) — 12 August 2012
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Conclusion:
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Extra Slides
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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Summary: Model ComparisonRate Decline Models
Model Relations Diagnostic Plots Recommendation
Power-law exponential
● Use diagnostic relation
Duong Model ● Use diagnostic relation
● Do not match boundary flow regimes.
Modified Duong ModelLogistic Growth Model (LGM)
Modified LGM
]ˆexp[ˆ)( nigi tDtDqtgq
DtDntD ni
1ˆ)(
)1(
1exp)( 1 mm
gig tmatqtq
m
p
g atGq
],1[],1[)1(
exp)(1
1
tDmDmaDtD
tqtq
DNGDNG
mDNGDNG
mg
]exp[ tDatGq
DNGm
p
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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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 diagnostic plot can be used.
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
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]ˆexp[ˆ)( nigi tDtDqtgq
)1(
1exp)( 1 mm
gig tmatqtq
2
)1(
)()( n
n
g taaKnttq
tDt
matqtq DNG
mmg 1
1exp)( 1
1
],1[],1[)1(exp)( 11 tDmDmaDtDtqtq DNGDNG
mDNGDNGmg
]exp[)(
)( 2
)1(
tDta
aKnttq LGMn
n
g
21
]exp[)1()(]exp[)(
nLGM
LGMn
LGMg ttDRa
tDnKttDatq
PLE
Duong
LGM
Modified LGM MODEL 2
Modified LGM MODEL 1
Modified Duong MODEL 2
Modified Duong MODEL 1
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 4
7/40
DtDntD n
i1ˆ)( 2)ˆ(
)1(ˆ)(n
i
ni
ntDtDntnDtb
matmttD 1)(2)()()( m
mm
mtatattmttb
)()1()( n
n
tattnanatD
2
222
))1(()1()1(2)1()( n
nn
tnanatntnanatb
mDNG at
tmDtD )( 2))((
)()(tDmtat
tatmttbDNG
m
mm
]exp[)( tDattmDtD DNG
mDNG
2)(]exp[
)(]exp[]exp[)(tDmttDat
tDmatmttDttDtbLGM
mLGM
LGMm
LGMm
LGM
)()1()1()( n
LGMn
LGM
tattDnttDnatD
2
222
))1()1(()1()1(2)1()(tDnttDnatntnanatb
LGMn
LGM
nn
PLE
Duong
LGM
Modified Duong MODEL 2
Modified Duong MODEL 1
Modified LGM MODEL 1
],1[],1[)1(exp)( 11 tDmDmaDtDtqtq DNGDNG
mDNGDNGmg
Slid
e —
48/
38
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege 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 - (MODEL 2)
]exp[ tDatGq
DNGm
p
],1[],1[exp)( 11 tDmDmaDDaqtG DNGDNG
mDNGDNGp
]exp[)( tDattmDtD DNG
mDNG
2)(]exp[
)(]exp[]exp[)(tDmttDat
tDmatmttDttDtbLGM
mLGM
LGMm
LGMm
LGM
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 4
9/40
Power Law Exponential (PLE) ModelLoss Ratio Relation
Basis for PLE Model
Rate-Time Relation
Loss-Ratio Derivative
DtDntD n
i1ˆ)(
]ˆexp[ˆ)( nigi tDtDqtgq
2)ˆ()1(ˆ)(
ni
ni
ntDtDntnDtb
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
0/40
Duong Time-Rate Relationq/Gp vs. Production Time Log-Log Plot
m
p
atGq Basis for Duong Model
Rate-Time Relation
)1(
1exp)( 1
1mm
g tmatqtq
Cumulative-Time Relation
)1(
1exp 11 m
p tma
aqG
Loss-RatiomatmttD 1)(
2)()()( m
mm
mtatattmttb
Loss-Ratio Derivative
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
1/40
Logistic Growth Model (LGM)K/Q(t) -1 vs. Production Time Log-Log Plot
ntatQK ˆ1)(
Basis for LGM
Rate-Time Relation
Cumulative-Time Relation
Loss-Ratio
Loss-Ratio Derivative
2
)1(
)ˆ(ˆ
)( n
n
g taKntatq
n
n
p taKtG
ˆ
)()1()( n
n
tattnanatD
2
222
))1(ˆˆ()1()1(ˆ2)1(ˆ)( n
nn
tnnaatntnanatb
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
2/40
Modified Duong Model (Model 1)Loss Ratio Relation
Basis for Modified Duong Model
Rate-Time Relation
Loss-Ratio Derivative
mDNG atmtDtD 1)(
tDt
matqtq DNG
mmg 1
1exp)( 1
1
2))(()()(tDmtat
tatmttbDNG
m
mm
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
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Modified Duong Model (Model 2)q/Gp vs. Production Time Log-Log Plot
Basis for Modified Duong Model (Model 2)
Rate-Time Relation
Cumulative-Time Relation
Loss-Ratio
Loss-Ratio Derivative
]exp[ tDatGq
DNGm
p
],1[],1[)1(exp)( 11 tDmDmaDtDtqtq DNGDNG
mDNGDNGmg
],1[],1[exp)( 11 tDmDmaDDaqtG DNGDNG
mDNGDNGp
]exp[)( tDattmDtD DNG
mDNG
2)(]exp[
)(]exp[]exp[)(tDmttDat
tDmatmttDttDtbLGM
mLGM
LGMm
LGMm
LGM
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
4/40
Modified Logistic Growth Model (Model 1)Loss Ratio Relation
Basis for Modified Logistic Growth Model(Model 1)
Rate-Time Relation
Loss-Ratio Derivative
LGMn
n
Dtat
tnnaatD
)ˆ()1(ˆˆ
)(
]exp[)ˆ(
ˆ)( 2
)1(
tDta
Kntatq LGMn
n
g
2
222
))1()1(ˆ()1()1(ˆ2)1(ˆ)(tDnttDnatntnanatb
LGMn
LGM
nn
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories
Status Presentation — Yohanes ASKABE — Texas A&M UniversityCollege Station, TX (USA) — 12 August 2012
Integration of Production Analysis and Rate-Time Analysis via Parametric Correlations Montney Shale Case Histories Sl
ide
— 5
5/40
Modified Duong Model (Model 2)
Basis for Modified LGM (Model 2)
Rate-Time Relation
Cumulative-Time Relation
K/Q(t) -1 vs. Production Time Log-Log Plot
RtDtatQK
LGMn
g
]exp[ˆ1)(
21
]exp[)1(ˆ)(]exp[ˆ
)(n
LGM
LGMn
LGMg
ttDRatDnKttDatq
nLGM
LGMn
g ttDRatDKttQ]exp[)1(ˆ]exp[)(
Loss-Ratio
Loss-Ratio Derivativedtdq
qD g
g
/1
dtdqq
dtd
Ddtdb
g
g
/1