fmm petrel plug-in (fast marching method)
TRANSCRIPT
FMM Petrel Plug-In(Fast Marching Method)
Atsushi Iino, Hye Young Jung
April 28, 2017
Outline
2
• Motivation
• Background
• FMM‐plug in
FMM plug‐in Features
Plug‐in Workflow
• Demonstration
Motivation
3
• Drainage volume and pressure depletion are important in unconventional
reservoirs
• Quickly generalize the concept of drainage volume to account for complex
geologic stratigraphy, reservoir heterogeneity and well/fracture geometry
Background
4
Radius of Investigation (ROI)for homogeneous reservoir
(Lee, 1982)
Generalization of ROI for heterogeneous reservoir
(Datta‐Gupta et. al., 2011))
tc
ktr
4
1)(
)(
tc
k
x
x
Diffusive Time‐of‐FlightSpeed (diffusivity)‘Peak’ arrival time(Impulse source)
Eikonal eq.:
Pressure Front Propagation
High
Low
Travel Time Calculations by Fast Marching Method
6
Fast Marching Method (FMM)*
• Efficiently solves eikonal eq. for Diffusive Time‐of‐Flight (DTOF)
• Sequential calculation of shortest path from a source outwards W
A
B
C
D E
F
G
H
I
Diffusive Time-of-Flight Map
*Dijkstra (1959), Sethian (1996)
Application to Unconventional Reservoirs:Drainage Volume Calculation Using Fast Marching Method
7
Geological Model Drainage Volume
Fracture System
Generalization of Radial Diffusivity EquationUsing Diffusive Time-of-Flight as a 1-D Spatial Coordinate
8
Homogeneous reservoir Heterogeneous reservoir
Radius Diffusive Time‐of‐Flight
Rapid Simulation of Unconventional Reservoirs:3-D to 1-D Formulation
9
FD FD
Permeability Diffusive Time of Flight
Spatial Heterogeneity Drainage Volume
1 2 NN-1
FMM
Drainage pore volume (ft3)
1-D -coordinate
Rate Calculation
BHP Calculation
Assign ∆
Numerical Flow Simulation
Well
9
CPU Time: Orders of Magnitude Faster Computation than Commercial FD Simulator
10
Significant gain in computational efficiency• Dual Porosity Model, Horizontal well with 15 HFs• BHP constraint • 20 years forecast
Rapid Compositional Simulation Using Fast Marching Method
11
Natural Fracture
Matrix
Hydraulic Frac
Initial pressure
0
0.5
1
1.5
2000 3000 4000 5000 6000 7000
Tra
ns
mis
sib
ilit
y m
ult
iplie
r
Pressure, psi
• 0.4 million cells with reservoir heterogeneity
• Multi‐stage hydraulic fractures
• 3‐phase and 7‐component
• Dual‐porosity
• High water saturation around well
• Permeability reduction due to compaction
• Primary depletion + CO2 Huff‐n‐Puff (5‐cycle)
Fracture Permeability
Fracture SwiRock compaction
12
Simulation Results
0
10
20
30
40
GO
R, M
scf/
stb
FMM_GORFDSim_GOR
0
200
400
600
Oil
Rat
e, s
tb/d
FMM_QoFDSim_Qo
0
0.025
0.05
800 1000 1200 1400 1600 1800
CO
2 M
ole
fr
acti
on
in O
il
Days
FMM_XCO2FDSim_XCO2
0
50
100
150
Incr
. Oil,
Mst
b
FMMFDSim
0
5
10
15
20
CO
2 In
j. R
ate
(MM
scf/
d) FMM_Qinj
FDSim_Qinj
0
200
400
600
800
Cu
m C
O2
Inj
(MM
scf)
FMM_Qinj
FDSim_Qinj
Inj. BHP=3500psi
GOR=0.55 Mscf/stbbefore Huff-n-Puff
No CO2 in oilbefore Huff-n-Puff
Day
Incremental Oil Recovery=(Cum. Oil) – (Cum. Oil@end of primary depletion)
Prod. BHP = 2500 psi
CO2 Huff-n-Puff
Qo
Cum. oil
Line: FMM, Symbol: FDSim
Line: FMM, Symbol: FDSim
Qw
Cum. water
32% increase in incremental oil than do‐nothing case
CO2 inj. rate
CO2 inj. total
Oil rate
Incremental oil
Production GOR
CO2 mole fraction in oil
Primary depletion 5-cycle Huff-n-PuffSpeed‐up factor x 320 (compared to commercial FD simulator)
0
100
200
300
400
0
500
1000
Cu
m.
Oil
(Mst
b)
Oil
Ra
te,
stb
/d
FMM_Qo FDSim_Qo
FMM_CumOil FDsim_CumOil
0
50
100
150
200
0
1000
2000
3000
4000
0 250 500 750 1000
Cu
m.
Wat
er (
Mst
b)
Wat
er R
ate,
stw
b/d
Days
FMM_Qw FDSim_Qw
FMM_CumWat Fdsim_CumWat
Primary depletion
Qo
Cum. oil
Line: FMM, Symbol: FDSim
Line: FMM, Symbol: FDSim
Qw
Cum. water
FMM Petrel Plug-in
13
FMM Plug-in Features
14
• Future plan
Multi‐phase black oil simulation
Compositional simulation
• Current version
Drainage volume calculation (single‐phase)
1‐D simulation (single‐phase)
FMM Petrel Plug-in Workflow
15
Drag and drop properties
Generate the simulation model
Run the FMM simulation
Import and visualize results
Visualizing Results in Petrel
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(a) (c)
(b) (d)
(a) Diffusive Time of Flight; (b) Drainage Volume; (c) BHP; (d) Rate
Evolution of Drainage Volume with Time
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(a) 10 days (b) 2 months (c) 3 months
(d) 1 year (e) 10 years
Visualizing Pressure on the Grid
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Initial Pressure = 4971 psi Pressure at the last time step
Training Session :Petrel Plug-in
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FMM Petrel Plug-in User Interface
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Model for Demonstration
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Reservoir dimension 1000 ft x 2000 ft x 120 ft
The number of gridblocks
100 x 200 x 10
Well data1 Producer
Horizontal WellRate constrained : 500 MSCF/D
Hydraulic Fractures (4)Half Length 300 ft
Width 2 ft
Porosity 0.05
PermeabilityMatrix
Avg. = 7.23e‐4 md
0.1
Fracture 100 md
Results from Democase
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Gas Rate BHP
Results from Democase
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Tau Time =
Pressure