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

16

(a) (c)

(b) (d)

(a) Diffusive Time of Flight; (b) Drainage Volume; (c) BHP; (d) Rate

Evolution of Drainage Volume with Time

17

(a) 10 days (b) 2 months (c) 3 months

(d) 1 year (e) 10 years

Visualizing Pressure on the Grid

18

Initial Pressure = 4971 psi Pressure at the last time step

Training Session :Petrel Plug-in

19

FMM Petrel Plug-in User Interface

20

Model for Demonstration

21

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

22

Gas Rate BHP

Results from Democase

23

Tau Time = 

Pressure