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Fundamentals of Reservoir Simulation
d
l f
i i l i
‐‐‐‐‐‐‐‐‐‐
Rhombo Exercise –
Exercise – Day 1
y
Etienne MOREAU ‐ May 2009

Course Outline

Day 1 : Reservoir Description

• Quiz:
Q
Grid definition,, Reservoir
layering,
rock
&amp;
fluid
properties
• Practice : Flow simulations
(Appraisal well)

Day 2 : Initial state &amp; Aquifers
• Quiz : Initial state &amp; aquifer
influx calculations
• Practice : Flow simulations
(Development well)

Day 4 : History matching
• Quiz
Q : Sensitivityy runs
• Practice : Flow simulations
(final screening)

Day 5 : Production forecasting
• Quiz : General overview &amp;
production constraints
• Practice : Flow simulations (Do
nothing &amp; alternate cases)

Day 3 : History matching

• Quiz : General overview &amp; well
representation
• Practice : Flow simulations;
Well history match (1st
screening)

Grid definition: Quiz

Look at the following sentences. Establish for each one if it is true
or false.
1. Grid ggeometryy can varyy with time.
2. Any grid has locally three main flow directions.
3. Grid axis should be locallyy orthogonal.
g
4. CPG geometry depends on pillars definition.
5. Each CPG cell is defined by six corners.
6. CPG geometry can deliver variable axis orientation.
7. One cell can communicate with a maximum of 6 neighbours.
8. Grid blocks are referred by three indexes (I, J, K)
9. Grid blocks (I,J,K) and (I+1, J+1, K+1) are neighbours
10. Any locally orthogonal grid is suitable for one given reservoir

Grid definition: Sugar box geometry
XY grid

XZ Cross Section

3D View

Grid definition: Sugar box geometry
1 cell can communicate with
6 neighbours
6 neighbours

3 main flow directions

I , J , K‐1

I+1, J , K

Cell a
I J1 K
I , J‐1, K
I , J+1 , K

I‐1, J , K

I , J , K+1

Cell b
Cell b

Grid definition: Corner Point Geometry
1 cell is defined by it’s corners

Pillar lines

Horizontal axis can have variable
orientation

Grid definition : Corner Point Geometry
1 cell is defined by it’s corners
All corner points belong to pillar lines

1 cell can communicate with
6 neighbours
I , J , K‐1

I+1, J , K

Cell a
I J‐1
I , J
1, K
K
I , J+1 , K

I‐1, J , K

Pillar lines

Cell b
I , J , K+1

Grid definition : Example
T2
T3

T5
T1

T4

Reservoir layering: Quiz

Look at the following sentences. Establish for each one if it is true
or false.
1. Reservoir layering
y
g should be defined before XY ggrid.
2. Reservoir layering is derived from well data.
3. Reservoir layering
y
g is derived from fault ggeometry.
y
4. Reservoir layering should respect wells’ correlation.
5. Reservoir layering should respect flow units.
6. Reservoir layering should respect facies distribution.
7. Reservoir layering should respect initial pressure distribution.
8. Reservoir layering should respect pressure evolution with time.
9. Reservoir layering should respect maximum flooding surfaces
10. There are specific porosity permeability relationships per
layer.

Reservoir layering: Identification of well trajectories

Reservoir layering: Use of log Correlation
210/15‐3

210/15a‐6

210/15‐2

210/15a‐5

210/15a‐T4

Tarbert3
Tarbert2
Tarbert1
Ness4
Ness3
Ness2

Ness1

Etive
Rannoch2

Rannoch1

Broom

Reservoir layering: Identification of flow Units
1960

‐25 psi
p

1980

T3
2000

2020

Depth (m TVDSSS)

a6

2060

T5

744 kg/m3
744 kg/m3

2040

T4

2080

1025 kg/m3

2100

2120

2140
2750

2800

2850

2900

2950
Pressure (psia)
(
)

3000

3050

3100

3150

‐240 psi
240 i

Rock properties: Quiz

Look at the following sentences. Establish for each one if it is true
or false.
1. Main input
p data are p
porosityy &amp; p
permeability.
y
2. Cell pore volume is equal to its porosity times its gross volume.
3. NTG is the ratio between net &amp; ggross volumes.
4. Cell porosity is a net porosity.
5. Rock compressibility refers to pore compressibility.
6. Average horizontal perm. is the harmonic mean of net perm.
7. K.H is equal to horizontal permeability times gross thickness.
8. Average vertical perm. is an harmonic mean of the net perm.
9. Upscaled data depend on flow units geometry.
10. It is recommended to upscale Phi‐K laws derived from core
analysis

Rock properties: Main parameters

Non reservoir
Non
reservoir
Reservoir

NTG 

Net thickness
Gross thickness

Porosityy
Permeability
Fluid Saturation

Rock properties: Main parameters (example)
NTG

Porosity

1

0.01

0.1

0.33

PermX (mD)
PermX (mD)

10,000
0

0.9

1

Initial Soil

Rock properties: Net thickness and porosity

Cell Volume : Vt x y z
Cell Volume : Vt = x . y . z
Net Volume : Vu = Vu1 + Vu2
Porous Volume : Vp = 1 . Vu1 + 2 . Vu2

Facies 1 (1, Vu1)
Net Thickness : Hu = Ht . Vu / Vt
Facies 2 (2, Vu2)
y
= Vp / Vu
p
Porosity : 

Non reservoir

Rock properties: Pore compressibility

Vp

Vp ‐ Vp

Vs

Vs+Vs

Pf

Pf Pf
Pf ‐

ΔVt  Δ Vp  ΔVs

Ct 
C

Vp
Vs
Cp 
Cs
Vt
Vt

Vt Ct  Vp Cp  Vs Cs

Rock properties: Pore compressibility

1 dVp
Vp dP

Pores :

Cp 

Solid :

Cs  

Total :

Ct 

1 dVs
Vs dP

1 dVt
Vt dP

Pore compressibility and total compressibility are not identical :

Ct =  . Cp ‐ (1 ‐ ) . Cs

Rock properties: Horizontal &amp; Vertical Permeability

Rock properties: Horizontal Permeability
P
Kx1, h1

Q1  Kx1 h1 P

Kx2, h2

Q2  Kx2 h2 P

Q   Qi
i

Hu   h i
i

Qn  Kxn hn P

Kxn, hn

NTG  Hu /Ht

Q iQi

  Kxi hi
ΔP
ΔP
i

Kx Hu 

Rock properties: Vertical Permeability
Kz1, h1

P1  Q h1 / Kz1

Kz2, h2

P2 = Q h2 / Kz2

ΔP   ΔPi
i

Ht   hi
i

Kzn, hn

Pn = Q hn / Kzn

Ht ΔP iΔPi
h

 i
Kz Q
Q
i Kzi

Rock properties: Identification of Phi – K laws

EF3 : Fine micaceous sands
EF4 : Upper shoreface
EF5 : Estuarine channel
EF6 :Medium to coarse sands
EF7 : Calcareous sands

Rock properties: Data upscaling
AVERAGE SHALINESS = 10%

Rock properties: Data upscaling

PORE ‐ GRAIN

MICRO

CORE

MACRO
CELL
MEGA
GIGA

FIELD

Rock properties: Permeability calculations

Core

Well

Geomodel

Flow  model

Data

Permeability

Permeability

Permeability

Transmissivity

Group

Facies

Flow Unit

Cell

Calculation

Technique

K‐Phi
K‐Phi
laws
laws
Correlation

Composition

Average

Average

Geomodelling

Homoge‐

neisation

Fluid properties: Quiz

Look at the following sentences. Establish for each one if it is true
or false.

• 1
1. B.O.
B O model uses volume factors,
factors solution ratios and viscosities
• 2. B.O. model applies for constant or variable initial sat. pressure.
• 3.
3 Volume factor,
factor solution ratio and viscosity depend on
temperature.
• 4. Oil volume factor is maximum at bubble p
point p
pressure.
• 5. Oil stock volume increases with oil volume factor.
• 6. Under Saturated Oil volume factor is decreasingg with p
pressure
• 7. Oil density is derived from stock density and volume factor.
point p
pressure: True
• 8. Oil densityy is minimum at bubble p
• 9. Oil compressibility depends on Bo, Rs and oil viscosity.
p
y is set to zero.
• 10. Water compressibility

Fluid properties: Main data
Identification of reservoir fluids
• Hydrocarbons
• Brines

Hydrocarbons
• Surface &amp; reservoir conditions.
• Liquid vapour equilibriums
• Physical properties : density, viscosity, compressibility
• Composition.

Brines
• Surface &amp; reservoir conditions
• Physical
Ph i l properties
ti : density,
d it viscosity,
i
it compressibility
ibilit
• Composition (salinity).

Hydrocarbons : Surface &amp; reservoir conditions (1)

GAS

Vapor
Recovery
System

P stockk
T stock

(c)

(c)

OIL
Separator

Stock(b)
Tank

P

(b)

(a)

(a)

T

P res
T res

Hydrocarbons: Surface &amp; reservoir conditions (2)

Bo 

Volume
V
l
off liquid
li id in
i reservoir
i conditions
diti
Volume of liquid in stock condtions

Bg 

Volume of gas in reservoir conditions
Volume of gas in stock condtions
Volume of gas
Volume of liquid
----------

GOR 

141,5
,
 131,5
131 5 (d  oil
il density
d it en g/cm3)
/ 3)
d

API 

Fluid properties: Influence of reservoir temperature

Small variations of composition
p
P
Volatile oil
C
O3

Condensate gas
Wet gas
G4
G5

Dry gas
G6

Black oil
O2

d l
O1
S2

S3
T2

S4
T3

S5
T4

S6
T5

T6

TF

S1
T1

Fluid properties: Black oil assumptions

Bottom hole temperature is constant with time.

Produced oil and gas in standard conditions have constant
compositions. It is possible to define "oil" and "gas" as pseudo
components.

Oil and gas in bottom hole conditions are mixtures of pseudo
components "oil " and "gas". Volumes in reservoir conditions
depends on pressure and concentrations.

Fluid properties : Black‐oil relationships

GAS COMPONENT
GAS COMPONENT

OIL COMPONENT
OIL COMPONENT

(gs)

(os)

Rs

STOCK TANK
CONDITIONS

GAS FLUID
RESERVOIR
CONDITIONS

1

1

OIL FLUID

Bgg
Bo

Fluid properties : Black oil representation

Bo

µo

Saturated
oil

Undersaturated
oil

Undersaturated
oilil

Saturated
oilil

P

P

Pb

Bg

Rs

µg

Bg

µg
Saturated
oil

Undersaturated
oil

P

Pb

Black oil : Compressibility calculations

OIL

GAS
B R
Bg Rs

Bo

Bo ‐ Bo

Bg

P

P ‐ P

P

Vo = ‐Bo + Bg Rs

1  Bo
Rs 
 Bg

Bo  P
P 

P ‐ P

Vg = Bg

Cg  

1 Bg
Bg P

Co  

Bg + Bg

Fluid properties : PVT Region

Constant Saturation Pressure
• All samples collected at initial state have the same saturation
pressure.
• Measurements of Bo(P), Rs(P), o(P) for one sample give values
of Bo, Rs, o everywhere in the reservoir at anytime.

Variable Saturation Pressure
• All samples collected at initial state have a saturation pressure
varying with an understandable law (e.g; saturation pressure
depends on depth)

• Measurements of Bo(P,Pb), Rs(P,Pb), o(P,Pb) for one sample
give values of Bo(Pb), Rs(Pb), o(Pb) everywhere in the reservoir
at anytime.
anytime

PVT Region : Constant saturation pressure

GOC

Spl2 (P = Pb)

GOC

Spl3 (P &lt; Pb)

Spl1 (P &gt; Pb)
DEPLETED RESERVOIR

INITIAL STATE

PVT Region : Oil description (Constant initial Pb)

R
Rs

Spl2

Bo

Spl2

Spl1

Spl1

Spl3

Spl3
oil
saturated

oil
saturated

oil
undersaturated

P

Pb

oil
undersaturated

P

Pb

µo

Pb

Spl3

Spl1
Spl2

Spl2
Spl3

oil
undersaturated

oil
saturated

z

Pb

P

Spl1

P

PVT Region : Variable Saturation Pressure

Spl2 (P2 = Pb2)

Spl4 (P4 = Pb4)

P

P

Spl1 (P1 &gt; Pb1)
Spl1 (P1 &gt; Pb1)
Spl3 (P3 &gt; Pb3)

Pb
P

Depth

P

Depth

DEPLETED RESERVOIR

INITIAL STATE

Pb

PVT Region : Oil description (Variable initial Pb)

Spl2
p

Spl2
l

Rs

Spl4

Bo

Spl4
Spl1

Spl1
Spl3
p

Spl3
P

P
µo

Pb

Spl3
Spl4

Spl1

Spl2
Spl1

Spl2

Spl3
P

z

P

Spl4
l

Course Outline

Day 1 : Reservoir Description

• Quiz:
Q
Grid definition,, Reservoir
layering,
rock
&amp;
fluid
properties
• Practice : Flow simulations
(Appraisal well)

Day 2 : Initial state &amp; Aquifers
• Quiz : Initial state &amp; aquifer
influx calculations
• Practice : Flow simulations
(Development well)

Day 4 : History matching
• Quiz
Q : Sensitivityy runs
• Practice : Flow simulations
(final screening)

Day 5 : Production forecasting
• Quiz : General overview &amp;
production constraints
• Practice : Flow simulations (Do
nothing &amp; alternate cases)

Day 3 : History matching

• Quiz : General overview &amp; well
representation
• Practice : Flow simulations;
Well history match (1st
screening)

Flow Simulations: Introduction

General context
• Reservoir has been discovered by an exploration well
• Available data are cores, logs, initial pressure and well test.

Exercise objectives
• Simulate the well test realized on the exploration well
• Reconcile well test data with log and core data

Data review
• Geometry, Rock &amp; Fluid properties, Well test data

Flow simulations
• Two layering
y
g will be tested
• Two types of horizontal grids will be tested :

− Fine layers (2m thick) or coarse layers (10 m thick)

Flow simulations: Data review
Reservoir description
− Top reservoir derived from seismics and well location
− Reservoir thickness observed along well path
− Initial pressure derived from MDT measurements &amp; well test
analysis
l i

Rock properties
p p
− Porosity and permeability derived from cores
− KH derived from well test Fluid properties
− Maximum oil rel. perm. and capillary pressure derived from
f
SCAL

Fluid
udp
properties
ope t es
− PVT properties derived from DST sample

Work to do

Reservoir description: Top reservoir

Reservoir description: Core data
NET POROSITY (% )
17%

19%

21%

23%

25%

0

1960

1960

1965

1965

1970

1970

1975

1975
DEPT
TH (m TVDss)

DEPT
TH (m TVDss)

15%

NET PERMEABILITY (mD)

1980

1985
1990

400

600

800

1000

1980

1985
1990

1995

2000

2000

2005

2005

2010

2010
LOG

1995

LOG

200

Rock properties: Poro Perm relationship
1000

PERMEABILITY
Y (mD)

100

10

1

14%

16%

18%
20%
POROSITY (%)

22%

24%

0

Rock properties: Reservoir thin layering
NET PERMEABILITY (mD)

NET POROSITY (% )
17%

19%

21%

23%

25%

1960

1960

1965

1965

1970

1970

1975

1975

1980

1985

1990

DEPTH (m TVDss)

DEPTH (m TVDss)

15%

0

200

400

600

800

1980

1985

1990

1995

2000

2000

2005

2005

2010

2010

1995

Rock properties: Reservoir thick layering
NET POROSITY (% )
15%

17%

19%

21%

NET PERMEABILITY (mD)
23%

25%

0

1960

1965

200

300

400

500

1965

1970

1970

1975

1975
DEPTH (m TVDss)

1980

1985

1990

1980

1985

1990

1995

2000

2000

2005

2005

2010

2010

1995

Rock properties: Water‐Oil Saturation functions

W/O Relative permeabilities
Krw

W/O Capillary Pressure

Krow

Pcow

1

1

0,8

0,8
Capilla
ary Pressurre

Relative Permeabiliity

DEPTH (m TVDss)

100

1960

0,6

0,4

0,6

0,4

02
0,2

02
0,2

0

0
0,2

0,4

0,6

Water Saturation

0,8

1

0

0,2

0,4

0,6

Water Saturation

0,8

1

0

Rock properties: Gas‐Oil Saturation functions

G/O Relative permeabilities
Krog

Pcog

1

1

0,8

0,8
Capilla
ary Pressurre

Relative
e Permeabillity

Krg

G/O Capillary Pressure

0,6

0,4

02
0,2

0,6

0,4

02
0,2

0

0
0,2

0,4
0,6
Gas Saturation

0,8

1

0

0,2

0,4
0,6
Gas Saturation

0,8

1

0

1,2

150

1 16
1,16

130

Solution
n Gas (m3 / m3)

Formation vo
olume factor (vol//vol)

Fluid properties: PVT functions (oil)

1,12

1 08
1,08

1,04

110

90

70

1

50
100

150

200

250

300

100

150

Pressure (bar)

200

250

300

250

300

Pressure (bar)

2

860

Oil viscosity (mP
Pa.s)

Oil Density (kg/m
m3)

855

850

845

1,8

1,6

14
1,4

835

1,2
100

140

180

220

P
Pressure
(b
(bar))

260

300

100

150

200
P
Pressure
(bar)
(b )

840

Fluid properties: PVT functions (gas)
0,012

0,01

1 03
1,03

Z factor

Formation
n volume factor (v
vol/vol)

1,05

0,008

1,01

0 99
0,99

0,006

0,97
0,004
100

150

200

250

0 95
0,95

300

100

Pressure (bar)

150

200

250

300

250

0,06

200

0,045

Oil viscosity (mP
Pa.s)

Gas Density (kg//m3)

Pressure (bar)

150

100

0,03

0 015
0,015

100

150

200

250

300

100

150

200
Pressure (bar)

P
Pressure
(b
(bar))

250

300

0

50

Reservoir description: Work to do

Look at the ECLIPSE data file

Identify the following data
• Grid definition
− Total number of cells
− Cell dimensions along each coordinate
− Volume of the smallest cell

• Reservoir geometry
− Top reservoir at well location
− Reservoir thickness (in true vertical depth)
− Perforated interval along well path

• Initial state

− Initial pressure at datum
− Depth of initial Water Oil Contact and Gas Oil Contact

Rock properties: Work to do
Look at the ECLIPSE data file

Identify the following data
• NTG &amp; average porosity per layer (fine &amp; coarse layering)
• Average permeability per layer (fine &amp; coarse layering)
• NTG; average porosity &amp; permeability (entire well)
• SCAL data : Maximum oil rel.
rel perm &amp; capillary pressure

Porosity permeability relationship
• Calculate the p
porosityy cut‐off equivalent
q
to a 0.6 mD/cp
/ p mobilityy
cut‐off
• Identify the poro perm relationship for fine &amp; coarse layering

Fluid properties: Work to do
Look at the ECLIPSE data file

Identify the following data
• Oil, gas &amp; water density and viscosity in stock conditions
• Initial saturation pressure versus depth
• Oil volume factor and solution gas ratio at initial pressure

Calculate the followingg p
parameters
• Oil and water density at initial pressure
pressure
• Oil and ggas densityy at saturation p
• Water oil mobility ratio at initial pressure &amp; saturation pressure
• Water oil transition height
g

Flow simulations: Appraisal well

Well 1 has been tested. Following data are available

Test 1 to 4
• Perforated interval
• Flow period : duration &amp; stabilized flow rate
• Shut‐in period : duration &amp; pressure build‐up

Work to do

Flow simulations : Well test results (RTZ grid)

RTZ grid ‐ 25 layers
(2 m per layer)

Flow simulations : Well test results (RTZ grid)

RTZ grid  ‐ 5 layers
(10 m per layer)

Flow simulations : Well test results (XYZ grid)

XYZ grid ‐ 25 layers
(2 m per layer)

Flow simulations : Well test results (XYZ grid)

XYZ grid  ‐ 5 layers
(10 m per layer)

Flow simulations: Work to do
Look at the ECLIPSE data files

Identify the following data for each test
• Perforated intervals, time schedule, &amp; flow‐rate
• Minimum &amp; maximum time steps duration

Simulate well tests and visualize followingg results
• Initial pressure and initial saturation versus space
• Oil flow rate and bottom hole flowingg p
pressure versus time
• Well productivity index versus time

Wellll productivity
W
d i i analysis
l i
• Calculate KH &amp; skin factor from permeability distribution, taking
into account a reduction by 10 of the permeability 1m around
the well bore.
• Ca
Calculate
cu ate tthee co
corresponding
espo d g p
productivity
oduct ty index.
de

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