1 Rhombo .pdf
À propos / Télécharger Aperçu
Ce document au format PDF 1.7 a été généré par PScript5.dll Version 5.2.2 / Acrobat Distiller 9.2.0 (Windows), et a été envoyé sur fichier-pdf.fr le 07/05/2012 à 00:51, depuis l'adresse IP 41.228.x.x.
La présente page de téléchargement du fichier a été vue 1648 fois.
Taille du document: 3.4 Mo (30 pages).
Confidentialité: fichier public
Aperçu du document
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
&
fluid
properties
• Practice : Flow simulations
(Appraisal well)
Day 2 : Initial state & Aquifers
• Quiz : Initial state & 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 &
production constraints
• Practice : Flow simulations (Do
nothing & alternate cases)
Day 3 : History matching
© 2010 ‐ IFP Training
• Quiz : General overview & 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
© 2010 ‐ IFP Training
•
•
•
•
•
•
•
•
•
•
Grid definition: Sugar box geometry
XY grid
XZ Cross Section
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
Cell b
Cell b
Grid definition: Corner Point Geometry
1 cell is defined by it’s corners
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
Cell b
I , J , K+1
Grid definition : Example
T2
T3
T5
T1
T4
© 2010 ‐ IFP Training
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.
© 2010 ‐ IFP Training
•
•
•
•
•
•
•
•
•
•
Reservoir layering: Identification of well trajectories
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
‐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 & p
permeability.
y
2. Cell pore volume is equal to its porosity times its gross volume.
3. NTG is the ratio between net & 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
© 2010 ‐ IFP Training
•
•
•
•
•
•
•
•
•
•
Rock properties: Main parameters
Non reservoir
Non
reservoir
Reservoir
NTG
Net thickness
Gross thickness
Porosityy
Permeability
Fluid Saturation
© 2010 ‐ IFP Training
Rock properties: Main parameters (example)
NTG
Porosity
1
0.01
0.1
0.33
PermX (mD)
PermX (mD)
10,000
0
0.9
© 2010 ‐ IFP Training
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 :
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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 :
© 2010 ‐ IFP Training
Ct = . Cp ‐ (1 ‐ ) . Cs
Rock properties: Horizontal & Vertical Permeability
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
Rock properties: Data upscaling
AVERAGE SHALINESS = 10%
© 2010 ‐ IFP Training
Rock properties: Data upscaling
PORE ‐ GRAIN
MICRO
CORE
MACRO
CELL
MEGA
GIGA
FIELD
© 2010 ‐ IFP Training
Rock properties: Permeability calculations
Core
Well
Geomodel
Flow model
Data
Permeability
Permeability
Permeability
Transmissivity
Group
Facies
Flow Unit
Cell
Adjacent Cells
Calculation
Technique
K‐Phi
K‐Phi
laws
laws
Correlation
Composition
Average
Average
Geomodelling
Homoge‐
© 2010 ‐ IFP Training
neisation
Fluid properties: Quiz
Look at the following sentences. Establish for each one if it is true
or false.
© 2010 ‐ IFP Training
• 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 & reservoir conditions.
• Liquid vapour equilibriums
• Physical properties : density, viscosity, compressibility
• Composition.
Brines
• Surface & reservoir conditions
• Physical
Ph i l properties
ti : density,
d it viscosity,
i
it compressibility
ibilit
• Composition (salinity).
© 2010 ‐ IFP Training
Hydrocarbons : Surface & reservoir conditions (1)
GAS
Vapor
Recovery
System
P stockk
T stock
(c)
(c)
OIL
Separator
Stock(b)
Tank
P
(b)
(a)
(a)
T
© 2010 ‐ IFP Training
P res
T res
Hydrocarbons: Surface & 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
© 2010 ‐ IFP Training
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
Dead oil
d l
O1
S2
S3
T2
S4
T3
S5
T4
S6
T5
T6
TF
© 2010 ‐ IFP Training
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.
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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)
© 2010 ‐ IFP Training
• 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 < Pb)
Spl1 (P > Pb)
DEPLETED RESERVOIR
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
Spl1
P
PVT Region : Variable Saturation Pressure
Spl2 (P2 = Pb2)
Spl4 (P4 = Pb4)
P
P
Spl1 (P1 > Pb1)
Spl1 (P1 > Pb1)
Spl3 (P3 > Pb3)
Pb
P
Depth
P
Depth
DEPLETED RESERVOIR
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
Spl4
l
Course Outline
Day 1 : Reservoir Description
• Quiz:
Q
Grid definition,, Reservoir
layering,
rock
&
fluid
properties
• Practice : Flow simulations
(Appraisal well)
Day 2 : Initial state & Aquifers
• Quiz : Initial state & 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 &
production constraints
• Practice : Flow simulations (Do
nothing & alternate cases)
Day 3 : History matching
© 2010 ‐ IFP Training
• Quiz : General overview & 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 & Fluid properties, Well test data
Flow simulations
• Two layering
y
g will be tested
• Two types of horizontal grids will be tested :
− Rectangular or radial grid
© 2010 ‐ IFP Training
− 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 & 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
© 2010 ‐ IFP Training
Reservoir description: Top reservoir
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
1995
LOG
200
Rock properties: Poro Perm relationship
1000
PERMEABILITY
Y (mD)
100
10
1
14%
16%
18%
20%
POROSITY (%)
22%
24%
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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 )
© 2010 ‐ IFP Training
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
© 2010 ‐ IFP Training
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
Give your comments
© 2010 ‐ IFP Training
− 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 & average porosity per layer (fine & coarse layering)
• Average permeability per layer (fine & coarse layering)
• NTG; average porosity & permeability (entire well)
• SCAL data : Maximum oil rel.
rel perm & 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 & coarse layering
Give your comments
© 2010 ‐ IFP Training
Fluid properties: Work to do
Look at the ECLIPSE data file
Identify the following data
• Oil, gas & 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 & saturation pressure
• Water oil transition height
g
© 2010 ‐ IFP Training
Flow simulations: Appraisal well
Well 1 has been tested. Following data are available
Test 1 to 4
• Perforated interval
• Flow period : duration & stabilized flow rate
• Shut‐in period : duration & pressure build‐up
Work to do
© 2010 ‐ IFP Training
Flow simulations : Well test results (RTZ grid)
© 2010 ‐ IFP Training
RTZ grid ‐ 25 layers
(2 m per layer)
Flow simulations : Well test results (RTZ grid)
© 2010 ‐ IFP Training
RTZ grid ‐ 5 layers
(10 m per layer)
Flow simulations : Well test results (XYZ grid)
© 2010 ‐ IFP Training
XYZ grid ‐ 25 layers
(2 m per layer)
Flow simulations : Well test results (XYZ grid)
© 2010 ‐ IFP Training
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, & flow‐rate
• Minimum & 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 & 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
© 2010 ‐ IFP Training