piroska lorinczi, paul w.j. glover, saud al-zainaldin, hassan al … · 2020. 4. 23. · saddam...
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Piroska Lorinczi, Paul W.J. Glover, Saud Al-Zainaldin, Hassan Al-Ramadhan, Saddam Sinan, George Daniel, I. Obielum
Co
nve
nti
on
al R
eser
voir
Mo
del
ling
2
A justified educated guessing game:
Physical properties obtained from few wells
Data incomplete and variability completely unknown at smaller scales ( say < 50 m)
Interpolated in the inter-well volume using variogram-filtered krigging
No information available for accurate well placement
No information about reservoir heterogeneity measured or used
No information about reservoir anisotropy measured or used in modelling and simulation
Introduction AFRMs Generic Models Conditioned Models The Future
Frac
tal R
eser
voir
Mo
del
ling
3Introduction AFRMs Generic Models Conditioned Models The Future
AFRMs can depict and control heterogeneity
AFRMs can depict and control xy, yz and zx anisotropy
AFRM accuracy can be verified
AFRM allows generic sensitivity tests for heterogeneity, anisotropy, well placement and orientation
AFRM is more accurate than conventional models in simulations
AFRM contains information at all scales larger than cell size
AFRMs can be fully reservoir-conditioned
… in this presentationWhat fractals can do for you …
How to make Advanced Fractal Reservoir Model (AFRMs)
Generic fractal modelling
The effect of heterogeneity on oil production data
The effect of anisotropy on oil production data
The effect of well placement and orientation
Conditioned fractal reservoir modelling
How to use AFRMs with real reservoirs
The Future
Creating flexible software for modelling
4Introduction AFRMs Generic Models Conditioned Models The Future
5Introduction AFRMs Generic Models Conditioned Models The FutureIntr
od
uct
ion
to
Fra
ctal
sStructured objects exhibiting self-similar behaviour at all scales.
Well-defined structure at a given scale: Full spatial correlation
Random distributions: No spatial correlation
Fractal: Partial spatial correlation
6Introduction AFRMs Generic Models Conditioned Models The Future
Scal
es a
nd
var
iab
ility Interpolation of wells:
Only large scale variability is taken account of
Fractal Interpolation (FSMA):
Takes account of all data from the reservoir scale to the cell scale
Interpolation of wells with seismic input: Range of scales in inter-well volume extended to seismic resolution
7
Piroska Lorinczi, Saud Al-Zainaldin
Introduction AFRMs Generic Models Conditioned Models The Future
How is it possible to make fractal reservoir models which
have:
o 3D
o controlled heterogeneity
o controlled anisotropy
o can be fully validated, and
o can be used to model poroperm curves
8Introduction AFRMs Generic Models Conditioned Models The Future
9Introduction AFRMs Generic Models Conditioned Models The Future
1D FT
2D
3D
FT
FT
Fou
rier
Filt
erin
g m
eth
od
in x
D
10Introduction AFRMs Generic Models Conditioned Models The Future
Data required: Physical and fractal dimension and two anisotropy factors
The Fourier Filtering methodFractal dimension and anisotropy controlledExact and repeatable structure defined by a unique random number key
Fractal Volume (D= 3.1 | cxy=cyz=1)
11Introduction AFRMs Generic Models Conditioned Models The Future
Fractal volumes for different heterogeneities (fractal dimensions) and the same isotropy
Data required: Physical and fractal dimension and two anisotropy factors
Fractal Volume (D= 3.1 | cxy=cyz=1)
Fractal Volume (D= 3.5 | cxy=cyz=1)
Fractal Volume (D= 3.9 | cxy=cyz=1)
Incr
eas
ing
Het
ero
gen
eity
12Introduction AFRMs Generic Models Conditioned Models The Future
Test
ing
the
frac
tal
dim
ensi
on
s D = 3.097
D = 3.498
D = 3.898
13Introduction AFRMs Generic Models Conditioned Models The Future
Fractal volumes for different heterogeneities (fractal dimensions) and the same isotropy
Porosity map (D= 3.4 | cxy= 1 | cyz=1)
Porosity map (D= 3.4 | cxy= 1 | cyz=5)
Porosity map (D= 3.4 | cxy= 1 | cyz=3)
Incr
eas
ing
An
iso
tro
py
14Introduction AFRMs Generic Models Conditioned Models The Future
Test
ing
the
anis
otr
op
ies
D = 3.397
D = 3.423
D = 3.437
15Introduction AFRMs Generic Models Conditioned Models The Future
16Introduction AFRMs Generic Models Conditioned Models The Future
Co
nd
itio
nin
g to
res
ervo
irp
rop
erti
es
Data required: Mean and standard deviation of each parameter
Porosity map (D= 3.5 | cxy= 1 | cyz=6)
Grain size map (D= 3.5 | cxy= 1 | cyz=6)
Cementation exponent map (D= 3.5 | cxy= 1 | cyz=6)
17Introduction AFRMs Generic Models Conditioned Models The Future
18Introduction AFRMs Generic Models Conditioned Models The Future
Using the RGPZ method for clastic rocks
or its carbonate or generic modifications appropriately.
Cal
cula
tin
g p
erm
eab
ility
Permeability map (D= 3.1 | cxy= 1 | cyz=3)
Distinct less connected channel
Layer 16
Permeability map (D= 3.5 | cxy= 1 | cyz=3)
Permeability map (D= 3.9 | cxy= 1 | cyz=3)
Distinct connected channel
19Introduction AFRMs Generic Models Conditioned Models The Future
Syn
thet
ic p
oro
per
mp
lots
Typical poroperm plot for D=3.4, different fractal volumes of main parameters and typical standard deviations of input fractal volumes
Increasing standard deviationsof input fractal volumes increases scatter
Using the same map for all input parameters collapses the poroperm plot
Pe
rme
ab
ilit
y k
(m
D)
Porosity f (%)P
erm
ea
bil
ity k
(m
D)
Porosity f (%) Porosity f (%)
Pe
rme
ab
ilit
y k
(m
D)
20Introduction AFRMs Generic Models Conditioned Models The Future
21Introduction AFRMs Generic Models Conditioned Models The Future
Water saturation
Capillary pressures
Capillary pressure
Entry pressure
Relativepermeabilities
Brooks-Corey-Mualem
Data required: Pore throat conversion factor, interfacial tension, wetting angle
22Introduction AFRMs Generic Models Conditioned Models The Future
Wat
er s
atu
rati
on
Water saturation depends on l,which depends on the fractal dimension
Water saturation map (l = 0.9)
Water saturation map (l = 1.4)
Water saturation map (l = 2)
23Introduction AFRMs Generic Models Conditioned Models The Future
Rel
ativ
e p
erm
eab
iliti
es
Can be calculated with any of the 4 main models –here the Brooks-Corey-Mualem model
What is the effect of:
o Heterogeneity
o Anisotropy
o Well Placement
o Orientation
on reservoir production from a model reservoir?
24
Saud Al-Zainaldin, George Daniel, Saddam Sinan, Piroska Lorinczi
Introduction AFRMs Generic Models Conditioned Models The Future
A T
ypic
al F
inis
hed
AFR
M
25
All the input parameters needed for full simulation.
Fully specified, unique structure, repeatable model. Not stochastic.
Introduction AFRMs Generic Models Conditioned Models The Future
Porosity map
Grain size map
Poroperm cross-plot
Cementation exponent map
Permeability map
Water saturation map
Relperm curves
Permeability map (D = 3.5 | cxy= 1 | cyz=1)
Sim
ula
tio
n f
or
test
ing
the
effe
ct o
f h
eter
oge
nei
ty a
nd
an
iso
tro
py
26Introduction AFRMs Generic Models Conditioned Models The Future
• Finite-difference RoxarTempest® Black-Oil simulator (ver. 7.0.4)
• Anisotropy causes striping in the x-lateral direction
27Introduction AFRMs Generic Models Conditioned Models The Future
Frac
tal c
apill
ary
pre
ssu
re
and
wat
er s
atu
rati
on
sPermeability map (D = 3.1 | cxy= 1 | cyz=3)
Permeability map (D = 3.5 | cxy= 1 | cyz=3)
Permeability map (D = 3.9 | cxy= 1 | cyz=3)
28Introduction AFRMs Generic Models Conditioned Models The FutureEffe
ct o
f ch
angi
ng
het
ero
gen
eity
: O
il P
rod
uct
ion
Rat
esHomogeneous reservoirs (low D) produce at a higher rate for longer than heterogeneous reservoirs (higher D)
Greater anisotropy c reduces production rate slightly at each time point
c = 1: Isotropic
c = 5: Anisotropic
29Introduction AFRMs Generic Models Conditioned Models The Future
Effe
ct o
f ch
angi
ng
het
ero
gen
eity
:W
ater
cu
t
Homogeneous reservoirs (low D) keep the water cut lower for longer than heterogeneous reservoirs (higher D).
Greater anisotropy c leads to earlier water breakthrough
c = 1: Isotropic
c = 5: Anisotropic
30Introduction AFRMs Generic Models Conditioned Models The Future
Effe
ct o
f ch
angi
ng
het
ero
gen
eit
y &
an
iso
tro
py
Water Breakthrough Time Oil Production Rate Cumulative Oil Productionx106
Fractal dimension Fractal dimension Anisotropy factor
Anisotropy factorAnisotropy factorAnisotropy factor
Wa
ter
Bre
ak
thro
ug
h D
ate
OP
R (
Ms
tb/d
ay)
Cu
m.
Pro
du
cti
on
(M
stb
)
Wa
ter
Bre
ak
thro
ug
h
Rela
tive
(%
da
ys
)
OP
R R
ela
tive
(%
)
Cu
m.
Pro
du
cti
on
(%
)
31Introduction AFRMs Generic Models Conditioned Models The Future
Effe
ct o
f an
iso
tro
py:
Pro
du
ctio
n
• Higher anisotropy• Higher anisotropic
flow• Advance water
break-through• Slightly increased
residual oil• No change in
production rates
Water saturation maps
32Introduction AFRMs Generic Models Conditioned Models The Future
• Higher heterogeneity• Higher fractal
dimension• Less spatial
correlation• Less distinct channels
of high permeability• Lower production
ratesEffe
ct o
f h
eter
oge
ne
ity:
P
rod
uct
ion
Permeability map (D= 3.1 | cxy= 1 | cyz=3)
Permeability map (D= 3.5 | cxy= 1 | cyz=3)
Permeability map (D= 3.9 | cxy= 1 | cyz=3)
Layer 16
Distinct connected channel
Distinct less connected channel
33Introduction AFRMs Generic Models Conditioned Models The Future
Wel
l pla
cem
ent
in
iso
tro
pic
res
ervo
irs Tests done for:
• 3 configurations of random well placement
• Combinations of Injectors I and/or producers P in low or high permeability zones
• 1 to 10 producers and 1 to 5 Injectors
• For conventional and tight reservoirs
• Fractal Dimensions 3.1, 3.5 and 3.9• Oil production profile, Oil recovery
factor, Water cutWell placements I and P in high permeability (k>120 mD cut-off)
54 profiles, each with 15 curves
34Introduction AFRMs Generic Models Conditioned Models The Future
Typ
ical
wel
l pla
cem
ent
resu
lts
Near-homogeneous D=3.1
Heterogeneous D=3.9
Ra
te (
Ms
tb/d
ay)
Number of production wells
Number of production wells
AO
PR
(M
stb
/day
)A
OP
R (
Mst
b/d
ay)
Ra
te (
Ms
tb/d
ay)
AO
PR
(M
stb
/da
y)
AO
PR
(M
stb
/da
y)
Near-homogeneous D=3.1
Heterogeneous D=3.9
No. of production wells
No. of production wells
35Introduction AFRMs Generic Models Conditioned Models The Future
Wel
l pla
cem
ent
con
clu
sio
ns
• Well numbers important but well placement not important for producer only scenarios (irrespective of reservoir type or fractal dimension)
• AOPR increases significantly by adding injector wells (irrespective of reservoir type or fractal dimension)
• AOPR benefits from placing both producers and injectors in high permeability zones
• Time to water break-through not consistently related to a particular well placement but is affected by heterogeneity
36Introduction AFRMs Generic Models Conditioned Models The Future
Wel
l Ori
enta
tio
nan
d A
nis
otr
op
y • AFRMs created with different heterogeneities and anisotropies
• Define simple injector-producer well pattern
• Rotate well pattern with respect to AFRM
• Simulate major reservoir production parameters at each orientation
37Introduction AFRMs Generic Models Conditioned Models The Future
Wel
l ori
enta
tio
nan
d a
nis
otr
op
yProduction rate initially higher in anisotropic direction,becoming isotropic by late production
How can AFRMs be used to represent real reservoirs?
38Introduction AFRMs Generic Models Conditioned Models The Future
Hassan Al-Ramadhan, Piroska Lorinczi
39Introduction AFRMs Generic Models Conditioned Models The Future
Co
nd
itio
nin
g to
real
res
ervo
irs The fractal
interpolation method allows data to be retained at all scales.
Fun
dam
enta
l dif
fere
nce
s
40Introduction AFRMs Generic Models Conditioned Models The Future
Krigged interpolationFractal interpolation
The fractal interpolation is not identical to the gold standard referenceBut it contains information over the whole range of frequencies, whereas the
conventional interpolation contains only long wavelength information.
41Introduction AFRMs Generic Models Conditioned Models The Future
D = 2.6
Conventional interpolation Emphasises highs and lows with information lost in the mid-range.• High frequency information lost.• Poroperms are artificially quasi-linear.
Fractal interpolation and scale conservation
Fractal interpolation Depth of information in the mid-range retained but not at the expense of the highs and lows.• Contains information at all frequencies.• Poroperms are more realistic.
Permeability HistogramPorosity HistogramPorosity Map
baPermeability Map
Grain Size
Pe
rme
ab
ilit
y
xx
PorosityP
oro
sity
Water SaturationPoroperm Cross-plot Relative Permeabilities
f ge
Poroperm (%)
Pe
rme
ab
ilit
y,
k (
mD
)
z
y xSw (-)
kr
(-)
Wa
ter
Sa
tura
tio
n
yy
Water Saturation
Cementation Exponent
Poroperm Cross-plot
Permeability Histogram
Relative Permeabilities
Grain-size HistogramPorosity HistogramPorosity Map
f ge
c d
baGrain-size Map
Poroperm (%)
Pe
rme
ab
ilit
y,
k (
mD
)
z
y xSw (-)
kr
(-)
Wa
ter
Sa
tura
tio
n
Pe
rme
ab
ilit
y
Permeability
Grain Size
Gra
in
Siz
ex
y
Permeability Map
x
x
x
yCementation Exponent
y
Ce
me
nta
tio
n E
xp
on
en
t
Cementation Exponent
Porosity
Po
rosi
ty
42Introduction AFRMs Generic Models Conditioned Models The Future
The FRACTAL INTERPOLATION mimics the reference model very well. It contains information over all wavelength scales.
The conventional KRIGGED INTERPOLATION contains only long wavelength information
Consequently, production data is simulated from a fractal model of the reservoir
Frac
tal I
nte
rpo
lati
on ON
Reference Standard Fractal Interpolation Krigged
Porosity Porosity Porosity
43Introduction AFRMs Generic Models Conditioned Models The Future
Frac
tal i
nte
rpo
lati
on
ve
rsu
s kr
iggi
ng
44Introduction AFRMs Generic Models Conditioned Models The Future
Homogeneous Reservoir (D=3.0) – Both krigged and fractal interpolations match the reference well.
Heterogeneous Reservoirs (D=3.5 and 3.9) – Kriggedinterpolations badly underestimate production rates, while fractal interpolation matches the gold standard reference well.Fr
acta
l in
terp
ola
tio
n
vers
us
krig
gin
g
…Putting it all together.
45Introduction AFRMs Generic Models Conditioned Models The Future
The
AFR
M a
dva
nta
ge
46
AFRMs can depict and control heterogeneity
AFRMs can depict and control xy, yz and zx anisotropy
AFRM accuracy can be verified
AFRM allows generic sensitivity tests for heterogeneity, anisotropy, well placement and orientation
AFRM is more accurate than conventional models in simulations
AFRM contains information at all scales larger than cell size
AFRMs can be fully reservoir-conditioned
Introduction AFRMs Generic Models Conditioned Models The Future
The
Futu
re
47Introduction AFRMs Generic Models Conditioned Models The Future
To do:
Create methods for deriving fractal dimensions and anisotropies from seismic attribute data
Synthesise all methodologies and code into a professional UOI
Run a number of case study scenarios in clastic, carbonate and unconventional reservoirs
48
AFRMs are a powerful new approach to creating realistic 3D geological models of
reservoirs for simulation…
…giving insight into how heterogeneity and anisotropy affect reservoir production at all scales and capable of being conditioned to
represent real reservoirs.
Introduction AFRMs Generic Models Conditioned Models The Future