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2
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Advances and Challenges in Dynamic Characterization of
Naturally Fractured Reservoirs Rodolfo G. Camacho-Velázquez
OUTLINE
3
Objectives
Motivation
Background on fractals and naturally
fractured vuggy reservoirs (NFVRs)
Results with fractal and 3ϕ–2k models
Conclusions about proposed models
Current and Future Vision
Objectives • Advances in characterization of Naturally
Fractured Vuggy Reservoirs (NFVRs, 3ϕ–2k) and NFRs with fractures at multiple scales with non-uniform spatial distribution, poor connectivity (fractal).
• Reservoir characterization challenges and current- future vision.
4
4 Acuña & Yortsos, SPEFE 1995
No se puede mostrar la imagen en este momento.
5
Motivation
Naturally Fractured Reservoirs
Dual-Porosity
Fractal Fractured-Vuggy (3φ-2k)
5
More general continuous models
Background on fractals Fractures are on a wide range of scales. There are zones with clusters of fractures and others where fractures are scarce.
6
dmf=1.78 dmf= 1.65 dmf= 1.47
Acuña & Yortsos, SPEFE 1995 ; N= number of parts from original figure, L= scale of measurement.
•Statistical method to describe structure of a fractured medium and identified by a power law fractal dimension, dmf.
•Fracture networks characterized by: length, orientation, density, aperture, and connectivity. Power laws to quantify these properties.
•Conventional uniform fracture distribution, fractures at a single scale, and good fracture connectivity. Fractals fractures at different scales, poor connectivity and non-uniform distribution careful location of wells.
Background on fractals
7
No se puede mostrar la imagen en este momento.
8
Some of the most prolific fields produce from Naturally Fractured Vuggy Reservoirs (NFVRs).
The effect of vugs on permeability depends on their connectivity.
Fluids are stored in the matrix, fractures and vugs. Core perm. and φ in vuggy zones are likely to be pessimistic.
Background on NFVRs
8
Background on NFVR
• Vugs affect flow & storage. Fractures network generally contributes < 1% of porous volume. Vuggy ϕ can be high.
• Vug network normally has good vertical permeability.
• The degree of fracturing and the presence of vugs are greater at the top of the anticline.
• Vug size, orientation, connectivity, and distribution are caused by deposit environment and diagenetic processes they are difficult to characterize.
9
Slides of core segments with halos around vugs. Increasing ϕ and k may be due to directly connected vugs and vugs connected through their halos. Vuggy kv may be > fracture kf.
Background on NFVRs
Casar & Suro, SPE 58998, Stochastic Imaging of Vuggy Formations.
10
No se puede mostrar la imagen en este momento.
11
Results with Fractal Modeling
F ractal Naturally Fractured Reservoir With Matrix ParticipationS=0 , CD=0 , w=0 .05 s= 0.0 l=0.0 00 1 q=0 .8
1
1 0
10 0
1 00 0
1.E-0 1 1.E+0 0 1.E+0 1 1.E+0 2 1.E+0 3 1.E+0 4 1.E+0 5 1.E+0 6 1.E+0 7Dimensionless Time, tD
Dim
ensi
onle
ss W
ellb
ore
Pres
sure
, PwD q=0.8
q=0.6
q=0.4q=0.2
Long Times Ap prox.
Sh ort Times Ap prox.
Warr en & R oot So lution
Short T ime
Long T imeNumerical Solut ion
Fractal Naturally Fractured Reservoir With Matrix Participation
Dim
ensi
onle
ssW
ellb
ore
Pre
ssur
e, P
WD
Dimensionless Time, TD
Warren & Root Solution
Short Time
Long Time
410,05.07.1,0,0 −===== λωmfD dCs
θ = 0.8θ = 0.6θ = 0.4θ= 0.2Long Times Approx.Short Times Approx.
Numerical Solution
1.E-01 1.E+071.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+061.E+001
10
100
1000
F ractal Naturally Fractured Reservoir With Matrix ParticipationS=0 , CD=0 , w=0 .05 s= 0.0 l=0.0 00 1 q=0 .8
1
1 0
10 0
1 00 0
1.E-0 1 1.E+0 0 1.E+0 1 1.E+0 2 1.E+0 3 1.E+0 4 1.E+0 5 1.E+0 6 1.E+0 7Dimensionless Time, tD
Dim
ensi
onle
ss W
ellb
ore
Pres
sure
, PwD q=0.8
q=0.6
q=0.4q=0.2
Long Times Ap prox.
Sh ort Times Ap prox.
Warr en & R oot So lution
Short T ime
Long T imeNumerical Solut ion
Fractal Naturally Fractured Reservoir With Matrix Participation
Dim
ensi
onle
ssW
ellb
ore
Pre
ssur
e, P
WD
Dimensionless Time, TD
Warren & Root Solution
Short Time
Long Time
410,05.07.1,0,0 −===== λωmfD dCs
θ = 0.8θ = 0.6θ = 0.4θ= 0.2Long Times Approx.Short Times Approx.
Numerical Solution
1.E-01 1.E+071.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+061.E+001
10
100
1000
Fractal Solution
Transient Behavior :
11
( )( )( )
sttp DDwD +−−Γ
+=
−ν
ν
ν
ωννθ
112)(
12
22
++−
=θ
θν mfd
Warren & Root solution (dmf=2, θ=0)
Flamenco & Camacho,SPEREE, Feb, 2003
s (skin)=0, dmf (fractal dimension)=1.7, ω (storativity ratio)=0.05, λ (interporosity flow parameter)=0.0001 Conductivity
Index
t = constant2* t
= c
onst
ant
1 (p
i-pw
f)
Results with fractal modeling Slope = ʋ = 0.326, difference between coordinates to the origin is 0.4786, wich yields ʋ = 0.3322 ~ slope. This is another indication of fractal behavior.
12
Results with fractal modeling 1-ϕ Fractured Reservoirs, Decline Curves, Bounded
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
tD
qw
D
OP, reD=5x102 OP ,reD=2x103 MGN, γ=0.93, reD=5x102 MGN, γ=0.93, reD=2x103 LTA-OP (Eq. 20) LTA-MGN (Eq. 21) Euclidean, reD=5x102 Euclidean, reD=2x103
( ) DtbbDD e
batq 21
2
1)( −≈
13
Fractals
Homogeneous
Dimensionless Time, tD
D
imen
sion
less
Rat
e, q
D
OP-- O’ Shaughnessy & Procaccia. 1985. Physical Review; MGN--Metzler et. al. 1994. Physica Camacho-V., R.G., et al., SPE REE, June 2008
long-time approximation with OP long-time approximation with MGN
,reD (drainage radius)= 500
MGN, reD=500 MGN, reD=2X103
=c 3
*q
= constant2* t
2- ϕ, Influence of reD, closed reservoir
Results with fractal modeling
14
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
tD
qw
D
reD=5x102 reD=1x103 reD=2x103 reD=4x103 STA (Eq. C9) LTA (Eq. C24) Euclidian (Warren and Root)
dmf=1.4, θ=0.2, ω=0.15, λ=1x10-5, σ=0.1
2-ϕ, Warren & Root
( )21
2
1 1)( hhtDD
Deh
gtq −−≈
ω
D
imen
sion
less
Rat
e, q
D
Dimensionless Time, tD
Fractals
long-time approximation
=c 3
*q
= constant2* t
Results with fractal modeling
15
Fig. 14. Pressure and production histories, field case.
1500
2000
2500
3000
3500
4000
4500
5000
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 1.4E+05 1.6E+05 1.8E+05 2.0E+05
t (hrs)
p wf (
psi)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
q o (B
PD)
Fig. 14. Pressure and production histories, field case.
1500
2000
2500
3000
3500
4000
4500
5000
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 1.4E+05 1.6E+05 1.8E+05 2.0E+05
t (hrs)
p wf (
psi)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
q o (B
PD)
B
otto
mho
le w
ellb
ore
pres
sure
, pw
f (ps
i)
O
il ra
te, q
o (S
TB/D
)
Production time, t (hrs) Camacho et. al.: “Decline Curve Analysis of Fractured Reservoirs with Fractal Geometry,” SPEREE, 2008
Pressure and production histories
Results with fractal modeling
Rate Normalized by ∆p
y = 2.6149e-2E-05x
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 1.4E+05 1.6E+05 1.8E+05 2.0E+05
t (hrs)
q/∆p
(BPD
/psi
)
Fig. 15. Rate normalized by the pressure drop versus time, field case.
y = 2.6149e-2E-05x
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 1.4E+05 1.6E+05 1.8E+05 2.0E+05
t (hrs)
q/∆p
(BPD
/psi
)
Fig. 15. Rate normalized by the pressure drop versus time, field case.16
O
il R
ate
/ pre
ssur
e dr
op, q
o/ Δ
p (S
TB/D
)/psi
Production time, t (hrs)
y = 185.8x0.5926
1.E+00
1.E+01
1.E+02
1.E+03
1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
∆t (hrs.)
∆p,
∆p'
(psi
)
Fig. 13. Pressure build-up test, field case.
y = 185.8x0.5926
1.E+00
1.E+01
1.E+02
1.E+03
1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
∆t (hrs.)
∆p,
∆p'
(psi
)
Fig. 13. Pressure build-up test, field case.Shut-in time, Δt (hrs)
Pr
essu
re in
crem
ent,
Δp
&
Pres
sure
Der
ivat
ive,
Δp´
’
θ = 0 re= 351 ft
k = 0.068 md
Results with fractal modeling
1-φ and 2-φ, show power-law transient behavior fractal dimension (fracture density).
PSS, both 1-φ and 2-φ, show a Cartesian straight line for pressure response porous volume evaluation.
Rate during boundary-dominated flow presents typical semilog behavior porous volume eval.
Transient and boundary-dominated flow data should be used to fully characterize fractal NFRs, obtaining better estimates of permeability and drainage area.
17
Results with 3 ϕ – 2 k modeling
ω (storativity ratio), λ (interporosity flow parameter), c (compressibility), ϕ (porosity), κ (permeability ratio), k (permeability), l (flow direction), σ (interporosity-flow
shape factor), rw (wellbore radius)
Results with 3 ϕ – 2 k modeling Transient Behavior, Connected & Unconnected Vugs
1.E
-03
1.E
-02
1.E
-01
1.E
+00
1.E
+01
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08Dimensionless Time, tD
Connected vugs, ωv =1e-03, ωf =1e-03, λvf =1e-05, λmv=1e-08
Dim
ensi
onle
ss P
ress
ure,
pD
= c
onst
ant*
Δp
D
imen
sion
less
Pre
ssur
e D
eriv
ativ
e, p
D’
λmf =1e-07, κ=0.1
λmf =0.001, κ=0.1
λmf =1e-07, κ=0.5
λmf =0.001, κ=0.5
λmf =0.001, κ=1.0
19 = constant2* t
Results with 3 ϕ – 2 k modeling Decline Curves for Connected & Unconnected Vugs
1.E
-04
1.E
-03
1.E
-02
1.E
-01
1.E
+00
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08
ωf =1e-03, ωv =1e-01, λmf =1e-03, λvf =1e-05, λmv =1e-06
Connected Vugs, κ= 0.5, reD= 2000
Unconnected Vugs, κ= 1.0, reD= 2000
Connected Vugs, κ= 0.5, reD= 500
Unconnected Vugs, κ= 1.0, reD= 500
Warren & Root, reD= 500
Warren & Root, reD= 2000
Dimensionless Time, tD
Dim
ensi
onle
ss F
low
Rat
e, q
D =
con
stan
t 3*q
20 = constant2* t
At 3280 – 3281 m depth there is a cavern with a vertical length of 1 - 1.5 m.
Breccioid zone showing connected vugular porosity. There is good vertical communication through the vugs.
Results with 3 ϕ – 2 k model
21
Camacho-V., R., et. al., SPE 171078, 2014
1E-3 0.01 0.1 1 10Time [hr]
0.01
0.1
1
Pre
ssur
e [k
g/cm
²]
Well 1-KS Pressure Parameter Fit 1 Fit 2 Fit 3
2-φ fit
22
Camacho-V., R., et. al.: SPE171078, 2014
Fit 1 Fit 2 Fit 3
Pr
essu
re in
crem
ent,
Δp
& p
ress
ure
deriv
ativ
e, Δ
p´, p
si’
Shut-in time, Δt (hrs)
Results with 3 ϕ – 2 k modeling Well 1-KS, multiple fittings, total penetration
Results with 3 ϕ – 2 k modeling Fixing ωv & ωf from well logs, Total Penetration
23
Well 1-KM Well 1-KS pressure pressure
Δ
pws
& P
ress
ure
Der
ivat
ive,
Δp´
’
Δ
pws
& P
ress
ure
Der
ivat
ive,
Δp´
’ Shut-in time, Δt (hrs) Shut-in time, Δt (hrs)
ωv ωf κ s 0.63 0.013 1.0 7.91
λmf λmv λvf kT
1.03E-07 1.76E-07 1.00E-09 2.11E+04
ωv ωf κ s 0.64 0.041 1.0 7.92
λmf λmv λvf kT
3.61E-08 1.00E-09 1.44E-08 3.37E+04
Tekel 1-KS, múltiples ajustes con modelo de 3 ϕ – 2 k Penetración parcial
Pressure data Fit 1 Fit 2
Parameter Fit 1 Fit 2
24
Pr
essu
re in
crem
ent,
Δp
& P
ress
ure
Der
ivat
ive,
Δp´
, psi
’
Shut-in time, Δt (hrs)
Results with 3 ϕ – 2 k modeling Well 1-KS, Partial Penetration
Tekel 1-KM, múltiples ajustes con modelo de 3 ϕ – 2 k Penetración parcial
Results with 3 ϕ – 2 k modeling Well 1-KM, Partial Penetration
Parameter Fit 1 Fit 2
Pressure data Fit 1 Fit 2
25
Shut-in time, Δt (hrs)
Pr
essu
re in
crem
ent,
Δp
& P
ress
ure
Der
ivat
ive,
Δp´
, psi
’
Results with 3 ϕ – 2 k modeling Overview of dynamic characterization– Well 1
2 ϕ – 1 k, total penetration (Warren-Root) KS: ω= 0.62, KM: ω= 0.40 Values from well logs: - KS: ωv= 0.64, ωf= 0.04 KM: ωv = 0.63, ωf = 0.01
3 ϕ – 2 k, total penetration - KS: ωv = 0.98, ωf = 8X10-4, κr = 0.96 - KM: ωv = 0.99, ωf = 1X10-4, κr = 0.75
3 ϕ – 2 k, partial penetration - KS: ωv = 0.7, ωf = 0.023, κr = 0.8, κz = 0.001 - KM: ωv = 0.51, ωf = 0.12, κr = 0.9, κz = 0.9
26
Ausbrooks, R. et al, SPE 56506
• 3 ϕ - 2 k better match of pressure tests than 2 ϕ model, obtaining more information about 3 media (matrix- fractures - vugs).
• (ωv + ωf) ≠ ω (2 ϕ, Warren-Root) use of traditional 2 ϕ simulators for NFVRs is not justified.
• Partial penetration effects information about vertical communication of vugs and fractures.
• Confirmed that vugs’ vertical communication can be significant, which is relevant for reservoirs with an active aquifer.
Results with 3 ϕ – 2 k modeling
27
Fractal & 3 ϕ - 2 k models better characterization key driver for maximizing production and recovery. Proposed models explanations for
production performance that can not be obtained with traditional 2 ϕ simulators. Additional information from these models useful to: prevent / anticipate mud losses during drilling evaluate vertical communication for NFVRs evaluate productive potential of NFRs anticipate efficiency of secondary and EOR determine better distribution of wells
Conclusions about proposed models
28
Current and Future Vision
It is important to consider other alternatives that best describe heterogeneities, such as the 3ϕ – 2k models for NFVRs and fractal models
29
Reservoir Complexity
Fractures at different scales, not all interconnected, non-uniform distribution, presence of vugs, heterogeneous & anisotropic
Static Characterization
Dynamic Characterization 2 φ
Advances in characterization
Advances in simulation
Fractal NFRs
3ϕ-2k, NFVRs
Main message There are two new models that
provide more reservoir information with the same input data
30
Reservoir complexity
Static characterization
Dynamic characterization 2 φ
Advances in characterization
Advances in simulation
Fractal NFRs
3ϕ-2k, NFVRs
Reservoir complexity
Static characterization
Dynamic characterization 2 φ
Advances in characterization
Advances in simulation
Thank you Are there any questions?
31
Fractal NFRs
3ϕ-2k, NFVRs
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