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2

Society of Petroleum Engineers Distinguished Lecturer Program www.spe.org/dl

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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