The SPE Foundation through member donations and a contribution from Offshore Europe

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1 Primary funding is provided by The SPE Foundation through member donations and a contribution from Offshore Europe The Society is grateful to those companies that allow their professionals to serve as lecturers Additional support provided by AIME Society of Petroleum Engineers Distinguished Lecturer Program

2 Advances and Challenges in Dynamic Characterization of Naturally Fractured Reservoirs Rodolfo G. Camacho-Velázquez Society of Petroleum Engineers Distinguished Lecturer Program 2

3 OUTLINE 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 3

4 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 Acuña & Yortsos, SPEFE

5 No se puede mostrar la imagen en este momento. Motivation Naturally Fractured Reservoirs Fractal Fractured-Vuggy (3φ-2k) Dual-Porosity More general continuous models 5 5

6 Background on fractals Fractures are on a wide range of scales. There are zones with clusters of fractures and others where fractures are scarce. dmf=1.78 dmf= 1.65 dmf= 1.47 ; N= number of parts from original figure, L= scale of measurement. Acuña & Yortsos, SPEFE

7 Background on fractals 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. 7

8 No se puede mostrar la imagen en este momento. Background on NFVRs 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. 8 8

9 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

10 Background on NFVRs 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. Casar & Suro, SPE 58998, Stochastic Imaging of Vuggy Formations. 10

11 No se puede mostrar la imagen en este momento. Dimensionless Wellbore Pressure, P WD Dimen sionless = constant W el lbor e Pressu re, P wd 1 (p i -p wf ) Results with Fractal Modeling Transient Behavior : Fractal Naturally Fractured Reservoir With Matrix Participation Fractal Naturally Fractured Reservoir With Matrix Participation 4 s (skin)=0, d mf (fractal S=0, CD=0 s = dimension)=1.7, 0,, C w=0 D =.05 0, d s= mf = 0.0 l=0.0 ω = , ω 1 q (storativity =0 λ =.8 10 ratio)=0.05, Conductivity λ (interporosity flow parameter)= Index Long Time q=0.8 θ = 0.8 2ν 1 q=0.6 θ = 0.6 Fractal Num er Solution ical S o lut( ion 2 + θ ) Long Time ν q=0.4 θ = 0.4 pwd ( td ) = t Numerical Solution D + s ν q=0.2 θ= 0.2 νγ( 1 ν )( 1 ω ) Long Times Times Ap prox. Approx. Sh Short Times Times Ap prox. Approx. 2 d + θ ν = mf θ + 2 Short Time Short Time Warr en & R oot So lution Warren & Root Solution Warren & Root solution (d mf =2, θ=0) 1 1.E E E E E E E E E+07 7 Flamenco & Camacho,SPEREE, Feb, 2003 D imensionless Time, td Dimensionless Time, Tt D = constant 2 * t 11 11

12 Results with fractal modeling Slope = ʋ = 0.326, difference between coordinates to the origin is , wich yields ʋ = ~ slope. This is another indication of fractal behavior. 12

13 Results with fractal modeling 1-ϕ Fractured Reservoirs, Decline Curves, Bounded 1.E+00 =c 3 *q 1.E-01 Homogeneous Dimensionless q Rate, wd q D 1.E-02 1.E-03 1.E-04 1.E-05 Fractals,r ed (drainage radius)= 500 OP, r ed =5x10 2 OP,r ed =2x10 3 MGN, rγ=0.93, r ed =5x10 2 ed =500 MGN, rγ=0.93, r ed =2x10 3 ed =2X10 3 LTA-OP long-time (Eq. approximation 20) with OP LTA-MGN long-time approximation (Eq. 21) with MGN Euclidean, r ed =5x10 2 a1 ( b b ) t D Euclidean, r ed =2x10 q D ( t D ) e b 2 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 = constant 2 * t Dimensionless Time, t D OP-- O Shaughnessy & Procaccia Physical Review; MGN--Metzler et. al Physica Camacho-V., R.G., et al., SPE REE, June 2008 t D 13

14 Results with fractal modeling 2- ϕ, Influence of r ed, closed reservoir =c 3 *q Dimensionless q wd Rate, q D 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 Fractals r ed =5x10 2 r ed =1x10 3 r ed =2x10 3 q r ed =4x10 3 D STA (Eq. C9) LTA (Eq. C24) Euclidian (Warren and Root) ( t long-time approximation D ) g ω e h ( h h ) d mf =1.4, θ=0.2, ω=0.15, λ=1x10-5, σ=0.1 2-ϕ, Warren & Root 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 t D 1 2 Dimensionless t D Time, t D = constant 2 * t 14

15 Results with fractal modeling Bottomhole wellbore p wf (psi) pressure, pwf (psi) Pressure and production histories E E E E E E E E E E E+05 t (hrs) Production time, t (hrs) Fig. 14. Pressure and production histories, field case. Camacho et. al.: Decline Curve Analysis of Fractured Reservoirs with Fractal Geometry, SPEREE, q o (BPD) Oil rate, qo (STB/D) 15

16 Rate Normalized by p Oil Rate / pressure drop, q/ p (BPD/psi) qo/ Δp (STB/D)/psi 1.E+02 1.E+01 1.E+00 Results with fractal modeling 1.E+03 θ = 0 r e = 351 ft k = md Pressure increment, Δp & Pressure Derivative, p, p' (psi) Δp y = 185.8x E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 y = e -2E-05x 1.E-01 1.E E E E E E E E E E E E+05 t (hrs) Production time, t (hrs) Fig. 15. Rate normalized by the pressure drop versus time, field case. 1.E+02 1.E+01 t (hrs.) Shut-in time, Δt (hrs) Fig. 13. Pressure build-up test, field case. 16

17 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

18 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)

19 Results with 3 ϕ 2 k modeling Dimensionless Pressure, p D = constant*δp Dimensionless Pressure Derivative, p D Transient Behavior, Connected & Unconnected Vugs 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 Connected vugs, ω v =1e-03, ω f =1e-03, λ vf =1e-05, λ mv =1e-08 λ mf =1e-07, κ=0.1 λ mf =0.001, κ=0.1 λ mf =1e-07, κ=0.5 λ mf =0.001, κ=0.5 λ mf =0.001, κ=1.0 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 Dimensionless Time, t D = constant 2 * t

20 Results with 3 ϕ 2 k modeling Dimensionless Flow Rate, q D = constant 3 *q ω f =1e-03, ω v =1e-01, λ mf =1e-03, λ vf =1e-05, λ mv =1e-06 Connected Vugs, κ= 0.5, r ed = 2000 Unconnected Vugs, κ= 1.0, r ed = 2000 Connected Vugs, κ= 0.5, r ed = 500 Unconnected Vugs, κ= 1.0, r ed = 500 Warren & Root, r ed = 500 Warren & Root, r ed = 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-04 1.E-03 1.E-02 1.E-01 1.E+00Decline Curves for Connected & Unconnected Vugs Dimensionless Time, t D = constant 2 * t 20

21 Results with 3 ϕ 2 k model Breccioid zone showing connected vugular porosity. There is good vertical communication through the vugs. At m depth there is a cavern with a vertical length of m. Camacho-V., R., et. al., SPE ,

22 Results with 3 ϕ 2 k modeling Well 1-KS, multiple fittings, total penetration Well 1-KS Pressure increment, Δp & pressure derivative, Δp, psi Pressure Parameter Fit 1 Fit 2 Fit 3 Fit 1 Fit 2 Fit 3 Pressure [kg/cm²] φ fit E Time [hr] Shut-in time, Δt (hrs) Camacho-V., R., et. al.: SPE171078,

23 Δpws & Pressure Derivative, Δp Results with 3 ϕ 2 k modeling Fixing ωv & ωf from well logs, Total Penetration Well 1-KM Shut-in time, Δt (hrs) pressure Δpws & Pressure Derivative, Δp Well 1-KS Shut-in time, Δt (hrs) pressure ω v ω f κ s λ mf λ mv λ vf k T 1.03E E E E+04 ω v ω f κ s λ mf λ mv λ vf k T 3.61E E E E+04 23

24 Pressure increment, Δp & Pressure Derivative, Δp, psi Results with 3 ϕ 2 k modeling Tekel 1-KS, múltiples ajustes con modelo de 3 ϕ 2 k Penetración parcial Well 1-KS, Partial Penetration Pressure data Fit 1 Fit 2 Shut-in time, Δt (hrs) Parameter Fit 1 Fit 2 24

25 Pressure increment, Δp & Pressure Derivative, Δp, psi Results with 3 ϕ 2 k modeling Tekel 1-KM, múltiples ajustes con modelo de 3 ϕ 2 k Penetración parcial Well 1-KM, Partial Penetration Pressure data Fit 1 Fit 2 Shut-in time, Δt (hrs) Parameter Fit 1 Fit 2 25

26 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 = ϕ 2 k, total penetration - KS: ωv = 0.98, ωf = 8X10-4, κr = KM: ωv = 0.99, ωf = 1X10-4, κr = ϕ 2 k, partial penetration - KS: ωv = 0.7, ωf = 0.023, κr = 0.8, κz = KM: ωv = 0.51, ωf = 0.12, κr = 0.9, κz = 0.9 Ausbrooks, R. et al, SPE

27 Results with 3 ϕ 2 k modeling 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. 27

28 Conclusions about proposed models 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 28

29 Reservoir Complexity Fractures at different scales, not all interconnected, non-uniform distribution, presence of vugs, heterogeneous & anisotropic Current and Future Vision Advances in characterization Static Characterization Fractal NFRs Dynamic Characterization 3ϕ-2k, NFVRs Advances in simulation 2 φ It is important to consider other alternatives that best describe heterogeneities, such as the 3ϕ 2k models for NFVRs and fractal models 29

30 Main message There are two new models that provide more reservoir information with the same input data Advances in characterization Advances in simulation Fractal NFRs Reservoir complexity Static characterization Dynamic characterization 2 φ 3ϕ-2k, NFVRs 30

31 Thank you Are there any questions? Advances in characterization Advances in simulation Fractal NFRs Reservoir complexity Static characterization Dynamic characterization 2 φ 3ϕ-2k, NFVRs 31

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