Radial- Basis Function Network Applied in Mineral Composition Analysis Shaochang Wo & Peigui Yin January 13, 2010, Denver
Mineral composition in the Minnelusa Formation can be calculated from the sonic, neutron, and density log suite Theoretically!! = 1 1 1 1 1 N A D Q f A D Q f A D Q f A D Q f t H H H H t t t t φ ρ φ φ φ φ ρ ρ ρ ρ Δt : sonic travel time (μs/ft) ρ: density (g/cm 3 ) H: hydrogen index (dimensionless) φ: fractional volume φ N : neutron porosity (%) SUBSCRIPTS f: fluid-filled pore space Q: quartz D: dolomite A: anhydrite (James W. Schmoker and Christopher J. Schenk, 1988)
M-N Plot for Mineral Identification M = 0.01 ( t f t b ) ρ ρ b f N φn = 1 ρ ρ b f Δt f : sonic travel time in pore fluid Δt b : bulk sonic travel time ρ f : fluid density ρ b : bulk density φ N : neutron porosity (limestone units, fractional)
0.95 0.9 0.85 0.8 Dolomite Quartz M 0.75 0.7 Anhydrite 0.65 0.6 0.55 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 N
100 90 Estimated Quartz in Matrix from MN Plot, % 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Observed Quartz in Thin Section, %
100 90 Estimated Dolomite in Matrix from MN Plot, % 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Observed Dolomite in Thin Section, %
100 90 Estimated Anhydrite in Matrix from MN Plot, % 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Observed Anhydrite in Thin Section, %
Radial-Basis Function Network Input Hidden Output x 1 G 1 Fixed input = 1 w x 1 w0 2 (bias) G j w j Σ f x p G n w n
Parameters in A Generalized RBF network f ( x) = M i= 1 w G( x t i i ) w i : weights t i : centers : the weighted norm
Regularization Theory - Supervised Learning as an Ill-Posed Hypersurface (Tikhonov, 1963; Poggio and Girosi, 1989) N = ( ( )) 2 + λ i i i= 1 H[ f ] y f x Pf 2 f: RBF network λ: regularization parameter P: stabilizer
Hybrid Learning Methods: A Combination of Self-Organized and Supervised Learning Self-organized selection of centers standard k-means clustering algorithm (Lloyd) moving center algorithm (Moody) Learning the weighted norm (widths) normalized inputs heuristic and supervised learning Supervised learning for weights least-mean-square (LMS) algorithm
SPE 59553 A New Technique to Determine Porosity and Deep Resistivity from Old Gamma Ray and Neutron Count Logs S. Wo, SPE, W. W. Weiss, SPE, R. S. Balch, SPE, New Mexico Petroleum Recovery Research Center, L. R. Scott, SPE, Lynx Petroleum Consultants, and R. P. Kendall, SPE, Los Alamos National Laboratory
Clustering View of the Cross-Plot Porosity 1 Normalized Neutron Count Rate 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Normalized Phi: 1~0.7 Normalized Phi: 0.7~0.3 Normalized Phi: 0.3~0 0 0.2 0.4 0.6 0.8 1 Normalized Gamma Ray
3550 Porosity, % 0 10 20 Porosity, % 0 10 20 Porosity, % 0 10 20 Training 3600 Testing 3650 Depth, ft 3700 3750 3800 3850
Cases with the middle interval for exclusion testing Correlation Coefficient (CC) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Training Testing 1 10 100 1000 Number of Centers
Cases with the bottom interval for exclusion testing Correlation Coefficient (CC) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Training Testing 1 10 100 1000 Number of Centers
Key Features of This Approach Point-count data from thin sections are used for the training of RBF networks Lithological facies are identified as clusters (the locations of RBF centers) on M-N plot Individual mineral volume is estimated by a weighted interpolation of RBFs taking M & N as inputs The method is applicable to formations with more than three minerals and can include Pe as the 3 rd input
Simulation of Fractured Tensleep Reservoirs Shaochang Wo Michael Presho January 13, 2010, Denver
The Tensleep Reservoirs in Wyoming Most reservoirs are naturally fractured Local compartments by Mineral-filled fractures Often with edge (or bottom) water driven Oil-wet or mixed-wet sandstone rocks Decades of production history 2008 total produced oil: ~7 million barrels 2008 average water cut: 98.8%
Gouge-filled Fractures in Tensleep Outcrops (from Peigui Yin)
Single-Permeability Model by Averaging Fracture Spacing (D) K cm Fracture Aperture (e) Width of Cemented Band (w)
K K K cm fm f = = K K m m 3 e = 12D ( w e) + + K K f m K c K D c ( D w) D : fracture spacing e : fracture aperture w : K K K K K m f c cm width of cemented band : matrix permeability : fracture permeability : permeability of cemented band fm : effective permeability parallel to fracture orientation : effective permeability normal to fracture orintation
Effect of Fracture Spacing on Permeability Ratio (Kc = 5 md, e = 0.1 mm, w =0.01 ft) 1 Km = 250 md Permeability Ratio, Kcm/Kfm 0.8 0.6 0.4 100 md 30 md 5 md 0.2 0 0.1 1 10 100 1000 Fracture Spacing, ft
Line Pattern - Parallel Line Pattern 90 Degree Fracture Orientation Fracture Orientation Fracture Orientation Fracture Orientation 9-Spot Pattern 5-Spot Pattern
(K m = 30 md, K f = 110 md, K c = 5 md, D = 20 ft, e = 0.2 mm, w = 0.5 ft) 90-Degree 9-spot Parallel
A single porosity/permeability system is often not capable to model fractured reservoirs when Permeability contrast ( true K f to K m ) > 100:1 Fracture spacing > 30 ft
Dual Porosity/Permeability Model of Single Phase Flow t p C p k f tf f f f = ϕ τ µ ) ( t p C p k m tm m m m = + ϕ τ µ ) ( ( m ) f m p p k = µ σ τ + + = 2 2 2 3 1/ ) ( z mz y my x mx mz my mx L k L k L k k k k S σ Fracture: Matrix: Transfer Function:
Simulation of Tracer Injection in Fractured Reservoir As part of Michael Presho s Ph.D. research Developing a numerical method of dual-continuum model to simulate tracer flow in fractured reservoirs, where the pressures in matrix and fracture systems were solved by finite element method combined with a Gauss-Seidel iteration Simulation results of tracer plume propagation on finegrid single-porosity models are used as benchmark Providing a better understanding of the effect of shape factor, fracture spacing, and grid size on the pressure distribution and fluid flow in a dual-continuum model
Transfer Function for Multiphase Flow (i.e. Oil, Water, & Gas Phases) Fluid Expansion Gravity Drainage Imbibition Relative Permeability Molecular Diffusion Transfer function of oil-water 2-phase flow with gravity effect τ w kmkrw σ z = σ {( p f pm) + ( ) γ w( hwf hwm)} µ σ w (Kazemi and Gilman 1993)
East Salt Creek (ESC) Tensleep Top structure top used in the simulation model
ESC: Well 14-10
ESC: Well 11-10 C Sand D Sand
ESC Tensleep: Oil Producing Zones Average Average Average Gross Net Average Average Original Average Productive Thickness Thickness Porosity Permeability Sw Sor Area ft ft % md % % acre A Sand (Zone 1) 44 10.6 11.2 51.8 27.5 19.9 927.4 B Dolomite 10 B Sand (Zone 2) 52 11.2 11.7 17.8 31.5 24.3 752.3 C Dolomite (Zone 3) 32 C Sand (Zone 4) 30 7.1 9.5 38 28.5 22.8 424.2 D Dolomite 10 D Sand (Zone 5) 30 7.7 11.4 81.8 25.7 20.1 234.5
ESC Tensleep: Well Perforation (Before 12/31/1977) Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well A-8 A-9 A-10 A-11 A-12 A-13 A-14 A-15 C-1 C-2 C-3 D-1 Fed. 1 Gov. 1 Gov. 2 A Sand (Zone 1) Δ Δ Δ Δ B Dolomite B Sand (Zone 2) Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ C Dolomite (Zone 3) Δ C Sand (Zone 4) Δ Δ D Dolomite D Sand (Zone 5) Δ
ESC Tensleep Model: matrix permeability by layers
ESC Tensleep Model: a simulated fracture permeability realization
ESC Tensleep Model: initial oil saturation
Well A-8 produced from D Sand: initial oil saturation
Well A-8 produced from D Sand: matrix oil saturation after 7-year production
Well A-8 produced from D Sand: fracture oil saturation after 7-year production
Ongoing Simulation Study Forward simulations with a range of parameter combinations in fracture model setting σ, K f (K fx & K fy ), K rf, P cf, D f Using ESC production/injection well patterns to configure well locations on the structure Constant BHFP for production well control Actual water rate for water injector control Attaching different tracers to the injected water and the influxed water from aquifer Looking for more effective injection pattern
Fly Ash Project Updates Shaochang Wo, Peigui Yin Xina Xie, Matthew Johnson Norman Morrow January 13, 2010, Denver
Potential Applications of Fly Ash in EOR For Improving Water Shutoff Treatment Fly ash + polymer-gel For Improving Water Injection Profile Fly ash + polymer Fly ash + polymer + bentonite + coagulant For Use in Combination with CO2 flooding Surfactant flooding Steam flooding
Project Status Collected ten fly ash samples, including samples from all major Wyoming power plants Purchased a GilSonic Ultraseiver for sieve analysis Completed chemical composition analysis on collected fly ash samples and selected Jim Bridger fly ash for lab and field tests Selected a field test site in the Wall Creek-2 formation at ROMTC Designed and constructed a pressure apparatus to measure the compressive strength of fly ash under reservoir conditions
Project Status (continued) Viscosities of various polymer solutions have been measured under room and reservoir temperatures An optimal polymer solution has been identified to suspend JB fly ash Ongoing works including lab core flooding tests to examine fly ash transport and straining in fractures and the design of fly ash injection for the pilot test site Samples of flooded cores will be scanned by Micro- CT at Australia National University to provide 3-D view of fly ash straining (2.5μm resolution)
No Straining Observed in Large Fracture Opening (Wall Creek-2 Core 2797) 0.6 Wallcreek 2797(Kg = 10.6 md) Wf = 200 to 300 microns fly ash size = 40 to 60 microns (5 wt%) Injection pressure, psi 0.4 0.2 q = 4.0 ft/d q = 1.0 ft/d 0 0 10 20 30 40 50 60 70 Injection time, min
Straining Occurred in Smaller Fracture Opening 8 6 (Berea Sandstone Core F1) Berea F1 (Kg = 88 md) Wf = 100 to 200 micron fly ash size = 40 to 60 micron (20 wt%) q = 4.0 ft/d Injection pressure, psi 4 2 0 0 20 40 60 80 100 120 Injection time, min
The 2 nd Wall Creek Reservoir at Teapot Dome Consisting of two, Northern and Southern, separated reservoirs Faulted and fractured reservoir formation Average Depth, ft 2900 Average gross pay thickness, ft 60 Average net pay thickness, ft 45 Average permeability, md 30 Average porosity, % 16 Initial reservoir pressure, psia 1000 Oil gravity, o API 36 Oil viscosity at 60 o F, cp 1-2 Estimated OOIP in the northern reservoir, MMB 39 Oil recovery in the northern reservoir, % 17 Current water cut, % 93%
Teapot Dome Wall Creek-2: Producing Well BHP
A Fracture Observed in the core from Well 26-AX-21
85 86 16 87 Selected a Test Site in Wall Creek-2 at RMOTC
Well 86-A-20 Production History
Proposed Field Injection Test Conducting a injection profile survey in Well 86-A- 20 to locate open fracture zone(s) Isolating open fracture zones(s) for fly ash injection Injection with low fly ash concentration (5~10 wt%) to monitor well injectivity and the response from the 3 observation wells Injection with higher fly ash concentration (20+ wt%) if no significant pressure increase observed In case dramatic reduction in injectivity occurs, turn the test into a water shutoff treatment
Thank You!