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Radial- Basis Function Network Applied in Mineral C omposition
Analysis
Shaochang Wo & Peigui Yin
Janu ary 13 , 2010, D e nve r
Mineral composition in the MinnelusaFormation can be calculated from the sonic, neutron, and density log suite – Theoretically!!
∆
=
∆∆∆∆
11111N
A
D
Q
f
ADQf
ADQf
ADQf t
HHHH
tttt
φρ
φφφφ
ρρρρ
Δt : sonic travel time (μs/ft)ρ: density (g/cm3)H: hydrogen index (dimensionless)φ: fractional volumeφN: neutron porosity (%)
SUBSCRIPTSf: fluid-filled pore spaceQ: quartz D: dolomiteA: anhydrite
(James W. Schmoker and Christopher J. Schenk, 1988)
M-N Plot for Mineral Identification
fb
bf ttM
ρρ −∆−∆×
=)(01.0
fb
NNρρφ−−
=1
Δtf: sonic travel time in pore fluidΔtb: bulk sonic travel time ρf: fluid densityρb: bulk densityφN: neutron porosity (limestone units, fractional)
Anhydrite
Dolomite
Quartz
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
M
N
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Esti
mat
ed Q
uart
z in
Mat
rix
from
MN
Plo
t, %
Observed Quartz in Thin Section, %
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Esti
mat
ed D
olom
ite
in M
atri
x fr
om M
N P
lot,
%
Observed Dolomite in Thin Section, %
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Esti
mat
ed A
nhyd
rite
in M
atri
x fr
om M
N P
lot,
%
Observed Anhydrite in Thin Section, %
Radial-Basis Function Network
Input Hidden Output
Σ f
Fixed input = 1
(bias)
1G
jG
nG
1x
px
1w
jw
nw
2x 0w
Parameters in A Generalized RBF network
it
iw : weights : centers
: the weighted norm
)()(1∑=
−=M
iii txGwxf
Regularization Theory - Supervised Learning as an Ill-Posed Hypersurface
(Tikhonov, 1963; Poggio and Girosi, 1989)
2
1
2 ))((][ PfxfyfHN
iii∑
=
+−= λ
f: RBF networkλ: regularization parameterP: 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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
No
rmalized
Neu
tro
n C
ou
nt R
ate
Normalized Gamma Ray
Normalized Phi: 1~0.7
Normalized Phi: 0.7~0.3
Normalized Phi: 0.3~0
Clustering View of the Cross-Plot Porosity
0 10 20
Porosity, %
0 10 20
Porosity, %
3550
3600
3650
3700
3750
3800
3850
0 10 20Porosity, %
Dep
th,
ft
Training
Testing
Cases with the middle interval for exclusion testing
00.10.20.30.40.50.60.70.80.9
1
1 10 100 1000
Number of Centers
Cor
rela
tion
Coe
ffic
ient
(C
C)
Training
Testing
Cases with the bottom interval for exclusion testing
00.10.20.30.40.50.60.70.80.9
1
1 10 100 1000
Number of Centers
Cor
rela
tion
Coe
ffic
ient
(C
C)
Training
Testing
• 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 3rd input
Key Features of This Approach
Simulat ion of FracturedTensleep Reservoirs
Shaochang WoMichael Presho
Janu ary 13 , 2010, D e nve r
• 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%
The Tensleep Reservoirs in Wyoming
Gouge-filled Fractures in Tensleep Outcrops(from Peigui Yin)
Fracture Spacing (D)
Width of Cemented Band (w)Fracture Aperture (e)
Kcm
Single-Permeability Model by Averaging
D
eK
KKK
wDKewK
DKKK
f
fmfm
cm
cmcm
12
)()(
3
=
+=−+−
=
orintation fracture tonormalty permeabili effective :
norientatio fracture toparallelty permeabili effective :
band cemented ofty permeabili :
typermeabili fracture :
typermeabilimatrix :
band cemented of width :
aperture fracture :
spacing fracture :
cm
fm
c
f
m
K
K
K
K
K
w
e
D
0
0.2
0.4
0.6
0.8
1
0.1 1 10 100 1000
Per
mea
bili
ty R
atio
, Kcm
/Kfm
Fracture Spacing, ft
Effect of Fracture Spacing on Permeability Ratio(Kc = 5 md, e = 0.1 mm, w =0.01 ft)
Km = 250 md
5 md
30 md
100 md
Frac
ture
O
rien
tatio
n
Frac
ture
O
rien
tatio
n
Line Pattern - Parallel Line Pattern – 90 Degree
Frac
ture
O
rien
tatio
n
Frac
ture
O
rien
tatio
n
9-Spot Pattern 5-Spot Pattern
(Km = 30 md, Kf = 110 md, Kc = 5 md, D = 20 ft, e = 0.2 mm, w = 0.5 ft)
Parallel
9-spot
90-Degree
A single porosity/permeability system is often not capable to model fractured reservoirs when– Permeability contrast (“true Kf” to Km) > 100:1
– Fracture spacing > 30 ft
Dual Porosity/Permeability Model of Single Phase Flow
t
pCp
k ftfff
f
∂∂
=−∇•∇ ϕτµ
)(
tp
Cpk m
tmmmm
∂∂
=+∇•∇ ϕτµ
)(
)( mfm pp
k−=
µστ
++= 2223/1)( z
mz
y
my
x
mx
mzmymx Lk
L
k
Lk
kkkSσ
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 fine-grid 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
(Kazemi and Gilman 1993)
)}()(){( wmwfwz
mfw
rwmw hhpp
kk−+−= γ
σσ
µστ
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
Average Average AverageGross Net Average Average Original Average Productive
Thickness Thickness Porosity Permeability Sw Sor Areaft ft % md % % acre
A Sand (Zone 1) 44 10.6 11.2 51.8 27.5 19.9 927.4B Dolomite 10B Sand (Zone 2) 52 11.2 11.7 17.8 31.5 24.3 752.3C Dolomite (Zone 3) 32C Sand (Zone 4) 30 7.1 9.5 38 28.5 22.8 424.2D Dolomite 10D Sand (Zone 5) 30 7.7 11.4 81.8 25.7 20.1 234.5
ESC Tensleep: Oil Producing Zones
ESC Tensleep: Well Perforation(Before 12/31/1977)
Well Well Well Well Well Well Well Well Well Well Well Well Well Well WellA-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 ΔB DolomiteB Sand (Zone 2) Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ ΔC Dolomite (Zone 3) ΔC Sand (Zone 4) Δ ΔD DolomiteD 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
• Forward simulations with a range of parameter combinations in fracture model setting– σ, Kf (Kfx & Kfy), Krf, Pcf, Df
• 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
Ongoing Simulation Study
F ly Ash Project U pdates
Shaochang Wo, Peigui YinXina Xie, Matthew Johnson
Norman Morrow
Janu ary 13 , 2010, D e nve r
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
• 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
• 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)
Project Status (continued)
No Straining Observed in Large Fracture Opening(Wall Creek-2 Core 2797)
0
0.2
0.4
0.6
0 10 20 30 40 50 60 70
Inje
ctio
n pr
essu
re, p
si
Injection time, min
Wallcreek 2797(Kg = 10.6 md)Wf = 200 to 300 micronsfly ash size = 40 to 60 microns (5 wt%)
q = 4.0 ft/D
q = 1.0 ft/D
0
2
4
6
8
0 20 40 60 80 100 120
Inje
ctio
n pr
essu
re, p
si
Injection time, min
Berea F1 (Kg = 88 md)Wf = 100 to 200 micronfly ash size = 40 to 60 micron (20 wt%)q = 4.0 ft/D
Straining Occurred in Smaller Fracture Opening(Berea Sandstone Core F1)
The 2nd Wall Creek Reservoir at Teapot Dome
Consisting of two , Northern and Southern, separated reservoirsFaulted and fractured reservoir formation
Average Depth, ft 2900Average gross pay thickness, ft 60Average net pay thickness, ft 45Average permeability, md 30Average porosity, % 16Initial reservoir pressure, psia 1000Oil gravity, oAPI 36Oil viscosity at 60 oF, cp 1-2Estimated OOIP in the northern reservoir, MMB 39Oil recovery in the northern reservoir, % 17Current water cut, % 93%
Teapot Dome Wall Creek-2: Producing Well BHP
A Fracture Observed in the core from Well 26-AX-21
86
85
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!