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

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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

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100

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Esti

mat

ed D

olom

ite

in M

atri

x fr

om M

N P

lot,

%

Observed Dolomite in Thin Section, %

0

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Esti

mat

ed A

nhyd

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om M

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lot,

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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

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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

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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)

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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

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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!