Fracture Diagnostics Using Low Frequency EM Induction and ... · 8/24/2016 DOE Project Review, Sharma, University of Texas at Austin 3 Concept • Transform a hydraulic fracture into

$Page 1: Fracture Diagnostics Using Low Frequency EM Induction and ... · 8/24/2016 DOE Project Review, Sharma, University of Texas at Austin 3 Concept • Transform a hydraulic fracture into$
DOE Project Review, Sharma, University of Texas at Austin8/24/2016 1

Mukul M. SharmaYaniv Brick, Peng Zhang, Javid Shiriyev,

Ali E. Yilmaz, Carlos Torres-VerdinUniversity of Texas at Austin

Jeff Gabelmann, Robert HoustonE-Spectrum

DE-FE0024271

Fracture Diagnostics Using Low Frequency EM Induction and Electrically

Conductive Proppant


Project Objectives

The primary objective of the project is to build andtest a downhole fracture diagnostic tool that can beused to estimate the orientation and length of the‘propped’ fracture and to map the distribution ofproppant in the fracture.

Specifically, our objectives are to:– Develop a forward model for the proposed technology taking into account

real geological and reservoir constraints.– Test proppants in the laboratory for electrical and material properties for

their suitability in deployment in the field.– Design, build and field test a prptotype low frequency electromagnetic tool.– Invert the field data to estimate the propped fracture geometry, and present

a map showing the distribution of proppant in the fracture.


Concept

• Transform a hydraulic fracture into a highly conductive plane using conductive proppants.

• One transmitter, two receiver set to measure electromagnetic response.

Transmitter

Receiver 1Receiver 2

Fracture filled with electrically conductive proppant

Electromagnetic waves


Forward Model


Tx Rx1

Shale background

a

Tx-Rx distance

Rx2

Rx2-Rx1 spacing

Fracture

Borehole

Simulated Scenario

shale 3 mρ = Ω3

eff 10 mρ −= Ω


• Short-spacing measurement

• Long-spacing measurementCenter of the receivers

Tx Rx1 Rx2

=Rx2 1.5 mrRx1= 1.2 mr

Tx Rx1 Rx2

=Rx2 19.2 mrRx1= 18 mr

Simulated Scenario

3Rx2 Rx1 Rx1 Rx2[ ( ) ( )( / ) ]uv uv uvH H H r rD = - -r r

u-component H field due to v-

directed magnetic dipole

• Primary and bucking coil configuration


• Primary (formation) and secondary (fracture) magnetic fields computed for co-axial and co-planar scenarios

• Field notations:– Magnetic field (fracture + formation):– uv indicates:

• aa – co-axial measurement, pp – co-planar measurement– Voltage after cancellation [volts]:

• Secondary field increases with facture size and effective conductivity and decreases with Tx-Rx distance.

form fracv v v= +H H H

Simulated Scenario

Tx Rx1 Rx2

3 30 turn Rx2 Rx1 Rx1 Rx2ˆRe [ ( ) ( ) / ]uv v vU j AN r rωµ∆ = − ⋅ −u H r H r


VJÞVJ

• Scattered (secondary) electric fieldV

V shale forV

fracm (( )[ ])s s- + =E JE J

Model: Volume Electric Field Integral Equation (VEFIE)


Þ

• Basis and Galerkin testing

VJ

VJ

3( )O NComputational cost: (direct method)2( )O N (iterative method)( : 70 000 250 000):N

Model: Method-of-Moments (MoM)

VV

form frac Galerkin test ingV shale

1 1V

1

( )

( ) [ ] ( )N N N NN

nn

I n

s s´ ´ ´

=

üïï= - ïï- ï ¾ ¾ ¾ ¾ ¾¾® =ýïï@ ïïïþå

JE E JZ I V

J r f r


Model: Numerical Solution and Fast Solver

• Method of Moments

– Discretization of the integral equation

– Computational cost

• Adaptive integral method:

– Auxiliary 3-D regular grid

– A 4-step procedure to approximate MOMmatrix

– Translational invariance

– 3-D FFTs

– Computational cost

2iter( )O N N

iter C C( ( log ))O N N N N+

1 1N N N N´ ´ ´=Z I V


Computational Complexity

• AIM iterative solver performance (new)– Problem: circular fracture (a=30m):– Number of unknowns: ~1.9M (dictated by higher conductivity)– Storage: ~91GB (~54.6TB with MoM)– 512 cores– Matrix fill time: 2.2 min (19 hr. if serial)– Solution per excitation average time: 8.3 sec. (1.18 hr. if serial)– For 2x200 excitations: 0.9 hr. (for a single fracture)

• MoM iterative solver performance (presented last year)– Problem: circular fracture (a=30m):– Number of unknowns: ~189k– Storage: ~546GB– 512 cores– Matrix fill time: 28 min (238 hr. if serial)– Solution per excitation average time: 45 sec. (6 hr. if serial)– For 2x200 excitations: 5 hr. (for a single fracture)

0.1 mρ = Ω

0.01 mρ = Ω


Simulations Summary

• Simulations are required for evaluation of tool design as well as for forward model as part of an inverse solver

• Integral equation-based solvers obviate the need in modelling formation background, larger fractures can be analyzed

• Adaptive Integral Method (AIM)-based fast iterative solver enable analysis of larger, more detailed fractures, with higher proppant conductivity

• Removal of borehole has little effect on the results while enabling optimal performance of AIM (greater acceleration)

• Fast run-time per excitation - corner stone of the inverse solver in progress


Simulations Summary

• High conductivity contrasts cause ill conditioning – results are scaled with fracture conductivity in post processing

• Hence, results are obtained with “pessimistic” proppant resistivity values and scaled to match values extracted from lab-experiment

• Planned:- Fast direct solver– (in progress) suitable for multiple

forward solutions and high conductivity contrasts- Inversion algorithm relying on a fast direct solution- Advanced formulation and complex modeling for cased

wells tools


Proppant Resistivity Measurements


Experimental Configuration

Conductive Proppant: Petroleum Coke• A 4-point probe method was used to do the measurements in a core holder• Alternating current (AC) was applied on the current-carrying electrodes,

while the voltage was measured on the voltage-sensing electrodes• Confining pressure can be applied. Saturation fluid could be tuned

1’’

~

V

A

1.5’’


Verification of the Experimental Method

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2

Rt (o

hm.m

)

Rw (ohm.m)

Sand pack saturated with brine

Rt= Rw(aΦ-m

)Sw-n

m 1.3Sw 1Φ 25.2%FF 4.55a 0.76

Archie’s Equation

A good fit to Archie’s Law


Verification of the Experimental Method

19

19.5

20

20.5

0.86

0.87

0.88

0.89

0.9

0.91

0 500 1000 1500 2000 2500 3000

Resi

stan

ce (o

hm)

Resi

stiv

ity (

ohm

.m)

Confining Pressure (psi)

Resistivity/Resistance VS Confining Pressure

Resistivity Resistance

Confining pressure applied

Φ=24.2%

Sea Water (Rw=0.18 ohm.m)

The setup worksproperly when confiningpressure is applied,although the contractionof the sleeve has asmall effect on thecalculations.


Resistivity measurements of petroleum coke with air

Preliminary Results

Density: 1.14 g/cm3

Porosity: 43.9%End point: 3.2x10-4

Density: 1.27 g/cm3

Porosity: 37.6%End point: 2.4x10

-4

mΩ⋅mΩ⋅


Resistivity measurements of petroleum coke in a fracture

Preliminary Results

1 mmfW =

The resistivity remains relatively steady around , i.e., an order of magnitude higher than that obtained for the cylindrical pack.

33 10 m−× Ω⋅


Key Observations

• The electric resistivity of the proppant we plan to use, under confining stress, was measured to be in the range of 2 x 10-4 .

• This value is four orders of magnitude smaller than the resistivity of a typical shale. This is very important since it provides an excellent resistivity contrast with the shale.

• The initial packing density affects the resistivity at low stress but not at high stress.

• The resistivity is not very sensitive to the fluid saturation since the conductance is controlled by the conductivity of the solid grains.

mΩ⋅


Towards a Parametric Inversion Algorithm


• We already know from simulations of simple fracture geometries:– The voltage detected are proportional to fractures’ conductivity

– increases as the fracture area increases, until it reaches to a saturation point

– Coaxial measurements are more sensitive to fracture’s conductivity, area, shape and position, while cross-polarized measurements ( …) are more sensitive to fractures’ angle

Yang, K., C. Torres-Verdin, and A.E. Yilmaz. 2015. IEEE Transactions, 53(8), 4605-4615.

Before Inversion

uvU∆uvU∆

zzU∆xzU∆

• In order to do inversion, we need to know:– What information the tool offers corresponding to different fracture

geometries

– What signals should be used for inversion in order to recognize different model parameters


Towards more realistic fractures:• Asymmetrical proppant distributions• Complex fractures• Curved fractures• Lab measured proppant conductivity

Can the tool differentiate these fractures?

Before Inversion


• The relative signal strength decreases as the propped area reduces proportionalityof the secondary fields to fracture size

Example - Proppant Distribution

Effect of proppant distribution (coaxial measurements)

• The curves reach their peak values when the center of the two receivers is roughly atzero ability to detect fracture’s location

-3 -2 -1 0 1 2 30

100

200

300

400

500

600

700

800

Center of Receivers (m)

(∆U

frac

zz-∆

Uno

-fra

czz

)/∆U

no-f

rac

zz (%

)

(a.1)(a.2)(a.3)

(a. 1)

(a. 2)

(a. 3)

150 ft25 ft

x

y

z Short spacing, coaxial

-6 -4 -2 0 2 4 6-20

-10

0

10

20

30

40

50

60

70

80


( ∆U

frac

zz- ∆

Uno

-fra

czz

)/ ∆U

no-f

rac

zz (%

)

(a.1)(a.2)(a.3)

Long spacing, coaxial

• The separation of the curves for the long-spacing configuration is more pronounced.The long-spacing detector is more sensitive to longer fractures.


-6 -4 -2 0 2 4 6-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2


(∆U

frac

yz-∆

Uno

-fra

cyz

)/∆U

no-f

rac

yz (%

)

(a.1)(a.2)(a.3)

(a. 1)

(a. 2)

(a. 3)

150 ft25 ft

x

y

z

-3 -2 -1 0 1 2 3-100

-80

-60

-40

-20

0

20

40

60

80

100


(∆U

frac

yz-∆

Uno

-fra

cyz

)/∆U

no-f

rac

yz (%

)

(a.1)(a.2)(a.3)

Short spacing, cross-polarized Long spacing, cross-polarized

• The cross-polarized measurement is less sensitive to the propped fracture’s area

• The more symmetrical fractures induce significantly lower voltage levels at thereceiver compared to that of the single sided distribution (less symmetrical inducedstronger signals)

• This configuration is more sensitive to the fracture’s asymmetry, and it providescomplementary information that can improve shape classification of the proppedfracture


Effect of proppant distribution (cross-polarized measurements)



Key conclusions:

• the EM logging technique enables the differentiation betweendifferent spatial distributions of proppant.

• To detect spatial asymmetry in fractures, a combination of co-axial and cross-polarized measurements should be used.

• While co-axial measurements provide information on fracturearea, distinguishing asymmetrical fractures from symmetricalones is possible based on cross-polarized measurements.

• Long-spacing configuration is preferred to distinguish betweenvarious spatial distributions of proppant in large-size fractures.


Example - Complexity of Fractures

• Use multiple planar elliptical fractures ofa 5mm total width and a 1 cm separationto approximate the complex fracture.

• No significant difference is observedbetween the various cases. The tool’sresponse depends only on the proppedfracture volume, and not on itscomplexity.

Therefore, it is sufficient to model a thincomplex fracture as a single thin bulkvolume of a constant effective thickness

Complex fractures VS planar fractures

Short spacing, coaxial


Example - Curved Fractures

Curved fracture VS planar fractureMajor radius 10m, minor radius 3mTwo wings are bent 30 º

• Measurement with long-spacingconfiguration shows some differences inboth coaxial and coplanarmeasurements.

• These differences are more likelyeffects of differences in area

-40

-30

-20

-10

0

10

20

30

40

50

60

-6 -4 -2 0 2 4 6

Rel

ative

SIg

nal S

treng

th (

%)

Centers of Receivers (m)

long spacing, coaxialPlanar

Bent

-700

-600

-500

-400

-300

-200

-100

0

100

200

-6 -4 -2 0 2 4 6

Rel

ative

Sig

nal S

treng

th (

%)


long spacing, coplanar

Planar


Parametric Inversion Approach2

1

2

1

[F ( ) ( )]( )

[ ( )]

n

truei ii

n

trueii

m F mE m

F m

=

=

-=

å

å/ /

(frac) (no-frac)

(no-frac)

( ) ( )( ) 100%

( )

zz xz zz xzi i

i zzi

U m U mF m

U m

D - D= ´

D

Objective function

[ ; ; ; ; ]m z Aa s l=

Relative signal strength

Model parameters

a : angle (º) s : conductivity (S/m)

A : area (m2) l : aspect ratio (m)

Goal: Minimize the objective function w.r.t all model parameters !

z : position (m)


Optimization Algorithm - GSS

Golden section search (GSS)

• To find the minimum of in the interval

1. Let be the initial interval

2. Set

3. Set

4. If , ; else

5. If (stopping criteria met) return; else go to Step 3

( )f x [ , ]lo hix x

[ , ]lo hix x

1 (1 )lo hix cx c x= + −

2 (1 ) lo hix c x cx= − +

( ) ( )1 2f x f x< 1 2 2, , hix x x x→ 1 2 1, ,lox x x x→


Example for InversionStarting from a simple case

True model Initial guess

ra

b

Position: 0 mConductivity: 30 S/mOrientation: Area: Aspect Ratio: 3.33

2π×10×3 m0°

Position: 3 mConductivity: 100 S/mOrientation: Area: Aspect Ratio: 1

2 2π×7 m0°

x

y

z


| | 0.254Eλ∂

=∂

| | 0.044Eα∂

=∂

| | 7.532EZ∂

=∂

| | 0.298Eσ∂

=∂

| | 0.007EA∂

=∂

The Order of Searching

α z σ are independent model parameters

A λ are coupled model parameters

Start searching using short-spacing configuration


Searching for Angle

-20 -15 -10 -5 0 5 100

0.5

1

1.5

2

2.5

3

3.5

4x 109

Angle of Fracture (°)

Obj

ectiv

e Fu

nctio

n E

• Cross-polarized results• Searching interval: [-30, 30]• Accuracy: 2• Number of forward Simulations: 7


-2 -1.5 -1 -0.5 0 0.5 1 1.56.5

7

7.5

8

8.5

9

9.5

10

10.5

11

Position (m)

Obj

ectiv

e Fu

nctio

n E

Searching for Location

• Searching interval: [-4, 4]• Accuracy: 0.1• Number of forward Simulations: 8

-3 -2 -1 0 1 2 30

10

20

30

40

50

60

70

80


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter position search


Searching for Conductivity

20 25 30 35 40 45 50 55 60 65 700

0.5

1

1.5

2

2.5

Conductivity (S/m)

Obj

ectiv

e Fu

nctio

n E

• Searching interval: [10, 100]• Accuracy: 10• Number of forward Simulations: 4-3 -2 -1 0 1 2 30

5

10

15

20

25


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter conductivity search


• Inversion results (stops after one iteration)

(True)

Reason: data from short-spacing configuration doesn’t provide information about proppant far from wellbore.

What if we switch to data from long-spacing configuration?

Searching for Area and Aspect Ratio

A λ are coupled model parameters !

255 mA = 1λ =294 mA = 3.3λ =


Searching for Area

60 70 80 90 100 110 120 1300

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Area (m2)

Obj

ectiv

e Fu

nctio

n E

• Searching interval: [20, 200]• Accuracy: 5• Number of forward Simulations: 8-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter first area search


Searching for Aspect Ratio

• Searching interval: [1, 8]• Accuracy: 1• Number of forward Simulations: 4

2 2.5 3 3.5 4 4.5 50

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Aspect Ratio

Obj

ectiv

e Fu

nctio

n E

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter first AR search


• Searching interval: [50, 110]• Accuracy: 2• Number of forward Simulations: 7

Searching for Area (2nd)

70 75 80 85 90 95 1002

4

6

8

10

12

14x 10-3

Area (m2)

Obj

ectiv

e Fu

nctio

n E

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter second area search


• Searching interval: [1, 4]• Accuracy: 0.5• Number of forward Simulations: 3

Searching for Aspect Ratio (2nd)

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 31.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2x 10-3

Aspect Ratio

Obj

ectiv

e Fu

nctio

n E

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6


(∆U

frac

zz-∆

Uno

-frac

zz)/∆

Uno

-frac

zz (%

)

TrueAfter second AR search


Inversion Summary

• Total number of forward simulations is 41• Total computational time needed ~50 min (256 processors)• Data should be chosen based on the rough estimation of fracture size

especially for inversion of fracture size and aspect ratio

Future plans for inversion:• Automation of searching • Adding noise to synthesized data• Using real data (recorded by experiments)

TruePosition: 0 mConductivity: 30 S/mOrientation: Area: Aspect Ratio: 3.33

294 m0°

InversionPosition: 0 mConductivity: 30 S/mOrientation: Area: Aspect Ratio: 2.5

284 m0°


Shallow Earth Experiment for Prototype Tool


Prototype Tool: Shallow Earth Experiment

• Smaller scale experiment in a controlled environment (not field deployable)

• Necessary for:– Refining/Improving design towards a field deployable tool

– Verifying measurement methodology

– Recording realistic data to be used by inverse algorithms in development


Test Site Tool Specifications

Constraints:- Wellbore Size Limitation: diameter of the coil is restricted to 4”

- Thickness of Wire used in transmitter and receiver

- Eccentricity: misalignment of receiver axis with respect to

transmitter axis can result in errors due to different signal level in

different configurations

- Target Frequency: Larger fractures require lower frequencies.

Requirements:- Magnetic dipole moment: Preferably at least N*S*I = 150 Am2

- Three receivers: short (6’), intermediate (20’), long Tx-Rx spacing (60’)


Proposed Experiment

Tx Rx1

Formation

Rx2

Conductive Target

Borehole

Air

𝑎𝑎 ≈ 1𝑚𝑚

Tx-Rx 6’

1’


Proposed Experiment

Not necessarily large size low conductivity target, induction number can be kept constant for fracture

Detectable signal level is ~10 μV

-3 -2 -1 0 1 2 310-10

10-8

10-6

10-4

10-2

100

Receivers' distance from fracture [m]

∆Ufra

c- ∆U

bore

co-axialco-planar

𝑇𝑇𝑥𝑥 − 𝑅𝑅𝑥𝑥 = 6 ft𝑟𝑟𝑅𝑅𝑥𝑥𝑅 − 𝑟𝑟𝑅𝑅𝑥𝑥𝑅 = 1 ft

𝑚𝑚 = 150 Am𝑅𝑓𝑓 = 100 Hz

𝜌𝜌𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 10−7 Ωm𝜌𝜌𝑏𝑏𝑡𝑡𝑏𝑏𝑏𝑏𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 3 Ωm

𝑁𝑁 = 60𝐴𝐴 = 𝜋𝜋 0.06𝑅 m𝑅

𝛿𝛿 = 𝜎𝜎𝜎𝜎𝜎𝜎𝑙𝑙𝑅

𝜎𝜎: conductivity of target𝜎𝜎: electric permeability𝜎𝜎: angular frequency𝑙𝑙: length of target


Induction Coil Shallow Earth Test


Field Test Facility:


Transmitter and Receiver

Mono Axis Transmitter CoilTri Axial Receiver Coils


Modified Drill Dog Surface System

Key components:• Electronics for driving the transmitter• Novel electronics and software for high

resolution signal processing


Conclusion

• A new numerically efficient simulator was built to solve Maxwell’s equations in 3-D.

• Simulations were conducted to show that induction measurements can be used to detect electrically conductive proppant in fractures.

• For these highly conductive targets, measurements are expected to be sensitive to all target parameters, i.e. fracture location, propped fracture area, length and orientation.

• A Field Deployable Prototype Tool is being built.

• A shallow earth experiment is being planned to test theprototype tool.


Thank DOE for funding the project

DE-FE0024271

Documents

Fracture Diagnostics Using Low Frequency EM Induction and ... · 8/24/2016 DOE Project Review, Sharma, University of Texas at Austin 3 Concept • Transform a hydraulic fracture into