Method and Apparatus for Determining the Permeability of Earth Formations

• US 20080306692A1
• Filed: 12/21/2005
• Published: 12/11/2008
• Est. Priority Date: 12/21/2004
• Status: Active Grant

• Current Assignee: Sondex Wireline Limited (GE Aerospace)
• Original Assignee: Sondex Wireline Limited (GE Aerospace)
• Inventors: Pain, Christopher, Saunders, Jonathan Howard, Singer, Julian
• Granted Patent: US 8,682,587 B2
• Time in Patent Office: Days
• US Class Current: 702/11
• CPC Class Codes: G01V 1/50 Analysing data
• CPC Class Codes: G01V 11/007 using the seismo-electric effect

Abstract

A method and apparatus for determining the fluid permeability of an earth formation is described. An instrument comprising an acoustic source and acoustic and electrokinetic sensors is located in a borehole at a site of interest. The acoustic source is fired and the resulting variations in pressure and electric field generated are measured and recorded. The Biot equation, and an equation for the streaming potential coupled to fluid displacement terms, is solved using finite element analysis to give an expected pressure waveform and electrokinetic waveform based on estimated earth formation properties. By comparison of the measured waveforms and those calculated from the equations, the actual permeability of the earth formation can be deduced.

Claims

1. A method of determining the permeability of a downhole earth formation, comprising the steps of:

generating an acoustic signal at a first point in a borehole;

detecting, as an acoustic response at a second point in the borehole, variations in pressure resulting from the acoustic signal;

detecting as an electric response at the second point in the borehole, variations in the electric field resulting from the acoustic signal;

determining the permeability of the earth formation using the detected acoustic and electric responses, and by solving the Biot equation and an expression for the streaming potential given in terms of the fluid and solid displacement.

2. The method of claim 1, comprising:

solving the Biot equation to give a predicted acoustic response;

solving the expression for the streaming potential to give a predicted electric response; and

comparing the predicted acoustic and electric response, with the pressure and electric response detected in the borehole.

3. The method of claim 1, comprising generating an acoustic signal at two or more frequencies, such that at least one unknown in the Biot equations, separate to permeability, can be determined or compensated for.

4. The method of claim 3, wherein the at least one unknown includes the mudcake impedance, the zeta potential, or a zeta potential dependent variable.

5. The method of claim 3, comprising:

selecting a predicted value of permeability, mudcake impedance and zeta potential or zeta potential dependent variable;

calculating a predicted pressure and electric response at each frequency, based on the predicted values;

comparing the predicted pressure and electric responses with those measured in the borehole;

adjusting the selected values of permeability, mudcake impedance, and zeta potential or zeta potential dependent variable, to minimize the difference between the predicted and measured responses at each frequency.

6. The method of claim 5, wherein minimizing the difference uses the adjoint or local search technique.

7. The method of claim 3, comprising determining the ratio of the electric response to the acoustic response to give a normalised electric field NEF value.

8. The method of claim 7, comprising:

i) determining the NEF for at least a first, second and third frequency, assuming that the permeability and at least one unknown variable in the Biot equation is known;

ii) calculating the ratio of the NEF at the first frequency to that at the second frequency, and the ratio of the NEF at the first frequency to that at the third frequency;

iii) repeating steps i) and ii) for different values of permeability and the unknown variable to generate a look-up table;

iv) determining the ratio of the measured electric response to the measured acoustic response at the first, second and third frequency, to give a measured NEF value;

v) determining the value of the permeability and/or the unknown variable based on the measure NEF, and the look-up table.

9. The method of claim 8, wherein the unknown variable is either mudcake impedance, zeta potential or zeta potential dependent variable.

10. The method of claim 8, wherein the first, second and third frequencies are chosen such that the NEF is substantially independent of the zeta potential, or zeta potential dependent variable.

11. The method of claim 1, wherein the permeability, mudcake impedance, zeta potential or zeta potential dependent variable are determined using a neural network trained to predict waveforms from parameters of the earth formation.

12. The method of claim 1, wherein the Biot equations and the equation for streaming potential are solved using finite element analysis.

13. The method of claim 12, wherein the Biot equation and the equation for streaming potential are solved using a forward model.

14. The method of claim 12, wherein the equation for the streaming

$\mathrm{potential}$



is 



C 

ψ

_ = b _ , where 



b = - ∫

Ω



N i 

∇

·

L x 

η

φ

k 

( u . - U . ) ·





V .

15. The method of claim 13, wherein the Biot equations are given by:

(λ

+2μ

)grad div u+γ

grad div U=ρ

₁₁ü

+ρ

₁₂Ü

+b({dot over (u)}−

{dot over (U)})+W_mcφ

(u−

U);

 

 

i)

and

γ

grad div u+R grad div U=ρ

₁₂ü

+ρ

₂₂Ü

−

b({dot over (u)}−

{dot over (U)})−

W_mcφ

(u−

U), 

 

ii)

expressed in the form;

$A<br><br>\frac{\partial <br><br>\underset{\_}{p}}{\partial <br><br>t}+B<br><br>\frac{\partial <br><br>\underset{\_}{U}}{\partial <br><br>t}+L<br><br>\underset{\_}{U}=\underset{\_}{s},<br><br>\mathrm{and}<br><br><br><br>\frac{\partial <br><br>\underset{\_}{U}}{\partial <br><br>t}=\underset{\_}{p}$

where A,B and L are matrices containing combinations of the discretised material properties in Equations i) and ii), and s and p are vectors containing terms related to the source and pressure respectively.

16. The method of claim 1, wherein the acoustic response is processed in dependence on the Stonely Wave component only.

17. The method of claim 3, wherein the acoustic source is arranged to generate acoustic signals in the range 0.1 to 20 kHz.

18. The method of claim 3, wherein the acoustic source is arranged to generate acoustic signals at 0.5 kHz, 1 kHz, and 2 kHz.

19. The method of claim 4, wherein the zeta potential dependent variable is the electrokinetic coupling coefficient L_x.

21. The apparatus of claim 20, wherein the processing means comprises a processor having program code stored thereon, which when executed causes the processor to control the acoustic source, acoustic receiver, electrode, to perform the steps of any of methods claims 1 to 19.

26. A computer readable medium, on which computer code is stored, the computer code when executed by a computer causing the computer to perform the steps of claim 1.

20. Apparatus for determining the permeability of a downhole earth formation, comprising:

an acoustic source for generating an acoustic signal at a first point in a borehole;

an acoustic receiver disposed at a location separated from the acoustic source, the acoustic receiver being arranged to detect, as an acoustic response, variations in pressure resulting from the acoustic signal;

an electrode disposed at a location separated from the acoustic source, the electrode being arranged as an electric response, variations in the electric field resulting from the acoustic signal;

processing means for determining the permeability of the earth formation using the detected pressure and electric responses, wherein the processor is arranged to solve the Biot equation and an expression for the streaming potential given in terms of the fluid and solid displacement.

22. The apparatus of claim 20, wherein the apparatus comprises a tool body, on which the acoustic source, acoustic receiver and electrode are mounted, the acoustic source being mounted at a separate location from that of the acoustic receiver and electrode.

23. The apparatus of claim 20, wherein the acoustic receiver and electrode are co-located at substantially the same location.

24. The apparatus of claim 20, comprising at least two acoustic sources.

25. The apparatus of claim 20, wherein the acoustic receivers are hydrophones or geophones.