Two methods of determining permeabilities of naturally fractured rocks from laboratory measurements

1. A method for measuring a fracture permeability and a matrix permeability of a naturally fractured cylindrical rock sample, comprising:

sealing a first flat end of the naturally fractured cylindrical rock sample;

sealing a second flat end of the naturally fractured cylindrical rock sample;

immersing the naturally fractured cylindrical rock sample in a fluid;

attaching an axial strain sensor and a radial strain sensor to a curved surface of the naturally fractured cylindrical rock sample;

attaching a signal generator to the first flat end of the naturally fractured cylindrical rock sample;

attaching a signal receiver to the second flat end of the naturally fractured cylindrical rock sample;

generating a harmonic excitation using the signal generator at a plurality of frequencies;

recording, using the signal receiver, the harmonic excitation at each of the plurality of frequencies;

calculating an elastic wave propagation attribute at each of the plurality of frequencies; and

inverting the elastic wave propagation attribute at each of the plurality of frequencies to determine the fracture permeability and the matrix permeability of the naturally fractured cylindrical rock sample.

2. The method of claim 1 ,

wherein the naturally fractured cylindrical rock sample is immersed in a fluid at atmospheric pressure.

3. The method of claim 1 ,

wherein the elastic wave propagation attribute is selected from the group consisting of a first compressional wave propagation velocity, a shear wave propagation velocity, a first compressional wave attenuation, a shear wave attenuation, an axial strain, and a radial strain.

4. The method of claim 1 ,

wherein the inverting the elastic wave propagation attribute, further comprises:

determining a characteristic frequency of the naturally fractured cylindrical rock sample; and

determining the fracture permeability and the matrix permeability of the rock based on the characteristic frequency of the naturally fractured cylindrical rock sample and a theory of dual-porosity dual-permeability poroelastodynamics.

5. The method of claim 1 ,

wherein the inverting the elastic wave propagation attribute, further comprises:

determining a value of the fracture permeability and a value of the matrix permeability of the naturally fractured cylindrical rock sample which minimizes a measure of a difference between a measured and a predicted value of the elastic wave propagation attribute, summed over a plurality of frequencies.

6. The method of claim 5 ,

wherein the predicted value of the elastic wave propagation attribute is determined using the theory of dual-porosity dual-permeability poroelastodynamics.

7. The method of claim 5 , further comprises:

summing over a plurality of frequencies using a weighted-sum, wherein one or more elastic wave propagation attributes are assigned more importance than another elastic wave propagation attributes.

8. The method of claim 5 ,

wherein the measure of the difference between a measured value of the elastic wave propagation attribute and a predicted value of the elastic wave propagation attribute, summed over a plurality of frequencies is the square of the differences between the measured and the predicted value summed over the plurality of frequencies.

9. A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:

generating a harmonic excitation using the signal generator and recording the harmonic excitation using the signal receiver at a plurality of frequencies;

calculating an elastic wave propagation attribute for the plurality of frequencies; and

inverting the elastic wave propagation attribute for the plurality of frequencies to determine the fracture permeability and the matrix permeability of the naturally fractured cylindrical rock sample.

10. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

selecting, the elastic wave propagation attributes from the group consisting of a first compressional wave propagation velocity, a shear wave propagation velocity, a first compressional wave attenuation, a shear wave attenuation, an axial strain, and a radial strain.

11. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

determining a characteristic frequency of the naturally fractured cylindrical rock sample; and

determining the fracture permeability and the matrix permeability of the rock based, at least in part, on the characteristic frequency of the naturally fractured cylindrical rock sample and a theory of dual-porosity dual-permeability poroelastodynamics.

12. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

determining the value of the fracture permeability and the value of the matrix permeability of the naturally fractured cylindrical rock which minimize a measure of the difference between a measured and a predicted value of the elastic wave propagation attribute, summed over a plurality of frequencies.

13. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

predicting the value of the elastic wave propagation attributes based, at least in part, using a theory of dual-porosity dual-permeability poroelastodynamics.

14. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

summing over a plurality of frequencies using a weighted-sums wherein one or more elastic wave propagation attributes are assigned more weight than other elastic wave propagation attributes.

15. The non-transitory computer readable medium of claim 9 , wherein the instructions further comprise functionality for:

wherein, the measure of the difference between a measured value of the elastic wave propagation attribute and a predicted value of the elastic wave propagation attribute, summed over a plurality of frequencies is the square of the differences between the measured and the predicted value summed over the plurality of frequencies.