Method and system to estimate fracture aperture in horizontal wells

1. A method for estimating a cumulative fracture aperture in a microscopically anisotropic formation penetrated by a well, comprising:

measuring a vertical resistivity (Rv) of the microscopically anisotropic formation using a TMD (transverse magnetic dipole) logging tool and a horizontal resistivity (Rh) of the microscopically anisotropic formation using a LMD (longitudinal magnetic dipole) logging tool;

measuring with one of the logging tools at least one of a mud resistivity (R mud ) or a matrix resistivity (R matrix ); and

estimating the cumulative fracture aperture using the resistivity measurements, wherein the estimating comprises simultaneously solving the following two equations:

R v =V hf ·R mud +(1 −V hf )· R matrix

and

1 /R h =V hf ·1 /R mud +(1 −V hf )·1 /R matrix

wherein V hf is the cumulative fracture aperture.

2. The method of claim 1 , wherein the well is a horizontal well or a highly deviated well.

3. The method of claim 1 , wherein the horizontal resistivity (Rh) and the mud resistivity (R mud ) are measured, and wherein the estimating is performed using the equation:

1 /Rh=V hf /R mud ,

wherein V hf is the cumulative fracture aperture and V hf is much less than 1.

4. The method of claim 1 , wherein the vertical resistivity (Rv) and the matrix resistivity (R matrix ) are measured, and wherein the estimating is performed using the equation:

Rv =(1 −V hf )· R matrix ,

wherein V hf is the cumulative fracture aperture and V hf is much less than 1.

5. The method of claim 1 , further comprising identifying fractured intervals using the estimated cumulative fracture aperture.

6. The method of claim 1 , further comprising estimating formation porosity or formation permeability using the estimated cumulative fracture aperture.

7. A system for estimating a cumulative fracture aperture in a microscopically anisotropic formation penetrated by a well, comprising:

a TMD (transverse magnetic dipole) logging tool, a LMD (longitudinal magnetic dipole) logging tool, and a processor having a memory storing a program having instructions to cause the processor to perform:

measuring a vertical resistivity (Rv) of the microscopically anisotropic formation using the TMD logging tool and a horizontal resistivity (Rh) of the microscopically anisotropic formation using the LMD logging tool;

measuring a mud resistivity (R mud ) or a matrix resistivity (R matrix ); and

estimating the cumulative fracture aperture using the resistivity measurements as a function of pressures in the well;

wherein the program has instructions to use the vertical resistivity (Rv), the horizontal resistivity (Rh), the matrix resistivity (R matrix ), and the mud resistivity (R mud ) to estimate the cumulative fracture aperture by simultaneously solving the following two equations:

R v =V hf ·R mud +(1 +V hf )· R matrix

and

1 /R h =V hf ·1 /R mud +(1 −V hf )·1 /R matrix

wherein V hf is the cumulative fracture aperture.

8. The system of claim 7 , wherein the program has instructions to use the horizontal resistivity (Rh) and the mud resistivity (R mud ) to estimate the cumulative fracture aperture using the equation:

1 /Rh=V hf /R mud ,

wherein V hf is the cumulative fracture aperture and V hf is much less than 1.

9. The system of claim 7 , wherein the program has instructions to use the vertical resistivity (Rv) and the matrix resistivity (R matrix ) to estimate the cumulative fracture aperture using the equation:

Rv =(1 −V hf )· R matrix ,

wherein V hf is the cumulative fracture aperture and V hf is much less than 1.

10. A method comprising:

using a logging tool to measure a vertical resistivity (Rv) and a horizontal resistivity of a formation;

using the logging tool to measure at least one of a mud resistivity (R mud ) or a matrix resistivity of the formation (R matrix );

determining a cumulative fracture aperture (V hf ) by solving each of a first expression in which Rv is expressed as a function of R mud , R matrix , and V hf and a second expression in which the reciprocal of Rh is expressed as a function of V hf , the reciprocal of R mud , and the reciprocal of R matrix .

11. The method of claim 10 , wherein the first expression is:

R v =V hf ·R mud +(1 ·V hf )· R matrix

and wherein the second expression is:

1 /R h =V hf ·1 /R mud +(1 −V hf )·1 /R matrix .

12. The method of claim 11 , wherein when R mud <<R matrix , the first expression is simplified to R v ≅(1−V hf )·R matrix , and wherein the second expression is simplified to R h ≅V hf /R mud .