Effective medium theory of acidized carbonate matrix resistivity employed to calculate the apparent geometric parameters of the wormholes

1. A method, comprising:

emplacing a resistivity logging tool in a borehole;

stimulating an interval of a formation in the borehole;

obtaining at least one resistivity log of the interval of the formation, wherein the resistivity log comprises a survey of one or more depths into the formation;

determining a radial invasion of a stimulating fluid into the interval of the formation;

inverting the radial invasion to obtain an input and entering the input into an effective medium model;

solving the effective medium model and generating an effective wormhole radius profile and thickness for the interval of the formation;

estimating wormhole density within an effective wormhole radius from a borehole image log;

estimating an average wormhole diameter as a function of depth for the interval of the formation; and constraining the inverted radial invasion in the effective medium model.

2. The method of claim 1 , further comprising:

transitioning the borehole to production and producing hydrocarbons from the borehole.

3. The method of claim 1 , wherein obtaining at least one resistivity log of the interval of the formation comprises obtaining a first resistivity log prior to stimulating the interval of the formation and obtaining a second resistivity log subsequent to stimulating the interval of the formation; and wherein determining a radial invasion of the stimulating fluid into the interval of the formation comprises comparing the first resistivity log with the second resistivity log.

4. The method of claim 3 , wherein the first resistivity log is obtained from a pilot well or lateral well.

5. The method of claim 1 , further comprising:

characterizing the effective wormhole radius as having an overall wormhole type selected from a group consisting of face dissolution, conical, and dominant.

6. The method of claim 1 , further comprising:

estimating wormhole density within the effective wormhole radius from a borehole image log.

7. The method of claim 1 , further comprising:

establishing an empirical correlation between the generated effective wormhole radius and thickness and productivity enhancement for the formation; and

estimating a productivity enhancement from a stimulating treatment.

8. The method of claim 1 , wherein the resistivity logging tool measures in real-time.

9. The method of claim 8 , wherein the resistivity is monitored at a fixed depth as a function of time.

10. The method of claim 1 , wherein the resistivity tool is an array induction imaging tool.

11. The method of claim 1 , wherein determining a radial invasion of the stimulating fluid into the interval of the formation comprises comparing the at least one resistivity log with a second log obtained prior to stimulating the interval, wherein the second log is an output from a logging tool selected from a group consisting of: acoustic tools, dielectric tools, gamma ray tools, and neutron tools.

12. The method of claim 11 , wherein the resistivity tool is configured on a drill string.

13. The method of claim 11 , wherein the resistivity tool is configured on a coiled tubing.

14. A method, comprising:

emplacing a resistivity logging tool in a borehole;

stimulating an interval of a formation;

logging resistivity with the resistivity logging tool at a depth of interest from a first time point to a second time point during stimulating the interval of the formation;

determining a radial invasion of a stimulating fluid into the interval of the formation;

inverting the radial invasion to obtain an input and entering the input into an effective medium model;

solving the effective medium model and generating an effective wormhole radius profile and thickness along the interval of the formation;

estimating wormhole density within an effective wormhole radius from a borehole image log;

estimating an average wormhole diameter as a function of depth for the interval of the formation; and constraining the inverted radial invasion in the effective medium model.

15. The method of claim 14 , further comprising:

transitioning the borehole to production and producing hydrocarbons from the borehole.

16. The method of claim 14 , further comprising:

characterizing the effective wormhole radius as having an overall wormhole type selected from a group consisting of: face dissolution, conical, and dominant.

17. The method of claim 14 , further comprising:

establishing an empirical correlation between the generated effective wormhole radius and thickness and productivity enhancement for the formation; and

estimating a productivity enhancement from a stimulating treatment.

18. A system comprising:

a resistivity logging tool disposed in a borehole during a stimulating operation;

a processor carried on the logging tool configured to:

log resistivity with the resistivity logging tool at a depth of interest from a first time point to a second time point during stimulating an interval of a formation;

determine a radial invasion of a stimulating fluid into the interval of the formation;

invert the radial invasion to obtain an input and entering the input into an effective medium model;

solve the effective medium model and generate an effective wormhole radius and thickness for the interval of the formation;

estimating wormhole density within the effective wormhole radius from a borehole image log;

estimating an average wormhole diameter as a function of depth for the interval of the formation; and constraining the inverted radial invasion in the effective medium model.