Determining invaded zones in resistivity logging

1 . A method comprising:

disposing a tool into a borehole, wherein the tool is communicatively coupled to an information handling system configured to control the tool and comprises:

a survey electrode and one or more guard electrodes configured to transmit a current into at least a formation surrounding the borehole; and

one or more monitor electrodes configured to obtain one or more measurements from at least the formation surrounding the borehole, wherein the survey electrode, the one or more guard electrodes, the one or more monitor electrodes, or any combination thereof enable identification of one or more invasion zones in the formation;

controlling, via the information handling system, the tool to identify an invasion zone in the formation by:

transmitting, via the survey electrode or the one or more guard electrodes, the current into the formation;

obtaining, via the one or more monitor electrodes, the one or more measurements;

evaluating, via the information handling system, the one or more measurements, wherein evaluating the one or more measurements comprises:

performing a first inversion on the one or more measurements to form a first inversion set;

performing a second inversion on the one or more measurements to form a second inversion set;

forming a misfit of the first inversion and a misfit of the second inversion based at least on the first inversion set and second inversion set;

determining a weighting inversion coefficient based at least on the misfit of the first inversion and the misfit of the second inversion; and

combining the first inversion set, the second inversion set, and weighting inversion coefficient to form one or more inversion products; and

determining, via the information handling system, invasion zone information associated with the formation based on the one or more inversion products.

2 . The method of claim 1 , wherein one or more inversion products are borehole diameter d bh , mud resistivity R m , invasion diameter d xo , invasion resistivity R xo , and/or formation resistivity R t .

3 . The method of claim 1 , wherein the first inversion comprises a step radial model without invasion.

4 . The method of claim 3 , wherein the second inversion comprises a step radial formation model with invasion.

5 . The method of claim 4 , further comprising forming a misfit ratio as a ratio between the misfit of the first inversion and the misfit of the second inversion.

6 . The method of claim 5 , further comprising forming a first decision boundary and a second decision boundary.

7 . The method of claim 6 , wherein the first decision boundary is formed by an adjustable threshold based on the misfit ratio and the second decision boundary is greater than the first decision boundary.

8 . The method of claim 7 , wherein determining the weighting inversion coefficient is performed by:

winv

=

{

0

if

⁢

Ratio

misfit

<

Thres

⁢

1

Ratio

misfit

-

Thres

⁢

1

Thres

⁢

2

-

Thres

⁢

1

if

⁢

Thres

⁢

1

≤

Ratio

misfit

≤

Thres

⁢

2

1

if

⁢

Ratio

misfit

>

Thres

⁢

2

wherein Thres1 is the first decision boundary, Thres2 is the second decision boundary, and Ratio misfit is the misfit ratio.

9 . The method of claim 8 , further comprising calculating a final inversion result for an invasion diameter by:

dxo

final

=

winv

×

dxo

inv

wherein dxo final is the final inversion result for the invasion diameter, winv is the weighting inversion coefficient, and dxo inv is an invasion diameter result of the second inversion.

10 . The method of claim 8 , further comprising calculating a final inversion result for an invasion zone resistivity by:

Rxo

final

=

winv

×

Rxo

inv

+

(

1

-

winv

)

×

Rt

n

-

inv

wherein Rxo final is the final inversion result for the invasion zone resistivity, winv is the weighting inversion coefficient, Rxo inv is the invasion zone resistivity result of the second inversion, and Rt n-inv is a formation resistivity result of the first inversion.

11 . The method of claim 8 , further comprising calculating a final inversion result for the formation resistivity by:

Rt

final

=

winv

×

Rt

inv

+

(

1

-

winv

)

×

Rt

n

-

inv

wherein Rt final is the final inversion result for the formation resistivity, winv is the weighting inversion coefficient, and Rt inv is a formation resistivity result of the second inversion.

12 . The method of claim 1 , further comprising performing a statistical analysis on the one or more inversion products, wherein a statistical analysis may comprise a median, a mean filter or any other statistical data operation to remove one or more spikes from the one or more inversion products.

13 . A non-transitory storage computer-readable medium storing one or more instructions that, when executed by a processor, cause the processor to:

transmit, via a survey electrode or one or more guard electrodes, a current into a formation surrounding a borehole, wherein the survey electrode and one or more guard electrodes are disposed on a tool disposed in the borehole;

obtain, via one or more monitor electrodes disposed on the tool, one or more measurements of the formation, wherein the one or more monitor electrodes, the survey electrode, the one or more guard electrodes, or any combination thereof enable identification of one or more invasion zones in the formation;

control the tool to identify an invasion zone in the formation by,

performing a first inversion on the one or more measurements to form a first inversion set;

performing a second inversion on the one or more measurements to form a second inversion set;

forming a misfit of the first inversion and a misfit of the second inversion based at least on the first inversion set and second inversion set;

determining a weighting inversion coefficient based at least on the misfit of the first inversion and the misfit of the second inversion; and

combining the first inversion set, the second inversion set, and/or weighting inversion coefficient to form one or more inversion products; and

determine invasion zone information associated with the formation based on the one or more inversion products.

14 . The non-transitory storage computer-readable medium of claim 13 , wherein the first inversion comprises a step model without invasion and the second inversion comprises a step radial formation model with invasion.

15 . The non-transitory storage computer-readable medium of claim 14 , wherein the one or more instructions, that when executed by the processor, further cause the processor to form a misfit ratio as a ratio between the misfit of the first inversion and the misfit of the second inversion.

16 . The non-transitory storage computer-readable medium of claim 15 , wherein a first decision boundary is formed by an adjustable threshold based on the misfit ratio.

17 . The non-transitory storage computer-readable medium of claim 16 , wherein a second decision boundary is greater than the first decision boundary.

18 . The non-transitory storage computer-readable medium of claim 17 , wherein the determining weighting inversion coefficient is calculated by:

winv

=

{

0

if

⁢

Ratio

misfit

<

Thres

⁢

1

Ratio

misfit

-

Thres

⁢

1

Thres

⁢

2

-

Thres

⁢

1

if

⁢

Thres

⁢

1

≤

Ratio

misfit

≤

Thres

⁢

2

1

if

⁢

Ratio

misfit

>

Thres

⁢

2

wherein Thres1 is the first decision boundary, Thres2 is the second decision boundary, and Ratio misfit is the misfit ratio.

19 . The non-transitory storage computer-readable medium of claim 18 , wherein the determining weighting inversion coefficient is calculated by:

dxo

final

=

winv

×

dxo

inv

wherein dxo final is the final inversion result for the invasion diameter, winv is weighting inversion coefficient, and dxo inv is an invasion diameter of the second inversion.

20 . The non-transitory storage computer-readable medium of claim 13 , wherein the one or more instructions, that when executed by the processor, further cause the processor to perform a statistical analysis on the one or more inversion products, wherein a statistical analysis may comprise a median, a mean filter or any other statistical data operation to remove one or more spikes from the one or more inversion products.