Fracturing a subsurface formation based on the required breakdown pressure accounting for filter cake

1. A method for fracturing a formation, the method comprising:

drilling a wellbore into the formation;

measuring a time-dependent permeability and a time-dependent thickness of a filter cake formed by a first drilling mud;

determining a time-dependent permeability model based on the measured time-dependent permeability of the filter cake;

determining a time-dependent thickness model of the filter cake based on the measured time-dependent thickness of the filter cake;

measuring a permeability of the formation;

selecting a breakdown pressure model based on (i) the time-dependent thickness of the filter cake, (ii) the time-dependent permeability of the filter cake, and (iii) the permeability of the formation;

using the selected breakdown pressure model to predict the breakdown pressure of the formation, wherein using the selected breakdown pressure model comprises using the time-dependent thickness model of the filter cake and the time-dependent permeability model of the filter cake in the breakdown pressure model;

determining a critical mud weight based on the predicted breakdown pressure; and

pumping a second drilling mud into the wellbore to fracture the formation, the second drilling mud having a mud weight within 10% of the critical mud weight.

2. The method of claim 1 , further comprising:

extracting one or more samples from the formation; and

performing a filtration experiment on at least one of the one or more samples by pumping the first drilling mud through the at least one sample to measure the time-dependent permeability of the filter cake and the time-dependent thickness of the filter cake.

3. The method of claim 2 , wherein determining the time-dependent permeability model of the filter cake comprises determining one or more parameters to a first exponential formula based on data from the filtration experiment, and determining the time-dependent thickness model of the filter cake comprises determining one or more parameters to a second exponential formula based on the data from the filtration experiment.

4. The method of claim 3 , wherein the first exponential formula is k m =a 1 (1+exp(−t/tau 1 )) and the second exponential formula is d m =a 2 (1−exp(−t/tau 2 )), where a 1 , tau 1 , a 2 , and taut are determined based on the data from the filtration experiment.

5. The method of claim 2 , further comprising:

performing a core flooding test or a field mini-frac test on at least one of the one or more samples to determine the permeability of the formation;

performing a tensile test on at least one of the one or more samples to determine a tensile strength of the formation; and

using the tensile strength to predict the breakdown pressure.

6. The method of claim 2 , further comprising:

pumping the first drilling mud into the wellbore while the wellbore is being drilled to form the filter cake;

pumping a cleaning fluid into the wellbore after the wellbore is drilled to at least partially remove the filter cake from the wellbore;

using the filtration experiment to determine one or more effects of the cleaning fluid on the filter cake;

updating the time-dependent permeability model based on the one or more effects of the cleaning fluid on the filter cake; and

updating the time-dependent thickness model based on the one or more effects of the cleaning fluid on the filter cake.

7. The method of claim 1 , further comprising:

pumping the first drilling mud into the wellbore while the wellbore is being drilled to form the filter cake;

completing the wellbore; and

extracting one or more hydrocarbons from the wellbore after the wellbore has been completed.

8. The method of claim 7 , wherein the filter cake is located on a wall of the wellbore and the method further comprises using at least one of a logging device or a sensor to measure the permeability and the thickness of the filter cake within the wellbore.

9. The method of claim 1 , wherein selecting the breakdown pressure comprises automatically selecting the breakdown pressure by a processor.

10. A method for fracturing a formation, the method comprising:

drilling a wellbore into the formation;

measuring a permeability and a thickness of a filter cake formed by a first drilling mud;

measuring a permeability of the formation;

selecting a breakdown pressure model from at least three breakdown pressure models based on (i) the thickness of the filter cake, (ii) the permeability of the filter cake, and (iii) the permeability of the formation, wherein at least one of the at least three breakdown pressure models accounts for a time-dependent permeability of the filter cake and a time-dependent thickness of the filter cake;

using the selected breakdown pressure model to predict the breakdown pressure of the formation;

determining a critical mud weight based on the predicted breakdown pressure; and

pumping a second drilling mud into the wellbore to fracture the formation, the second drilling mud having a mud weight within 10% of the critical mud weight.

11. The method of claim 10 , further comprising:

determining whether the thickness of the filter cake is greater than zero; and

determining whether the permeability of the formation is greater than a predetermined permeability,

wherein the breakdown pressure model is selected based on whether the thickness of the filter cake is greater than zero and whether the permeability of the formation is greater than the predetermined permeability.

12. The method of claim 11 , wherein the predetermined permeability is a permeability between 1 μD and 100 μD.

13. The method of claim 11 , wherein selecting the breakdown pressure model comprises responsive to determining that the thickness of the filter cake is not greater than zero and that the permeability of the formation is greater than the predetermined permeability, selecting a first breakdown pressure model of the at least three breakdown pressure models that neglects filter cake effects and neglects time-dependency.

14. The method of claim 10 , further comprising:

determining a permeability ratio of the permeability of the filter cake and the permeability of the formation;

determining whether the permeability ratio is below a predetermined ratio;

determining whether the thickness of the filter cake is approximately constant with respect to time; and

responsive to determining that the permeability ratio is below the predetermined ratio and that the thickness of the filter cake is approximately constant with respect to time, selecting a second breakdown pressure model of the at least three pressure breakdown models that includes filter cake effects and neglects time-dependency.

15. The method of claim 14 , wherein the predetermined ratio is a ratio between 1% and 10%.

16. The method of claim 14 , wherein selecting the breakdown pressure model comprises responsive to determining that the thickness of the filter cake is not approximately constant with respect to time, selecting a third breakdown pressure model of the at least three breakdown pressure models that includes filter cake effects and includes time-dependency.

17. The method of claim 16 , wherein the third breakdown pressure model accounts for changes in the thickness of the filter cake as a function of position and the second model neglects changes in the thickness of the filter cake as a function of position.

18. The method of claim 10 , wherein selecting the breakdown pressure comprises automatically selecting the breakdown pressure by a processor.

19. The method of claim 10 , further comprising:

extracting one or more samples from the formation;

performing a filtration experiment on at least one of the one or more samples by pumping the first drilling mud through the at least one sample to measure the permeability of the filter cake and the thickness of the filter cake;

determining a time-dependent thickness model of the filter cake based on data from the filtration experiment;

determining a time-dependent permeability model of the filter cake based on data from the filtration experiment;

wherein the at least one breakdown pressure model that accounts for the time-dependent permeability of the filter cake and the time-dependent thickness of the filter cake uses the time-dependent thickness model and the time-dependent permeability model to predict the breakdown pressure.

20. The method of claim 19 , wherein the time-dependent permeability model is a first exponential formula of k m =a 1 (1+exp(−t/tau 1 )) and the time-dependent thickness model is a second exponential formula of d m =a 2 (1−exp(−t/tau 2 )), where a 1 , tau 1 , a 2 , and tau 2 are determined based on the data from the filtration experiment.