Downhole inflow control

1. An apparatus comprising:

a funnel comprising:

a first end;

a second end;

a wall spanning from the first end to the second end, the wall defining a longitudinal axis through the first end and the second end, the wall having a first cross-sectional area at the first end and a second cross-sectional area at the second end, the first cross-sectional area and the second cross-sectional area perpendicular to the longitudinal axis, the first cross-sectional area greater than the second cross-sectional area;

a plurality of inlet ports, wherein a first inlet port of the plurality of inlet ports is disposed on the first end of the funnel, and a second inlet port of the plurality of inlet ports is disposed on the wall of the funnel; and

an outlet port disposed on the second end of the funnel;

a core disposed within the funnel, the core defining a first outer diameter, wherein the outlet port has an inner diameter that is less than the first outer diameter of the core;

a first coating disposed on and surrounding an outer surface of the core, the first coating defining a second outer diameter, the first coating configured to dissolve at a first dissolution rate in response to being exposed to water;

a second coating disposed on and surrounding an outer surface of the first coating, the second coating defining a third outer diameter, the second coating configured to dissolve at a second dissolution rate different from the first dissolution rate in response to being exposed to water; and

a third coating disposed on and surrounding an outer surface of the second coating, the third coating defining a fourth outer diameter, the third coating configured to dissolve in response to being exposed to a hydrocarbon.

2. The apparatus of claim 1 , wherein the second dissolution rate of the second coating is less than the first dissolution rate of the first coating.

3. The apparatus of claim 2 , wherein the first coating has a first thickness, the second coating has a second thickness, and a difference between the first thickness and the second thickness is less than 0.1 centimeters.

4. The apparatus of claim 3 , wherein the third coating has a third thickness, and a difference between the third thickness and the first thickness is less than 0.1 centimeters.

5. The apparatus of claim 4 , wherein the third thickness is in a range of from about 50% to about 100% of the first thickness.

6. The apparatus of claim 5 , wherein

the core coated with the first coating, the second coating, and the third coating is disposed between the first end and the second end of the funnel.

7. The apparatus of claim 6 , wherein the second inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a first distance from the first end along the longitudinal axis, wherein the wall has a third cross-sectional area at the first distance, the third cross-sectional area perpendicular to the longitudinal axis, the third cross-sectional area having an inner diameter that is less than the third outer diameter and greater than the second outer diameter.

8. The apparatus of claim 7 , wherein a third inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a second distance from the first end along the longitudinal axis, wherein the wall has a fourth cross-sectional area at the second distance, the fourth cross-sectional area perpendicular to the longitudinal axis, the fourth cross-sectional area having an inner diameter that is less than the second outer diameter and greater than the first outer diameter.

9. A method comprising:

disposing an apparatus within a wellbore formed in a subterranean formation, the apparatus comprising:

a funnel comprising:

a plurality of inlet ports and an outlet port;

a first end;

a second end; and

a wall spanning from the first end to the second end, the wall defining a longitudinal axis through the first end and the second end, the wall having a first cross-sectional area at the first end and a second cross-sectional area at the second end, the first cross-sectional area and the second cross-sectional area perpendicular to the longitudinal axis;

wherein a first inlet port of the plurality of inlet ports is disposed on the first end of the funnel, and the outlet port is disposed on the second end of the funnel;

a core disposed within the funnel, the core defining a first outer diameter, wherein the outlet port has an inner diameter that is less than the first outer diameter of the core;

a first coating disposed on and surrounding an outer surface of the core, the first coating defining a second outer diameter, the first coating configured to dissolve at a first dissolution rate in response to being exposed to water;

a second coating disposed on and surrounding an outer surface of the first coating, the second coating defining a third outer diameter, the second coating configured to dissolve at a second dissolution rate different from the first dissolution rate in response to being exposed to water; and

a third coating disposed on and surrounding an outer surface of the second coating, the third coating defining a fourth outer diameter, the third coating configured to dissolve in response to being exposed to a hydrocarbon;

receiving, by the plurality of inlet ports of the funnel, wellbore fluid from the subterranean formation, the wellbore fluid comprising a hydrocarbon and water;

directing, by the funnel, the wellbore fluid to the core;

contacting the third coating with the hydrocarbon of the wellbore fluid to dissolve the third coating;

in response to dissolving the third coating, moving the core toward the outlet port and exposing the second coating to the wellbore fluid;

contacting the second coating with the water of the wellbore fluid to dissolve the second coating;

in response to dissolving the second coating, obstructing, by the core with the second and third coatings dissolved, fluid communication between a first portion of the plurality of inlet ports and the outlet port, such that fluid flow through the apparatus and out of the outlet port decreases;

contacting the first coating with the water of the wellbore fluid to dissolve the first coating; and

in response to dissolving the first coating, obstructing, by the core with the first, second, and third coatings dissolved, fluid communication between a remaining portion of the plurality of inlet ports and the outlet port, such that fluid flow through the apparatus and out of the outlet port is prevented.

10. The method of claim 9 , wherein the second dissolution rate of the second coating is less than the first dissolution rate of the first coating.

11. The method of claim 10 , wherein the first coating has a first thickness, the second coating has a second thickness, and a difference between the first thickness and the second thickness is less than 0.1 centimeters.

12. The method of claim 11 , wherein the third coating has a third thickness, and a difference between the third thickness and the first thickness is less than 0.1 centimeters.

13. The method of claim 12 , wherein the third thickness is in a range of from about 50% to about 100% of the first thickness.

14. The method of claim 13 ,

wherein the core coated with the first coating, the second coating, and the third coating is disposed between the first end and the second end of the funnel.

15. The method of claim 14 , wherein a second inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a first distance from the first end along the longitudinal axis, wherein the wall has a third cross-sectional area at the first distance, the third cross-sectional area perpendicular to the longitudinal axis, the third cross-sectional area having an inner diameter that is less than the third outer diameter and greater than the second outer diameter, such that a center of the core with the second and third coatings dissolved is disposed between the second inlet port and the outlet port, thereby obstructing fluid communication between the first portion of the plurality of inlet ports and the outlet port.

16. The method of claim 15 , wherein a third inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a second distance from the first end along the longitudinal axis, wherein the wall has a fourth cross-sectional area at the second distance, the fourth cross-sectional area perpendicular to the longitudinal axis, the fourth cross-sectional area having an inner diameter that is less than the second outer diameter and greater than the first outer diameter, such that the center of the core with the first, second, and third coatings dissolved is disposed between the third inlet port and the outlet port, thereby obstructing fluid communication between the plurality of inlet ports and the outlet port, such that fluid flow through the apparatus and out of the outlet port is prevented.

17. A system comprising:

a tubular disposed within a wellbore formed in a subterranean formation; and

an inflow control device disposed on the tubular, the inflow control device configured to control flow of wellbore fluid from the wellbore and into the tubular, the inflow control device comprising:

a funnel comprising:

a first end;

a second end;

a wall spanning from the first end to the second end, the wall defining a longitudinal axis through the first end and the second end, the wall having a first cross-sectional area at the first end and a second cross-sectional area at the second end, the first cross-sectional area and the second cross-sectional area perpendicular to the longitudinal axis, the first cross-sectional area greater than the second cross-sectional area;

a plurality of inlet ports, wherein a first inlet port of the plurality of inlet ports is disposed on the first end of the funnel, and a second inlet port of the plurality of inlet ports is disposed on the wall of the funnel; and

an outlet port disposed on the second end of the funnel;

a core disposed within the funnel, the core defining a first outer diameter, wherein the outlet port has an inner diameter that is less than the first outer diameter of the core;

a first coating disposed on and surrounding an outer surface of the core, the first coating defining a second outer diameter, the first coating configured to dissolve at a first dissolution rate in response to being exposed to water;

a second coating disposed on and surrounding an outer surface of the first coating, the second coating defining a third outer diameter, the second coating configured to dissolve at a second dissolution rate different from the first dissolution rate in response to being exposed to water; and

a third coating disposed on and surrounding an outer surface of the second coating, the third coating defining a fourth outer diameter, the third coating configured to dissolve in response to being exposed to a hydrocarbon.

18. The system of claim 17 , wherein

the core coated with the first coating, the second coating, and the third coating is disposed between the first end and the second end of the funnel,

the second inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a first distance from the first end along the longitudinal axis, wherein the wall has a third cross-sectional area at the first distance, the third cross-sectional area perpendicular to the longitudinal axis, the third cross-sectional area having an inner diameter that is less than the third outer diameter and greater than the second outer diameter, and

a third inlet port of the plurality of inlet ports is disposed on the wall of the funnel at a second distance from the first end along the longitudinal axis, wherein the wall has a fourth cross-sectional area at the second distance, the fourth cross-sectional area perpendicular to the longitudinal axis, the fourth cross-sectional area having an inner diameter that is less than the second outer diameter and greater than the first outer diameter.