Downhole inflow control

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 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.

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 plurality of inlet ports and an outlet port;
• 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.