Configurable programmable check valve for well operations

A well production system comprising:

• a tubular body disposed in a wellbore;
• a valve assembly disposed on the tubular body, the valve assembly comprising:
• a first funnel comprising a plurality of inlet ports exposed to a pressure of an interior of the tubular body;
• a second funnel comprising a plurality of inlet ports exposed to a pressure of an exterior of the tubular body, the first funnel and the second funnel narrowing towards a connecting port, the connecting port defined by, and penetrating through, a pressure wall at least partially isolating the pressure of the interior of the tubular body from the pressure of the exterior of the tubular body;
• a first ball enclosed within the first funnel, the first ball configured to dissolve in response to contact with a first specified fluidic material;
• and
• a second ball enclosed within the second funnel, the second ball comprising a coating around a core, the coating configured to dissolve in response to contact with a second specified fluidic material.

A method of well operations, the method comprising:

• disposing, in a wellbore, a tubular body with a wellbore valve assembly disposed thereon, the valve assembly comprising:
• a first funnel comprising a plurality of inlet ports exposed to a pressure of an interior of the tubular body;
• a second funnel comprising a plurality of inlet ports exposed to a pressure of an exterior of the tubular body, the first funnel and the second funnel narrowing towards a connecting port, the connecting port defined by, and penetrating through, a pressure wall at least partially isolating the pressure of the interior of the tubular body from the pressure of the exterior of the tubular body;
• a first ball enclosed within the first funnel, the first ball configured to dissolve in response to contact with a first specified fluidic material;
• and
• a second ball enclosed within the second funnel, the second ball comprising a coating around a core, the coating configured to dissolve in response to contact with a second specified fluidic material;
• with the tubular body disposed in the wellbore and the first ball in an un-dissolved state, increasing a pressure of the interior of the tubular body such that the pressure of the interior of the tubular body exceeds a pressure of the exterior of the tubular body, thereby urging the first ball against the connecting port;
• and
• then, reducing the pressure in the interior of the tubular body such that the pressure of the exterior of the tubular body exceeds the pressure of the interior of the tubular body such that the first ball is pushed away from the ball seat, thereby permitting a flow of fluid through the connecting port from the exterior of the tubular body to the interior of the tubular body, wherein:
• (i) the first ball at least partially dissolves in response to contact with the first specified fluidic material in the flow of fluid through the connecting port from the exterior of the tubular body to the interior of the tubular body;
• and
• (ii) the coating of the second ball at least partially dissolves in response to contact with the second specified fluidic material in the flow of fluid through the connecting port from the exterior of the tubular body to the interior of the tubular body.