Bottom hole assembly for rotary drilling

A well system, comprising:

• a drill string conveyable into a wellbore;
• a housing coupled to a downhole end of the drill string and defining a flow channel therethrough for receiving a fluid from the drill string;
• a drill bit coupled to the housing and operable to drill a geologic formation and thereby extend the wellbore;
• a first flow path defined through the drill bit between a first inlet port and a first nozzle, the first inlet port being in fluid communication with the flow channel to permit a first portion of the fluid received from the drill string to flow through the first flow path and exit the drill bit through the first nozzle;
• a pump disposed in the housing and having a pump inlet in fluid communication with the flow channel to receive a second portion of the fluid received from the drill string, the pump being configured to pressurize and discharge the second portion of the fluid through a pump outlet, wherein the pump comprises:
• a cylinder axially fixed to the housing and including the pump inlet and the pump outlet;
• a piston partially received within the cylinder;
• a self-reversing screw rotatable relative to the piston;
• and
• a follower block attached to the piston;
• a power source coupled to the housing and operable to drive the pump, wherein the power source generates rotary power, and the self-reversing screw rotates in response to the power source;
• and
• a second flow path defined through the drill bit and separate from the first flow path, the second flow path extending between a second inlet port and a second nozzle, the second inlet port being in fluid communication with the pump outlet to permit the pressurized second portion of the fluid to flow through the second flow path and exit the drill bit through the second nozzle,
• wherein the follower block reciprocates the piston relative to the cylinder in response to the rotation of the self-reversing screw to intake a second portion of the fluid into the cylinder through the pump inlet and discharge the second portion of the fluid from the pump outlet into the second flow path.

A method of drilling a geologic formation, comprising:

• rotating a drill string to rotate a drill bit at a downhole end of the drill string against the geologic formation;
• pumping a fluid downhole through the drill string using a surface pump while rotating the drill string;
• discharging a first portion of the fluid from a first nozzle of the drill bit at a first discharge pressure;
• flowing a second portion of the fluid into a pump disposed in the drill string;
• rotating a rotor of a mud motor coupled to the drill string in response to fluid flow through the mud motor to generate rotational power;
• and
• transferring the rotational power to the pump through a transmission coupled to the pump to drive the pump to thereby discharge the second portion of the fluid from the pump into a flow path of the drill bit while rotating the drill string;
• discharging the second portion of the fluid from a second nozzle of the drill bit at a second discharge pressure greater than the first discharge pressure;
• and
• disconnecting the transfer of rotational power from the transmission to the pump when a predetermined torque threshold is reached.