Reducing friction in a drill string and cleaning a wellbore

An apparatus comprising:

• a stator fluidically coupled to and rotationally fixed to a pipe, the stator comprising a bore configured to receive and flow fluid from the pipe, the stator comprising a helically undulated outer surface and two fluid ports configured to fluidically couple the helically undulated outer surface with the bore;
• a rotor rotationally coupled to and residing outside the stator, the rotor comprising a helically undulated internal surface to form, with the helically undulated outer surface of the stator, a progressive cavity extending from one of the two fluid ports to the other of the two fluid ports and configured to receive fluid from the bore of the stator to allow the fluid to rotate the rotor as the fluid flows along the progressive cavity;
• and
• a flow regulation assembly coupled to the bore between the two ports and configured to divert an amount of fluid flowing toward the progressive cavity by decreasing an amount of fluid flowing past the flow regulation assembly.

A method comprising:

• receiving, by a processor and from a sensor, fluid information including a pressure of a drilling fluid flowing along a bore of a drilling sub, the drilling sub comprising:
• a stator fluidically coupled to and rotationally fixed to a drill string, the stator comprising the bore configured to receive and flow the drilling fluid from the drill string, the stator comprising a helically undulated outer surface,
• a rotor rotationally coupled to and residing outside the stator, the rotor comprising a helically undulated internal surface to form, with the helically undulated outer surface of the stator, a progressive cavity configured to receive the drilling fluid from the bore of the stator to allow the drilling fluid to rotate the rotor as the fluid flows along the progressive cavity,
• a valve coupled to the bore, and
• a cam assembly coupled to and configured to move the valve to regulate a flow of drilling fluid along the bore;
• determining, by the processor and based on the fluid information, a flow rate of the drilling fluid required to actuate the cam assembly to regulate a flow of fluid along the bore to change a rotational speed of the rotor;
• and
• transmitting, to a receiver, the flow rate to be used by a controller or an operator to change a flow rate of the drilling fluid.