A pumping system for the production of hydrocarbons with a high gas fraction, said system comprising a stationary production unit and a subsea pumping module installed on the sea bed alongside an oil production well, comprising: a first transport pipe connecting an outlet pipe from the pumping module to the stationary production unit; a second transport pipe connecting the pumping module to the annulus of the production well for the supply of drive fluid to a well pump installed at the bottom of the production well draining a reservoir; a third transport pipe connecting the outlet of the well pump to a hydrocarbon inlet pipe of the pumping module designed to deliver to the top of the module a flow of oil from said production well having a high associated gas fraction; and a flow valve located in the second transport pipe that is used to regulate how much fluid pumped by the pumping module to the first transport pipe is diverted to the second transport pipe to act as drive fluid for the well pump; the pumping module further comprising: separator equipment connected to the inlet pipe and being for separating the oil into gas and liquid phases which then respectively flow in two separate streams; a first pump, being a pump of the ESP type, designed to pump the liquid phase that has been separated by the separator equipment; a second pump, being a jet pump, designed to pump the gas phase separated by the separator equipment; an outlet pipe connected to the outlets of the first and second pumps and being for transporting mixed oil and gas away from the subsea module. a first transport pipe connecting an outlet pipe from the pumping module to the stationary production unit; a second transport pipe connecting the pumping module to the annulus of the production well for the supply of drive fluid to a well pump installed at the bottom of the production well draining a reservoir; a third transport pipe connecting the outlet of the well pump to a hydrocarbon inlet pipe of the pumping module designed to deliver to the top of the module a flow of oil from said production well having a high associated gas fraction; and a flow valve located in the second transport pipe that is used to regulate how much fluid pumped by the pumping module to the first transport pipe is diverted to the second transport pipe to act as drive fluid for the well pump; the pumping module further comprising: separator equipment connected to the inlet pipe and being for separating the oil into gas and liquid phases which then respectively flow in two separate streams; a first pump, being a pump of the ESP type, designed to pump the liquid phase that has been separated by the separator equipment; a second pump, being a jet pump, designed to pump the gas phase separated by the separator equipment; an outlet pipe connected to the outlets of the first and second pumps and being for transporting mixed oil and gas away from the subsea module. separator equipment connected to the inlet pipe and being for separating the oil into gas and liquid phases which then respectively flow in two separate streams; a first pump, being a pump of the ESP type, designed to pump the liquid phase that has been separated by the separator equipment; a second pump, being a jet pump, designed to pump the gas phase separated by the separator equipment; an outlet pipe connected to the outlets of the first and second pumps and being for transporting mixed oil and gas away from the subsea module.