Downhole transmission with wellbore fluid flow passage

A method of lifting wellbore fluid to a surface, comprising:

• running an electric submersible pump (ESP) assembly into a wellbore, wherein the ESP assembly comprises an electric motor comprising a first drive shaft, a seal section comprising a second drive shaft coupled to the first drive shaft, a gas separator comprising a third drive shaft that is configured to receive rotational power directly or indirectly from the second drive shaft, a first downhole transmission assembly comprising a flow passage fluidically coupled to a liquid phase discharge port of the gas separator, a fourth drive shaft coupled to the third drive shaft of the gas separator, a fifth drive shaft, and a first transmission that mechanically couples the fourth drive shaft to the fifth drive shaft, wherein the first transmission is configured to turn the fifth drive shaft at a slower angular speed than the angular speed of the fourth drive shaft, and a centrifugal pump assembly having a sixth drive shaft coupled to the fifth drive shaft;
• providing electric power to the electric motor;
• drawing wellbore fluid into a downhole end of the gas separator;
• flowing wellbore fluid via the liquid phase discharge port of the gas separator to a downhole end of the flow passage of the first downhole transmission assembly;
• flowing wellbore fluid an uphole end of the flow passage of the first downhole transmission assembly to an inlet of the centrifugal pump assembly;
• turning the fourth drive shaft at a first angular speed;
• turning the fifth drive shaft at a second angular speed by the first transmission of the first downhole transmission assembly, wherein the second angular speed is less than the first angular speed;
• turning the sixth drive shaft at the second angular speed;
• and
• flowing the wellbore fluid out an outlet at an uphole end of the centrifugal pump assembly.

A method of assembling an electrical submersible pump (ESP) assembly at a wellbore location, comprising:

• lowering an electric motor having a first drive shaft at least partly in the wellbore;
• coupling a downhole end of a seal section having a second drive shaft to an uphole end of the electric motor and coupling the second drive shaft to the first drive shaft;
• lowering the seal section at least partly into the wellbore;
• coupling a downhole end of a gas separator having a third drive shaft directly or indirectly to an uphole end of the seal section and coupling the third drive shaft directly or indirectly to the second drive shaft;
• lowering the gas separator at least partly into the wellbore;
• coupling a downhole end of a first downhole transmission assembly to an uphole end of the gas separator, wherein the first downhole transmission assembly comprises a flow passage fluidically coupled to a liquid phase discharge port of the gas separator, a fourth drive shaft coupled to the third drive shaft of the gas separator, a fifth drive shaft, and a first transmission that mechanically couples the fourth drive shaft to the fifth drive shaft, wherein the first transmission is configured to turn the fifth drive shaft at a slower angular speed than the angular speed of the fourth drive shaft, and a centrifugal pump assembly having a sixth drive shaft coupled to the fifth drive shaft;
• and
• coupling a downhole end of the centrifugal pump assembly to an uphole end of the first downhole transmission and coupling the sixth drive shaft to the fifth drive shaft, wherein an inlet of the centrifugal pump assembly is fluidically coupled to the flow passage of the first downhole transmission.