Generating downhole motor torque and RPM of a downhole motor with a drilling fluid having a compressible portion

1 . A method for identifying an output of a downhole motor, comprising:

at a surface location, combining an incompressible fluid and a compressible fluid, resulting in a drilling fluid having an incompressible portion including the incompressible fluid and a compressible portion including the compressible fluid, the compressible portion having a surface compressible density and a surface compressible flow component;

measuring a downhole temperature and a downhole pressure of the drilling fluid;

calculating a downhole compressible fraction of the drilling fluid using the downhole temperature and the downhole pressure;

determining a motor torque and a rotational rate of a downhole motor using the downhole compressible fraction of the drilling fluid;

recommending an equipment type based on the motor torque and the rotational rate; and

when the motor torque or the rotational rate is outside of a threshold range, adjusting the incompressible portion or the compressible portion of the drilling fluid.

2 . The method of claim 1 , further comprising transmitting the downhole temperature and the downhole pressure to a surface location.

3 . The method of claim 2 , wherein transmitting the downhole temperature and the downhole pressure includes transmitting in real-time.

4 . The method of claim 1 , wherein, when the motor torque and the rotational rate are within the threshold range, maintaining the incompressible portion and the compressible portion of the drilling fluid.

5 . The method of claim 1 , wherein the downhole temperature is a first downhole temperature and the downhole pressure is a first downhole pressure, and further comprising:

measuring a second downhole temperature and a second downhole pressure of the drilling fluid;

calculating a second downhole compressible fraction of the drilling fluid using the second downhole temperature and the second downhole pressure; and

determining a second motor torque and a second rotational rate of the downhole motor using the second downhole compressible fraction of the drilling fluid.

6 . The method of claim 5 , further comprising, when the second motor torque or the second rotational rate are outside the threshold range, adjusting the incompressible portion or the compressible portion of the drilling fluid.

7 . The method of claim 1 , wherein, when the motor torque or the rotational rate is above a high threshold, adjusting the incompressible portion or the compressible portion includes reducing the incompressible portion or the compressible portion.

8 . A system for identifying an output of a downhole motor, comprising:

a processor; and

a memory in electronic communication with the processor, the memory including instructions that cause the processor to:

at a surface location, cause drilling equipment to combine an incompressible fluid and a compressible fluid, resulting in a drilling fluid having an incompressible portion of the incompressible fluid and a compressible portion of the compressible fluid, the compressible fluid having a surface compressible density and a surface compressible flow component;

measure a downhole temperature and a downhole pressure of the drilling fluid;

calculate a downhole compressible fraction of the drilling fluid using the downhole temperature and the downhole pressure;

determine a motor torque and a rotational rate of a downhole motor using the downhole compressible fraction of the drilling fluid;

recommend an equipment type based on the motor torque and the rotational rate; and

when the motor torque or the rotational rate is outside of a threshold range, adjust the incompressible portion or the compressible portion of the drilling fluid.

9 . The system of claim 8 , wherein, when the motor torque or the rotational rate is above a high threshold, adjusting the incompressible portion or the compressible portion includes reducing the incompressible portion or the compressible portion.