Drilling mud flow metering system and method

A mud flow measurement method implemented by a mud flow measurement system including a Coriolis meter having a measuring tube and two or more vibration sensors, a differential pressure sensor positioned to generate a signal corresponding to a pressure drop across the Coriolis meter in response to the multiphase mud flow flowing through the mud flow measurement system, and a flow pipe configured to direct a portion of the multiphase mud flow from a well to the Coriolis meter and the differential pressure sensor, the method comprising:

• selecting a calibration curve corresponding to a drilling mud injected into the well from a library of calibration curves for the Coriolis meter corresponding to different types of drilling muds;
• determining a measured density based on a signal from the Coriolis meter and the selected calibration curve;
• determining a differential pressure across the Coriolis meter based on one or more signals generated by the differential pressure sensor;
• and
• computing a calculated mass flow rate, Qmass, of the multiphase mud flow using equation
• Q
• mass
• =
• C
• d
• ⁢
• A
• t
• 1
• -
• β
• 4
• ⁢
• 2
• ⁢
• ρ
• *
• Δ
• ⁢
• P
• where Cd is a calibration constant, At is a cross-sectional area of the measurement tube of the Coriolis meter, β is a ratio of an internal diameter of the flow pipe and an internal diameter of the measuring tube of the Coriolis meter, ρ is the density of the multiphase mud, and ΔP is the differential pressure across the Coriolis meter determined from the differential pressure sensor, wherein
• ρ is the measured density determined from the Coriolis meter.

A mud flow measurement system comprising a flow pipe, a Coriolis meter, a differential pressure sensor, and a mud flow measurement module, wherein:

• the flow pipe is configured to direct a portion of the multiphase mud flow from a well to the Coriolis meter and the differential pressure sensor;
• the Coriolis meter comprises a measuring tube and two or more vibration sensors;
• the measuring tube is induced to oscillate;
• the vibration sensors are positioned at different locations along the measuring tube;
• each vibration sensor is configured to generate a signal in response to the multiphase mud flow through the Coriolis meter from the well;
• the differential pressure sensor is positioned to generate a signal corresponding to a pressure drop across the Coriolis meter in response to the multiphase mud flow flowing through the mud flow measurement system;
• and
• the mud flow measurement module is coupled to the Coriolis meter and the differential pressure sensor, and is configured to
• select a calibration curve corresponding to a drilling mud injected into the well from a library of calibration curves for the Coriolis meter corresponding to different types of drilling muds,
• determine a measured mass flow rate based on the signal from each of the vibration sensors of the Coriolis meter and the selected calibration curve,
• determine a differential pressure across the Coriolis meter based on one or more signals generated by the differential pressure sensor, and
• compute a calculated density, p, of the multiphase mud flow based on the measured mass flow rate from the Coriolis meter and the differential pressure across the Coriolis meter.