Ultrasonic differential travel time flow measurement in liquids with suspended granular solids

Abstract

Flow rates in homogeneous liquids can be determined by simultaneously transmitting ultrasonic pulses in opposite directions along the same path and measuring the travel time difference between the pulses travelling with versus against the flow. We discuss the feasibility of extending this measurement technique to flows of a liquid with suspended granular solids. Two new factors limit the accuracy of the flow measurement for this mixture. First, the solids cause spreading and attenuation of the ultrasonic pulse, reducing the travel time measurement accuracy. Second, the flow moves slightly over the travel time of the pulse, such that the oppositely directed pulses do not encounter exactly the same medium. We present lab experiments on a liquid with suspended granular solids similar to the drilling fluids which are circulated through the bit during the drilling of oil and gas wells. The flow measurement accuracy is predicted as a function of the wavelength, grain size, volume fraction of solids, path length and flow velocity.