## Measurement of fluid viscosity in pipes using multimode ultrasonic guided wave attenuation

Remi A. Kippersunda,b,*, Per Lundeb,a and Kjell-Eivind Frøysaa

a Christian Michelsen Research AS (CMR), P.O. Box 6031 Postterminalen, N-5892 Bergen, Norway

b University of Bergen, Department of Physics and Technology, P.O. Box 7803, N-5020 Bergen, Norway

High-viscous fluid flow is becoming increasingly important in petroleum industry, in connection with flow measurement and flow assurance. Fluids undergoing rheological changes are important for process control. Density, adiabatic bulk modulus and viscosity constitute important liquid properties, and quantification of such may provide important information about the status and progress of the industrial process. Non-invasive methods for fluid characterization are of interest in this context, for operational and cost-saving reasons and to avoid interference with the industrial process.

The velocity and attenuation of elastic waves transmitted in fluid loaded solid waveguides are affected by the sound velocity, density and viscosity of the surrounding fluid. An elastic wave travelling in a solid causes deformation of the solid-fluid interface, inducing fluid motion. The coupling mechanism between the motion in the solid and the fluid depends on the geometry of the waveguide and the type of elastic wave employed. Torsional and longitudinal guided waves in pipes provide different information about the interior fluid in this context.

In the present work, attenuation of ultrasonic guided elastic waves in fluid-filled pipes is investigated theoretically and experimentally. Torsional waves in the pipe wall are excited and detected using externally mounted circumferential piezoelectric transducer arrays. The attenuation of multi-modal waveguide signals propagating in the pipe wall is used to extract the fluid density • viscosity product, employing theoretical models for ultrasonic wave propagation in plane and circumferentially layered elastic-fluid media. A multitude of modes are excited simultaneously to employ a wide frequency band, and time-reversal techniques are investigated to improve sensitivity. Measurements and simulation results are presented for fluids of different fluid viscosities.