Velocity measurement in porous media using steady-state free precession—Analytical solution to the Bloch–Torrey equation with flow

In this study, fluid velocity is measured in a porous medium using a magnetic resonance steady state free precession (SSFP) technique. As shown theoretically and experimentally in this study, the SSFP measurement under steady flow conditions produces a periodic steady state magnetization with a strong flow sensitivity. The Bloch-Torrey equations were solved analytically using a Fourier series to predict the distortion of the steady state response due to flow. The analytical solution accurately describes the measured steady state longitudinal magnetization and transverse magnetization phase to permit the determination of the fluid velocity in a Bentheimer sandstone core plug non-invasively.