Modelling of T1 dispersion effects on fluid polarization in oil flow

In this article we use numerical simulations to study the effect of T₁ dispersion on fluid polarization buildup in oil flow to characterize the sensitivity of both a conventional NMR concept (ROI located inside the polarization magnet) and a Earth's field NMR concept (ROI outside and downstream of the polarization magnet) to T₁ dispersion of flowing samples. As a polarization field in both concepts we use a 90 cm long Halbach magnet. The T₁ dispersion behavior of the oils is based on a set of crude oils that span a viscosity range of 0.7 cP up to 2·10⁴ cP and T₁ relaxation measurements for Larmor frequencies between 10 kHz and 20 MHz. Numerical simulations based on solving the Bloch-Torrey equation for the longitudinal magnetization component show that fluid polarization levels in a ROI of a Earth's field NMR system concept are much more strongly affected by T₁ dispersion than in the conventional NMR system concept. As a result, we may conclude that the Earth's field NMR system design is less robust for measuring flowing samples that show strong T₁ dispersion behavior. In comparison, the conventional NMR system design is relatively insensitive to the effect of T₁ dispersion, as T₁ dispersion effects were found to form a relatively small correction to the magnetization buildup. The conventional NMR system design consequently is the preferred implementation of a NMR system that operates on fluids with strong T₁ dispersion behavior. We show that in the presence of T₁ dispersion s = vT₁(0)/L_m* may be used as a governing parameter for fluid polarization buildup, where T₁(0) is the T₁ relaxation time in the center of the polarization magnet, and we show how an modified analytical uniform field model can be used to describe fluid polarization for a uniform flow velocity distribution in the presence of T₁ dispersion with an accuracy within 1% for the samples and field distribution considered in this study at industrially relevant flow velocities.