We use pulsed field gradient nuclear magnetic resonance to probe molecular displacements in preasymptotic Stokes flow through a pack of beads with bead diameter d=100±20μm, through a Bentheimer sandstone, and a Portland carbonate rock core, for a common range of flow velocities v and interrogation times Δ. For flow through the bead pack the length scale of the pore is well defined, as are the Peclet number Pe∊[20–80] and the Reynolds number Re<0.1. Probability distributions of molecular displacements P(ζ) are determined. The mean displacement ⟨ζ⟩, the variance σ2≡⟨(ζ−⟨ζ⟩)2⟩ and the skewness γ3≡⟨(ζ−⟨ζ⟩)3⟩ of P(ζ) are determined by a self-consistent cumulant analysis designed to minimize the systematic errors to which any cumulant analysis of non-Gaussian distributions is susceptible. Systematic errors in σ and γ arising from surface relaxation effects and flow displacements through the internal fields of rocks are quantified.

We report small angle neutron scattering (SANS) experiments on two crude oils. Analysis of the high-Q SANS region has probed the asphaltene aggregates in the nanometer length scale. We find that the radius of gyration decreases with increasing temperature. We show that SANS measurements on crude oils give similar aggregate sizes to those found from SANS measurements of asphaltenes redispersed in deuterated toluene. The combined use of SANS and V-SANS on crude oil samples has allowed the determination of the radius of gyration of large scale asphaltene aggregates of approximately 0.45 microm. This has been achieved by the fitting of Beaucage functions over two size regimes. Analysis of the fitted Beaucage functions at very low-Q has shown that the large scale aggregates are not simply made by aggregation of all the smaller nanoaggregates. Instead, they are two different aggregates coexisting.

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We derive an analytic solution for the magnetization of spins diffusing in a constant gradient field while applying a long stream of rf pulses, which is known as the steady-state free precession (SSFP) sequence. We calculate the diffusion-dependent amplitude of the free induction decay (FID) and higher order echoes for pulses with arbitrary flip angle α and pulse spacing TR. Stopped-SSFP experiments were performed in a permanent gradient field and the amplitudes of the first three higher order echoes were measured for a range of values of α and TR. Theoretical results are in excellent agreement with experimental results, using no adjustable parameters. We identify various diffusion regimes in a rather large parameter space of pulsing and relaxation times, diffusion coefficient, and flip angle and discuss the interplay of the relevant time scales present in the problem. This “phase diagram” provides a road map for designing experiments which enhance or suppress the sensitivity to diffusion. We delineate the limits of validity of the widely used ansatz put forth by Kaiser, Bartholdi, and Ernst in their seminal paper.

We determine the intrinsic longitudinal dispersivity l(d) of randomly packed monodisperse spheres by separating the intrinsic stochastic dispersivity l(d) from dispersion by unavoidable sample dependent flow heterogeneities. The measured l(d), scaled by the hydrodynamic radius r(h), coincide with theoretical predictions [Saffman, J. Fluid Mech. 7, 194 (1960)] for dispersion in an isotropic random network of identical capillaries of length l and radius a, for l/a=3.82, and with rescaled simulation results [Maier et al., Phys. Fluids 12, 2065 (2000)].

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The propagator for molecular displacements P(zeta, t) and its first three cumulants were measured for Stokes flow in monodisperse bead packs with different sphere sizes d and molecular diffusion coefficients D(m). We systematically varied the normalized mean displacement /d and diffusion length L(D)=sqrt[2D(m)t]/d. The experimental results map onto each other with this scaling. For L(D)/d<0.2 the propagator remains non-Gaussian, and thus an advection diffusion equation is not obeyed, for mean displacements measured up to >10d. A Gaussian shape is approached for large mean displacements when L(D)>0.3d.

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