Nuclear-magnetic-resonance relaxation rates for fluid confined to closed, channel, or planar pores

Abstract

Fast-field-cycling nuclear-magnetic-resonance (FFC NMR) experimentation measures the spin-lattice relaxation rate T1-1=R1 as a function of NMR frequency f. It is a proven technique for probing the nanoscale dynamics of H1 spins over multiple timescales. In many porous systems, fluid is confined to quasi-zero-dimensional (closed), quasi-one-dimensional (channel), or quasi-two-dimensional (planar) pores. Expressions are presented for R1(f) providing simulated dispersion curves for closed, channel, and planar pores where relaxation is associated with fluid movement relative to fixed relaxation centers in the solid. It is shown that fluid confined to nanosized (1-5 nm) spaces can be identified by submillisecond relaxation times for any geometry. The shape and magnitude of R1(f) is shown to be sensitive to pore geometry at low frequency only if relaxation is dominated by the motion of pore bulk fluid. Relaxation in most porous material is dominated by slow-moving surface fluid. Here, the pore geometry can only be distinguished if the relaxation center density is known a priori and then only at very low frequency. Systems containing mixtures of closed, channel, and planar pores of similar characteristic dimension h would present as three peaks at low frequency with closed pores providing the largest R1 and planar pores the smallest. Pore size and shape variability in real systems is shown to diminish the ability to distinguish the three peaks. We show that the ratio T1/T2, where T2 is the spin-spin relaxation time, is a complex function of h, the surface diffusion time constant τ, and NMR frequency for f>1 MHz. It is shown that measurements of T1/T2 at 20 MHz in cement paste and hydrocarbon rock capture information on both τ and h.