The Relation of Pore Size to NMR T2 Diffusional Relaxation in Porous Media

Abstract

Abstract A thorough understanding of the NMR relaxation mechanisms of fluids in rocks is of central importance to modern NMR log interpretation. The T1 and T2 bulk fluid response and surface relaxivity are currently better characterized than is the T2 diffusional relaxation. This latter T2 relaxation mechanism is a phasing incoherency which develops as the molecules that bear the proton spins diffuse across strong internal field gradients generated by the susceptibility contrast between rock and pore fluid when a sample is placed in a magnetic field. The CPMG T2 measurement pulse sequence is unable to refocus the spins effectively when they are subject to such a time-varying internal field, and the observable signal decays. To characterize this diffusional loss mechanism, the proton T2 relaxation rate at 2 MHz in synthetic mono-disperse porous media was studied as a function of pore size, pore fluid and CPMG inter-pulse spacing τ. The results are compared to higher field data (85 MHz) and to relaxations in Berea sandstone and Bedford limestone. In addition, the effects of a static applied gradient G were investigated. Over the entire range of τ, the T2 diffusional relaxation rate had a well-defined inverse dependence on pore radius. As expected, mono-disperse samples were adequately characterized by a single exponential decay. For small values of the refocusing time τ (the CPMG inter-pulse spacing), the T2 diffusional relaxation rate was proportional to τ. For large τ, this relaxation was independent of τ. The relationship of the effects of τ and G on T2 relaxation are developed to quantitatively explain how the CPMG T2 measurements in static field gradients of logging tools differ from the results done with lab spectrometers without gradients.