The effect of spatial variation in surface relaxivity on nuclear magnetic resonance relaxation rates

Nuclear magnetic resonance (NMR) relaxation measurements are sensitive to the physiochemical environment of water in saturated porous media and can provide information about the properties of geologic material. Interpretation of NMR data typically relies on three assumptions: that pores within the geologic material are effectively isolated such that the diffusion of a proton between pores is limited (i.e., there is weak coupling); that relaxation occurs in the fast-diffusion regime; and that surface relaxivity rho(2) is uniform throughout the measured volume. We investigated the effect of spatial variation in rho(2) on the NMR relaxation measurement and evaluated two equations relating rho(2) to the NMR relaxation rate for samples containing two types of surfaces, each with a different surface relaxivity. One equation was valid when there is weak diffusional coupling between pores, the other is valid when there is strong diffusional coupling. We prepared a suite of samples composed of quartz sand and an iron-coated quartz sand. NMR relaxation occurred in two distinct regions: the weak- and strong-coupling regions. In the weak-coupling region, the equation did not accurately represent the relationship between the two rho(2) values and the NMR relaxation rate, suggesting that further research is required to understand the effect of spatially variable rho(2) in this relaxation region. In the strong-coupling region, the equation accurately represented the relationship between the two values of rho(2) and the NMR relaxation rate. The results from these laboratory experiments represented a first step towards accounting for spatial variability in rho(2) in the interpretation of NMR data.