Nuclear magnetic relaxation and the internal geometry of sedimentary rocks

In this paper we study nuclear magnetic relaxation in the pore fluid within a detrital sedimentary rock. Bloch equations are introduced for the magnetization and solved for the case of uniform magnetization, yielding a single relaxation rate linearly related to the surface to volume ratio of the pore space. The surface magnetization is then eliminated and a closed set of equations for the bulk magnetization is developed. These equations are solved in detail in a spherical pore. The results show that local uniformity within a pore is set up rapidly. We show how to partition the pore space into individual pores separated by throats and obtain a set of coupled relaxation equations for the magnetization within each pore. The equations have the form encountered in the theory of disordered materials. When the throat size is sufficiently small, the relaxation function yields directly the probability distribution of the surface to volume ratios of individual pores. Otherwise, geometric information about pores and throats is enfolded in the relaxation function.