Nuclear Magnetic Relaxation in Porous Media

Nuclear magnetic relaxation of protons in water contained in a porous medium is discussed, taking into consideration connections between the pores. Bloch equations and boundary conditions are set up for the longitudinal component of the magnetization. By means of Green's functions, defined for the individual pores, these equations are converted to a set of integral equations. Green's functions are written out explicitly for spherical pores. The integral equations are used to obtain an approximate set of equations for the average magnetization in each pore. These equations are solved to first order in the areas of the throats connecting the pores. The total magnetization in the sample yields the probability distribution of the surface to volume ratios of individual pores, with the throat areas included in the pore surface area. The probability depends on the pore volume fraction, the throat areas, and the difference between surface to volume ratios of connected pores.