Nuclear Magnetic Relaxation of Pore Space Saturated With Oil and Water

Abstract

AbstractIn this paper, the basic characteristics of transverse relaxation of oil‐water saturated pore model have been discussed. Via eigenfunction expansion method, the Bloch equations controlled by diffusion effect have been solved for two simple geometrical pore space, slab and sphere, when saturated with oil and water. From the derived formulae, it can be found that nuclear magnetic relaxation is controlled by multi relaxation modes, and is associated with pore size, surface relaxivity, diffusion coefficient of pore fluid, and oil saturation. Numerical results show that for water saturated pore space, relaxation is mainly determined by pore size. And for small water‐saturated pore, the relaxation is dominated by the smallest relaxation mode and the corresponding relaxation time is proportional to pore size. Whereas for large pore space, multi exponential relaxation modes compose the pore water relaxation process, even when pore size is homogeneous. And under this situation, there is no longer a linear function between relaxation time and pore size. For water‐oil double‐phase saturated pore space, when pore size is small and as oil saturation increases, water relaxation time decreases linearly. However, when pore dimension is rather large, multiple exponential relaxation modes turn to be a single exponential mode due to the increase of oil saturation. And at the same time, the variation of relaxation time with oil saturation is non‐linear. With the formulae in the paper, the responses of the pore space model abstracted from real rock core have been calculated. Comparing with experiment results, there is close agreement.