Numerical analysis of nuclear magnetic resonance relaxation-diffusion responses of sedimentary rock

Physics

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The nuclear magnetic resonance (NMR) relaxation-diffusion response of porous reservoir rock is frequently used, e.g. in oil field applications, to extract characteristic length scales of pore space or information about saturating fluids. External gradients are typically applied to encode for diffusion. In reservoir rocks, field inhomogeneities due to internal gradients can even at low fields be strong enough to interfere with this encoding. Furthermore, the encoding for diffusion coefficients of fluids takes a finite amount of time, during which diffusing fluid molecules can experience restricted diffusion. Both effects can combine to make the interpretation of the diffusion dimension of a relaxation-diffusion measurement difficult. We use x-ray-CT images of porous rock samples to define the solid and fluid phases of reservoir rock and simulate the full experimental pulse sequence, taking into account the static applied field, external gradients and internal gradients as a function of susceptibility of each component, and surface and bulk relaxation properties of fluids and fluid-fluid and fluid-solid interfaces. We carry out simulations of NMR relaxation-diffusion measurements, while explicitly tracking the time-dependent diffusion coefficient in each fluid as well as associated local gradients. This allows us to quantify the influence of restricted diffusion and internal gradients for common choices of experimental parameters.

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