Numerical Simulations of NMR Responses in Fractal Pore-space with the Finite Element Method

A finite element technique for simulating NMR responses in a complex porous media is developed to investigate the effects of rough inner surfaces to the NMR response of fluids in rocks. The influence on the NMR response (i.e. decay times and intensities) by changing physical and geometrical parameters of the inner surface is investigated. Attention is focused to the effect of increasing inner surface whereas volume maintains constant. The finite element program allows to investigate the NMR response of any complex two-dimensional pore-space. Simulations are designed and conducted for fully water saturated rocks. It shows that roughness shifts the T2 (distribution) to lower values and the intensities of higher modes are not negligible in rough, high surface relaxivity but still fast diffusion condition. A multi-exponential function describes the decay. Commonly used permeability vs. T2 (distribution) relationships vary in rough inner surface conditions. Estimations with the logarithmic mean of T2 (distribution) give a realistic trend for the permeability. The NMR response of fluids in a pore with rough inner surface in the fast diffusion regime between 0.1 and 1 is adequately described only by a multi-exponential function.