Numerical simulation study on the effect of temperature on the restricted diffusion in porous media

It is of great significance to study how temperature affects the restricted diffusion in pores for an accurate evaluation of reservoir physical properties by using nuclear magnetic resonance (NMR) diffusion-transverse relaxation (D-T ₂) spectrum under reservoir temperature conditions. In this paper, we simulate the restricted diffusion and two-dimensional (2D) NMR D-T ₂ spectra of water molecules at different temperatures using random-walk method. The one-dimensional (1D) restricted diffusion simulation results show that the diffusion coefficient in the pore at room temperature decays with the diffusion time and eventually reaches a plateau. Under the condition of long-time diffusion, the ratio of restricted diffusion coefficient to bulk diffusion coefficient at different temperatures tends to be the same constant. With the increase in temperature, the simulated D-T ₂ spectra also gradually move upward. The simulated D-T ₂ spectra at all temperatures are consistent with the Padé interpolation equation. In addition, the results calculated by Padé interpolation equation demonstrate that the degree of temperature influence on the D-T ₂ spectrum of rock is quantitatively related to the pore radius, porosity and cementation index.