Magnetization Evolution in Network Models of Porous Rock under Conditions of Drainage and Imbibition

Abstract

Surface-enhanced relaxation of nuclear magnetization in fully and partially saturated water-wet porous media is studied using a pore network simulator. The simulator is based on a description of the pore space in terms of a regular cubic lattice of pores and throats following respective size distributions. The latter are obtained from geometric characterization of 3D stochastic replicas of real porous rock samples. Concepts of percolation theory are used to simulate the pore-scale distribution of a strongly wetting phase under conditions of quasistatic drainage by or imbibition against a nonwetting phase. The results of these simulations compare favorably with experimental mercury intrusion/retraction curves. The equations governing magnetization evolution in a connected pore system are then solved by matrix diagonalization for different values of wetting-phase saturation along the primary drainage and secondary imbibition paths. Analysis of the corresponding spectra of decay rates provides new insights regarding the influence of pore structure (pore and throat size distributions, spatial correlation), surface relaxation strength, and fluid distribution on diffusive coupling between pores. For pore and throat size distributions and surface relaxation strength representative of sandstones, diffusive coupling is quite important, especially under conditions of partial saturation. Remarkably, simulations show that correlated heterogeneity is the main reason pores appear poorly coupled with respect to NMR relaxation—an assumption underlying the correspondence between pore size and relaxation time distributions. Finally, for a given value of wetting-phase saturation, the history of saturation change (drainage or imbibition) is shown to have a profound effect on the spectrum of decay rates.