A FRACTAL-MONTE CARLO APPROACH TO MODEL OIL AND WATER TWO-PHASE SEEPAGE IN LOW-PERMEABILITY RESERVOIRS WITH ROUGH SURFACES

Abstract

The capillary pressure and relative permeability are the key parameters to affect the transport properties of low-permeability reservoirs. In this paper, the Fractal-Monte Carlo technique is applied to predict the oil and water relative permeabilities of low-permeability reservoirs with rough surfaces by considering the effect of tortuosity of capillaries and capillary pressure as well as roughness of capillary walls. The oil and water relative permeabilities are expressed as a function of the pore size, the area fractal dimension of pores, porosity, the water saturation, the capillary pressure, the relative roughness, the tortuosity fractal dimension and the microstructural parameters of low-permeability reservoirs with rough surfaces. It is observed that the average capillary pressure for water phase decreases with the increase of water saturation. On the other hand, it is found that the average capillary pressure for water phase increases with tortuosity fractal dimension and relative roughness. It can be found that the oil relative permeability of low-permeability reservoirs with rough surfaces increases with the increase of driving pressure. On the contrary, it can be observed that the oil and water relative permeabilities of low-permeability reservoirs with rough surfaces decrease with the increase of tortuosity fractal dimension and relative roughness. The predicted oil and water relative permeabilities obtained by the proposed Fractal-Monte Carlo simulation are shown to have a good agreement with the available experimental results. The proposed probability models for capillary pressure and relative permeability well revealed the physical mechanisms of transport properties of low-permeability reservoirs with rough surfaces.