A Comprehensive Model for Oil–water Relative Permeabilities in Low-Permeability Reservoirs by Fractal Theory

Abstract

Oil–water relative permeability curve is an important parameter for analyzing the characters of oil and water seepages in low-permeability reservoirs. The fluid flow in low-permeability reservoirs exhibits distinct nonlinear seepage characteristics with starting pressure gradient. However, the existing theoretical model of oil–water relative permeability only considered few nonlinear seepage characteristics such as capillary pressure and fluid properties. Studying the influences of reservoir pore structures, capillary pressure, driving pressure and boundary layer effect on the morphology of relative permeability curves is of great significance for understanding the seepage properties of low-permeability reservoirs. Based on the fractal theory for porous media, an analytically comprehensive model for the relative permeabilities of oil and water in a low-permeability reservoir is established in this work. The analytical model for oil–water relative permeabilities obtained in this paper is found to be a function of water saturation, fractal dimension for pores, fractal dimension for tortuosity of capillaries, driving pressure gradient and capillary pressure between oil and water phases as well as boundary layer thickness. The present results show that the relative permeabilities of oil and water decrease with the increase of the fractal dimension for tortuosity, whereas the relative permeabilities of oil and water increase with the increase of pore fractal dimension. The nonlinear properties of low-permeability reservoirs have the prominent significances on the relative permeability of the oil phase. With the increase of the seepage resistance coefficient, the relative permeability of oil phase decreases. The proposed theoretical model has been verified by experimental data on oil–water relative permeability and compared with other conventional oil–water relative permeability models. The present results verify the reliability of the oil–water relative permeability model established in this paper.

Pore-Throat Combination Characteristics and Their Effect on Gas–Water Seepage Behavior in Tight Sandstone Gas Reservoirs of the Dingbian Area, Ordos Basin, North China

“…To better understand this complex behavior, the relative permeability curves of all samples were corrected in this study, taking into consideration the slippage effect. The relative permeability curves for different types of pore-throat structures are presented in Figure , and the corresponding characteristic parameters are listed in Table , as shown in this paper …”

Pore Structure and Permeability Characterization of Tight Sandstone Reservoirs: From a Multiscale Perspective

“…Yan et al analyzed the relationship between the fractal dimension and pore structure based on fractal theory and MIP, exploring the fractal characteristics of reservoirs with different pore types . Su and Li proposed permeability calculation formulae that considered a fractal dimension. , Luo et al established a dual-medium permeability prediction model that considered fracture stress sensitivity based on the fractal dimension of the rock matrix and the tortuosity of the fracture aperture . As numerical simulation methods gradually became the mainstream method for quantitatively characterizing permeability, a numerical simulation based on micro-CT images can be used to construct a three-dimensional digital rock core reconstruction model, and then calculate its absolute permeability value through single-phase fluid simulation.…”

Determination of Starting Pressure Gradient of Oil and Water in Low-Permeability Reservoirs Using Genetic Algorithm

“…Xie et al [5] established the seepage model of the multi-stage fractured horizontal well considering stress sensitivity and the starting pressure gradient in order to evaluate its productivity, and Li and Zhang [6] presented the production calculation model in consideration of variable starting pressure gradient in the ultra-low permeability reservoir. Ye et al [7] presented the fractal model for calculation of the starting pressure gradient considering the fractal dimension of the tight oil reservoir, and Su et al [8] built the analytical model for the permeability of oil and water in the lowpermeability reservoir based on the fractal theory for porous media. Ke et al [9] studied the effect of the starting pressure gradient on the remaining oil distribution in the heavy-oil reservoirs, and Tian et al [10] addressed the different factors that affect the starting pressure gradient in the tight sandstone gas reservoirs with high water saturation.…”