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In this paper, a novel fractal model for the invasion depth of fluid through the tortuous capillary bundle with roughened surfaces in porous media is proposed. The capillary pressure effect is considered in the proposed model. The proposed model is expressed as a function of structure parameters of porous media, including the relative roughness, the fractal dimension for pore size distribution, the contact angle, the density, the gravitational acceleration, the tortuosity and porosity. The invasion depth can be quantitatively characterized by the proposed model. By using the fractal theory, the effect of relative roughness on the invasion depth is discussed. It is observed that the invasion depth decreases with increasing the relative roughness of the tortuous capillary bundle with roughened surfaces. In addition, it is found that the invasion depth increases with the increase of the invasion time. The proposed model predictions are in good agreement with the available experimental data. Each parameter in our model has clear a distinct physical meaning, which may contribute to comprehend the better understanding of seepage mechanisms.

Many scholars have studied the interporosity flow function (IFF) and shape factor. However, the existing research does not consider the complex microstructure of dual media and the influence of fluid types on interporosity flow. In this paper, the anisotropic IFF and shape factor model of power-law fluid in smooth and rough fracture dual media are established by using the rough capillary bundle model and considering the influence of the microstructure of dual media and the type of fluid. The relationship between IFF, shape factor, and relative roughness in dual media is studied. It is found that the relative roughness is inversely proportional to the IFF and inversely proportional to the shape factor. In addition, the model is compared with the existing research and experimental data to verify the rationality of the model.

In this work, a new gas transport model for shale reservoirs is constructed by embedding randomly distributed roughened tree-like bifurcation networks into the matrix porous medium. We constructed apparent permeability models for different shale gas flow mechanisms based on fractal theory, taking into account the effects of relative roughness and surface diffusion. The effects of bifurcation structure parameters as well as shale gas parameters on different apparent permeabilities are systematically analyzed. It is found that the permeability generally shows a decreasing trend with the increase in pore pressure, but the effect on viscous flow is inconsiderable. In addition, larger porosity, fractal dimension and bifurcation levels lead to increased permeability of different mechanisms. Whereas, the increase in the bifurcation levels implies a greater flow resistance, resulting in a decreased permeability. In addition, The relative roughness hinders the development of total permeability but favors surface diffusion permeability. Moreover, larger length ratios and diameter ratios are beneficial to the shale gas flow.

In this paper, the gas-water two-phase flow characteristics of rock media are studied based on fractal theory and the relative roughness model, and the analytical model of gas-water relative permeability of rock pores with relative roughness is derived. Through numerical simulation, it is found that the maximum flow velocity in the rough microchannel is greater than the maximum flow velocity in the smooth microchannel, but the average flow velocity in the rough microchannel is less than the average flow velocity in the smooth microchannel. The theoretical model results show that the dimensionless permeability of gas-water two-phase flow is inversely proportional to the fractal dimension of relative roughness and tortuosity, and the relative permeability of gas-water two-phase flow is inversely proportional to the relative roughness. The correctness of the model is verified by comparing it with the relevant experimental data.

Turbulent flow over rough boundaries is a common occurrence in nature and the subject of much interest in a range of disciplines. It has long been recognized that the geometry of the boundary (or surface) dictates the flow and turbulence structure on a mean and instantaneous time scale. However, the mechanisms linking flow characteristics to roughness geometry remain poorly quantified, which has implications for our understanding of a variety of processes, particularly those occurring in the near-boundary region. It has been demonstrated that temporal and spatial variations in flow structure are sensitive to a range of geometric parameters describing the boundary geometry. We review the experimental evidence for rough boundary/flow interactions across different disciplines. A synthesis reveals that (1) different approaches have led to the adoption of a variety of parameters that are used to describe boundary roughness, and (2) that different criteria are used to evaluate the relative effects of boundary roughness. Moreover, (3) much of the experimental data relates to idealized surfaces that do not reflect the complexity of natural boundaries, or (4) is taken in low Reynolds number flows, and generally cannot be applied to aquatic flows in nature. The implications for our understanding of near-bed aquatic processes in turbulent boundary layers are discussed, and suggestions for future research approaches are presented.