Flow In Rough-walled Fractures Research Articles

Pore-scale insight into the effect of porous walls on fluid flow in rough-walled fractures

This study investigates the influence of porous walls on fluid flow behavior in single rough-walled fractures. A series of direct numerical simulations (DNS) were conducted to examine fluid flow through rough-walled fractures surrounded by porous walls under various hydraulic gradients. The simulation results clearly demonstrate the progressively significant impact of porous walls on flow characteristics as porosity increases. Regression analyses indicate that the Forchheimer's law, which characterizes the nonlinear flow of rock fractures, remains valid in the presence of porous walls. Moreover, increased porosity enhances fluid exchange and leads to an increased ability for single fractures to transmit fluid. Two double-parameter equations were established to quantitatively characterize the effects of porous walls on hydraulic conductivity of the fracture and fluid exchange between porous walls and the fracture. Further analysis revealed that the angle between the fracture profile and main flow direction profoundly influences the inflow/outflow exchange between the fracture and its adjacent porous walls. Moreover, the pore-scale results indicate that it is unreasonable to equate the effect of porous walls with slip boundaries as suggested in previous studies. The results and findings of this study deepen our understanding of flow behavior at the interface between the rough-walled fracture and adjacent porous walls, and they serve as a basis for accurately simulating large-scale fracture networks that consider the hydraulic contribution of fracture walls.

Pore-Scale Simulation of Gas and Water Two-Phase Flow in Rough-Walled Fractures Using the Volume of Fluid Method

The gas and water flow behavior in rough-walled hydrophilic fractures at the pore scale is crucial for understanding the gas production characteristics of naturally fractured formations. This paper presents a systematic analysis of the gas and water flow characteristics in both the single-fracture and Y-shaped junction fracture models using the volume of fluid (VOF) method. Numerical simulations showed that the gas/water rate ratio is the most significant factor influencing gas bubble/slug geometry, phase distribution, and saturation. The effect of fracture roughness and tortuosity is less significant than the gas/water ratio, whereas the total fluid rate has a negligible effect. For Y-shaped junction models, the phase distribution and referential pathways are predominantly controlled only by the channel aperture ratio, whereas the effect of the intersecting angle and fluid flow rate can be neglected.

Effects of wettability on relative permeability of rough-walled fracture at pore-scale: A lattice Boltzmann analysis

Abstract Two-phase flow in fractured geo-material plays a significant role in various subsurface processes. In this study, the realistic issues regarding two-phase flow in rough-walled fractures (RWFs) with different surface wettability are initially investigated with an improved approach based on the free energy multiphase lattice Boltzmann model and a novel rough-walled discrete fracture network model. After validation with analytical solutions, the proposed model is applied to investigate the co-current flow of two immiscible fluids in RWFs at different surface wettability conditions, and the impact of contact angle and fracture aperture on fluid flow distribution, velocity field, and relative permeability curves are further clarified. For fluid initially distributed near the surface, its relative permeability increases monotonically with its saturation. For fluid flowing as the bulk phase, when its saturation is low, its relative permeability decreases with the decrease of its saturation. However, when its saturation is high (about 0.6–0.9), its relative permeability in RWFs exposes instabilities and could be lower than that in smoothed wall fractures, meaning additional flow resistance exists in RWFs. According to our simulation results and theoretical analysis, this phenomenon is mainly caused by the wettability-related microscale fluid distribution. In RWFs with small aperture, the fluid–solid surface interaction dominates, the distribution and flow pattern of fluid flowing near the surface alters the “apparent roughness” of the fracture and further impact the relative permeability curves.

Pore-scale study of the effects of surface roughness on relative permeability of rock fractures using lattice Boltzmann method

Two-phase flow in fractured geo-material plays a significant role in various subsurface processes. Despite some success in studying two-phase flow in ideal smooth-walled fractures, the more realistic issues regarding two-phase flow in rough-walled fractures are still not well understood. In this study, an improved approach based on free energy lattice Boltzmann model is proposed to analyze the two-phase immiscible flow in the rough-walled fracture and to further estimate the relative permeability curves. The proposed model is validated by comparison with analytical results of individual fracture, and good agreement is achieved in general. Then it is used to investigate the effects of wall roughness and the initial phase distribution patterns on the co-current flow of two immiscible fluids. The simulation results demonstrate that roughness impacts phase distribution, flow patterns and relative permeability curves in a single rough-walled fracture. Rough surface increases two-phase interference and flow resistance, and an unsteady flow state appears for the non-wetting phase (NWP) when the wetting phase (WP) saturation is small. In addition, the NWP flow can either be lubricated or be resisted by the WP depending on the flow patterns and the WP saturation.

Numerical modeling of non-Newtonian fluid flow in fractures and porous media

Non-Newtonian fluids having Bingham or power-law rheology are common in many applications within drilling and reservoir engineering. Examples of such fluids are drilling muds, foams, heavy oil, hydraulic-fracturing and other stimulation fluids, and cement slurries. Despite the importance of non-Newtonian rheology, it is rarely used in reservoir simulators and fracture flow simulations. We study two types of non-Newtonian rheology: the truncated power-law (Ostwald-de Waele) fluid and the Bingham fluid. For either of the two types of non-Newtonian rheology, we construct relationships between the superficial fluid velocity and the pressure gradient in fractures and porous media. The Bingham fluid is regularized by means of Papanastasiou-type regularization for porous media and by means of a simple hyperbolic function for fracture flow. Approximation by Taylor expansion is used to evaluate the fluid velocity for small pressure gradients to reduce rounding errors. We report simulations of flow in rough-walled fractures for different rheologies and study the effect of fluid parameters on the flow channelization in rough-walled fractures. This effect is known from previous studies. We demonstrate how rheologies on different domains can be included in a fully-unstructured reservoir simulation that incorporates discrete fracture modeling (DFM). The above formulation was implemented in the open-source MATLAB Reservoir Simulation Toolbox (MRST), which uses fully implicit discretization on general polyhedral grids, including industry standard grids with DFM. This robust implementation is an important step towards hydro-mechanically coupled simulation of hydraulic fracturing with realistic non-Newtonian fluid rheology since most hydraulic fracturing models implemented so far make use of oversimplified rheological models (e.g., Newtonian or pure power-law).

Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water) flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.

Redirection and channelization of power-law fluid flow in a rough-walled fracture

Flow of non-Newtonian fluids in rough-walled rock fractures is common in many technological processes in oil and gas industry. A numerical study of power-law fluid flow in rough-walled fractures is carried out under the assumptions of the lubrication theory approximation. It is shown that, in a self-affine fracture, varying the exponent of the power-law fluid may lead to a redirection of flow compared to a Newtonian fluid flow field. This effect is observed even though the fracture landscape is isotropic, i.e. no preferential flow paths have been created in the model by e.g. relative displacement of the fracture faces. In another fracture, one that contains an obstacle represented by a spot of zero aperture, the spread of the flow around the obstacle is again controlled by the power exponent of the fluid. The fluid being more shear-thinning leads to a channelization of the flow in such a fracture. “Channelization” here refers to the fluid velocity component in the direction of the applied pressure gradient becoming larger as compared to the velocity component in the direction normal to the overall flow direction as the fluid becomes more shear-thinning. A channelization is also observed in a fracture containing a local zone of an elevated aperture. The effects of rheology on the spread and redirection of flow in a fracture of variable aperture are crucial for optimization of transport and placement of particles or tracers in natural and man-made fractures.