Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.

Effects of Gravity on Foam Behavior in Roughened Model Fractures

Summary In this study, to investigate how gravity affects foam in open vertical fractures, we report foam experiments in three 1-m-long, 15-cm-wide glass-model fractures. Each fracture has a smooth wall and a roughened wall. Between the two walls is a slit-like channel representing a single geological fracture. Three model fractures (Models A, B, and C) share the same roughness and have different hydraulic apertures of 78, 98, and 128 µm, respectively. We conduct foam experiments by horizontal injection in the three model fractures placed horizontally and sideways (i.e., with the model fractures turned on their long side), and in Model A placed vertically with injection upward or downward. Direct imaging of the foam inside the model fracture is facilitated using a high-speed camera. We find that foam reaches local equilibrium (LE; where the rate of bubble generation equals that of bubble destruction) in horizontal-flow experiments in all three model fractures and in vertical-flow experiments in Model A. In fractures with a larger hydraulic aperture, foam is coarser because of less in-situ foam generation. In the vertical-flow experiments in Model A, we find that the properties of the foam are different in upward and downward flow. Compared with downward flooding, upward flooding creates a finer-texture foam, as sections near the inlet of this experiment are in a wetter state, which benefits in-situ foam generation. Moreover, less gas is trapped during upward flooding, as gravitational potential helps overcome the capillarity and moves bubbles upward. In the sideways-flow experiments, gravity segregation takes place. As a result, drier foam propagates along the top of the fractures and wetter foam along the bottom. The segregation is more significant in fractures with a larger hydraulic aperture. At foam quality 0.8, gas saturation is 27.7% greater at the top than the bottom for Model C, and 19.3% and 10.8% for Models B and A, respectively. Despite the gravity segregation in all three model fractures, water and gas are not completely segregated. All three model fractures thus represent a capillary transition zone, with greater segregation with increasing aperture. Our results suggest that the propagation of foam in vertical natural fractures meters tall and tens of meters long, with an aperture of hundreds of microns or greater, is problematic. Gravity segregation in foam would weaken its capacity in the field to maintain uniform flow and divert gas in a tall fracture over large distances.

Mechanical and hydraulic properties of the excavation damaged zone (EDZ) in the Opalinus Clay of the Mont Terri rock laboratory, Switzerland

Construction of cavities in the subsurface is always accompanied by excavation damage. Especially in the context of deep geological nuclear waste disposal, the evolving excavation damaged zone (EDZ) in the near field of emplacement tunnels is of utmost importance concerning safety aspects. As the EDZ differs from the intact host rock due to enhanced hydraulic transmissivity and altered geomechanical behavior, reasonable and location-dependent input data on hydraulic and mechanical properties are crucial. Thus, in this study, a hydromechanical characterization of an EDZ in the Mont Terri underground rock laboratory, Switzerland, was performed using three different handheld devices: (1) air permeameter, (2) microscopic camera and (3) needle penetrometer. The discrete fracture network (DFN), consisting of artificially induced unloading joints and reactivated natural discontinuities, was investigated by a portable air permeameter and combined microscopic imaging with automatic evaluation. Geomechanical and geophysical characterization of the claystone was conducted based on needle penetrometer testing at the exposed rock surface. Within the EDZ, permeable fractures with a mean hydraulic aperture of 84 ± 23 µm are present. Under open conditions, self-sealing of fractures is suppressed, and cyclic long-term fracture aperture oscillations in combination with closure resulting from convergence processes is observed. Based on measured needle penetration indices, a uniaxial compressive strength of 30 ± 13 MPa (normal to bedding) and 18 ± 8 MPa (parallel to bedding) was determined. Enhanced strength and stiffness are directly related to near-surface desaturation of the claystone and a sharp decrease in water content from 6.6 wt % to 3.7 wt %. The presented methodological approach is particularly suitable for time-dependent monitoring of EDZs since measurements are nondestructive and do not change the actual state of the rock mass. This allows for a spatially resolved investigation of hydraulic and mechanical fracture apertures, fracture surface roughness, and physico-mechanical rock parameters and their intra-facies variability.

Numerical Simulation of the Nonlinear Flow Properties in Self-Affine Aperture-Based Fractures

In order to study the effect of fracture geometry on the nonlinear flow properties in aperture-based fractures, a fractal model based on the self-affinity is proposed to characterize the three-dimensional geometry of rough-walled fractures. By solving the N–S (Navier–Stokes) equation directly, the relationships between the Forchheimer-flow characteristics, fractal dimension, and standard deviation of the aperture have been obtained. The Forchheimer equation is validated to describe the nonlinear relationship between flow rate and pressure gradient. For lower flow rate, the influence of the fractal dimension almost can be ignored, but the linear coefficient increases and the hydraulic aperture decreases with increasing standard deviation of the aperture, respectively. For larger flow rate, the nonlinear coefficient increases with the growth of the standard deviation of the aperture and fractal dimension. Thus, an empirical relationship between the nonlinear coefficient, fractal dimension, and standard deviation of aperture is proposed. In addition, the critical Reynolds number decreases with the increase of the standard deviation of the aperture and the fractal dimension, and the numerical results are generally consistent with the experimental data.

A semi-analytical approach to model drilling fluid leakage into fractured formation

Loss of circulation while drilling is a challenging problem that may interrupt operations and contaminate the subsurface formation. Analytical modeling of fluid flow in fractures is a tool that can be quickly deployed to assess drilling mud leakage into fractures. A new semi-analytical solution is developed to model the flow of non-Newtonian drilling fluid in fractured formation. The model is applicable for various fluid types exhibiting yield-power law (Herschel-Bulkley). We use finite-element simulations to verify our solutions. We also generate type curves and compare them to others in the literature. We then demonstrate the applicability of the proposed model for two field cases encountering lost circulations. To address the subsurface uncertainty, we combine the semi-analytical solutions with Monte Carlo and generate probabilistic predictions. The solution method can estimate the range of fracture conductivity, parametrized by the fracture hydraulic aperture, and time-dependent fluid loss rate that can predict the cumulative volume of lost fluid.

Hydromechanical Investigations on the Self-propping Potential of Fractures in Tight Sandstones

The hydromechanical properties of single self-propping fractures under stress are of fundamental interest for fractured-rock hydrology and a large number of geotechnical applications. This experimental study investigates fracture closure and hydraulic aperture changes of displaced tensile fractures, aligned tensile fractures, and saw-cut fractures for two types of sandstone (i.e., Flechtinger and Fontainebleau) with contrasting mechanical properties, cycling confining pressure between 5 and 30 MPa. Emphasis is placed on how surface roughness, fracture wall offset, and the mechanical properties of the contact asperities affect the self-propping potential of these fractures under normal stress. A relative fracture wall displacement can significantly increase fracture aperture and hydraulic conductivity, but the degree of increase strongly depends on the fracture surface roughness. For smooth fractures, surface roughness remains scale-independent as long as the fracture area is larger than a roll-off wavelength and thus any further displacement does not affect fracture aperture. For rough tensile fractures, these are self-affine over a larger scale so that an incremental fracture wall offset likely leads to an increase in fracture aperture. X-ray microtomography of the fractures indicates that the contact area ratio of the tensile fractures after the confining pressure cycle inversely correlates with the fracture wall offset yielding values in the range of about 3–25%, depending, first, on the respective surface roughness and, second, on the strength of the asperities in contact. Moreover, the contact asperities mainly occur isolated and tend to be preferentially oriented in the direction perpendicular to the fracture wall displacement which, in turn, may induce flow anisotropy. This, overall, implies that relatively harder sedimentary rocks have a higher self-propping potential for sustainable fluid flow through fractures in comparison to relatively soft rocks when specific conditions regarding surface roughness and fracture wall offset are met.

Effects of Gas Trapping on Foam Mobility in a Model Fracture

In enhanced oil recovery, foam can effectively mitigate conformance problems and maintain a stable displacement front, by trapping gas and reducing its relative permeability in situ. In this study, to understand gas trapping in fractures and how it affects foam behavior, we report foam experiments in a 1-m-long glass model fracture with a hydraulic aperture of 80 $$\upmu $$ μ m. One wall of the fracture is rough, and the other is smooth. Between the two is a 2D porous medium representing the aperture in a fracture. The fracture model allows direct visualization of foam inside the fracture using a high-speed camera. This study is part of a continuing program to determine how foam behaves as a function of the geometry of the fracture pore space (AlQuaimi and Rossen in Energy & Fuels 33: 68-80, 2018a). We find that local equilibrium of foam (where the rate of bubble generation equals that of bubble destruction) has been achieved within the 1-m model fracture. Foam texture becomes finer, and less gas is trapped as interstitial velocity, and pressure gradient increase. Shear-thinning rheology of foam has also been observed. The fraction of trapped gas is significantly lower in our model (less than 7%) than in 3D geological pore networks. At the extreme, when velocity increases to 7 mm/s, there is no gas trapped inside the fracture. Our experimental results of trapped-gas fraction correlate well with the correlation of AlQuaimi and Rossen (SPE J 23: 788-802, 2018b) for fracture-like porous media. This suggests that the correlation can also be applied to gas trapping in fractures with other geometries. Article Highlights We have made a lab-scale 1-meter-long transparent glass model representing a geological fracture with roughened surface, and we have implemented a direct method of image analysis to quantify the texture of bubbles in the fracture and to link the texture with the strength of the foam; We have successfully created surfactant-stabilized foam flow inside the fracture and examined its stability along the 1-meter-long fracture; We explain the mechanism of gas trapping in fractures and how it affects foam behavior. We also discuss how viscous force and capillary force affect gas trapping in fractures at our experimental conditions. Graphic Abstract