Fluid Flow In Fracture Networks Research Articles

A CLUSTERED FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR FRACTURED COAL

The fracture network in fractured coal is the main channel of coal seam gas flow. Not only the geometric topology properties (such as fractal characteristics) of a single fracture but also the connection topology properties (interconnection characteristics between fractures) of the fracture network have an important impact on the fluid flow in fracture networks. In this study, the connection topology properties of the fracture network in the fractured coal are explored based on the complex network theory for the first time. The property parameters such as the fracture node degree, the clustering coefficient, and the average path length are analyzed. It shows that the average clustering coefficient of the fracture network in fractured coal is larger, and the average path length is smaller. The connection property of the fracture network in the fractured coal presents a typical “small-world” clustering model. Further, by considering the fractal characteristics of the single fracture and the clustering characteristics of the fracture network, an improved clustered fractal discrete fracture network (DFN) model is developed. Then, based on the lattice Boltzmann method, the permeability properties of the generated clustered fractal DFNs are analyzed. The results show that the permeability of DFNs is positively correlated with the average clustering coefficient of fracture network, and negatively correlated with the fractal dimension of fracture. Therefore, the topological clustering characteristics of fracture networks and the fractal characteristics of fractures cannot be ignored in describing the fluid flow in the fracture network, and our clustered fractal DFN model provides a new idea for guiding the optimization design in DFN engineering.

Flow of non-Newtonian fluids in single fractures and fracture networks: Current status, challenges, and knowledge gaps

Flow of non-Newtonian fluids in rock fractures is ubiquitous in engineering practice and involves e.g. cement flow in tunnel grouting, drilling fluid flow when a fracture is met during drilling, and flow of fracturing fluids in hydraulic fracturing. In this review article, basic information about rheological behavior of non-Newtonian fluids is provided in Section 1. In Section 2, a summary of equations for the flow of non-Newtonian fluids between smooth parallel plates is provided, and knowledge gaps are identified, including those in two-phase flow. In Section 3, non-Newtonian fluid flow in fracture networks is reviewed, and outstanding research tasks are identified. The article concludes with a summary of current challenges in Section 4. Amongst the main knowledge gaps and challenges identified in the review and relevant for engineering geological practice are fracture flow of thixotropic fluids; two-phase flow regimes and instabilities associated with it; flow of non-Newtonian fluids through (and their mixing with Newtonian fluids at) fracture intersections; efficient algorithms for network flow at arbitrary pressure gradients; leak-off of non-Newtonian fluids through fracture walls; modelling of non-Newtonian fluids that include environmental effects and the resulting multiple couplings and multiphysics.

An efficient adaptive implicit scheme with equivalent continuum approach for two-phase flow in fractured vuggy porous media

This work investigates numerical method and equivalent continuum approach (ECA) of fluid flow in fractured porous media. The commonly used discrete fracture model (DFM) without upscaling needs full discretization of all fractures. It enjoys the merit of capturing each fracture accurately but will get in trouble with mesh partition and low computational efficiency, especially when a complex geometry is involved. In this study, we develop an efficient implicit scheme with adaptive iteration, in which an improved ECA is devised and then integrated in this scheme. Numerical studies show that the proposed numerical scheme improves the convergence condition and computational efficiency. Then, a test is conducted to demonstrate the feasibility of using superposition principle of permeability tensor in upscaling. Based on these, different strategies are applied to simulate fluid flow in fracture networks with a complex geometry. It is demonstrated that the proposed ECA is able to reproduce the results computed by DFM. The accuracy depends on resolution of background grids. The presented method enjoys a low computational cost and desirable convergence performance compared with the standard DFM in which equivalent continuum is not considered.

Using 87Sr/86Sr LA-MC-ICP-MS Transects within Modern and Ancient Calcite Crystals to Determine Fluid Flow Events in Deep Granite Fractures

The strontium isotope signature (87Sr/86Sr) of calcite precipitated in rock fractures and faults is a frequently used tool to trace paleofluid flow. However, bedrock fracture networks, such as in Precambrian cratons, have often undergone multiple fracture reactivations resulting in complex sequences of fracture mineral infillings. This includes numerous discrete calcite crystal overgrowths. Conventional 87Sr/86Sr analysis of dissolved bulk samples of such crystals is not feasible as they will result in mixed signatures of several growth zonations. In addition, the zonations are too fine-grained for sub-sampling using micro-drilling. Here, we apply high spatial resolution 87Sr/86Sr spot analysis (80 µm) in transects through zoned calcite crystals in deep Paleoproterozoic granitoid fractures using laser ablation multi-collector inductively coupled plasma mass spectrometry (LA-MC-ICP-MS) to trace discrete signs of paleofluid flow events. We compare the outermost calcite growth zone with 87Sr/86Sr values of the present-day groundwater sampled in the same boreholes to distinguish potential modern precipitates. We then connect our results to previously reported radiometric dating and C and O isotope signatures to understand the temporal history and physicochemical evolution of fluid flow within the fractures. Comparisons of modern calcite precipitated in a borehole over a period of 17 years with modern waters prove the concept of using 87Sr/86Sr as a marker for fluid origin in this environment and for how 87Sr/86Sr changed during marine water infiltration. Intermittent calcite precipitation over very long time spans is indicated in calcite of the currently open fractures, showing an evolution of 87Sr/86Sr from ~0.705–0.707—a population dated to ~1.43 billion years—to crystal overgrowth values at ~0.715–0.717 that overlap with the present-day groundwater values. This shows that high spatial resolution Sr isotope analysis of fine-scaled growth zonation within single calcite crystals is applicable for tracing episodic fluid flow in fracture networks.

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

The mechanism and quantitative descriptions of nonlinear fluid flow through rock fractures are difficult issues of high concern in underground engineering fields. In order to study the effects of fracture geometry and loading conditions on nonlinear flow properties and normalized transmissivity through fracture networks, stress-dependent fluid flow tests were conducted on real rock fracture networks with different number of intersections (1, 4, 7, and 12) and subjected to various applied boundary loads (7, 14, 21, 28, and 35 kN). For all cases, the inlet hydraulic pressures ranged from 0 to 0.6 MPa. The test results show that Forchheimer’s law provides an excellent description of the nonlinear fluid flow in fracture networks. The linear coefficient a and nonlinear coefficient b in Forchheimer’s law J=aQ+bQ2 generally decrease with the number of intersections but increase with the boundary load. The relationships between a and b can be well fitted with a power function. A nonlinear effect factor E=bQ2/(aQ+bQ2) was used to quantitatively characterize the nonlinear behaviors of fluid flow through fracture networks. By defining a critical value of E = 10%, the critical hydraulic gradient was calculated. The critical hydraulic gradient decreases with the number of intersections due to richer flowing paths but increases with the boundary load due to fracture closure. The transmissivity of fracture networks decreases with the hydraulic gradient, and the variation process can be estimated using an exponential function. A mathematical expression T/T0=1-exp⁡(-αJ-0.45) for decreased normalized transmissivity T/T0 against the hydraulic gradient J was established. When the hydraulic gradient is small, T/T0 holds a constant value of 1.0. With increasing hydraulic gradient, the reduction rate of T/T0 first increases and then decreases. The equivalent permeability of fracture networks decreases with the applied boundary load, and permeability changes at low load levels are more sensitive.

Critical hydraulic gradient for nonlinear flow through rock fracture networks: The roles of aperture, surface roughness, and number of intersections

Transition of fluid flow from the linear to the nonlinear regime has been confirmed in single rock fractures when the Reynolds number (Re) exceeds some critical values, yet the criterion for such a transition in discrete fracture networks (DFNs) has received little attention. This study conducted flow tests on crossed fracture models with a single intersection and performed numerical simulations on fluid flow through DFNs of various geometric characteristics. The roles of aperture, surface roughness, and number of intersections of fractures on the variation of the critical hydraulic gradient (Jc) for the onset of nonlinear flow through DFNs were systematically investigated. The results showed that the relationship between hydraulic gradient (J) and flow rate can be well quantified by Forchheimer's law; when J drops below Jc, it reduces to the widely used cubic law, by diminishing the nonlinear term. Larger apertures, rougher fracture surfaces, and a greater number of intersections in a DFN would result in the onset of nonlinear flow at a lower Jc. Mathematical expressions of Jc and the coefficients involved in Forchheimer's law were developed based on multi-variable regressions of simulation results, which can help to choose proper governing equations when solving problems associated with fluid flow in fracture networks.

Stress-controlled localization of deformation and fluid flow in fractured rocks

Abstract The discrete-element method (UDEC — Universal Distinct Element Code) was used to numerically model the deformation and fluid flow in fracture networks under a range of loading conditions. A series of simulated fracture networks were generated to evaluate the effects of a range of geometrical parameters, such as fracture density, fracture length and anisotropy. Deformation and fluid flow do not change progressively with increasing stress. Instability occurs at a critical stress and is charzacterized by the localization of deformation and fluid flow usually within intensively deformed zones that develop by shearing and opening along some of the fractures. The critical stress state may be described in terms of a driving stress ratio, R = (fluid pressure — mean stress)/1/2 (differential stress). Instability occurs where the R ratio exceeds some critical value, R C , in the range – 1 to −2. At the critical stress state, the vertical flow rates are characterized by a large increase in both their overal magnitude and degree of localization. This localization of deformation and fluid flow develops just prior to the critical stress state and may be characterized by means of multifractals. The stress-induced criticality and localization displayed by the models is an important phenomenon, which may help in the understanding of deformation-enhanced fluid flow in fractured rock masses.

Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self-affine surfaces

Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures' apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures' surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K approximately <delta>(beta), where <delta> is the average aperture of the fractures in the network and the exponent beta may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re approximately O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures' surfaces.

Fractal Scaling and Fluid Flow in Fracture Networks in Rock: ABSTRACT

Fractal Scaling and Fluid Flow in Fracture Networks in Rock: ABSTRACT

Challenging models for flow in unsaturated, fractured rock through exploration of small scale processes

Fluid flow in unsaturated, fractured rock is studied with respect to applied environmental problems ranging from remediation of existing contaminated sites to evaluation of potential sites for isolation of hazardous or radioactive wastes. Spatial scales for such problems vary from meters to kilometers with temporal scales from months to tens of thousands of years. Because such scales often preclude direct physical exploration of system response and detailed site characterization, we are regularly forced to use our understanding (or misunderstanding) of the underlying physical processes to predict large scale behavior. It is essential that conceptual models used as the basis for prediction be firmly grounded in physical reality. In this paper, we provide examples of how recent advances in understanding of small‐scale processes within discrete fractures may influence the behavior of fluid flow in fracture networks and ensembles of matrix blocks sufficiently to impact the formulation of intermediate‐scale effective media properties. We also explore, by means of a thought experiment, how these same small‐scale processes could couple to produce a large‐scale system response inconsistent with current conceptual models of flow through unsaturated, fractured rock.