Flow In Fractured Rock Research Articles

Mass transport in biological tissues: Comparisons between single- and dual-porosity models in the context of saline-infused Radiofrequency Ablation

Conventional method for modelling mass transport in biological tissues is based on the single-porosity (SP) model, which assumes a homogeneous pressure and concentration in the vasculature. Over the years, the dual-porosity (DP) model, which was originally derived for describing water flow in fractured rocks, has seen an increase in its application to describe flow in biological tissues. In DP models, two porous continua (the interstitium and the vasculature) co-exist within the same space. Flows in both continua are modelled explicitly, which allows for a more accurate representation of the hydraulic interaction between the interstitium and the vasculature. This raises the question on the validity and accuracy of the SP model for describing saline transport in biological tissues. This paper seeks to answer this question by performing a comparative study on the numerical predictions obtained using the SP and DP models in the context of saline-infused radiofrequency ablation (RFA). The results suggest that the SP model has a tendency to underestimate the saline penetration depth inside the tissue. Results from the present study are applicable only in the context of saline-infused radiofrequency ablation. They should not be generalized to other medical and biological applications, as comparison between the SP and DP models for these applications may yield observations that are different from those in the present study.

The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks

Rock fractures are major conduits for fluid flow in fractured rocks, and the convective heat transfer between rock fracture surfaces and circulating fluid is a critical issue in heat recovery in fractured rocks. It has been demonstrated that fracture surface roughness has a significant influence on the mechanical, hydraulic, thermal and transport behavior of single fractures. This study aimed to assess the effects of local surface roughness of fractures on fluid flow and heat transfer processes at the macroscopic scale of fracture networks. Two distributions of Joint Roughness Coefficient (JRC) were determined based on the JRC data in Oskarshamn/Forsmark, Sweden and Bakhtiary, Iran. Two empirical models relating hydraulic apertures to mechanical apertures were considered. A total of ninety-one realizations that considered different JRC distributions and empirical models of mechanical-hydraulic apertures were studied. The results show that fracture surface roughness can affect the fluid flow and heat transfer processes in fracture networks to various extents, mainly depending on the empirical models of mechanical-hydraulic apertures. In other words, the role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks is critical, when using a model of mechanical-hydraulic apertures that predicts significant reduced hydraulic apertures. Discrete fracture networks models with the normal distribution of JRC are less permeable than those with the lognormal distribution of JRC, using the fitting parameters of in-situ JRC data.

Modelling Methods Attached to the Research of Groundwater Flow in Fractured Rocks – Theories, Laboratory and Numerical Modelling

There are serious efforts worldwide to better understand and model groundwater flow in fractured rocks and karst aquifers. This study summarizes the major theories and idealizations used for describe flow in fractured rocks and presents a laboratory model and numerical models which were made for this purpose. The laboratory model originally made by Ollős and Nemeth in 1960 was rebuilt in MODFLOW-CFP. The usability of both modelling method was analysed. Based on the experience of this modelling an existing cave system was modelled with CFP. The Molnar Janos Cave – a karst cave almost filled with water – was analysed with the tool of numerical modelling to better understand the flow in cave conduits.

Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs

The Distinct Element Method (DEM) represents a rock mass as an assembly of blocks (polygonal or polyhedral). Contacts between blocks correspond to discontinuities (i.e., fractures or joints) that can exhibit non-linear mechanical behavior, including slip and opening. If flow in rock fracture is approximated using the lubrication equation, coupled hydro-mechanical DEM models can be used for simulation of rock mass treatment by fluid injection. However, this approach has a limited capability for simulating fracture propagation. The synthetic rock mass (SRM) concept overcomes this limitation. In SRM, the bonded particle model (BPM), which is an assembly of circular or spherical particles bonded to each other, represents deformation and damage of intact rock. If pre-existing discontinuities are represented in the BPM, the resulting model, referred to as SRM, has the capability of simulating hydraulic fracturing in naturally fractured reservoirs. The model delivers a pattern of hydraulic fractures that evolves in response to both intact rock fracturing and sliding and opening of pre-existing joints.

Numerical modeling of porous flow in fractured rock and its applications in geothermal energy extraction

Understanding the characteristics of hydraulic fracture, porous flow and heat transfer in fractured rock is critical for geothermal power generation applications, and numerical simulation can provide a powerful approach for systematically and thoroughly investigating these problems. In this paper, we present a fully coupled solid-fluid code using discrete element method (DEM) and lattice Boltzmann method (LBM). The DEM with bonded particles is used to model the deformation and fracture in solid, while the LBM is used to model the fluid flow. The two methods are two-way coupled, i.e., the solid part provides a moving boundary condition and transfers momentum to fluid, while the fluid exerts a dragging force to the solid. Two widely used open source codes, the ESyS_Particle and the OpenLB, are integrated into one code and paralleled with Message Passing Interface (MPI) library. Some preliminary 2D simulations, including particles moving in a fluid and hydraulic fracturing induced by injection of fluid into a borehole, are carried out to validate the integrated code. The preliminary results indicate that the new code is capable of reproducing the basic features of hydraulic fracture and thus offers a promising tool for multiscale simulation of porous flow and heat transfer in fractured rock.

Modelling of Groundwater Flow in Fractured Rocks

Traditional groundwater flow modelling is based on the Darcy's law which is valid when the flow is laminar. However, the water flow in fractured aquifers can be non-laminar in discontinuities and in this case the Darcy's law is not valid. That is why a numerical solver is needed which is able to model both laminar and non-laminar flows. The MODFLOW-CFP by USGS is one of the programs that can be used for this issue.Additionally to numerical experiments physical modelling can be also a useful and effective tool to explore the flow in fractured media in details. Besides some international published case studies exists a less-known Hungarian conduit model by Öllős & Németh (1960). In this study the Öllős-Németh's conduit model was rebuilt in the modified MODFLOW-CFP (CFPv2). The goal of this modelling study was to reach good agreement between the results of the numerical model and the measurements. After having studied many numerical cases and by means of sensibility analysis, the CFP model was verified. Based on the verification the model is applicable to simulate non-laminar flows in fractured rocks not only in laboratory-scale but even in real cases.Following the international practice the MODFLOW-CFP is a usable tool to learn more about a well-developed karst aquifer in Hungary. Using the numerical model the flow in this karst area can be described in detail and more precisely.

Evaluation of Hydraulic Aperture of the Joints of Behesht Abad Dam Foundation, Iran

The fluid flow in rock fractures during shear processes has been an important issue in rock mechanics. During shearing, because of the stiffer rock matrix, most deformation occurs in the joints, in the form of normal and shear displacement. Since the joints are rough, deformations will also change the joint aperture and fluid flow. In this article, the hydraulic apertures of the joints of dolomitic limestone foundation of Behesht Abad dam are investigated. Firstly, geological data during a site investigation phase in dam site is gathered, and then related calculations are done and the hydraulic conductivity of the joints is evaluated. The results indicate that the hydraulic conductivity of the joints is reasonable.

A New Geometrical Model of Fluid Flow in Rock Fractures for Valid Application of the Cubic Law

The cubic law (CL) is one of the most commonly applied physical laws for flow through rock fractures and fractured media, but many studies indicate that the CL is often not adequate. We investigate the establishment conditions of valid applying the “cubic law” to flow in fractures. A dimensional analysis of the N-S equations yields three conditions for the applicability of cubic law, as a leading order approximation in a local fracture segment with parallel walls. These conditions may not be met in many natural rock fractures as whole and demonstrate that the “cubic law” should be exactly applied in local segments (local cubic law, LCL). In this way, a new 2D discrete equivalent model for natural rough fractures is introduced, and its equivalent aperture and flow formulation are derived. By comparing the developed model and experimental results of different fractures, good accuracy was found, and the model was validated. The model could be useful for theory studies of flows through real rock fractures.

Prediction of permeability in dual fracture media by multivariate regression analysis

Abstract One of the most important characteristics of naturally fractured rocks for simulating the flow in the hydrocarbon reservoir is permeability. There are two major approaches in modeling fluid flow in fractured rocks: the discrete fracture network (DFN) model which is a special case of DFM models where fractures and matrix of rock mass are treated explicitly. DFN models consider the flow only in fracture pattern and neglect the rock matrix conductivity, and the dual porosity (DP)/dual fracture (DF) model. In the latter method two overlaid media are considered: rock matrix and fractures. In this study the permeability of 2D fractured and permeable rock matrix is calculated using a distinct element method when the rock matrix is modeled by Voronoi tessellations. Totally 860 models of the synthetic fracture networks were generated based on different fracture features with different fracture densities and aperture patterns and different sizes of Voronoi tessellations that exemplify different grain sizes in rock matrix and micro-apertures. According to the literature, this is the first case which such sensitivity analysis about the effect of geometrical parameters of fractures and grain patterns is considered which is the main objective of this research work. The results show a significant difference between calculated permeability of dual fracture models and discrete fracture network (DFN) models. Using all calculated models permeability, a practical equation is proposed that consists of different statistical and fractal characteristics of fracture patterns using multivariate regression analysis (MRA). High correlation coefficient value was emerged between different input parameters. Thus the principal component regression (PCR) was used to eliminate this problem.

Brittle structures focused on subtle crustal heterogeneities: implications for flow in fractured rocks

Host rock mechanical heterogeneities influence the spatial distribution of deformation structures and hence predictions of fault architecture and fluid flow. A critical factor, commonly overlooked, is how rock mechanical properties can vary over time, and how this will alter deformation processes and resultant structures. We present field data from an area in the Borborema Province, NE Brazil, that demonstrate how temporal changes in deformation conditions, and consequently processes, exert a primary control on the spatial distribution and geometric attributes of evolving deformation structures. Furthermore, each temporal deformation phase imparted different hydraulic architecture. The earliest flowing structures are localized upon subtle ductile heterogeneities. Following fault formation, both fault core and damage zone were flow conduits. In later stages of faulting pseudotachylyte welding created a low-permeability fault core and annealed high-permeability fractures within the fault damage zone. Modern flow occurs along a zone of later open shear fractures, defined by the mechanical strength contrast between the host rock and annealed fault. This second hydraulically conductive zone extends hundreds of metres from the edge of the annealed fault damage zone, creating a flow zone far wider than would be predicted using traditional fault scaling relationships. Our results demonstrate the importance of understanding successive deformation events for predicting the temporal and spatial evolution of hydraulically active fractures.

Detailed measurement of the magnitude and orientation of thermal gradients in lined boreholes for characterizing groundwater flow in fractured rock

• TVP measures the detail variations in the thermal gradient within a lined borehole. • Components of the thermal gradient vector characterize fracture flow through rock. • Complex thermal patterns exist in a lined borehole adjacent to fractures. • Data are reproducible and consistent with three nearby multilevel installations. • Variations in “thermal stratigraphy” are similar to hydro-stratigraphic layers. Recent developments have led to revitalization of the use of temperature logging for characterizing flow through fractured rock. The sealing of boreholes using water-filled, flexible impermeable liners prevents vertical cross connection between fractures intersecting the hole and establishes a static water column with a temperature stratification that mimics that in the surrounding formation. Measurement of the temperature profile of the lined-hole, water column (using a high sensitivity single-point probe achieving resolution on the order of 0.001 °C) has identified fractures with active flow under ambient groundwater conditions (without cross connecting flow along the borehole). Detection of flow in fractures was further improved with the use of a heater to create thermal disequilibrium in the active line source (ALS) technique and eliminate normal depth limitations in the process. This paper presents another advancement; detailed measurement of the magnitude and direction of the thermal gradient to characterize flow through fractured rock. The temperature within the water column is measured along the length of the lined hole using a temperature vector probe (TVP): four high sensitivity sensors arranged in a tetrahedral pattern oriented using three directional magnetometers. Based on these data, the horizontal and vertical components of the thermal field, as well as the direction of temperature gradient are determined, typically at depth intervals of less than 0.01 m. This probe was assessed and refined by trials in over 30 lined boreholes; the results from two holes through a fractured dolostone aquifer in Guelph, Ontario are used as exampled. Since no other device exists for measuring flow magnitude and direction under the ambient flow condition created by lined holes, the performance of the TVP is assessed by examining the reproducibility of the temperature measurements through an ALS test, and by the consistency of the results relative to other types of larger-scale information from the study area. Temperature profiles were measured in lined holes under both ambient thermal conditions and subject to ALS heating of the entire length of the holes to demonstrate resolution and reproducibility. The hydraulic gradient in three-dimensional space, based on pressure measurements from three depth discrete, multilevel monitoring systems in nearby holes, was used to independently estimate variations in groundwater flow directions. The characteristics of the hydraulic and thermal regimes are compared to assess response to changes in flow in a fractured rock system. When used in the lined holes, the level of detail provided by this multi-sensor probe is much greater than that provided by a single-sensor probe and this detail strongly supports inferences concerning the relative magnitude and direction of the flow. The results of this study indicate that the details of the thermal gradient can be measured and provides superior results compared to a conventional one dimensional temperature profile, thereby substantially enhancing the characterization of groundwater flow in fractured rock.

Simulation of groundwater flow in fractured rocks using a coupled model based on the method of domain decomposition

Groundwater flow in fractured rocks is modeled using a coupled model based on the domain decomposition method. In the model, the fractured porous medium is divided into two non-overlapping sub-domains. One is the rock matrix, in which the medium is described using a continuum model. The other consists of deep fractures and fissure zones, where the medium is described using a discrete fracture network (DFN) model. The two models are coupled through the continuity of the hydraulic heads and fluxes on the common boundaries. The coupled model is used to simulate groundwater flow in a hydropower station. The results show that the model simulates groundwater levels that are in agreement with the measured groundwater levels. Furthermore, the model’s parameters relating to deep fractures and fissure zones are verified by comparing three different models (the continuum model, coupled model, and DFN model). The results show that the coupled model can capture and duplicate the hydrogeological conditions in the study domain, whereas the continuum model overestimates and the DFN model underestimates the measured hydraulic heads. A sensitivity analysis shows that fracture aperture has a considerable effect on the groundwater level. So, when the fracture aperture is large, the coupled model or DFN model is more appropriate than the continuum model in the fracture domain.

Discrete-dual-porosity model for electric current flow in fractured rock

The identification of fractures and the characterization of their properties are of critical importance in a wide variety of research fields and applications. To this end, geophysical methods are of significant interest as they can provide information regarding the spatial distribution of a number of subsurface physical properties in a rapid and noninvasive manner. Electrical resistivity surveying, in particular, has been shown in several previous investigations to exhibit sensitivity to the presence of fractures, suggesting that geoelectrical experiments may contain important information regarding how fractures are distributed and connected in the subsurface. However, a lack of suitable numerical modeling tools for electric current flow in fractured media has prevented a detailed and systematic exploration of this concept. To address this issue, we present a novel discrete-dual-porosity modeling approach that is specifically tailored to the electrical resistivity problem. With our approach, an analytical formulation for fracture-matrix current flow exchange at the fracture scale is integrated into a discrete-fracture-network model, which is then combined with a block-scale finite-volume representation of the rock matrix. Our methodology allows for low-cost and accurate simulation of electric current flow through both the fractures and matrix, and is readily applicable to complex fracture networks at relatively large scales. Although formulated here in two dimensions, this work represents an important first step toward investigating the effect of fracture-network characteristics on bulk electrical properties, as well as toward the simulation of geoelectrical survey data in realistic fractured-rock environments.

Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes

This paper experimentally investigates the role of shear processes on the variation of critical Reynolds number and nonlinear flow through rough-walled rock fractures. A quantitative criterion was developed to quantify the onset of nonlinear flow by comprehensive combination of Forchheimer's law and Reynolds number. At each shear displacement, several high-precision water flow tests were carried out with different hydraulic gradients then the critical Reynolds number was determined based on the developed criterion. The results show that (i) the Forchheimer's law was fitted very well to experimental results of nonlinear fluid flow through rough-walled fractures, (ii) the coefficients of viscous and inertial pressure drops experience 4 and 7 orders of magnitude reduction during shear displacement, respectively, and (iii) the critical Reynolds number varies from 0.001 to 25 and experiences 4 orders of magnitude enlargement by increasing shear displacement from 0 to 20 mm. These findings may prove useful in proper understanding of fluid flow through rock fractures, or inclusions in computational studies of large-scale nonlinear flow in fractured rocks.

Flow Modeling in Rock Fracture for Long Time Simulation of Geothermal Reservoirs

AbstractThe exploitation of geothermal power is an energy source with great potential for the future. But the exploration and development of deep geothermal energy is connected with high cost and risk, these require a reliable numerical prediction. The analysis of geothermal reservoir is usually interested in long time physical properties (e.g. 50–100 years). Typical CFD simulation tool could be used somehow, but the computational effort may be limited due to incompatibility of small scale heterogeneities. Here we developed flow modeling in rock fracture, which describe the different characteristic flow in different dimension. The fluid flow in tube is described by one dimensional flow (1D flow), while flow in rock fracture is modeled as two dimensional flow (2D flow) on fracture plane. The 1D flow in tube and 2D flows in fracture are coupled to represent three dimensional flows in reservoirs. The solution of coupling system (1D and 2D flow) is obtained by iterative procedure, while the flow inside 2D fracture is calculated by cellular automaton. This algorithm is relatively fast for calculating flow inside rock fracture, especially for long time behavior of 3D–geothermal reservoir. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental Investigation of Seepage Properties of Fractured Rocks Under Different Confining Pressures

The effectiveness of transmitting underground water in rock fractures is strongly influenced by the widths of the fractures and their interconnections. However, the geometries needed for water flow in fractured rock are also heavily controlled by the confining pressure conditions. This paper is intended to study the seepage properties of fractured rocks under different confining pressures. In order to do this, we designed and manufactured a water flow apparatus that can be connected to the electro-hydraulic servo-controlled test system MTS815.02, which provides loading and exhibits external pressures in the test. Using this apparatus, we tested fractured mudstone, limestone and sandstone specimens and obtained the relationship between seepage properties and variations in confining pressure. The calculation of the seepage properties based on the collection of water flow and confining pressure differences is specifically influenced by non-Darcy flow. The results show that: (1) The seepage properties of fractured rocks are related to confining pressure, i.e. with the increase of confining pressure, the permeability $$ k $$ decreases and the absolute value of non-Darcy flow coefficient $$ \beta $$ increases. (2) The sandstone coefficients $$ k $$ and $$ \beta $$ range from $$ 1.03 \times 10^{ - 18} $$ to $$ 1.53 \times 10^{ - 17} $$ m2 and $$ - 1.13 \times 10^{17} $$ to $$ - 2.35 \times 10^{18} $$ m−1, respectively, and exhibit a greater change compared to coefficients of mudstone and limestone. (3) From the regression analysis of experimental data, it is concluded that the polynomial function is a better fit than the power and logarithmic functions. The results obtained can provide an important reference for understanding the stability of rock surrounding roadways toward prevention of underground water gushing-out, and for developing underground resources (e.g. coal).

Modeling spatial fracture intensity as a control on flow in fractured rock

Spatial fracture intensity (P 32, fracture area by volume) is an important characteristic of a jointed rock mass. Although it can hardly ever be measured, P 32 can be modeled based on available geological information such as spatial data of the fracture network. Flow in a mass composed of low-permeability hard rock is controlled by joints and fractures. In this article, models were developed from a geological data set of fractured andesite in LanYu Island (Taiwan) where a site is investigated for possible disposal of low-level and intermediate-level radionuclide waste. Three different types of conceptual models of spatial fracture intensity distribution were generated, an Enhanced Baecher’s model (EBM), a Levy–Lee Fractal model (LLFM) and a Nearest Neighborhood model (NNM). Modeling was conducted on a 10 × 10 × 10 m synthetic fractured block. Simulated flow was forced by a 1% hydraulic gradient between two vertical x–z faces of the cube (from North to South) with other boundaries set to no-flow conditions. Resulting flow vectors are very sensitive to spatial fracture intensity (P 32). Flow velocity increases with higher fracture intensity (P 32). R-squared values of regression analysis for the variables velocity (V/V max) and fracture intensity (P 32) are 0.293, 0.353, and 0.408 in linear fit and 0.028, 0.08, and 0.084 in power fit. Higher R 2 values are positively linked with structural features but the relation between velocity and fracture intensity is non-linear. Possible flow channels are identified by stream-traces in the Levy–LeeFractal model.

Inversion of a set of well-test interferences in a fractured limestone aquifer by using an automatic downscaling parameterization technique

This work inverts interference hydraulic tests from a karstic aquifer modeled as a single continuum with heterogeneous hydraulic properties (hydraulic conductivity K and specific storage capacity Ss). An automatic technique of parameterization is proposed to solve the inverse problem. Sought parameters are located at the nodes of a parameter grid made of triangular elements and independently superimposed onto the calculation grid of the flow problem. The parameter grid can be refined within the process of inversion so that the solution is improved locally because increasing the number of parameters better depicts spatial heterogeneity. Applied to hydraulic tests carried out at the Hydrogeological Experimental Site (HES) of Poitiers–France, this Adaptative Multi-scale Triangulation (AMT) method of parameterization reveals that hydraulic conductivity K and hydraulic diffusion K/Ss are structured in space as correlated stochastic continuums. This structure is not imposed a priori but is found as the mere consequence of inverting drawdown data. The sought stochastic continuums are discussed and compared to previous results obtained by processing the same data with various techniques. Even though interference data show evidences of local karstic features, the hydraulic bulk behavior of the aquifer is that of a diffusive continuous medium. This reinforces the idea that at mid to large scales, flow in fractured rocks can also be handled with relevance by means of a continuous heterogeneous approach. This result would extend to fractured aquifers with local draining in open conduits as is the case in this study.

A new geometrical model for non-linear fluid flow through rough fractures

Summary Fractures in rock mass are the main flow paths and introduce as a most important attribute in rock mass hydraulic behavior. The non-linear fluid flow through rock fractures was studied in this paper. Computational domain of an artificial three-dimensional fracture is generated and used for CFD simulations. Both laminar and turbulent flow simulations were performed for a wide range of flow rates. Also, a new non-linear fluid flow formulation was developed on the basis of some geometrical and kinematical assumptions for fracture and fluid flow, respectively. Based on comparison between simulation results and developed formulation, a new geometrical model has been proposed for non-linear fluid flow through rough fractures, which suggests a polynomial expression, like Forchheimer law, to describe the dependence of pressure drop on flow rate. Finally, this model has been evaluated with experimental results of a fracture with different geometries. The results show that the predicted pressure drop for turbulent flow simulation was roughly 3–17% more than those for laminar one at the Reynolds number of 4.5–89.5, respectively. Moreover, a good accuracy was found between the proposed model and turbulent flow simulation results. These findings may prove useful for computational studies of flows through real rock fractures, or inclusions in simulators for large-scale flow in fractured rocks.

Multiple Well‐Shutdown Tests and Site‐Scale Flow Simulation in Fractured Rocks

A new method was developed for conducting aquifer tests in fractured-rock flow systems that have a pump-and-treat (P&T) operation for containing and removing groundwater contaminants. The method involves temporary shutdown of individual pumps in wells of the P&T system. Conducting aquifer tests in this manner has several advantages, including (1) no additional contaminated water is withdrawn, and (2) hydraulic containment of contaminants remains largely intact because pumping continues at most wells. The well-shutdown test method was applied at the former Naval Air Warfare Center (NAWC), West Trenton, New Jersey, where a P&T operation is designed to contain and remove trichloroethene and its daughter products in the dipping fractured sedimentary rocks underlying the site. The detailed site-scale subsurface geologic stratigraphy, a three-dimensional MODFLOW model, and inverse methods in UCODE_2005 were used to analyze the shutdown tests. In the model, a deterministic method was used for representing the highly heterogeneous hydraulic conductivity distribution and simulations were conducted using an equivalent porous media method. This approach was very successful for simulating the shutdown tests, contrary to a common perception that flow in fractured rocks must be simulated using a stochastic or discrete fracture representation of heterogeneity. Use of inverse methods to simultaneously calibrate the model to the multiple shutdown tests was integral to the effectiveness of the approach.