scaling invariance of crack surfaces the morphology of fractured rock surfaces is studied in terms of their scaling invariance fresh brittle fractures of granite and gneiss were sampled with a mechanical laboratory profilometer and 1 1 dimensional parallel profiles were added to build actual maps of the surfaces a first step in the scaling invariance description is a self affine analysis using three independent methods the root mean square and the maximum minimum difference of the height are shown to follow a power law with the sample length the return probability and the fourier spectrum are also computed all these approaches converge to a unique self affine exponent 0 80 analysis over a broad statistical set provides a reproducibility error of 0 05 no significant differences between the isotropic granite and the markedly anisotropic gneiss appear for the scaling exponents an analysis of the profilometer shows that the two main drawbacks of the setup are not significant in these analyses the systematic errors of the scaling analysis are estimated for the different methods isotropy of the scaling invariance within the mean fracture plane is shown either with the result obtained from different fracture orientations or with the two dimensional fourier spectrum of the surface topography itself the analysis is brought further into the multifractal framework the structure functions are shown to have power law behavior and their scaling exponent varies nonlinearly with the moment order finally the corresponding conserved process belongs to a universal multifractal class with 1 5 for the levy index and c1 0 3 for the fractal codimension of the mean singularities the three indices and c1 completely characterize the scale invariance the multifractal behavior is significant for physical properties which depend on high order moments like contact according to this study and that of other groups the self affine exponent is constant over a large range of scales and for different fracture modes and various materials this opens the possibility that there exists a form of universality in the cracking process it appears that only the prefactor of the roughness is dependent on material and mode

simulation of groundwater exchange between an unconfined aquifer and a discrete fracture network with laminar and turbulent flows abstract in this study a new approach is developed to simulate groundwater flow through both an overlying unconfined aquifer and an underlying discrete fracture network the groundwater exchange between the aquifer and the fracture network including magnitude and direction is explicitly simulated based on the mass conservation which depends on a variety of parameters related to flow and network characteristics in the overlying unconfined aquifer we approximate the flow using the dupuit assumptions in the underlying fracture network we use the cubic law and forchheimer s law to iteratively simulate laminar or turbulent flow in individual fractures depending on the reynolds number explicitly separating laminar and turbulent flows in the fractures results in a system of nonlinear equations which is iteratively solved while the flow from the overlying unconfined aquifer is a small portion of the overall flow in the underlying fracture network incorrect use of the laminar or turbulent flow equation in the fractures can lead to significant errors in simulating the flow exchange as apertures increase both the portion of the total flowrate in the aquifer and the portion of the flow in the fractures coming from the aquifer decrease as the overall hydraulic gradient increases both the portion of the total flow in the aquifer and the portion of the fracture flow that comes from the aquifer increase the portion of the total flow in the aquifer increases with the aquifer thickness while the portion of fracture flow coming from the overlying aquifer decreases

fluid flow through rough fractures in rocks i high resolution aperture determinations abstract full characterisation of rough fracture surfaces and the resulting variable apertures is an important step in the drive towards an improved understanding of the factors which control fluid flow through rocks a number of surface profiling techniques exist such as needle or laser profiling however these techniques are difficult and time consuming to apply to the total area of a fracture because they involve measuring a large number of parallel profiles which are then difficult to align accurately hence although a single profile may have high resolution in the z direction and the direction of the profile the fracture surface has a much lower resolution due to alignment errors we have developed and improved considerably a previously existing optical concept for obtaining the topography of a fracture surface where the information about surface heights is measured simultaneously the method relies on the construction of high fidelity transparent models of the fracture surface which are imaged while covered with dyed and undyed water the resulting images are converted to topography by a simple calibration procedure that makes use of the lambert beer law this method utilises in house optiprof software which provides considerably more control over the imaging process than previous attempts at optical profiling we have applied the technique to a range of rock fractures and test pieces and have found the technique to work reliably with lateral resolutions of 15 m and a vertical resolution of 15 m although all these could be improved by increasing the pixel count and the bit depth of the camera respectively

multiscale fracture network characterization and impact on flow a case study on the latemar carbonate platform a fracture network arrangement is quantified across an isolated carbonate platform from outcrop and aerial imagery to address its impact on fluid flow the network is described in terms of fracture density orientation and length distribution parameters of particular interest is the role of fracture cross connections and abutments on the effective permeability hence the flow simulations explicitly account for network topology by adopting discrete fracture and matrix description the interior of the latemar carbonate platform dolomites italy is taken as outcrop analogue for subsurface reservoirs of isolated carbonate build ups that exhibit a fracture dominated permeability new is our dual strategy to describe the fracture network both as deterministic and stochastic based inputs for flow simulations the fracture geometries are captured explicitly and form a multiscale data set by integration of interpretations from outcrops airborne imagery and lidar the deterministic network descriptions form the basis for descriptive rules that are diagnostic of the complex natural fracture arrangement the fracture networks exhibit a variable degree of multitier hierarchies with smaller sized fractures abutting against larger fractures under both right and oblique angles the influence of network topology on connectivity is quantified using discrete fracture single phase fluid flow simulations the simulation results show that the effective permeability for the fracture and matrix ensemble can be 50 to 400 times higher than the matrix permeability of 1 0 10 14 m2 the permeability enhancement is strongly controlled by the connectivity of the fracture network therefore the degree of intersecting and abutting fractures should be captured from outcrops with accuracy to be of value as analogue

connectivity permeability and channeling in randomly distributed and kinematically defined discrete fracture network models a major use of dfn models for industrial applications is to evaluate permeability and flow structure in hardrock aquifers from geological observations of fracture networks the relationship between the statistical fracture density distributions and permeability has been extensively studied but there has been little interest in the spatial structure of dfn models which is generally assumed to be spatially random i e poisson in this paper we compare the predictions of poisson dfns to new dfn models where fractures result from a growth process defined by simplified kinematic rules for nucleation growth and fracture arrest davy et al 2010 2013 this so called kinematic fracture model is characterized by a large proportion of t intersections and a smaller number of intersections per fracture several kinematic models were tested and compared with poisson dfn models with the same density length and orientation distributions connectivity permeability and flow distribution were calculated for 3d networks with a self similar power law fracture length distribution for the same statistical properties in orientation and density the permeability is systematically and significantly smaller by a factor of 1 5 to 10 for kinematic than for poisson models in both cases the permeability is well described by a linear relationship with the areal density p32 but the threshold of kinematic models is 50 larger than of poisson models flow channeling is also enhanced in kinematic dfn models this analysis demonstrates the importance of choosing an appropriate dfn organization for predicting flow properties from fracture network parameters

multi scale approach to invasion percolation of rock fracture networks summary a multi scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed inside fractures fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field the channel network is characterized and reduced to a vectorized artificial channel network acn different realizations of acns are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties typical situations in fracture networks are parameterized by fracture inclination flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures using these scaling relations obtained from the finer scales we simulate the invasion process of immiscible fluids into saturated discrete fracture networks which were studied in previous works

flow bearing structures of fractured rocks insights from hydraulic property scalings revealed by a pumping test abstract a long duration pumping test conducted over 151 days in a fractured sandstone and shale formation displays a nonstandard drawdown response and anomalous pressure diffusion which cannot be properly interpreted using existing frameworks e g homogeneous double porosity boundary conditions and fractal models an alternative framework with simple geometry and more complex hydraulic properties is thus proposed to interpret such kind of drawdown responses the analytical development allows first to demonstrate all scaling relations in this interpretation framework then and most importantly the multi scale hydraulic test provides consistent scalings of transmissivity t to storativity s over distances ranging from 83 to 383 m in a faulted area drawdown analysis in several monitoring wells shows persistent decrease of transmissivity in highly channelized fracture flow structures in one structure the cubic dependency of transmissivity to storativity identifies a well defined fault and also demonstrates the validity of poiseuille flow at a scale rarely investigated in the other structure the linear dependency of transmissivity to storativity indicates that the flow bearing structure is the surrounding fracture network well designed pumping tests combined with scaling analysis driven by geological evidence thus provide essential information on flow bearing structures for site characterization and modeling tasks at least for moderate to low permeable fractured rocks the scaling of transmissivity to storativity appears to be more informative than any separate interpretation of hydraulic property scaling exponents

the relationship of the degree of interconnection to permeability in fracture networks the problem of determining the permeability of a rock mass containing a system of finite fractures is highly dependent on both the degree of interconnection between fractures and the heterogeneity of individual fracture characteristics this paper examines how degree of interconnection affects both magnitude and nature of the fracture permeability the interconnection between given fracture sets is a complex function of 1 fracture density i e the number of fractures per unit volume and 2 the fracture extent or size unfortunately neither the density nor the extent of fractures is easily determined from borehole data however fracture frequency can be directly measured in a borehole because it is simply the number of fractures intersected per unit length of the borehole the frequency is a measure of the product of fracture density and size because the probability of a fracture intersecting a borehole is proportional to this product the effect of the degree of interconnection was investigated by numerically simulating flow in fracture networks where fracture size and density varied inversely while the product of these two parameters was held fixed directional permeabilities of a number of such networks were determined and the hydraulic behavior of each fracture system was compared to that of an ideal porous medium the permeability of the rock matrix between the fractures was assumed to be low enough to be negligible the results show that as fracture length increases the degree of interconnection increases thus for a given fracture frequency as measured in a borehole the permeability of the system increases as fracture length is increased and density is proportionally decreased also fracture systems with shorter but more dense fractures behave less like porous media than do systems with longer but less dense fractures knowledge of fracture frequency and orientation alone is inadequate when determining permeability or deciding the important question of whether a given system behaves like a porous medium for many cases where these parameters can be measured in the borehole it is critical to know fracture length in order to predict the degree of fracture network interconnection however for certain cases where fractures are larger than some critical size it may not be necessary to know fracture lengths exactly

the geology and genesis of the cleveland tin deposit western tasmania fluid inclusion and stable isotope studies the cleveland tin copper deposit comprises several lenses of pyrrhotite cassiterite stannite chalcopyrite mineralization represented by a series of interlayered chert shale beds and mineralized units occurring within an early cambrian succession of spilitic basalt mafic pyro clastic argillite chert and limestone overlain by a sequence of micaceous turbiditic graywacke and argillite south and east of the deposit is the late devonian meredith granite ore paragenesis is divided into four stages with a superimposed mineralogical zonation i quartz fluorite wolframite molybdenite cassiterite as stockwork veins in the footwall rocks ii quartz tourmaline fluorite chlorite pyrrhotite chalcopyrite cassiterite stannite as stratabound lenses parallel to the host rocks with sphalerite and arsenopyrite common at the extremities of the sulfide lenses and quartz veins with sphalerite arsenopyrite chalcopyrite and galena surrounding the deposit iii quartz arsenopyrite stannite as veins and iv fluorite carbonate quartz filling veins and vugs an extensive alteration halo in the hanging wall of the sulfide lenses is defined by increased replacement of pyroxene by actinolite nearer to the ore accompanied by an increase in k rb sn and zn and a decrease in na but is not reflected by the whole rock delta 18 o values fluid inclusion and stable isotope data reveal a systematic trend in depositional temperatures and a marked consistency in composition of the hydrothermal fluid fluids of stages i and ii were low to moderately saline 8 14 nacl but while stage i fluids were of low co 2 content the co 2 content of stage ii fluids was locally high the co 2 in stage ii fluids was probably derived from dissolution of limestone the salinity of the fluid decreased slightly to 7 to 11 percent nacl and was very low in co 2 during stage iv fluid temperatures are estimated at about 480 degrees c for stage i and 500 degrees c for stage ii and 250 degrees to 300 degrees c during stage iv the calculated delta 18 o composition of the water in the hydrothermal fluid was about 8 7 per mil for stage i 10 2 per mil for stage ii and 9 5 per mil for stage iv the delta 34 s values of the sulfides were near to 0 per mil 0 2 to 5 5 per mil throughout the mineralization the consistent salinity and the isotopic compositions indicate a magmatic source for the mineralizing fluid and a lack of mixing with meteoric water the cleveland deposit originated from the metasomatic replacement of limestone beds by tin bearing low to moderately saline fluids of initially low co 2 content derived from a granitic source related to the meredith granite

a comprehensive model combining laplace transform finite difference and boundary element method for the flow behavior of a two zone system with discrete fracture network abstract this paper provides a comprehensive model for the flow behavior of a two zone system with discrete fracture network the discrete fracture network within the inner zone is represented explicitly by fracture segments the laplace transform finite difference method is used to numerically model discrete fracture network flow with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions boundary element method and line source functions in the laplace domain are employed to derive a semi analytical flow solution for the two zone system by imposing the continuity of flux and pressure on discrete fracture surfaces the semi analytical two zone system flow model and the numerical fracture flow model are coupled dynamically the main advantage of the approach occurring in the laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined discrete times thus stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics the model is validated by comparison with the results from an analytical solution and a fully numerical solution flow regime analysis shows that a two zone system with discrete fracture network may develop six flow regimes fracture linear flow bilinear flow inner zone linear flow inner zone pseudosteady state flow outer zone pseudoradial flow and outer zone boundary dominated flow especially local solutions for the inner zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term in the inner zone pseudosteady state flow period the discrete fractures along with the boundary of the inner zone will act as virtual closed boundaries due to the pressure interference caused by fracture network and the mobility contrast of the two zones the dimensionless fracture conductivity of the fracture network determines the characteristics of the bilinear flow and the inner zone linear flow the mobility ratio m and storability ratio fs primarily influence the flow behavior of the middle to later time for a larger m the ending time of the inner zone pseudosteady state flow will be advanced and the beginning time of the outer zone pseudoradial flow will be delayed and the larger m also results in increasing of the values of the transient responses in these two periods duration of the outer zone pseudoradial flow becomes longer as fs increases the development of the outer zone boundary dominated flow is therefore postponed finally idealization of dual porosity model for the two zones will introduce two dips on the pressure derivatives on the log log plot depending on the interporosity flow parameter the time of the two dips varies however the dips are not very appreciable for the transient dual porosity model when the permeability of matrix system or fracture density is relatively high

what factors control mechanical erosion rates mechanical erosion rates are important factors in understanding how continents evolve mechanical erosion is much faster than chemical erosion especially for highly elevated regions of the earth s surface it is a principal way in which mountain ranges are removed exposing deep metamorphic roots which comprise much of the older portions of the continental masses in addition there has to be a long term balance between erosion and mountain building a new data set allows us to explore in greater detail some of the many factors which control mechanical erosion rates the most important factors are some expression of the average slope of a drainage basin some measurement of the amount of water available for erosion some environmental measurements and also a measurement of basin length for which we have no good explanation the estimate of global mechanical erosion rate obtained here is considerably lower than those obtained by some other workers some of whom have concentrated on the fact that smaller river basins tend to get eroded faster than larger basins and it is mainly smaller basins which have not been measured and which are therefore not allowed for by simple arithmetic averaging of observed erosion rates it is shown here that although smaller basins are eroded faster this is mainly because they are steeper than larger basins we also show that extrapolation of current data to smaller basins does not work because the observed continental area which is draining to the ocean cannot be attained by the simplest extrapolation scheme

fractal relations for the diameter and trace length of disc shaped fractures analytic relations are developed between the fractal parameters of a random isotropic population of disc shaped fractures and the parameters of the corresponding population of fracture traces expressed in outcrop these relations indicate that a fractal distribution of fracture diameters translates to a fractal distribution of trace lengths and that the parameters for diameter may be uniquely determined from the parameters for trace length probabilistic results demonstrate the accuracy of the analytic relations and identify nonideal behaviors at the limits of the computed trace length data it is expected that these relations will be useful in the three dimensional characterization of fracture systems in rock from in situ trace length data

beyond laboratory scale prediction for channeling flows through subsurface rock fractures with heterogeneous aperture distributions revealed by laboratory evaluation the present study evaluates aperture distributions and fluid flow characteristics for variously sized laboratory scale granite fractures under confining stress as a significant result of the laboratory investigation the contact area in fracture plane was found to be virtually independent of scale by combining this characteristic with the self affine fractal nature of fracture surfaces a novel method for predicting fracture aperture distributions beyond laboratory scale is developed validity of this method is revealed through reproduction of the results of laboratory investigation and the maximum aperture fracture length relations which are reported in the literature for natural fractures the present study finally predicts conceivable scale dependencies of fluid flows through joints fractures without shear displacement and faults fractures with shear displacement both joint and fault aperture distributions are characterized by a scale independent contact area a scale dependent geometric mean and a scale independent geometric standard deviation of aperture the contact areas for joints and faults are approximately 60 and 40 changes in the geometric means of joint and fault apertures m em joint and em fault with fracture length m l are approximated by em joint 1 102 l0 1 and em fault 1 103 l0 7 whereas the geometric standard deviations of both joint and fault apertures are approximately 3 fluid flows through both joints and faults are characterized by formations of preferential flow paths i e channeling flows with scale independent flow areas of approximately 10 whereas the joint and fault permeabilities m2 kjoint and kfault are scale dependent and are approximated as kjoint 1 10 12 l0 2 and kfault 1 10 8 l1 1

topography of natural and artificial fractures in granitic rocks implications for studies of rock friction and fluid migration abstract the topography of fractures and joints has a strong influence on their frictional strength and fracture permeability important aspects of the surfaces are the size distribution and density of contact spots between the surfaces which can be calculated using topographic data for a variety of tensile fracture surfaces in granite including both natural joints and man made fractures spectral and statistical properties are similar suggesting that man made fractures in granites can be acceptable substitutes for natural fractures in some experimental situations the topographic data indicate that fracture surfaces at scales from 0 1 to 200 mm are approximately fractal and statistically self affine a log log plot of power spectral density vs spatial frequency calculated from the fracture surfaces indicates a spectral slope of 2 3 0 2 yielding a fractal dimension d between 2 25 and 2 45 shear fracture surfaces are also fractal but have anisotropic roughness which develops during the fracture initiation process the amount of anisotropy that develops on the shear fracture surfaces is small in comparison to that exhibited by natural fault surfaces which include anisotropy that results from post failure wear and from surface evolution for fractures like those measured in this study simple simulations indicate that the aperture size and number density of wall to wall contacts between the surfaces change non linearly with relative shear displacement of the surfaces it is possible to make preliminary estimates of how the permeability and frictional properties of fractures and joints depend on the size distribution and character of the contact spots furthermore given that artificial fractures can be generated numerically with statistical properties similar to those of natural or man made fractures it is reasonable for systematic studies of the effects of roughness on friction and fluid flow to use computer designed surfaces to provide a range of variability that is not easily accessible in the laboratory

fracture size and transmissivity correlations implications for transport simulations in sparse three dimensional discrete fracture networks following a truncated power law distribution of fracture size we characterize how different fracture size transmissivity relationships influence flow and transport simulations through sparse three dimensional discrete fracture networks although it is generally accepted that there is a positive correlation between a fracture s size and its transmissivity aperture the functional form of that relationship remains a matter of debate relationships that assume perfect correlation semi correlation and non correlation between the two have been proposed to study the impact that adopting one of these relationships has on transport properties we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution the distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same we observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used while fracture network geometry plays the principal role in determining where transport occurs within the network the relationship between size and transmissivity controls the flow speed these observations indicate dfn modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics this article is protected by copyright all rights reserved

a note on the angular correction applied to fracture intensity profiles along drill core we derive the angular correction that has to be applied to borehole fracture intensities to recover the actual three dimensional distribution when the fracture networks have a length distribution we assume that the fracture intensity is calculated from the fractures that fully transect the core because of the length distribution the classical terzaghi correction which involves the cosine of fracture dip is no longer valid solutions have been calculated in the specific case of fractal fracture networks with power law length distribution we show that the terzaghi correction may significantly overestimate the frequency of fractures subparallel to the borehole the correction procedure proposed here was tested on a fracture database recorded at a study site for a repository of spent nuclear fuel located in se sweden with three outcrop maps and three boreholes a consistency between the dip distributions of outcrops and boreholes was achieved when applying the angular correcting term calculated with the power law length distribution deduced from outcrop maps

understanding hydraulic fracturing a multi scale problem despite the impact that hydraulic fracturing has had on the energy sector the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres we characterize flow and transport in shale formations across and between these scales using integrated computational theoretical and experimental efforts methods at the field scale we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir at the core scale we use triaxial fracture experiments and a finite discrete element model to study dynamic fracture crack propagation in low permeability shale we use lattice boltzmann pore scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore scale flow and transport phenomena including multi phase flow and fluids mixing a mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs finally we discuss the potential of co2 as an alternative working fluid both in fracturing and re stimulating activities beyond its environmental advantages this article is part of the themed issue energy and the subsurface

discrete fracture network model of the vapor zone leakages at the copahue geothermal field abstract the volcano hosted geothermal system of copahue is one of the most promising resources of renewable energy in argentina it is driven by a layered reservoir composed of a steam cap above a deep liquid dominated reservoir we study the surficial leakages of the shallow steam zone by performing a discrete fracture network model and a 3d forward strain stress model of the upper caprock unit the hydrothermal zones linked to steam cap leakages are subordinated to deep rooted n60 striking faults associated damage zones exhibit higher values of fracture intensity vertical and anisotropy of permeability than the host rocks joints and cross joints likely control leakage zones where the formers are subject to high dilation tendency the anfiteatro monocline might constitute the northwestern boundary of the shallow steam zone variations of h2o co2 ratio helium isotopic signature and co2 between hydrothermal zones are explained in terms of petrophysical properties of the upper ignimbrites and changes in their structural control our results suggest that the upper caprock ignimbrite avoids the decompression of the reservoir because it provides the low fractured and low permeability layer that seals the geothermal system conversely ignimbrites affected by the extensional faults system enhance the shallow vapor zone given its high fracture density and permeability

single fractures under normal stress the relation between fracture specific stiffness and fluid flow abstract fracture specific stiffness and fluid flow through a single fracture under normal stress are implicitly related through the geometry of the void space and contact area that comprise the fracture data from thirteen different rock samples each containing a single fracture show that relationships between fracture specific stiffness and fluid flow through a fracture fall into two general classes of behavior fractures either fall on a loosely defined universal curve relating fluid flow to fracture specific stiffness or else the flow is weakly dependent on fracture specific stiffness the second relationship shows that flow decreases slowly with increasing fracture specific stiffness the first relationship shows that flow decreases rapidly for increases in fracture specific stiffness to understand this behavior computer simulations on simulated single fractures were performed to calculate fluid flow fracture displacement and fracture specific stiffness as a function of normal stress simulated fractures with spatially correlated and uncorrelated aperture distributions were studied fractures with spatially uncorrelated aperture distributions tend to exhibit a weak dependence of fluid flow on fracture specific stiffness because these fractures tend to have multiple connected paths across the sample which can support flow with uniformly distributed contact area thus an increment in stress will increase the stiffness of the fracture without greatly reducing the amount of fluid flow on the other hand fractures with spatially correlated aperture distributions tend to belong to the universal relationship because correlated fractures tend to have only one or two dominant flow paths and the contact area is limited to a few regions resulting in a compliant fracture thus an increment in stress on a spatially correlated fracture will result in an increase in stiffness and rapid decrease in fluid flow these spatial correlations in fracture void geometry can be differentiated in the laboratory based on the observed fracture specific stiffness fluid flow relationship for a single fracture under normal loading

effect of advective flow in fractures and matrix diffusion on natural gas production although hydraulic fracturing has been used for natural gas production for the past couple of decades there are significant uncertainties about the underlying mechanisms behind the production curves that are seen in the field a discrete fracture network based reservoir scale work flow is used to identify the relative effect of flow of gas in fractures and matrix diffusion on the production curve with realistic three dimensional representations of fracture network geometry and aperture variability simulated production decline curves qualitatively resemble observed production decline curves the high initial peak of the production curve is controlled by advective fracture flow of free gas within the network and is sensitive to the fracture aperture variability matrix diffusion does not significantly affect the production decline curve in the first few years but contributes to production after approximately 10 years these results suggest that the initial flushing of gas filled background fractures combined with highly heterogeneous flow paths to the production well are sufficient to explain observed initial production decline lastly these results also suggest that matrix diffusion may support reduced production over longer time frames

a review of existing methods used to evaluate the hydraulic conductivity of a fractured rock mass we review the existing methods for evaluating the hydraulic conductivity of a rock mass rock mass permeability may be assessed using empirical analytical and numerical approaches empirical methods use data from in situ field tests to derive the relationship between depth and permeability by applying a curve fitting method and establishing the relationship between hydraulic conductivity and a geological index analytical methods rely on darcy and cubic laws to estimate the permeability of a rock mass by taking into account the geometrical characteristics of the joint sets analytical equations of the flow rate into underground excavations are also developed by solving the laplace equation for homogeneous and isotropic aquifers under various boundary conditions numerical modeling can evaluate the outcomes of both empirical and analytical approaches and vice versa and can provide a sensitivity analysis of the parameters that affect rock mass permeability the importance of stress and joint set characteristics is often investigated via numerical modeling as are the scale effect and directional permeability in this review paper we provide a comprehensive review of these approaches for studying rock mass permeability we summarize the advantages and disadvantages of existing methods and highlight potential future research directions

flow enhancement of a rough fracture we study experimentally and numerically the permeability of a rough fracture at laboratory scale when viscous forces are dominating low reynolds number the experimental setup includes a granite fracture surface 10 10 cm opened in mode i it allows a continuous opening of the fracture parallel to its mean plane the fracture roughness is measured and characterized in terms of self affine heterogeneities its isotropy is checked the departure from the cubic law is measured as a function of the aperture opening for mean separations between 4 0 and 10 3 mm and the pressure drop orientation by rotating the fracture by 90 degrees a strongly anisotropic hydraulic behavior is observed and results from the geometrical heterogeneities that exist up to the fracture macro scale

the impact of in situ stress and outcrop based fracture geometry on hydraulic aperture and upscaled permeability in fractured reservoirs abstract aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs this uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical and diagenetic processes that control aperture in the absence of cement bridges and high pore pressure fractures in the subsurface are generally considered to be closed however experimental work outcrop analyses and subsurface data show that some fractures remain open and that aperture varies even along a single fracture however most fracture flow models consider constant apertures for fractures we create a stress dependent heterogeneous aperture by combining finite element modeling of discrete fracture networks with an empirical aperture model using a modeling approach that considers fractures explicitly we quantify equivalent permeability i e combined matrix and stress dependent fracture flow fracture networks extracted from a large outcropping pavement form the basis of these models the results show that the angle between fracture strike and 1 has a controlling impact on aperture and permeability where hydraulic opening is maximum for an angle of 15 at this angle the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress averaging the heterogeneous aperture to scale up permeability probably results in an underestimation of flow indicating the need to incorporate full aperture distributions rather than simplified aperture models in reservoir scale flow models

influence of fracture scale heterogeneity on the flow properties of three dimensional discrete fracture networks dfn while permeability scaling of fractured media has been so far studied independently at the fracture and network scales we propose a numerical analysis of the combined effect of fracture scale heterogeneities and the network scale topology the analysis is based on 2 106 discrete fracture network dfns simulations performed with highly robust numerical methods fracture local apertures are distributed according to a truncated gaussian law and exhibit self affine spatial correlations up to a cutoff scale lc network structures range widely over sparse and dense systems of short long or widely distributed fracture sizes and display a large variety of fracture interconnections flow bottlenecks and dead ends at the fracture scale accounting for aperture heterogeneities leads to a reduction of the equivalent fracture transmissivity of up to a factor of 6 as compared to the parallel plate of identical mean aperture at the network scale a significant coupling is observed in most cases between flow heterogeneities at the fracture and at the network scale the upscaling from the fracture to the network scale modifies the impact of fracture roughness on the measured permeability this change can be quantified by the measure a2 which is analogous to the more classical power averaging exponent used with heterogeneous porous media and whose magnitude results from the competition of two effects i the permeability is enhanced by the highly transmissive zones within the fractures that can bridge fracture intersections within a fracture plane ii it is reduced by the closed and low transmissive areas that break up connectivity and flow paths citation de dreuzy j r y meheust and g pichot 2012 influence of fracture scale heterogeneity

simple mathematical model of a rough fracture a simple mathematical model of rough walled fractures in rock is described which requires the specification of only three main parameters the fractal dimension the rms roughness at a reference length scale and a length scale describing the degree of mismatch between the two fracture surfaces fractured samples collected from natural joints and laboratory specimens have been profiled to determine the range of these three parameters in nature it is shown how this surface roughness model can be implemented on a computer allowing future detailed study of the mechanical and transport properties of single fractures and the scale dependence of these properties

fracture network characterization using stress based tomography information on structural features of a fracture network at early stages of enhanced geothermal system egs development is mostly restricted to borehole images and if available outcrop data however using this information to image discontinuities in deep reservoirs is difficult wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities based on this we introduce stress based tomography in a bayesian framework to characterize the fracture network and its heterogeneity in potential egs reservoirs in this procedure first a random initial discrete fracture network dfn realization is generated based on prior information about the network the observations needed to calibrate the dfn are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes a markov chain monte carlo mcmc sequence is employed to update the dfn iteratively by a fracture translation within the domain the markov sequence compares the simulated stress profile with the observed stress profiles in the borehole evaluates each iteration with metropolis hastings acceptance criteria and stores acceptable dfn realizations in an ensemble finally this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map indicating possible fracture locations and lengths we test this methodology to reconstruct simple synthetic and more complex outcrop based fracture networks and successfully image the significant fractures in the domain

hydrogeophysical characterization of transport processes in fractured rock by combining push pull and single hole ground penetrating radar experiments the in situ characterization of transport processes in fractured media is particularly challenging due to the considerable spatial uncertainty on tracer pathways and dominant controlling processes such as dispersion channeling trapping matrix diffusion ambient and density driven flows we attempted to reduce this uncertainty by coupling push pull tracer experiments with single hole ground penetrating radar gpr time lapse imaging the experiments involved different injection fractures chaser volumes and resting times and were performed at the fractured rock research site of ploemeur in france h network hplus ore fr en for the gpr acquisitions we used both fixed and moving antenna setups in a borehole that was isolated with a flexible liner during the fixedantenna experiment time varying gpr reflections allowed us to track the spatial and temporal dynamics of the tracer during the push pull experiment during the moving antenna experiments we clearly imaged the dominant fractures in which tracer transport took place fractures in which the tracer was trapped for longer time periods and the spatial extent of the tracer distribution up to 8 meters at different times this demonstrated the existence of strongly channelized flow in the first few meters and radial flow at greater distances by varying the resting time of a given experiment we identified regions affected by density driven and ambient flow these experiments open up new perspectives for coupled hydrogeophysical inversion aimed at understanding transport phenomena in fractured rock formations

synthetic rough fractures in rocks natural fractures serve a very important function in the transport of fluid through rocks as well as in the flow of electrical charge and heat the creation of numerically synthesized fractures can aid the study of the physical processes connected with fractures synthetic fracture is the term used to describe fractures that are created numerically in such a way that they share the same mean geometrical characteristics as specific natural fractures measured by profiling by a process known as tuning we have modified methods for producing synthetic rough surfaces whose geometric properties are tuned to mimic natural fracture surfaces in rocks in order to create synthetic fractures that are statistically identical to those found in rocks one important such modification has been the incorporation of a method that allows the surfaces to be matched at long wavelengths and unmatched at short wavelengths with the degree of matching varying smoothly in between as it does for real fractures we have compared numerically synthetic fractures created using the new method with fractures created using an existing technique that uses a mismatch wavelength as a sudden discontinuity between matched and unmatched behavior as well as data from fractures in real rocks this comparison has shown that the new technique provides much more realistic numerically synthesized fractures than previous methods synthetic fractures created with the new method have been used in normal closure and fluid flow modeling and the results are reported in a companion paper

a novel three dimensional discrete fracture network model for investigating the role of aperture heterogeneity on fluid flow through fractured rock masses abstract effect of anisotropic aperture on the hydraulic properties of single rock fractures has been systematically investigated yet the aperture variability of individual fractures in 3d discrete fracture networks dfns is commonly negligible by using parallel plate fractures the present study proposed a 3d dfn model with fractures having heterogeneous apertures to estimate the influence of fracture variability on fluid flow in total a set of 1280 3d models with increasing fracture densities and fracture lengths are generated and the fluid flow through the models is simulated using a developed numerical code the influences of aperture heterogeneity and network topology on the flow pattern and permeability of 3d dfns are estimated the results show that the network topology provides a first order frame of geometrical connectivity and the heterogeneous aperture further allows the flow to select some most transmissive channels within these connected fractures the dfn model with identical apertures generates a large number of medium flow rate regions whereas the dfn model with fractures having heterogeneous apertures results in extremely low and high flow rate regions the permeability ratio of the two models is widely spread in terms of a small variation in the average mechanical aperture as a result of strong dependence on the aperture distribution the average permeability ratio increases significantly first and then approaches to 1 0 with increasing the average mechanical aperture this allows for the definition of a critical mechanical aperture above which the permeability can be properly predicted using the dfn model with fractures having identical apertures and below which the permeability is much altered by the aperture variability and the dfn model with fractures having heterogeneous apertures should be employed

hydraulic properties of fractured rock masses with correlated fracture length and aperture permeability of fractured rocks is investigated considering the correlation between distributed fracture aperture and trace length based on a newly developed correlation equation the influence of