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Keywords: Dershowitz

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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 53rd U.S. Rock Mechanics/Geomechanics Symposium, June 23–26, 2019

Paper Number: ARMA-2019-0504

... Simulation Upstream Oil & Gas Cottrell Reservoir Characterization stiffness property complex reservoir golder associate fracture network stimulation workflow fracture equation Symposium natural fracture

**Dershowitz**stiffness hydraulic fracture rock mass stress condition interaction...
Abstract

ABSTRACT: Proper understanding of the in-situ stress conditions is essential to safe, efficient, and productive development of many unconventional resources, including shale gas and oil and coal seam gas, as well as tight sandstones and carbonates. Hydraulic fracture propagation geometry, and the geometry of both inflated and reactivated natural fractures, can be difficult to predict due to their complex interaction with the natural faults and fractures, the mechanical properties of surrounding formations, and the in-situ stress field. This paper presents a combined workflow consisting of the Discrete Fracture Network (DFN) algorithm and the Finite Element Method (FEM), which provides a three-dimensional basis for simulating the interaction between natural fracture geometry, rock mechanical properties, and the in-situ stress conditions. Furthermore, the developed framework also provides an improved basis for simulation of hydraulic fracture and reactivated natural fracture geometry, including both the interaction with the pre-existing geologic setting, and the interactions which occur between adjacent, simultaneous hydraulic fractures, or during refracturing operations. The developed workflow allows the basic natural fracture network to be geomechanically upscaled to allow prediction of the elastic rock mechanical properties as a function of both the elastic properties and the spatially varying fracture network. This work importantly demonstrates the coupled DFN-FEM simulation strategy as an efficient approach for providing detailed understanding of fracture reservoir development during stimulation. 1. INTRODUCTION Driven by many decades of experience in its use, hydraulic fracturing stimulation represents a proven means to enhance rock mass permeability in tight reservoir rocks. The use of hydraulic fracturing assists in more efficient hydrocarbon recovery and ultimately an increase in the ultimate economic recovery. From a subsurface perspective, the design of hydraulic fracturing treatments requires developed understanding of several key steps, including (i) characterizing the geology and rock mass properties, (ii) estimating the orientation and magnitudes of the in-situ stress conditions, and (iii) designing the completion and selecting the desired treatment fluid (see Bourtembourg, 2011).

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 53rd U.S. Rock Mechanics/Geomechanics Symposium, June 23–26, 2019

Paper Number: ARMA-2019-2205

... complex reservoir calculation

**Dershowitz**hydraulic fracturing stability analysis rock slope stability Reservoir Characterization Upstream Oil & Gas wedge stability wedge analysis mass failure identification reservoir geomechanics strength tensor assumption discrete fracture...
Abstract

ABSTRACT: Kinematic rock slope stability typically considers the primary loading force as a combination of the self-weight of the rock blocks themselves, and the water pressure in fractures. When major facilities exist or are planned near rock slopes, kinematic stability analysis also needs to consider the effect of the weight of the facilities themselves, induced fluid pressures, and local variations in geostatic stresses. This paper presents an approach for the incorporation of vertical, lateral, and shear stresses from civil and mining facilities on rock slope kinematic stability. The approach is built on the use of a fully three-dimensional discrete fracture network (DFN) model to identify potential rock wedges, and hybrid discrete/continuum approach to assess the shear and normal effective stresses on the natural and (potentially) induced fractures that define those wedges. The approach uses a variant of Oda (1985) geomechanical upscaling to evaluate the three-dimensional effective rock modulus, and a hybrid finite element approach to calculate effective stresses.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 52nd U.S. Rock Mechanics/Geomechanics Symposium, June 17–20, 2018

Paper Number: ARMA-2018-945

... fluid modeling data mining metals & mining reservoir geomechanics Upstream Oil & Gas fracture network complex reservoir filling body mining activity

**Dershowitz**Existence gob-side entry Reservoir Characterization discrete fracture network hydraulic fracturing displacement...
Abstract

ABSTRACT: An innovative approach to the gob-side entry retaining non-pillar mining is being used to increase the coal seam re cycling rate and productivity in China’s coal mining. The retained entry with a sidewall formed by gob caved-in filling rocks is unique in this method and the stability of caved-in material is critical to ensure efficient and safe mining activities. In this paper a numerical investigation on the stability of the gob-side entry is conducted using a discrete fracture network (DFN) model developed by the Massachusetts Institute of Technology (MIT), GEOFRAC, in combination with discrete element modelling (UDEC). The proposed method is applied to a case study of a gob-side retained entry in an underground coal mine in China. Fracture traces are measured along the gob-side wall of the entry, and statistical methods are used to estimate the fracture intensity and the mean fracture areas, which are the key inputs to GEOFRAC. Fracture networks generated by GEOFRAC estimate the rock blocks in the filling body, and simulations with UDEC are done to evaluate the stability of the gob-side entry. Two models are developed, one considering the generated fractures and the other considering no fractures within the gob-side filling. The results show the effects of considering the fractures in the filling body on the distribution of displacement and field stress in the gob-side entry zone. Also, the stability under the mining impact loading, due to periodic roof caving, is simulated, providing the basis for the optimization of the design of the entry support.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Golden Rocks 2006, The 41st U.S. Symposium on Rock Mechanics (USRMS), June 17–21, 2006

Paper Number: ARMA-06-1029

... [3]. equation of state flow in porous media Upstream Oil & Gas dfn epm approach fracture network shaft hydraulic fracturing Fluid Dynamics hybrid discrete fracture network connectivity WCF Implementation grout fluid modeling complex reservoir DFN EPM model

**Dershowitz**...
Abstract

ABSTRACT: This paper describes the development of a hybrid discrete fracture network/continuum (DFN/EPM) model for an underground rock research laboratory. This model is based on a 9 km scale discrete fracture network (DFN) model, which includes a combination of conductive discrete fractures and partially sealing, non-planar sub-vertical faults. In addition, the overlaying sedimentary rock sequences are modeled using the conventional continuum (EPM) approach. INTRODUCTION Discrete fracture network (DFN) models are increasingly popular in civil, mining, and oil reservoir projects because of their ability to realistically model the important effects of fracture connectivity and fault sealing. With increased use, the scale of DFN modeling has increased, with production modeling occurring at scales of kilometers to tens or even hundreds of kilometers. At these scales, water conducting fractures (WCF) and flow barrier (fault) fracture counts increase to the order of 106 to 109, which is beyond the range of current computer hardware. This paper describes the development of a hybrid DFN/EPM model, in which EPM (volume) elements are integrated with DFN (triangular) elements. This hybrid DFN/EPM approach is an extension of dual permeability features of Golder Associates? FracMan code [1]. Since 1989, FracMan has included a capability to model EPM (volume) elements within the DFN model to represent rock matrix effects. This paper describes an extension of this capability to allow EPM elements to be used for (a) Sedimentary and intensely fractured strata, and (b) fractured granite at distance from the area of primary concern. Both EPM and DFN elements can be used for (a) steady state and transient flow of slightly compressible fluids, (b) group flux (well) boundaries, and (c) moving phreatic surfaces. The advantage of this approach is that it allows increased modeling detail using DFN (triangular) elements in areas of concern, while facilitating increased model size through the use of EPM elements elsewhere. Other hybrid DFN/EPM models include ConnectFlow [2] and Frac3DVS [3].

Proceedings Papers

#### Stochastic Fracture Modeling For Stability Assessment of Underground Facilities In Crystalline Rocks

Publisher: American Rock Mechanics Association

Paper presented at the DC Rocks 2001, The 38th U.S. Symposium on Rock Mechanics (USRMS), July 7–10, 2001

Paper Number: ARMA-01-1483

... hydraulic fracturing fracture intensity probability function west-east direction prediction block statistics key block fracture orientation

**Dershowitz**clab site fracture statistics hypothesis fracture model Rock Mechamcs tn the Nattonal Interest, Elsworth, Ttnucct & Heasley (eds), ¸2001...
Abstract

ABSTRACT : Predictions of key blocks in underground excavations are uncertain, subject to the natural variation of rock properties. This study illustrates how stochastic fracture concept could be applied to make such predictions more realistic. The methodology was tested on the rock cavern sited in crystalline basement in southeast Sweden. Fracture mapping in boreholes was used to evaluate input variables to the stochastic model. Prior to model derivation, spatial pattern of fracture intensities was investigated by nonparametric statististics, variogram and spectral analysis. Fracture model incorporating fracture orientations, size, location pattern and termination mode was generated. Subsequently, the key block statistics along the cavern was computed. Probabilistic predictions of the number of block and block weight were obtained. To illustrate the value of the predictions made, the block analysis was done for two different tunnel orientations. Some noticeable differences in distribution parameters were observed. The presented methodology offers the possibility to optimize tunnel location and predict rock support. 1 INTRODUCTION One of the major hazards to proper functioning of an underground object is related to sliding of rigid rock blocks formed by intersecting rock discontinuities. Work done by Warburton (1981) and Goodman & Shi (1985) belong to the most important contributions in identification of unstable rock blocks from given orientation of fractures with respect to dimensions, shape and orientation of an underground facility.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Vail Rocks 1999, The 37th U.S. Symposium on Rock Mechanics (USRMS), June 7–9, 1999

Paper Number: ARMA-99-0777

... fracture intensity. Relationships between fracture trace intensity (2-d) and fracture intensity (3-d) are discussed by

**Dershowitz**& Herda (1992) and Mauldon (1994). This paper discusses an unbiased estimator of fracture trace intensity based on a count of fracture trace intersections with a circular...
Abstract

INTRODUCTION ABSTRACT: This paper presents a simple derivation of the unbiased fracture trace intensity estimator n/4r, where n is the number of intersections between fracture traces and a circular scanline of radius r. The use of circular scanlines eliminates the orientation bias associated with straight scanlines while still achieving the time efficiency of scanlines. Application of the estimator to synthetic and real fracture trace maps is discussed. The utility and efficiency of the circular scanline intensity estimator make it a valuable tool for fracture studies. Fracture traces, for present purposes, are the intersections of planar fractures with an exposed planar surface such as a bedding plane, rock face or mine drive wall. The traces appear as straight line segments with ends that may be either exposed or hidden beyond the boundaries of the exposure (i.e. censored). Fracture trace intensity, with /timension L-', is defined as the mean length of fracture traces per unit area of the planar sampling region. For parallel fractures of infinite length, trace intensity may be considered equal to frequency (Priest & Hudson 1981). Intensity can be considered as roughly the product of mean size and density. Estimators for mean fracture trace length and trace density, using circular windows are discussed in a companion paper (Mauldon et al. 1999). Fracture trace intensity is useful for characterizing fractured rocks to determine their hydraulic and mechanical behavior (Brown 1970, Oda 1982, 1985, 1993, Barton & Larson 1985, Narr 1991, Wu & Pollard 1995, Kulatilake et al. 1996). Trace intensity is determined from a two- dimensional (2-d) sample and as such, serves as a proxy for the volumetric fracture intensity. Relationships between fracture trace intensity (2-d) and fracture intensity (3-d) are discussed by Dershowitz & Herda (1992) and Mauldon (1994). This paper discusses an unbiased estimator of fracture trace intensity based on a count of fracture trace intersections with a circular scanline. In current geologic and rock engineering practice, straight scanlines and fracture trace maps (Fig. 1) are commonly used to estimate fracture intensity (Priest & Hudson 1981, LaPointe & Hudson 1985, Schaeffer 1991, Dershowitz & Herda 1992, Wu & Pollard 1995, Becker & Gross 1996). Straight scanlines provide a fast method for recording fracture attributes, but yield a sample biased by fracture orientation with respect to the scanline (Terzaghi 1965, Wathugala et al. 1990, Priest 1993, Mauldon 1994, Mauldon & Mauldon 1997). Fracture trace maps reduce this sampling bias by sampling an area rather than a single direction, but are highly labor-intensive and therefore costly.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Vail Rocks 1999, The 37th U.S. Symposium on Rock Mechanics (USRMS), June 7–9, 1999

Paper Number: ARMA-99-0431

... discontinuous rock is significantly less developed. Reservoir Characterization orientation Rock mechanics machine learning Upstream Oil & Gas roughness

**Dershowitz**Artificial Intelligence Euclidean Distance discontinuity reservoir geomechanics bore hole hole discontinuity data Priest...
Abstract

ABSTRACT: This paper describes a new and cost effective method of analyzing hard rock discontinuities from oriented core bore hole data. This algorithm uses multivariate cluster analysis to group discontinuities (joints) into sets based on orientation and spatial position (spacing) along the bore hole, and to display the data in a three dimensional stereonet. Although drift or surface exposure mapping data allows better characterization of discontinuities, bore hole data is often more readily available, because of lower costs. In addition, bore hole data may be more useful because bore holes can be drilled to the exact location where the ground needs to be characterized and bore hole data is usually available earlier in the life cycle of an engineering project. INTRODUCTION 1.1 Discontinuities in Rock Mechanics The characterization of the structure of rock masses is an important consideration in engineering projects in rock. Often it is the nature of the discontinuities (joints, fractures, bedding planes, faults, and other breaks in the continuity of the rock) and not of the intact rock that governs the mechanical and hydrological behavior of the rock mass (Fig. 1). With a few exceptions, most of the rock masses that engineers deal with are influenced to some extent or another by discontinuities. In rock engineering analysis it is necessary to understand the mechanical and hydrological behavior of rock masses in order to predict such aspects of design as: 1. The stability of a rock mass (how likely is it that the rock will fail, and how catastrophic will the failure be?); 2. The degree of remediation and/or ground support required (how do we make it safe?); 3. The expected amount of deformation as a result of applied structural loads (how much movement do we have to design for?); 4. The amount of effort needed to excavate the rock (do we need to use explosives, and if so how much?); 5. The degree and effect of water infiltration (how do we keep it dry?.). While we understand much about the mechanical properties of intact, solid rock, our understanding of discontinuous rock is significantly less developed.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Vail Rocks 1999, The 37th U.S. Symposium on Rock Mechanics (USRMS), June 7–9, 1999

Paper Number: ARMA-99-0785

... hydraulic fracturing trace density rocky creek reservoir geomechanics llantwit major pavement trace length estimator mean fracture trace length Wellbore Design

**Dershowitz**application density estimator Reservoir Characterization Upstream Oil & Gas estimator mean trace length...
Abstract

INTRODUCTION ABSTRACT: Mean fracture trace length and trace density are important parameters in the characterization of fractured rock with applications in hydrogeology, oil recovery and rock engineering. Estimating these parameters from field data is beset with problems due to censoring and length bias. The paper presents simple distribution-free estimators for mean trace length and density that automatically correct for sampling bias. The estimators use samples collected with circular windows placed at random on exposed pavements or rock surfaces. Use of the estimators is demonstrated by application to synthetic and real data sets. This paper describes easy-to-use estimators for fracture trace density and mean fracture trace length using circular sampling windows (Fig. 1). Trace density is here defined as the mean number of trace centers per unit area of the sampling plane. Mean fracture trace length is the mean length of the entire population of traces. Unless both ends of a trace are visible within a sampling window, the location of the trace center is unknown. Therefore, mean trace length and trace density must both be inferred, which is the purpose of these new estimators. The estimators are distribution independent and automatically correct for errors from censoring and length bias, making the estimators an improvement on existing methodologies. The results of these techniques yield useful information about the trace density and mean trace length of a fracture population, which may be used Figure 1. Ci?ular window, scanline and irregular rock pavement window samples of fracture traces. Solid traces where visible on the pavement. to tackle many problems in geology and engineering. For example, trace density and mean trace length are used for estimating elastic rock properties, fracture porosity, path length and connectivity for fluid flow, and mechanical behavior of fractured rock (Segall & Pollard 1983, Long et al. 1985, Amadei & Savage 1993, Elsworth & Mase 1993, Hu & Huang 1993, Dershowitz & LaPointe 1994, Kulafilake et al. 1996, Zhang et al. 1996, Odling 1997). The estimators are simplified from special cases of more general models developed for sampling windows of arbitrary convex shape (Mauldon 1998). When circular windows are used as the sampling domain, the estimators are independent of both the trace orientation distribution and of the trace length distribution (each of which may be either discrete or continuous). Thus, they are entirely distribution independent. The performance of these estimators is demonstrated by Monte Carlo simulation of synthetic fracture sets, and also by application to fracture trace maps from rock pavements (Fig. 2b, c) in Wales, UK, and South Carolina, USA.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 35th U.S. Symposium on Rock Mechanics (USRMS), June 5–7, 1995

Paper Number: ARMA-95-0725

... conceptual models incorporated in the commercially available software package FracMan (

**Dershowitz**et al. 1993). Combined geometric-mechanical models consist of geometric modeling procedures which attempt to duplicate typical. 'mechanical processes. Examples are the model by Martel et al. (1991) in which...
Abstract

ABSTRACT: Hierarchical geometric-mechanical models attempt to capture the relations between the geometry of rock fracture systems and the underlying geologic mechanisms of fracturing. The two-dimensional enhanced hierarchical model can represent complex fracture trace patterns. Since two-dimensional representations of fracture patterns are insufficient for many applications, a three-dimensional hierarchical model is being developed. The model generates hierarchically related sets of fractures using a sequence of three stochastic processes: Poisson plane process, Poisson line process, and a combined translation-rotation process. The modeling that is presented in this paper is still geometric but relations to the underlying mechanisms are discussed as well. INTRODUCTION Modeling of fracture systems for use in a number of engineering applications ranging from slope reliability analysis to analysis and design of foundations and tunnels on and in rock masses, to flow and transport in fractured rock masses has been the objective of many research efforts. In the opinion of the authors of this paper, one can group the fracture system models in three categories: 1. Mechanical Models; 2. Geometric Models; and 3. Combined GeometricMechanical Models. From the point of view of engineers and scientists, mechanical modeling is the most desirable approach in that one tries to duplicate the actual fracture nucleation and propagation mechanisms which have acted throughout the geologic history, under varying applied stress conditions. However, so far, only relatively simple fracture patterns can be replicated by the mechanical models, be they experimentally or numerically based. In particular, the three dimensional characteristics and the often pervasive clustering can be modeled to a limited extent only. Further development is likely to lift some of these limitations. Prime examples of mechanical models are the models developed by the Stanford Group (see e.g. Wu and Pollard 1992). Purely geometric models, often called conceptual models, are the most widely used category. Geometric modeling started with statistical evaluation of pole diagrams for orientation on the one hand, and the development of simple deterministic block or wedge models on the other hand. Today a wide variety of stochastic models exist. Many of them are threedimensional and capture, at least to a certain extent, the clustering of geometric fracture characteristics. Since they simulate what is observed rather than what caused the fracture pattern, it is not easy to produce complete representations from the usually available information such as boreholes and outcrops. Examples of advanced geometric models are the conceptual models incorporated in the commercially available software package FracMan (Dershowitz et al. 1993). Combined geometric-mechanical models consist of geometric modeling procedures which attempt to duplicate typical. 'mechanical processes. Examples are the model by Martel et al. (1991) in which fractal-like objects are created in two dimensions using so called Iterated Function Systems conditioned on geologic information, and the two-dimensional Hierarchical Model developed at MIT (see e.g. Lee et al. 1990). In the latter, the hierarchy of fracture genesis is modeled by creating fracture sets in sequence and by incorporating dependencies (or independencies if applicable) between different fracture sets in this process. In our developments at MIT we worked originally on purely geometric models (e.g. Baecher et al. 1977; Veneziano 1978) and simultaneously looked into the mechanical aspects of fracture behavior (Einstein et al. 1983). However, the latter involved engineering application rather than an inv

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 34th U.S. Symposium on Rock Mechanics (USRMS), June 28–30, 1993

Paper Number: ARMA-93-0689

... decades, considerable effort has been devoted to developing quantitative approaches to studying groundwater flow in fractured rock masses (e.g., Snow; 1969, Louis; 1969, Long et al.; 1982,

**Dershowitz**et al.; 1991). The Stripa Project in Sweden provides an excellent example of such efforts to validate...
Abstract

ABSTRACT INTRODUCTION The flow of groundwater through fractured rock may be complex because the spatial distribution of hydraulic properties is strongly affected by the heterogeneous geometry of the fracture system and the surface geometries of the individual fractures. Over the last two decades, considerable effort has been devoted to developing quantitative approaches to studying groundwater flow in fractured rock masses (e.g., Snow; 1969, Louis; 1969, Long et al.; 1982, Dershowitz et al.; 1991). The Stripa Project in Sweden provides an excellent example of such efforts to validate methods for modelling flow in fractures (e.g., Ollson ;1992, Dershowitz et al.; 1989). The approaches to model validation have generally used field studies, however, these have drawbacks connected with the uncertainties of the pressure conditions and actual geometry of the fractures. Laboratory tests provide better control on experimental variables, but have disadvantages of scale. This paper describes a laboratory experiment which has the flexible control of hydraulic conditions while having the realistic complexity of natural fracture networks. The effectiveness of the proposed method is proved from test results using a rock containing multiple fractures. Experiments performed with well defined boundary conditions and fracture systems will contribute significantly understanding fundamental physical mechanisms associated with flow through fracture networks. DESCRIPTION OF THE EXPERIMENT The unique feature associated with the proposed test is the capability of injecting or extracting water at numerous "windows" located on the surfaces under controlled hydraulic pressure. As shown in Figure 1, this is realized by attaching a gasket with lattice windows on each surface of a 30 cm cube. The whole system is shown schematically in Figure 2. A water saturated block sample covered by gaskets is placed in a polyaxial loading frame, and a uniform water pressure is applied to press the gaskets on the rock surface. Each of the windows, or "panels, is thus hydraulically isolated from the other panels, and flux or pressure can be independently controlled in each panel. By selecting proper combinations of hydraulic conditions, one can conduct injection tests under variety of flow conditions, i.e., from a simple one-dimensional flow test to a more complex panel-to-panel injection test to study fluid flow in a rock with heterogeneous features.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 33rd U.S. Symposium on Rock Mechanics (USRMS), June 3–5, 1992

Paper Number: ARMA-92-0543

...) represents a combination of stochastic discrete fracture network modelling (

**Dershowitz**, 1984) with dual porosity modelling. The geometry of fractures is modelled explicitly to capture the heterogenous connectivity typical of fractured rock masses (Figure 2). Interaction between fluids in fractures and rock...
Abstract

ABSTRACT: Discrete feature analysis provides the crucial link between the com- plex geometries and structural control of reservoir geology and the regular, rectangu- lar geometries of the finite difference continua approaches used in reservoir engineer- ing. This paper summarizes the theory of discrete feature analysis, and three applica- tions of the approach to fractured reservoirs and hazardous waste. INTRODUCTION The geometry of discontinuities and openings such as faults, fractures, lithologic contacts, and karst features can have a significant effect on the hydraulic behavior of fractured rock masses. These discrete features frequently cause rock masses,to exhibit heterogeneous connections, discontinuous flow and head fields, and non- linear flow behavior. This paper presents applications of a new, multiphase/ multiporosity approach for numerical modelling of fractured rock masses. This approach incorporates a stochastic description of discrete feature geometry and properties, with each fracture coupled to one or more rock block models (Miller, 1990). Dual porosity continuum modelling has been used for at least 15 years to represent the non-linear behavior of rock with high permeability/low hydraulic storage fractures and low permeability/high hydraulic storage rock matrix. This approach is particu- larly useful where fracturing is intense or regular, such that discrete feature geometry does not have a strong effect on behavior. The dual porosity discontinuum approach (Figure 1) represents a combination of stochastic discrete fracture network modelling (Dershowitz, 1984) with dual porosity modelling. The geometry of fractures is modelled explicitly to capture the heterogenous connectivity typical of fractured rock masses (Figure 2). Interaction between fluids in fractures and rock blocks is mod- elled by coupling a rock block volume to each fracture. Flow between rock blocks and fractures is solved by coupling heads between fracture elements and a matrix block associated with each fracture. This equation can be solved as a one dimen- sional finite difference equation, or by an approximate method based upon the War- 'en and Root (1963) pseudo steady state approach, which assumes that flux into or our of the matrix blocks equals the change in storage within the blocks according to the equation.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 33rd U.S. Symposium on Rock Mechanics (USRMS), June 3–5, 1992

Paper Number: ARMA-92-0551

... correlation

**Dershowitz**Stockholm fracture Water Resource Research packer test model 2 borehole Fracture Zone fracture model fractured rock conductivity ABSTRACT: Conductivity estimates Kp, from packer tests are the normal basis for sto- chastic continuum (SC) models of sparsely fractured...
Abstract

ABSTRACT: Conductivity estimates Kp, from packer tests are the normal basis for sto- chastic continuum (SC) models of sparsely fractured rock. The scale of the tests is often much smaller than the scale on which the rock acts as an equivalent porous medium (EPM). Therefore extrapolation of test results to the scale of blocks in a SC model, based on continuum assumptions, is questionable. This paper demonstrates an alternative method for extrapolation of Kp, data, based on discrete fracture network (DFN) model- ing. 3-D rock blocks were simulated based on fracture geometric and packer test data from Finnsjtn, Sweden. Constant-pressure packer tests were simulated in these blocks, and the results were compared with field data to validate the fracture model. Effective block-scale conductivities Kb, were estimated by modeling steady-state flow through the blocks. Probabilistic estimates were obtained of the relationship between Kp, estimates and Kb, for block scales from 15 to 50 m. The DFN model predicts that the correlations between Kp, and Kb, are poor, even for the smaller blocks. INTRODUCTION Predictive modeling of water flow in sparsely fractured, low-permeability rock is required for design of high-level nuclear waste repositories and other types of under- ground facilities such as gas storage caverns. Problems in modeling this rock arise from the tendency for the flow to be concentrated within fractures. Interconnections among fractures to form flow paths can be highly irregular on scales of concern for site model- ing. This is evident from the high variability of heads seen in the vicinity of tunnels in tight, sparsely fractured rock. To model this rock, its strongly heterogeneous and effectively random nature must be represented. Two types of models which do this are: -Discrete fracture network (DFN) models. -Stochasticontinuum (SC) models. DFN models represent the discrete flow paths explicitly, whereas SC models represent blocks of the rock mass in terms of an "equivalent porous medium" (EPM). The more detailed representation used in DFN models has thus far restricted use of these models to rock volumes smaller than (200 m)3. SC models are viewed as being more tractable for site-scale modeling. Unfortunately, the properties of rock blocks on the scale of the constituent blocks of SC models cannot be measured directly in the field. Therefore it is difficult to obtain answers to two critical questions: -Does the rock behave as an EPM on the block scale? -If so, then how should the block-scale conductivities be estimated from packer tests? The first question has been treated extensively in the literature (e.g., Long et al., 1982; Khaleel, 1989). This paper focuses primarily on the second question, which has not thus far been examined using a discrete fracture approach.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 33rd U.S. Symposium on Rock Mechanics (USRMS), June 3–5, 1992

Paper Number: ARMA-92-0757

... applications. INTRODUCTION Fracture patterns are described in terms of distributions for orientation, size, shape, spatial location, and intensity (

**Dershowitz**and Einstein, 1988). Of these, intensity is one of the most important, but the least well characterized. Fracture intensity is generally noted in...
Abstract

ABSTRACT: A class of fracture intensity measures in one, two, and three dimensions has been defined that allows for the definition of fracture frequency without requiring reference to specific sets or orientations. Measure P?2 (fracture area per unit volume) was found to be the most useful measure for fracture intensity in three dimensions. Relationships between intensity measures are described based on solutions from the field of stochastic geometry. The use of these measures significantly improves the consistency of discrete fracture analysis and modelling for mechanical and hydrologic applications. INTRODUCTION Fracture patterns are described in terms of distributions for orientation, size, shape, spatial location, and intensity (Dershowitz and Einstein, 1988). Of these, intensity is one of the most important, but the least well characterized. Fracture intensity is generally noted in terms of fracture spacing St, the mean distance between fractures within a given set, as measured along a particular line such as' a borehole or scanline (Figure 1). This measure is relatively easy to determine the field, but is not useful for describing fractures in two or three dimensions. It is also dependent upon the subjective definition of fracture sets in the field. In three dimensional analysis, fracture intensity is generally defined as the number of fracture centers per unit volume, P,?. This measure is useful only where fractures are much smaller than the region being analyzed, such that fracture centers represent individual fractures, rather man fragments of fractures that may be within or outside the region. In addition, Pa? can only be related to fracture spacing St through the fracture size and orientation distributions. The goal of this paper is to define a consistent set of fracture intensity measures in one, two, and three dimensions, together with the relationships between them.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 28th U.S. Symposium on Rock Mechanics (USRMS), June 29–July 1, 1987

Paper Number: ARMA-87-0433

... complex reservoir modeling conceptual model Artificial Intelligence JINX fracture termination borehole intersection hydraulic fracturing Einstein Simulation fracture network application fracture statistics rock mass Upstream Oil & Gas dimension Rock mechanics

**Dershowitz**...
Abstract

ABSTRACT ABSTRACT JINX is a computer program for discrete fracture modeling of fractured rock masses for rock mechanics and hydrologic applications. The program incorporates conceptual models for fracture geometry based upon disks, polygons, and serially defined polygons with terminations at both fracture intersections and within intact rock. This paper describes the features of the JINX program and its application to practical problems. 1. INTRODUCTION The discrete fracture network modeling package JINX (Joints in Networks) was developed originally at the Massachusetts Institute of Technology under the sponsorship of the Army Research Office (ARO), and has since been extended by Golder Associates under the sponsorship of the Battelle-Office of Waste Technology Development (OWTD) of the U.S. Department of Energy Repository Technology Program (RTP). The program was designed to facilitate rock mechanics and hydrologic modeling of two and three dimensional discrete fracture networks. The discrete fracture network modeling approach has been implemented by a number of researchers over the past five years (Dershowitz, 1979; Long, 1983; Dershowitz, 1984; Robinson, 1985). The basic assumption of the approach is that the properties of fractured rock masses are determined by the behavior of individual fractures rather than by the rock mass as a continuum. As a result, the rock mass is modeled as a network of discrete elements representing the fractures (Figure 1). This approach has been applied to rock slope stability (see e.g., Einstein et.al, 1979), rock tunnel stability (Goodman and Shi, 1984), rock mass deformation (Dershowitz and Einstein, 1980), and more recently to groundwater flow (Long et al, 1985) and solute transport (Smith, Mase, and Schwartz, 1985). The approach of all of these models has been to define the rock mass by a specific conceptual model for rock fracture geometry, such as two dimensional Poisson (random) fibers, or Poisson disks. The philosophy of the of the JINX fracture network modeling package is to provide a common model within which many different conceptual models can be evaluated, under the assumption that different conceptual models are appropriate for different rock masses. At present, seven conceptual models have been implemented. For all of these models, JINX allows the same rock mechanics and hydrological analyses to be carried out. 2. ROCK FRACTURE CONCEPTUAL MODELS The disk model (Figure 1) (Baecher, Lanney, and Einstein, 1978) in which fractures are represented by randomly located circular or eltpttcal disks. The Veneztano (1979) polygon model (Figure 2), in which polygonal fractures are defined by a process of random (Potsson) lines on planes oriented according to any desired orientation distribution. Polygons on each plane are defined independently, so that there is no facility for defining fracture terminations at intersections. The fracture model defined by Dershowitz (1984) (Figure 3), in which polygonal fractures are defined on fracture planes by a process of Poisson lines resulting from the intersection of fracture planes. This model can model fracture terminations at fracture intersections or intact rock, but requires that fracture termination and size be defined indirectly through the intensity of fracture planes. The fundamental assumption of the JINX package is that different rock masses require different rock mass conceptual models. Figures 1 through 4 present the conceptual models implemented to date: