Average Fracture Spacing Research Articles

Characterization methods for natural fractures distribution in shale and tight reservoirs

Aperture distribution and spatial arrangement are fundamental characteristics of natural fractures. Since it is impossible to directly measure the aperture of all existing fractures, a power law (fractal model) has been commonly used to describe fracture apertures, which has also been extended to estimate fracture spacing and macrofractures density. Although a power law (fractal model) has commonly been used to describe fracture apertures, data points in small and large fracture size ranges tend to deviate from this distribution. In this study, a Variable Shape Distribution (VSD) method was derived from a fractal theory to model fracture size distribution. The VSD method was compared with seven other commonly used models. Eleven fracture datasets collected from five countries on four continents were regressed using these methods. The scale-free methods of the VSD and power law models showed more advantages than the scale-dependent methods. The VSD method was found to best fit all variable aperture size distribution patterns, with an average coefficient of determination of 0.99. The average fractal dimension for all samples calculated by the VSD method (1.36) was slightly higher than that of the power law (1.06). This study is unique in showing that the VSD method can solve a boundary characterization problem that has been widely neglected in previous studies. With the assumption of an even fracture distribution, the VSD method was further applied to estimate average fracture spacing, predict a threshold fracture length that controls the linkage of fractures, and predict fractures outside of the measurement range. This study not only proposes an advanced fractal method to model aperture size distributions in shale and tight rocks but also helps to better understand the importance of fractal dimensions and boundary characterizations.

Allocating transmissivities from constant head tests for the development of DFN models

Constant head tests are commonly used for field measurements of fracture transmissivity. As a bulk transmissivity is measured for each test section, it is frequently unclear how this transmissivity relates to the hydraulic properties of individual fractures. The goal of this study is to determine if constant head tests conducted at scales larger than the average fracture spacing can be used to generate discrete fracture network (DFN) models that describe transport. The methodology involved generating DFNs using measurements from constant head tests conducted at lengths both above and below the average fracture spacing at a site in Ontario, Canada. Transport predictions from DFNs produced from different scales of hydraulic tests were compared to determine if a method for proportioning larger-scale test results to obtain a DFN representative of the smaller-scale tests could be established. The results of this study indicate that the choice of method used to apportion bulk transmissivities has a significant impact on transport simulations, with a difference in mass arrival of over a factor of two at travel distances less than 50 m. While the most appropriate method is case specific, the error resulting from the choice needs to be considered when using DFN models.

A systematic study of internal gas generation in shale source rocks using analog experiments

A two-dimensional Hele-Shaw cell was created to study and visualize hydrocarbon source rock (i.e., shale) elastic-brittle fracture and fracture network propagation mechanisms triggered by internal gas generation and gas build up during maturation of organic components. An analog immature source rock was created using a mixture of gelatin, sugar, and live yeast in pre-determined proportions. This mixture was poured into the Hele-Shaw cell and allowed to gel. The internal gas generated as a result of sugar fermentation by yeast caused pressure build up within the gel that ultimately resulted in the activation of dissipation mechanisms such as gas diffusion and deformation of the gel matrix. These mechanisms are analogous to shale maturation and fluid generation. Image analysis was employed to study and characterize key events such as fracture nucleation, propagation, and coalescence versus time. Derivative parameters such as fracture growth rate, fracture tip pressure, and fracture spatial distribution, among others, were calculated using the image-sourced data and applying Linear Elastic Fracture Mechanics (LEFM) principles. Results showed that the experiments are repeatable within a consistent response range and additional parameters were identified to be useful input for numerical modelling, including nucleation sites, fracture merging angle, merging to nucleation ratio, and fracture connectivity. For a volume of about 100 cm3 of 11.6% wt. food-grade gelatin solution with 0.25% wt. yeast and a sugar/yeast ratio of 3, measured average total gas production was 35 cm3 (at standard conditions). On an average gelatin matrix area of 400 cm2, the average total fracture length and fracture density are 106 cm and 0.15 fractures/cm2, respectively. Average maximum calculated fracture tip pressure and maximum fracture velocity are 0.92 psi and 5.85 × 10−4 cm/s, respectively. Fracture connectivity was more frequent in the second half of the gas generation process and greater for the older and longer fractures. Average final fracture spacing was 4.42 cm. Connection angles between fractures tended to be closer to 0° than to 90°. Photoelasticity imaging techniques were applied to the experimental setup to visualize the stress field within the sample. The difference of principal stresses was estimated at 3.70 × 103 Pa for the tested material late in the maturation process. Results suggest interdependence of gas pressure, gas diffusion, and transient stress field states. The range of laboratory-scaled data are useful as benchmarking parameters for numerical modelling of source rock maturation including geomechanics.

Numerical simulation of electricity generation potential from fractured granite reservoir using the MINC method at the Yangbajing geothermal field

Field tests indicate that after hydrofracturing the fracture spacing in an Enhanced Geothermal System (EGS) reservoir may be within 0.33–300 m. For EGS reservoirs with large fracture spacing, it is unreasonable to assume the local thermodynamic equilibrium between water and rock when simulating the heat production process, and temperature gradient between the rock and circulating water must be considered. The multiple interacting continua (MINC) model is an effective method for calculating the temperature gradient between the rock and the circulating water in the EGS reservoirs. In this work we evaluated the electricity generation potential from the 950–1350 m deep fractured granite reservoir at the Yangbajing geothermal field by the MINC method with TOUGH2 software, and analyzed the main factors influencing the system production performance. The results indicate that the system attains an electric power generation potential of 22.2–19.3MW, a reservoir impedance of 0.25–0.39 MPa/(kg/s), a pump power of 0.93–1.78 MW and an energy efficiency of 23.92–10.82 during an exploitation period of 30 years under reference conditions, showing good heat production performance. The main factors influencing the production performance are fracture spacing, fracture permeability, injection temperature and water production rate. Within a certain range, measures to improve the electricity generation performance are to reduce the average fracture spacing, to increase the fracture permeability, or to adopt more reasonable injection temperature and water production rate.

High-resolution stratigraphic characterization of natural fracture attributes in the Woodford Shale, Arbuckle Wilderness and US-77D Outcrops, Murray County, Oklahoma

Natural fracture aperture-size, spacing, and stratigraphic variation in fracture density are factors determining the fluid-flow capacity of low-permeability formations. In this study, several facies were identified in a Woodford Shale complete section. The section was divided into four broad stratigraphic zones based on interbedding of similar facies. Average thicknesses and percentages of brittle and ductile beds in each stratigraphic foot were recorded. Also, five fracture sets were identified. These sets were split into two groups based on their trace exposures. Fracture linear intensity (number of fractures normalized to the scanline length [[Formula: see text]]) values were quantified for brittle and ductile beds. Individual fracture intensity-bed thickness linear equations were derived. These equations, along with the average bed thickness and percentage of brittle and ductile lithologies in each stratigraphic foot, were used to construct a fracture areal density (number of fracture traces normalized to the trace exposure area [[Formula: see text]]) profile. Finally, the fracture opening-displacement size variations, clustering tendencies, and fracture saturation were quantified. Fracture intensity-bed thickness equations predict approximately 1.5–3 times more fractures in the brittle beds compared with ductile beds at any given bed thickness. Parts of zone 2 and almost entire zone 3, located in the upper and middle Woodford, respectively, have high fracture densities and are situated within relatively organic-rich (high-GR) intervals. These intervals may be suitable horizontal well landing targets. All observed fracture cement exhibit a lack of crack-seal texture. Characteristic aperture-size distributions exist, with most apertures in the 0.05–1 mm (0.00016–0.0032 ft) range. In the chert beds, fracture cement is primarily bitumen or silica or both. Fractures in dolomite beds primarily have calcite cement. The average fracture spacing indices (i.e., bed thickness-fracture spacing ratio) in brittle and ductile beds were determined to be 2 and 1.2, respectively. Uniform fracture spacing was observed along all scanlines in the studied beds.

Determining the REV for Fracture Rock Mass Based on Seepage Theory

Seepage problems of the fractured rock mass have always been a heated topic within hydrogeology and engineering geology. The equivalent porous medium model method is the main method in the study of the seepage of the fractured rock mass and its engineering application. The key to the method is to determine a representative elementary volume (REV). The FractureToKarst software, that is, discrete element software, is a main analysis tool in this paper and developed by a number of authors. According to the standard of rock classification established by ISRM, this paper aims to discuss the existence and the size of REV of fractured rock masses with medium tractility and provide a general method to determine the existence of REV. It can be gleaned from the study that the existence condition of fractured rock mass with medium tractility features average fracture spacing smaller than 0.6 m. If average fracture spacing is larger than 0.6 m, there is no existence of REV. The rationality of the model is verified by a case study. The present research provides a method for the simulation of seepage field in fissured rocks.

Fracture clustering effect on amplitude variation with offset and azimuth analyses

Traditional amplitude variation with offset and azimuth (AVOAz) analysis for fracture characterization extracts fracture properties through analysis of reflection AVOAz to determine anisotropic parameters (e.g., Thomsen’s parameters) that are then related to fracture properties. The validity of this method relies on the basic assumption that a fractured unit can be viewed as an equivalent anisotropic medium. As a rule of thumb, this assumption is taken to be valid when the fracture spacing is less than [Formula: see text]. Under the effective medium assumption, diffractions from individual fractures destructively interfere and only specular reflections from boundaries of a fractured layer can be observed in seismic data. The effective medium theory has been widely used in fracture characterization, and its applicability has been validated through many field applications. However, through numerical simulations, we find that diffractions from fracture clusters can significantly distort the AVOAz signatures when a fracture system has irregular spacing even though the average fracture spacing is much smaller than a wavelength (e.g., [Formula: see text]). Contamination by diffractions from irregularly spaced fractures on reflections can substantially bias the fracture properties estimated from AVOAz analysis and may possibly lead to incorrect estimates of fracture properties. Additionally, through Monte Carlo simulations, we find that fracture spacing uncertainty inverted from amplitude variation with offset (AVO) analysis can be up to 10%–20% when fractures are not uniformly distributed, which should be the realistic state of fractures present in the earth. Also, AVOAz and AVO analysis gives more reliable estimates of fracture properties when reflections at the top of the fractured layer are used compared with those from the bottom of the layer.

Closed form flow model of a damped slug test in a fractured bedrock borehole

Summary An existing closed form model is modified to describe the damped response of groundwater in a fractured bedrock borehole with variable apertures and dips to a slug test. The existing theory, which requires single sized horizontal fractures, is accurately calibrated by slug test data from three uncased bedrock boreholes in the Dedham Granite and an observation well screened just below the contact surface with a till drumlin. Apertures and dips vary however, so the ability of the modified theory to accommodate different sizes and inclinations improves upon the physical validity of its predecessor when fracture information accompanies slug test data. Geophysical logs identify a large number and dip of fractures in the uncased boreholes in the Dedham Granite in this regard. A lognormally distributed, horizontal aperture calibration of the slug tests in the uncased boreholes retains the accuracy of the single size model, and yields aperture statistics more consistent with literature values. The slug test in the screened observation well is accurately calibrated with the modified horizontal theory for discrete (two) sizes, based upon the average fracture spacing found in the uncased boreholes. All four results yield comparable compressibility estimates, which depend on fracture spacing but not size or dip. The calibrated aperture size and calculated fracture porosity and permeability decrease with length of the borehole into the Dedham Granite. The measured dip and aperture for flowing and nonflowing fractures in one of the boreholes accurately calibrates the modified theory. The inclusion of dip reduces the calibrated permeability because of the increased ellipsoidal area at the interface of the borehole and the inclined fractures.

Control of folding and faulting on fracturing in the Zagros (Iran): The Kuh-e-Sarbalesh anticline

The Kuh-e-Sarbalesh anticline (Fars region), shows a strong and poorly studied curvature in the vicinity of the Kazerun transfer zone. Here we investigated this structure by analyzing the orientation and distribution of fractures in the Oligocene-Early Miocene Asmari Formation (a major reservoir rock of the Zagros petroleum system) and paleo-burial conditions. Far away from the Kazerun Fault, the orientation of fractures is similar to that observed in other folds in the Zagros: two tensional fracture sets (F1 and F2) develop respectively parallel and perpendicular to the fold axis, whereas two shear fracture sets (dextral F3 and sinistral F4) develop at 30° from F2. Closer to the Kazerun fault, F1 and F2 become less abundant, whereas F3 fractures do prevail. F3 dextral shear fractures are associated with dextral shear zones (SZ3). Within SZ3, sets of tensional fractures (F5) occur. F4 shear planes are less abundant than F3 sets and are sometimes associated with sinistral shear zones (SZ4). Within SZ4, sets of tensional fractures (F6) occur. The frequency of F3 and SZ3 structures increases from south to north, suggesting a control by dextral shear along the Kazerun Fault. Average fracture spacing is around 20cm and fracturing saturation values is larger than 0.7, at 20km distance from the Kazerun fault whilst spacing is smaller than 1cm and saturation is as low as 0.32 (typical of well-developed fracture systems) close to the fault highlighting a strong strain gradient from south to north. The orientation of F1 and F2 fracture sets changes from south to north according to the clockwise rotation of the northern part of the fold with respect to the southern part. Inorganic thermal parameters derived from X-ray diffraction analysis of clay minerals indicate that the Asmari formation was deformed at burial depths of 3km (assuming a geothermal gradient of 20°C/km). We suggest that the progressive differential advancement of the thrust front produced the curved shape of the Kuh-e-Sarbalesh anticline with associated rotation of the pre-/early-folding F1 and F2 fracture sets observed in the field, consistently with a dextral shear associated with the Kazerun transfer fault.

Microseismic Clouds: Modeling and Implications

Summary Microseismic measurements provide qualitative information about the location of a fracture stimulation. However, there is also quantitative information to consider, a fact that has largely been neglected. We have developed a geomechanical model to predict the extent of shear failure during fracture stimulation of a well. The model identifies different types of failures, tensile and shear, which will occur on natural fractures or vertical planes of weakness. It is a “screening model,” meaning it takes a global perspective where point-by-point details of natural fracture distribution, fluid leakoff, and failure prediction are not emphasized. By matching the model to the extent of the microseismic cloud of shear failure, we obtain an injection permeability and porosity which characterize the volume of the microseismic cloud, which we assume to be a quasi-uniform fracture network with a system permeability enhancement. The model can be applied to any formation in which the microseismic distribution in each fracture stage is widespread, as happens in many tight shales (i.e., not elongated, as in a dominant vertical fracture). From our modeling studies, a high injection permeability (>100 md) is required to pressure the formation and achieve failure out as far as the microseismic events extend. Low injection porosity (<0.1%) is required for the fracture fluid to leak off that far (this is typically much less than formation porosity of 3–5%). These numbers are symptomatic of fracture-controlled flow. Reports on interference with offset wells support this interpretation. As a case history, the method and results for sequential stimulation of two sister horizontal wells in the Barnett shale are described. The geomechanical model is matched to the composite cloud of all microseismic events measured in that well. Not all wells in a field have microseismic data, but the first few wells usually do, and modeling of these cases can provide useful directives for future wells. For example, the injection permeability can provide information on average fracture spacing and aperture width during injection, and these can be important for tailoring proppant size to acess the fracture network in gas and oil plays in tight shales.

Pressure Transient Analysis of Multi-stage Hydraulically Fractured Horizontal Wells

The horizontal well with multiple transverse fractures has proven to be an effective way to exploit tight reservoirs economically. Due to the nature of ultralow permeability, it would take a significant long period of time for a well producing in transient flow regimes. Therefore, pressure transient analysis for such a well is important in both evaluation of fracturing treatment by estimating fracture and reservoir parameters and prediction of the long-term production behavior of wells in oil recovery. This paper discusses the analysis of pressure-transient responses of horizontal wells intercepting multiple infinite-conductivity transverse fractures. Then a numerical model is utilized to simulate the whole well flow regimes and pressure transient characteristics of multiple fractured horizontal wells. Accordingly, appropriate analytical pressure-transient models and analysis procedures are provided to determine fracture properties, i.e. average fracture half-length and spacing and estimate the oil in place in the stimulated reservoir volume.

Two-Dimensional Integral Equation Solution of Advective-Conductive Heat Transfer in Sparsely Fractured Water-Saturated Rocks with Heat Source

AbstractSaturated sparsely fractured granite (average fracture spacing on the order of meters) is currently studied as the host rock for a potential high-level nuclear waste repository in China. As part of an effort to study the coupling of waste-decay induced heat conduction in the rock matrix and heat convection in the fractures, a mathematical model is proposed for two-dimensional advective-conductive heat transfer in sparsely fractured water-saturated rocks with heat source(s), and an integral-equation solution scheme is developed by using discrete Laplace transform and numerical integration. The model and solution procedure is verified against an analytical solution for a single-fracture case with 1D perpendicular-to-fracture heat conduction. Illustrative calculations reveal, among other things, that significant interactions exist between the heat source intensity and the locations, apertures, and water velocities of the fractures, and that the influence of water in the fractures on the temperature i...

Effect of Materials Characteristics on Average Crack Spacing of Reinforced Concrete Specimen

The goal of the present work is to investigate the influence of concrete on failure mode and stress distribution of the reinforced concrete specimens under axial tension by using a numerical test code named Realistic Failure Process Analysis. It can be found that, the periodically distributed fracture spacing phenomenon and tension stiffening phenomenon exist in the failure process of the reinforced concrete structure. Besides, the effect of concrete characteristics on the mechanical behavior and crack spacing of reinforced concrete was also studied in three samples with different concrete strength. The concrete strength value is considered to be an important factor not only to significantly influence the average crack spacing but also to influence the initial peak load of the specimen. In addition, the average fracture spacing is increased and the initial peak load is also increase with the increasing of the concrete strength value, but the mechanical capacities of the concrete has little influence on the ultimate load capacities of the specimen. Keywords: Numerical test; reinforcement concrete, crack distribution, 3D

Stress Distribution Rule of Reinforced Concrete Specimen under Uniaxial Tension

A numerical test code named RFPA (Realistic Failure Process Analysis) was used to investigate the stress filed transformation process of the reinforced concrete specimen under uniaxial tensile loading. The periodically distributed fracture spacing phenomenon exists in the reinforced concrete structure and the concrete cover thickness was an important factor influence the average crack spacing and crack number. The numerical simulation results show that the stress fields on the concrete between the two adjacent cracks go through a variation process from tensile stress to compressive stress with the increasing of the concrete cover thickness value. It is clear that the stress distribution and fracture spacing were related to the concrete cover thickness under the condition that the materials characteristics were certain (such as concrete and reinforcement materials).In addition, if there was a new crack produced, the location was sure in the middle of the two adjacent cracks since the maximum stress occurred in the middle of the two adjacent cracks. So, it indicates that the concrete cover thickness can influence the average fracture spacing and the crack number in the reinforced concrete prism specimen.

Quantification of fracture networks in non-layered, massive rock using synthetic and natural data sets

Two quantitative measures – correlation dimension and maximum Lyapunov exponent – are investigated for quantifying fracture spacing in massive, non-layered rock. The correlation dimension, a measure of fractal dimension, characterizes some aspects of fracture distribution. Relative to other fractal methods used in structural geology, the correlation dimension provides a more rigorous mathematical calculation of the fractal dimension and is particularly robust in cases where data is limited. The maximum Lyapunov exponent calculation also provides quantification of observed distributions of fracture spacing, emphasizing variations in adjacent spacing measurements. The two methods are tested on two different synthetic data sets, to elucidate their usefulness in distinguishing between different distributions, and their sensitivity to population size, average fracture spacing, and standard deviation. Both methods provide accurate results for small population sizes and for a range of average fracture spacings. These methods are then used together to quantify two different fracture sets in the granitoids of the Sierra Nevada Batholith. The results indicate that the different fracture sets – inferred to form from different tectonic processes – have distinctive and quantifiable differences in patterns of fracture spacing.

Effect of reinforcement speciality on average fracture spacing of reinforced concrete specimen

A numerical test code named RFPA (realistic failure process analysis) was used to investigate the crack distribution rule of reinforced concrete specimens under axial tension. The results indicate that, the periodically distributed fracture spacing phenomenon exists in the failure process of the reinforced concrete structure. Besides, the effect of reinforcement characteristics on the mechanical behavior and average crack spacing of reinforced concrete was also studied in five samples with different elastic moduli of the reinforcement. The elastic modulus value of the reinforcement is considered to be an important factor not only to significantly influence the average crack spacing but also to control the ultimate strain of the specimen. In addition, the average crack spacing is increased and the ultimate strain of the specimen is also increased with the decrease of the elastic modulus of the reinforcement.

Isotopic effects in fracture-dominated reactive fluid–rock systems

A mathematical model is presented that describes the effects of pore fluid aqueous diffusion and reaction rate on the isotopic exchange between fluids and rocks in reactive geo-hydrological systems where flow is primarily through fractures. The model describes a simple system with parallel equidistant fractures, and chemical transport in the matrix slabs between fractures by aqueous diffusion through a stagnant pore fluid. The solid matrix exchanges isotopes with pore fluid by solution–precipitation at a rate characterized by a time constant, R (yr −1), which is an adjustable parameter. The effects of reaction on the isotopes of a particular element in the fracture fluid are shown to depend on the ratio of the diffusive reaction length for that element ( L) to the fracture spacing ( b). The reaction length depends on the solid–fluid exchange rate within the matrix, the partitioning of the element between the matrix pore fluid and the matrix solid phase, the porosity and density of the matrix, and the aqueous diffusivity. For L/ b < 0.3, fluid–rock isotopic exchange is effectively reduced by a factor of 2 L/ b relative to a standard porous flow (single porosity) model. For L/ b > 1, the parallel fracture model is no different from a porous flow model. If isotopic data are available for two or more elements with different L values, it may be possible to use the model with appropriate isotopic measurements to estimate the spacing of the primary fluid-carrying fractures in natural fluid–rock systems. Examples are given using Sr and O isotopic data from mid-ocean ridge (MOR) hydrothermal vent fluids and Sr isotopes in groundwater aquifers hosted by fractured basalt. The available data for MOR systems are consistent with average fracture spacing of 1–4 m. The groundwater data suggest larger effective fracture spacing, in the range 50–500 m. In general, for fractured rock systems, the effects of fracture–matrix diffusive exchange must be considered when comparing isotopic exchange effects for different elements, as well as for estimating water age using radioactive and cosmogenic isotopes.

Fracture Length Estimation from Borehole Image Logs

We describe a method to estimate fracture length for circular fractures from borehole image logs. The relative frequency of fractures, which have complete circumference trace on image logs is related to fracture length. A simple functional relationship can be derived for the relative frequency of complete fracture traces in terms of average fracture inclination to borehole, borehole diameter and fracture length. This formulation however, tends to underestimate fracture length because a constant length is assumed. A more accurate length estimate can be obtained by assuming that fracture length is linearly correlated to fracture aperture or spacing. Cumulative frequency distribution of fracture aperture and spacing can be obtained from borehole image logs. The problem then transforms itself to finding the scaling factor between fracture length and aperture (or spacing) from the relative frequency of fractures with complete traces. The product of the scaling factor and average fracture spacing (or aperture) gives the average fracture length.

Fracture spacing and orientation distributions for two‐dimensional data sets

A new, automated method is developed for the measurement and display of fracture spacing and orientation from two‐dimensional (2‐D) fracture maps. Separate histograms of fracture spacing are calculated at different orientations through the 2‐D data set. The histograms for all orientations are plotted together, reducing the biasing effects associated with one‐dimensional (1‐D) sampling of a fracture population. Quantitative measurements of fracture strike anisotropy and fracture density are incorporated in the plot. No prior measurements are needed of parameters such as fracture spacing, orientation, or width. The data do not have to be preprocessed into a numerical vector format, saving time and reducing user bias. The method retains the relative frequency of different ranges of fracture spacings, which are lost in other fracture frequency measures such as fracture intensity/density. Thus the presence of any dominant (rather than average) fracture spacing and fracture clustering is highlighted. The method provides a quantitative, statistically unbiased representation of fracture orientation and spacing and is illustrated on synthetic and real fracture data sets at a range of scales (from meters to tens of kilometers). Its application to a seismic energy scattering problem is also discussed.

Estimating Average Fracture Spacing in Subsurface Rock

Knowledge of the spacing of fractures in reservoir rocks (i.e., the distance between parallel fractures in a subsurface joint set) can lead to a better understanding of the production characteristics of a reservoir and serve to quantify the relative degree of deformation in subsurface rocks. In this paper, I present a new method for estimating the spacing of subsurface fractures; this new method is easy to use from the standpoint of both data collection and data analysis. The average fracture spacing method can be applied with boreholes of any orientation relative to a fracture set. The method is especially powerful when it is used for the relatively common case of a borehole nearly parallel to a fracture set (e.g., vertical borehole intersecting vertical fractures). Average fracture spacing is estimated from an analytical solution based on observed borehole-fracture intersections and observed fracture porosity; the only data required are the dimensions of the core (or imaged borehole) and the total height of all sampled fractures. Because the likelihood of intersecting fractures increases when a well is deviated perpendicular to the fractures of a set, fracture reservoirs commonly are candidates for deviated boreholes. An informed decision on borehole deviation requires predicting the fracture intersection frequency as a function of both deviation magnitude and direction. A new method, based on probabilities of borehole-fracture intersections, uses spacing and height data from subsurface joint-like fractures and the borehole diameter to predict fracture intersection frequencies for all possible well deviations. Fracture intersection frequency solutions are presented with respect to a conventional geographic reference frame, thus simplifying even the most complex three-dimentional situations.