Geological Fracture Research Articles

Elastic Properties of Fractured Rock Masses With Frictional Properties and Power Law Fracture Size Distributions

AbstractWe derive the relationships that link the general elastic properties of rock masses to the geometrical properties of fracture networks, with a special emphasis to the case of frictional crack surfaces. We extend the well‐known elastic solutions for free‐slipping cracks to fractures whose plane resistance is defined by an elastic fracture (shear) stiffness ks and a stick‐slip Coulomb threshold. A complete set of analytical solutions have been derived for (i) the shear displacement in the fracture plane for stresses below the slip threshold and above, (ii) the partitioning between the resistances of the fracture plane on the one hand and of the elastic matrix on the other hand, and (iii) the stress conditions to trigger slip. All the expressions have been checked with numerical simulations. The Young's modulus and Poisson's ratio were also derived for a population of fractures. They are controlled both by the total fracture surface for fractures larger than the stiffness length lS (defined by ks and the intact matrix elastic properties) and by the percolation parameter of smaller fractures. These results were applied to power law fracture size distributions, which are likely relevant to geological cases. We show that if the fracture size exponent is in the range −3 to −4, which corresponds to a wide range of geological fracture networks, the elastic properties of the bulk rock are almost exclusively controlled by ks and the stiffness length, meaning that the fractures of size lS play a major role in the definition of the elastic properties.

Seismic inversion for geologic fractures and fractured media

Amplitude variation with offset (AVO) inversion attempts to use the available surface seismic data to estimate the density, P-wave velocity, and S-wave velocity of the earth model. Under linear slip interface theory, synthetic seismograms for models with fractures prove that fractures are also reflection generators. Consequently, observed reflections are not necessarily due to lithologic variations only, but they could be due in part to the effect of fractures. To obtain approximate equations for AVO inversion for fractured media, denoted by AVO with fracture (AVOF), we derived new equations for PP-wave reflection and transmission coefficients that are based on nonwelded contact boundary conditions. In particular, along with the fracture compliances, azimuth has also been taken into account in the equations because the fractures can have any orientation. The new approximate AVOF equations for a horizontally fractured medium with impedance contrast are developed by simplifying the equations for the new PP-wave reflection and transmission coefficients. In the new approximate AVOF equations, the reflection coefficients are divided into a welded contact part (a conventional impedance contrast part) and a nonwelded contact part (a fracture part). This makes the equations flexible enough to separately invert for the rock properties of the fracture and the background medium in the case of a fractured medium with impedance contrast. The new approximate AVOF equations state that fractures could cause the seismic reflectivity to be frequency dependent, and that the fractures not only influence the wave amplitude but also change the wave phase. The linear least-squares and nonlinear conjugate gradient inversion algorithms are applied to estimate the elastic reflectivity using the new approximate AVOF equations. The inverted results for seismic data for a horizontally fractured medium with impedance contrast are evaluated to find a more accurate delineation of the subsurface rock properties.

Edge detection in potential filed using the correlation coefficients between the average and standard deviation of vertical derivatives

Edge detection is an essential task in the interpretation of potential field data. Many existing edge detection methods are the functions composed by the horizontal derivative and vertical derivative of potential field data. The edges recognized by those methods are bigger than the true edges and when the depths of the geological bodies are different, the edges will be detected fuzzy and difficult to identify the edges accurately. In this paper, we present a new method to delineate the edges of the sources, which is based on the correlation coefficients between the average and standard deviation of vertical derivatives in a sliding window. The algorithm of this method is very simple. The zero value of the correlation coefficients is used to delineate the geological edges. It's clear to see the edges with the zero contours which will lead to continuous and clear detected edges and the method shows the edges more precisely. Moreover, the anomalies in different depths can be detected in the same degree and are insensitive to noise. The measure is initially applied on the synthetic gravity and magnetic data. The tests of theoretical models indicate that the new method could detect the edges of models in different depths and the position is in good accordance with the models' edges. Finally, this method is applied to gravity data from a portion of Vientiane Basin, Laos. As a result, the method is helpful in recognizing geologic fractures clearly. Moreover, it shows more geologic details with smaller window size and gives superior results with higher quality data.

Análisis de fracturas geológicas extraídas por teledetección en imágenes Landsat TM, ejemplo de la zona de Imilchil-Tounfite (Alto Atlas central, Marruecos)

En este trabajo se han aplicado metódos estadísticos de datos obtenidos por teledetección, para la cartografía de lineamientos en afloramientos del Jurásico en la zona de Imilchil-Tounfite, Alto Atlas Central de Marruecos. Las técnicas analíticas utilizadas incluyen el análisis de componentes principales (PCA) aplicado a las bandas visible y infrarrojos, que permite crear nuevas imágenes con una mejor interpretación visual, y filtros direccionales N0°, N45°, N90° y N135° con una matriz de 5.5 para mejorar rasgos en las direcciones perpendiculares correspondientes y obtener una buena discriminación de esas estructuras. Los resultados preliminares ponen de manifiesto una fractura geológica dominante de tendencia ENE-SW con un 52% del total de lineamientos, una segunda tendencia ONO-S (23%), una tercera serie de fracturas orientada NE-SW (20%) y, por último, una serie de menor importancia de fracturas tendencia NW-SE (5%). Las relaciones estadísticas entre las fracturas y la superficie afectada por un lado y la longitud de la fractura, por otra parte, muestra una red de fracturación bien estructurada. El mapa final de lineamientos constituye una contribución para completar la geología de la zona y como ayuda a las prospecciones mineras e hidrogeológicas en la zona de Imilchil-Tounfite.

Multi-criterion based well placement and control in the water-flooding of naturally fractured reservoir

In the optimization of naturally fractured reservoirs, it is required to take into account their complex flow behavior due to high conductivity fractures. In this regard, the possible effects of fractures must be included in the optimization procedure. In a water-flooding project, fast water breakthrough from injection to production wells may be occurred because of high permeability fractures. To consider the effect of the fracture system, a multi-criterion optimization procedure is proposed in this work. For this contribution, Non-dominated Sorting Genetic Algorithm version II (NSGA-II) is implemented for the optimization purposes. Considering the effect of the fracture system on the flow behavior and consequently, development scenarios, the water breakthrough time is regarded as the objective in addition to ultimate oil recovery. The procedure is applied for well placement and control problems subject to maximization of the cumulative oil production and minimization of water front velocity (or respectively maximization of water breakthrough time). The problems cover design of well configuration and also time-varying bottom-hole pressures. Geological fracture uncertainty in terms of fracture permeability realizations is taken into account for the last optimization problem. This enables decision-makers to select the best scenario by a trade-off between the objectives which are maximization of expected reservoir performance and reducing the risk associated with the worst-case scenario. For this optimization problem under uncertainty, the significance of water breakthrough time expected value as an objective on the robust optimization problem is investigated.

Fluid trapping during capillary displacement in fractures

The spatial distribution of fluid phases and the geometry of fluid–fluid interfaces resulting from immiscible displacement in fractures cast decisive influence on a range of macroscopic flow parameters. Most importantly, these are the relative permeabilities of the fluids as well as the macroscopic irreducible saturations. They also influence parameters for component (solute) transport, as it usually occurs through one of the fluid phase only. Here, we present a numerical investigation on the critical role of aperture variation and spatial correlation on fluid trapping and the morphology of fluid phase distributions in a geological fracture. We consider drainage in the capillary dominated regime. The correlation scale, that is, the scale over which the two facing fracture walls are matched, varies among the investigated geometries between L/256 and L (self-affine fields), L being the domain/fracture length. The aperture variability is quantified by the coefficient of variation (δ), ranging among the various geometries from 0.05 to 0.25. We use an invasion percolation based model which has been shown to properly reproduce displacement patterns observed in previous experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. We show that when the in-plane curvature is considered, the amount of trapped fluid mass first increases with increasing correlation scale Lc and then decreases as Lc further increases from some intermediate scale towards the domain length scale L. The in-plane curvature contributes to smoothening the invasion front and to dampening the entrapment of fluid clusters of a certain size range that depends on the combination of random aperture standard deviation and spatial correlation.

A calculation method of optimal water injection pressures in natural fractured reservoirs

Abstract Injection pressures usually play a great role in the stimulation of low permeability fractured reservoirs. In this study, the stress state around an injection well was analyzed, and a three-collinear fracture model was established. Based on this model, the mode II fracture criterion was expressed in terms of a new form without stress intensity factor and fracture toughness involved. Based on this new form of fracture criterion, a calculation method of water injection pressures was proposed, and its effectiveness has been confirmed by the measurement results from Fuyu reservoir of Toutai oilfield. The factors that affecting optimal injection pressures have been investigated, and the results show that the water injection pressure is largely affected by the state of natural factures and the in-situ stress; According to Fuyu reservoir geological property and natural fracture distribution, the water injection pressure has been predicted and the result agrees well with that adopted in Fuyu reservoir. This study will have a beneficial application in the design and optimization of hydraulic fracturing in naturally fractured reservoirs.

The geospatial relationship of geologic strata, geological fractures, and land use attained by a time-series aridity index in a semiarid region.

In a vast semiarid region of the Baja California Peninsula, remote sensing and GIS techniques were applied to moderate resolution images of Landsat 5 TM to explore the geospatial correlation among the grid aridity index (AI), shapefiles of geologic strata, land use, and geological fractures. A dataset of randomized sample points in a time-series of one hydrologic year along with vector file GIS delineated geologic fractures-including the area between their left/right parallel buffer lines-was used as mask analysis. MANOVA results were significant (p<0.05) for geologic strata, land use, and basin. Overall results reveal the effects of soil texture on water retention on deeper soil horizons and the rate of vertical motion of rainwater. Despite the fact that geologic fractures underlie a large number of biotic communities, in both latitude and longitude gradients of the peninsula, no statistical significance was observed among the fractures themselves or the areas between their parallel buffer lines. One pulse rainfall event was documented by the AI grid maps enabling a robust vegetative response in early summer to an abnormal amount of rain provided by tropical storm Julio. AI grids appear to be useful for characterizing an ecosystem's dynamism. New options are suggested for this research strategy by expanding the number of datasets and incorporating geographic exclusion areas.

BDDC for mixed‐hybrid formulation of flow in porous media with combined mesh dimensions

SummaryWe extend the balancing domain decomposition by constraints (BDDC) method to flows in porous media discretised by mixed‐hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are modelled by one‐dimensional or two‐dimensional elements inside three‐dimensional domains. In this set‐up, the global problem and the substructure problems have a symmetric saddle‐point structure, containing a ‘penalty’ block due to the combination of meshes. We show that the problem can be reduced by means of iterative substructuring to an interface problem, which is symmetric and positive definite. The interface problem can thus be solved by conjugate gradients with the BDDC method as a preconditioner. A parallel implementation of this algorithm is incorporated into an existing software package for subsurface flow simulations. We study the performance of the iterative solver on several academic and real‐world problems. Numerical experiments illustrate its efficiency and scalability. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Laboratory measurements of guided-wave propagation within a fluid-saturated fracture

A fluid-saturated flat channel between solids, such as a fracture, is known to support guided waves—sometimes called Krauklis waves. At low frequencies, Krauklis waves can have very low velocity and large attenuation and are very dispersive. Because they propagate primarily within the fluid channel formed by a fracture, Krauklis waves can potentially be used for geological fracture characterization in the field. Using an analogue fracture consisting of a pair of flat slender plates with a mediating fluid layer—a trilayer model—we conducted laboratory measurements of the velocity and attenuation of Krauklis waves. Unlike previous experiments using ultrasonic waves, these experiments used frequencies well below 1 kHz, resulting in extremely low velocity and large attenuation of the waves. The mechanical compliance of the fracture was varied by modifying the stiffness of the fluid seal of the physical fracture model, and proppant (fracture-filling high-permeability sand) was also introduced into the fracture to examine its impact on wave propagation. A theoretical frequency equation for the trilayer model was derived using the poroelastic linear-slip interface model, and its solutions were compared to the experimental results.

Mapping of tecto-lineaments and investigate their association with earthquakes in Egypt: a hybrid approach using remote sensing data

This study integrates quantitative methods to detect surface and near-surface geological linear structures from digital elevation model. A set of altitude, slope and shaded relief maps was enhanced by applying Sobel filter with 10% threshold and percentile stretch to detect geological fractures and their displacements over regional scale. Topographic fabric grain algorithm, which classifies point lines into the ridge/valley and quantifies the degree to which all the ridges and valleys are aligned in the same direction, was used to auto-detect lineaments. About 1300 linear features were computed and their orientations were statistically analysed using rose diagrams. The enhanced morphometric maps successfully visualized fault zones and their displacements and detected the regional fault zones cutting across the entire Egypt. Their trends were found to be in the NE–SW, NNE–SSW, NW–SE, NNW–SSE, N–S, E–W and WNW–ESE directions. The results obtained using the integrated methods were compared with those in geological and seismic maps of Egypt and showed strong agreement in several places. This proposed method may be useful for mapping concealed geological structures, where geophysical surveying is difficult and geological information not available.

Pressurized Poroelastic Inclusions: Short-term and Long-term Asymptotic Solutions

This paper provides semi-analytical, asymptotic short-term and long-term solutions for the volume change and corresponding leak-off volume of a fluid-saturated, three-dimensional poroelastic inclusion, considering fluid exchange with the surrounding poroelastic medium. Considering possibly different material properties and different fluid pressure of hydrocarbon-bearing formations or proppant-filled fractures in comparison to those of the surrounding geological structures, fractures or whole reservoirs can be regarded as inclusions. The problem-solving approach used in our study is inspired by the theory of inclusions and modal decomposition technique previously developed and used to solve several poroelasticity problems. Previous studies on the topic, however, have not incorporated the hydraulic communication between the inclusion and the surrounding medium; therefore, fluid pressure changes in the surrounding rock due to fluid pressure changes in the inclusion were ignored. An example of this problem would be a pressurized stationary fracture, which, depending on pressure, might have fluid exchange with the surroundings. Numerical examples considering inclusions with different aspect ratios and material properties are provided to better describe the significance of fluid exchange.

An automated approach for conditioning discrete fracture network modelling to in situ measurements

Creation of a geological fracture network model conditioned to in situ geometric measurements is of great importance to geoprofessionals, as fractures dominate pathways for fluid flow, a major concern for many engineering applications. This paper introduces and applies the Stochastic Nelder Mead simplex method to automatically calibrate stochastic parameters of geometric characterisations of a discrete fracture network model. This method can overcome the non-convergence of a previous exploratory approach on the classic Nelder Mead method by others, and is an effective substitution to the manual trial-and-error method and is complementary to existing conditional simulation approaches. The procedure to integrate the Stochastic Nelder Mead with a discrete fracture network is presented in detail, and a case study was conducted. Results show that the improved model can better handle the stochastic nature of the underlying system and effectively simulates the observed number and mean trace length of these fractures, although the model results underestimate its standard deviation. Simulated distributions of trace lengths and spacings are within acceptable ranges except for some small offsets, which can be adjusted during model runs.

Automatic detection of near surface geological and hydrological features and investigating their influence on groundwater accumulation and salinity in southwest Egypt using remote sensing and GIS

This study employs two automated algorithms, the topographic fabric and the deterministic eight-node (D8), to reveal near surface geological fractures and their associated paleodrainages network from a 90 m DEM of the Shuttle Topographic Radar Mission sensor. The topographic fabric algorithm, which calculates the slope and aspect which define a vector normal to the earth’s surface and then compute direction cosines of normal vector at each point, was used to auto-detect fault zones. The deterministic eight-node (D8) algorithm, which determines in which neighbouring pixel any water in a central pixel will flow naturally, was used to delineate paleodrainages concealed beneath sand sheets. Seven sets of geological structures were recognized. Their major trends were found to be in the S46°W, S58°W, S81°W, N107°W, N–S, E–W and N152°W and share similar trends of the revealed paleodrainages. The results suggest a strong spatial relationship between the features extracted from DEM and groundwater potential.

Channeling and stress during fluid and suspension flow in self-affine fractures.

The flow of fluids and particulate suspensions in realistic models of geological fractures is investigated by lattice Boltzmann numerical simulations. The walls are synthetic self-affine fractal surfaces combined to produce a tight fracture, the fluid is a viscous Newtonian liquid, and the particles are rigid noncolloidal solid spheres. One focus is channeling phenomena, where we compare the fracture aperture, the preferred paths for fluid flow, and the preferred paths for suspended particles. The preferred paths are found to be somewhat similar for pure fluid and particulates and not immediately related to the fracture aperture map. We further investigate the (tensor) stress exerted on the fracture walls. Wall roughness tends to decrease stress by reducing the flow velocities adjacent to it, an effect enhanced by the presence of particulates. Last, we examine the stress probability distributions and their spatial correlation functions.

SIMULATION AND ASSESSMENT OF SHALE OIL LEAKAGE DURING IN SITU OIL SHALE MINING

Whether there is a risk of shale oil leakage along the depleted wells or multi-level geological fractures during in situ oil shale mining was predicted using the geological data from the Songliao Basin and survey wells in Fuyu county of Jilin province, China. The simulation results obtained employing the Transport of Unsaturated Groundwater and Heat 2 (TOUGH2) software indicate that oil leakage along depleted wells would entail greater risks to the upper aquifer, while the leakage along multi-level geological fractures would involve higher risks to the lower aquifer close to the shale beds. The distributions of shale oil saturation under the original and 1.3-fold formation pressures are slightly different, and the pollution halo somewhat increased only in an aquifer 40-50 m underground. The shale oil saturation in the leaking channel may be 0 during the leaking process.

A Fully Integrated Approach for Better Determination of Fracture Parameters Using Streamline Simulation; A gas condensate reservoir case study in Iran

Many large oil and gas fields in the most productive world regions happen to be fractured. The exploration and development of these reservoirs is a true challenge for many operators. These difficulties are due to uncertainties in geological fracture properties such as aperture, length, connectivity and intensity distribution. To successfully address these challenges, it is paramount to improve the approach of characterization and simulation of fractured reservoirs.In this study, a fully integration of all available data and methods have been used for generating stochastic discrete fracture network (DFN)such as outcrop study, core description, petrophysical and image logs and also for better result validation, streamline simulation has been conducted. In this comprehensive process a real gas condensate fractured carbonate reservoir has been used.Firstly, three main fracture sets were defined that have fold-related fractures, then the fracture intensity and DFN model using fracture drivers correlation were generated. After that, permeability of the developed DFNs was calibrated with available well test permeability. Then, a streamline simulation was used because of its high computational speed, high accuracy and good visualization for the repeated nature of history matching of a dual porosity model in the gas condensate reservoir. So, with running streamline simulation, three realizations (High, Medium and Low) ranked based on the objective function values. These three realizations are common realization that are well known with optimistic, most likely and pessimistic scenarios. Finally, comprehensive history matching was done for all the three-selected realizations.The overall goal is to develop a representative fluid flow simulation model for improving gas cycling procedure in gas condensate reservoir. This method has great application in the high resolution fractured reservoir modeling due to using actual fracture parameters. Also, it can be used for model ranking, screening and optimum dynamic model calibration for reduction of the history matching complexity without being manipulated by reservoir engineer.

Groundwater potential modelling using remote sensing and GIS: a case study of the Al Dhaid area, United Arab Emirates

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEM and LANDSAT images of spatial resolution 30 m were used to construct groundwater potential zones (GPZ) map by integrating geological fractures, drainage network, slope and relief, and convergence index maps of the study area. Weight and score of each map were developed according to their level of contribution toward groundwater accumulation and spatial distribution of groundwater wells. The area that has very high potential for groundwater is located at the foot of Oman Mountains and Al Dhaid Depression covering an area of about 59.33 km², which is 4.40% of the study area. Further hydrological map and data on hydraulic properties of shallow aquifer, as recorded from observation wells in the regions, have been used to validate the produced GPZ map. The validation result showed sufficient agreement between the produced GPZ map.

Natural hazards susceptibility mapping in Kuala Lumpur, Malaysia: an assessment using remote sensing and geographic information system (GIS)

Intensive geological fractures and their associated karst features in tropical regions are often associated with unpredictable environmental and geotechnical engineering problems. This requires precise modelling using modern techniques. A 20 m spatial resolution Digital Elevation Model (DEM), a Geographic Information System (GIS) and Weighted Spatial Probability Modelling (WSPM) were integrated to predict the occurrence of flooding, landslides, sinkholes and earth subsidence in Kuala Lumpur, Malaysia. Five essential thematic layers were extracted using set of automated algorithms and then they were weighted. Layers included were geological fractures, stream network, micro-depressions, slope and lithological contact. All these thematic layers were assigned weights according to their level of contributions to the occurrence of flooding, landslide, sinkholes and earth subsidence. The map demonstrated that areas having very high geohazard susceptibility show an area of 4.155 km2 (8%), whereas the areas characterized by low susceptibility for the occurrence of geohazard is approximately 16.394 (31.5%) of total Kuala Lumpur area. The natural hazard probability model was validated by comparing its results with the published landslide locations and geophysical and geotechnical maps of Kuala Lumpur and the comparison showed strong agreement.

Topology of fracture networks

We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed within modern network theory. We test the mapping for two-dimensional geological fracture outcrops and find that the equivalent networks are small-world and dissasortative. By anlayzing the Discrete Fracture Network model, which is used to generate artifical fracture networks, we also find small world networks. However, the networks turn out to be assortative.