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Collaborating Authors
Zimmerman, R.W.
Abstract Numerical simulations have been conducted to model the deformation, damage, and fracture growth caused by the plunge of a spherical drill bit insert into a brittle rock. The deformation of the rock, which is initially homogeneous and isotropic, is modeled using the finite element method. Fracture geometry evolves as a function of fracture growth, and the rock domain is continuously re-meshed to capture this geometric change. Contact forces are applied radially over the contact area as a function of the depth of the plunge. A series of simulations is presented, having varying initial flaw distributions, and which capture the fracture pattern formation during the progressive indentation of the insert into the rock. The ensuing patterns depict the formation of horizontal and Hertzian fractures. A large fracture density is created around the contact area. The complexity of the internal fracture structure is less apparent at the surface of the deformed rock, as compared to the internal fracture pattern. Fracturing leads to the formation of surface chips in the form of tilted elliptical domains parallel to the rock surface. Early stages of chipping are not always apparent from the fracture pattern at the surface of the rock. Results are in good agreement with experimental observations.
- Europe > United Kingdom (0.28)
- North America > United States (0.28)
Abstract Some rocks, such as shales, are highly anisotropic in their mechanical behavior. In such rocks, the value of the maximum principal stress that causes shear failure depends not only on the confining stress, but also on the angle ß between the maximum principal stress and the normal vector to the bedding plane. Triaxial compression experiments were carried out on two types of organic-rich mudstones at different bedding angles ß and confining pressures s3. Two triaxial compression datasets from experiments and 10 datasets from the literature were fit to the Pariseau and the Jaeger plane-of-weakness (JPW) models. Results show that Pariseau’s model is more accurate for 10 of the 12 anisotropic rocks, whereas the JPW model is more accurate for the other two rocks, which were both rocks that had a low degree of strength anisotropy. Post-test examination of computerized tomography (CT) and thin-section images shows that for highly laminated organic-rich shales, there is a transition regime of angles ß lying between angles of about 10°ß<35°, wherein the failure surface follows an irregular path that may jump between the weak plane and intact rock. In this regime, the strength of the rock is lower than the strength predicted by the JPW model.
- North America > United States > Texas (0.97)
- South America > Argentina > Neuquén Province > Neuquén (0.31)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- South America > Argentina > Patagonia > Neuquén > Neuquen Basin > Vaca Muerta Shale Formation (0.99)
- North America > United States > Texas > East Texas Salt Basin > Cotton Valley Group Formation > Bossier Shale Formation (0.99)
- North America > United States > Louisiana > East Texas Salt Basin > Cotton Valley Group Formation > Bossier Shale Formation (0.99)
- North America > United States > Arkansas > East Texas Salt Basin > Cotton Valley Group Formation (0.99)
- Well Completion > Hydraulic Fracturing (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Shale gas (0.97)
A Multi-modal Approach to 3D Fracture And Fragmentation of Rock Using Impulse-Based Dynamics And the Finite Element Method
Paluszny, A. (Department of Earth Science and Engineering Imperial College) | Tang, X.H. (Department of Earth Science and Engineering Imperial College) | Zimmerman, R.W. (Department of Earth Science and Engineering Imperial College)
ABSTRACT: A numerical method combining the finite element method (FEM) and impulse-based dynamics is proposed for the simulation of 3D fracture and fragmentation. As opposed to existing methods, fragments are not represented as a conglomeration of primitive shapes; instead, their geometry is represented using solid modeling techniques. This allows for continuum-mechanics-based fracture propagation analysis to be carried out within each fragment, with fragment interaction and movement simulated using impulse-based dynamics. This approach models multi-body interaction of non-convex 3D objects which fall, collide, and fragment using impulse-based dynamics, as opposed to a penalty-based method. Instead, object trajectories are used to estimate time-of-impact, and contact between bodies is modeled by collisions at contact locations. This approach allows material properties to be explicitly defined at the macro-scale. A 3D fracture engine models fracture propagation in the individual 3D continua based on local stress intensity factor measurements using the reduced virtual integration technique, as well as decoupled geometry and mesh representation, and on the evaluation of local failure and propagation criteria. Fractures that reach free boundaries lead to further fragmentation. The framework, presented as a multi-modal toolkit, is suitable for meso-scale simulations, and is demonstrated by a mining-specific block caving application. 1. INTRODUCTION Fragmentation simulation involves capturing two main processes: damage and cracking of single bodies, and dynamics/collision between fragments. The analysis of damage and cracking in single bodies includes challenges such as defining initial material properties and rock heterogeneities, crack nucleation, and propagation of multiple cracks. Modeling collisions between fragments includes capturing processes such as collision detection, force transfer due to impact and compression, and energy loss during collision. Challenges include accurate geometric representation of fragments and cracks, accurate mechanical computations of movement and energy transfer, efficient processing of large volumes of data, and incorporating dynamically defined boundary conditions.
A Conceptual Empirical Approach for the Overall Strength of Unwelded Bimrocks
Sonmez, H. (Hacettepe University) | Kasapoglu, K.E. (Hacettepe University) | Coskun, A. (Hacettepe University) | Tunusluoglu, C. (Canakkale Ondokuzmart University) | Medley, E.W. (Geosyntec Consultants) | Zimmerman, R.W. (Imperial College)
Abstract Design and engineering facilities are often constructed in complex geological mixtures or fragmented rocks such as mélanges, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentines. These types of geological materials are generally chaotic and mechanically and/or spatially heterogeneous rock masses, which are composed of relatively strong rock inclusions, surrounded by weaker matrix, and may be considered as bimrocks (block-in-matrix-rocks; Medley, 1994). The preparation of standard and representative cores from these types of rock masses for conventional laboratory experiments is almost impossible. In the literature, there are a few attempts to overcome this difficulty by developing empirical approaches based on case histories and laboratory studies on bimrocks. However, despite these attempts, there is no widely accepted empirical approach in the rock mechanics community. In this study, some conceptual equations, which are open to improvement, were generated by considering literature findings to predict strength of unwelded bimrocks.
- Asia > Middle East > Turkey (0.31)
- North America > United States > California > Alameda County (0.15)
- Geology > Rock Type (0.49)
- Geology > Geological Subdiscipline > Geomechanics (0.36)
ABSTRACT: A simple model of a rock fracture is developed. The void space of the fracture is assumed to consist of parallel, periodically spaced tubular channels of elliptical cross-section. The apertures of the channels follow some arbitrary statistical distribution law. The normal stiffness of the fracture, and the hydraulic transmissivity of the fracture, can then be related to the aperture distribution function. The model is tested by inverting stress-strain data from a naturally-occurring fracture in granite to determine the aperture distribution function, and then using this aperture distribution function to predict the variation of permeability with stress. The predicted variation of transmissivity with stress shows good agreement with the measured values. 1. INTRODUCTION Both the mechanical and hydraulic behaviors of rock fractures are controlled by the morphology of the fracture surfaces. It is therefore expected that the mechanical compliance (normal and shear) and hydraulic transmissivity of a fracture should be related to one another [1,2]. Although this is undoubtedly true, the relationship is indirect and very complex, and thus far no simple correlations have yet been found between the mechanical and hydraulic properties of a fracture. A schematic diagram of a cross-section of a rock fracture (Fig. 1) shows two nominally-parallel rough rock surfaces that are in contact at some points. These contacting asperities impart stiffness to the fracture. The regions where the surfaces are not in contact form pathways for fluid flow. Fig. 1. Schematic of a rough-walled rock fracture, showing regions of contact and regions of open flow paths. (available in full paper) As the normal stress on a fracture increases, the mean aperture decreases, causing the transmissivity to decrease. Due to roughness and asperity contact, however, the change in mean aperture is not exactly equivalent to the joint closure. Furthermore, although transmissivity is proportional to the cube of the mean aperture, it also depends on the variance of the aperture, and the amount of contact area [3]. Consequently, the transmissivity of a fracture that is deforming under a normal load does not vary in direct proportion to the cube of the mean aperture. Numerous models have been proposed to attempt to relate the compliance and the transmissivity to the fracture morphology. But models for fracture compliance have naturally tended to focus on the rough fracture walls (for example, [4]), whereas fluid flow models have tended to focus their attention on the void spaces [3]. Consequently, it is difficult to draw connections between these two types of models. Among the works that have specifically atempted to relate the normal stiffness of a fracture to its transmissivity, through some micromechanical model, include Tsang and Witherspoon [5], Pyrak-Nolte and Morris [2], and Murdoch and Germanovich [6]. In the present paper we present a simple geometrical model of the void space of a fracture, which attempts to capture the basic features of fracture closure and fluid flow, and which has the advantage of allowing explicit mathematical expressions to be developed for the normal compliance and transmissivity.
- Well Completion > Hydraulic Fracturing (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (0.66)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (0.49)
ABSTRACT ABSTRACT: Uniaxial compression tests on rocks, if conducted at stresses below failure, typically show nonlinearity in the stress-strain curve, and hysteresis. Walsh (J. Geophys. Res., 1965) explained this behavior in terms of frictional sliding along the faces of closed cracks. Although well known and widely cited, Walsh’s model has not previously been developed in sufficient detail to be used for quantitative predictions. We revisit and extend his model, by including the effect of the stress required to close an initially open crack, and we examine the unloading process in detail. Our analysis leads to closed-form expressions for the loading and unloading portions of the stress-strain curve, as functions of elastic modulus of the uncracked rock, the crack density, the characteristic aspect ratio, and the crack friction coefficient. The model provides a good fit to the loading and unloading portions of the stress-strain curves, for experimental data on sandstones taken from the literature. 1 INTRODUCTION The mechanical behavior of rocks is to a great extent controlled by the presence of cracks and crack-like voids. This is true both with regards to the elastic behavior of the rock (see Jaeger et al. 2007), and with regards to inelastic processes such as yielding and failure (Paterson & Wong 2005). In 1965, Walsh (1965a, b ,c) published a set of three papers that provide the conceptual basis of much of our understanding of the influence of cracks on elastic rock deformation. Under hydrostatic loading (Walsh 1965a), open cracks initially (i.e., at low stresses) contribute an excess compliance to the rock. But each crack closes up at a stress that is roughly equal to aE , where E is the Young’s modulus of the uncracked rock, and a is the initial aspect ratio of the crack.
Abstract Water production in gas and oil wells is one of the major problems faced by the petroleum industry. Polymers and gels can be efficient materials for controlling excessive water production in gas and oil wells. The injection of gelant solutions into the near-wellbore formation can reduce the permeability of the formation to water much more so than to oil. Such gelants are known as relative permeability modifiers. In this experimental study, tetramethylorthosilicate (TMOS) has been used as the oil soluble gelant. TMOS is soluble in the oil phase, and reacts with water to form a semi-solid gel that is capable of modifying the permeability of the rock. As the water is transformed into gel, the permeability of the medium to water is reduced. Due to the increase in volume of the "water phase", the oil permeability is reduced to a lesser extent. A series of static and dynamic gelation and flow experiments have been performed in test tubes. These were followed by flow tests conducted in transparent glass micromodels to determine the end-point relative permeability for oil and water before and after gelant injection. Our results show that the gel formation depends on the concentration of the gelant in the oil phase, the oil/water ratio, the amount of total gelant solution injected, and the time of flow of the gelant solution into the water phase. It was observed that the volume of gel obtained after gelation increases as the TMOS concentration increases, at a fixed oil/water ratio. The degree of permeability reduction for both oil and water is directly related to the amount of gelant injected. The results we have obtained can be used for pre-screening the efficiency of TMOS treatments. Introduction An increase in water percentage during the production of crude oil from oil and gas reservoirs increases the production costs, and also creates water disposal problems. This problem has consequently attracted the interest of many researchers in the search for methods of reducing water production. Several methods have been used to control water production by reducing the relative permeability to water while avoiding, to the extent possible, any reduction in the relative permeability to oil. One approach has been to inject polymer solution into the production well, along with a cross-linker. The polymer solution and the cross-linker then react to form an annulus of gel around the production well. Once formed, the cross-linked gel is retained within the reservoir rock. This gel has the effect of modifying the flow of the two phases, oil and water. Hence, these polymers/gels are known as known as relative permeability modifiers (RPM), and the phenomenon they induce is known as disproportionate permeability reduction (DPR). Ideally, the aim of the treatment is to reduce the effective permeability for water flow, with no reduction in oil permeability. Such treatments may lead to significant reduction in water production, and hence a reduction in production costs. Sodium or potassium silicate solutions have been used to form totally blocking gels within the reservoir. Recently, organically modified silicates have been found to produce an effective gel that can modify the relative permeability of the reservoir rock. Tetramethylorthosilicate (also known as tetramethoxysilane, or TMOS) is one of the most widely known alkoxides, and can be hydrolyzed and condensed under relatively wide range of conditions to form a rigid, porous gel.
- Research Report > New Finding (1.00)
- Research Report > Experimental Study (0.86)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.34)
Abstract Polymers in the form of either solutions or gels are being used to control water production, especially when oil bearing and water zones cannot be isolated. Results of field treatments have varied widely, but often no obvious reason can be given for the success or the failure of the treatment. The lack of understanding of the basic mechanisms by which polymers influence the flow of water and oil hinders a wider application of this process. The achievement of a disproportionate permeability reduction (DPR - reducing the water permeability while producing minimum reduction in the oil permeability) is crucial, and several mechanisms have been proposed to explain this effect. Among those mechanisms, polymer adsorption and lubrication effect are being thought as the main reason for DPR when polymers (without cross-linker) are used. This paper presents a mechanistic study of the effect of polymer injection on single and two-phase flow. Experiments have been performed in glass micromodels, under both water-wet and oil-wet conditions. The oil and water end-point permeabilities have been obtained, before and after the injection of a cationic polyacrylamide, while observing the fluid distribution and flow patterns. During polymer injection, under water-wet conditions, polymer layers were seen to form and build-up on the crevices between the grains. This mechanism is known as adsorption-entanglement. Data on this phenomenon are scarce, and this paper presents the first visualization study of this phenomenon in porous media. In water-wet models there was a significant permeability reduction to water, while there was no significant reduction in oil permeability. The entanglement of polymer reduces the area available for water to flow, whereas the oil, occupying the centre of the larger pores, was nearly unaffected by the polymer entanglement. In oil-wet models, where polymer layers were not observed, the oil and water effective permeability before and after polymer injection remained unchanged. Our results confirm that adsorption-entanglement for water-wet media, which produces the build-up of the polymer layers on the grain crevices, is a basic mechanism by which polymers can modify the flow characteristics and thus preferentially reduce the water relative permeability. Introduction Several methods aimed at reducing water inflow into production wells have been proposed and tested in the field. These methods generally consist of placing a barrier across the water-producing zone. The barrier consists of, for example, cements, resins, suspensions of solid particles, or paraffin waxes. Unfortunately, these methods have the disadvantage of blocking the oil or gas flow as well as the water inflow. More recently, polymers have been successfully used to reduce the water flow. The success of polymer treatments is based on reducing the water permeability while producing minimum reduction in the oil permeability, this phenomenon is known as disproportionate permeability reduction (DPR). However, until now, there is no consensus on the mechanisms by which the polymer produces the DPR.
Abstract Water production from oil and gas reservoirs is increasing world-wide, as more reservoirs are becoming mature. In order to control water production, polymers or gels are injected into production wells to either block the flow, or to reduce water permeability. In the latter case the polymers/gels are known as relative permeability modifiers. In these treatments, a gel is often formed in-situ through a chemical reaction, creating a semi-solid material that is capable of modifying the permeability. To visualise the processes that occur during the flow of water and oil through a porous rock containing gel, experiments were conducted in transparent glass models in which the flow events can be observed. To form the gel in-situ, a novel alkyl silicate gelant was used, which is soluble in the oil phase, and which, when in contact with water, reacts to convert the water phase into a gel. From the flow observations, the underlying physics can be extracted and the basic mechanisms understood (reduction in effective pore size distribution, gel-bounded water, wetting films of free water, etc.). These mechanisms were used to develop a conceptual model, which consists of three main elements: pore space (bundle of capillary tubes), occupancy of the phases (fluid and gel distribution), and flow equations. The output from the conceptual model is the capillary pressure as a function of total water saturation and end-point relative permeability. The results from this model successfully represent the disproportionate permeability reduction observed in micromodels and core experiments, verifying the mechanisms included in the model. This model may be quickly and easily used to study the influence of pore size distribution, gelant concentration, and initial water saturation, before undertaking laboratory or more complex modelling studies. Introduction High water production in association with crude oil is one of the major production difficulties for the petroleum industry, with water often comprising more than 50% of the produced fluids. Coning due to bottom water drive and production from high permeability, watered-out layers during water flooding are among the main causes. Water handling and disposal costs often shorten the economic life of a well. Disposal of produced water is also an environmental concern, especially offshore. One method to control water production that has been used with some success is to inject gelant solutions into the near well-bore formation. After the gel has been formed, in general, they reduce the permeability to water much more so than to oil; this phenomenon is known as disproportionate permeability reduction (DPR). The ideal treatment will reduce the water effective permeability without affecting the oil permeability. Although many successful polymer gels experiments and field applications have been reported in the literature, the exact mechanisms by which this disproportionate permeability reduction occurs are not understood. However, as the fluids used before and after treatment remain unchanged, some modifications in the saturation, fluid distribution and flow should occur at the pore level due to the presence of the gel. The mechanisms and causes of DPR could vary with the polymer or gel system and the particular conditions studied. Several mechanisms have been proposed and verified under certain conditions, but still there is no consensus regarding its validity. In this study a silicate gel is produced in-situ by using a relatively new gelant system. This gel system has been proposed as a means to reduce excess water production by treating the production wells, i. e., near-wellbore treatment. As the gelant is oil soluble, it could be injected into the formation without precipitation. Therefore, this chemical system should not damage the oil producing zones. During shut-in period the reaction takes place converting the water into gel while ensuring oil continuity.
- Europe (0.68)
- North America > United States (0.46)
Abstract This paper describes the implementation of a Genetic Algorithm (GA) to carry out hydrocarbon reservoir characterisation by conditioning the reservoir simulation model to production data (history matching) on a predefined geological and structural model. The proposed technique combines the advantages of the pilot point method for the description of petrophysical properties, with the advantages of GAs for global optimisation. The modified GA uses a complex genome, which is divided into seven separate chromosomes for different types of reservoir parameters. Chromosomes containing the pilot point information are three-dimensional real number structures which include information for the wells, while the chromosomes for all other parameters are one-dimensional arrays. Specially designed crossover and mutation operators have been created to work with the non-standard genome structure. Results from tests on several GA design issues are presented, including crossover and mutation operators, encoding, selection, and other population strategies such as elitism. In addition, a comparison is made with a standard Simulated Annealing algorithm. Introduction Reservoir characterisation requires the incorporation into the reservoir models of all knowledge available, so that better predictions of reservoir performance can be achieved. The process makes use of measurements made in the field to restrict the range of values that the parameters might take. The measurements used are wide-ranging and include seismic data, data from geological analogues, core and log data from wells, well test data, and production data. Many previous attempts have been made to automate this process, posing the inverse problem as an optimisation problem and using some optimisation technique to match the numerical results to the measurements. Papers describing this process include Tan and Kalogerakis, Oliver et al., Deschamps et al., Wu et al., and Floris et al. Most of these attempts have used gradient-type methods. Search methods such as simulated annealing (SA) and genetic algorithms (GA) have also been applied to address the optimisation problem. GAs have been used in reservoir engineering in several works, including those by Sen et al., Bush and Carter, Guerreiro et al., and Romero and Carter. Genetic Algorithms (GAs) were invented by John Holland as an abstraction of biological evolution, drawing on ideas from natural evolution and genetics for the design and implementation of robust adaptive systems. Over the last 20 years, GAs have received much attention because of their potential as optimisation techniques for complex functions. Their main drawback, however, is that they can be computationally intensive, and therefore very expensive. This paper describes in detail the formulation of a modified GA using non-standard genome and genetic operators, as proposed by Romero et al. The method is computationally efficient, in that it requires only a modest number of forward simulations. The paper deals with some of the main GA design issues, and presents optimisation results on its application to a synthetic reservoir model constructed as part of the PUNQ project. Results with respect to the history matching at well level, and to the petrophysical property fields can be found in Ref. 12. Genetic Algorithm Genetic Algorithms (GAs) are heuristic type methods that can be applied to the optimisation of complex functions. They are randomised search algorithms based on an analogy to the mechanics of natural selection according to Darwinian evolutionary theory and the ‘survival of the fittest’ principle. GAs draw ideas from genetics to describe solutions to the problem under consideration as ‘individuals’, and mimic natural evolution by starting with an initial population of feasible solutions (individuals) to the problem being addressed.
- Europe (1.00)
- North America > United States > Texas (0.46)
- North America > United States > California (0.29)