Multiscale Fracture Research Articles

Numerical investigation of fluid-loss mechanisms during hydraulic fracturing flow-back operations in tight reservoirs

Multi-stage hydraulic fracturing is widely applied in tight reservoir exploitation. Production is enhanced significantly if hydraulic fractures can connect to sweet spots with enhanced permeability due to the presence of micro- (and induced) fractures. However, less than 50% of fracturing fluids are typically recovered. This study models the mechanisms of water loss and retention in fracture–matrix system and investigates their associated time scales under different reservoir conditions. Numerical simulation results are analyzed to identify circumstances under which these phenomena might be beneficial or detrimental to subsequent production. A series of mechanistic simulation models consisting of both hydraulic fractures and stochastically-distributed secondary fractures are constructed to simulate imbibition, fluid re-distribution, and flow-back during shut-in and cleanup. Water imbibition into the matrix would help to displace hydrocarbons into nearby micro- and hydraulic fractures, and this process could lead to an increase in initial rate. Although other mechanisms including water loss in desiccated matrix and water trapping in induced secondary fractures were proposed in literature, detailed understanding of these water-trapping mechanisms is still lacking. Fluid-loss and retention mechanisms in matrix and induced fractures are systematically investigated. Impacts of secondary fracture distributions and properties, matrix permeability, multiphase flow functions, initial saturation, water injection rate and shut-in duration on fluid retention and the associated time scales are assessed. This work presents a quantitative study of the controlling factors of water retention. It investigates the roles of multi-scale fractures in flow-back behavior and ensuing recovery performance. The results highlight the crucial interplay between shut-in duration and properties of connected fractures in the short- and long-term production performances. The results would have considerable impacts on understanding and improving current industry practice on fracturing design and assessment of stimulated reservoir volume.

Three-dimensional cellular automata modelling of cleavage propagation across crystal boundaries in polycrystalline microstructures

A three-dimensional cellular automata (CA) with rectilinear layout is used in this work to create and cleave polycrystalline microstructures. Each crystal is defined by a unique randomly generated orientation tensor. Separate states for grains, grain boundaries, crack flanks and crack fronts are created. Algorithms for progressive cleavage propagation through crystals and across grain boundaries are detailed. The mesh independent cleavage criterion includes the critical cleavage stress and the length scale. Resolution of an arbitrary crystallographic plane within a 26-cell Moore neighbourhood is considered. The model is implemented in Fortran 2008 coarrays. The model gives realistic predictions of grain size and mis-orientation distributions, grain boundary topology and crack geometry. Finally, we show how the proposed CA model can be linked to a finite-element model to produce a multi-scale fracture framework.

Finite Element Method Using a Characteristic-Based Split for Numerical Simulation of a Carbonate Fracture-Cave Reservoir

Fracture-cave carbonate reservoirs occur widely in source rocks and are prospects for exploitation worldwide. However, the presence of massive caves and multiscale fracture systems results in extremely complex fluid flow patterns. Therefore, in this paper, a discrete network model for fracture-cave reservoirs was established to study fluid flow characteristics and pressure distributions in complex flow regimes. In this study, the cave system was treated as a free-flow region, and the fluid flow in fracture systems followed the Navier-Stokes and Darcy equations, respectively. After discrete modeling, the Galerkin finite element method was used for numerical calculation of the single-phase free flow; the method maintains a high-precision result with low grid orientations during the simulation. In addition, because only one linear equation requires solving at each step, the solution is obtained quickly. Moreover, based on the proposed discrete media network model of fracture-cave reservoirs and the finite element numerical calculation method, a corresponding simulator was also developed. The finite element numerical simulation method based on the characteristic-based split (CBS) algorithm has proven to be applicable to complex flow problems in fracture-cave reservoirs.

A DYNAMIC DISCRETE FRACTURE APPROACH FOR MODELING MULTIPHASE FLOW AND TRANSPORT IN FRACTURED POROUS MEDIA

A numerical study was conducted to analyze multiphase fluid flow and transport processes in naturally fractured rocks during long-term waterflooding operations, particularly the dynamic discrete fracture models present for simulation of natural fracture, induced fracture, and fracture−matrix interactions. Different flow mechanisms for porous media, such as the non-Darcy model, fracture growth with respect to poroelastic stresses, and matrix−fracture transfer were considered. The method was solved by using the discrete fracture control-volume method. Results were obtained in terms of water cut, output, and pressure distribution for various fractured porous media. Comparisons for simulation results and purely analytical solutions show an excellent match. The new model allows us to better understand the flow behavior caused by multiscale fracture systems. The results from this investigation showed that the pressure drop across porous media increased with the length of dynamic fracture. In addition, water injection rate and injection-production ratio play an important role in determining the fracture growth. The proposed simulation method can be used to optimize injection pressures and rates, and water quality for maximizing oil recovery.

Fluid identification based on frequency-dependent AVO attribute inversion in multi-scale fracture media

A key problem in seismic inversion is the identification of the reservoir fluids. Elastic parameters, such as seismic wave velocity and formation density, do not have sufficient sensitivity, thus, the conventional amplitude-versus-offset (AVO) method is not applicable. The frequency-dependent AVO method considers the dependency of the seismic amplitude to frequency and uses this dependency to obtain information regarding the fluids in the reservoir fractures. We propose an improved Bayesian inversion method based on the parameterization of the Chapman model. The proposed method is based on 1) inelastic attribute inversion by the FDAVO method and 2) Bayesian statistics for fluid identification. First, we invert the inelastic fracture parameters by formulating an error function, which is used to match observations and model data. Second, we identify fluid types by using a Markov random field a priori model considering data from various sources, such as prestack inversion and well logs. We consider the inelastic parameters to take advantage of the viscosity differences among the different fluids possible. Finally, we use the maximum posteriori probability for obtaining the best lithology/fluid identification results.

Laboratory Experiment, Production Performance Prediction Model, and Field Application of Multi-slug Microbial Enhanced Oil Recovery

Because of heterogeneous formations and multi-scale fractures, the accurate evaluation of microbial enhanced oil recovery is faced with numerous difficulties. For the purpose of evaluating the production performance of multi-slug microbial enhanced oil recovery, this work studied the influence of microbial activity on the properties of oil and porous rock and the effect of microbial slug compositions on oil recovery. A mathematical model was built on the basis of the experiment, using the Buckley–Leverett theory and production decline laws. The model is a combination of the characteristic curve of the water cut change and the exponential decline law of oil production, which could predict oilfield production performance, including water breakthrough time, cumulative oil production, and relationship between the water cut and water saturation of the flood front. In comparison to the numerical simulation method, this approach has no additional restrictions because of grid orientation effects, which were found to be suitable for predicting production performance of either large-scale or whole block. The predicted values of the model were compared to the measured values of a field test, indicating that the model predicted the performance of microbial enhanced oil recovery precisely. More specifically, the maximum prediction error of a single well was less than 10%, and the prediction error of the whole block was less than 3%, suggesting the suitability of the model in predicting production performance. In conclusion, it is believed that the multi-slug seems to be a better approach for enhanced oil recovery and that the mathematical model would accurately predict the production performance of microbial enhanced oil recovery.

Experimental and Numerical Investigation of Multiscale Fracture Deformation in Fractured–Vuggy Carbonate Reservoirs

Fractures intersected with borehole are extremely sensitive to borehole pressure fluctuations, which causes the fractures to evolve into loss channels during well operations. This paper presents fracture deformation and pressure distribution within a single fracture, by combining experimental study of micro-fractures with numerical analysis of macro-fractures based on ANSYS software. Additionally, the deformable behavior of fracture considering the fluid–solid coupling effect is investigated, and the pressure distribution within the fracture during mud loss process is numerically simulated. It is revealed that fracture mouth expanded to the biggest as borehole fluid pressure transfers from fracture mouth to fracture tip, which results in lost circulation frequently due to the solid particles of drilling fluid failing to plug rapidly and effectively the opened fracture. To avoid lost circulation incidents, the acid-soluble lost circulation materials should be added according to the fracture deformation behavior before drilling the reservoirs with strong stress sensitivity.

Multiscale Fracture in Peeling of Highly Oriented Pyrolytic Graphite

Micromechanical cleavage is one of the methods used for isolation of single-and few-layer graphene sheets from bulk graphite. On the surface of peeled graphite flakes, nanosteps of precisely multiple-layer thickness are often observed. The nanosteps are believed to be termination edge of graphene sheets and formed by tearing graphene sheets sandwiched in the mouth of a main cleavage crack during the peeling process. In the present work, we introduce a continuum model to examine the peeling process that involves multiple fractures: the main cleavage fracture at the microscale, delamination of a graphene sheet from bulk graphite at the nanoscale, and tearing fracture of graphene at the atomistic scale. We apply von Karman's plate theory to model the graphene layer, the elastic fracture mechanics for the microscale cleavage crack, and a cohesive zone model for the nanoscale interlayer delamination and for the lattice-scale tearing fracture as well. With a reliable empirical interlayer potential, we could reveal the characteristic length scales involved in the multiscale fracture process. We show that the graphene layer is locally stretched to fracture in mode-I when von Karman's finite deflection effect in a plate is invoked, although the loading by the sandwiching cleavage crack faces is nominally tearing in mode-III.

Multi-scale fracture and fluid response characteristic in seismic data: Numerical simulation analysis

The exchange of fluid between fractures and rock matrix is considered to be a main factor influencing the calculated anisotropic elastic properties. Theoretical study shows that the fracture scales also have the same impact on it. To identify the multi-scale fracture, numerical analysis was introduced to analyze the variation of velocity and attenuation with the changes of the multi-scale fracture, frequency and fluid factor based on the equivalent medium model. The results show that the elastic parameters are frequency dependent, including the attenuation. This frequency dependence is related to the fracture scale and fluid properties of rocks. Within the various fracture scales with different velocity dispersion, the shear wave splitting depends on the frequency, and the scale of fracture is the leading factor, small scale is sensitive to high frequency, while low frequency to large scale. In the seismic frequency band, Thomsen parameters decreased with increasing frequency as well as the increasing of the fracture scale. Thus, seismic data may be an indication to distinguish the anisotropy caused by the fracture or micro-crack and also used to distinguish fracture scale.

Multi-scale fracture network analysis from an outcrop analogue: A case study from the Cambro-Ordovician clastic succession in Petra, Jordan

A regional multi-scale fracture network is prominently exposed in the Cambro-Ordovician sedimentary succession in south-western Jordan. This succession consists of marine deposits, overlain by heterogeneous deltaic sediments, culminating in 500 m of massive to cross-bedded fluvial sandstones. A data set acquired from high-resolution satellite imagery and field measurements enables the quantification of the geometry and spatial characteristics of the fracture network in three dimensions.Five directional fracture sets are identified from the satellite data with mean strikes of 000°, 040°, 065°, 120°, and 145°. Large fracture zones (longer than 600 m), composed of tightly spaced joints confined in fracture swarms, exhibit a log-normal trace-length distribution and the fracture swarms are regularly spaced. The trace-length distribution of intermediate fractures (40–600 m long) exhibits power-law characteristics and the fractures are clustered, reflecting different fracture system styles and stratigraphic controls as a function of scale. The small-scale fracture network is strongly dependent on the distribution of bedding plane discontinuities throughout different parts of the succession. The multi-scale fracture network is categorized in a three-tier hierarchical fracture model that reflects underlying stratigraphic controls in the study area. This type of model can be used to improve the representation of fracture networks in fluid flow simulations of fractured reservoirs with hybrid models that combine elements of discrete fracture networks and continuum models.

Fracture evolution in oil-producing sills of the Rio Grande Valley, northern Neuquén Basin, Argentina

Oil-producing sills are commonly considered atypical reservoirs, although they can hold significant exploration potential. The need for a better understanding of fracture properties and petroleum system characteristics for this and similar igneous rock plays is the main motivation of our study. We explore the evolution of this play type by an analysis of the Los Cavaos oil field, located in the Malargue fold belt of the Neuquen Basin, Argentina, integrating multiscale fracture data from outcrops and subsurface. The field was created by a combination of intrusions and mild Miocene-Pliocene inversion. Production stems from thick cavity zones in naturally fractured andesitic sills emplaced in Upper Jurassic shale source rocks. Orientation patterns, fracture spacing, and length of fracture sets in the sill are consistent over several orders of magnitude. Large multiply connected and weakly cemented fractures are responsible for excellent interconnectedness in the reservoir. Fracture density is correlated with fault proximity, indicating a cogenetic evolution during active deformation. Abundant fractures in core with strike-slip to oblique striations support transpressional overprint during and after fracture formation. Although it is challenging to separate cooling from tectonic fractures, we propose two phases of fracturing, marked by a coexistence of subvertical and oblique fractures together with transpressional striae. Petrographic evidence suggests initial local oil expulsion and migration through microfractures, with opening displacements of 0.01 to 1 mm, followed by subsequent charging of the evolving intrasill cavity system as well as the bulk fracture system during cooling and mild deformation. We suggest that the observed patterns may be extrapolated to sills in similar geotectonic settings.

A dual representation of multiscale fracture network modelling: application to a giant UAE carbonate field

The network of faults and fracture corridors assumed to act as preferential fluid pathways between reservoir units in a Type III Lower Cretaceous reservoir in Abu Dhabi is evident on 3D seismic data, but its elements are too numerous to be efficiently picked by hand. Alternative modelling techniques with increased levels of complexity and accuracy were tested for incorporation into the 3D model: deterministic fault patches, geobodies, and multipoint statistics, the latter to correct for the difference in corridor location observed between seismic and well data. Seismic and matrix properties guided the modelled distribution of unit-bound fractures outside the corridors. The new dual-scale approach to fracture network modelling applied in this study uses discrete fracture networks to represent the large fractures that provide connectivity between the grid cells, and describes statistically, with an implicit fracture model, the small fractures that probably enhance matrix permeability and anisotropy. A model comprising only discrete fractures would have taken hours to run, and the smallest fractures would have been neglected for computational limitations; whereas creation and upscaling of the hybrid model was performed in few minutes, enabling future implementation of iterative workflows for more rigorous statistics and calibration of intermediate and final results.

Structural-temporal theory of fracture as a multiscale process

The paper reports on a structural-temporal approach to analysis of multiscale fracture of solids. A practical procedure is proposed for estimating the strength characteristics of material on one scale from test data on another scale.

A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks

The simulation of flow in fractured media requires handling both a large number of fractures and a complex interconnecting network of these fractures. Networks considered in this paper are three-dimensional domains made up of two-dimensional fractures intersecting each other and randomly generated. Due to the stochastic generation of fractures, intersections can be highly intricate. The numerical method must generate a mesh and define a discrete problem for any discrete fracture network (DFN). A first approach [Erhel, de Dreuzy, and Poirriez, SIAM J. Sci. Comput., 31 (2009), pp. 2688–2705] is to generate a conforming mesh and to apply a mixed hybrid finite element method. However, the resulting linear system becomes very large when the network contains many fractures. Hence a second approach [Pichot, Erhel, and de Dreuzy, Appl. Anal., 89 (2010), pp. 1629–1643] is to generate a nonconforming mesh, using an independent mesh generation for each fracture. Then a Mortar technique applied to the mixed hybrid finite element method deals with the nonmatching grids. When intersections do not cross or overlap, pairwise Mortar relations for each intersection are efficient [Pichot, Erhel, and de Dreuzy, 2010]. But for most random networks, discretized intersections involve more than two fractures. In this paper, we design a new method generalizing the previous one and that is applicable for stochastic networks. The main idea is to combine pairwise Mortar relations with additional relations for the overlapping part. This method still ensures the continuity of fluxes and heads and still yields a symmetric positive definite linear system. Numerical experiments show the efficiency of the method applied to complex stochastic fracture networks. We also study numerical convergence when reducing the mesh step. This method makes it easy to perform mesh optimization and appears to be a very promising tool to simulate flow in multiscale fracture networks.

Sedimentary and diagenetic controls on the multiscale fracturing pattern of a carbonate reservoir: The Madison Formation (Sheep Mountain, Wyoming, USA)

A multidisciplinary approach has been applied to characterize the Madison Formation in the Sheep Mountain anticline at different scales, in order to illustrate the relationship between sedimentology, diagenesis and fracturing pattern. Sedimentary facies are organized into three types of elementary facies sequences showing different vertical evolutions of their petrophysical properties. This is controlled by the double influence of the initial sedimentary facies and the diagenetic evolution. Three main sets of fractures (related to the Sevier and Laramide compressive phases and to the folding of Sheep Mountain) have been described at three orders of scale. At small scale, the Sevier-related set I and folding related set III are the most abundant. Set II, dated from the early stage of the Laramide compression, exhibits the highest fracture intensity. There is also a clear faciologic control on the fracture intensity. Small-scale mechanical units correspond to entire facies sequences when no or little petrophysical property contrasts between beds are observed. Conversely, small-scale mechanical units correspond to each bed of a facies sequence in the case of high contrasts of petrophysical properties between beds. At intermediate scale, set II is not present and sets I and III show the highest fracture intensities. The latter are partly controlled by the mechanical unit thickness. Intermediate and large-scale mechanical unit distribution is mainly controlled by the overall faciologic vertical stacking pattern and by the position across the Sheep Mountain anticline (forelimb or backlimb). Sheep Mountain outcrops provide a good spatial representation of the carbonate reservoir heterogeneities from the micro- to the field scale, illustrating the complexity of fractured-carbonate reservoirs.

Local/global model order reduction strategy for the simulation of quasi‐brittle fracture

SUMMARYThis paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. Copyright © 2011 John Wiley & Sons, Ltd.

Coupling effect of primary voids and secondary voids on the ductile fracture of heat-treatable aluminum alloys

Ductile fracture of commercial aluminum alloys is controlled not only by the primary voids but also by the secondary voids, which are respectively nucleated at cracked constituents and at decohered dispersoid. In this paper, experiment and modeling were carried out to study the combined effect of the two populations of voids on the ductile fracture in two kinds of heat-treatable aluminum alloys, i.e., Al–Cu–Mg alloys and Al–Mg–Si alloys. Different heat treatments were applied to the alloys to achieve various combinations of the two voids, which were subsequently related to the mechanical properties. A multiscale fracture model was proposed to describe quantitatively the relationships between parameters of the two voids and the ductility and fracture toughness of heat-treatable aluminum alloys. It is revealed experimentally and theoretically that the presence of secondary voids will reduce the ductile properties especially when the intervoid spacing is less than about 0.5 μm. All calculations are in good agreement with experimental results.

Multiscale fracture simulation of three-point bending asphalt mixture beam considering material heterogeneity

A multiscale modeling frame combining macroscale and mesoscale is proposed in basis of the aggregate generation and packing algorithm so that the heterogeneity feature of asphalt mixture can be involved in the computational model. In this frame, the mesoscopic scale is used in some concerned local regions and the macroscopic scale is used in the other regions. As examples, a series of two-dimensional multiscale models of cracked three-point bending asphalt mixture beam are created and then the effects of crack location and aggregate distribution near the crack on cracking behaviors are evaluated. Finally, some important conclusions are concluded.

Phenomena of Multicale Fracture of Brittle Materials and its Application to Teaching in Strength Theory

Multi-scale science is the challenge and opportunity of science in the 21th century, and turbulence of liquid and fracture of solid will be the classical problems of multi-scale mechanics. The failure process of brittle materials displayed a multi-scale mechanics feature that amounts of micro damages grow large trans-scale and nonlinear and evolve to a macro catastrophic transition in the end. So, the concepts of scale and hierarchy of material are inescapable in strength theory to be used explaining solid fracture, it is the main puzzle of the strength theory at present. In the paper, in order to show the phenomena of multi-scale fracture, numeric method is used to simulate the failure process of brittle material, during which micro cracks initiate, grow large, aggregate and in the end form a run-through fracture band in the sample. The result of the numeric simulation shows that the micro cracks of a meso-scale size initiate due to tensile strain and the sample of a macro-scale size breaks down due to tensile-shearing strain under uniaxial tensile or due to compression-shearing strain under uniaxial compression. It powerfully disabused the puzzles in teaching strength theory of brittle material. The further discussion concluded that for a brittle material grain of meso-scale size, the theory of Maximum Tensile Strain is reasonable in explaining the strength, as for a brittle material sample of a macro-scale size, the mohr-columb theory is reasonable for its strength owing to the two important factors of cohesive strength and friction factorwere introduced.

Hydrothermal coupling in a self-affine rough fracture

The influence of the multiscale fracture roughness on the heat exchange when a cold fluid enters a fractured hot solid is studied numerically on the basis of the Stokes equation and in the limit of both hydrolubrication and thermolubrication. The geometrical complexity of the fracture aperture is modeled by small self-affine perturbations added to a uniform aperture field. Thermal and hydraulic properties are characterized via the definition of hydraulic and thermal apertures both at microscopic and macroscopic scales and obtained by comparing the fluxes to the ones of flat fractures. Statistics over a large number of fracture configurations provide an estimate of the average behavior and its variability. We show that the long-range correlations of the fracture roughness induces strong channeling effects that significantly influence the hydraulic and thermal properties. An important parameter is the aspect ratio (length over width) of the fracture: we show, for example, that a downstream elongated rough fracture is more likely to inhibit the hydraulic flow and subsequently to enhance the thermal exchange. Fracture roughness might, in the opposite configuration, favor strong channeling which inhibits heating of the fluid. The thermal behavior is in general shown to be mainly dependent on the hydraulic one, which is expressed through a simple law.