: A fully implicit method for coupled fluid flow and geomechanical deformation in fractured porous media is presented. Finite-volume and finite-element discretization schemes are used, respectively, for the flow and mechanics problems. The discrete flow and mechanics problems share the same conformal unstructured mesh. The network of natural fractures is represented explicitly in the mesh. The behavior of the fractured medium due to changes in the fluid pressure, stress, and strain fields is investigated. The methodology is validated using simple cases for which analytical solutions are available, and also using more complex "realistic" test cases.
Fluid flow in fractured rocks has been a very difficult problem that has stymied many workers. A major cause of this problem is the disconnect between the geology of fractured rocks and the assumptions of Darcy’s Law. Darcy’s Law is based on the average permeability over a uniform mass of rock or soil, but the permeability of fractured rock is anything but uniform, and tends to be log-normally distributed with a high degree of variability. Darcy’s Law requires the arithmetic mean permeability but log-normal distributions are centered around the geometric mean. If the variability is low, the geometric mean will be close to the arithmetic mean so that the error is not serious. However, if the variability is high, as is typical of fractured rock, the geometric mean can be several orders of magnitude lower than the arithmetic mean, resulting in profound error and failed calculations. This paper shows how to obtain the arithmetic mean of the log-normal distribution so that permeability data from fractured rock can be used in Darcy’s Law.
In this paper, we present the results from laboratory and In Situ rock fracture experiments where calibrated Acoustic Emission (AE) sensors were implemented. By removing sensor distortions, we were able to study the size and magnitude of AE sources in two unique environments. The laboratory experiment was conducted on a cubic sample of Fontainbleau sandstone under true-triaxial stress conditions (σ1 > σ2 > σ3). The In Situ experiment was conducted on a 0.7 m x 0.7 m x 1.1 m rectangular prism of Lac du Bonnet granite located on the side of an underground tunnel during a large-scale excavation response test. For both sets of data, corner Frequency (fo) and moment magnitude (Mw) were found to be inside the ranges 190 kHz < fo < 750 kHz and -7.2 < Mw < -6.5, respectively and all source parameters appeared to obey scaling relationships derived for larger earthquakes.
A constitutive model that couples elastic-plastic and damage theories is developed to predict the mechanical behavior of a shale from the Mont Terri rock laboratory (Opalinus Clay). The framework of continuum damage mechanics allows to predict the degradation of the elastic parameters with strains, while the coupling with plasticity correctly reproduces the irreversible strains typical of hard clayey materials. The yield surfaces (one for damage and one for plasticity) are postulated and the evolution equations of the internal variables are derived throughout the application of normality rule. Thermodynamic consistency of the model is investigated. The plastic behavior is described with a non-linear strain hardening function and is coupled with an isotropic damage model suitable for brittle and quasi-brittle geomaterials. The model is integrated with an implicit scheme that guarantees convergence and accuracy. Numerical simulations carried out with the proposed model in triaxial conditions well reproduced observed behavior from experiments.
The Numerical Manifold Method (NMM) with a two-cover-meshing system is an ideal method to handle boundaries, considering its flexibility with no need to adjust mathematical nodes onto boundaries, the meshing efficiency and its integration precision. In this study, we derived different forms of Lagrange multiplier methods (LMMs) and jump function methods (JFMs) for boundary constraints in the frame of NMM. These approaches for boundary constraints make full use of the aforementioned advantages of NMM and are established based on a clear physical meaning of water flow by an energy-work seepage model. The LMM approaches are discontinuous approaches in which Lagrange Multipliers provide links between discontinuous physical covers cut by material interfaces, whereas the JFM approaches are continuous, in which the discontinuities of material interfaces are realized by introducing jump terms across a continuous medium. The boundary constraint approaches developed in this study were coded into an NMM water flow model. We compared simulation results involving Dirichlet boundary conditions and idealized faulted rock using LMM and JFM with analytical solutions, and prove that both methods provide accurate results, with additional degrees of freedom introduced (or eliminated by special physical meaning). Based on these results, we recommend the LMM considering its accuracy and efficiency, flexibility, especially when involving intense geometric change or fracture intersections. Last, we apply and demonstrate the LMM approach in a simplified model of flow through porous rock with a major fault and a tunnel and arrived at convincing results.
Heterogeneous proppant placement (HPP) technologies offer improved hydraulic fracturing performance through the creation of channels within the propped fracture. We present an investigation into the fundamentals of HPP utilizing a general fracture closure prediction capability that can consider arbitrary proppant placement within potentially rough fractures combined with a rigorous statistical analysis. We applied our simulator to extensive parameter study with several thousand scenarios relevant to HPP. We then employed global sensitivity analysis (GSA) to highlight which formation- and proppant-related factors most impact HPP performance. The results allow us to rigorously quantify the impact of parametric uncertainty on the predicted fracture conductivity under stress. Our results highlight the robustness of the HPP concept and allow us to quantify and rank the sources of uncertainty in predicting HPP performance and clearly identify the fundamental parameters that control HPP conductivity.
This paper describes a workflow involving a reservoir flow simulator coupled with a finite element geomechanical simulator. Multi-stage hydraulic fracturing jobs are modeled by simulating injection of water into the reservoir - using stage spacing, stage sizes and pump rates as parameters to the well models. Constitutive models are specified for fracture propagation and shear failure due to induced stress changes in the reservoir. Coupling is also provided through stress dependent flow transmissibility multiplier tables. Simulation based sensitivity studies are carried out on stage spacing and stage size as well as strength of the reservoir rock . Maps of the ratio between deviatoric stresses (at the actual stress states) and failure are built as a function of space and time (for the duration of the fracturing job). These maps can be correlated against maps of recorded microseismicity and used to better understand the mechanism and growth of the stimulated reservoir volume. This workflow attempts to reconcile flow and geomechanical behavior of the reservoir without requiring detailed reservoir characterization.
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.
Leforta, Vincent (LFC-R, UMR5150, University Pau & Pays Adour) | Gr&$233;goirea, David (LFC-R, UMR5150, University Pau & Pays Adour) | Grasslb, Peter (University of Glasgow) | Pijaudier-Cabota, Gilles (LFC-R, UMR5150, University Pau & Pays Adour)
Characterizing the change of the transport properties during the propagation of macrocracks in a quasi-brittle material (rocks, hard soils,…) is one of the challenges of current research on hydraulic fracturing. Analyzing such change of properties is a way to determine the extent of the Stimulated Reservoir Volume (SRV). The degradation of quasi-brittle materials encompasses micro-crack propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located progressively within the so-called Fracture Process Zone (FPZ). The shape and growth of the FPZ, and its interaction with boundaries, lead to typical phenomena such as size effects, boundary effects and shielding effects. In this paper, we consider synthetic quasi-brittle materials (mortar or concrete) that mimic the mechanical behavior of natural rock, and develop analysis tools based on mesoscale simulations that enable the study of characteristic lengths during damage and failure of such materials.
Recent advances in high power plasma torch technology provide an apparatus to replace the conventional perforation methods in oil and gas wells. High power plasma torches are capable of cutting and removing rocks textures efficiently and they might be considered as one of the appropriate substitutions for current shaped charge perforation methods. According to its advantages the conventional shaped charge methods that one the important one is increasing permeability considerably and no need to have costly re-perforation operations to decreasing new formation damage named by perforation skin. Plasma torch perforation is gone along with heat flux generation. As the temperature increases during plasma torch operation, thermal energy accumulates the matrix expansion. This expansion generate thermal stresses induce the rock texture. Furthermore, thermal stresses exceeds the rock strength, thermal fractures will form in texture that mainly depend on rock thermal properties, pore size distribution, applied thermal stresses and confining and pore pressures. In this paper, the results of experimental studies on implementation of high power plasma torch in perforation and fracture initiation in oil and gas wells is presented. Also, numerically analyzing of generating these thermal fractures during plasma torch perforation will facilitate hydraulic fracturing operation.