The paper presents further developments of the boundary element technique for solving three-dimensional problems of piecewise homogeneous elastic media containing multiple cracks of arbitrary non-planar shapes (previous results were reported in [1, 2]). In the developed technique, the elastic fields are represented by integral identities. Triangular elements are used to discretize the boundaries and polynomial (linear and quadratic) approximations of the unknown variables are adopted. In-plane components of the fields and geometrical parameters are arranged in various complex-valued combinations to simplify the integration. No singular integrals are involved since the limit, as the field point approaches the boundary, is taken after the integration. Analytical integration over each element is reduced to that over the contour of the element via application of Cauchy- Pompeiu representation . The collocation method is used to set up the system of linear algebraic equations to find the boundary unknowns. Geoengineering applications of the method are discussed.
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.
We report a field study on solution mining of magnesium chloride from bischofite layers in the Netherlands at depths between 1500 and 1850 m. Subsidence that was observed in the area is due to part of the brine production being realized by cavern squeeze; some of which were connected. We used an earlier developed inversion scheme to quantify the distribution of the squeeze volumes from the subsidence measurements. We incorporated in it the creep behavior of the rock salt as a convolution between the time-dependent response of a squeeze event and the actual production history. With a Maxwell viscoelastic behavior in the salt with realistic time constant, we achieved a good result for the subsidence values and for the observed ratio between subsidence bowl volume and squeeze volume. With the new understanding we created physics-based forecasts for different production scenarios and provided an estimate for the remaining time and the producible volumes before the maximum allowed amount of subsidence is reached. After completely stopping production, our model predicted a rebound of the subsidence.
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.
: 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.
Proppant additives play an essential role in hydraulic fracturing as they provide support, which retains the fracture opening after the pumping is shut off. From a production point of view, a larger proppant size provides better permeability, while, at the same time, gravitational settling may cause significant distortion of the particle distribution inside the fracture for heavier particles. This study uses a recently developed model for proppant transport, that has been implemented for Khristianovich-Zheltov- Geertsma-De Klerk (KGD) and pseudo-3D (P3D) fracture geometries, to quantify the effect of particle settling. The proppant transport model is based on an empirical constitutive relation for the slurry that accounts for: i) a non-uniform particle distribution across the fracture width due to shear-induced migration, which distorts the parabolic velocity profile, ii) slip velocity in the direction of flow, which, in the limit of a jammed state, leads to Darcy’s law, and iii) gravitational settling. While the gravitational settling is the biggest concern when dealing with larger particle sizes, other effects may include earlier jamming due to proppant stalling in between the walls and higher permeability of the proppant plug, which promotes the fracture propagation in front of the jammed region.
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 crack damage progression in crystalline rocks is approximated in laboratory by means of rigorous strain measurement and/or monitoring of Acoustic Emission (AE) activity. When both means are used, they are treated independently for quantification of damage in the rock. This paper is investigating a new method to combine the AE and strain data in a unified function to calculate the balance of stored and released energy in the rock due to loading (strain energy) and micro-cracking respectively. This method introduces a new solution for measurement and quantification of crack damage in rock and also provides a tool to investigate the brittleness of different rock types. Unconfined Compressive Strength (UCS) testing of six different rock types with strain measurement and AE monitoring was performed for this study. The application of the new method to the data collected from the UCS tests indicates the difference between the behaviour of the various rock types in terms of sudden energy release at the onset of CI threshold and the difference in the storability of strain energy before and after CI and CD thresholds.
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.