Dual virtual element method for discrete fractures networks

Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to compute the pressure field and Darcy velocity in the system. The first allows a normal flow out of a fracture at the intersections, while the second grants also a tangential flow along the intersections. For the numerical discretization, we use the mixed virtual finite element method as it is known to handle grid elements of, almost, any arbitrary shape. The flexibility of the discretization allows us to loosen the requirements on grid construction, and thus significantly simplify the flow discretization compared to traditional discrete fracture network models. A coarsening algorithm, from the algebraic multigrid literature, is also considered to further speed up the computation. The performance of the method is validated by numerical experiments

High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients, which in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of partial differential equations, one enforcing stress equilibrium and another governing phase-field evolution. The two equations are coupled through an energy degradation function that models the loss of stiffness in the bulk material as it undergoes damage. In the present work, we introduce a new parametric family of degradation functions aimed at increasing the accuracy of phase-field models in predicting critical loads associated with crack nucleation as well as the propagation of existing fractures. An additional goal is the preservation of linear elastic response in the bulk material prior to fracture. Through the analysis of several numerical examples, we demonstrate the superiority of the proposed family of functions to the classical quadratic degradation function that is used most often in the literature.Comment: 33 pages, 30 figure

Transport of polymer particles in a oil-water flow in porous media: enhancing oil recovery

We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.Comment: 20 pages, 9 Figures Submitted to Transport in Porous Medi

Post-injection normal closure of fractures as a mechanism for induced seismicity

Understanding the controlling mechanisms underlying injection-induced seismicity is important for optimizing reservoir productivity and addressing seismicity-related concerns related to hydraulic stimulation in Enhanced Geothermal Systems. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations, and the shear slip of pre-existing fractures. Previous experiments indicate that fracture deformation in the normal direction reverses as the pressure decreases, e.g., at the end of stimulation. We hypothesize that this normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for post-injection seismicity. To test this hypothesis, hydraulic stimulation is modeled by numerically coupling fracture deformation, pressure diffusion and stress alterations for a synthetic geothermal reservoir in which the flow and mechanics are strongly affected by a complex three-dimensional fracture network. The role of the normal closure of fractures is verified by comparing simulations conducted with and without the normal closure effect

Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids

In this paper, we consider anisotropic diffusion with decay, and the diffusivity coefficient to be a second-order symmetric and positive definite tensor. It is well-known that this particular equation is a second-order elliptic equation, and satisfies a maximum principle under certain regularity assumptions. However, the finite element implementation of the classical Galerkin formulation for both anisotropic and isotropic diffusion with decay does not respect the maximum principle. We first show that the numerical accuracy of the classical Galerkin formulation deteriorates dramatically with increase in the decay coefficient for isotropic medium and violates the discrete maximum principle. However, in the case of isotropic medium, the extent of violation decreases with mesh refinement. We then show that, in the case of anisotropic medium, the classical Galerkin formulation for anisotropic diffusion with decay violates the discrete maximum principle even at lower values of decay coefficient and does not vanish with mesh refinement. We then present a methodology for enforcing maximum principles under the classical Galerkin formulation for anisotropic diffusion with decay on general computational grids using optimization techniques. Representative numerical results (which take into account anisotropy and heterogeneity) are presented to illustrate the performance of the proposed formulation

Laboratory tests in out-of-hours services in Norway. Studies with special emphasis on use and consequences of C-reactive protein test in children

Background: Children with infections and respiratory symptoms have the highest contact rate with Norwegian out-of-hours (OOH) services, especially in the youngest age group, and during the winter season. Many contacts are non-urgent in a strict medical sense. Onsite measurement of C-reactive protein (CRP) is the most frequent laboratory test in Norwegian OOH, used in 60% of all contacts with children with infections and respiratory diseases. The aim of CRP is to differentiate between bacterial infections, viral and/or non-serious infections and to keep the use of antibiotics as low as possible. Nevertheless, the use of antibiotics has increased since the test was introduced as a point of care test until 2013. Several studies have investigated the diagnostic value of laboratory tests for children with fever, but not in primary health care where the prevalence of serious bacterial infections is low. Objective: Investigate the use of laboratory tests at Norwegian out-of-hours services and which characteristics of the doctor, patient, diagnoses and geography that affects it. Compare the RGPs’ rate of CRP use at daytime and at OOH in consultations with children. Evaluate if pre-consultation CRP screening affects the choice of treatment Identify predictors for prescription of antibiotics and referral to hospital for children at OOH services. Design/method: The first and second papers are from two cross-sectional registry based studies, based on electronic compensation claims from consultations in primary care. The third study (third paper) was a randomized controlled observational study at OOH-services in Norway, including children 20 mg/L, signs on ear examination and use of paracetamol during the previous 24 hours. A high respiratory rate, low oxygen saturation and signs of auscultation were predictors for referral to hospital. In addition, parents’ assessment of the seriousness was significantly associated with prescription of antibiotics and referral to hospital. Conclusion: Paper I and II: CRP is extensively used at Norwegian OOH services and the differences in use cannot be explained by different diagnoses. Paper III: CRP screening of children with fever or respiratory symptoms will not reduce the prescription of antibiotics. Paper IV: Predictors for prescription are signs on ear examination, slightly elevated CRP values and the parents’ assessment. Disturbed respiration is the most important sign predicting hospital admission