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Understanding deformations and fluid flow in fractured rocks is of central importance for many subsurface flow applications. Thus, numerical frameworks are needed that capture the coupled mechanical and hydraulic behaviour, including scenarios with complex fracture networks. This paper employs the extended finite volume method to represent fracture manifolds in a poroelastic matrix domain and to compute shear and tensile displacements of fracture segments. However, using embedded fractures with non‐conforming grids can lead to severe convergence issues while computing shear slip and tensile opening of intersecting and parallel fractures, particularly if they have similar slopes. Our proposed solution of this problem is to slightly deform the fracture geometry by merging critical segments. We discuss and show examples of which attributes the merged segment has to adopt to ensure the correct slip behaviour at an intersection. Thereby it is crucial that the flow topology remains unaltered. Analysing failures of kinked fractures and fracture intersections show the flexibility of the devised algorithm. Moreover, it is demonstrated that deformation and opening patterns of a natural network with more than 200 fractures are qualitatively predicted very well. This method is a simple solution to treat multiple fracture segments in a grid cell, hence it can be used for any model embedding fractures in non‐conforming grids. [ABSTRACT FROM AUTHOR]

Summary: Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed‐stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two‐ and three‐dimensional matrices. The convergence criterion for sequentially implicit fixed‐stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied. [ABSTRACT FROM AUTHOR]

In subsurface aquifers, dispersion of contaminants is highly affected by the heterogeneity of the hydraulic conductivity field. As an alternative to Monte Carlo simulations on probable conductivity fields, stochastic velocity processes have been introduced to assess the uncertainty in the transport of contaminants. In continuum‐scale simulations, discrete velocity models (such as correlated continuous time random walk) focus on modeling plume dispersion in the longitudinal direction. There are alternative continuous velocity processes (such as the polar Markovian velocity process [PMVP]) that are able to accurately model transport in both longitudinal and transverse directions. Importantly, the PMVP model correctly predicts the limited spreading of the ensemble contaminant plume in the transverse direction. However, the stochastic differential equations used in the PMVP model have specific drift and diffusion functions that are designed for the exponential correlation structure. In this paper, a new discrete velocity process is described that is applicable to modeling transport in two‐dimensional conductivity fields for both Gaussian and exponential correlation structures. This method is simple, in a sense that it does not require modeling the functional form of the drift and diffusion functions. The new method is validated against Monte Carlo simulations for both correlation structures with high variances of log conductivity. Key Points: A discrete temporal Markov model is proposed for modeling transport in correlated porous mediaThe proposed model is significantly more flexible compared to its continuous counterpart based on SDEsThe proposed model can correctly predict the spreading of the ensemble plume in both longitudinal and transverse directions [ABSTRACT FROM AUTHOR]

Abstract: Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the lognormal permeability distribution, the transport of a passive tracer is non‐Fickian. Here we model this non‐Fickian dispersion in random porous networks using discrete temporal Markov models. We show that such temporal models capture the spreading behavior accurately. This is true despite the fact that the slow velocities are strongly correlated in time, and some studies have suggested that the persistence of low velocities would render the temporal Markovian model inapplicable. Compared to previously proposed temporal stochastic differential equations with case‐specific drift and diffusion terms, the models presented here require fewer modeling assumptions. Moreover, we show that discrete temporal Markov models can be used to represent dispersion in unstructured networks, which are widely used to model porous media. A new method is proposed to extend the state space of temporal Markov models to improve the model predictions in the presence of extremely low velocities in particle trajectories and extend the applicability of the model to higher temporal resolutions. Finally, it is shown that by combining multiple transitions, temporal models are more efficient for computing particle evolution compared to correlated CTRW with spatial increments that are equal to the lengths of the links in the network. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model to predict flow-induced shear failure along pre-existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence. [ABSTRACT FROM AUTHOR]

Objective Oxygen transport to parenchymal cells occurs mainly at the microvascular level and depends on convective RBC flux, which is proportional in an individual capillary to the product of capillary hematocrit and RBC velocity. This study investigates the relative influence of these two factors on tissue PO2. Methods A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity, and RBC flow on tissue oxygenation around capillaries. Predicted tissue PO2 levels are compared with a detailed computational model. Results Hematocrit is shown to have a larger influence on tissue PO2 than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained, and the discrepancies are explained. Significant dependence of MTCs on RBC velocity at low hematocrit is demonstrated. Conclusions For a given RBC flux in a capillary, the PO2 in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing IVR to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as those that occur in functional hyperemia in the brain. [ABSTRACT FROM AUTHOR]

In subsurface aquifers, dispersion of contaminant, or tracer, is mainly driven by spatial fluctuations in the flow field caused by heterogeneity of the hydraulic conductivity. Measurements of conductivity, however, are usually sparse. To assess the resulting uncertainty in the transport of tracers, Monte Carlo (MC) methods are usually applied, where the transport statistics are sampled over a large number of probable hydraulic conductivity realizations. In this paper, an alternative method is described that provides accurate transport statistics at a computational expense that is 3 orders of magnitude lower than conventional MC. The new method is applicable for conductivity fields with multivariate Gaussian characterization involving conductivity measurements for both small and high log-conductivity variances. The new method is validated against MC for different dispersion scenarios, where the region of interest spans tens of log-conductivity correlation lengths. [ABSTRACT FROM AUTHOR]

The probability density function (PDF) of the local concentration of a contaminant, or tracer, is an important component of risk assessment in applications that involve flow in heterogeneous subsurface formations. In this paper, a novel joint velocity-concentration PDF method for tracer flow in highly heterogeneous porous media is introduced. The PDF formalism accounts for advective transport, pore-scale dispersion (PSD), and molecular diffusion. Low-order approximations (LOAs), which are usually obtained using a perturbation expansion, typically lead to Gaussian one-point velocity PDFs. Moreover, LOAs provide reasonable approximations for small log conductivity variances (i.e., σ Y2 < 1). For large σ Y2, however, the one-point velocity PDFs deviate significantly from the Gaussian distribution as demonstrated convincingly by several Monte Carlo (MC) simulation studies. Furthermore, the Lagrangian velocity statistics exhibit complex correlations that span a wide range of scales, including long-range correlations due to the formation of preferential flow paths. Both non-Gaussian PDFs and complex long-range correlations are accurately represented using Markovian velocity processes (MVPs) in the proposed joint PDF method. LOA methods can be generalized to some extent by presuming a certain shape for the concentration PDF (e.g., a β PDF fully characterized by the concentration mean and variance). The joint velocity-concentration PDF method proposed here does not require any closure assumptions on the shape of the marginal concentration PDF. The Eulerian joint PDF transport equation is solved numerically using a computationally efficient particle-based approach. The PDF method is validated with high-resolution MC reference data from Caroni and Fiorotto (2005) for saturated transport in velocity fields, which are stationary in space and time, for domains with σ Y2 = 0.05, 1, and 2 and Péclet numbers ranging from 100 to 10,000. PSD is modeled using constant anisotropic dispersion coefficients in both the reference MC computations and our PDF method. [ABSTRACT FROM AUTHOR]