Penny-shaped fractures revisited

All methods of seismic characterization of fractured reservoirs are based on effective media theories that relate geometrical and material properties of fractures and surrounding rock to the effective stiffnesses. In exploration seismology, the first-order theory of Hudson is the most popular. It describes the effective model caused by the presence of a single set of thin, aligned vertical fractures in otherwise isotropic rock. This model is known to be transversely isotropic with a horizontal symmetry axis (HTI). Following the theory, one can invert the effective anisotropy for the crack density and type of fluid infill of fractures, the quantities of great importance for reservoir appraisal and management.Here I compute effective media numerically using the finite element method. I deliberately construct models that contain a single set of vertical, ellipsoidal, non-intersecting and non-interconnected fractures to check validity of the first-order Hudson’s theory and establish the limits of its applicability. Contrary to conventional wisdom that Hudson’s results are accurate up to crack density e ≈ 0.1, I show that they consistently overestimate the magnitudes of all effective anisotropic coefficients ε^(V), δ^(V), and γ^(V). Accuracy of theoretically derived anisotropy depends on the type of fluid infill and typically deteriorates as e grows. While the theory gives | ε^(V)|, |δ^(V)|, |γ^(V)| and close to the upper bound of the corresponding numerically obtained values for randomly distributed liquid-filled fractures, theoretical predictions of ε^(V), δ^(V) are not supported by numerical computations when the cracks are dry. This happens primarily because the first-order Hudson’s theory makes no attempt to account for fracture interaction which contributes to the final result much stronger for gas- than for liquid-filled cracks. I find that Mori-Tanaka’s theory is superior to Hudson’s for all examined crack densities and both types of fluid infill.The paper was presented at the 11th International Workshop on Seismic Anisotropy (11IWSA) held in St. John’s, Canada in 2004.     

Détermination expérimentale des paramètres équivalents d'un milieu poreux hétérogène en écoulements uniforme ou radial

Tracer tests are carried out in a heterogeneous porous medium that has a 3D correlated random distribution of the permeabilities. The fitting of numerical models provides the values of equivalent permeability and macrodispersivity characterizing a 2D homogeneous horizontal medium. Different flow configurations are studied: uniform, radial and pump and treat (doublet). The fitted parameter sets are independent of the flow type, except for the doublet. They are greater than the values predicted by stochastic theories, due to the small number of correlation lengths explored by the tracer and the limited extension of the experimental set-up. To cite this article: C. Danquigny, P. Ackerer, C. R. Geoscience 337 (2005).     

Fracture mechanics analysis of multiple cracks in anisotropic media

This paper presents a single‐domain boundary element method (BEM) for linear elastic fracture mechanics analysis in the two‐dimensional anisotropic material. In this formulation, the displacement integral equation is collocated on the un‐cracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. A special crack‐tip element was introduced to capture exactly the crack‐tip behavior. A computer program with the FORTRAN language has been developed to effectively calculate the stress intensity factors of an anisotropic material. This BEM program has been verified having a good accuracy with the previous researches. Furthermore, by analyzing the different anisotropic degree cracks in a finite plate, we found that the stress intensity factors of crack tips had apparent influence by the geometry forms of cracks and media with different anisotropic degrees. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: mesh effect and discretization error estimation

Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger‐amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger‐amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger‐amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts. Copyright © 2014 John Wiley & Sons, Ltd.     

A model for moisture and heat flow in fractured unsaturated porous media

The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd.     

Hydrologic response of engineered media in living roofs and bioretention to large rainfalls: experiments and modeling

The hydrologic response of engineered media plays an important role in determining a stormwater control measure's ability to reduce runoff volume, flow rate, timing, and pollutant loads. Five engineered media, typical of living roof and bioretention stormwater control measures, were investigated in laboratory column experiments for their hydrologic responses to steady, large inflow rates. The inflow, medium water content response, and outflow were all measured. The water flow mechanism (uniform flow vs. preferential flow) was investigated by analyzing medium water content response in terms of timing, magnitude, and sequence with depth. Modeling the hydrologic process was conducted in the HYDRUS‐1D software, applying the Richards equation for uniform flow modeling, and a mobile–immobile model for preferential flow modeling. Uniform flow existed in most cases, including all initially dry living roof media with bimodal pore size distributions and one bioretention medium with unimodal pore size distribution. The Richards equation can predict the outflow hydrograph reasonably well for uniform flow conditions when medium hydraulic properties are adequately represented by appropriate functions. Preferential flow was found in two media with bimodal pore size distributions. The occurrence of preferential flow is more likely due to the interaction between the bimodal pore structure and the initial water content rather than the large inflow rate.     

The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on the 2‐phase porous theory

The effective stress concept for solid‐fluid 2‐phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot‐type theory for 2‐phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, m, corresponds to the inverse of the B value by Bishop and was obtained during the step loading of the cell pressure. In addition, the m values were evaluated by comparing them with theoretically obtained values based on the solid‐fluid 2‐phase mixture theory. The experimental m values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi‐phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.     

Building a model-based personalised recommendation approach for tourist attractions from geotagged social media data

When travelling, people are accustomed to taking and uploading photos on social media websites, which has led to the accumulation of huge numbers of geotagged photos. Combined with multisource information (e.g. weather, transportation, or textual information), these geotagged photos could help us in constructing user preference profiles at a high level of detail. Therefore, using these geotagged photos, we built a personalised recommendation system to provide attraction recommendations that match a user's preferences. Specifically, we retrieved a geotagged photo collection from the public API for Flickr (Flickr.com) and fetched a large amount of other contextual information to rebuild a user's travel history. We then created a model-based recommendation method with a two-stage architecture that consists of candidate generation (the matching process) and candidate ranking. In the matching process, we used a support vector machine model that was modified for multiclass classification to generate the candidate list. In addition, we used a gradient boosting regression tree to score each candidate and rerank the list. Finally, we evaluated our recommendation results with respect to accuracy and ranking ability. Compared with widely used memory-based methods, our proposed method performs significantly better in the cold-start situation and when mining ‘long-tail’ data.