High-Resolution Micro-Continuum Approach to Model Matrix-Fracture Interaction and Fluid Leakage

Understanding the fundamental mechanism of fracture-matrix fluid exchange is crucial for the modeling of fractured reservoirs. Traditionally, high-resolution simulations for flow in fractures often neglect the matrix-fracture leakage influence on the fracture hydraulic properties, i.e., assuming impermeable fracture walls. This work introduces a micro-continuum approach to capture the matrix-fracture leakage interaction and its effect on the rock fractures’ hydraulic properties. Because of the multiscale nature of fractured media, full physics Navier-Stokes (NS) representation everywhere in the whole domain is not feasible. We thus employ NS equations to describe the flow in the fracture, and Darcy’s law to model the flow in the surrounding porous rocks. Such hybrid modeling is achieved using the extended Darcy-Brinkman-Stokes (DBS) equation. With this approach, a unified conservation equation for flow in both media is applied by choosing appropriate parameters (e.g., porosity and permeability) for the corresponding domains. We apply an accurate Mixed Finite Element approach to solve the extended DBS equation. Various sensitivity analyses are conducted to explore the leakage effects on the fracture hydraulic properties by varying surrounding matrix permeability, fracture roughness, and Reynolds number (Re). Streamline profiles show the presence of back-flow phenomena, where in-flow and out-flow are possible between the matrix and the fractures. Further, zones of stagnant (eddy) flow are observed around locations with large asperities of sharp corners under high Re conditions. Numerical results show the significant effects of roughness and inertia on flow predictions in fractures for both impermeable and leaky wall cases. Besides, the side-leakage effect can create non-uniform flow behavior within the fracture that may differ significantly from the case with impermeable wall conditions. And this matrix-fracture leakage influence on hydraulic properties of rock fractures matters especially for cases with high matrix permeability, high fracture roughness, and low Re values. In summary, we present a high-resolution micro-continuum approach to explore the flow exchange behavior between the fracture and rock matrix, and further investigate the static and dynamic effects, including variable Reynold numbers, mimicking flow near and away from the wellbore. The approach and results provide significant insights into the flow of fluids through fractures within permeable rocks and can be readily applied in field-scale reservoir simulations.

Determination of representative elementary volume (REV) for jointed rock masses exhibiting scale-dependent behavior: a numerical investigation

Representative elementary volume (REV) is defined as the usual size of a rock mass structure beyond which its mechanical properties are homogenous and isotropic, and its behavior can be modeled using the equivalent continuum approach. Determination of REV is a complex problem in rock engineering due to its definition ambiguity and application area. This study is one of the first attempts to define a REV for jointed rock masses using the equivalent continuum approach. It is aimed to numerically search a ratio between the characteristic size of an engineering structure and pre-existing joint spacing, which are the two most important contributing elements in assessing REV. For this purpose, four hypothetical engineering cases were investigated using the RS2 (Phase2 v. 9.0) finite element (FE) analysis program. An underground circular opening with a constant diameter, an open-pit mine with varying bench heights, a single bench with a constant height, and an underground powerhouse cavern with a known dimension were executed for possible changes in the safety factor and total displacement measurements under several joint spacing values. Different cut-off REVs were calculated for FE models depending on the type of excavation and measurement method. An average REV size of 19.0, ranging between a minimum of 2 for tunnels and a maximum of 48 for slopes, was found in numerical analysis. The calculated sizes of REV were significantly larger than the range of values (5 to 10) commonly reported in the relevant geotechnical literature.

Pushover Tests on Unreinforced Masonry Wallettes Retrofitted with an Innovative Coating: Experimental Study and Finite Element Modelling

This paper investigates the mechanical contribution of an innovative coating applied on masonry wallettes compared to a traditional one. In both cases, the multifunctional coatings were insulating coatings intended for thermal refurbishment, but they could also be used to retrofit masonry. Uncoated specimens as well as coated ones were submitted to pushover tests to establish the strength gain. URM walls experienced brittle failures while the coated walls exhibited significant strength gains and strong ductility. The corresponding finite element models were developed. The behaviour of the URM walls was reproduced accurately in terms of strength and failure pattern. Models involving the coatings were used to partially retrieve the behaviour and to highlight the issues of a continuum approach.

Determination of representative elementary volume (REV) for jointed rock masses exhibiting scale-dependent behavior: A numerical investigation

Representative elementary volume (REV) is defined as the usual size of a rock mass structure beyond which its mechanical properties are homogenous and isotropic, and its behavior can be modeled using the equivalent continuum approach. Determination of REV is a complex problem in rock engineering due to its definition ambiguity and application area. This study is one of the first attempts to define a REV for jointed rock masses using the equivalent continuum approach. It is aimed to numerically search a ratio between the characteristic size of an engineering structure and pre-existing joint spacing, which are the two most important contributing elements in assessing REV. For this purpose, four hypothetical engineering cases were investigated using the RS2 (Phase2 v. 9.0) finite element (FE) analysis program. An underground circular opening with a constant diameter, an open-pit mine with varying bench heights, a single bench with a constant height, and an underground powerhouse cavern with a known dimension were executed for possible changes in the safety factor and total displacement measurements under several joint spacing values. Different cut-off REVs were calculated for FE models depending on the type of excavation and measurement method. An average REV size of 19.0, ranging between a minimum of 2 for tunnels and a maximum of 48 for slopes, was found in numerical analysis. The calculated sizes of REV were significantly larger than the range of values (5 to 10) commonly reported in the relevant geotechnical literature.

Numerical simulation of resistance sintering of titanium by a porous continuum approach

This paper presents a numerical model for the simulation of resistance sintering. It involves an electro-thermo-mechanical coupling, where each model is simulated as a continuum with the influence of porosities included through the distribution of relative density, i.e. the ratio of the apparent density to that of the corresponding fully dense bulk material. For the mechanical response, this involves a plasticity model based on a porous formulation. Other material data have to be supplied as a function of relative density and temperature, as for example the electrical resistivity. The numerical modeling is compared to experimentally resistance sintered titanium with good agreement in terms of pre-compaction and developed relative density and temperature during the sintering process.