A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

In this work we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structure where the high strain core is surrounded by the so called damage zones, characterized by the presence of smaller fractures which enhance the permeability of the medium. To obtain reliable simulation outcomes these damage zone, as well as the fault, have to be accurately described. The new model proposed in this work considers both these two regions as lower dimensional and embedded in the rock matrix. The model is presented, analyzed, and tested in several configurations to prove its robustness and ability to capture many important features, such as hight contrast and heterogeneity of permeability

A multi-layer reactive transport model for fractured porous media

An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here the transported solute may precipitate and form a salt, or vice-versa. This phenomenon has been observed and reported in real outcrops. By changing its physical properties this layer might substantially alter the global flow response of the system and thus the actual transport of solute: the problem is thus non-linear and fully coupled. The aim of this work is to propose a new mathematical model for reactive flow in fractured porous media, by approximating both the fracture and these surrounding layers via a reduced model. In particular, our main goal is to describe the layer thickness evolution with a new mathematical model, and compare it to a fully resolved equidimensional model for validation. As concerns numerical approximation we extend an operator splitting scheme in time to solve sequentially, at each time step, each physical process thus avoiding the need for a non-linear monolithic solver, which might be challenging due to the non-smoothness of the reaction rate. We consider bi- and tridimensional numerical test cases to asses the accuracy and benefit of the proposed model in realistic scenarios

A mathematical model for thermal single-phase flow and reactive transport in fractured porous media

In this paper we present a mathematical model and a numerical workflow for the simulation of a thermal single-phase flow with reactive transport in porous media, in the presence of fractures. The latter are thin regions which might behave as high or low permeability channels depending on their physical parameters, and are thus of paramount importance in underground flow problems. Chemical reactions may alter the local properties of the porous media as well as the fracture walls, changing the flow path and possibly occluding some portions of the fractures or zones in the porous media. To solve numerically the coupled problem we propose a temporal splitting scheme so that the equations describing each physical process are solved sequentially. Numerical tests shows the accuracy of the proposed model and the ability to capture complex phenomena, where one or multiple fractures are present

Modeling and simulation in tribology across scales: An overview

This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions

Aeronautical engineering: A continuing bibliography with indexes (supplement 193)

This bibliography lists 682 reports, articles and other documents introduced into the NASA scientific and technical information system in October 1985

Modelling of hydraulic fracturing in unconventional reservoirs

Hydraulic fracturing (HF) is a process of fluid injection into the well in order to create tensile stresses in the rock to overcome the tensile strength of the formation. In this study, the development and application of a fuzzy model to predict the efficiency of hydraulic fracturing is presented with application in a coal mine as an unconventional reservoir. The most important parameters affecting the HF process of a coal seam are: dip, thickness, seam uniformity, roof and floor conditions, reserve of coal seam and coal strength. In the developed model, the efficiency of hydraulic fracturing of coal seams is calculated as a dimensionless numerical index within the range 0-100. The suggested numerical scale categorizes the efficiency of HF of seams to very low, low, medium, high and very high, each one being specified by a numerical range as a subset of the above range (0-100). HF in the coal bed in PARVADEH 4 Tabas mine in Iran is investigated as a case study. The results show that the developed model can be used to identify seams that have high potential for HF Moreover, a three-phase hydro-mechanical model is developed for simulating hydraulic fracturing. The three phases include: porous solid, fracturing fluid and reservoir fluid. Two numerical simulators (ANSYS Fluent for fluid flow and ANSYS Mechanical for geomechanical analysis) are coupled together to model multiphase fluid flow in hydraulically fractured rock undergoing deformations, ranging from linear elastic to large, nonlinear inelastic deformations. The two solvers are coupled, using system coupling in ANSYS Workbench. The coupled problem of fluid flow and fracture propagation is solved numerically. The fluid flow model involves solving the Navier-Stokes equations using the finite volume method. The flow model is coupled with the geomechanics model to simulate the interaction between fluid flow inside the fracture with rock deformations. For any time step, the pore pressures from the flow model are used as input for the geomechanics model for the determination of stresses, strains, and displacements. The strains derived from the gomechanics model are in turn used to calculate changes to the reservoir parameters that are fed as input to the flow model. This iterative process continues until both (fluid and solid) models are converged. The laboratory-scale study of hydraulic fracturing in the Second White Specks (SWS) shale was simulated using the developed model. The numerical and experimental results were compared. Comprison of the results shows that the numerical model can predict the behaviour of the shale under hydraulic fracturing with a good accuracy

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics