The aim of this work is to numerically investigate the particulate flow applied to filling fractures in wellbores during the drilling operation. In order to do so, the drill hole is considered in the vertical position and the fracture is defined transversal to the borehole. The wellbore is assumed to be impermeable throughout its entire length, except for the fluid inlet, outlet and the fracture point. The fracture is impermeable so that the fluid loss occurs only at its end. The analysis procedure is divided into two parts: the first one regards to the fluid loss due to the presence of a fracture in a channel (which is treated as a single-phase flow). This is a necessary step to correctly determine the boundary condition at the end of fracture by associating the amount of fluid to be lost according to a specific pressure. In the second part, the fracture filling process with the fluid-solid flow is accomplished as some of the particles carried along the channel flow take the fluid path being eventually lost through the fracture. The fracture filling process is finished when the fluid loss reduction achieves a steady plateau, despite the complete fracture obturation provided by the particles deposition. The particulate flow is numerically modeled via an Eulerian-Lagrangian approach. The Dense Discrete Phase Model (DDPM) deals with the phase coupling; the particle collisions (which happen mainly inside the fracture) are modeled through the Discrete Element Method (DEM). Results are shown in terms of both the historic of the fluid loss and the channel inlet pressure. The influence of geometric (fracture length), particle injection (diameter, concentration and density) and flow parameters (Reynolds number and fluid dynamic viscosity) over the length, height and position of the particle bed formed along the fracture as well the filling time is investigated. A better understanding of the fracture filling process is provided since all sensitivity parameters can alter not only the geometric characteristics of the bed and the steady state fluid loss, but also the time required to finish the process. The Reynolds number increases with the particles bed initial position and due to the higher flow velocity the bed length is increased as well. However, the bed height is reduced and the time required to partially obturate the fracture is raised. For safety issues in the operation during the filling process the increase of Re has shown a smaller pressure buildup in the system. To improve the fluid loss reduction at the end of the filling process, a decrease of Re and an increase of fluid viscosity is required. Such reduction is more dramatic when the diameter and the density of the particles are decreased.

The lid-driven flow inside a porous square cavity is numerically simulated. The porous media is modelled on the microscopic scale (heterogeneous porous medium) with a square heat conductive single block representing the solid constituent. Conversely, the fluid relies between the block and the cavity surfaces. A vertical positive thermal gradient, obtained by keeping the sliding-lid temperature T H higher than the base one T C , aligned with the gravity force enables a gravitational stable condition where the buoyant-induced flow does not occurs spontaneously. Instead, the flow comes about as the cavity top surface slides with constant velocity. Conservation equations are applied separately for each constituent and are coupled by boundary conditions at the fluid to solid interface (block surface). The Boussinesq-Oberbeck approximation accounts for the buoyant effects. The equations are solved via the finite volume method with the use of the SIMPLE algorithm for the pressure-velocity coupling and QUICK interpolation scheme for the treatment of the advection terms. The aim of the present work is to investigate how variations on the flow parameters and the block size affect the thermal process throughout the cavity. A top lid velocity based Reynolds number evaluates the intensity of the forced convection process while the Grashof number is associated with the intensity of buoyancy. The flow parameters cover only the laminar regime, such as 10 2 ≤ Re ≤10 3 and 10 3 ≤ Gr ≤10 7 . The Re and the Gr numbers are also analyzed by the means of the Richardson number, Ri , which accounts the relative predominance of buoyancy over the inertia effects. Moreover, a clear fluid cavity and enclosure configurations with three different block dimensions, namely B = 0.3, 0.6 and 0.9, are simulated. The heat transfer across the cavity can be characterized as a competitive effect, since the flow is hindered as the buoyancy effect rises. Results show that an increase in Re , or decrease in Gr , enhances the heat transfer, revealing a convection dominant regime. Alternatively, an increase in Gr , or a decrease in Re , leads the fluid to a stagnant-prone condition where a conduction dominant regime is verified. Thus, the surface-average Nusselt number, Nu av , tends to unity as the flow is confined to the adjacency of the sliding-lid. The placement of the single block in the cavity can enhance or hinder the heat transferred, depending on the flow regime. For instance, if a B = 0.6 block is inserted in the presence of a convection dominant regime, the Nu av is increased. Conversely, if the fluid is quiescent, a B = 0.6 block alters the flow path and the Nu av decreases. Intense blockage effects are observed for larger values of B since the block interferes on the flow more significantly. For a convection dominant regime, for instance, a B = 0.9 block causes the Nu av to drop. However, in the presence of stagnant fluid, the same obstacle forces the flow to circumvent it. Thus, the Nu av number increases, indicating that heat transfer mode returns to a convective pattern.

In this study, the natural convection inside a fluid filled enclosure containing several solid obstructions and heated from the side is simulated numerically as to determine the effects of the solid thermal conductivity and volume-fraction. The solid obstructions are conducting, disconnected square blocks, uniformly distributed inside the enclosure. The mathematical model follows a continuum approach, with balance equations of mass, momentum and energy presented for each one of the constituents (i.e., fluid and solid) inside the enclosure. The equations are then solved numerically via the finite-volume method. The effects of varying the solid-fluid thermal conductivity ratio (K), the fluid volume-fraction or porosity (φ), the number of solid blocks (N) and the heating strength (represented by the Rayleigh number, Ra) on the natural convection process inside the enclosure are investigated parametrically. The Nusselt number based on the surface-averaged heat transfer coefficient along the heated wall is chosen to characterize the convection strength inside the enclosure. The results indicate a competing effect caused by the proximity of the solid blocks to the heated and cooled walls of the enclosures, vis-a`-vis hindering the boundary layer growth, hence reducing the heat transfer effectiveness, and at the same time enhancing the heat transfer when K is large. An analytical estimate of the minimum number of blocks beyond which the convection hindrance becomes predominant is presented and validated by the numerical results.