Flow through Packed and Fluidized Beds
Chemical engineering operations commonly involve the use of packed and fluidized beds. These are devices in which a large surface area for contact between a liquid and a gas (absorption, distillation) or a solid and a gas or liquid (adsorption, catalysis) is obtained for achieving rapid mass and heat transfer, and particularly in the case of fluidized beds, catalytic chemical reactions. You will find a good deal of information about flow through packed and fluidized beds in the book by McCabe, Smith, and Harriott (1) and Perry’s Handbook (2). Here, only a brief summary is given. First, let us consider flow through a packed bed.
Modeling of hydraulic fracturing in rocks : a multiscale and fluid-solid coupling approach
This dissertation investigates the implications of the fluid flow on the behaviour of the particle-scale structure of a porous hard rock, based on the Discrete Element Method (DEM). This project is driven by the need to contribute towards a better understanding of the mechanical behaviour of porous rock formations under intense injection conditions and the influence of natural pre-existing rock damage to the hydraulic fracturing mechanism. The proposed numerical scheme incorporates different methods for computing both the solid and co-existing fluid phases. The solid phase (rock sample) has been characterized as a collection of discrete interacting particles, bound by spring-like contacts according to the DEM. Meanwhile, the fluid phase has been modelled by discretising the Navier-Stokes equations for porous media, utilising the fluid coupling algorithm embedded in the Particle Flow Code (PFC3D) software by Itasca. 
The outcome of this dissertation suggests that the DEM approach is an advanced computational method that can reproduce accurate rock models, adequately describe the inter-particle dynamics and thus contribute towards direct numerical and experimental comparisons, and interpret the geo-mechanical behaviour of the rock materials. Furthermore, this study identifies the importance of shear cracking in the hydraulic fracturing models, whereas conventional theory relates hydraulic fracturing with tensile cracking. Finally, this study focuses on the influences of various parameters, such as the external stress regime, fluid viscosity and pre-existing fractures, on the mechanical behaviour of the rock material in the particle-scale and the hydraulic fracturing process as a whole. 
This work is in an early stage and it aims to simulate hydraulic fracturing experiments with the use of a 3D modelling and the DEM approach, and to investigate the micromechanical response of the rock. Further research may include areas such as the 3D modelling of pre-cracked rocks using a larger variety of fracture angles.
Pressure drops in the flow of gases through packed and distended beds of spherical particles
Pressure drop measurements were made across packed and distended beds having five layers of smooth plastic spheres, 1.23 in. in diamter, arranged in cubic, body-centered cubic, and face-centered cubic orientations of void fractions varying from 0.354 to 0.882. The distended beds were prepared by separating the spheres with permanently attached short lengths of fine rigid wire. Friction factors were calculated from the overall pressure drop measurements with the Ergun equation and were plotted against the corresponding modified Reynolds number which ranged from 2,550 to 64,900. A single relationship resulted for both types of beds which is independent of the geometric orientation and void fraction of the spheres of the bed. 
 
To eliminate entrance and exit effects of the air flowing through the bed pressure drop measurements were also made across the middle layer of each distended bed. Again a single relationship between the corresponding friction factors and modified Reynolds number was obtained which is independent of the geometric orientation and void fraction of the bed. 
 
From the two relationships between friction factors and modified Reynolds number the ratio Pk/fk for a packed or distended bed having five layers of spheres is 1.13. This ratio should decrease with increasing number of layers of spheres and approach the limiting value of 1 when the number of layers becomes very large.