Advection fluid phase

A general overview was provided of porous media characteristics, fluid flow in porous media, advection and dispersion in porous media, and phase partitioning and reactive processes in porous media. Four questions were posed in the introduction, and it was suggested that the answers to those questions could be used to highlight the important features of a particular porous media transport problem. By the very nature of porous media, the answer to the first question (i.e., which phases are present ) will at least include a solid phase and one fluid phase, composed of either a liquid or a gas. If multiple phases are present in the void space, then the distribution of the liquid and gas in the pore space will be a function of capillary pressure. 

Transport of stable isotopes in a moving fluid phase is called advection. Here infiltrating fluids move the isotopic species of interest. Fluid flow is restricted to connected pore spaces. The amount of connected pore space and the manner of connection determines the permeability of a rock. Mixing of stable isotope ratios by a flowing fluid on grain boundary intersections, micro crack intersections, and fracture intersections results in dispersion. Dispersion is similar to diffusion (at least mathematically), since this is a mixing process. 

The model has a reactive module, which solves reaction kinetics and equilibrium reactions, and a transport module, which incorporates the advection-dispersion equation. The transport/reaction equation is formulated for each redox acceptor in the fluid phase as follows... 

The evolution of the interface and advection of the phase-indicator function is accomplished by reconstructing the interface within each computational cell and computing the volume flux that occurs from each cell to its immediate neighbors under the prevaihng flow. The surface reconstruction problem [11] is one of finding an interface with the correct unit normal vector which divides the computational cell into two regions, each occupied by the respective fluid phase. One popular way to accomplish this is using the Piecewise Linear Interface Calculation or Con-... 

Macromixing refers to the processes of advection caused by the turbulent flow, which transport fluid particles and which, through the roll-up and stretching of sheets, assist in fragmenting the fluid phase into small-scale entities. As a result, concentration gradients within the fluid domain are considerably strengthened. These phenomena have already been described and illustrated in Figures 10.1 and 10.4. 

Data for the bulk fluid, line A, indicate that vz varies as a function of z but maintains a value near 0.75 of maximum velocity. The periodicity of vx and vy is clearly evident in the graph of line A and a 1800 out of phase coupling of the components is seen with one positive when the other is negative. This indicates a preferred orientation to the plane of the oscillatory flow and this feature was seen in all the biofilms grown throughout this study. The secondary flow components are 0.1-0.2 of the maximum axial velocity and are spatially oscillatory. The significant non-axial velocities indicate non-axial mass transport has gone from diffusion dominated, Pe = 0, in the clean capillary, to advection dominated, Pe 2 x 103, due to the impact of the biofilm. For comparison, the axial Peclet number is Pe L 2x 10s. Line B intersects areas covered by biomass and areas of only bulk... 

Following the release of a toxicant into an environmental compartment, transport processes will determine its spatial and temporal distribution in the environment. The transport medium (or fluid) is usually either air or water, while the toxicant may be in dissolved, gaseous, condensed, or particulate phases. We can categorize physical transport as either advection or diffusion. 

Other models directly couple chemical reaction with mass transport and fluid flow. The UNSATCHEM model (Suarez and Simunek, 1996) describes the chemical evolution of solutes in soils and includes kinetic expressions for a limited number of silicate phases. The model mathematically combines one- and two-dimensional chemical transport with saturated and unsaturated pore-water flow based on optimization of water retention, pressure head, and saturated conductivity. Heat transport is also considered in the model. The IDREAT and GIMRT codes (Steefel and Lasaga, 1994) and Geochemist s Workbench (Bethke, 2001) also contain coupled chemical reaction and fluid transport with input parameters including diffusion, advection, and dispersivity. These models also consider the coupled effects of chemical reaction and changes in porosity and permeability due to mass transport. 

The volume of fluid (VOF) approach simulates the motion of all the phases rather than tracking the motion of the interface itself. The motion of the interface is inferred indirectly through the motion of different phases separated by an interface. Motion of the different phases is tracked by solving an advection equation of a marker function or of a phase volume fraction. Thus, when a control volume is not entirely occupied by one phase, mixture properties are used while solving governing Eqs (4.1) and (4.2). This avoids abrupt changes in properties across a very thin interface. The properties appearing in Eqs (4.1) and (4.2) are related to the volume fraction of the th phase as follows ... 

The advection-reaction-dispersion equation defined by Eq. 2.60 is for an isothermal single phase flow in one dimension. The fluid is incompressible. Gravity and capillary forces are not included. For multiphase flow, because chemicals are usually injected in the water phase, the advection term in the previous equation should be multiplied by water fraction f , and the left side should be multiplied by water saturation Sw When dispersion is also neglected, Dl = 0. Equation 2.60 therefore becomes... 

The PBE is a simple continuity statement written in terms of the NDE. It can be derived as a balance for particles in some fixed subregion of phase and physical space (Ramkrishna, 2000). Let us consider a finite control volume in physical space O and in phase space with boundaries defined as dO. and dO., respectively. In the PBE, the advection velocity V is assumed to be known (e.g. equal to the local fluid velocity in the continuous phase or directly derivable from this variable). The particle-number-balance equation can be written as... 

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