Solute transport fluid flow coupling

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. 

Figure2 Ohnishi et al. (1985) and Chijimatsu et al. (2000)) and reactive-mass transport model (inside the box named Chemical in Figure 2). This is a system of governing equations composed of Equations (l)-(9), which couple heat flow, fluid flow, deformation, mass transport and geochemical reaction in terms of following primary variables temperature T, pressure head y/, displacement u total dissolved concentration of the n master species C< > and total dissolved and precipitated concentration of the n" master species T,. Here we set master species as the linear independent basis for geochemical reactions, and speciation in solution and dissolution/precipitation of minerals are calculated by a series of governing equations for geochemical reaction. Now we adopt equilibrium model for geochemical reaction (Parkhurst et al. (1980)), mainly because of reliability and abundance of thermodynamic data for geochemical reaction.

The MOTIF code is a three-dimensional finite-element code capable of simulating steady state or transient coupled/uncoupled variable-density, variable- saturation fluid flow, heat transport, and conservative or nonspecies radionuclide) transport in deformable fractured/ porous media. In the code, the porous medium component is represented by hexahedral elements, triangular prism elements, tetrahedral elements, quadrilateral planar elements, and lineal elements. Discrete fractures are represented by biplanar quadrilateral elements (for the equilibrium equation), and monoplanar quadrilateral elements (for flow and transport equations). 

SIMULATION OF COUPLED FLUID FLOW AND SOLUTE TRANSPORT IN A ROUGH FRACTURE... 

The processes can be considered as three initially independent processes. These include the undrained load-deformaiion-failure process and the fluid and heat flow processes. The fluid flow process may include solute transport. Other mechanisms include swelling of shale caused by change in water potential resulting from the other processes. The main coupling parameters are stress, pore pressure and temperature. 

Increasingly since the mid-1970s, with the advent of high-speed digital computers, process-based mathematical models of coupled subsurface fluid flow, solute transport, and geochemistry have been used to assess subsurface water contamination impacts. 

Dynamic factors are among the key variables to be optimized in an SFE process. In addition to extracting the analytes, the primary function of the supercritical fluid is to transport the solutes to the collecting vessel or to an on-line coupled chromatograph or detector. Ensuring efficient transportation of the analytes following separation from the matrix entails optimizing three mutually related variables, namely the flow-rate of the supercritical fluid, the characteristics of the extraction cell and the extraction time. These factors must be carefully combined in order to allow the flow-cell to be vented as many times as required. 

The basic discretization of the two-fluid model equations is similar to the approximations of the corresponding transport equations for single phase flow. A minor difference is that the two-fluid model equations contain the novel phase fraction variables that have to be approximated in an appropriate manner. More important, to design robust, stable and accurate solution procedures with appropriate convergence properties for the two-fluid model equations, emphasis must be placed on the treatment of the interface transfer terms in the phasic momentum, heat and mass transport equations. Because of these extra terms, the coupling between the different equations is even more severe for multiphase flows than for single phase flows. 

Mass-transport (i.e., diffusion or electromigration) effects are particularly acute in the cases of cracking, pitting, and crevice corrosion, whereby occlusion effects can create highly concentrated solutions that move an otherwise stable system into regions of thermodynamic instability at the local level [13,14,41 3, 79-82]. When porous films or particular solution flow conditions exist, mass-transport effects should also be taken into account [83, 84]. Molecular dynamics and Monte Carlo simulations of interfaces over the past few decades have provided some insight into the concentration gradients that occur close to the electrochemical interface [85-91], and these, coupled with computational fluid dynamics simulations, can indicate the extent to which mass-transport effects can dominate an overall corrosion scenario [92]. 

The dynamics is obtained hy numerical solving a set of the coupled Boltzmann-BGK transport equations (d. eqn [35]) on a spatial lattice in discrete time steps with a discrete set of microscopic vdodties. At each time step, the prohahility density evolved hy each LB equation is adverted to nearest neighhoting lattice sites and modified by molecular collisions, which are local and conserve mass and momentum. As a result, a LB fluid is shown to obey the Navier-Stokes equation (in the limit of a small lattice spacing and small time step). For dilute polymer solutions, the method typically involves phenomenological coupling between the polymer chain and the flowing fluid in the form of a linear friction term based on an effective viscosity. 

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