Coupled fluid flow-reaction model

Some applications of the coupled fluid flow-reaction model were carried out to the ore-forming process (e.g., Lichtner and Biino, 1992). However, a few attempts to understand quantitatively the precipitations of minerals from flowing supersaturated fluids in the submarine hydrothermal systems have been done (Wells and Ghiorso, 1991). Wells and Ghiorso (1991) discussed the silica behavior in midoceanic ridge hydrothermal system below the seafloor using a coupled fluid flow-reaction model. 

Baumgartner L. P. and Ferry J. M. (1991) A model for coupled fluid-flow and mixed-volatile mineral reactions with applications to regional metamorphism. Contrib. Mineral. Petrol. 106, 273-285. 

In this book we considered mass transfer and elemental migration between the atmosphere, hydrosphere, soils, rocks, biosphere and humans in earth s surface environment on the basis of earth system sciences. In Chaps. 2, 3, and 4, fundamental theories (thermodynamics, kinetics, coupling model such as dissolution kinetics-fluid flow modeling, etc.) of mass transfer mechanisms (dissolution, precipitation, diffusion, fluid flow) in water-rock interaction of elements in chemical weathering, formation of hydrothermal ore deposits, hydrothermal alteration, formation of ground water quality, seawater chemistry. However, more complicated geochemical models (multi-components, multi-phases coupled reaction-fluid flow-diffusion model) and phenomenon (autocatalysis, chemical oscillation, etc.) are not considered. 

A modelling approach that could fulfil this need is based on the stationary-state approximation to coupled fluid flow and water-rock interaction (Lichtner 1985, 1988). This model represents the chemical evolution of an open, flow-through system as a sequence of relatively long-lived stationary states of the system, which are linked in time by short-lived transients. The basis for the model is the observation that within a representative elemental volume of a rock-water system, the aqueous concentration of any particular species is generally much less than its concentration in minerals. Long periods of time are therefore necessary to dissolve, or precipitate, minerals such that the spatial distribution of mineral abundances, surface area, porosity and permeability is altered significantly. Each time interval represents a stationary state of the system, in which fluid composition, reaction rates and the distribution of primary and alteration minerals vary only as a function of position in the flow path, not of time. 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

FORTRAN computer program that predicts the species, temperature, and velocity profiles in two-dimensional (planar or axisymmetric) channels. The model uses the boundary layer approximations for the fluid flow equations, coupled to gas-phase and surface species continuity equations. The program runs in conjunction with CHEMKIN preprocessors (CHEMKIN, SURFACE CHEMKIN, and TRAN-FIT) for the gas-phase and surface chemical reaction mechanisms and transport properties. The finite difference representation of the defining equations forms a set of differential algebraic equations which are solved using the computer program DASSL (dassal.f, L. R. Petzold, Sandia National Laboratories Report, SAND 82-8637, 1982). 

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. 

Ferry JM, Dipple GM (1991) Fittid flow, mineral reactions and metasomatism. Geology 19 211-214 Ferry JM, Dipple GM (1992) Models for coupled fittid flow, mineral reaction, and isotopic alteration during contact metamorphism The Notch Peak Aureole, Utah Am Mineral 77 571-577 Ferry JM, Rumble D in (1997) Formation and destraction of periclase by fluid flow in two contact aureoles. Contrib Mineral Petrol 128 313-334... 

The most recent computations of chemical reaction paths couple chemical kinetics, path calculations, and fluid flow models. This can be accomplished by alternating between fluid flow and reaction path calculations in small time steps, with reaction kinetics included as we have described above. Several examples of this type are summarized by Brimhall and Crerar (1987, pp. 302-306). With this kind of approach it should ultimately become possible to model the detailed physical and chemical evolution of quite complex natural mineral systems. With inclusion of three-dimensional space as well as temperature and pressure gradients, there are challenges for the foreseeable future. 

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.

Clearly there is no theoretical limit to the complexity of the reactions that might be considered in this way. In addition, it is quite possible to couple this type of calculation with other types, such as fluid flow, heat flow, pressure changes, diffusion, permeability changes, deformation, and so on, because these other model calculations also are carried out iteratively in a large series of small steps. Thus, for example, after carrying out a Af step in a reaction path model, we could then take a small step in a heat flow model, then a small step in a fluid flow model, and then return to the reaction model, and so on. The heat... 

Throughout this process, there will be tradeoffs between the levels of detail included in the different aspects of the model. For example, in a simple batch reactor model, one can include thousands of chemical species and reactions, whereas in a detailed three-dimensional fully coupled model of fluid flow, heat transfer, and chemical reactions, one might be limited to less than 20 chemical species and a similar number of reactions. With continuous advances in both computational hardware and... 

Above-mentioned reaction, diffusion and advection influence mass transfer in rock-water system. It is generally difficult to solve the differential equation including all these mechanisms. Thus, the two coupled models at constant temperature and pressure will be explained below. They are (1) reaction-fluid flow model, (2) reaction-diffusion model, (3) diffusion-fluid flow model. In addition to these coupled models, model taking into account the change in temperature will be considered. 

Chemical equilibrium and mass transfer mechanisms (chemical reactions, diffusion, fluid flow (advection), adsorption, etc.) (Chaps. 1,2, and 3) are examined in order to illustrate the compositional variation that exists within water (ground water, hydrothermal solution, seawater) and weathered and hydrothermally altered rocks and soils. To better understand the subsystems of the earth, equilibrium and mass transfer coupling models are apphed to the seawater system, as an example of a low-temperature exogenic system, and hydrothermal systems, as an example of high-temperature endogenic systems (Chap. 4). 

In spite of the success of CFD simulations for the multiphase turbulent fluid flow in stirred-tank bioreactors (see Section 3.4), their application to coupled material balance equations in case of more complicated reaction networks is still limited by the required computing power. Even in case of successful approaches for model reduction, the number of compounds necessary for reliable portrayal of cellular dynamics in response to spatial variation of extracellular compounds may be still too large. An interesting method to overcome these numerical difficulties is the general hybrid multizonal/CFD [27-36], which gave momentum to the application of CFD modeling for bioreactors. 

Instead of assigning different shear rates, he employed different breakage rate expressions for the two zones. The problem of coupling population balance models with fluid flow models has received some attention recently and coupled PB-CFD models have been developed for a wide variety of processes such as fluidization [70], gas-liquid reactions in bubble columns [71] and nanoparticle synthesis in flame aerosol reactors [72]. Complete description of aggregation in turbulent environments requires simultaneous solution of basic balance equations for mass, momentum, energy and concentration of species present along with population balances for particles/aggregates of different size classes. 

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