Numerical models transport-flow coupling

The previous example was calculated with a common numerical model for flow-and conservative transport. The simulation of natural attenuation processes however, requires three-dimensional transport coupled with complex biochemical and chemical reactions. In the following example the numerical model TBC (Transport, Biochemistry and Chemistry Schafer et al., 1998A) is used to simulate natural attenuation processes in a heterogeneous aquifer. 

All numerical models incorporate significant assumptions and approximations, and their predictions must always be regarded as estimates. Solution of the RANS equations, for example, requires some form of closure assumption dealing with the Reynolds stress terms. Since the Reynolds stress terms and the mean flow terms are coupled by the equations, inaccuracies in the closure approximations can affect the predicted mean flow fleld. Furthermore, the boundary conditions imposed on the model require the assumption of velocity profiles and momentum transport rates, which may themselves be approximated. Similar approximations are inherent in any of the various techniques used to compute the wind fleld, with further assumptions being present in each of the dispersion models. 

There has been considerable attention given to the development of 2 and 3-D numerical models to approximate the coupled two-phase mass and heat transport within unit cells, see [5, 7, 8, 15, 17, 22, 25, 29, 30, 38, 39, 37]. However, these approaches have either not fully resolved the multiphase flow, advecting the liquid as suspended droplets in the gas flow, or used isothermal models in which the vapor and liquid are treated as a combined mixture, or have experienced convergence difficulties for physically reasonable values of the parameters. The majority of the treatments are at steady-state, and none has treated the transient evolution of the free surface separating the two-phase and dry regions in the hydrophobic GDL. 

The transport rates fj will be determined by the turbulent flow field inside the reactor. When setting up a zone model, various methods have been proposed to extract the transport rates from experimental data (Mann et al. 1981 Mann et al. 1997), or from CFD simulations. Once the transport rates are known, (1.15) represents a (large) system of coupled ordinary differential equations (ODEs) that can be solved numerically to find the species concentrations in each zone and at the reactor outlet. 

The coupled code developed by Steefel and Lasaga (1994) for multicomponent reactive transport with kinetics of precipitation and dissolution of minerals has been developed further into the OS3D/GIMRT code (Steefel and Yabusaki, 1996). This model has been applied to reaction fronts in fracture-dominated flow systems (Steefel and Lichtner, 1998). Eurther developments for nonuniform velocity helds by Yabusaki et al. (1998) required the use of massively parallel processing computers, although ... the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. ... 

Due to the strong coupling and the non-linearity of the transport equations determining a reactor model, the usefulness of the numerical methods are conditional on being able to solve the set of PDE s accurately. This is difficult for most flows of engineering interest. 

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