Streamtube Approach

In the numerical streamtube model, the restriction to nearly uniform flow fields, commonly associated with the streamtube approach, is eliminated by introducing non-planar injection and control surfaces which are perpendicular to the mean flow direction, thus accounting for non-uniform velocity fields (Fig. 7.2). Furthermore, the numerical approach allows to consider even complex physico-chemical relationships among the solutes regarded as well as between the solute and the solid phase. 

Some examples illustrating possible arrangements of injection and control surfaces are given in Fig. 7.3. The model concept can be applied to field-scale situations but as well to small-scale problems, for example laboratory columns (Fig. 7.3a). In a 

Sold phase Hetero0on OMS son maMx (Miotogy, giSln Si2M) 

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Yabusaki, S. B., C. I. Steefel and B. D. Wood, 1998, Multidimensional, multicomponent subsurface reactive transport in non-uniform velocity fields code verification using an advective reactive streamtube approach. Journal of Contaminant Hydrology 30,299-331. 

Modelling Reactive Transport of Organic Solutes in Groundwater with a Lagrangian Streamtube Approach... 

Figure 7.1 Conceptual basis of the streamtube approach (a) aquifer domain between an injection and a control plane, (b) pdf of travel time as description of flow field variability in the aquifer domain.

SMART is applicable if integral information on contaminant behaviour in groundwater is sufficient. If point information is needed a conventional FD or FE model has to be used. Although it is obvious that the streamtube approach is not as flexible as real 3D models , decoupling of conservative transport and physico-chemical processes allow to model three-dimensional contaminant transport in a convenient and computationally efficient way, especially if only one representative streamtube must be modelled. Computation times, as observed by Peter et al. (chapter 14) are much lower compared to MT3D simulations. It should also be mentioned, that the streamtube approach possesses some advantages compared to real 3D models even if each and every streamtube has to be modelled by means of a numerical model in order to evaluate F. Since only one dimensional advective-reactive transport must be modelled, numerical solutions based on discrete or mechanistical approaches, free of numerical dispersion, can be applied. In SMART this is done by a so-called parceltracking approach where contaminant transport is described by means of a continuous series of water volumes ( parcels ) as described in Finkel et al. (1998). 

These findings show that the one-dimensional streamtube model SMART is able to appropriately represent the mean transport behaviour for travel distances larger than 100 m, which corresponds to approximately two to four correlation lengths at the investigated site. Single realisations caimot be simulated satisfactorily using the streamtube approach. 

The model utilizes the "streamtube approach introduced by Higgins and Leighton. Each sand layer of the reservoir is divided into a number of tubes connecting the injector to the producer in 1/8 of a five-spot. Each tube is divided into a number... 

Two model approaches are compared by simulating reactive transport of acenaphthene in a heterogeneous porous medium. In a Monte Carlo approach a Lagrangian onedimensional streamtube model is used to assess the transport behaviour at field scale for distances of up to 800 m. Aquifer properties are taken from results of field experiments characterising a test site in a shallow quaternary sand and gravel aquifer. The results of the streamtube model are compared to model results of a two-dimensional Eulerian model. Both models account for kinetic sorption, described as diffusive transport in intra-particle pores. 

Natural attenuation is controlled by numerous processes, which include sorption, intraparticle diffusion as weU as biological and chemical degradation. In order to be able to quantify respectively predict the fate and transport of contaminants, appropriate models that are able to deal with the complexity and interactions of the involved processes need to be developed. Due to insufficient information on the spatial distribution of transport parameters in the subsurface, stochastic methods are a preferred alternative to deterministic approaches. In the present paper a one-dimensional Lagrangian streamtube model is used to describe the reactive transport of acenaphthene as a sample organic compoimd at field scale. As the streamtube model does not consider the heterogeneity of hydrogeochemical parameters but only hydraubc heterogeneity, model results from the streamtube model are compared in a Monte Carlo approach to results of a two-dimensional Eulerian model. 

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