Groundwater mass transport

Cederberg, G. A., R. L. Street and J. O. Leckie, 1985, A groundwater mass transport and equilibrium chemistry model for multicomponent systems. Water Resources Research 21, 1095-1104. 

Beginning in the late 1980s, a number of groups have worked to develop reactive transport models of geochemical reaction in systems open to groundwater flow. As models of this class have become more sophisticated, reliable, and accessible, they have assumed increased importance in the geosciences (e.g., Steefel et al., 2005). The models are a natural marriage (Rubin, 1983 Bahr and Rubin, 1987) of the local equilibrium and kinetic models already discussed with the mass transport... 

Such models are known as reactive transport models and are the subject of the next chapter (Chapter 21). We treat the preliminaries in this chapter, introducing the subjects of groundwater flow and mass transport, how flow and transport are described mathematically, and how transport can be modeled in a quantitative sense. We formalize our discussion for the most part in two dimensions, keeping in mind the equations we use can be simplified quickly to account for transport in one dimension, or generalized to three dimensions. 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

In the next chapter (Chapter 27) we show calculations of this type can be integrated into mass transport models to produce models of weathering in soils and sediments open to groundwater flow. In later chapters, we consider redox kinetics in geochemical systems in which a mineral surface or enzyme acts as a catalyst (Chapter 28), and those in which the reactions are catalyzed by microbial populations (Chapter 33). 

At the same time, reaction modeling is now commonly coupled to the problem of mass transport in groundwater flows, producing a subfield known as reactive transport modeling. Whereas a decade ago such modeling was the domain of specialists, improvements in mathematical formulations and the development of more accessible software codes have thrust it squarely into the mainstream. 

We will try our hand at applying the diffusion equation to a couple of mass transport problems. The first is the diffusive transport of oxygen into lake sediments and the use of oxygen by the bacteria to result in a steady-state oxygen concentration profile. The second is an unsteady solution of a spill into the groundwater table. 

The reactions in zero-valent iron are heterogeneous due to the strong dependence of the reaction rate on the surface area of the iron (Burris et al., 1995). The surface reaction proceeds in four steps. First, the reactant undergoes mass transport from the groundwater to the iron surface (Matheson and Tratnyek, 1994). Second, the contaminant is absorbed onto the surface of the iron, where the chemical reaction occurs. Third, the reaction products desorb from the surface, which allows the site to become available for another reaction (Burris et al., 1996a). Finally, the products of the reaction return to the groundwater. Rate limitation could occur at any step. Where it may not be the sole limitation, mass transport plays an essential role in the kinetics of dechlorination (Matheson and Tratnyek, 1994). 

Advection is the transport of dissolved contaminant mass due to the bulk flow of groundwater, and is by far the most dominant mass transport process [2]. Thus, if one understands the groundwater flow system, one can predict how advection will transport dissolved contaminant mass. The speed and direction of groundwater flow may be characterized by the average linear velocity vector (v). The average linear velocity of a fluid flowing in a porous medium is determined using Darcy s Law [2] ... 

Concentration gradients are leveled out by diffusion by means of molecular motion. The vector of diffusion is generally much smaller than the vector of convection in groundwater. With increasing flow velocity diffusion can be neglected. In sediments, in which the kf value is very low, and consequently the convective proportion is very small or even converging towards zero (e.g. for clay), the diffusion could become the controlling factor of mass transport. 

All chemical reactions comprise at least two species. For models of transport processes in groundwater or in the unsaturated zone reactions are frequently simplified by a basic sorption or desorption concept. Hereby, only one species is considered and its increase or decrease is calculated using a Ks or Kd value. The Kd value allows a transformation into a retardation factor that is introduced as a correction term into the general mass transport equation (chapter 1.1.4.2.3). 

Reactive transport. Mass transfer combined with mass transport commonly refers to geochemical reactions during stream flow or groundwater flow. 

Bredehoeft J. D. and Pinder G. F. (1973) Mass transport in flowing groundwater. Water Resour. Res. 9, 194-210. 

The flow of groundwater in a sedimentary basin results from the combined influence of the different driving forces for groundwater flow (mechanical, thermal, chemical and electrical driving forces) and the hydraulic conductivity of the subsurface. The transport of grovmdwater, heat and electricity, the mass transport of chemical components and the deformation of the solid part of the subsurface are coupled processes. 

The high permeability of fractures causes them to preferentially focus fluid flow. The effectiveness of fractures as mass transport systems for fluids is evident from a casual examination of mineralisation in fractured rocks and leakage of groundwater at fracture outcrops. Similarly, these fractures act as preferential hydrocarbon pathways, focusing their flow from source beds to surface. 

Figure 8. The longitudinal dispersion for tracers from colunrn experiments and groundwater tracer studies is proportional to the length of the flow system studied. A typical value for the dispersion is roughly one tenth of the length of the system. While not much is known about dispersion in high temperature flow systems, it is nevertheless likely that a similar correlation exists. Hence dispersion will be important for a system of any size where mass transport occurs by fluid infdtration. Data from Gelhar et al. (1985).

Hendricks Franssen, H.-J., Inverse Stochastic Modeling of Groundwater Flow and Mass Transport, Ph.D. Thesis, Universidad Politecnica de Valencia, Proquest Information and Leamging, Ann Harbor, 363 pp. 

---