Groundwater velocity

Groundwater monitoring is a necessary component in any investigation of subsurface contamination. A wide variety of information can be gleaned from the data including groundwater velocity and direction, and contaminant identification and concentration. These data can be combined with other observations to infer various characteristics of the contamination. Examples are source and timing of the release, and future location of the contaminant plume. 

Plutonium is transported by the groundwater in fractures in the rock (usually <1 mm wide). A typical groundwater velocity (vw) at >100 m depth in Swedish bedrock is 0.1 tn/y. The fractures are filled with crushed, weathered, clayish minerals, which have a high capacity to sorb the plutonium. Assuming instantaneous and reversible reactions, the sorption will cause the plutonium to move considerably slower (with velocity vn) than the groundwater. The ratio between these two velocities is referred to as the retention factor (RF), defined by... 

The value of groundwater velocity within a rock or sediment, then, invariably exceeds that of specific discharge. 

The accounting for diffusion in these models, in fact, is in many cases a formality. This is because, as can be seen from Equations 20.19 and 20.21, the contribution of the diffusion coefficient D to the coefficient of hydrodynamic dispersion D is likely to be small, compared to the effect of dispersion. If we assume a dispersivity a of 100 cm, for example, then the product av representing dispersion will be larger than a diffusion coefficient of 10-7-10-6 cm2 s-1 wherever groundwater velocity v exceeds 10 9-10-8 cm s 1, or just 0.03-0.3 cm yr-1. 

Substituting the transport laws for advection and dispersion (Eqns. 20.11 and 20.20), and noting that groundwater velocity v is related to specific discharge q according to Equation 20.7, gives... 

Here, Rj is reaction rate (mol cm-3 s-1), the net rate at which chemical reactions add component i to solution, expressed per unit volume of water. As before, Q is the component s dissolved concentration (Eqns. 20.14—20.17), Dxx and so on are the entries in the dispersion tensor, and (vx, vy) is the groundwater velocity vector. For transport in a single direction, v, the equation simplifies to,... 

Retardation also arises when a fluid undersaturated or supersaturated with respect to a mineral invades an aquifer, if the mineral dissolves or precipitates according to a kinetic rate law. When the fluid enters the aquifer, a reaction front, which may be sharp or diffuse, develops and passes along the aquifer at a rate less than the average groundwater velocity. Lichtner (1988) has derived equations describing the retardation arising from dissolution and precipitation for a variety of reactive transport problems of this sort. 

A notable aspect of this equation is that L appears within it as prominently as the rate constant k+ or the groundwater velocity vx, indicating the balance between the effects of reaction and transport depends on the scale at which it is observed. Transport might control fluid composition where unreacted water enters the aquifer, in the immediate vicinity of the inlet. The small scale of observation L would lead to a small Damkohler number, reflecting the lack of contact time there between fluid and aquifer. Observed in its entirety, on the other hand, the aquifer might be reaction controlled, if the fluid within it has sufficient time to react toward equilibrium. In this case, L and hence Da take on larger values than they do near the inlet. 

Extrapolation of laboratory results to the field scale is at best qualitative because of the complexity of the geochemical and hydrological systems in the Bengal Basin. Movement of As-contaminated groundwater towards a well screened in the uncontaminated aquifer is likely to contain both vertical and horizontal components of flow. For modeling purposes presented here, a relatively slow interstitial groundwater velocity of 3 m/yr (Stollenwerk et al. 2007) is compared with a more rapid interstitial velocity of 30 m/yr (McArthur et al. 2008). 

Recovery of DNAPL is a very slow process that is alfected by those factors encountered with LNAPL (i.e., relative permeability, viscosity, residual hydrocarbon pool distribution, site-specific factors, etc ). Dissolution of a DNAPL pool is dependent upon the vertical dispersivity, groundwater velocity, solubility, and pool dimension. Dispersivities for chamolid solvent are estimated for a medium to coarse sand under laboratory conditions on the order of 1(L3 to 1(H m. Thus, limited dispersion at typical groundwater velocities is anticipated to be slow and may take up to decades... 

This result implies that the TNT will move through the subsurface at a rate that is 1/30 the rate of the groundwater velocity. You also note that if the TNT concentrations anywhere in the plume are above 1 x 10 6 M, then the AiXNTd llll[e would be smaller (second term in the denominator of Eq. 11-20 won t be negligible) and the retardation factor will correspondingly decrease. 

The groundwater velocity field is determined by Darcy s law after the head distribution from solution of (1) has been determined ... 

The reactive transport of contaminants in FePRBs has been modeled using several approaches [179,184,186,205-208]. The simplest approach treats the FePRB as an ideal plug-flow reactor (PFR), which is a steady-state flow reactor in which mixing (i.e., dispersion) and sorption are negligible. Removal rates (and therefore required wall widths, W) can be estimated based on first-order contaminant degradation and residence times calculated from the average linear groundwater velocity [Eq. (27)]. The usefulness of... 

One of the simplest forms of the ADE that has been applied to an FePRB includes both dispersion and sorption [205]. A one-dimensional steady-state ADE was used to estimate W for 1000-fold reduction in contaminant concentrations at a groundwater velocity of 1 ft day-1. Applying the model to chlorinated aliphatic compounds (using rate coefficients summarized in Ref. 86) gave the results shown in Fig. 11. These estimates,... 

Nonequilibrium sorption due to mass-transfer limitations (including slow external or internal diffusion) and sorption to two different sorbents have been incorporated into a single ADE to evaluate the conditions under which mass-transfer processes may be important [206]. Simulations with this model, using mass-transfer parameters estimated from empirical correlations, reveal nonequilibrium conditions (i.e., mass-transfer limitations) when groundwater velocities increase (such as those that might occur in a funnel-and-gate system). 

Mechanical dispersion has been shown to be proportional to the average linear velocity, and can be modeled using the following equation, where the coordinate axes have been aligned so that groundwater velocity is in the x-di-rection [3] ... 

Mathematical models for mass transfer at the NAPL-water interface often adopt the assumption that thermodynamic equilibrium is instantaneously approached when mass transfer rates at the NAPL-water interface are much faster than the advective-dispersive transport of the dissolved NAPLs away from the interface [28,36]. Therefore, the solubility concentration is often employed as an appropriate concentration boundary condition specified at the interface. Several experimental column and field studies at typical groundwater velocities in homogeneous porous media justified the above equilibrium assumption for residual NAPL dissolution [9,37-39]. 

For each hydraulic conductivity field generated, the associated variable hydraulic head field and groundwater velocity field were determined. Each variable hydraulic head field was evaluated numerically by solving the following steady state two-dimensional groundwater flow equation for a heterogeneous confined aquifer [50] ... 

Numerous empirical correlations for the prediction of residual NAPL dissolution have been presented in the literature and have been compiled by Khachikian and Harmon [68]. On the other hand, just a few correlations for the rate of interface mass transfer from single-component NAPL pools in saturated, homogeneous porous media have been established, and they are based on numerically determined mass transfer coefficients [69, 70]. These correlations relate a dimensionless mass transfer coefficient, i.e., Sherwood number, to appropriate Peclet numbers, as dictated by dimensional analysis with application of the Buckingham Pi theorem [71,72], and they have been developed under the assumption that the thickness of the concentration boundary layer originating from a dissolving NAPL pool is mainly controlled by the contact time of groundwater with the NAPL-water interface that is directly affected by the interstitial groundwater velocity, hydrodynamic dispersion, and pool size. For uniform... 

This correlation is valid for groundwater velocities in the range from 0.1 to... 

This correlation can be applied to circular pools by setting a=b=r. It should be noted that the Eq. (95) is valid for groundwater velocities in the range from 0.1 to 1.0 m/d, and elliptic/circular pools with semiaxes axb in the range 2.5X2.5 m to 5.0X5.0 m. 

Marine, I.W. (1979) The use of naturally occurring helium to estimate groundwater velocities for studies of geologic storage of radioactive waste. Waste Resourc. Res. 15, 1130-1136. 

Complications in the estimation of groundwater ages are not unique to For example, diffusion can create major errors in estimated ages when applying the H/ He method in areas where the groundwater velocity is less than —0.01 m yr. In such cases He will diffuse upwards, and little information regarding travel times will be preserved in the He concentrations (Schlosser et al., 1989). Similar comphcations are inherent in the use of other tracers as well (see, e.g., Phillips, 2000 Sudicky and Frind, 1981 Varni and Carrera, 1998). 

---