Pore water velocity

Diffusivity in water Molecular diffusion is defined as the transport of molecules (e.g., organic compounds) in either liquid or gaseous states. Typically, molecular diffusion is not a major factor under the majority of enviromnental conditions. However, in saturated aquifers with low pore water velocities (i.e., <0.002 cm/sec), diffusion can be a contributing factor in the transport of organic compounds. 

Brusseau, M. L., The influence of solute size, pore water velocity, and intraparticle porosity on solute dispersion and transport in soil , Water Resour. Res., 29,1071-1080 (1993). 

Triazines and metabolites remain in the surface soil as a result of sorption processes. In intact soil cores containing a silt loam soil, atrazine leaching was primarily influenced by sorption-related nonequilibrium at low pore water velocities and by a combination of both transport- and sorption-related nonequilibrium at high pore water velocities (Gaber et al., 1995). 

Selim et al. (1976b) developed a simplified two-site model to simulate sorption-desorption of reactive solutes applied to soil undergoing steady water flow. The sorption sites were assumed to support either instantaneous (equilibrium sites) or slow (kinetic sites) first-order reactions. As pore-water velocity increased, the residence time of the solute decreased and less time was allowed for kinetic sorption sites to interact (Selim et al., 1976b). The sorption-desorption process was dominated by the equilib-... 

Mathematical derivations of potassium transport and transformation processes may be formulated as follows. The following new terms can be defined C, concentration of potassium in solution phase Si, amount of potassium in exchangeable phase S2, amount of potassium in nonexchangeable phase S5, amount of potassium in primary mineral phase wPW, pore water velocity Dc, dispersion coefficient and d, depth or distance below soil surface. 

Akratanakul, S., Boersma, L., and Klock, G. O. (1983). Sorption processes in soils as influenced by pore water velocity. 2. Experimental results. Soil Sci. 135, 331-341. 

D = dispersion coefficient v = average pore water velocity p = bulk density 0 = saturated water content x = distance in the direction of flow t = time. 

Adams, F., Burmester, C., Hue, N. V., and Long, F. L. (1980). Comparison of column-displacement and centrifuge methods for obtaining soil solution. Soil Sci. Soc. Am. J. 44, 733—735. Amoozegar-Fard, A. D., Nielsen, D. R., and Warrick, A. W. (1982). Soil solute concentration distribution for spatially varying pore water velocities and apparent diffusion coefficients. Soil Sci. Soc. Am.J. 46, 3—9. 

The movement of chemicals undergoing any number of reactions with the soil and/or in the soil system (e.g., precipitation-dissolution or adsorption-desorption) can be described by considering that the system is in either the equilibrium or nonequilibrium state. Most often, however, nonequilibrium is assumed to control transport behavior of chemical species in soil. This nonequilibrium state is thought to be represented by two different adsorption or sorption sites. The first site probably reacts instantaneously, whereas the second may be time dependent. A possible explanation for these time-dependent reactions is high activation energy or, more likely, diffusion-controlled reaction. In essence, it is assumed that the pore-water velocity distribution is bimodal,... 

Model input parameters were based on independent field and laboratory observations that used subsurface media similar to that at the WAG 5 field facility. The mean pore-water velocity (v) of the fracture regime was estimated from measured... 

Breakthrough curves from column experiments have been used to provide evidence for diffusion of As to adsorption sites as a rate-controlling mechanism. Darland and Inskeep (1997b) found that adsorption rate constants for As(V) determined under batch conditions were smaller than those necessary to model breakthrough curves for As(V) from columns packed with iron oxide coated sand the rate constants needed to model the breakthrough curves increased with pore water velocity. For example, at the slowest velocity of 1 cm/h, the batch condition rate constant was 4 times smaller than the rate constant needed to model As adsorption in the column experiment. For a velocity of 90 cm/h, the batch rate constant was 35 times smaller. These results are consistent with adsorption limited by diffusion of As(V) from the flowing phase to sites within mineral aggregates. Puls and Powell (1992) also measured more retardation and smaller rate constants for As(V) at slower flow velocities where there was sufficient time for diffusion to adsorption sites. 

The velocity of a contaminant in groundwater is slowed by the presence of organic matter in the soil into which the contaminant will partition. Under equilibrium partitioning conditions, contaminant velocity is related to the pore water velocity by... 

For naphthalene in a particular aquifer, R has been found experimentally to equal 70. If the pore water velocity from a source to a well at a distance of 1000 m is 5 X 10 cm/s, what is the travel time of naphthalene to the well ... 

The pore water velocity, v = 5 x 10 cm/s, and the retardation factor, R = 70, are given in the problem statement. Thus, the velocity of the naphthalene is determined... 

Equation (3.4.34) can be altered by making assumptions as to the influence of molecular diffusion and rate of water flow. For example, if the molecular diffusion is negligible and the dispersion carries with the pore-water velocity,... 

Pore water velocity Average fluid velocity inside a porous medium. 

Davidson, J.M., and R.K, Chang. 1972. Transport of picloram in relation to soil physical conditions and pore water velocity. Soii Sci. Soc. Am. Proc. 36 257-261. 

Here c is the solute concentration, [ML-3 ], Ds is the solute dispersion coefficient, [L2T], and v is the average pore-water velocity, [LHM ]. This equation describes movement of particles participating in Fickian diffusion-like transport and simultaneously transported with the mean pore velocity. 

Although anomalous diffusion is expected in fractal pore systems, the presence of anomalous diffusion does not prove that the porous media is fractal. A heterogeneity along transport pathways may result in an anomalous transport regardless of the presence or the absence of self-similarity of the pore space (Beven et al., 1993). The physical interpretation of Levy motions does not presume the presence of fractal scaling in the porous media in which the motions occur (Klafter et al, 1990). The applicability of the FADE may be closely related to the distribution of pore-water velocities. In saturated media, the presence of heavy-tailed distributions of the hydraulic conductivity directly implies the validity of the FADE (Meer-schaert et al., 1999 Benson et al., 1999). The heavy-tailed hydraulic conductivity distributions were found in geologic media (Painter, 1996 Benson et al., 1999). Heavy-tailed velocity distributions can also be expected in unsaturated and structured soils, and therefore the FADE may be a useful model in these conditions. 

Models that are used to predict transport of chemicals in soil can be grouped into two main categories those based on an assumed or empirical distribution of pore water velocities, and those derived from a particular geometric representation of the pore space. Velocity-based models are currently the most widely used predictive tools. However, they are unsatisfactory because their parameters generally cannot be measured independently and often depend upon the scale at which the transport experiment is conducted. The focus of this chapter is on pore geometry models for chemical transport. These models are not widely used today. However, recent advances in the characterization of complex pore structures means that they could provide an alternative to velocity based-models in the future. They are particularly attractive because their input parameters can be estimated from independent measurements of pore characteristics. They may also provide a method of inversely estimating pore characteristics from solute transport experiments. 

Velocity-based models use the distribution of pore water velocities to predict the spreading of a solute in time and space. No attempt is made to directly link the distribution of pore water velocities or solute spreading to characteristics of the pore space. As a result, the model parameters must be either estimated inversely (Parker van Genuchten, 1984 Toridc el al.. 1995) or inferred from the hydraulic conductivity-water content function (Slcenlmisel al., 1990 Scotler Ross, 1994). 

Equation [1] assumes the porous medium is homogeneous and isotropic (i.e., K and v do not vary in space or with direction), that flow is laminar, and that individual solute molecules sample a normal (Gaussian) distribution of pore water velocities in a time-independent fashion (the ergodic hypothesis) (Sposito et al., 1979). It can be shown (e.g., Bear, 1961) that the v and K in Eq. [1] are related to the mean (u) and variance (o2) of a normal distribution of distances traversed by the solute over the time increment At by,... 

Mixing due to the microscopic distribution of pore water velocities, known as hydrodynamic dispersion, is illustrated in Fig. 3-2. Figure 3-2A shows the pore water velocity profile, v(y) for Poiseuille flow in a uniform capillary tube of radius r. Additional spreading can occur due to the irregular shape of natural pores as compared to ideal cylinders (Fig. 3-2B). 

---