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<br />t"- <br /><<::l" <br />~ <br />N <br />C. <br />o <br /> <br />\~~, ~.:<. <br /> <br />, ' <br /> <br />Unlike the movement of ground water, which can be defined entirely by advective processes, the <br />transport of solutes at a macroscopic scale is governed by mechanisms that approximate the effects of <br />mixing of waters with differing solute concentrations. which are moving both faster and slower than the <br />average (advective) velocity. These mechanisms are referred to as hydrodynamic dispersion and molecular <br />diffusion. Hydrodynamic dispersion (D) represents the mixing of fluids that deviate from the average <br />advective or solute flux (Voss, 1984, p. 38), If flow could be defined at a microscopic scale. an averaging <br />of the velocities would not be necessary and the mechanical component of hydrodynamic dispersion would <br />not be needed. Because fluid travels at rates and in directions that differ from the average advective flux, <br />the incorporation of hydrodynamic dispersion is required to account for uncertainties in the true flow field, <br />Generally. the better defined the heterogeneities within a given flow system, the smaller ~"component,of <br />dispersion necessary to describe the solute front. Molecular diffusion. sometimes referred to as ionic <br />diffusion, is a mixing process caused by a concentration gradient within the fluid (Freeze and Cherry, 1979. <br />p. 103), This process can produce a measurable flux if the fluid velocities are extremely small. In most <br />zones of active ground-water circulation. however, mixing caused by hydrodynamic dispersion is much more <br />rapid than molecular diffusion. Consequently. the effects of molecular diffusion often are ignored when <br />the length of the flow path is hundreds or thousands of meters. <br /> <br />Use of hydrodynamic dispersion in the model requires specific values for longitudinal and transverse <br />dispersivity, which, simply stated, represent mixing lengths parallel to and normal to the mean flow <br />direction. The dispersion tensor, D. for an isotropic medium is related to dispersivity as follows: <br /> <br />rD.. D,.,J (4) <br />D e lD", D" <br /> <br />D.. e v'(dLv;+dTv,'), <br /> <br />D" e v'(drv;+dLv,'). <br /> <br />D e D - v'(d -d \ (v.v). <br />AY yx L Tj I J.' <br /> <br />i *j, <br /> <br />i ~ x, y, dL llll <XLV, <br /> <br />j := X, y, dT "" a,.v, <br /> <br />where v = <br />dL = <br /> V = <br /> x <br />dT = <br /> V = <br /> , <br />aL = <br />ex,. = <br /> <br />average fluid velocity, in meters per second; <br />longitudinal dispersion coefficient, in meters squared per second; <br />magnitude of x-component of v, in meters per second; <br />transverse dispersion coefficient, in meters squared per second; <br />magnitude of y-component of v, in meters per second; <br />longitudinal dispersivity, in meters; and <br />transverse dispersivity, in meters; <br /> <br />For anisotropic media. calculation of the dispersion coefficients becomes more rigorous. Voss (1984. <br />p, 50-54) gives a detailed discussion of the effects of anisotrupy on the dispersion equations, <br /> <br />Dispersivity in a heterogeneous aquifer is scale-dependent. Dispersivity will increase with increases <br />in both solute reSidence time and displacement distance as the dispersion process develops, but it may <br />approach a constant asymptotic value (Sudicky. 1986. p. 2069) that usually is reached when travel distances <br />of hundreds of meters are involved, A constant dispersivity is assumed for the simulations in this study. <br /> <br />-28- <br />