User's guide of Proceessing Modflow 5.0

Processing Modflow 113
MOC3D < Dispersion & Chemical Reaction...
The types of reactions incorporated into MOC3D are restricted to those that can be represented
by a first-order rate reaction, such as radioactive decay, or by a retardation factor, such as
instantaneous, reversible, sorption-desorption reactions governed by a linear isotherm and
constant distribution coefficient (K ).
d
Use the Dispersion / Chemical Reaction (MOC3D) dialog box (Fig. 3.36) to specify the
required data for each model layer as described below.
< Simulate Dispersion: Check this option, if dispersion should be included in the simulation.
-1
< First order decay rate 8 [T ] typically represents represents radioactive decay of both the
free and sorbed solute. A radioactive decay rate is usually expressed as a half-life (t ). The
1/2
half-life is the time required for the concentration to decrease to one-half of the original
value. 8 is calculted by:
8 ' ln2
t 1/2
F ' &D @ dC
dx
D ( ' T @ D
(3.32)
2 -1
< Effective molecular diffusion coefficient [L T ] describes the diffusive flux of a solute in
water from an area of greater concentration toward an area where it is less concentrated. The
mass flux is proportional to the concentration gradient and is given by Fick’s first law:
(3.33)
-2 -1 2 -1
where F [ML T ] is the mass flux of solute per unit area per unit time; D [L T ] is the
-3 -3 -1
diffusion coefficient; C [ML ] is the solute concentration and dC/dx [ML L ] is the
concentration gradient. In porous media, the solute mass cannot move as fast as the water,
because the ions must flow through a longer pathways through the pore space and because
of adsorption on the soil matrix. To account for this effects, an effective diffusion coefficient
*
D must be used.
(3.34)
According to Freeze and Cherry (1979), T ranges from 0.5 to 0.01 for laboratory studies of
diffusion of nonadsorbed ions in porous geologic materials. The diffusion coefficients D of
+ + 2+ 2+ - - 2-
the major ions (Na , K , Mg , Ca , Cl , HCO 3 , SO 4 ) are temperature-dependent and range
-9 -9 2
from 1× 10 to 2× 10 m /s at 25 °C (Robinson and Stokes, 1965). At 5°C the coefficients
are about 50% smaller. The molecular diffusion coefficient is generally very small and
3.6.2 MOC3D