User's guide of Proceessing Modflow 5.0

126 Processing Modflow
3 -1
where n j,i,k [-] is the porosity of the porous medium in the cell [j, i, k]; K d [L M ] is the
distribution coefficient that depends on the solute species, nature of the porous medium, and
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other conditions of the system; and D b [ML ] is the bulk density of the porous medium. The
bulk density is the ratio of the mass of dried soil to total volume of the soil.
¯C j,i,k ' K f @ C a
j,i,k
R j,i,k ' 1 % D b
n j,i,k
¯C j,i,k ' K L @ ¯S @ C j,i,k
1 % K L @ C j,i,k
R j,i,k ' 1 % D b
n j,i,k
@ a @ C a&1
j,i,k @ K f
@
K L @ ¯S
(1 % K L @ C j,i,k ) 2
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where K [L M ] is the Langmuir constant and ¯S
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[MM ] is the maximum amount of the
)CRCT i,j,k ' & )t
@ 81@C i,j,k % 82@ Ri,j,k Db @ ¯C i,j,k
ni,j,k -1 -1
where 8 1 [T ] is the first-order rate constant for the dissolved phase; 8 2 [T ] is the first-order
rate constant for the sorbed phase; )t is the transport time-step; and ¯C j,i,k is the mass of the
solute species adsorbed on the solids per unit bulk dry mass of the porous medium at the
3.6.3 MT3D
The Freundlich isotherm is a non-linear isotherm, which can be expressed in eq. 3.43.
The retardation factor at the beginning of each transport step is calculated by eq. 3.44.
(3.43)
(3.44)
where C j,i,k is the solute concentration in the cell in the cell [j, i, k] at the beginning of each
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transport step; a [-] is the Freundlich exponent; and K f [L M ] is the Freundlich constant.
The Langmuir non-linear sorption isotherm is described by eq. 3.45. The retardation
factor at the beginning of each transport step is calculated by 3.46.
L
solute that can be adsorbed by the soil matrix.
(3.45)
(3.46)
For more information on the mathematical description of adsorption and transport of
reactive solutes in soil, the user can refer to Travis (1978) or Bear and Verruijt (1987).
< Simulate the radioactive decay or biodegradation: Check this box to simulate the effect
of the first-order irreversible rate reactions. The concentration change due to the chemical
reaction from one transport step to another transport step at cell [j, i, k] can be expressed as
(3.47)