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in which the exchange of Fe 2 + between the solid and liquid is rapid and the
overall rate depends only on the approximately first-order oxidation of sorbed
Fe 2 + . Although this rate is independent of pH, the distribution of Fe 2 + between
the solid and liquid is not and it is therefore necessary to allow for pH changes
in calculating the rate.
4.4.2
SIMULTANEOUS DIFFUSION AND OXIDATION IN SOIL
Kirk et al . (1990b) and Kirk and Solivas (1994) used the above understanding
of oxidation kinetics to develop a model of soil oxygenation. The model allows
for the diffusion of O 2 into the soil, the diffusion of Fe 2 + towards the oxidizing
surface, the rate of formation and concentration profile of the Fe(OH) 3 formed,
and the diffusion by acid - base transfer of the acidity formed: H 3 O + diffusing
away from the zone of acidification and HCO 3 (derived from CO 2 ) towards it.
The principal equations are as follows, expressedinplanargeometrysoastobe
able to test the predictions against experimentally measured reactant profiles.
(1) For the diffusion and reaction of O 2 :
D LO θf [O 2 ] L
∂x
[O 2 ]
∂t
∂x
1
=
4 S 1 S 2
( 4 . 40 )
where [O 2 ]and[O 2 ] L are the concentrations of O 2 in the whole soil and
solution, respectively, S 1 is the rate of Fe 2 + oxygenation, S 2 is the rate of O 2
consumption in microbial respiration, and the other parameters are as defined
in Chapter 2.
(2) For the diffusion and reaction of Fe 2 + :
D LI θf [Fe 2 + ] L
∂x
[Fe 2 + ]
∂t
∂x
=
S 1
( 4 . 41 )
where [Fe 2 + ]and[Fe 2 + ] L are the concentrations of mobile Fe 2 + in the whole
soil and solution, respectively.
(3) For the diffusion and reaction of soil acidity (Section 2.2)
2 . 303 θf (D LH [H 3 O + ] L + D LC [HCO 3 ] L ) pH
∂x
[HS]
∂t
∂x
=−
+
2 S 1
( 4 . 42 )
where [HS] is the concentration of titratable soil acid.
Applying Equation (4.39) to the structured-soil system, and ignoring the slow
oxidation of Fe 2 + in solution, gives
S 1 = ρk S [O 2 ] L [Fe 2 + ] S
( 4 . 43 )
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