Anoxic conditions formation formulas

The rates of sulfur and nitrogen compounds transformation processes in the model describe by the following equations:

Am = KAm [Norg] FAm (O2) - ammonification;
Nf1 = KNf1 [NH4+] FNf (O2) - first stage of nitrification;
Nf2 = KNf2 [NO2-] FNf (O2) - second stage of nitrification;
Nr1 = KNr1 [NO3-] FNr (O2) - nitrate reduction;
Nr2 = KNr2 [NO2-] FNr (O2) - denitrification;
Th1 = KTh1 [H2S] FTh (O2) - first stage of hydrogen sulfide oxidation;
Th2 = KTh2 [S0] FTh (O2) - second stage of hydrogen sulfide oxidation;
Th3 = KTh3 [S2O32-] FTh (O2) - third stage of hydrogen sulfide oxidation;
Sr1 = m1 KSr1 [Norg] FSr (O2) - first stage of sulfate reduction;
Sr2 = KSr2 [S2O32-] FSr (O2) - second stage of sulfate reduction;
Td = KTd [H2S] FTd (NO3-) - thiodenitrification;
As = p1Th1 + p1Th2 + p1Th3 + p2Nf1 + p2Nf2 + p3Td - ammonium assimilation by autotrophic microorganisms (chemosynthesis in nitrogen unites).
Where, Ki - constants of corresponding reactions, mi - stoicheometric coefficients, Fi (O2), Fi (NO3-) - dependencies of reaction rates from oxygen and nitrate content respectively, pi - the quantity of consumed nitrogen of NH4+ in unite of consumed substrate (S 2-, S0, S2O32-, NH4+, NO2-).
Thus, the general form of the source equations for all blocks of the model is:
RNorg = -Am - m2Nr1 - m3Nr2 - m4Sr1 + As;
RNH4+ = Am + m4Sr1 - Nf1 - As;
RNO2- = Nf1 - Nf2 + Nr1 - Nr2;
RNO3- = Nf2 - Nr1 - m5Td;
RH2S = -Th1 + Sr2 - Td;
RS0 = Th1 - Th2;
RS2O32- = Th2 - Th3 + Sr1 - Sr2;
RSO42- = Th3 - Sr1 + Td;
RO2 = -m6Th1 - m7Th2 - m8Th3 - m9Nf1 - m10Nf2 - m11Am, where mi (i = 2-11) - stoicheometric coefficients of the model.

Table. Constants and coefficients used in the model.

Constant (coefficient), Value in the modelLiterature estimates Source
Constant of ammonification KAm, day-1 0.01 0.01-0.1 Volkov, 1984; Modeling of transport..., 1979
Constant of the first stage of nitrification KNf1, day-1 0.1 0.001- 0.13 Modeling of transport..., 1979
Constant of the second stage of nitrification KNf2, day-1 0.3 0.01-0.63 Modeling of transport..., 1979
Constant of the first stage of nitrate reduction KNr1, day-1 0.16 -
Constant of the second stage of nitrate reduction KNr2, day-1 0.22 -
Constant of the first stage of hydrogen sulfide oxidation KTh1, day-1 0.45 0.01-0.3 Sorokin Yu. et. al., 1991
Constant of the second stageof hydrogen sulfide oxidation KTh2, day-1 0.7 0.01-0.7 Sorokin Yu. et. al., 1992
Constant of the third stage of hydrogen sulfide oxidation KTh3, day-1 0.4 0.01-0.5 Sorokin Yu. et. al., 1991; Sorokin D., 1991
Constant of the first stage of sulfate reduction KSr1, day-1 0.001 10-6 - 10-4 Volkov, 1984
Constant of the second stage of sulfate reduction KSr2, day-1 0.004
Stoicheometric coefficient of sulfate reduction (Redfield model) m1, mgS/molN 0.106 Ivanenkov, 1979
Stoicheometric coefficient of the first stage of nitrate reduction m2 0.08 Anderson et. al., 1982
The same m3 0.11 Anderson et. al., 1982
Stoicheometric coefficient of sulfate reduction Redfield model), m4,molN/mgS 9.43 Ivanenkov, 1979
Stoicheometric coefficient of thiodenitrification m5, molN/mgS 41.5 Volkov, 1984
Stoicheometric coefficient of the first stage of H2S oxidation m6, mlO2/mgS 0.34 Volkov, 1984
The same for the second stage m7, mlO2/mgS 0.34 Kondratieva, 1983
The same for the third stage m8, mlO2/mgS 0.70 Kondratieva, 1983
Stoicheometric coefficient of the first stage of nitrification m9, mlO2/molN 0.03 Kondratieva, 1983
The same for the second stage m10, mlO2/molN 0.01 Kondratieva, 1983
Stoicheometric coefficient of the ammonification (Redfield model) m11, mlO2/molN 0.17 Ivanenkov, 1979
p1, molN/mgS 3.0 -
p2, day-1 0.2 -
p3, molN/mgS 12.5 -
Percentage of the suspended organic nitrogen of the total organic one a, % 10 6-14 Skopintsev, 1975
Vertical speed of particles sinking W, m day-1 50 30-376; Muramoto et. al., 1991; Modeling of transport..., 1979
Coefficient of the vertical turbulence diffusion Az, cm2/sec 0.4 0.05-1.0 Skopintsev, 1975; Lewis, Landing, 1991
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