BIOLOGICAL Cr(VI) REMOVAL COUPLED WITH BIOMASS GROWTH, BIOMASS DECAY, AND MULTIPLE SUBSTRATE LIMITATION

Supplementary data

The following set of reactions were used to represent the proposed model in GEPASI 3

Reaction / Kinetic expression / Process
1 / XNG ® XGA / kA XNG / Activation (start up)
2 / XNG ® / b XNG / Endogenous decay
3 / Cr + S + NH + XGA ® Cr + S + NH + 2XGA / RX / Growth of XGA
4 / XGA ® / b XGA / Endogenous decay
5 / Cr + S + NH + XGA ® Cr + S + NH + XGNA / RCrG/RC / Inactivation by Cr(VI)
6 / Cr + S + NH + XGNA ®
Cr + S + NH + XGNA + XGA / RX / Growth of XGNA
7 / XGNA ® / b XGNA / Endogenous decay
8 / Cr + S + NH + XGA ® Cr + NH + XGA / RS / Consumption of S
9 / Cr + S + NH + XGNA ® Cr + NH + XGNA / RS / Consumption of S
10 / Cr + S + NH + XGA ® Cr + S + XGA / iN,BM RX / Consumption of NH
11 / Cr + S + NH + XGNA ® Cr + S + XGNA / iN,BM RX / Consumption of NH
12 / XNG ® NH + XNG / (iN,BM - iN,P) b XNG / Production of NH by decay
13 / XGA ® NH + XGA / (iN,BM - iN,P) b XGA / Production of NH by decay
14 / XGNA ® NH + XGNA / (iN,BM - iN,P) b XGNA / Production of NH by decay
15 / XNG ® P + XNG / fP b XNG / Production of P by decay
16 / XGA ® P + XGA / fP b XGA / Production of P by decay
17 / XGNA ® P + XGNA / fP b XGNA / Production of P by decay
18 / Cr + S + NH + XGA ® S + NH + XGA / RCrG / Consumption of Cr by growth
19 / Cr + XNG ® XNG / RCrD / Consumption of Cr by decay
20 / Cr + XGA ® XGA / RCrD / Consumption of Cr by decay

In terms of GEPASI, reaction kinetics of 1, 2, 4, 7, and 12 to 17 were defined as Mass Action (irreversible) Kinetic using the button Kinetics that appears in the main screen of the program (Model Definition). Rates (r) of those reactions are expressed as follows:

where k is the rate constant and Zi is the concentration of compound i. For example, reaction 13 defines the release of NH during the decay of XGA. It must be pointed out that XGA concentration not depends on reaction 13 because XGA appears on both sides this reaction. The net effect of reaction 13 is to increase the NH concentration at a rate (r) that is proportional to XGA; in this example, the rate constant (k) represents the following group of constants of the proposed model:

k = (iN,BM - iN,P) b

For the reactions 3, 5, 6, 8 to 11, and 18 to 20, the following kinetic expressions were defined using the button Kinetic Types in the main screen of the program:

(SD1)

(SD2)

(SD3)

(SD4)

where X denotes XGA or XGNA, depending on the represented reaction. Note that if the kinetic expression has more than one substrate, the order in which the substrates are written in the reaction defines their association with the symbols in the kinetic function; for this reason, substrates of reactions 3, 5, 6, 8 to 11, 18 to 20, and in eqs.(SD1), (SD2), (SD3), and (SD4) were written following the same order: Cr, S, NH, X.

The following functions were defined using the button Functions:

CODS = S + P (SD5)

TSS = iSS (XNG + XGA + XGNA) (SD6)

(SD7)

where J(Ri) corresponds to the flux of the reaction Ri. Because S, P, and biomass concentrations are expressed in oxygen units, equation (SD7) is the result of the conservation of the Theoretical Oxygen Demand. Equations (SD5), (SD6), and (SD7) allow calculating the observable variables CODS, TSS, OUR based on the model outputs S, P, XNG, XGA, XGNA, and model coefficients.

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