A series of experiments has been performed to investigate the biodegradation of two

pollutants $$ toluene and methane $$ using a biofilter.

Using the information in the Data Section below, answer the following questions.

$($a$)$ Assuming Monod kinetics apply, use the data in Tables B$-1$ and B$-2$ overleaf to

determine the parameters $\backslash$mu max and KM for each pollutant.

$($b$)$ It has been suggested that the pollutants may be affecting cell growth rates at

certain levels. The Haldane model has been proposed as a potential alternative

to the Monod model, and proposed key parameters are presented in Table B$-3$

overleaf.

$($i$)$ For each pollutant, present a graphical comparison of the two models with

the experimental data for varying initial pollutant concentration.

$($ii$)$ What do your results tell you about the suitability of the two models for

describing the biodegradation of toluene?

$($iii$)$ What do your results and the data tell you about the impact of methane as a

substrate for this biofilter?

$($iv$)$ What are the potential weaknesses in this experimental analysis?

Data Section

Monod Kinetic Model:

$\backslash$mu $=$

$\backslash$mu maxS

KM $+$ S

Haldane Kinetic Model:

$\backslash$mu $=$

$\backslash$mu maxS

KH $+$ S $+$ SK$2$i

$\backslash$mu $=$ specific growth rate $[$day$1]$

$\backslash$mu max $=$ maximum specific growth rate $[$day$1]$

S $=$ substrate concentration $[$g m$3]$

KM $=$ Monod constant $[$g m$3]$

KH $=$ Haldane constant $[$g m$3]$

Ki $=$ Haldane inhibition constant $[$g m$3]$ Table B$-1$ Cell mass concentration profile for toluene biodegradation, with varying initial concentrations of toluene

S$0,$ toluene $[$g m$3]1\mathrm{.}02\mathrm{.}54\mathrm{.}05\mathrm{.}08\mathrm{.}0$

Time $[$days$]$ X $[$g m$3]$

$0\mathrm{.}000\mathrm{.}5000\mathrm{.}5000\mathrm{.}5000\mathrm{.}5000\mathrm{.}500$

$0\mathrm{.}010\mathrm{.}5060\mathrm{.}5120\mathrm{.}5150\mathrm{.}5160\mathrm{.}515$

$0\mathrm{.}020\mathrm{.}5120\mathrm{.}5250\mathrm{.}5310\mathrm{.}5320\mathrm{.}531$

$0\mathrm{.}030\mathrm{.}5190\mathrm{.}5380\mathrm{.}5470\mathrm{.}5490\mathrm{.}547$

$0\mathrm{.}040\mathrm{.}5250\mathrm{.}5510\mathrm{.}5630\mathrm{.}5660\mathrm{.}564$

$0\mathrm{.}050\mathrm{.}5310\mathrm{.}5640\mathrm{.}580\mathrm{.}5840\mathrm{.}581$

$0\mathrm{.}060\mathrm{.}5380\mathrm{.}5780\mathrm{.}5980\mathrm{.}6030\mathrm{.}599$

$0\mathrm{.}070\mathrm{.}5440\mathrm{.}5920\mathrm{.}6160\mathrm{.}6220\mathrm{.}617$

$0\mathrm{.}080\mathrm{.}5510\mathrm{.}6070\mathrm{.}6350\mathrm{.}6420\mathrm{.}636$

Table B$-2$ Cell mass concentration profile for methane biodegradation, with varying initial concentrations of methane

S$0,$ methane $[$g m$3]1\mathrm{.}02\mathrm{.}54\mathrm{.}05\mathrm{.}08\mathrm{.}0$

Time $[$days$]$ X $[$g m$3]$

$0\mathrm{.}0020\mathrm{.}00020\mathrm{.}00020\mathrm{.}00020\mathrm{.}00020\mathrm{.}000$

$0\mathrm{.}0120\mathrm{.}01520\mathrm{.}02720\mathrm{.}03520\mathrm{.}04020\mathrm{.}052$

$0\mathrm{.}0220\mathrm{.}03020\mathrm{.}05520\mathrm{.}07120\mathrm{.}08020\mathrm{.}104$

$0\mathrm{.}0320\mathrm{.}04520\mathrm{.}08220\mathrm{.}10720\mathrm{.}12020\mathrm{.}157$

$0\mathrm{.}0420\mathrm{.}06020\mathrm{.}10920\mathrm{.}14220\mathrm{.}16020\mathrm{.}209$

$0\mathrm{.}0520\mathrm{.}07520\mathrm{.}13720\mathrm{.}17820\mathrm{.}20120\mathrm{.}262$

$0\mathrm{.}0620\mathrm{.}09020\mathrm{.}16420\mathrm{.}21420\mathrm{.}24120\mathrm{.}315$

$0\mathrm{.}0720\mathrm{.}10620\mathrm{.}19220\mathrm{.}24920\mathrm{.}28120\mathrm{.}368$

$0\mathrm{.}0820\mathrm{.}12120\mathrm{.}21920\mathrm{.}28520\mathrm{.}32220\mathrm{.}421$

Table B$-3$ Proposed Haldane model parameters for different pollutants; n $=$ the last digit of your Student ID

Parameter Toluene Methane

$\backslash$mu max $[$day$1]17\mathrm{.}15+0\mathrm{.}05$n $0\mathrm{.}19$

KH $[$g m$3]13\mathrm{.}21\mathrm{.}35$

Ki $[$g m$3]2\mathrm{.}518\mathrm{.}33+0\mathrm{.}1$n