Exponential growth in a batch process. You're running a CHO process in a batch reactor. Biomass

$(x)$ is formed from substrate $($S$).$ Using the data tabulated below, determine the specific growth rate

$()$ using the exponential growth model. Reminder: Be sure to account for the lag phase.

Mass balances and rates in a batch fermenter. You are running a $5L$ batch fermentation process

that produces biomass $(x)$ and consumes substrate $($S$).$ You have the following plots: $(1)ln(x\frac{t}{x_0})$

vs time and $(2)(S(t)-S_o)$ vs $(x(t)-x_o)$ :

a$.$ Calculate the specific growth rate $()$ and the doubling time $({}_d).$

b$.$ Calculate the specific substrate consumption rate $(q_s).$

c$.$ Given: $M{W}_s=26\frac{g}{C}-$mol and $M{W}_x=24\frac{g}{C}-$mol. How many grams of $S$ is consumed per

grams of $x$ produced?

d$.$ Now you're going to scale up the process from $5$L to $1000L.$ Assume you run the $5L$ and $1000L$

processes at the same conditions $($initial concentrations, temperature, $pH,$ etc.$).$ Compare the

values of the variables$/$parameters listed below between the $5L$ process and the $1000L$

process. Which will be higher in the $1000L,$ and which will be the same at both scales?

${}_d$

$q_5$

Substrate concentration at $t=2d$

Mass of substrate at $t=2d$

e$.$ Assume that your $3$ day, $5L$ batch process produces $5g$ of Product $P.$ If the yearly demand for

$P$ is $100kg,$ can your $1000L$ process meet the demand? Assume that it takes $6$ hours to clean

and sterilize the fermenter between batches.