What amount of sugar beet is required for plant of this size? Is

that feasible in Denmark?

What is the scale of the plant fermenter to reach the given

production in the campaign period?

What if yeast cannot be recycled $-$ how much sucrose and sugar

beets is then needed? Assume that production of yeast biomass

has a yield of $0\mathrm{.}5$ tons cells$/$tons hexose

Informations for this problem:

Photosynthesis $-$ formation of hexoses:

$6C{O}_2+6H_{2}O{C}_6{H}_{12}{O}_6+6O_2$

Sucrose is formed from glucose and fructose:

$2C_6{H}_{12}{O}_6{C}_{12}{H}_{22}{O}_{11}+H_{2}O$

Water $75\%$

Sugar $16-18\%$

Raw fibers $5-6\%$

Other $2-3\%$

Weights approx. $650g$

$10$ beets $=1kg$ sugar

In $2012,$ the production was $2,771,220$ tons of sugar beet from roughly $39,800$ ha$.$

The sugar beets are processed at two sugar factories in Denmark $($roughly equal size$).$ The campaign in $2012/13$ ran from September $12$ to January $26(134$ days$).$

The sugar $($sucrose$)$ content was on average $18\mathrm{.}1\%,$ which in

historical perspective was in the high end.

Plant size:

A realistic production size for the campaign is at $100,000m^3$ ethanol per year $($ethanol density: $789\frac{g}{l})$

Assume ethanol yield from hexose was $92\%$ of maximum

A final ethanol concentration $10\%(\frac{v}{v})$ is reached in $10$ hours using a cell density of $12\%(\frac{w}{w})$

Fermentation is operated in batch

Reactor tank filling max $80\%,$ and filling$/$empty takes $2\mathrm{.}5$ hours each $($pump rate max $500\frac{m^3}{h})$ with a down time of $2$ hours

Yeast is recycled