Problem $1.$ Biomass Utilization:

Biomass from agriculture and forests is a large source of renewable energy and fuel. It can be burned for

heating, electricity generation, or biofuel production. If used in its raw form, it is carbon dioxide neutral

since it is part of the carbon cycle. In this problem we use woody biomass whose chemical formula can be

assumed to be $C_6{H}_{12}{O}_6.$ The original biomass is $85\%$ wood and $15\%$ moisture.

Technology I: Combustion

One way to utilize biomass is to burn it in air in an adiabatic combustion chamber and use the product

stream to generate steam. The generated steam is then used in a steam cycle to produce work. Dry biomass

and air enter the combustion chamber at atmospheric conditions. You may consider $1$ mole of dry biomass

as your basis of calculation.

a$.$ If the combustion is stoichiometric, calculate the temperature of the product stream assuming

complete combustion.

b$.$ The combustion product stream is used to generate steam while its temperature drops to $50C.$ The

maximum temperature of the steam power cycle is $550C,$ while the ambient temperature is $25C.$

Calculate the maximum possible efficiency for the combustion system and the maximum efficiency

of the power cycle $($both based on the logarithmic mean temperature$).$

c$.$ If the second law efficiency of the power cycle is $60\%,$ calculate the work produced by the plant per

mole of biomass.

d$.$ What is the actual overall efficiency of this configuration in reference to the utilized fuel $($first law

efficiency$)?$

$2,360K$;$68\mathrm{.}47$&:$42\mathrm{.}3\%6$;$633k\frac{l}{m}ol$;$15\mathrm{.}9\%]$

Technology II: Gasification

In this process, one mole of dry biomass and $6\mathrm{.}5$ moles of $H_{2}O$ enter a steam reformer at atmospheric

conditions to produce a mixture of $CO,C{O}_2,H_2,$ and $H_{2}O$ at $500C.$ Next, the mixture goes through a water$-$

gas shift $($WGS$)$ reactor to convert $CO$ to $C{O}_2.$ In the WGS reactor, one mole of $H_{2}O($at $25C)$ is added for

every mole of $CO$ originally in the mixture. The mixture leaves the WGS reactor at $100C.$ The resulting

mixture is used in the fuel cell to generate work. A schematic is shown in the following figure:

e$.$ Calculate the hydrogen mole fraction in the gas leaving the steam reformer. Due to the relatively

high temperature inside the reformer, it can be assumed that the biomass reforming reaction

proceeds to completion and the WGS reaction $($occurring inside the reformer$)$ reaches equilibrium.

Obtain the WGS pressure equilibrium constant $($Kp$)$ from Smith, Van Ness, Abbot Textbook or from

any published WGS $Kp(T)$ correlation.

f$.$ What is the heat transfer required in the steam reformer?

Due to the relatively low temperature inside the WGS reactor, the WGS reaction can be assumed

irreversible and proceed to completion. Calculate the hydrogen mole fraction in the gas leaving

the WGS reactor.

h$.$ Evaluate the overall process efficiency, including the reforming and WGS process, if no waste heat

is recuperated.

Additional information:

LHV of woody biomass is $21\frac{M}{k}g.$

Thermodynamic properties: