P$8-16$ Solar energy capture has great potential to help meet the world's growing energy demand, which is $12$

terawatts in $2010$ and is expected to rise to $36$ terawatts in $2050($cf$.$ P$3-15$ B$).$ Professor Al Weiner and his

students at the University of Colorado are engaged in developing methods of utilizing solar$-$thermal

energy. In solar$-$thermal reactors, mirrors are used to focus and concentrate the sun's energy on a

flow$-$type cavity reactor where temperatures as high as $1200C$ can be realized, as shown below.

The switch grass is fed to the $1200C$ solar$-$thermal reactor. At these temperatures, biomass can be con$-$

verted to $CO$ and $H_2,$ i$.$e$.,$ syn gas, which then can be used for liquid fuels. Switch grass, which is approx$-$

imately $\frac{2}{3}$ cellulose $(C_6{H}_{10}{O}_5)$ and $\frac{1}{3}$ lignin $(C_{10}{H}_{12}{O}_3)$ will be fed with steam to produce $CO,H_2$ and a

small amount of ash, which we will neglect. In order to simplify this process into a tractable home prob$-$

lem, we assume the switch grass is volatilized immediately upon entering the plug$-$flow reactor and that

the reactions and postulated rate laws are

$(1)$ Cellulose: $C_6{H}_{10}{O}_5(C)+H_{2}O(W)6H_2+6CO$

$(2)$ Lignin: $,C_{10}{H}_{12}{O}_3(L)+7H_{2}O(W)13H_2+10CO$

$[$AIChEJ$.55,$ p$.286(2009)].$ Also see Science p$.326,1472(2009).$

The rate laws and constants are hypothesized to be

$-r_{1C}=k_{1C}{C}_C{C}_W$

$-r_{2L}=k_{2L}{C}_L{C}_W^2$

with $k_{1C}=3{10}^4\frac{\frac{d{m}^3}{(mol)}}{s}$ and $k_{2L}=1\mathrm{.}4{10}^7\frac{\frac{d{m}^3}{(mol)}}{s}$

Total gas concentration in the feed and reactor with $C_{T0}=\frac{P_0}{R{T}_0}=\frac{1(atm)}{(0\mathrm{.}082)(1473)}=0\mathrm{.}00828mo\frac{l}{d}{m}^3$ with

the entering molar flow rates of cellulose, lignin, and water are $F_{C0}=0\mathrm{.}00411mo\frac{l}{s}$ and $F_{L0}=0\mathrm{.}00185$

$mo\frac{l}{s},F_{W0}=0\mathrm{.}02mo\frac{l}{s},$ respectively.

$($a$)$ Plot and analyze the molar flow rates as a function of PFR volume up to $V=0\mathrm{.}417d{m}^3.$

$($b$)$ Plot and analyze $Y_C,Y_W,Y_L,$ and tilde$(S{)}_{C\frac{O}{H_2}}$ down the reactor. Describe what you find.

$($c$)$ Repeat $($a$)$ for different molar flow rates of water.