Digester $1($CSTR $1)$ Balance

Biomass Balance

$(1+)Q{x}_0+r_{x1}V=(1+)Q{x}_1$ Equation $1$

Substrate Balance

$(1+)Q{S}_0-rs1V=(1+)Q{S}_1$ Equation $2$

Digester $2($CSTR $2)$ Balance

Biomass Balance

$(1+)Q{x}_1+r_{x2}V=(1+)Q{x}_2$ Equation $3$

Substrate Balance

$(1+)Q{S}_1-rs2V=(1+)Q{S}_2$ Equation $4$

Digester $3($CSTR $3)$ Balance

Biomass Balance

$(1+)Q{x}_2+r_{x3}V=(1+)Q{x}_3$ Equation $5$

Substrate Balance

$(1+)Q{S}_2-rs3V=(1+)Q{S}_3$ Equation $6$

The six equation and six unknown $(x_1,x_2,x_3,S_1,S_2,V)$ is to be solved using the solver in excel as well as hand calculation.

Kinetic Equations is used for the above eqns.

$\backslash$mu $=\backslash$mu max S $/$ Ks $+$ S

rx $=\backslash$mu max $($S $/$ Ks $+$ S$)*$X $-$ KdX

rs $=\backslash$mu X$/$Y

The knowns are as follows

Q $($L$/$hr$)-25,000$

kd $(1/$hr$)-0\mathrm{.}0025$

Ks $($mgO$2/$L$)-100$

$\backslash$mu max $(1/$hr$)-0\mathrm{.}18$

Y $($mgVSS mg$/$O$2)-0\mathrm{.}6$

alpha$-0$

X$0($mgVSS$/$L$)-0$

S$0($mgO$2$ L$-1)-400$

S$3($mgO$2$ L$-1)-5$

Unknown which have to be find are;$-$

X$1,$X$2,$X$3,$S$1,$S$2,$VOLUME$($V$)$

Please attach a excel sheet in which solver is used and also the hand calculation solution of the same and mostly in both the ways answer should be nearly equal.

thanks.