Chapter 6, Problem 6.1P

To determine

The sludge and refuse needed to meet the required $\text{C}/\text{N}$ ratio.

Answer to Problem 6.1P

The sludge requirement is $50\%$ .

The refuse requirement is $50\%$ .

Explanation of Solution

Given:

Required $\text{C}/\text{N}$ ratio is $20:1$ .

  $\text{C}/\text{N}$ ratio refuse is $24:1$ .

  $\text{C}/\text{N}$ ratio sludge is $16:1$ .

Calculation:

Assume the refuse fraction be $X_r$ .

Write the equation to calculate the sludge fraction.

  $S_F=\left(1-X_r\right)$ ..... (I)

Here, the sludge fraction is $S_F$ .

Write the equation to complete the mass balance on carbon.

  $\begin{array}{l}20=24X_r+16\left(1-X_r\right)\\ 5=6X_r+4-4X_r\\ 2X_r=1\\ X_r=0.5\end{array}$

Calculate the value of $X_r$ in percentage.

  $\begin{array}{c}{X}_r=\left(0.5\times 100\right)\%\\ =50\%\end{array}$

Calculate the sludge fraction.

Substitute $0.5$ for $X_r$ in Equation (I).

  $\begin{array}{c}{S}_F=1-0.5\\ =\left(0.5\times 100\right)\%\\ =50\%\end{array}$

Conclusion:

Thus, the mass balance on carbon is calculated first to find out the answer.