Question 10.10: Canister carbon systems are typically used for emission stre...

The HAP density, D_{HAP}, is calculated first using

D_{HAP} = PM/RT                                                                              (9)
D_{HAP} = (1 atm) (58 lb/lb-mole)/(0.7302 ft³ atm/lb-moleºR)(460+90)(ºR)
D_{HAP} = 0.144 lb/ ft³

Using Eq. (4), the inlet HAP loading, M_{HAP}, is determined:

M_{HAP} = 6.0 \times 10^{−5} (HAP_{e})(Q_{e})(D_{HAP})                                   (4)
M_{HAP} = 6.0 \times 10^{−5} (700 ppmv of acetone)(2,000 ft³/min) (0.144 lb/ft³)
M_{HAP} = 12.10 lb acetone/h

The carbon requirement, C_{req}, is determined using

C_{req} = M_{HAP}  θ_{ad} /W_{c}                                                                        (11)

The working capacity value, W_{c}, is usually 50\% of the equilibrium capacity (W_{e}). Using Eq. (1) and values from Table 1, the W_{e} is calculated as follows:

W_{e} = k  (P_{partial})^{m}                                                                               (1)

where

P_{partial} = (HAP_{e}) (14.696 \times 10^{−6})                                                           (2)
P_{partial} = (HAP_{e}) (14.696 \times 10^{−6}) = (700 ppmv) (14.696 \times 10^{−6}) = 0.01029 psia

Note: _{}^{a}\textrm{Each} isotherm is of the form: W_{e} = kP^{m}. (See text for definition of terms).
Data are for adsorption on Calgon-type “BPL” carbon (4 \times 10 mesh).
_{}^{b}\textrm{Equations }should not be extrapolated outside of these ranges

Then, from Eq. (1), the equilibrium capacity is obtained.

W_{e} = k  (P_{partial})^{m}                                                                               (1)

From Table 1, k = 0.412 and m = 0.389.

Substituting these values into Eq.(1) yields the equilibrium capacity:

W_{e} = (0.412) (0.01029  psia)^{0.389}
W_{e} = 0.06945 lb acetone/lb carbon

Because the working capacity, W_{c}, is usually 50\% of equilibrium capacity (W_{e}),

W_{c} = 0.50  W_{e} = 0.50 (0.069 lb acetone/lb carbon) = 0.0345 lb acetone/lb carbon

The carbon requirement is calculated using

C_{req} = M_{HAP}  θ_{ad} /W_{c}                                                                        (11)
C_{req} = (12.10 lb of acetone/h)(40 h)/(0.0345 lb acetone/lb carbon)
C_{req} = 14,029 lb of carbon

Typically, each canister contains 150 lb of carbon; therefore, the required canister number (RCN) is calculated as follows:

RCN = (14,029 lb carbon)/(150 lb carbon/canister)
RCN = 93.5 canisters, therefore use 94 canisters