A coal-fired power plant equipped with a SO2 scrubber is required to achieve an overall SO2 removal efficiency of 85%. The existing scrubber is 95% efficient. Rather than treating the entire gas stream to 95% removal, the plant proposes to treat part of the flue gas to 95% removal, and to bypass the remainder around the scrubber. Calculate the fraction of the flue gas stream that can be bypassed around the scrubber (i. e., Qbypass/Q) and still satisfy the regulatory requirement.

bypassed fraction B will be B = 0.105 (10.5%)

Explanation:

doing a mass balance of SO₂ at the exit

total mass outflow of SO₂ = remaining SO₂ from the scrubber outflow + bypass stream of SO₂

F * (1-er) = Fs * (1-es) + Fb

where

er = required efficiency

es = scrubber efficiency

Fs and Fb = total mass inflow of SO₂ to the scrubber and to the bypass respectively

F = total mass inflow of SO₂

and from a mass balance at the inlet

F = Fs + Fb

therefore the bypassed fraction B=Fb/F is

F * (1-er) = Fs * (1-es) + Fb

1-er = (1-B) * (1-es) + B

1-er = 1-es - (1-es) * B + B

(es-er) = es*B

B = (es-er) / es = 1 - er/es

replacing values

B = 1 - er/es=1-0.85/0.95 = 2/19 = 0.105 (10.5%)