Page 342 - Elements of Chemical Reaction Engineering Ebook

Sec. 6.:3 Algorithm for Solution to Complex Reactions 31 3

Species B: rB = 1.25 r,A + 0.75 r2A + r3B (E6- 8.14)

Species C: rc = - r,A + 2 rgB + r4c (E6- 8.15)
Species D: rD = - 1.5 - 1.5 rfA - r4c (E6-8.16)

r2A
Species E: rE= ---- 5 (E6-8.17)
6r4c
2
Species F: rF = -2r3B = x,,c,~c, (E6-8.18)

Finally, we write mole balances on each species.

Mole balances:

dF.4 - 2
Species A: -- rA = rIA + ‘2A + 3 r4C (E6-8.19)
dV
dFB -
Species B: -- rB = 1.25 rIA + 0.75 r2A + r3B (E6-8.20)
dV

Species C: dFc -- - rc= -r1A+2r3B+r4C (E6-8.21)
Solutions to these dV
equations are most
easily obtained with
an ODE solver Species D: dLD = rD = --l.5rlA- l.5r2A-r4c (E6-8.22)
dV

‘2A - 5
dFE =
Species E: - rE=-- 2 g4c (E6-8.23)
dV
--
Species F: dFF - rF = -2r3B (E6- 8.24)
dV
Total: FT = FA+FB+Fc+FD+FE+FF (E6-8.25)

Conibining
Rather than combining the concentrations, rate laws, and mole balancles to
write everything in terms of the molar flow rate as we did in the past, it is more con-
venient here to write our computer solution (either POLYMATH or our own pro-
gram) using equations for rIA, FA, and so on. Consequently, we shall write
Equations (E6-8.9) through (E6-8.12) and (E6-8.19) through (E6-8.25) as individual
lines, and let the computer combine them to obtain a solution.
The comesponding POLYMATH program written for this problem is shown in
Table E6-8.1 and a plot of the output is shown in Figure E6-8. I. One notes that
there: is a maximum in the concentration of NO (i.e., C) at approximately 1.5 dmi.