Question

You found that the PFR in your chemical plant has loose screws and has a continuous leak along its axial direction. The volumetric flow rate along the axial direction decreases as a result of the leak and is Differential Slice z= 0 z+Az Leaky PFR Fila Fleak: a function of axial position, Z, as follows: v(z) = vo 1-3) → B is to be carried out isothermally and The first order gas phase reaction A isobarically. a. b. Determine an expression for FA.leak, in terms of dv/dz, CA, Az. Write a mole balance on a differential slice of the reactor. Assume the PFR has a constant cross-sectional area A. Obtain an equation in terms of Az, dv/dz, F CA, A., K, and z. Be sure to include the term for the amount of A lost through the leak in a differential volume element-denoted by FA,leak . Allow Az to approach 0 and obtain a differential equation for conversion X in terms of dv/dz, dX/dz, A, FAO, Ca, K, and z. Your dependent variables should be v and X while the independent variable should be z. on for dx/dz. Use I) to simplify further the equation. Integrate to find X as a function of z. d. e.

Answer 1

Sowtions: Given that Let, Balance on "':- Ile=0/leak + Reacted differential size z +02 - >FA13.02 F Ale (more of a iniet = Molex of left + moier of A leaked y + morer of A reacted. FAIZ = FAIz toz + FM leave iz + (re)dv FAIZ - FA/2+42 = FA, leak /2 + (-VA)dv od FA = Fon Sear]z + (-VA) dv FA, leak/2 - -DFA - (-YA.)dv FA, leak'= -dFA - KCAM DV - 0 NA = Rute of Reaction = CAM a) Pust (W) :: I'm solving after furt (b). Vecak = V(3)-1(3+02) dvlean = Vo (- )- vo (?- 3+12) sto ( 12 ) = vo I FA, leak /2 = Cadrlear for az slice Fardeak)2 = CAVAD 3 - 0 Put it in ean- :.SCA Y A3 = -AFA - Keandv] mole Balance equation dy= Ac dz dr-vow me of differential slice - FA CA VO 82 + x candy - 3

change in flow rate of Leaked 'A' A reacted *) fig - fout :) If. Azt0 Then we will use {-FAL = CA V t K CAM AL} divide qn - By og - DFA da = CA No + KCA? AC 1. dFA = FAdx divide . 30, use the entire e che non + x CAT AL co/4 = Fe(3) US (3) 7(2) hoy * ( 59. (B)) "A Yo (i-/-) ! Fo (3) at the dat ** (Fata) you on c) La Thank you i, ...

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