11-Lect-Pressure Drop in Reactors0

0165 lb1 w 1 ac c p0 w 1 ac zc 0 g 1 1501

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Unformatted text preview: in terms of y = P/P0: dy € α TFT α €T =− = − (1 + εX ) dW 2 y T0 FT 0 2y T0 Pressure Drop in Reactors where FT = 1 + εX FT 0 and α ≡ 2β 0 1 − φ ) Ac ρ c P0 ( Lecture 11 - Page 6 Chemical Reaction Engineering - Musgrave € € € 3 For isothermal conditions: dy α = − (1 + εX ) dW 2y If εX is negligible or zero (equalmolar rxn): FA0 FA dW = (1 − φ ) Ac dz € dy α =− dW 2y P € Which is solved by: € where: P 1/ 2 y= = (1 − αW ) P0 α≡ 2β 0 € α = 0.0165 lb−1 W € (1 − φ ) Ac ρc P0 W = (1 − φ ) Ac zρc β0 ≡ Ⱥ G ȹ 1 − φ ȹȺ150(1 − φ )µ + 1.75GȺ ȹ 3 ȹȺ ρ 0 gc Dp ȹ φ ȺȺ Dp Ⱥ Lecture 11 - Page 7 Or in terms of z: € 1/ 2 P ȹ 2β 0 z ȹ where: y= = ȹ 1 − ȹ P0 ȹ P0 Ⱥ Pressure Drop in Reactors Chemical Reaction Engineering - Musgrave € € € FA0 FA FA0 FA dW = (1 − φ ) Ac dz For a PFR, rather than a PBR: € P Ⱥ 4 fG 2V Ⱥ 1/ 2 = Ⱥ1 − Ⱥ = [1 − α cV ] P0 Ⱥ Ac ρ 0 P0 DȺ 1/ 2 D = pipe diameter f = Fanning friction factor If we have large volumetric flow rate and small pipe diameters, the pressure drop can be significant. € Pressure Drop in Reactors Chemical Reaction Engineering - Musgrave Lecture 11 - Page 8 4 1. Mole Balance PBR CSTR Batch 1. Mole Balance dW = 2. Rate Law 2. Rate Law -rA=f(CA) -rA=g(CA) -rA=h(CA) FA 0 dX −rA + −rA + = kCA CA = FA υ υ = υ 0 (1 + εX ) P0T PT0 3. Stoichiometry Flow Batch 3. Stoichiometry € Flow Gas € Gas Liquid Gas Liquid 4. Combine dV=dV(X) dt=dt(X) € CA = CA 0 (1 − X ) P (1 + εX ) P0 € CA = CA 0 (1 − X ) P P0 5. Evaluate V=V(X) t=t(X) 4. Combine € dW = FA 0 dX −€+ r A dW = FA 0 dX kCA • 1st order • Equimolar • Irreversible • Gas phase • PBR Pressure Drop in Reactors dW = € 5. Evaluate FA 0 dX Ⱥ € P Ⱥ kȺCA 0 (1 − X ) Ⱥ P0 Ⱥ Ⱥ Chemical Reaction Engineering - Musgrave € Lecture 11 - Page 9 5. Evaluate dW = FA 0 dX Ⱥ P Ⱥ kȺCA 0 (1 − X ) Ⱥ P0 Ⱥ Ⱥ εX Negligible y= α≡ P 1/ 2 = [1 − αW ] P0 2β 0 Because ε is zero we can use: € y= P 1/ 2 = [1 − αW ] P0 dW = α≡ 2β 0 (1 − φ ) Ac ρc P0 (1 − φ ) Ac ρc P0 € € € Which gives: β0 ≡ Ⱥ G ȹ 1 − φ ȹȺ150(1 − φ )µ + 1.75GȺ ȹ...
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