Question

2. Flow Past a Sphere Consider a bulk flow of product gas B that contains a small amount, 1.5 mol%, of unreacted reactant A. To convert the remaining reactant A into product B, a fluidized bed reactor is used that contains spherical catalyst particles of 1 mm in diameter. The particles are fluidized to such an extent that each particle can be considered as a single sphere acting independently of each other in the mass transfer and reaction process. The overall process involves the mass transfer of A to the particle surface where a reaction occurs at the external surface that is described by a reaction flux Na = kscAs, where k, is the reaction rate constant and CAs is the concentration of A at the catalyst surface. The gas mixture flows at a velocity of 10 m/s and at a temperature and pressure of 500 K and 1 atm, respectively. At these conditions, the mass diffusivity of A in B is 2.50 x 10-5 mʻls and the kinematic viscosity of B is 3 x 10-5 mº/s, and the surface reaction rate constant is 0.2 m/s. 1 (a) Using an appropriate convective mass transfer correlation, determine the convective mass transfer coefficient and the molar rate of consumption of A (in mol/s) at steady state with each catalyst particle.

Answer 1

Solution - to Given dp YA date definedus 1x 103 m diameter of sphorical particle mok fraction of A in plagas minture = 0.015 sook temperature of bulk gus minture u minterre Tatry pressure og bulk gay minture lom/ = velocity of Diffusivity y 4 in B 25x10 sm kinmates viscosity of B 3x10 mins 0.2 m the surface reaction rate constant Pt coles the gas DAB Rs 220m La CAS bulk gey yow ap le CAPP ah Z1oox402.10 < 800 2 <Rep 0.6 < sc <2.7 using correlation for mass transfer for flow ovcar a sphire 0.552 Resso - 10 (73) x 10-309) sh - 2 + 0.552 335 33 hep 3 x10-5 mins partick reynolds number Sc 3x10 mg DAB WA NI 2.5X10 S (m/s) Schmidt 2 - 1-2 number C-

Bulbs tiduting the value in egoth get most Sh = 2 + 0.552 (333-337°*(1.233 sh • 12.7 6 plom letisim 2 zog Alod Ritim oxing de 12,7 AB DAB ovlstorlove 12.7 x DAB slov - 105 mnts) Foly zis = 2018 E 12.7 x 2.5x105 10-3 رف 0.311 m/s ke de vesti ket is mus consectice mass trams for coefficient rate og mass transfer from bulk gas the surface can be given as M4 - - (2) to Colt weblod CARO - CAS) A in bulk Where CARO concentre rationg molt CARO Pt YA RJ 101.325 (theyx 0-015 8,314 (Kft. a) x 50 x 50004 of knol CARO 0.365 mol m3 the surface of rate of chemical reaction at the catalyst (21) ol glos MA Rg CAS - 137 9 3-oje stre 2 At steady Steady (IMA = NAID Re CCAMO - CAS) ks CAS

from here we get CAS m3 RC CAO Rstke 0.317 ats 0.365 mo 0.2 MB) + 0.317 ) CAS 0.223 mol m3 Substituting this value of CAs in eguth (3) get HA' (molts Rs CAS 0.2 (m5) x 0.223 mol m3 MA 0.0447 mol mas can be 4 consumption ở g molar rate The gire) as, S = MAXS Surface are a ef Contalyst a dp² 3.14 x(103)? 0.0447 mol *3.1 x8.14 x (103) me 0 14 x 10-6 mol .