Fixed Bed Models Homogeneous: Axial dispersion (steady) Fronts (unsteady) PFR Radial dispersion Membrane Heterogeneous (PFR): 1 st, nth order two consecutive

Chemical Imaging of Spatial Heterogeneities in Catalytic Solids at Different Length and Time Scales Bert M. Weckhuysen* Angew. Chem. Int. Ed. 2009, 48, 4910 – 4943 Selected examples of spatial heterogeneities occurring at different length scales: a) Selected frames (b) Coke and temperature profiles over an industrial reactor. c) Spatial gradients of the amount of transition-metal ion across an individualAl2O3 catalyst body. d) Spatial gradients of a reaction product across an individual zeolite crystal. e) Spatial gradients of metal, metal oxide, and metal carbide within an individual catalyst grain spanning several nanometers

Homogeneous Models Axial dispersion model (steady state) z z C A0 T0T0 T CACA For industrial gas reactors Pem ~ 2.

Properties: CSTR asymptote for infinite axial dispersivities. PFR asymptote for no dispersion Axial dispersion can be ignored for commercial reactors (L/d p >>1) when grad at feed is largest. Applies to isothermal positive-order kinetics. Can exhibit bistability (like CSTR)-BVP Can exhibit fronts (unsteady state-version)

First order isothermal

Unsteady-state version

Back to regular fixed bed: The Zeldovich-Frank Kamenetski approximation where k r =Aexp(-E/RT m ) is the rate constant at the maximal temperature, u s is the fluid velocity. c>0 implies front motion downstream.Note that increasing throughput (u s ) implies eventually extinction The condition for c=0 yields the critical fluid velocity that will not push the front downstream; that can be translated to

PFR model (steady state) Solution of PFR always unique Hotspot –reaction runaway (first order kinetics) Multiplicity exists in auto-thermal operation for exothermic reversible runs (e.g. N 2 +3H 2  2NH 3, SO 2 +1/2O 2  SO 3 ) Uniqueness criteria have been developed. T z

Temp runaway (analogy with thermal explosion) PFR-nonadiabatic case

Semenov theory of thermal explosion Nikolai Semenov Nobel Prize in Chemistry, 1956 Let’s analyze the behavior as if the depletion is slow

Semenov theory (1928)

Determining Ψ c 1 θ Ψ=ΨcΨ=Ψc 1 θ Ψ>0.37

Reactor Safety JOURNAL OF LOSS PREVENTION IN THE PROCESS INDUSTRIES, (2002) 15(3) p Acrylic reactor runaway and explosion accident analysis On May 18, 2001 a destructive fire and explosion accident occurred in an acrylic resin manufacturing plant located in the northern part of Taiwan. More than 100 people were injured and totally 46 plants including 16 high-tech companies nearby were severely damaged. The resulting blast wave destroyed and shattered many large and small windows of residences within half-a-kilometer. The immediate cause turned out to be a vapor cloud explosion and the blast mass was estimated to be equivalent to 1000 kg of TNT. However, the original cause was found to be a runaway reaction of a 6-ton reactor that contained methyl acrylate, methyl alcohol, acrylonitrile, isopropyl alcohol, acrylic acid, methacrylic acid, and benzoyl peroxide. The investigation and experimental runaway results revealed that during the runaway, the temperature had risen rapidly from 60degreesC to about degreesC and the maximum temperature rising rate could reach 192 K min(-1). Since the final temperature of the process was much higher than the boiling points of all the reactants, vapors generated inside the reactor were released to the atmosphere. Certain hazards analysis and calorimetric tests to ensure that similar runaway accident should not occur again were performed as part of this study.

Radial dispersion models: why would radial grad develop?

Membrane Reactors Figure 3: Changes in total olefin yield (f), cracking (y 3, triangles) and isomerisation (y N, squares) products with inverse flow rate during isobutane dehydrogenation in a Pd-tube packed with catalyst at 500 o C (Sheintuch and Dessau, 1996) Figure 4: SEM micrographs of the carbon membrane fibers.

6/20/2011NCSU Raleigh, NC, US19 Introduction- Pd membrane Fig. 1 Morphology of Pd/a-Al2O3 membrane. (a) top view, and (b) cross section.(Chem. Commun., 2006, 1142–1144)

Consider a packed tube and shell membrane reactor for the simple dehydrogenation reaction B-> C+H2. The steady-state balances over the three species in a PFR, with exchange of material between the tube and shell, F i is the molar flow of specie i (B,C or H), a i is the stoichiometric coefficient (-1,1 and 1), r - the reaction rate, P-the total pressure, y i is the mole fraction of specie i.

Extension I: Solar heating- CoMETHy (Compact Multifuel-Energy to Hydrogen converter ) 6/20/2011NCSU Raleigh, NC, US21

Hetero Model (PFR)-temp rise

Case 3: Two consecutive first order reactions A1->A2->A3, negligible film resistance

Reformer kinetic model