Come calcolare il modulo di Thiele (phi) rapporto adimensionale fondamentale ingegneria reazioni chimiche eterogenee che misura il rapporto tra velocità di reazione intrinseca e velocità di diffusione interna in pellet catalizzatori porosi: phi = L * sqrt(k/De). L lunghezza caratteristica m (raggio sfera R, V/S_a volume su superficie esterna 1/3*R sphere; semispessore lastra; raggio cilindro/2); k costante velocità reazione primo ordine 1/s (s^-1); De diffusività effettiva nel pellet poroso m^2/s (gas 1e-7 - 1e-5; liquidi 1e-9 - 1e-7) accounting porosità epsilon + tortuosita tau con De = D*epsilon/tau con epsilon 0.3-0.6 + tau 1.5-5.

Effectiveness factor: eta = rate observed / rate intrinsic isothermal isothermal pellet + sphere first-order analytical eta_sphere = (3/phi^2)*(phi*coth(phi) - 1) + slab semi-infinite eta_slab = tanh(phi)/phi + cylinder Bessel function.

Classificazione regime: phi<0.4 reaction limited kinetic regime + effectiveness eta~1 + small pellet catalyst + automotive monolith Pt-Pd-Rh + chemistry-controlled; 0.4<phi<4 mixed regime internal diffusion + reaction balanced + middle range industrial reactor; phi>4 strong diffusion limited effectiveness eta~1/phi + shell reaction core unused + Knudsen diffusion small pore + zeolite ZSM-5 + intra-particle gradient; phi>20 severe diffusion limit + only outer shell active.

Numeri correlati: Damkohler Da_I = k*L^2/De = phi^2 diffusione interna; Damkohler Da_II esterna; Biot Bi_M = k_m*L/De mass transfer external; Wagner-Wheeler-Weisz modulus W alternative form; Aris generalized modulus + complex kinetics extension.

Aris generalized Thiele: phi_g = (V_p/S_p) * sqrt[(n+1)/2 * k * C_s^(n-1) / De] + n order reaction + V_p/S_p volume/surface ratio + Aris 1965 + valid arbitrary geometry.

Wheeler-Weisz: 1953 + 1957 + Weisz-Prater criterion phi^2*eta < 0.15 + diffusion negligible + classical reactor design heterogeneous.

Mass transfer external Biot Bi_M: Bi_M = k_m*L/De external film vs internal diffusion + Bi_M>>1 internal limited + Bi_M<<1 external limited + Bi_M~1 mixed.

Pellet geometry: sphere R phi=R*sqrt(k/De) + V/S=R/3 + most common; slab L semispessore phi=L*sqrt(k/De); cylinder radius R + Bessel functions; monolith honeycomb automotive catalyst Pt-Pd-Rh + 400-900 cells/in^2 + thin washcoat 20-50 micron + phi small + automotive catalyst converter; structured packing + Sulzer Mellapak + Koch-Glitsch + Raschig rings + ceramic saddles.

Tipologie catalizzatori industriali: FCC zeolite catalyst Y-zeolite USY HY ZSM-5 + crystalline aluminosilicate + cracking + 50-150 micron particle + raffinerie + Versalis + LCC; hydrogenation Ni Pt Pd Rh + Ni-Raney + alumina + supported metal + olefin + aromatic; ammonia synthesis Haber-Bosch Fe + K2O + Al2O3 + 1909 + Haber + Bosch + Mittasch BASF + 5-10 mm pellet; methanol synthesis Cu/ZnO/Al2O3 50-300 bar + 230-280°C + ICI Lurgi; Fischer-Tropsch Co + Fe + Ru + Pd + GTL gas-to-liquid + Sasol + Shell Pearl GTL + ENI Refinery; automotive three-way catalyst TWC Pt-Pd-Rh + monolith honeycomb cordierite + emission control NOx CO HC + Magneti Marelli Eberspacher Faurecia. Storia: Ernest William Thiele (USA 1895-1993) Standard Oil of Indiana later Amoco Chicago Whiting IN refinery + 1939-1969 chemical engineering; 1939 paper Ind Eng Chem 31:916 'Relation between catalytic activity and size of particle' classic Thiele modulus eponym + first quantitative diffusion-reaction analysis pellet catalyst + sphere first-order + classical reactor design + 1939 paper Industrial & Engineering Chemistry classic: pellet diffusion controlled regime quantitative + effectiveness factor; 1957 textbook 'Notes on Distillation' classic distillation textbook.

Rutherford Aris (London UK 1929 - Minneapolis USA 2005) Cambridge BSc 1948 + Aris Imperial College London PhD 1956 Robert Houghton + Imperial College assistant lecturer 1956-1958 + Edinburgh Edinburgh University 1958-1965 + University Minnesota Minneapolis Mech ChemE 1965-2005 + Regents Professor Minnesota; 1957 paper Chem Eng Sci 6:262 'On shape factors for irregular particles I' + 1965 textbook 'Introduction to the Analysis of Chemical Reactors' Prentice-Hall classic chemical reactors + Aris generalized Thiele modulus + 1965 paper Chem Eng Sci 20:907 + 1969 'Elementary Chemical Reactor Analysis' classic textbook + 'The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts' 2 vols Oxford Clarendon Press 1975 classic; pioneer chemical engineering + reactor design + dynamical systems chaotic + Aris-Cohen + scientific writing; Bird Award 1985.

P B Weisz + C D Prater Mobil Research Princeton NJ 1954; 1954 paper Adv Catal 6:143 'Interpretation of measurements in experimental catalysis' classic Weisz-Prater criterion phi_W = phi^2*eta = (rate*L^2)/(De*C_s) + criterion phi_W<0.15 diffusion negligible + experimental design heterogeneous catalysis.

Ahlborn Wheeler (USA 1947) Esso Research Standard Oil New Jersey + 1947 paper Adv Catal 3:249 'Reaction rates and selectivity in catalyst pores' classic + Wheeler classical analysis pore catalyst.

Octave Levenspiel (Brooklyn NY 1926 - Corvallis OR 2017) Oregon State University ChemE 1958-2017; 1962 textbook 'Chemical Reaction Engineering' John Wiley classic textbook 3rd ed 1999 668 pagine + 1972 'The Chemical Reactor Omnibook' Wiley + classic chemical engineering education + Levenspiel reactors design.

Edward L Cussler MIT + Univ Minnesota 1967-2017; 'Diffusion: Mass Transfer in Fluid Systems' 3rd ed 2009 Cambridge classic textbook.

Charles Newton Satterfield (USA 1925-2006) MIT ChemE 1949-1989; 1980 textbook 'Heterogeneous Catalysis in Industrial Practice' McGraw-Hill classic. Eredita: Aris 'Mathematical Theory of Diffusion and Reaction in Permeable Catalysts' 2 vols 1975 Oxford classic + Bird-Stewart-Lightfoot 'Transport Phenomena' 2007 Wiley + Levenspiel 'Chemical Reaction Engineering' 3rd ed 1999 Wiley 668 pagine + Fogler 'Elements of Chemical Reaction Engineering' 5th ed 2016 Prentice-Hall 992 pagine classic + Hill-Root 'Chemical Engineering Kinetics and Reactor Design' 2nd ed 2014 Wiley; Satterfield 'Heterogeneous Catalysis in Industrial Practice' 1991 McGraw-Hill 554 pagine + Smith 'Chemical Engineering Kinetics' 3rd ed 1981 + Froment-Bischoff 'Chemical Reactor Analysis and Design' 3rd ed 2011 Wiley 880 pagine.

Italia ricerca catalisi eterogenea + Thiele + reattori chimici: CNR-ICCOM Istituto Chimica Composti Organometallici Firenze + Bari + Pisa 100 + catalisi omogenea + eterogenea + Pt Pd Rh; CNR-ITM Istituto Membrane Tecnologie Bologna + Rende CS 200 + catalitic membranes + zeolite; CNR-IAS Inquinamento Atmosferico Napoli 250; CNR-ISMN Istituto Studio Materiali Nanostrutturati Bari + Palermo + Roma 250 + nanocatalysts + supported metals; CNR-IMM Microelettronica Microsistemi Catania + Roma + Bologna + Lecce 600 + porous silicon + supported catalyst MEMS sensors; ENEA Casaccia + Brindisi + Trisaia + 11 centri 2700 + biomass gasification catalyst + hydrogen + Fischer-Tropsch; RSE Milano 1000 + fuel cells catalyst Pt; Politecnico Milano DEIB + DENG + LCM 7500 + Carlo Cercignani Boltzmann legacy + Renzo Piazza CFD + Marco Mauri thermal storage + Pio Forzatti catalisi heterogenea + Enrico Tronconi reactor engineering + Gianpiero Groppi automotive catalyst MMO + Giancarlo Cappelli reattori; Politecnico Torino DENERG + DIATI 5000 + Marco Carlo Masoero buildings + Marco Filippi indoor + Aldo Pietro Reggiani lubrication; Federico II Napoli DICMaPI + DII + DIETI 5000 + Vincenzo Russo unit operations + Maria Chiara Mosca chemical reactors + Antonio Apicella catalysis;

Bologna DICAM + DEI + DIN 4000 + Pier Luigi Dragoni HVAC + Francesco Trifirò industrial chemistry + Andrea Vaccari catalysis; Padova DII + DEI + ICEA 3000 + Massimo Brunetti drying + Carlo Maragoni polymers; Pisa DICI + DESTeC 2500 + Walter Grassi heat transfer + Daniele Testi heat pumps; Politecnico Bari DEI 2500; Sapienza Roma DICEA + DIMA + DIET 4000; Genova DICCA + DIBRIS 2000 + IIT 1700; Trento DICAM 1962; Salerno DIIN 1968; Firenze DIEF 1321; Cagliari DIMCM 1606; Universita Pisa DICI; Aquila DIIIE 1964 1200.

Italia industria petrolchimica + raffinerie FCC + catalisi: Eni SpA Roma 1953 32000 + raffinerie 5 sites Sannazzaro + Livorno + Taranto + Gela + Sarroch + FCC fluidized catalytic cracking zeolite USY HY + Versalis polimeri + Eni R&D San Donato Milanese 1500 + Eni Refining&Marketing; Saipem Milano 1957 32000 oil&gas EPC + offshore + reattori chimici design FCC; Tecnimont Milano Maire Tecnimont 6000 EPC + Methanol synthesis Cu/ZnO/Al2O3 Lurgi license; Snam Milano 6000; Italgas Torino 1837 4000; Versalis Eni 6000 + polipropilene PP HDPE LDPE LLDPE + olefins ethane cracker + zeolite ZSM-5; Polimeri Europa Versalis Eni 5000; API Group Roma 1933 1100 + raffinerie Falconara Marittima; IPLOM SpA Busalla GE 1947 200.

Italia industria automotive catalysts + emission control: Magneti Marelli (Marelli) 39000 + automotive catalysts converter Pt-Pd-Rh + Bologna + Bari + Crevalcore + GDi diesel common rail; Eberspacher Italia Brescia 1865 + 200 + emission control + automotive catalyst converter; Faurecia Italia (Forvia) 200 + emission control automotive; Brembo Stezzano 14000; FCA Stellantis Italia 50000 + Mirafiori Pomigliano Cassino + GDi catalyst converter; Ferrari Maranello 5500; Avio Aero Pomigliano 5000 GE Aviation + jet engine catalysts + emission control.

Italia industria farmaceutica + catalisi enzymatic + asymmetric: Chiesi Farmaceutici Parma 7000 + asymmetric synthesis API; Recordati 4500; Zambon 2500; Angelini Pharma Roma 5000; Menarini Firenze 17000; Bracco Diagnostica 3500; Italfarmaco 3000; Dompe 800.

Italia industria fertilizzanti + ammonia synthesis Haber-Bosch: Eni Italia + Versalis Ferrara 6000 + ammonia synthesis + nitrogen fertilizers urea ammonium nitrate; Yara Italia 200 + ammonia + urea + Italian distribution; Cifo Bologna fertilizers 800; Mantica Modena fertilizers 600.

Italia industria fuel cells + idrogeno + electro-catalysis: Snam Hydrogen 600 + green hydrogen distribution; Eni Plenitude + Versalis 1500 + green hydrogen; Solvay Italia + Solvay Belgium 600 + chlor-alkali electrolysis; De Nora Industrie Milano 1923 1600 + electro-catalysis + DSA Dimensionally Stable Anodes + Pt-Ru-Ir + ITO + chlor-alkali; Consorzio Italia 200.

Formula modulo Thiele

Definizione: phi = L * sqrt(k / De). L caratteristica + k 1° ordine 1/s + De effettiva m^2/s.

De effettiva: De = D * epsilon / tau + porosità epsilon 0.3-0.6 + tortuosita tau 1.5-5 + Knudsen + bulk + bulk dominate large pore + Knudsen dominant small pore.

Effectiveness factor analytical: eta_sphere = (3/phi^2)*(phi*coth(phi) - 1) + sphere first-order; eta_slab = tanh(phi)/phi; eta_cylinder Bessel.

Aris generalized: phi_g = (V_p/S_p) * sqrt[(n+1)/2 * k * C_s^(n-1) / De] + n order + arbitrary geometry.

Weisz-Prater criterion: phi_W = phi^2 * eta = rate*L^2/(De*C_s) + diffusion negligible if phi_W < 0.15.

Storia e contesto

Ernest William Thiele (USA 1895-1993) Standard Oil of Indiana later Amoco Chicago Whiting IN refinery + 1939-1969 chemical engineering + retired Amoco; 1939 paper Ind Eng Chem 31:916 'Relation between catalytic activity and size of particle' classic Thiele modulus eponym phi = R*sqrt(k/De) + first quantitative diffusion-reaction analysis pellet catalyst + sphere first-order + effectiveness factor eta + classical reactor design + 1939 IECh paper diffusion limited regime quantitative; 1957 textbook 'Notes on Distillation' classic distillation; pioneer pellet catalyst + reactor engineering + Standard Oil Whiting Indiana refinery FCC; Aris 1969 honor Thiele 80th birthday Special Issue Chem Eng Sci.

Rutherford Aris (London UK 1929 - Minneapolis USA 2005) Cambridge BSc 1948 Caius College + Aris Imperial College London PhD 1956 Robert Houghton + Imperial College assistant lecturer 1956-1958 + Edinburgh University 1958-1965 + University Minnesota Minneapolis ChemE 1965-2005 Regents Professor; 1957 paper Chem Eng Sci 6:262 'On shape factors for irregular particles I' shape factors generalize Thiele + 1965 textbook 'Introduction to the Analysis of Chemical Reactors' Prentice-Hall classic chemical reactors + Aris generalized Thiele modulus + 1965 paper Chem Eng Sci 20:907 + 1969 'Elementary Chemical Reactor Analysis' classic textbook + 'The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts' 2 vols Oxford Clarendon Press 1975 classic 800 pagine; pioneer chemical engineering + reactor design + dynamical systems chaotic + Aris-Cohen + scientific writing classic 'The Mere Rhetoric of Science' 1986; Bird Award 1985 American Chemical Society.

Paul B Weisz + Charles D Prater Mobil Research Princeton NJ 1954; 1954 paper Adv Catal 6:143 'Interpretation of measurements in experimental catalysis' classic Weisz-Prater criterion phi_W = phi^2*eta + observable rate-based criterion + diffusion negligible if phi_W<0.15 + experimental heterogeneous catalysis design + Mobil Princeton; Weisz also discoverer of zeolite shape selectivity Mobil ZSM-5.

Ahlborn Wheeler USA 1947 Esso Research Standard Oil New Jersey; 1947 paper Adv Catal 3:249 'Reaction rates and selectivity in catalyst pores' classic + Wheeler-Thiele analytical pore + Wheeler model heterogeneous catalysis.

Octave Levenspiel (Brooklyn NY 1926 - Corvallis OR 2017) Oregon State University ChemE 1958-2017; 1962 textbook 'Chemical Reaction Engineering' John Wiley & Sons classic textbook 3rd ed 1999 668 pagine + 1972 'The Chemical Reactor Omnibook' Wiley + 1979 'Engineering Flow and Heat Exchange' Plenum + 1989 + classic chemical engineering education + Levenspiel reactors design didactic style.

Edward Lansing Cussler (Bryn Mawr PA 1939-) Yale BS 1961 + Wisconsin-Madison PhD 1966 + MIT + Carnegie Mellon + University Minnesota 1980-2017; 'Diffusion: Mass Transfer in Fluid Systems' 3rd ed 2009 Cambridge classic textbook 631 pagine + Bioseparations 1989 + Cussler chair Minnesota ChemE.

Charles Newton Satterfield (Massachusetts 1925-2006) MIT ChemE 1949-1989 William Henry Dow Professor; 1980 textbook 'Heterogeneous Catalysis in Industrial Practice' McGraw-Hill 554 pagine classic + Mass Transfer in Heterogeneous Catalysis 1970 MIT Press classic + Trickle-Bed Reactors 1975.

Hugh Scott Fogler (USA 1939-) University Michigan Ann Arbor ChemE 1965-2018 Vennema Endowed Chair; 'Elements of Chemical Reaction Engineering' 5th ed 2016 Prentice-Hall 992 pagine classic textbook chemical engineering + 1992 LearnChemE web + Fogler Foundation Michigan; pioneer ChemE education + Sokrates Schmidt-Aris collaboration. Eredita: Aris 'Mathematical Theory of Diffusion and Reaction in Permeable Catalysts' 2 vols 1975 Oxford Clarendon Press classic 800 pagine + Bird-Stewart-Lightfoot 'Transport Phenomena' 2nd ed 2007 Wiley + Levenspiel 'Chemical Reaction Engineering' 3rd ed 1999 Wiley + Fogler 'Elements of Chemical Reaction Engineering' 5th ed 2016 Prentice-Hall + Hill-Root 'Chemical Engineering Kinetics and Reactor Design' 2nd ed 2014 Wiley; Satterfield 1980 + Smith 'Chemical Engineering Kinetics' 3rd ed 1981 + Froment-Bischoff 'Chemical Reactor Analysis and Design' 3rd ed 2011 Wiley 880 pagine.

Italia ricerca catalisi eterogenea + Thiele modulus + reattori chimici: CNR-ICCOM Istituto Chimica Composti Organometallici Firenze + Bari + Pisa 100 + catalisi omogenea + eterogenea + Pt Pd Rh; CNR-ITM Istituto Membrane Tecnologie Bologna + Rende CS 200 + catalitic membranes + zeolite + dehidrogenation; CNR-IAS Istituto Inquinamento Atmosferico Napoli + Roma + Sesto Fiorentino 250 + emission catalyst three-way; CNR-ISMN Istituto Studio Materiali Nanostrutturati Bari + Palermo + Roma 250 + nanocatalysts + supported metals + Au-TiO2 Pd-CeO2 + perovskite; CNR-IMM Istituto Microelettronica Microsistemi Catania + Roma + Bologna + Lecce 600 + porous silicon + supported catalyst MEMS; ENEA Agenzia Nazionale Nuove Tecnologie Energia Roma + Casaccia + Frascati + Brindisi + Trisaia + 11 centri 2700 + biomass gasification catalyst + hydrogen + Fischer-Tropsch + Cu/ZnO/Al2O3; RSE Ricerca Sistema Energetico Milano 1000 + fuel cells catalyst Pt-Ru + biomass; SOGIN SpA Roma 1100.

Italia università catalisi eterogenea + reattori chimici + Thiele: Politecnico Milano DEIB + DENG + LCM 7500 + Carlo Cercignani Boltzmann legacy 1939-2010 kinetic theory + Renzo Piazza CFD + Marco Mauri thermal storage + Pio Forzatti heterogeneous catalysis kinetics + Enrico Tronconi reactor engineering + Gianpiero Groppi automotive catalyst + monolith + Andrea Beretta + Stefano Pierucci kinetics + Giancarlo Cappelli reattori + Carlo Lubello biocatalysis; Politecnico Torino DENERG + DIATI 1859 5000 + Marco Carlo Masoero buildings + Vito Specchia catalysis + Stefania Specchia automotive catalyst Pt-Pd-Rh + Aldo Pietro Reggiani lubrication; Federico II Napoli DICMaPI + DII + DIETI 1224 5000 + Vincenzo Russo unit operations + Maria Chiara Mosca chemical reactors + Antonio Apicella catalysis + Alberto Servida ammonia methanol; Bologna DICAM + DEI + DIN 1088 4000 + Pier Luigi Dragoni HVAC + Francesco Trifirò industrial chemistry + Andrea Vaccari catalysis + Stefania Albonetti environmental catalysis; Padova DII + DEI + ICEA 1222 3000 + Renato Lazzarin HVAC + Massimo Brunetti drying + Marco Pertile microgravity; Pisa DICI + DESTeC 1343 2500 + Walter Grassi heat transfer + Daniele Testi heat pumps + Anna Maria Raspolli petrochemicals; Politecnico Bari DEI 1990 2500;

Sapienza Roma DICEA + DIMA + DIET 1303 4000; Genova DICCA + DIBRIS 1481 2000 + IIT 1700; Trento DICAM 1962; Salerno DIIN 1968; Firenze DIEF 1321; Cagliari DIMCM 1606; Universita Pisa DICI.

Italia industria petrolchimica + raffinerie FCC + catalisi heterogenea: Eni SpA Roma 1953 32000 + raffinerie 5 sites Sannazzaro de'Burgondi PV + Livorno + Taranto + Gela CL + Sarroch CA + FCC fluidized catalytic cracking zeolite USY HY ZSM-5 + Versalis polimeri + Eni R&D San Donato Milanese 1500 + Eni Refining&Marketing; Saipem Milano 1957 32000 oil&gas EPC + offshore + reattori chimici design FCC + Saipem catalysis department; Tecnimont Milano Maire Tecnimont 6000 EPC + Methanol synthesis Cu/ZnO/Al2O3 Lurgi license + ammonia + ethylene oxide + downstream petrochemicals; Snam Milano 1941 6000; Italgas Torino 1837 4000; Versalis Eni 6000 + polipropilene PP HDPE LDPE LLDPE + olefins ethane cracker + zeolite ZSM-5 + Mantua Brindisi Marghera + downstream Versalis renewables; Polimeri Europa Versalis Eni 5000; API Group Roma 1933 1100 + raffinerie Falconara Marittima; IPLOM SpA Busalla GE 1947 200; SARAS Sarroch Cagliari 1962 1500 + raffineria Sarroch Sardegna; Esso Italia Roma 200; Total Italia 200.

Italia industria automotive catalysts + emission control three-way TWC: Marelli (CK Holdings 2018 ex-Magneti Marelli Cofima Powertrain Bologna + Bari + Crevalcore BO 1919 39000 + automotive catalysts converter Pt-Pd-Rh + Marelli Plastics + GDi diesel common rail; Eberspacher Italia Brescia 200 + emission control + automotive catalyst converter; Faurecia Italia (Forvia) 200 + emission control automotive; Tenneco Italia 200; Brembo Stezzano BG 14000; FCA Stellantis Italy 50000 + Mirafiori Torino + Pomigliano + Cassino + Modena Maserati Ferrari + GDi catalyst converter; Ferrari Maranello MO 5500 + V8 V12 GDi catalyst; Lamborghini Sant'Agata Bolognese 2000; Maserati Modena 1000; Pagani Modena 200; Avio Aero Rivalta Pomigliano 5000 GE Aviation + jet engine catalysts + emission control.

Italia industria farmaceutica + catalisi enzimatica + asymmetric synthesis: Chiesi Farmaceutici Parma 1935 7000 + asymmetric synthesis API + foster Trimbow Atimos respiratory; Recordati Milano 1926 4500; Zambon Bresso MI 1906 2500; Angelini Pharma Roma 1919 5000; Menarini Firenze 1886 17000 leading Italian pharma; Bracco Diagnostica Milano 1927 3500; Italfarmaco Milano 1938 3000; Dompe Farmaceutici 800.

Italia industria fertilizzanti + ammonia synthesis Haber-Bosch + urea: Eni Italia + Versalis Ferrara 6000 + ammonia synthesis Fe + K2O + Al2O3 + nitrogen fertilizers urea ammonium nitrate Ferrara; Yara Italia 200 + ammonia + urea + Italian distribution; Cifo Bologna fertilizers 800; Mantica Modena fertilizers 600; Compo Italia 200; Adama Italia 200.

Italia industria fuel cells + green hydrogen + electro-catalysis: Snam Hydrogen Milano 600 + green hydrogen pipeline distribution; Eni Plenitude + Versalis Renewables 1500 + green hydrogen + biomass; Solvay Italia Bollate Rosignano 600 + chlor-alkali electrolysis Nafion membranes; De Nora Industrie Milano 1923 1600 + electro-catalysis + DSA Dimensionally Stable Anodes + Pt-Ru-Ir + ITO + chlor-alkali industrial; Industrie De Nora 1600; Hydrogenious LOHC Italy 100; NextChem Maire Tecnimont 200 + green hydrogen.

Tabella valori Thiele

• phi = L*sqrt(k/De): definizione
• De = D*epsilon/tau: porosità tortuosita
• eta_sphere = (3/phi^2)*(phi*coth(phi)-1)
• eta_slab = tanh(phi)/phi
• phi<0.4 reaction limited: eta~1
• 0.4<phi<4 mixed: balanced
• phi>4 diffusion limited: eta~1/phi
• phi>20 severe: outer shell only
• Aris generalized: V_p/S_p geometry
• Weisz-Prater criterion: phi^2*eta<0.15
• Damkohler Da_I = phi^2: equivalente
• Biot Bi_M = k_m*L/De: external
• FCC zeolite USY HY ZSM-5: Versalis
• Hydrogenation Ni Pt Pd Rh: alumina
• Ammonia Haber-Bosch Fe K Al: 1909
• Methanol Cu/ZnO/Al2O3: ICI
• Fischer-Tropsch Co Fe Ru: GTL
• TWC automotive Pt-Pd-Rh: cordierite
• Thiele USA 1939: Standard Oil Whiting
• Aris 1956 Imperial 1965 Minnesota: textbook
• Weisz-Prater Mobil 1954
• Wheeler Esso 1947
• Levenspiel Oregon 1962
• Cussler Minnesota: Diffusion
• Satterfield MIT 1980
• Italia Eni 32000: FCC raffinerie 5 sites
• Italia Versalis 6000: zeolite ZSM-5
• Italia Marelli 39000: TWC automotive
• Italia De Nora 1600: electro-catalysis DSA
• Italia Politecnico Milano LCM 7500: Forzatti Tronconi

Esempi numerici dettagliati

Esempio 1 - Pellet small reaction limited.

Esempio 2 - FCC zeolite cracking. L=5 mm, k=10 1/s, De=1e-6. phi = 0.005*sqrt(10/1e-6) = 15.8. Strong diffusion limited + eta~0.19 + outer shell active. Italia: Eni FCC raffinerie 5 sites + Versalis zeolite ZSM-5 USY.

Esempio 3 - Ammonia synthesis Haber-Bosch. L=3 mm, k=1 1/s, De=1e-7. phi = 0.003*sqrt(1/1e-7) = 9.49. Diffusion limited + eta~0.31. Italia: Eni Versalis Ferrara ammonia + Tecnimont Maire Lurgi license.

Esempio 4 - Automotive monolith TWC. L=50 micron washcoat, k=100 1/s fast, De=1e-6. phi = 5e-5*sqrt(100/1e-6) = 0.5. Mixed regime. Italia: Marelli 39000 + Eberspacher + Faurecia + Stellantis + Ferrari.

Esempio 5 - Severe diffusion limit. L=10 mm, k=100, De=1e-8. phi = 0.01*sqrt(100/1e-8) = 1000. eta~0.001 outer shell only + waste catalyst. Italia: Saipem reactor design + Politecnico Milano LCM Tronconi reactor engineering.

Limiti e considerazioni

1. Isothermal pellet assumption: real exothermic + Prater number beta + non-isothermal effectiveness multiple steady states.
2. First-order kinetics: real n=2 + power-law + Langmuir-Hinshelwood + Aris generalized.
3. External mass transfer: Bi_M finite + Damkohler external.
4. Pore structure heterogeneity: bidisperse + macropore + micropore zeolite.
5. Knudsen diffusion: small pore + Knudsen number + bulk + Knudsen mixed.
6. Catalyst deactivation: coke + sintering + poisoning + activity decay over time.
7. Diffusion-reaction multiple steady states: ignition extinction + autothermal.
8. Selectivity: parallel + series reactions + diffusion controlled selectivity decrease.
9. Surface reactions: surface diffusion + spillover + zeolite shape selectivity.
10. Reactor scale: pellet + bed + reactor geometry + gradients axial radial.

Errori comuni

Confondere phi e Damkohler: Da_I = phi^2 internal diffusion + Da_II external Bi.

L characteristic length: sphere R + slab L semispessore + cylinder R/2 + V_p/S_p Aris generalized.

De effective vs D bulk: De = D*epsilon/tau + porosità + tortuosita 1.5-5 + Knudsen small pore.

Order kinetics: Aris generalized phi_g = (V/S)*sqrt[(n+1)/2*k*C^(n-1)/De].

Weisz-Prater criterion: phi^2*eta<0.15 + diffusion negligible + observable rate.

Applicazioni pratiche

1. FCC fluidized catalytic cracking raffinerie: Italia Eni 32000 raffinerie 5 sites Sannazzaro Livorno Taranto Gela Sarroch + Versalis 6000 zeolite ZSM-5 USY HY + SARAS 1500 + API 1100 + IPLOM.
2. Ammonia synthesis Haber-Bosch fertilizers: Italia Eni Versalis Ferrara 6000 ammonia urea nitrogen + Tecnimont Maire Lurgi license + Yara Italia 200 + Cifo Mantica fertilizers + Compo + Adama.
3. Methanol synthesis Cu/ZnO/Al2O3: Italia Tecnimont Maire Tecnimont 6000 Lurgi license + Eni Versalis + ICI methanol Italian distribution.
4. Automotive three-way catalyst TWC Pt-Pd-Rh: Italia Marelli 39000 catalyst converter + Eberspacher 200 + Faurecia + Tenneco + Stellantis Mirafiori Pomigliano Cassino + Ferrari Lamborghini Maserati Pagani GDi.
5. Hydrogenation Ni Pt Pd Rh chemicals: Italia Versalis 6000 + Eni Refinery + Saipem reactor design + CNR-ICCOM Firenze + Politecnico Milano Forzatti Tronconi.
6. Fischer-Tropsch GTL gas-to-liquid: Italia Eni Plenitude + Versalis + Saipem GTL design + Sasol partner + biomass-to-liquid Cat Cracker.
7. Pharmaceutical asymmetric catalysis API: Italia Chiesi 7000 + Recordati 4500 + Zambon + Angelini 5000 + Menarini 17000 + Bracco 3500 + Italfarmaco + Dompe + asymmetric synthesis chiral.
8. Fuel cells PEM Pt-Ru electrocatalysis: Italia Snam Hydrogen 600 + Eni Plenitude 1500 + RSE 1000 fuel cells + De Nora 1600 DSA Pt-Ru-Ir.
9. Chlor-alkali electrolysis: Italia De Nora Industrie Milano 1600 DSA Dimensionally Stable Anodes + Solvay Italia Bollate 600 + Industrie De Nora.
10. Universita ricerca catalisi heterogenea: Politecnico Milano DEIB DENG LCM 7500 Forzatti Tronconi Groppi + Politecnico Torino DENERG Specchia + Federico II DICMaPI Russo + Bologna DICAM Trifirò Vaccari Albonetti + Genova DICCA + Pisa DICI Raspolli + IIT Genova + ENEA Casaccia 2700 + RSE Milano 1000.

Aggiornato a luglio 2026