How to calculate Thiele modulus phi catalyst effectiveness pellet

Calculate Thiele modulus phi = L*sqrt(k/De) ratio reaction rate to internal diffusion in heterogeneous catalyst pellet. phi<0.4 reaction limited eta~1; phi>4 diffusion limited eta~1/phi. Ernest Thiele 1939 + Aris 1965. ExxonMobil + Chevron FCC + Pfizer Merck pharmaceutical.

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Thiele modulus phi dimensionless ratio of intrinsic reaction rate to internal diffusion rate in porous catalyst pellets in heterogeneous chemical reaction engineering: phi = L * sqrt(k/De). L characteristic length m (sphere radius R, V_p/S_a volume to external surface ratio = R/3 sphere; slab semi-thickness; cylinder R/2); k first-order rate constant 1/s; De effective diffusivity in porous pellet m^2/s with De = D*epsilon/tau with porosity epsilon 0.3-0.6 + tortuosity tau 1.5-5.

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

Regimes: phi<0.4 reaction limited kinetic + eta~1 + small pellet + automotive monolith Pt-Pd-Rh; 0.4<phi<4 mixed internal diffusion + reaction balanced; phi>4 strong diffusion limited eta~1/phi + shell reaction core unused + FCC zeolite Knudsen; phi>20 severe diffusion outer shell only.

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

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

Industrial catalysts: FCC zeolite Y-zeolite USY HY + ZSM-5 + crystalline aluminosilicate + 50-150 micron particle + refineries; hydrogenation Ni Pt Pd Rh + alumina supported + olefin aromatic; ammonia Haber-Bosch Fe + K2O + Al2O3 + 1909 + 5-10 mm pellet + BASF Mittasch; methanol Cu/ZnO/Al2O3 50-300 bar + 230-280°C + ICI Lurgi; Fischer-Tropsch Co + Fe + Ru + GTL + Sasol Shell Pearl; automotive TWC three-way Pt-Pd-Rh + monolith honeycomb cordierite + 400-900 cells/in^2 + 20-50 micron washcoat + emission NOx CO HC. History: 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 + effectiveness factor + classical reactor design + 1957 'Notes on Distillation'.

Rutherford Aris (London UK 1929 - Minneapolis USA 2005) Cambridge BSc 1948 + Imperial College London PhD 1956 Robert Houghton + Edinburgh University 1958-1965 + University Minnesota Minneapolis ChemE 1965-2005 Regents Professor; 1957 Chem Eng Sci 6:262 'On shape factors for irregular particles I' + 1965 textbook 'Introduction to the Analysis of Chemical Reactors' Prentice-Hall + 'Mathematical Theory of Diffusion and Reaction in Permeable Catalysts' 2 vols 1975 Oxford classic 800 pages + Aris generalized Thiele modulus + 1969 Elementary; pioneer chemical engineering + dynamical systems + Bird Award 1985.

Paul B Weisz + Charles D Prater Mobil Research Princeton NJ 1954; 1954 Adv Catal 6:143 'Interpretation of measurements in experimental catalysis' Weisz-Prater criterion + Mobil + Weisz also discovered zeolite shape selectivity ZSM-5.

Ahlborn Wheeler Esso Research Standard Oil New Jersey 1947; 1947 Adv Catal 3:249 'Reaction rates and selectivity in catalyst pores' classic.

Octave Levenspiel (Brooklyn NY 1926 - Corvallis OR 2017) Oregon State University ChemE 1958-2017; 1962 textbook 'Chemical Reaction Engineering' Wiley classic + 'The Chemical Reactor Omnibook' 1972.

Edward L Cussler Univ Minnesota; 'Diffusion: Mass Transfer' 3rd ed 2009 Cambridge classic.

Charles N Satterfield (USA 1925-2006) MIT ChemE 1949-1989 Dow Professor; 1980 'Heterogeneous Catalysis in Industrial Practice' McGraw-Hill classic + 'Mass Transfer in Heterogeneous Catalysis' 1970 MIT Press.

H Scott Fogler (USA 1939-) Univ Michigan Ann Arbor ChemE 1965-2018 Vennema Endowed Chair; 'Elements of Chemical Reaction Engineering' 5th ed 2016 Prentice-Hall 992 pages classic. Legacy: Aris 'Mathematical Theory of Diffusion and Reaction' 2 vols 1975 Oxford classic + Bird-Stewart-Lightfoot 'Transport Phenomena' 2007 Wiley + Levenspiel 1999 + Fogler 2016 + Hill-Root 2014 + Satterfield 1980 + Smith 1981 + Froment-Bischoff 'Chemical Reactor Analysis' 2011 Wiley 880 pages.

USA research heterogeneous catalysis + Thiele + reactor design: NIST Gaithersburg MD 3500 + reference materials catalyst; NREL Golden CO 2900 + biomass catalysis; ORNL Oak Ridge TN 6500 + nuclear catalysis + carbon capture; Sandia Albuquerque NM 14000 CRF combustion catalyst; Argonne IL 3400 Center for Nanoscale Materials catalysis; PNNL Richland WA 4500; LBNL Berkeley 4400; Brookhaven Long Island NY 2600 + catalysis; NETL National Energy Technology Lab Pittsburgh + Morgantown WV 1500 + Fischer-Tropsch + biomass catalysis.

USA universities heterogeneous catalysis + Thiele: MIT Cambridge MA 11700 + ChemE Yuriy Romàn Leshchov catalysis + Bernhardt Trout + James Swan + Manolis Doxastakis catalysis MOF + George Stephanopoulos process + Charles Satterfield heritage + Edwin Thomas; Stanford CA 17000 + ChemE Stacey Bent ALD catalyst + Eric Shaqfeh + Andre Larizadeh + James Swan polymers; Caltech Pasadena 2400 + Mark Davis CalTech zeolite catalysis + John Brady; UC Berkeley 45000 + ChemE Alexis Bell catalysis + Dean Toste + Susan Muller; Princeton 8000 + ChemE Sankaran Sundaresan + Howard Stone + Annibal Vaschetto catalysis MOF; Cornell Ithaca NY 25000 + ChemE Lynden Archer polymer + Donald Koch; Georgia Tech Atlanta 36000 + ChemE Christopher Jones catalysis Scopus; UIUC Urbana 56000 + ChemE Hong Yang + Jian Xie catalysis fuel cells; Penn State 50000 + Bert Chandler catalysis + Doraiswamy + Ramkrishna; UT Austin 51000 + ChemE Henkelman catalysis DFT + Charles Mullins; Univ Michigan Ann Arbor 50000 + ChemE Robert Larson polymer + Suljo Linic catalysis; Purdue 47000 + ChemE Doraiswamy Ramkrishna + Fabio Ribeiro catalysis; Wisconsin-Madison 49000 + ChemE James Dumesic catalysis biomass + George Huber catalysis;

Minnesota 51000 + ChemE Aris heritage + Tsapatsis catalysis MOF + Andreas Stein materials catalysis; UCLA 45000; UC Davis 40000; Northwestern Evanston IL 22000 + ChemE Tobin Marks catalysis ALD + Linda Broadbelt; RPI Rensselaer 7000; Lehigh Bethlehem PA 7000 + Manoj Chaudhury surfaces; Case Western Reserve 11000; UMass Amherst 30000; WVU Morgantown 26000; Univ Delaware Newark 24000 + ChemE Dion Vlachos catalysis; Univ Pittsburgh 28000; Notre Dame 12000.

USA petrochemicals industry FCC + ammonia + methanol: ExxonMobil Irving TX 1882 62000 + refineries Baytown Beaumont Joliet Baton Rouge + FCC Houston Houston Refinery; Chevron San Ramon CA 1879 45000 + Richmond Pascagoula + FCC; Marathon Petroleum Findlay OH 1887 17000 + 13 refineries 3 million bpd FCC; Phillips 66 Houston TX 14000; Valero Energy San Antonio TX 9700 + 15 refineries; Honeywell UOP Des Plaines IL 1914 5000 + UOP FCC technology Universal Oil Products + Cyclar + Penex; BP America Chicago + Whiting IN 60000; Shell USA Houston 14000 Pearl GTL Qatar Fischer-Tropsch; Citgo Petroleum Houston TX 3500; CF Industries Holdings Deerfield IL 1946 3000 + ammonia urea fertilizer + 5 nitrogen plants USA; Nutrien Saskatoon Canada / USA 2018 27000 + ammonia urea + agriculture; Yara North America 800 + ammonia distribution; Mosaic Tampa FL 13000 + phosphate + potash + ammonia; Air Products and Chemicals Allentown PA 1940 21000 + industrial gases + Hydrogen + ammonia.

USA automotive catalysts emission control three-way TWC: BASF Catalysts Iselin NJ 4000 + automotive emission catalyst Pt-Pd-Rh + Catalysts Iselin Florham Park; Johnson Matthey USA West Deptford NJ 5000 + UK parent + automotive TWC + Pt-Pd-Rh + diesel SCR DPF; Umicore USA Rancho Dominguez CA 600 + Belgian parent automotive catalyst; Eberspacher USA 800 + emission control automotive; Tenneco Lake Forest IL 1888 70000 + emission control + clean air + DRiV catalysts; Faurecia Auburn Hills MI 25000 + clean mobility emission systems; Cummins Columbus IN 1919 73000 + diesel emission + SCR DEF AdBlue; Caterpillar Peoria IL 1925 105000 + diesel emission.

USA pharmaceutical asymmetric catalysis: Pfizer NY 1849 80000 + asymmetric synthesis API + Lipitor Viagra; Merck Kenilworth NJ 1891 73000; Johnson&Johnson NJ 1886 152000; Eli Lilly Indianapolis IN 1876 39000; AbbVie Lake Bluff IL 50000; Bristol-Myers Squibb NY 33000; Amgen Thousand Oaks CA 24000; Gilead Foster City CA 16000; Codexis Redwood City CA 2002 600 + biocatalysis + enzymatic asymmetric.

USA fuel cells electrocatalysis Pt-Ru: Plug Power Latham NY 2400 + PEM fuel cells + green hydrogen; Ballard Power Vancouver BC + Bend OR 1500; Bloom Energy San Jose CA 2000 + SOFC fuel cells; 3M St Paul MN 92000 + Nafion membranes ion-exchange; DuPont Wilmington DE 1802 28000 + Nafion + Krytox; FuelCell Energy Danbury CT 600 MCFC molten carbonate; Cummins Cellcentric 73000.

USA chlor-alkali electro-catalysis: Olin Clayton MO 1892 8500 + chlor-alkali; Westlake Chemical Houston TX 1986 16000; Occidental Petroleum Houston TX 1920 13000; Tronox Stamford CT 4500 chlor-alkali.

Thiele formula

Definition: phi = L*sqrt(k/De). L sphere R or V_p/S_a + k 1° order 1/s + De effective m^2/s.

De effective: De = D*epsilon/tau + porosity epsilon 0.3-0.6 + tortuosity tau 1.5-5.

Effectiveness: eta_sphere = (3/phi^2)*(phi*coth(phi)-1); eta_slab = tanh(phi)/phi.

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

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

History

Ernest Thiele (USA 1895-1993) Standard Oil Indiana Amoco Whiting IN refinery 1939-1969 + 1939 Ind Eng Chem 31:916 classic Thiele modulus + 1957 'Notes on Distillation'. Rutherford Aris (London 1929 - Minneapolis 2005) Cambridge + Imperial College PhD 1956 + Edinburgh + Minnesota 1965-2005 Regents Professor + 1965 textbook 'Introduction to Analysis of Chemical Reactors' + 'Mathematical Theory of Diffusion and Reaction' 1975 Oxford classic. Weisz + Prater Mobil Princeton 1954 + Weisz zeolite ZSM-5 selectivity. Wheeler Esso 1947. Levenspiel Oregon 1962 'Chemical Reaction Engineering' classic. Cussler Minnesota 'Diffusion' 2009. Satterfield MIT 1980. Fogler Michigan 2016 'Elements of CRE'. Bird-Stewart-Lightfoot 2007 + Aris 1975 + Levenspiel 1999 + Fogler 2016 + Froment-Bischoff 2011.

USA research: NIST Gaithersburg 3500; NREL Golden 2900 biomass; ORNL 6500 nuclear carbon capture; Sandia 14000 CRF; Argonne 3400 CNM catalysis; PNNL 4500; LBNL 4400; Brookhaven 2600; NETL Pittsburgh Morgantown 1500 Fischer-Tropsch.

USA universities: MIT 11700 Romàn Leshchov + Trout + Doxastakis MOF + Stephanopoulos + Satterfield heritage; Stanford 17000 Bent ALD; Caltech 2400 Davis zeolite + Brady; UC Berkeley 45000 Bell + Toste; Princeton 8000 Sundaresan + Stone + Vaschetto MOF; Cornell 25000 Archer + Koch; Georgia Tech 36000 Jones; UIUC 56000 Yang Xie fuel cells; Penn State 50000 Chandler + Ramkrishna; UT Austin 51000 Henkelman DFT + Mullins; Michigan 50000 Larson + Linic; Purdue 47000 Ribeiro; Wisconsin-Madison 49000 Dumesic biomass + Huber; Minnesota 51000 Aris heritage + Tsapatsis MOF + Stein; UCLA 45000; UC Davis 40000; Northwestern 22000 Marks ALD + Broadbelt; RPI 7000; Delaware 24000 Vlachos catalysis; UMass Amherst 30000; WVU 26000.

USA petrochemicals FCC: ExxonMobil 62000 Baytown Beaumont Joliet Baton Rouge FCC; Chevron 45000 Richmond Pascagoula; Marathon Petroleum 17000 13 refineries 3 Mbpd; Phillips 66 14000; Valero 9700 15 refineries; Honeywell UOP Des Plaines 5000 UOP FCC tech Cyclar Penex; BP America 60000; Shell USA 14000 Pearl GTL Qatar Fischer-Tropsch; Citgo 3500.

USA fertilizers ammonia: CF Industries Deerfield IL 3000 5 nitrogen plants; Nutrien 27000 ammonia urea; Yara NA 800; Mosaic Tampa 13000 phosphate ammonia; Air Products 21000 hydrogen ammonia.

USA automotive TWC: BASF Catalysts Iselin 4000 Pt-Pd-Rh; Johnson Matthey USA West Deptford 5000; Umicore USA 600; Tenneco 70000 emission DRiV; Faurecia 25000 clean mobility; Cummins 73000 diesel SCR AdBlue; Caterpillar 105000.

USA pharma asymmetric: Pfizer 80000; Merck 73000; JNJ 152000; Lilly 39000; AbbVie 50000; BMS 33000; Amgen 24000; Gilead 16000; Codexis Redwood City 600 biocatalysis.

USA fuel cells: Plug Power Latham 2400 PEM; Ballard Power 1500; Bloom Energy San Jose 2000 SOFC; 3M 92000 Nafion; DuPont 28000 Nafion Krytox; FuelCell Energy 600 MCFC; Cummins Cellcentric 73000.

USA chlor-alkali: Olin Clayton MO 8500; Westlake 16000; Occidental 13000; Tronox Stamford 4500.

Thiele values table

  • phi = L*sqrt(k/De): definition
  • De = D*epsilon/tau: porosity tortuosity
  • eta_sphere = (3/phi^2)*(phi*coth(phi)-1)
  • eta_slab = tanh(phi)/phi
  • phi<0.4 reaction limited
  • 0.4-4 mixed
  • phi>4 diffusion limited: eta~1/phi
  • phi>20 severe: outer shell
  • Aris generalized: V_p/S_p
  • Weisz-Prater: phi^2*eta<0.15
  • FCC zeolite: USY HY ZSM-5
  • Hydrogenation Ni Pt Pd Rh
  • Ammonia Haber-Bosch: Fe K Al
  • Methanol Cu/ZnO/Al2O3
  • TWC Pt-Pd-Rh: cordierite
  • Thiele USA 1939
  • Aris 1965 Minnesota
  • Weisz-Prater Mobil 1954
  • USA NIST 3500
  • USA ExxonMobil 62000: FCC
  • USA Honeywell UOP 5000: FCC tech
  • USA CF Industries 3000: ammonia
  • USA BASF Catalysts 4000: TWC
  • USA Johnson Matthey 5000: TWC
  • USA Pfizer 80000: asymmetric API
  • USA Plug Power 2400: PEM fuel cells

Numerical examples

Example 1 - Small pellet reaction limited. L=1 mm, k=0.1, De=1e-6. phi=0.316 eta~0.97. USA: BASF Catalysts + Johnson Matthey TWC.

Example 2 - FCC zeolite. L=5 mm, k=10, De=1e-6. phi=15.8 eta~0.19. USA: ExxonMobil Baytown + Chevron Richmond + Honeywell UOP.

Example 3 - Ammonia Haber-Bosch. L=3 mm, k=1, De=1e-7. phi=9.49 eta~0.31. USA: CF Industries + Nutrien + Yara NA + Mosaic Tampa.

Example 4 - Automotive TWC washcoat. L=50 micron, k=100, De=1e-6. phi=0.5 mixed. USA: BASF Catalysts Iselin + Johnson Matthey West Deptford + Umicore USA.

Example 5 - Severe diffusion limit. L=10 mm, k=100, De=1e-8. phi=1000 eta~0.001. USA: Sandia CRF + Argonne CNM catalysis research.

Limits and considerations

  1. Isothermal pellet: real exothermic + Prater number beta + multiple steady states.
  2. First-order kinetics: Aris generalized arbitrary order.
  3. External mass transfer: Bi_M finite + Damkohler external.
  4. Pore structure: bidisperse + macropore + micropore zeolite.
  5. Knudsen diffusion: small pore + Knudsen + bulk mixed.
  6. Catalyst deactivation: coke + sintering + poisoning.
  7. Multiple steady states: ignition extinction autothermal.
  8. Selectivity: parallel series diffusion controlled.
  9. Surface reactions: shape selectivity zeolite.
  10. Reactor scale: pellet + bed + gradients axial radial.

Common errors

Confusing phi and Damkohler: Da_I = phi^2 internal.

L characteristic length: sphere R + slab + V_p/S_p Aris.

De effective vs D bulk: De = D*eps/tau.

Order kinetics: Aris generalized.

Weisz-Prater: phi^2*eta<0.15 observable.

Practical applications

  1. FCC refineries: USA ExxonMobil 62000 Baytown + Chevron 45000 + Marathon 17000 + Phillips 66 + Valero + Honeywell UOP 5000 FCC tech + BP + Shell Pearl GTL.
  2. Ammonia Haber-Bosch fertilizers: USA CF Industries 3000 5 nitrogen plants + Nutrien 27000 + Yara NA + Mosaic 13000 + Air Products 21000 hydrogen.
  3. Methanol Cu/ZnO/Al2O3: USA Methanex Vancouver 1000 + Methanol Holdings + ICL Israel partnership.
  4. Automotive TWC Pt-Pd-Rh: USA BASF Catalysts 4000 + Johnson Matthey 5000 + Umicore 600 + Tenneco 70000 + Faurecia 25000 + Cummins 73000 + Caterpillar 105000.
  5. Hydrogenation Ni Pt Pd Rh: USA ExxonMobil + Chevron + Dow + DuPont chemicals.
  6. Fischer-Tropsch GTL: USA Sasol Houston Texas + Shell Pearl GTL Qatar + Air Products partnership.
  7. Pharma asymmetric synthesis: USA Pfizer 80000 + Merck 73000 + JNJ 152000 + Lilly 39000 + AbbVie 50000 + BMS + Amgen + Gilead + Codexis 600 biocatalysis.
  8. Fuel cells PEM Pt-Ru: USA Plug Power 2400 + Ballard 1500 + Bloom Energy 2000 SOFC + 3M Nafion + DuPont Nafion + FuelCell Energy MCFC + Cummins.
  9. Chlor-alkali electrolysis: USA Olin 8500 + Westlake 16000 + Occidental 13000 + Tronox 4500.
  10. Universities heterogeneous catalysis: MIT Trout Romàn + Stanford Bent + Caltech Davis zeolite + UC Berkeley Bell Toste + Princeton + Cornell Archer + Georgia Tech Jones + UIUC + Penn State Chandler + Wisconsin-Madison Dumesic biomass + Minnesota Aris heritage Tsapatsis + Northwestern Marks + Delaware Vlachos.

Updated July 2026

Frequently Asked Questions

What is the Thiele modulus?

phi = L*sqrt(k/De) dimensionless ratio intrinsic reaction rate to internal diffusion in heterogeneous porous catalyst pellets. phi<0.4 reaction limited eta~1; 0.4-4 mixed; phi>4 diffusion limited eta~1/phi outer shell. Ernest Thiele Standard Oil Whiting 1939 + Aris 1965 Minnesota generalized. USA: ExxonMobil 62000 FCC + CF Industries 3000 ammonia + BASF Catalysts 4000 TWC + Pfizer 80000.

How do I calculate Thiele?

Procedure: (1) phi = L*sqrt(k/De); (2) L characteristic m (sphere R, slab semi-thickness, V_p/S_p Aris); (3) k 1/s 1° order; (4) De effective m^2/s = D*eps/tau; (5) eta_sphere = (3/phi^2)*(phi*coth(phi)-1); (6) regime. Pellet small: phi=0.3 eta~1. FCC: phi=15 eta~0.2. USA: MIT Romàn + Caltech Davis zeolite + Wisconsin Dumesic.

What is the effectiveness factor?

Effectiveness factor eta = rate observed/rate intrinsic isothermal pellet sphere first-order analytical eta_sphere = (3/phi^2)*(phi*coth(phi)-1) + slab tanh(phi)/phi + cylinder Bessel + phi4 eta~1/phi diffusion limited. Thiele 1939 + Aris 1965 generalized. USA: ExxonMobil FCC + CF Industries ammonia + BASF Catalysts TWC.

What regimes does phi classify?

phi<0.4 reaction limited kinetic + eta~1 + small pellet TWC; 0.4<phi<4 mixed internal diffusion + reaction balanced; phi>4 diffusion limited eta~1/phi shell core unused FCC zeolite Knudsen; phi>20 severe outer shell only. USA: ExxonMobil Baytown FCC + CF Industries ammonia + BASF Catalysts TWC washcoat + Plug Power PEM.

Who was Ernest Thiele?

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 + effectiveness factor + classical reactor design + 1957 'Notes on Distillation'.

What is the Weisz-Prater criterion?

Weisz-Prater criterion Paul Weisz + Charles Prater Mobil Research Princeton NJ 1954 paper Adv Catal 6:143 + observable rate-based criterion phi_W = phi^2*eta = rate*L^2/(De*C_s) + diffusion negligible if phi_W<0.15 + experimental design heterogeneous catalysis Mobil + Weisz also discovered zeolite shape selectivity ZSM-5. USA: Caltech Davis zeolite + Honeywell UOP.

What are Thiele applications?

Applications: FCC refineries USA ExxonMobil 62000 + Chevron 45000 + Marathon 17000 + Honeywell UOP 5000 FCC tech; ammonia Haber-Bosch CF Industries 3000 + Nutrien 27000 + Yara NA + Mosaic 13000; methanol Cu/ZnO Methanex; automotive TWC Pt-Pd-Rh BASF Catalysts 4000 + Johnson Matthey 5000 + Umicore + Tenneco 70000; pharma asymmetric Pfizer 80000 + Merck 73000 + JNJ + Codexis 600 biocatalysis; fuel cells PEM Plug Power 2400 + Bloom Energy 2000 SOFC + 3M Nafion + DuPont; chlor-alkali Olin 8500 + Westlake 16000.

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