MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN
CONTENTS CHAPTER ONE REACTION MECHANISMS AND RATE EXPRESSIONS INTRODUCTION TYPICAL REACTION MECHANISMS REACTION MECHANISMS ELEMENTARY AND NON-ELEMENTARY REACTIONS TYPES OF INTERMEDIATE THE ARRHENIUS EQUATION AND THE COLLISION THEORY TRANSITION STATE THEORY CHAIN REACTIONS CATALYTIC REACTIONS GUIDELINES TO FORMULATING REACTION MECHANISM TESTING KINETIC MODELS CHAIN LENGTH REFERENCES CHAPTER TWO THERMODYNAMICS OF CHEMICAL REACTIONS CHEMICAL EQUILIBRIUM CRITERIA FOR EQUILIBRIUM REACTION EQUILIBRIUM IDEAL GAS MIXTURES REAL GASES—IDEAL GASEOUS SOLUTIONS REAL GASES LIQUID STATE DETERMINING THE FUGACITY AND THE FUGACITY COEFFICIENT PARTIAL MOLAR QUANTITIES EFFECT OF TEMPERATURE ON THE EQUILIBRIUM CONSTANT HEATS OF REACTION HEAT CAPACITIES OF GASES HEATS OF FORMATION APPENDIX CHAPTER THREE REACTION RATE EXPRESSION REACTION RATE EQUATION REACTION ORDERS DETERMINING THE ORDER OF REACTIONS EMPIRICAL RATE EQUATIONS OF THE NTH ORDER METHOD OF HALF-LIFE T1/2 PARALLEL REACTIONS HOMOGENEOUS CATALYZED REACTIONS AUTOCATALYTIC REACTIONS IRREVERSIBLE REACTIONS IN SERIES FIRST ORDER REVERSIBLE REACTIONS SECOND ORDER REVERSIBLE REACTIONS GENERAL REVERSIBLE REACTIONS SIMULTANEOUS IRREVERSIBLE SIDE REACTION PSEUDO-ORDER REACTION PRACTICAL MEASUREMENTS OF REACTION RATES REGRESSION ANALYSIS WEIGHTED LEAST SQUARES ANALYSIS PROBLEMS AND ERRORS IN FITTING RATE MODELS CHAPTER FOUR INDUSTRIAL AND LABORATORY REACTORS BATCH ISOTHERMAL PERFECTLY STIRRED REACTOR SEMI-BATCH REACTORS CONTINUOUS FLOW ISOTHERMAL PERFECTLY STIRRED TANK REACTOR CONTINUOUS ISOTHERMAL PLUG FLOW TUBULAR REACTOR CONTINUOUS MULTIPHASE REACTORS FLUIDIZED BED SYSTEM FLUID CATALYTIC CRACKING (FCC) UNIT DEEP CATALYTIC CRACKING UNIT DETERMINING LABORATORY REACTORS GUIDELINES FOR SELECTING BATCH PROCESSES CHAPTER FIVE INTRODUCTION TO REACTOR DESIGN FUNDAMENTALS FOR IDEAL SYSTEMS A GENERAL APPROACH IDEAL ISOTHERMAL REACTORS NUMERICAL METHODS FOR REACTOR SYSTEMS DESIGN REVERSIBLE SERIES REACTIONS THE SEMIBATCH REACTOR CONTINUOUS FLOW STIRRED TANK REACTOR (CFSTR) MULTI-STAGE CONTINUOUS FLOW STIRRED TANK REACTOR EQUAL SIZE CFSTR IN SERIES SPACE TIME (ST) AND SPACE VELOCITY (SV) FRACTIONAL CONVERSION, YIELD, AND SELECTIVITY IN REACTORS RELATIONSHIP BETWEEN CONVERSION, SELECTIVITY, AND YIELD PLUG FLOW REACTOR HETEROGENEOUS TUBULAR REACTOR DESIGN EQUATION FOR SYSTEMS OF VARIABLE DENSITY DESIGN EQUATIONS FOR HETEROGENEOUS REACTIONS COMPARISON OF IDEAL REACTORS CFSTR AND PLUG FLOW SYSTEMS DYNAMIC BEHAVIOR OF IDEAL SYSTEMS FLOW RECYCLE REACTOR CHAPTER SIX NON-ISOTHERMAL REACTORS OPERATING TEMPERATURE, REACTION TYPES, AND TEMPERATURE EFFECT OF OPERATING PARAMETERS ON EQUILIBRIUM CONVERSION ENERGY BALANCE AND HEAT OF REACTION ENERGY TRANSFERRED BETWEEN THE SYSTEM AND SURROUNDINGS BATCH REACTOR AUTOTHERMAL REACTORS CONVERSION IN AMMONIA SYNTHESIS TWO-DIMENSIONAL TUBULAR (PLUG FLOW) REACTOR PRESSURE DROP (?P) IN TUBULAR (PLUG FLOW) REACTORS THERMAL BEHAVIORS IN FLOW SYSTEMS EXOTHERMIC REACTIONS IN CFSTRS THERMAL BEHAVIOR OF A TUBULAR FLOW REACTOR VARIABLE COOLANT TEMPERATURE IN A CFSTR OPTIMAL DESIGN OF NON-ISOTHERMAL REACTORS MIMIMUM REACTOR VOLUME AT THE OPTIMUM TEMPERATURE PROGRESSION (OTP) OF A SINGLE CFSTR WITH A REVERSIBLE EXOTHERMIC REACTION OPTIMUM REACTOR SIZE CHAPTER SEVEN FLUID MIXING IN REACTORS MIXING AND AGITATION OF FLUIDS SIMILARITY MIXING TIME CORRELATION SCALE-UP OF MIXING SYSTEMS STATIC MIXERS HEAT TRANSFER IN AGITATED VESSELS LIQUID-SOLID AGITATION BATCH HEATING AND COOLING OF FLUIDS DESIGN OF MIXING SYSTEMS CHAPTER EIGHT RESIDENCE TIME DISTRIBUTIONS IN FLOW REACTORS THE RESIDENCE TIME DISTRIBUTION FUNCTIONS AND THEIR RELATIONSHIPS DETERMINING RTD FROM EXPERIMENTAL TRACER CURVES ANALYSIS OF RTD FROM PULSE INPUT RESIDENCE TIME DISTRIBUTION FOR A LAMINAR FLOW TUBULAR REACTOR E- AND F-CURVES FOR A SERIES OF STIRRED TANK REACTORS RTD FUNCTIONS FOR CSTRS WHERE N IS NOT AN INTEGER THE DISPERSION MODEL COMPARISON OF TANK IN SERIES (TIS) AND DISPERSION PLUG FLOW (DPF) MODELS RESIDENCE TIME DISTRIBUTION IN A STATIC MIXER GLOSSARY CHAPTER NINE MODELS FOR NON-IDEAL SYSTEMS BASICS OF NON-IDEAL FLOW SEGREGATED FLOW MODEL COMPLETE SEGREGATION MODEL WITH SIDE EXITS MAXIMUM MIXEDNESS MODEL (MMM) EFFECT OF MICROMIXING ON CONVERSION CHAPTER TEN APPLICATION OF COMPUTATIONAL FLUID DYNAMICS AND COMPUTATIONAL FLUID MIXING IN REACTORS THEORY AND FLUID FLOW EQUATIONS TURBULENCE ON TIME-AVERAGED NAVIER-STOKES EQUATIONS TIME-DEPENDENT TURBULENT MIXING AND CHEMICAL REACTION IN STIRRED TANKS REFERENCES AND RECOMMENDED READING NOMENCLATURE IMPROVE REACTORS VIA COMPUTATIONAL FLUID DYNAMICS CHAPTER ELEVEN BIOCHEMICAL REACTION KINETICS OF ENZYME-CATALYZED REACTIONS MODELS OF ENZYME KINETICS ENZYME KINETICS IN THE PRESENCE OF AN INHIBITOR FERMENTATION DESIGN OF BIOLOGICAL REACTORS VESSEL DESIGN AND ASPECT RATIO TYPES OF OPERATION CELL GROWTH MODELING BIOLOGICAL REACTORS GENERAL MODEL FOR A SINGLE VESSEL THE CHEMOSTAT BATCH FERMENTER FED-BATCH REACTOR SCALE-UP OF BIOREACTORS CHAPTER TWELVE SAFETY IN CHEMICAL REACTION ENGINEERING HAZARD EVALUATION IN THE CHEMICAL PROCESS INDUSTRIES HAZARD ASSESSMENT PROCEDURES THERMAL RUNAWAY CHEMICAL REACTION HAZARDS THE ?-FACTOR ONSET TEMPERATURE TEST INSTRUMENTS TWO-PHASE FLOW RELIEF SIZING FOR RUNAWAY REACTION VENT SIZING METHODS DISCHARGE SYSTEM INHERENTLY SAFE PLANTS IN REACTOR SYSTEMS HAZARD AND OPERABILITY STUDIES (HAZOP) CHAPTER THIRTEEN SCALE-UP IN REACTOR DESIGN DEVELOPMENT AND SCALE-UP OF REACTORS SIMILARITY CRITERIA SCALE-UP IN RELATION TO VARIOUS FACTORS HEAT EFFECT COEFFICIENTS OF PROCESS STABILITY DIMENSIONAL ANALYSIS AND SCALE-UP EQUATIONS MATHEMATICAL MODELING SCALE-UP OF A BATCH REACTOR HEAT TRANSFER MODEL JACKET ZONING OF A BATCH REACTOR THE OUTLET TEMPERATURE OF A SCALED-UP BATCH SYSTEM ASPECT RATIO (R) IN JACKET ZONING AND SCALE-UP OF A BATCH REACTOR CHAPTER ONE REACTION MECHANISMS AND RATE EXPRESSIONS INTRODUCTION THE FIELD OF CHEMICAL KINETICS AND REACTION ENGINEERING HAS GROWN OVER THE YEARS NEW EXPERIMENTAL TECHNIQUES HAVE BEEN DEVELOPED TO FOLLOW THE PROGRESS OF CHEMICAL REACTIONS AND THESE HAVE AIDED STUDY OF THE FUNDAMENTALS AND MECHANISMS OF CHEMICAL REACTIONS THE AVAILABILITY OF PERSONAL COMPUTERS HAS ENHANCED THE SIMULATION OF COMPLEX CHEMICAL REACTIONS AND REACTOR STABILITY ANALYSIS THESE ACTIVITIES HAVE RESULTED IN IMPROVED DESIGNS OF INDUSTRIAL REACTORS AN INCREASED NUMBER OF INDUSTRIAL PATENTS NOW RELATE TO NEW CATALYSTS AND CATALYTIC PROCESSES, SYNTHETIC POLYMERS, AND NOVEL REACTOR DESIGNS LIN [1] HAS GIVEN A COMPREHENSIVE REVIEW OF CHEMICAL REACTIONS INVOLVING KINETICS AND MECHANISMS CONVENTIONAL STOICHIOMETRIC EQUATIONS SHOW THE REACTANTS THAT TAKE PART AND THE PRODUCTS FORMED IN A CHEMICAL REACTION HOWEVER, THERE IS NO INDICATION ABOUT WHAT TAKES PLACE DURING THIS CHANGE A DETAILED DESCRIPTION OF A CHEMICAL REACTION OUTLINING EACH SEPARATE STAGE IS REFERRED TO AS THE MECHANISM MECHANISMS OF REACTIONS ARE BASED ON EXPERIMENTAL DATA, WHICH ARE SELDOM COMPLETE, CONCERNING TRANSITION STATES AND UNSTABLE INTERMEDIATES THEREFORE, THEY MUST TO BE CON- TINUALLY AUDITED AND MODIFIED AS MORE INFORMATION IS OBTAINED REACTION STEPS ARE SOMETIMES TOO COMPLEX TO FOLLOW IN DETAIL IN SUCH CASES, STUDYING THE ENERGY OF A PARTICULAR REACTION MAY ELUCIDATE WHETHER OR NOT ANY INTERMEDIATE REACTION IS PRODUCED ENERGY IN THE FORM OF HEAT MUST BE PROVIDED TO THE REACTANTS TO ENABLE THE NECESSARY BONDS TO BE BROKEN THE REACTANT MOLECULES BECOME ACTIVATED BECAUSE OF THEIR GREATER ENERGY CONTENT THIS CHANGE CAN BE REFERRED TO AS THE ACTIVATED COMPLEX OR TRANSITION STATE, AND CAN BE REPRESENTED BY THE CURVE OF FIGURE 1-1 THE COMPLEX IS THE LEAST STABLE STATE THROUGH WHICH THE REACTANTS PASS BEFORE FORMING THE PRODUCTS THE AMOUNT OF ENERGY REQUIRED TO RAISE THE REACTANT MOLECULES TO THIS STATE IS KNOWN AS THE ACTIVATION ENERGY, EA THIS ENERGY IS IMPORTANT IN DETERMINING THE RATE AT WHICH A REACTION PROCEEDS THE USE OF A CATALYST AFFECTS THE RATE OF REACTION BY ENABLING THE PRODUCTS TO FORM BY AN ALTERNATIVE ROUTE EACH STAGE HAS LOWER ACTIVA- TION ENERGY THAN THE UNCATALYZED REACTION ONCE THE REACTANTS HAVE ABSORBED SUFFICIENT ENERGY TO CROSS OVER THIS PEAK, ENERGY IS THEN RELEASED AS THE NEW BONDS ARE MADE IN YIELDING THE STABLE PRODUCTS FOR REACTIONS AT CONSTANT PRESSURE, THE DIFFERENCE BETWEEN THE AMOUNT OF ENERGY PROVIDED TO BREAK THE BONDS OF THE REACTANTS AND THAT EVOLVED DURING THE FORMATION OF NEW MOLE- CULES IS TERMED THE ENTHALPY OF REACTION, ?HR WHEN MORE ENERGY IS EVOLVED THAN ABSORBED, THE REACTION IS EXOTHERMIC, THAT IS, ?HR IS NEGA- TIVE AS SHOWN IN FIGURE 1-1 ALTERNATIVELY, WHEN LESS ENERGY IS EVOLVED THAN ABSORBED, THE REACTION IS ENDOTHERMIC, THAT IS, ?HR IS POSITIVE AS INDICATED BY FIGURE 1-2 PRODUCTS FORMED THROUGH AN EXOTHERMIC REACTION HAVE A LOWER ENERGY CONTENT THAN THE REACTANTS FROM WHICH THEY ARE FORMED ALTER- NATIVELY, PRODUCTS FORMED VIA AN EXOTHERMIC PROCESS HAVE A HIGHER FIGURE 1-1 POTENTIAL ENERGY CURVE FOR AN EXOTHERMIC REACTION MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN ENERGY CONTENT THAN THEIR REACTANTS IN GENERAL, EXOTHERMIC COMPOUNDS ARE MORE STABLE THAN ENDOTHERMIC COMPOUNDS THERE ARE CASES WHERE THE ACTIVATED COMPLEX EXISTS AS AN UNSTABLE INTERMEDIATE THIS IS OBSERVED IN REACTION PROFILE AS A TROUGH IN THE ACTIVATED PEAK OF THE CURVE THIS PRODUCES A DOUBLE HUMP AND AS THE MINIMUM IN THE TROUGH IS MORE MARKED, THAT IS, AS THE INTERMEDIATE BECOMES MORE STABLE, IT BECOMES MORE DIFFICULT TO SEPARATE THE INTER- MEDIATE FROM THE REACTION MIXTURE DURING THE COURSE OF THE REACTION FIGURE 1-3 SHOWS THE CURVE OF AN UNSTABLE INTERMEDIATE GENERALLY, ALL PRACTICAL REACTIONS OCCUR BY A SEQUENCE OF ELEMENTARY STEPS THAT COLLECTIVELY CONSTITUTE THE MECHANISM THE RATE EQUATION FOR THE OVERALL REACTION IS DEVELOPED FROM THE MECHANISM AND IS THEN USED IN REACTOR DESIGN ALTHOUGH THERE ARE CASES WHERE EXPERIMENTAL DATA PROVIDE NO INFORMATION ABOUT INTERMEDIATE CHEMICAL SPECIES, EXPERI- MENTAL DATA HAVE PROVIDED RESEARCHERS WITH USEFUL GUIDELINES IN POSTULATING REACTION MECHANISMS INFORMATION ABOUT INTERMEDIATE SPECIES IS ESSENTIAL IN IDENTIFYING THE CORRECT MECHANISM OF REACTION WHERE MANY STEPS ARE USED, DIFFERENT MECHANISMS CAN PRODUCE SIMILAR FORMS OF OVERALL RATE EXPRESSION THE OVERALL RATE EQUATION IS THE RESULT FIGURE 1-2 POTENTIAL ENERGY CURVE FOR AN ENDOTHERMIC REACTION MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN OF THE CORRECT MECHANISM AND IS DEVELOPED IN TERMS OF CONCENTRATIONS OF THE REACTANTS AND PRODUCTS IN THE CASE OF COMPLEX CHEMICAL REAC- TIONS, THE OVERALL RATE EQUATION MAY BE ERRONEOUS FOR REACTOR DESIGN THEREFORE, ASSUMPTIONS ARE EMPLOYED TO MAKE A SATISFACTORY KINETIC REPRESENTATION RESULTING IN THE DESIGN OF A RELIABLE REACTOR CHEMISTS AND ENGINEERS INTERPRET THE MECHANISMS IN DIFFERENT WAYS THE CHEMIST DEFINES THE REACTION MECHANISM AS HOW THE ELECTRON DENSITIES AROUND THE MOLECULE MOVE IN ORDER TO PROVIDE CHARGED AREAS, ALLOWING THE SECOND REACTANT TO ATTACH BECAUSE OF INDUCED OPPOSITE CHARGE THE ACTIVATED COMPLEX HAS A MODIFIED ELECTRON STRUCTURE THAT RESULTS IN PART OF THE COMPLEX BEING WEAKLY ATTACHED, THEREBY MAKING DETACHMENT POSSIBLE THE OVERALL REARRANGEMENT OF THE CHARGES AROUND THE MOLECULES GIVES THE PRODUCT OF THE REACTION THE CHEMICAL ENGINEER, ON THE OTHER HAND, OFTEN VIEWS THE MECHANISM IN TERMS OF ITS REACTION STEPS, WHERE EACH STEP CHANGES FROM ONE DISTINCT CHEMICAL SPECIES TO ANOTHER THIS REDUCES THE REACTION MECHANISM SO THAT IT CAN BE TREATED QUANTITATIVELY THE FOLLOWING DESCRIBES MANY TYPES OF REACTION MECHANISMS WITH A VIEW TOWARD DEVELOPING THEIR OVERALL RATE EXPRESSIONS FIGURE 1-3 POTENTIAL ENERGY CURVE FOR REACTIONS SHOWING THE UNSTABLE INTER- MEDIATE STATE MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN TYPICAL REACTION MECHANISMS CRACKING OF ALKANES (PARAFFINS CNH2N+2) PYROLYSIS OF ALKANES IS REFERRED TO AS CRACKING ALKANES FROM THE PARAFFINS (KEROSENE) FRACTION IN THE VAPOR STATE ARE PASSED THROUGH A METAL CHAMBER HEATED TO 400–700°C METALLIC OXIDES ARE USED AS A CATALYST THE STARTING ALKANES ARE BROKEN DOWN INTO A MIXTURE OF SMALLER ALKANES, ALKENES, AND SOME HYDROGEN ALKANES SMALLER ALKANES ALKENES H O C ? ? ? ???? + + FOR EXAMPLE: 400 CH CH CH CH CH CH CH CH CH H O C ? ? ? ???? + = + = + (1-1) PROPENE ETHENE MECHANISM THE REACTION PROCEEDS VIA A FREE RADICAL MECHANISM WITH HOMOLYTIC FISSION OCCURING BETWEEN THE CARBON-CARBON ATOMS THE MECHANISM OF REACTIONS FOR THE CRACKING OF PROPANE IS: CHAIN INITIATION: 1 CH CH CH CH CH CH ? ? + ? ? (1-2) CHAIN PROPAGATION: 2 CH CH CH CH H * * ? = + (1-3) 3 CH CH CH H H CH CHCH + ? + * ? (1-4) 4 CH CH CH CH CH CH CHCH + ? + * ? (1-5) CHAIN TERMINATION: 5 CH CH CH CH CH CH ?? = + (1-6) 6 CH CHCH CH CH CH CH CH CH ? ? = + (1-7) MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN SULFUR DIOXIDE OXIDATION THE OVERALL STOICHIOMETRIC EQUATION IS: SO O SO THAT EXISTS ON THE SUPPORT AT OPERATING CONDITIONS IN THE MOLTEN STATE THE MECHANISM OF REACTION IS: 1 SO V O SO V + + + + ? + [ (1-9) 2 O V V O + + [ ] + + ? [ (1-10) 3 O V V O ? + + ? + + [ ] [ (1-11) 4 O V V O ? + + ? + + [ (1-12) AMMONIA SYNTHESIS THE OVERALL STOICHIOMETRIC EQUATION IS: N H NH + ? (1-13) STUDIES OF AMMONIA SYNTHESIS ON IRON CATALYST SUGGEST THAT THE REACTION OCCURS THROUGH SURFACE IMINE RADICALS MECHANISM THE FOLLOWING ELEMENTARY STEPS ARE: 1 N2(G) ? 2N(ADS) (1-14) 2 H2(G) ? 2H(ADS) (1-15) 3 N(ADS) + H(ADS) ? NH(ADS) (1-16) MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN 4 NH H NH ADS ADS ADS ( ) ( ) ( ) + ? (1-17) 5 NH H NH ADS ADS ADS ( ) ( ) ( ) + ? (1-18) 6 NH NH ADS G ( ) ( ) ? (1-19) THE “ADS” DENOTES THE ADSORBED SPECIES AMMONIA OXIDATION THE OVERALL STOICHIOMETRIC REACTION FOR THE OXIDATION OF AMMONIA TO NITRIC OXIDE IS: NH O NO H O + ? + (1-20) THIS REACTION IS VERY RAPID AND HAS BEEN DIFFICULT TO STUDY MECHAN- ISTICALLY THE DIRECT OXIDATION OF AMMONIA, NH3, TO NITRIC OXIDE, NO, OVER PLATINUM CATALYST IS ONE OF THE MAJOR STEPS IN THE MANUFACTURE OF NITRIC ACID, HNO3 MECHANISM 1 O O ? ? (1-21) 2 NH O NH OH + ? ? (1-22) 3 NH OH NH H O ? + ? (1-23) 4 NH O HNO ?+ ? (1-24) 5 HNO NO OH 2 ? + ? (1-25) 6 OH H O O ? ? ? + (1-26) THE OXYGEN IS CHEMISORBED ON THE CATALYST THIS THEN REACTS WITH AMMONIA TO PRODUCE A CHEMISORBED IMIDE RADICAL THE IMIDE REACTS WITH A MOLECULAR OXYGEN TO YIELD NITRIC OXIDE STEAM REFORMING STEAM REFORMING IS AN IMPORTANT PROCESS TO GENERATE HYDROGEN FOR SUCH USES AS AMMONIA SYNTHESIS BECAUSE OF THE HIGH ENDOTHERMIC HEAT REACTION AND ITS RAPIDITY HIGH HEAT FLUXES WITH A DIRECT-FIRED FURNACE ARE REQUIRED ALTHOUGH MANY STEPS OF REACTIONS ARE POSSIBLE, THE TYPICAL REACTION STEPS ARE AS FOLLOWS: MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN 1 CH H O H CO + ? + (1-27) 2 CH H O H CO + ? + (1-28) 3 CO H O CO H + ? + (1-29) 4 CH CO CO H + ? + (1-30) 5 CO H C H O + + [ (1-31) 6 CH C H [ + (1-32) 7 CO C CO [ + (1-33) BIOCHEMICAL REACTION: CONVERSION OF GLUCOSE TO GLUCONIC ACID THE FERMENTATION OF GLUCOSE TO GLUCONIC ACID INVOLVES OXIDATION OF THE SUGAR IN THE ALDEHYDE GROUP (RCHO), THEREBY CONVERTING IT TO A CARBOXYL GROUP (RCOOH) THE CONVERSION PROCESS IS ACHIEVED BY A MICRO-ORGANISM IN THE FERMENTATION PROCESS THE ENZYME GLUCOSE OXIDASE THAT IS PRESENT IN THE MICRO-ORGANISM CONVERTS THE GLUCOSE TO GLUCONOLACTONE THE GLUCONOLACTONE IS FURTHER HYDROLYZED TO FORM THE GLUCONIC ACID THE ENZYME GLUCOSE OXIDASE IS USEFUL IN MEDICINAL APPLICATIONS WHERE GLUCOSE OR OXYGEN REMOVAL IS REQUIRED THIS ENZYME PREVENTS THE BROWNING REACTION, OR A MAILLAND REACTION, WHEN DRIED EGG POWDERS ARE DARKENED DUE TO A REACTION BETWEEN GLUCOSE AND PROTEIN ALSO, THE PRESENCE OF OXYGEN IN THE PRODUCTION AND STORAGE OF ORANGE SOFT DRINKS, DRIED FOOD POWDERS, CANNED BEVERAGES, SALAD DRESSING, AND CHEESE SLICES CAN BE AVOIDED BY ADDING GLUCOSE OXIDASE SINCE THE ACTIVITY OF THE ENZYME IS MAINTAINED FOR A LONG TIME AT STORAGE TEMPERATURE, SUCH ENZYME ADDITIONS INCREASE THE SHELF-LIFE OF FOOD PRODUCTS THIS IS ACHIEVED BY THE REMOVAL OF OXYGEN THAT DIFFUSES THROUGH FOOD PACKAGING [2] THE HYDROGEN PEROXIDE PRODUCED IN THE GLUCOSE OXIDASE CATALYZED REACTION HAS AN ANTIBACTERIAL ACTION THE ADDITION OF A CATALASE CATALYZES THE DECOMPOSITION OF HYDROGEN PEROXIDE TO WATER AND OXYGEN REACTION MECHANISMS THE REACTION MECHANISMS IN THE FERMENTATION OF GLUCOSE TO GLUCONIC ACID ARE: MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN 1 CELL GROWTH: GLUCOSE + CELLS ? MORE CELLS THAT IS: C6H12O6 + CELLS ? MORE CELLS (1-34) 2 GLUCOSE OXIDATION: GLUCOSE O GLUCONOLACTONE H O GLUCOSE OXIDASE + ? ? ????? + THAT IS: C H O O C H O H O + ? ? ????? + (1-35) 3 GLUCONOLACTONE HYDROLYSIS: GLUCONOLACTONE H O GLUCONIC ACID + ? THAT IS: C H O H O C H O COOH + ?? ? (1-36) 4 HYDROGEN PEROXIDE DECOMPOSITION: H O H O 2 O CATALASE ? ? ??? + (1-37) ANALYSIS OF THE RATE EQUATION AND KINETIC MODEL OF THE CONVERSION OF GLUCOSE TO GLUCONIC ACID IS DISCUSSED IN CHAPTER 11 ELEMENTARY AND NON-ELEMENTARY REACTIONS CONSIDER THE REACTION BETWEEN HYDROGEN AND BROMINE IN THE GAS PHASE: H BR HBR + ? (1-38) BODENSTEIN AND LIND [3] FIRST STUDIED THE THERMAL REACTION OVER THE TEMPERATURE RANGE OF 500–600 K THE RELATIVE REACTION RATES OF HYDRO- GEN AND BROMINE AND THE FORMATION OF HYDROGEN BROMIDE ARE: MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN ?( ) = ?( ) = +( ) R R R H BR HBR (1-39) AND, IF THE REACTION TOOK PLACE IN A SINGLE STEP, THEN THE RATE EXPRESSION MAY BE REPRESENTED AS: +( ) = R K C C HBR H BR (1-40) THE SLOPE OF A CONCENTRATION-TIME CURVE TO DEFINE THE RATE EXPRESSION CAN BE DETERMINED HOWEVER, EXPERIMENTAL STUDIES HAVE SHOWN THE REAC- TION CANNOT BE DESCRIBED BY SIMPLE KINETICS, BUT BY THE RELATIONSHIP: +( )= + R K C C K C C HBR H BR HBR BR (1-41) WHERE K1 AND K2 ARE THE RATE CONSTANTS THE REACTION BETWEEN HYDROGEN AND BROMINE IS AN EXAMPLE OF A NON-ELEMENTARY REACTION THE FOLLOW- ING STEPS ACCOUNT FOR THE RATE EXPRESSION: BR BR ? * (1-42) BR H HBR H * * + ? + (1-43) H HBR BR H * * + ? + (1-44) BR* AND H* BEING HIGHLY REACTIVE INTERMEDIATES TYPES OF INTERMEDIATE STABLE INTERMEDIATES STABLE INTERMEDIATES ARE THOSE WHERE CONCENTRATION AND LIFESPAN ARE COMPARABLE TO THOSE OF STABLE REACTANTS AND PRODUCTS AN EXAMPLE IS THE REACTION BETWEEN METHANE AND OXYGEN IN THE GAS PHASE AT 700 K AND 1 ATMOSPHERE THE OVERALL REACTION IS: CH O CO H O + ? + (1-45) MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN SUCCESSIVE SINGLE REACTIONS ARE: CH O CH O H O + ? + (1-46) (FORMALDEHYDE) CH O O CO H O + ? + (1-47) CO O CO + ? (1-48) H O H O O ? + (1-49) IN THESE REACTIONS, THE STABLE INTERMEDIATES ARE CH2O, CO, AND H2O2 ACTIVE CENTERS REACTIONS THAT ARE CATALYZED BY SOLIDS OCCUR ON THE SURFACES OF THE SOLIDS AT POINTS OF HIGH CHEMICAL ACTIVITY THEREFORE, THE ACTIVITY OF A CATALYTIC SURFACE IS PROPORTIONAL TO THE NUMBER OF ACTIVE CENTERS PER UNIT AREA IN MANY CASES, THE CONCENTRATION OF ACTIVE CENTERS IS RELATIVELY LOW THIS IS EVIDENT BY THE SMALL QUANTITIES OF POISONS PRESENT (MATERIAL THAT RETARDS THE RATE OF A CATALYTIC REACTION) THAT ARE SUFFICIENT TO DESTROY THE ACTIVITY OF A CATALYST ACTIVE CENTERS DEPEND ON THE INTERATOMIC SPACING OF THE SOLID STRUCTURE, CHEMICAL CONSTITUTION, AND LATTICE STRUCTURE GENERALLY, ACTIVE CENTERS ARE HIGHLY REACTIVE INTERMEDIATES PRESENT IN VERY SMALL CONCENTRATIONS WITH SHORT LIFESPANS FOR EXAMPLE, IN THE CASE OF H BR HBR + ? (1-50) H* AND BR* AND IN THE CASE OF CH CHO CH CO ? + (1-51) CH CHO CH CO ? ? ? , , MODELING OF CHEMICAL KINETICS AND REACTOR DESIGN