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Chemical Reaction Engineering 제 1 장 Mole Balance 반응공학 I

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Chapter 1. Mole Balance 1.1Definition of the Rate of Reaction, -r A 1.2 The General Mole Balance Equation 1.3 Batch Reactors 1.4 Continuous-Flow Reactors 1.4.1Continuous-Stirred Tank Reactor 1.4.2Tubular Reactor 1.4.3Packed-Bed Reactor 1.5 Industrial Reactors

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The first step to knowledge is to know that we are ignorant Socrates (470-399 B.C.)

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Chapter 1. Mole Balance Objectives After completing Chapter 1, the reader will be able to: Define the rate of chemical reaction. Apply the mole balance equations to a batch reactor, CSTR, PFR, and PBR. Describe two industrial reaction engineering systems. Describe photos of real reactors.

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The identity of a chemical species The species nicotine is made up of a fixed number of a specific atoms in the specific atoms in a definite molecular arrangement or configuration. The structure shown illustrates the kind, number, and configuration of atoms in the species nicotine on a molecular level.

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The identity of a chemical species C=C H H CH 3 C=C H CH 3 H 2-butene has four carbon atoms and eight hydrogen atoms; however the atoms in this compound can form two different arrangements. cis-2-butene trans-2-butene As a consequence of the different configurations, these two isomers display different chemical and physical properties. Therefore, we consider them as two different species.

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We say that chemical reaction has taken place when a detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms. The identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms. When has a chemical reaction taken place?

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Three basic chemical reactions: 1. Decomposition ( 분해반응 ) 2. Combination ( 결합반응 ) 3. Isomerization ( 이성질화반응 ) A species can lose its identity by 3 reactions

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Three basic chemical reactions: When has a chemical reaction taken place? CH(CH 3 ) 2 + C 3 H 6 Decomposition Combination CH 2 =C-CH 2 CH 3 CH 3 CH 3 C=CHCH 3 CH 3IsomerizationIsomerization 분자가 그들의 화학적 동일성을 잃을 때 어떤 특정 화학성분 의 분자의 일정 개수가 반응 또는 소실되었다고 말한다.

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Reaction rate The rate of a reaction can be expressed as the rate of disappearance of a reactant or as the rate of appearance of a product. Consider species A: A → B r A r A : the rate of formation of species A per unit volume -r A -r A : the rate of disappearance of species A per unit volume r B r B : the rate of formation of species B per unit volume

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2C 6 H 5 Cl + CCl 3 CHO (C 6 H 4 Cl) 2 CHCCl 3 + H 2 O Chlorobenzene Chloral DDT (Dichloro Diphenyl-Trichloroethane) What is –r A (–r´ A )? Solely a function of properties of reacting materials. (Concentration, temperature, pressure, catalyst or solvent) An intensive quantity. An algebraic function of concentration. such as. for homogeneous system: for heterogeneous system: The numerical value of the rate of reaction, -r A, is defined as the number of moles of chloral reacting (disappearing) per unit time per unit volume [mol/dm 3 ·s]. Fuming H 2 SO 4

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Sodium Hydroxide Concentration in Batch Reactor NaOH CH 3 COOC 2 H 5 NaOH + CH 3 COOC 2 H 5 CH 3 COONa + C 2 H 5 OH Time CACA Constant-volume batch reactor Ethyl Acetate Sodium Acetate

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Ideal Reactor Type Batch Reactor -uniform composition everywhere in the reactor -the composition changes with time Continuous-Stirred Tank Reactor (CSTR) -uniform composition everywhere in the reactor (well mixed) -same composition at the reactor exit Tubular Reactor (PFR) -fluid passes through the reactor with no mixing of earlier and later entering fluid, and with no overtaking. -It is as if the fluid moved in single file through the reactor -There is no radial variation in concentration (plug-flow reactor)

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Is Sodium Hydroxide Reacting? NaOH CH 3 COOC 2 H 5 C 2 H 5 OH, CH 3 COONa, and unreacted NaOH and CH 3 COOC 2 H 5 NaOH + CH 3 COOC 2 H 5 CH 3 COONa + C 2 H 5 OH CSTR Steady state: the product is continuously withdrawn from the tank at a rate equal to the total feed rate. C A @ 1P.M. = C A @ 3P.M.

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Balance on control volume A mole balance on species j, at any time, t, yields N j G j = r j · V F j0 FjFj control volume Rate of flow of j into the system (mole/time) Rate of generation of j by chem. rxn within the system (mole/time) Rate of accumulation of j within the system (mole/time) Rate of flow of j out of the system (mole/time) - + = in - out + generation = accumulation

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Rate of formation of species j by chem. rxn r j1 r j2 V1V1 V2V2 V Suppose that the rate of formation of species j for the reaction varies with the position in the control volume. The rate of generation, G j1, in terms of r j1 and sub- volume V 1 is If the total control volume is divided into M sub-volume, the total rate of generation is By taking the appropriate limits (i.e., let M → and V → 0) and making use of the definition of integral, we can rewrite the foregoing equation in the form From this equation, we can see that r j will be an indirect function of position, since the properties of the reacting materials (e.g., conc., temp.) can have different values at difference locations in the reactor.

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1.2 The General Mole Balance Equation (GMBE) With this GMBE, we can develop the design equations for the various types of industrial reactors: batch, semi-batch, and continuous-flow. Upon evaluation of these equations we can determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of reactants to products.

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1.3 Batch Reactors If the reaction mixture is perfectly mixed so that there is no variation in the rate of reaction throughout the reactor volume, we can take r j out of the integral and write the GMBE in the form 00 t NANA A → B No spatial variations in the rate of reaction (1-5) N A0

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What time is necessary to reduce the initial number of moles from N A0 to N A1 ? (1-6) Integrating with limits that at t = 0, N A = N A0 at t = t 1, N A = N A1

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1.3 Batch Reactors t NANA N A0 A B t NBNB N B1 t1t1 t1t1 N A1

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Constant Volume or Constant Pressure CH 3 -O-CH 3 → CH 4 + H 2 + CO Constant volume (variable pressure) Constant pressure (variable volume)

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1.4.1 Continuous-Stirred Tank Reactor (CSTR) The CSTR is normally run at steady state and is assumed to be perfect mixed. - No temporal, spatial variations in conc., temp., or rxn rate throughout the vessel - Conc. and temp at exit are the same as they are elsewhere in the tank - Non-ideal mixing, residence-time distribution model is needed 0 No spatial variations in the rate of reaction Design Equation for a CSTR F j0 FjFj

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1.4.1 Continuous-Stirred Tank Reactor (CSTR) Design Equation for a CSTR F j0 FjFj

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1.4.2 Tubular Reactor - The reaction rate will also vary axially. - To develop the PFR design equation, we shall divide (conceptually) the reactor into a number of sub-volumes so that within each sub-volume V, the reaction rate may be considered spatially uniform. Let F j (y) represent the molar flow rate of species j into volume V at y F j (y+ y) represent the molar flow rate of species j out of volume V at (y+ y) In a spatially uniform sub-volume V,

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1.4.2 Tubular Reactor 0 r j is a function of reactant concentration, which is function of the position y down the reactor. Steady state (1-8) Substitute V into Eq. 1-8 and divide by y to yield Taking the limit as y approaches zero, we obtain

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Tubular Reactor It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady, The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.

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Tubular Reactor It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady, The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.

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Tubular Reactor V FAFA F A0 A B V FBFB F B1 V1V1 V1V1 F A1

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Packed-Bed Reactor (PBR) For a fluid-solid heterogeneous system, the rate of reaction of a substance A is defined as The mass of solid is used because the amount of the catalyst is what is important to the –r’ A In - out + generation = accumulation No pressure drop No catalyst decay

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The first-order reaction (liquid phase rxn) A B is carried out in a tubular reactor in which the volumetric flow rate, v 0, is constant. (1) Derive an equation relating the reactor volume (V) to the entering concentration of A (C A0 ), the rate constant k, and the volumetric flow rate v 0. (2) Determine the reactor volume necessary to reduce the exiting concentration (C A ) to 10% of the entering concentration (C A0 ) when the volumetric flow rate (v 0 ) is 10 ℓ/min and the specific reaction rate, k, is 0.23 min -1. Example 1-1 How large is it? (PFR) C A0 v 0 CACA V r A =-kC A

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Example 1-1 How large is it? (PFR) (GMBE for tubular reactor) (first-order reaction) Tubular, 1 st order rxn

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The first-order reaction (liquid phase rxn) A B is carried out in a CSTR in which the volumetric flow rate, v 0, is constant. (1) Derive an equation relating the reactor volume (V) to the entering concentration of A (C A0 ), the rate constant k, and the volumetric flow rate v 0. (2) Determine the reactor volume necessary to reduce the exiting concentration (C A ) to 10% of the entering concentration (C A0 ) when the volumetric flow rate (v 0 ) is 10 ℓ/min and the specific reaction rate, k, is 0.23 min -1. P1-6 B How large is it? (CSTR) V r A =-kC A F j0 FjFj

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For CSTR, the mole balance on species A was shown to be P1-6 B How large is it? (CSTR) V r A =-kC A F j0 FjFj The CSTR is almost 4 times larger than the PFR for getting 90% conversion

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Reactor Differential Algebraic Integral Mole Balance on Different Reactor Batch CSTR PFR PBR

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Homework 1.P1-7 A 2.P1-9 A 3.P1-11 B 4.P1-15 B Due Date: Next Week

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