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Chemical Reaction Engineering 제 1 장 Mole Balance 반응공학 I.

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Presentation on theme: "Chemical Reaction Engineering 제 1 장 Mole Balance 반응공학 I."— Presentation transcript:

1 Chemical Reaction Engineering 제 1 장 Mole Balance 반응공학 I

2 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

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

4 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.

5 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.

6 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.

7 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?

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

9 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.

10 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

11 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

12 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

13 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)

14 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.

15 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

16 Rate of formation of species j by chem. rxn r j1 r j2 V1V1 V2V2 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.

17 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.

18 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

19 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

20 1.3 Batch Reactors t NANA N A0 A B t NBNB N B1 t1t1 t1t1 N A1

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

22 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

23 1.4.1 Continuous-Stirred Tank Reactor (CSTR) Design Equation for a CSTR F j0 FjFj

24 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,

25 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

26 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.

27 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.

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

29 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

30 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

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

32 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

33 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

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

35 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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