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제1장 Mole Balance Chemical Reaction Engineering 반응공학 I

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**Chapter 1. Mole Balance 1.1 Definition of the Rate of Reaction, -rA**

1.2 The General Mole Balance Equation 1.3 Batch Reactors 1.4 Continuous-Flow Reactors 1.4.1 Continuous-Stirred Tank Reactor 1.4.2 Tubular Reactor 1.4.3 Packed-Bed Reactor 1.5 Industrial Reactors

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**Socrates (470-399 B.C.) The first step to knowledge**

The first step to knowledge is to know that we are ignorant

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**Objectives Chapter 1. Mole Balance**

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 cis-2-butene trans-2-butene**

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. H H H CH3 C=C C=C CH3 CH3 CH3 H

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**When has a chemical reaction taken place?**

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.

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**A species can lose its identity by 3 reactions**

Three basic chemical reactions: 1. Decomposition (분해반응) 2. Combination (결합반응) 3. Isomerization (이성질화반응)

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**When has a chemical reaction taken place?**

Three basic chemical reactions: CH(CH3)2 + C3H6 Decomposition Combination CH2=C-CH2CH3 CH3 CH3C=CHCH3 Isomerization 분자가 그들의 화학적 동일성을 잃을 때 어떤 특정 화학성분의 분자의 일정 개수가 반응 또는 소실되었다고 말한다.

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**Reaction rate rA: the rate of formation of species A per unit volume**

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 rA: the rate of formation of species A per unit volume -rA: the rate of disappearance of species A per unit volume rB: the rate of formation of species B per unit volume

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What is –r A (–r´A )? 2C6H5Cl CCl3CHO (C6H4Cl)2CHCCl H2O Chlorobenzene Chloral DDT (Dichloro Diphenyl-Trichloroethane) Fuming H2SO4 The numerical value of the rate of reaction, -rA, is defined as the number of moles of chloral reacting (disappearing) per unit time per unit volume [mol/dm3·s]. 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:

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**Sodium Hydroxide Concentration in Batch Reactor**

NaOH + CH3COOC2H5 CH3COONa + C2H5OH Ethyl Acetate Sodium Acetate Constant-volume batch reactor NaOH CH3COOC2H5 CA Time

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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 + CH3COOC2H5 CH3COONa + C2H5OH CSTR NaOH CH3COOC2H5 1P.M. = 3P.M. C2H5OH, CH3COONa, and unreacted NaOH and CH3COOC2H5 Steady state: the product is continuously withdrawn from the tank at a rate equal to the total feed rate.

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**Balance on control volume**

Nj Gj = rj · V Fj0 Fj A mole balance on species j, at any time, t, yields Rate of flow of j into the system (mole/time) Rate of flow of j out of 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) - + = in out generation = accumulation

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**Rate of formation of species j by chem. rxn**

Suppose that the rate of formation of species j for the reaction varies with the position in the control volume. The rate of generation, DGj1, in terms of rj1 and sub-volume DV1 is DV1 DV2 V rj1 rj2 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 DV → 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 A → B NA (1-5) t**

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 rj out of the integral and write the GMBE in the form No spatial variations in the rate of reaction NA0 A → B NA (1-5) t

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**What time is necessary to reduce the initial number of moles**

from NA0 to NA1? Integrating with limits that at t = 0, NA = NA0 at t = t1, NA = NA1 (1-6)

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1.3 Batch Reactors A B NA0 NB1 NA NB NA1 t1 t1 t t

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**Constant Volume or Constant Pressure**

CH3-O-CH3 → CH4 + H2 + CO Constant volume (variable pressure) Constant pressure (variable volume)

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**1.4.1 Continuous-Stirred Tank Reactor (CSTR)**

Fj0 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 Fj No spatial variations in the rate of reaction Design Equation for a CSTR

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**1.4.1 Continuous-Stirred Tank Reactor (CSTR)**

Fj0 Design Equation for a CSTR Fj

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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 DV, the reaction rate may be considered spatially uniform. Let Fj(y) represent the molar flow rate of species j into volume DV at y Fj(y+D y) represent the molar flow rate of species j out of volume DV at (y+D y) In a spatially uniform sub-volume DV,

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Tubular Reactor Steady state (1-8) rj is a function of reactant concentration, which is function of the position y down the reactor. Substitute DV into Eq. 1-8 and divide by Dy to yield Taking the limit as Dy 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 A B FA0 FB1 FA FB FA1 V1 V1 V V

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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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**Example 1-1 How large is it? (PFR)**

CA0 v0 CA V rA=-kCA The first-order reaction (liquid phase rxn) A B is carried out in a tubular reactor in which the volumetric flow rate, v0, is constant. (1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow rate v0. (2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is 0.23 min-1.

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**Example 1-1 How large is it? (PFR)**

(GMBE for tubular reactor) (first-order reaction) Tubular, 1st order rxn

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**P1-6B How large is it? (CSTR)**

V rA=-kCA Fj0 Fj The first-order reaction (liquid phase rxn) A B is carried out in a CSTR in which the volumetric flow rate, v0, is constant. (1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow rate v0. (2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is 0.23 min-1.

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**P1-6B How large is it? (CSTR)**

For CSTR, the mole balance on species A was shown to be V rA=-kCA Fj0 Fj The CSTR is almost 4 times larger than the PFR for getting 90% conversion

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**Mole Balance on Different Reactor**

Reactor Differential Algebraic Integral Batch CSTR PFR PBR

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Homework P1-7A P1-9A P1-11B P1-15B Due Date: Next Week

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