TEKNIK REAKTOR KIMIA

Mole Balances, Conversion and Reactor Sizing

(Chapters 1 & 2, Fogler)

1: Mole Balances, Conversion & Reactor SizingTopics to be covered : Introduction to basic elements of reactor designQuick refresher of basic terminology/notationHomogeneous and heterogeneous reactionsReversible and irreversible reactionDefinition/notation of reaction rate.Development of general mole balance equation

1: Mole Balances, Conversion & Reactor SizingTopics to be covered : Common reactor typesKey characteristicsMole balance equations for common industrial reactors (batch and continuous)Introduction to the concept of reactant conversionReactor design of single-reaction systemsDefinition of conversionLevenspiel PlotsIntroduction of space time and residence time and few other concepts

Basic Elements of Reactor DesignReactor design usually involves the following:

Knowledge of nature of reaction Catalytic or Non-CatalyticHomogeneous or HeterogeneousReversible or Irreversible

Selection of operating conditionsTemperature, Pressure, ConcentrationsType of catalyst (if applicable)Flow rates

Basic Elements of Reactor Design

Selection of reactor type for a given application

Estimation of reactor volume required to process given amount (moles or molar rate) of raw material to desired amount of productsHow fast does the reaction occurs (reaction rates) dictates how large the reactor volume will be

Design of isothermal reactors involves solution of MOLE BALANCE equation onlyIn some cases, pressure drop must also be calculated

Our approach to reactor designOperations of most reactors are relatively complexTemperature is not uniform and/or constantMultiple reactions can occurFlow patterns are complex

To gain an insight into basic concepts relevant to reactor design, we will, first, consider simplified and/or ideal reactor systems.

Let us first familiarize ourselves with some common terminologies and notations that we will be using throughout the course

Terminologies and Definitions

Homogeneous Reactions: reactions that occur in a single-phase (gas or liquid)

NOx formationNO (g) + 0.5 O2 (g) NO2 (g)

Ethylene ProductionC2H6 (g) C2H4 (g) + H2 (g)

Heterogeneous Reactions: reactions that require the presence of two distinct phases

Coal combustionC (s) + O2 (g) CO2 (g)

SO3(for sulphuric acid production) SO2 (g) + 1/2 O2 (g) SO2 (g) Vanadium catalyst (s)Homogeneous & Heterogeneous ReactionsAside:What is the precise definition of a phase?

Reversible and Irreversible ReactionsIrreversible Reactions: Reactions that proceed uni-directionally under the conditions of interest

Reversible Reactions: Reactions that proceed in both forward and reverse directions under conditions of interest.

SO2 + 0.5 O2 SO3CH4 + 2O2 CO2+2H2OH2S H2 + 1/xSx

Form of Mole Balance EquationRate of INPUT Rate of OUTPUT + Rate of GENERATION Rate of CONSUMPTION = Rate of ACCUMULATIONNote: Rates refer to molar rates (moles per unit time).

Before we get into the details of the mole balance equation, we must introduce definition for reaction rate as well as associated notation.

( rA) = rate of consumption of species A= moles of A consumed per unit volume per unit time

(rA) = rate of formation of species A

Note: minus sign denotes consumption or disappearance.

Units of (rA) or ( rA)moles per unit volume per unit timemol/L-s or kmol/m3-s

Notation: Reaction Rate for Homogeneous ReactionsQuestion: Can we use (rA) to describe reaction rate of species that is actually being consumed in during a reaction ??

Notation: Reaction Rate for Heterogeneous ReactionsFor a heterogeneous reaction, rate of consumption of species A is denoted as (-rA')

Heterogeneous reactions of interest are primarily catalytic in nature. Consequently, the rates are defined in term of mass of catalyst present (why ?)

Units of (-rA')mol per unit time per mass of catalystmol/s-g or kmol/hr-kg catalyst

Rate of reaction has units of dCA/dt. Does the relationship: (-rA) = dCA/dt always hold true?Reactor operates at steady state, neither CAO nor CA are changing with timeLet us consider the following example of a flow reactor and evaluate if dCA/dt is equal to (-rA).

Reaction Rate and Rate LawReaction RateRate of reaction of a chemical species will depend on the local conditions (concentration, temperature) in a chemical reactor

Rate LawRate law is an algebraic equation (constitutive relationship) that relates reaction rate to species concentrations via a constant (?) that depends on temperature.Rate law is independent of reactor type

(-rA) = k [concentration terms]

e.g. (-rA) = k CA or (-rA) = k CA2

where, k is rate constant [k=f(T)]Note: a more appropriate description of functionality should be in terms of activities rather than concentration.Well learn more about rate laws .

General Mole Balance Equation (GMBE)Rate of INPUT Rate of OUTPUT + Rate of GENERATION = Rate of ACCUMULATIONControl Volume = VGA = (rate of formation of A) V= (rA)V=General mole balance equation is the foundation of reactor design.Could you write the GMBE in terms of consumption and NOT generation of a species ?

Common Reactor TypesBatch Reactor

Flow ReactorContinuous-Stirred Tank Reactor (CSTR)Plug Flow Reactor (PFR)Packed Bed Reactor (PBR)

Other Reactor TypesFluidized Bed ReactorTrickle Bed Reactor

Batch ReactorKey Characteristicsunsteady-state operation (by definition)no spatial variation of concentration or temperature, i.e. lumped parameter system (well-mixed)mainly used for small scale operationsuitable for slow reactionsmainly (not exclusively) used for liquid-phase reactioncharge-in/clean-up times can be large

General Mole Balance for a Batch ReactorReaction: A ProductsGeneral Mole Balance Equation (GMBE) for Batch Reactor may be written in differential form as in integral form as

Plug Flow Reactor (PFR)Key CharacteristicsSteady-state operationSpatial variation in axial direction but not in radial direction + no temporal variation, i.e. distributed system suitable for fast reaction mainly used for gas phase reactiontemperature control may be difficultthere are no moving parts

General Mole Balance for PFRReaction: A Products

Continuous Stirred Tank Reactor (CSTR)steady state operationused in seriesno spatial variation of concentration or temperature, i.e. lumped parameter system (well-mixed)mainly used for liquid phase reactionsuitable for viscous liquidPicture Source: http://www-micrbiol.sci.kun.nl/galleries/two.htmlFA0FACSTRs are also known as back-mix reactor

General Mole Balance for CSTRReaction: A ProductsGeneral Mole Balance Equation (GMBE) for a CSTR is of algebraic formFA0FA

Packed Bed Reactor (PBR)FA0FAKey CharacteristicsSimilar to PFR. Can be thought of as PFR packed with solid particles, which are almost always catalysts.Steady-state operationSpatial variation but no temporal variationMainly used for gas phase catalytic reaction although examples for liquid-phase reaction are also known.temperature control may be difficultThere are no moving partsPressure drop across the packed bed is an important consideration

Mole Balance for PBRDifferential FormIntegral FormFA0FAW = Weight of the packingReaction: A Products

Summary - Design Equations of Ideal ReactorsDifferentialEquationAlgebraicEquationIntegralEquationRemarks

Class Problem 1Calculating Reaction Rate in a CSTR1.0 L/min of liquid containing A and B (CAO=0.10 mol/L, CBO=0.01 mol/L) flow into a mixed flow reactor of volume VR=1.0 L. The materials in the reactor interact (react) in a complex manner for which the stoichiometery is unknown.The outlet stream from the reactor contains A, B and C at concentrations of CAf = 0.02 mol/L, CBf=0.03 mol/L and CCf=0.04 mol/L.

Find the rate of reactions of A, B and C at conditions of the reactor.

Human Body as a System of ReactorsMouthStomachSmall IntestineLarge IntestineWhat reactor type can we represent the various body parts with?Food

Single-Reaction Systems

Conversion (X) Batch Reactors Continuous (or Flow) Reactors

Further Discussions on ConversionLimiting reactant..

Maximum conversion for irreversible reactions

Maximum conversion for reversible reactions

Notes to be provided in the class.

Design Equation in Terms of ConversionREACTOR DIFFERENETIAL ALGEBRAIC INTEGRAL FORM FORM FORM

Levenspiel Plots: Illustration of Reactor Sizing for Single-Reaction Systems

Levenspiel PlotsPlug Flow Reactor (PFR)Continuous Stirred Tank Reactor (CSTR)Evaluated at X=XCSTRXPFRXPFR

Class Problem 2The following reaction is to be carried out isothermally in a continuous flow reactor:

A B

Compare the volumes of CSTR and PFR that are necessary to consume 90% of A (i.e. CA=0.1 CAO). The entering molar and volumetric flow rates are 5 mol/h and 0.5 L/h, respectively. The reaction rate for the reaction follows a first-order rate law:

(-rA) = kCA where, k=0.0001 s-1

[Assume the volumetric flow rate is constant.]

For same conversion, is the CSTR volume always higher than PFR volume ?

For a given conversion, can the CSTR volume be equal to PFR volume?X

Reactors in Series

PFR in SeriesXLet us compare two scenarios

(i) Single reactor achieving X3(ii) 3 reactors in series achieving X3

How is the total volume of 3 reactors in series related to single reactor ??

CSTR in SeriesFAO

X=0FA1

X=X1FA2

X=X2FA3; X=X3XCan we model PFR as a series of n equal volume CSTRs??Compare volume for the following 2 casesA single reactor achieving X33 reactors in series achieving X3

How is the total volume of 3 reactors in series related to single reactor ??

Closing Thoughts on Levenspiel PlotsLevenspiel Plots are useful means to illustrate the difference between PFR and CSTR behavior

Levenspiel plots are seldom used to design real world reactorsthe conditions (P, T, and reactant concentration) must be identical to that in the laboratory experiments.

If the rate law is given in terms of conversion (-rA) = g(X) or can be generated/derived by intermediate calculations, one can size PFR, CSTRs, and batch reactors.

Space Time & Residence Time

Class Problem 3The following aqueous-phase reaction are carried out isothermally in a laboratory-scale and an industrial-scale continuous stirred tank reactors: A B The reaction rate for the reaction follows a first-order rate law:

(-rA) = kCA where, k=0.1 min-1 at 50 oC

The operating conditions of the reactors are provided belowThe two reactors, vastly different in scale, and with different feed concentrations yield similar conversion. Why?

Industrial CSTRLab CSTRFeed concentration10%A in solution2% A in solutionReactor volume3600 L63 mLVolumetric flow rate40 L/min0.7 mL/min

Time is of EssenceThe extent of conversion of reactants in a chemical reactor is related to the time the chemical species spend in the reactor.

Two types of time-parameters are commonly used in chemical reaction engineeringspace time residence time

Space time is often used as a scaling parameter in reactor design

Space Time () : Time required to process 1 reactor volume of fluid at inlet conditions Actual Residence Time: The time actually spent by fluid inside the reactor.Space Velocity:

LHSV - Liquid Hourly Space VelocityGHSV - Gas Hourly Space Velocity

Space Time & Residence Time - Definitions

Illustration of difference betweenspace time (t) and residence time (tres)Under what practical conditions do we expect space time = residence time ?The Pop Corn Example

Reaction Rates of Some Known Systems Slow reaction Fast Reaction(requires large residence time) (short residence time)

Relative Rates of ReactionFor a reaction given below:

aA + bB cC + dD

How is (-rA) related to (-rB), (rC) and (rD) ?

Beberapa definisi..

aA + bB cC + dD.(20)(21)

.(22)FA0 = 0 CA0 ..(23)

..(24)

jika X = 0, CA = CA0jika X = X, CA = CA

(25) .(26)

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