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Chemical Reaction Engineering. Dr. Yahia Alhamed. Kinetics and Reaction Rate. What is reaction rate? It is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction can be expressed as:- - The rate of disappearance of a reactant or

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## Chemical Reaction Engineering

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**Chemical Reaction Engineering**Dr. Yahia Alhamed SABIC Chair in Catalysis at KAU**Kinetics and Reaction Rate**What is reaction rate? It is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction can be expressed as:- - The rate of disappearance of a reactant or - The rate of appearance of a product. SABIC Chair in Catalysis at KAU**Reaction Rate**Consider species A: -rA = the rate of formation of species A per unit volume rB = the rate of formation of species B per unit volume • EXAMPLE: If B is being formed at 0.2 moles per decimeter cubed per second, ie, rB = 0.2 mole/dm3/s • Then A is disappearing at the same rate: • -rA= 0.2 mole/dm3/s • The rate of formation (generation of A) is rA= -0.2 mole/dm3/s SABIC Chair in Catalysis at KAU**Reaction Rate**Consider species j: • rj is the rate of formation of species j per unit volume [e.g. mol/dm3*s] • rj is a function of concentration, temperature, pressure, and the type of catalyst (if any) • rj is independent of the type of reaction system (batch, plug flow, etc.) • rj is an algebraic equation, not a differential equation SABIC Chair in Catalysis at KAU**Rate Law Basics**• A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration. SABIC Chair in Catalysis at KAU**Reaction Rate for solid catalytic reactions**• For a catalytic reaction, we refer to -rA', which is the rate of disappearance of species A on a per mass of catalyst basis. • -r'A = rA/bulk density of the catalyst (ρb) SABIC Chair in Catalysis at KAU**Rate Law Basics**• A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration. • Power Law Model k is the specific reaction rate (constant) k is given by the Arrhenius Equation: Where:E = activation energy (cal/mol) • R = gas constant (cal/mol*K) • T = temperature (K) • A = frequency factor (units of A, and k, depend on overall reaction order) SABIC Chair in Catalysis at KAU**General Mole Balance**SABIC Chair in Catalysis at KAU**Batch Reactor Mole Balance**SABIC Chair in Catalysis at KAU**Constantly Stirred Tank Reactor Mole BalanceCSTR or MFR**SABIC Chair in Catalysis at KAU**Plug Flow Reactor (PFR) Mole Balance**The integral form is: This is the volume necessary to reduce the entering molar flow rate (mol/s) from FA0 to the exit molar flow rate of FA. SABIC Chair in Catalysis at KAU**Packed Bed Reactor Mole Balance**PBR The integral form to find the catalyst weight is: SABIC Chair in Catalysis at KAU**Space time and space velocity**• FA0 = CAo vo • θ = is called space time (s) = V/vo • Space velocity = 1/θ, where; • FA0 = Molar feed rate of key reactant A (mol/s) • CAo= Concentration of key reactant A in the feed (mol/m3) • vo=Volumetric flow rate of feed to the reactor (m3/s) • V = volume of the reactor • For constant volume systems v = vo where v is volumetric flow rate leaving the reactor SABIC Chair in Catalysis at KAU**Reactor Mole Balance Summary**SABIC Chair in Catalysis at KAU**Reactor Mole Balance Summary**SABIC Chair in Catalysis at KAU**Reactor Mole Balance Summary**SABIC Chair in Catalysis at KAU**Reactor Mole Balance Summary**SABIC Chair in Catalysis at KAU**Reactor Mole Balance Summary**SABIC Chair in Catalysis at KAU**Conversion**Consider the general reaction: aA + bB -cC + dD We will choose A as bases of calculation (i.e. Key reactant) The limiting reactant is usually taken as the key reactant Then: A + (b/a)B (c/a)C + (d/a)D XA = moles reacted/moles fed SABIC Chair in Catalysis at KAU**Batch Reactor Conversion**SABIC Chair in Catalysis at KAU**CSTR Conversion**Algebraic Form: There is no differential or integral form for a CSTR. SABIC Chair in Catalysis at KAU**PFR Conversion**PFR Differential Form: Integral Form: SABIC Chair in Catalysis at KAU**V**Design Equations SABIC Chair in Catalysis at KAU**Reactor Sizing (CSTR)**• Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor. • We do this by constructing a Levenspiel plot. • Here we plot either as a function of X. • volume of a CSTR is: SABIC Chair in Catalysis at KAU**Reactor Sizing (PFR)**For PFR th evolume of the reactor needed is given by the area under the curve =area SABIC Chair in Catalysis at KAU**Summary**SABIC Chair in Catalysis at KAU**Rate Law Basics**• A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration. • Power Law Model k is the specific reaction rate (constant) SABIC Chair in Catalysis at KAU**Examples of Rate Laws**• First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with SABIC Chair in Catalysis at KAU**Examples of Rate Laws**• First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with (2) Homogeneous reversible elementary reaction with and SABIC Chair in Catalysis at KAU**Examples of Rate Laws**• First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with (2) Homogeneous reversible elementary reaction with and • Second Order Reactions (1) Homogeneous irreversible non-elementary reaction with and • This is first order in ONCB, first order in ammonia and overall second order. At 188˚C SABIC Chair in Catalysis at KAU**Examples of Rate Laws**• Second Order Reactions (2) Homogeneous irreversible elementary reaction with SABIC Chair in Catalysis at KAU**Examples of Rate Laws**• Second Order Reactions (2) Homogeneous irreversible elementary reaction This reaction is first order in CNBr, first order in CH3NH2 and overall second order. (3) Heterogeneous catalytic reaction: The following reaction takes place over a solid catalyst: with SABIC Chair in Catalysis at KAU

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