Reactions and Reactors

Transcription

1 Reactions and Reactors ChE Reactive Process Engineering If we want to run a chemical process in order to convert some reactants (the reactor feed) to some product (the reactor effluent), we have to answer a number of basic questions: Formulate the reaction equation. -> What yield can we expect in an optimal case? -> How fast will the reaction proceed? -> What type of reactor would be best used for this reaction? -> What limits the yield in this reactor? L1-1

2 Stoichiometry ChE Reactive Process Engineering L1-2 Stoichiometry is is the the law law of of conservation of of the the number of of atoms during a reaction. Example: The combustion of natural gas (which is mostly methane) can be written as: or equivalently: Obviously, both reaction equations are balanced in that the number of C, H and O-atoms on each side of the equation match. The coefficients of the chemical symbols in a reaction the stoichiometric coefficients can be multiplied with any constant factor and the atom balance is still intact. There

3 Stoichiometry II ChE Reactive Process Engineering L1-3 Denoting the reactants and products with A, we can write the previous reaction equation as: We can also write this as a (pseudo-) mathematical equation, and convention demands that the stoichiometric numbers (not coefficients) of the reactants then be negative and those of the products be positive (this is pure convention!): The generalized form for any reaction equation hence becomes: S 1 ν A 0 where S is the total number of species participating in the reaction and ν are the stoichiometric numbers.

4 Stoichiometry: Limiting Reactants ChE Reactive Process Engineering Let s assume you want to make cheese sandwiches, each consisting of one slice of cheese between two slices of bread. As chemical engineers, we would write this as: : 2 Bd + Ch -> > Bd 2 Ch If you have 10 slices of bread and 7 slices of cheese, you will run out of bread after making the first 5 sandwiches. You are limited by the amount of bread. (olive optional) The same can happen in a chemical reaction: if you don t start with stoichiometric amounts of reactants, the reaction will stop as soon as the understoichiometric reactant is completely consumed. This reactant is called the limiting reactant. L1-4

5 Stoichiometry: Example ChE Reactive Process Engineering In a gas stove (and in gas-powered power plants), methane is combusted with air to give CO 2 and water. The reaction is strongly exothermic and hence a good (and rather clean! Why?) source of energy. (1) Write the (balanced) reaction equation: (2) Assuming that you run this reaction starting with one mole of methane for every 100 moles of air, how many moles of each of the initial reactants s will you have after the reaction went to completion? (3) Which reactant was hence the limiting reactant? L1-5

6 Stoichiometry: Multiple Reactions ChE Reactive Process Engineering L1-6 The previous form of our generalized stoichiometric equation is only applicable to a single reaction. Almost all systems of practical interest, however, involve multiple reactions. What does the formula look like then? Example: 2 + O 2 -> 2 O 2 O + O 2 -> 2 O 2 - A 1 A A A 3 A A 4 0 S 1 ν i A where R is the number of reactions, S is the total number of species participating in all reactions and ν i is the stoichiometric number of species in reaction i. 0 O x -formation due to oxidation of 2 in high-t combustion processes (cars and power plants) i i 1, 1, 2, 2,,, R

7 Reactions and Reactors ChE Reactive Process Engineering If we want to run a chemical process in order to convert some reactants (the reactor feed) to some product (the reactor effluent), we have to answer a number of basic questions: Formulate the reaction equation. -> Stoichiometry How fast will the reaction proceed? -> Kinetics What yield can we expect in an optimal case? -> Thermodynamics What type of reactor would be best used for this reaction? -> Reactor Design What limits the yield in this reactor? Kinetics vs mass transfer vs heat transfer limitations. L1-7

8 Reaction Kinetics: Basic Concepts ChE Reactive Process Engineering L1-8 Chemical reaction kinetics deals with the velocity or rate of chemical reactions. We wish to quantify the the (aka the ). This requires experimental measurements. We are also interested in developing theoretical models by which the underlying basis of chemical reactions can be understood at a microscopic molecular level. Chemical reactions are said to be processes : energy (usually thermal energy heat) must be introduced into the system so that chemical transformation can occur. Hence chemical reactions occur more rapidly when the system temperature is increased. In simple terms, an must be overcome before reactants can be transformed into products.

9 Reaction rates ChE Reactive Process Engineering While the reaction equation tells us, what reactants are converted into which products, it doesn t say anything about how fast this is happening. This reaction progress with time is described by the reaction rate: r Where r denotes the reaction rate, and [A] the concentration of a reactant A. A (Units of r are hence: concentration/time!) For a reaction R -> P, we have to distinguish the rate of appearance of product P: r P and the rate of disappearance of reactant R: r A L1-9

10 Reaction rates, cont d 10ChE Reactive Process Engineering L1-10 For stoichiometrically more complex cases, we need to be careful! Check this complex case: 2 R -> P The rate of appearance of the product P is still r P d[p]/dt and the rate of disappearance of the reactant R: r R - d[r]/dt The reactant R is consumed twice as fast as P is formed! Hence the rate is: r For a general reaction a A + b B -> c C + d D we can therefore write (simply based on stoichiometry!): r 1 da [ ] 1 db [ ] 1 dc [ ] 1 dd [ ] or: a dt b dt c dt d dt da [ ] r ν dt 1 r ν

11 Measures of Concentration 11ChE Reactive Process Engineering L1-11 The dimensions for concentrations are usually moles per volume: [CH 4 ] General form: C For gases, partial pressures are most often used: P Frequently, you will also find mole fractions: y We will largely follow LDS and use concentrations C throughout the class. P P

12 Reaction Rate Law 12ChE Reactive Process Engineering L1-12 The relation between concentrations and the rate of reactions is usually complex and can typically be expressed as a general rate law in the form: r k 1 Where the proportionality constant k is the rate coefficient and m the reaction order. Generally, m ν! (We will talk about an exception to this rule, so-called elementary reactions in the next class!) S m C typical power-law rate expression What does m 0 signify?

13 Reaction Order 13ChE Reactive Process Engineering L1-13 Let s take the rate law r k [A] x [B] y We say the reaction is: of order x in [A] of order y in [B] has an overall reaction order of (x+y) Rate laws can in general OT be derived from the reaction equation, i.e. the reaction order is in general OT equal to the stoichiometric coefficients! Rate laws have to be determined experimentally! The most common integral reaction orders are zero, one and two. However, for more complex reaction systems, non-integral reaction orders are very frequently encountered. Reaction orders can also become negative! This indicates an inhibition effect. Both reactants and products can have inhibiting effects on a reaction. Particularly product inhibition is often encountered in catalytic and in enzymatic reactions.

14 Reaction rates: Example 14ChE Reactive Process Engineering L1-14 Reaction rates typically refer to a particular reaction equation! Example: O formation 2 + O 2 -> 2 O ; let assume r k [ 2 ] [O 2 ] In terms of the change in concentration of each species, this becomes: r 2 r O2 r O What if we had written the reaction equation differently? 1 da [ ] r ν dt O 2 -> O r r would would be be different! different! -> How would this affect our rate law rf([ 2 ],[O 2 ])?

15 The Extent of a Reaction 15ChE Reactive Process Engineering L1-15 We ust saw that stoichiometry connects the rate laws for different reactants and products. This is due to the conservation of atoms, which requires that no atoms get lost in the course of a reaction. Hence, for our O-formation example, we can write for example a simple O-balance: O O2 const. Since this must be true at any moment in time during the reaction, we can also write: Δ O Δ O2 Or in a generalized form:, 0 ν χ Closed system! defining the reaction extent χ (Remark: the reaction extent is very often also denoted as ξ ).

16 Conversion 16ChE Reactive Process Engineering L1-16 An alternative way to quantify the reaction progress at any point in time is the (fractional) conversion X: X A A0 (1-X A ) or: What are the boundaries for X A? X A Unlike χ, which refers to a reaction equation, X i refers to a specific reactant (and always a reactant not a product!), that means: χ takes on one value for the whole equation, while X i will generally have different values for the different reactants participating in the same reaction! Why is that so?!? A0 A0 A

17 Conversion & Extent: Example 17ChE Reactive Process Engineering L1-17 Let s revisit our previous example: In a gas stove (and in gas-powered power plants), methane is combusted with air to give CO 2 and water: CH O > 2 CO H 2 O. (1) Assuming, as before, that you run this reaction starting with one e mole of methane for every 100 moles of air and the reaction runs to completion, what is the reaction extent and the conversion for each reactant? Initial: CH4,0 1, O2,0 20, 2,0 80 Final: CH4,f 0, O2,0 18, 2,0 80 X Conversion: CH 4 CH 4,0 CH 4, f CH 4,0 X A X O2 A0 A0 A O2,0 O2, f O2,0 X CH4 X O2 X 2 X 2 2,0 2, f 2,0

18 Conversion & Extent: Example 18ChE Reactive Process Engineering L1-18 Let s revisit our previous example: In a gas stove (and in gas-powered power plants), methane is combusted with air to give CO 2 and water: CH O > 2 CO H 2 O. (1) Assuming, as before, that you run this reaction starting with one e mole of methane for every 100 moles of air and the reaction runs to completion, what is the reaction extent and the conversion for each reactant? Initial: CH4,0 1, O2,0 20, 2,0 80 Final: CH4,f 0, O2,0 18, 2,0 80 Reaction Extent: χ ν,0 χ χ ν CH 4, f CH 4,0 CH 4 ν O2, f O2,0 O2

19 Conversion & Extent: Example 19ChE Reactive Process Engineering L1-19 Let s revisit our previous example: In a gas stove (as well as gas-powered power plants), methane is combusted with air to give CO 2 and water: CH O > 2 CO H 2 O. (2) If you achieve a conversion of methane of 20%, what is the conversion of oxygen and what is the final composition of your reaction mixture? CH4,0 1, O2,0 20, 2,0 80 From definition of conversion: X 0.2 CH 4 CH 4,0 CH 4, f CH 4,0 From stoichiometry: O2 2 CH4 O2,f O2,0 + O2 Final composition: CH4,f 0.8 * CH4,0 0.8 X O 2 O2,0 O2, f O 2,0 CH4,f mol, O2,f mol, 2,f mol