Reactor Theory: kinetics TVM 4145 Vannrenseprosesser / unit processes Reactor Theory: kinetics Prof. TorOve Leiknes torove.leiknes@ntnu.no

Reactor kinetics: What makes a reaction take place? How does a reaction start? What affects / influences a reaction? How fast does a reaction proceed?

Gibb’s free energy: Generally: The energy which is available for a reaction is the free energy of the reactionen: Δ G Reaction dergee 1.0 Equilibrium positive ΔG 0 negative Δ G All products All reactants Generally: product reactants

Activation energy? Reactants Products A B Energy catalyst effect DE B Reaction progress

Temperature dependence: Generally: reaction rate temperature increase of 10° C gives ca. 2-3 times increase in rate Arrhenius (1889) : for constant Eact Eact – activation energy R – the universal gas constant T – absolute temperature A – integration constant (frequency factor)

NB ! Empiric form most often used: Where: T is temperature in oC q is a process dependent constant NB ! Arrhenius: Enzyme reactions: Oxidation: Temperature oC Reaction rate Temperature oC Reaction rate Temperature oC Reaction rate

Definitions and classification of reactions: Generally: Elementary reactions: 1. 0.-order reactions; A P ; independent of [A] 2. 1.-order reactions; A P 3. 2.-order reactions; A+B P 2A P Composite reactions : 1. Reversible reactions; A+B C+D 2C C 2. Consecutive reactions; A B 3. Chain reactions; 2A A+B2 P+B B+A2 P+A A2+B2 2P

Reactions in water are often complex: Example Chlorination of phenol consecutive kinetics competing reactions Reaction pathways; Calculation results; P 2CP 4CP 24DCP 26DCP 246TCP X OH Cl Phenol PCP

0. order reactions : enzyme kinetics and biological treatment reactants absorbed on a surface integrared where: CAo CA t tk k0 CA can not be negative

1. order reactions : where: for non-reversible reactions CA CAo t lnCA integrated or where: Half-life: CA CAo t lnCA lnCAo t k1 Generally:

2. order reactions : where: For: t k2 t k2(CAo- CBo)/2.3 Generally: integrated (where a+b=2) where: For: t k2 log CA/CB log CAo/CBo t k2(CAo- CBo)/2.3 2A P A+B P (and Ao=Bo) Generally:

Other “cases”: Retardant: Autocatalytic: change in rate over time as f(concentration) where  is a characteristics constant Autocatalytic: spontaneous acceleration as time proceeds A + P P + P When: Rearranged: Several empirical models exist depending on the system

Enzyme kinetics Michaelis-Menton Biological reactions: Degradation of substrate is an enzyme-catalytic reaction Reactions follow thermodynamic principles Historic developments: Our understanding of mechanisms can be dated back to the 1800s 1892, 1902; do not follow a simple 2.order kinetics - Brown 1903; theory that enzymes form complexes with the substrate - Henri ca.1913; Henri’s experiments improved by Michaelis og Menton 1925; Briggs og Haldane reached the same expressions/equations Enzyme kinetics Michaelis-Menton

E + S ES E + P 1 2 3 Michaelis-Menton: Balance on ES; k1 k2 k3 k4 ES E + P Balance on ES; 1 Reaction rate is dependent on product formation; 2 Mass balance maintained; 3 Formation of ES from product is insignificant;

ES cannot be measured – rewrite equations in measureable parameters: Assume steady state: 1. 2. 3. 4. Michaelis constant / saturation constant 5. 6. Reaction rate 7. If We have vmax Substitute into 5.

So what…? Rewrite equation: Michaelis-Menton Assumptions: Rate [S] vmax Assumptions: only one substrate initial rate must be extrapolated concentration of E is constant [E] > [S]o for steady state conditions temp., pH, IS, are constant

Microbial growth kinetics: Growth of cell mass: Monod found that growth of microorganisms followed enzyme reactions: Growth of microorganisms = f(substrate used)

In summary To design a reactor we need to know… What components are to be transformed? How do they react? what is needed to make a reaction happen? how fast does a reaction occur? what factors affect / impact the reaction? How can we express / model the reaction?