Lecture 1: Reaction networks and critical effects Sudden change in behavior (bifurcation): bistability, periodic behavior, explosions When and why do we need a mathematical model? Model-based understanding and control Examples at different scales

Reactor Safety JOURNAL OF LOSS PREVENTION IN THE PROCESS INDUSTRIES, (2002) 15(3) p Acrylic reactor runaway and explosion accident analysis On May 18, 2001 a destructive fire and explosion accident occurred in an acrylic resin manufacturing plant located in the northern part of Taiwan. More than 100 people were injured and totally 46 plants including 16 high-tech companies nearby were severely damaged. The resulting blast wave destroyed and shattered many large and small windows of residences within half-a-kilometer. The immediate cause turned out to be a vapor cloud explosion and the blast mass was estimated to be equivalent to 1000 kg of TNT. However, the original cause was found to be a runaway reaction of a 6-ton reactor that contained methyl acrylate, methyl alcohol, acrylonitrile, isopropyl alcohol, acrylic acid, methacrylic acid, and benzoyl peroxide. The investigation and experimental runaway results revealed that during the runaway, the temperature had risen rapidly from 60degreesC to about degreesC and the maximum temperature rising rate could reach 192 K/ min. Since the final temperature of the process was much higher than the boiling points of all the reactants, vapors generated inside the reactor were released to the atmosphere.

CO+1/2O 2 ->CO 2 CO+NO -> 1/2N 2 +CO 2.

Negative order kinetics

Langmuir, Hinshelwood, Ertl

Langmuir-Hinshelwood Mechanism

Single crystal catalyst, Pd(111) Temperature series of measured hysteresis loops between 370 and 490 K. The CO2 rate is shown as a function of the CO fraction Y in the gas flux to the surface. The Journal of Chemical Physics, 7 February 2009 J. Chem. Phys. 130, (2009)

Analysis of catalytic reactions by PEEM Photoemission Electron Microscopes (PEEM's) record electrons emitted from a sample in response to the absoprtion of ionizing radiation. The electrons are accelerated by a strong electric field between the sample and the outer electrode of the objective lens, and the image is magnified hundred- or thousand- fold by a series magnetic or electrostatic electron lenses. An electron-sensitive detector records the electron emission. UV e-e- PEEM images the surface work function, which depends on the nature of the adsorbed species and coverage

Parametric analysis of reaction rate as a function of k 1

Steady state analysis k1k1

Limit Points Bistability can be analysed graphically, or numerically or formally For negligible desorption (k -1 =0) we find one solution at y=0 and two more solutions obtained from Find the extremum of k 1 by dk 1 /dy= 0. 2k 2 k 3 (1-2y)=k 3 +(2k 1 +k 3 ) dk 1 /dy This yields y lp and the boundary by substituting back into eq above The other boundary (wout proof) at k 1 =0, y lp =0 k lp k 1 y y lp

Limit points (2)

Single crystal catalyst, Pd(111) The Journal of Chemical Physics, 7 February 2009 J. Chem. Phys. 130, (2009)

Dynamics

Summary Critical effects in simple physicochemical systems Sudden changes in reaction rate Same operating conditions lead to multiple regimes Different regimes exhibit different parametric dependence This leads to critical effects What about the stability of different steady states? We will find out next time…