1. Time Invariants and Conservatively Perturbed Equilibrium (CPE)
Gregory Yablonsky,1 Daniel Branco,2,* Guy B. Marin,3 and Denis Constales2
2Department of Mathematical Analysis
3Laboratory for Chemical Technology
1Department of Energy, Environmental and Chemical Engineering
Washington University, Saint Louis MO 63130, USA
Krijgslaan 281 S-8, B-9000 Ghent, Belgium
Technologiepark 914, 9052 Ghent, Belgium
Introduction
A k 1 + ⇄ k 1 − B k 2 + ⇄ k 2 − C
New Ideas in planning kinetic experiments:
Dual experiments:
Symmetric initial conditions.
Thermodynamic invariants
Conservatively Perturbed Equilibrium (CPE)
Mass balance: linear invariant
Ao + Bo + Co = 1
Experiment # 1 (Ao, Bo, Co) = (1, 0, 0)
Experiment # 2 (Ao, Bo, Co) = (0, 1, 0)
Thermodynamic invariant from symmetric experiments
The thermodynamic invariants are modified Onsager relationships, in terms of non-steady-state concentrations. Experimental evidence for water-gas shift, ferrocyanide-ferricyanide and estherification reactions is presented [1-3]
Non-thermodynamic invariant from ratios of differences of SIC [4]
Scaled Incremental Conversion SIC
Differences of SIC
Experiment # 3 (Ao, Bo, Co) = (Ceq, Beq, Aeq)
Non-thermodynamic invariant from ratios of differences of SIC in CPE
Conservatively Perturbed Equilibrium
At balance conditions, some initial concentrations are equal to the equilibrium concentrations. The extreme time value depends exclusively on the kinetic coefficients.
Ratios of differences of SIC in CPE yield invariants expressions.
Substance B in CPE
References:
1- Yablonsky G.S., Gorban A.N., Constales D., Galvita V.V., Marin G.B., EPL 93, 2011, Hankins M.J., Yablonsky G.S., Kiss I.Z., PLOS ONE, 2017, 12(3): e Peng B., Yablonsky G.S., Constales D., Marin G.B., Muhler M., Chem. Eng. Sci., 2018, submitted. 4- Branco D., Yablonsky G.S., Marin G.B., Constales D., Chem. Eng. Sci., 2018, 184, 25,
ISCRE, Florence, 23/05/2018