Simulation of Water-Gas Shift Membrane Reactor for Integrated ...

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)12, 911-926reaction temperatures, at which the equilibriumCO conversion would otherwise be low, byextracting either CO 2 or H 2 from the reactionmixture.1.3 Water-Gas Shift Kinetics1.3.1 General Definition of Rate LawChemical kinetics investigates howdifferent experimental conditions can influencethe chemical reaction rate. The main factors thatcan speed up the reaction rate include increasein the concentrations of the reactants, increasein temperature or pressure at which the reactionoccurs and whether or not any catalysts are presentin the reaction.Usually, what appears to be a single stepconversion is in fact a multistep reaction and thus,the reaction mechanism is a step by step sequenceof elementary reactions. Each step has its ownrate law and molecularity (the number of speciestaking part in that step); therefore the slowest stepis the one that determines the overall reactionrate – the rate limiting step.Only for simple (elementary) reactionsa partial order of reaction is the same as thestoichiometric number of the reactant concerned.For stepwise reactions there is no generalconnection between stoichiometric numbers andpartial orders. Such reactions may have morecomplex rate laws and the orders of reaction are inprinciple always assigned to the elementary steps.By conducting experiments involvingreactants A and B, one would find that the rate ofthe reaction r is related to the concentrations [A]and [B] in a rate law as:r = k [A] a [B] b , (2)where k is the rate constant and the powers a andb are called the partial orders of the reaction. Theoverall order of the reaction is found by adding upthe partial orders. The rate constant is not a trueconstant because it is dependent on the reaction’stemperature T and the activation energy E a and isdefined via Arrhenius equation as:Ea−k = k ⋅eRT ⋅0 , (3)where k 0 is the pre-exponential factor.A pair of forward and backward reactionsmay define an equilibrium process where A and Breact into C and D and vice versa (a, b, c and d arethe stoichiometric coefficients):aA+ bB ⇔ cC+ d D(4)Assuming that above reactions areelementary, the reaction rate can be expressed as:r = k 1·[A] a·[B] b ‒ k 2·[C] c·[D] d , (5)where k 1 is the rate coefficient for the forwardreaction which consumes A and B; k 2 is the ratecoefficient for the backward reaction, whichconsumes C and D.In a reversible reaction, like WGSR,chemical equilibrium is reached when the rates ofthe forward and backward reactions are equal andthe concentrations of the reactants and products nolonger change (r = 0 in balance).1.3.2 Bradford Mechanisma) Backward WGSRBradford [4] assumed that the reactionmechanism would follow the simple gas-phasechain-reaction mechanism given below (Mindicates any gas-phase collision partner). Thechain is initiated by the gas-phase dissociationof hydrogen (Eq. (6)). Propagation steps arerepresented by reactions in Eqs. (7) and (8). Thetermination step corresponds to the gas-phase reassociationof H 2 in Eq. (9), consuming the chaincarriers.H2k1+ M ⎯⎯ →2H+M, (6)2H+ CO ←⎯⎯⎯⎯ →CO+OH, (7)2k−2k2 k2k3OH + H ←⎯⎯⎯⎯ →H O+H, (8)−3k−12 MH+ ⎯⎯ →H 2 + M. (9)With the assumption of low conversionand a stationary state for the concentrations ofthe intermediates (H and OH concentrations donot change significantly with respect to time), thefollowing rate equation r b is obtained,rdCOdtkk[ ] b = = ⎛ ⎝ ⎜ 1⎞−112 /12 /⎟ ⋅k2⋅[ H2] ⋅[ CO2]. (10)⎠914 Lotrič, A. ‒ Sekavčnik, M. ‒ Kunze, C. ‒ Spliethoff, H.