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

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)12, 911-926Table 2. Activation energies and pre-exponential factors for forward and backward WGSR obtained fromliterature; the rate constants for WGSR were calculated at operating temperature 1073 KSourceE af[J/mol]k 0f[(l/mol) 0.5 s -1 ]E ab[J/mol]k 0b[(l/mol) 0.5 s -1 ]k f[(cm 3 /mol) 0.5 s -1 ]k b[(cm 3 /mol) 0.5 s -1 ]Culbertson [8] 334.72 7.7·10 45·T-10 (i) / / 6.10 /Graven & Long [9] 281.58 5.0·10 12 238.49 9.5·10 10 3.10 7.37Bustamante [10] 253.55 1.52·10 10 218.40 6.65·10 8 0.22 0.49(i)The pre-exponential factor is also temperature dependant therefore the correct unit is K 10 (l/mol) 0.5 s -1 .xji , + 1n=nji , + 1Ri , + 1,(29)where j represents individual specie (H 2 , CO 2 , COor H 2 O).Similarly, the concentration of each specieswas calculated:nji , + 1 pRpRc ji , + 1 = ⋅ = x ji , + 1 ⋅ , (30)nRi , + 1 RT ⋅ RT ⋅where the pressure on the retentate side was heldat constant value p R = 50 bar. The partial H 2pressure on the retentate side was calculated as:p = x ⋅ p(31)RH2, i+ 1 RH2, i+1 R .In order to calculate heat duty the heat ofreaction DH R needs to be calculated. This wasdone by using the van’t Hoff Relation based onsource [6]:2 ∂∆HR=−R⋅T⋅ ln Keq( T, p ), (32)∂Twhere the logarithm of equilibrium constantK eq was obtained with the equation reported inBustamante [10] which was based on the studyfrom Singh and Saraf [7]:⎛ 9998.22 ⎞⎜ − 10 . 213 +T⎟⎜⎟ln K. Teq = 1.⋅ −3⎜ + 2 7456⋅10⋅ − ⎟.(33)1 987 ⎜−6 ⎜ −0.453⋅10⋅T2 ⎟− ⎟⎜⎝ −0. 201⋅lnT⎟⎠And the CO conversion X CO was deducedas follows:nCO, in − nCO,i+1XCO,i+1 =. (34)nCO,inb) Permeate side:Similarly as on the retentate side the Lawof Conservation of Mass must also apply for eachsection on the permeate side. The molar flow ofH 2 and N 2 mixture was calculated as:nPi , + 1 = nPi , −nH 2, i+1.(35)Because the molar flow of the N 2 sweepinggas is constant throughout the reactor, the molarflow of H 2 on the permeated side can be writtenas:n = n − n(36)PH2, i+ 1 Pi , + 1 N2.Samilarly as on the retentate side, themolar fraction of each species was calculatedusing the Eq.:nji , + 1x ji , + 1 = ,(37)nRi , + 1where j represents individual specie (H 2 or N 2 ).The partial H 2 pressure on the permeateside was calculated as:pPH2, i+ 1 = xPH2, i+1⋅ pP. (38)where the pressure on the permeate side was heldat the constant value p P = 1 bar.2.3 Model Design in Aspen PlusThe simulation was performed using theAspen Plus reactor model unit where chemicalreactions of WGS and side reactions (H 2 S andCOS formation) were modelled. The inputdata were temperature, pressure, molar flow,composition of syngas and formulas of chemicalreactions that take place inside the reactor. Theshortcoming of the model was that the programhad no information about the kinetics of the WGSRand hence no knowledge of the extent of the COconversion and the H 2 permeation through themembrane. These two parameters were calculatedbased on the kinetics of the WGSR and importedfrom Mathematica (see Fig. 4). That gave us moreaccurate predictions of the molar flow of H 2 in thepermeate stream and the achieved CO conversion918 Lotrič, A. ‒ Sekavčnik, M. ‒ Kunze, C. ‒ Spliethoff, H.