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

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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.
Strojniški vestnik - Journal of Mechanical Engineering 57(2011)12, 911 -926in the WGSMR. Based on these two parametersand the initial and boundary conditions (seesubchapter 2.1) the simulation of the WGSMRwas performed.The model of the MR was designed toachieve the isothermal temperature distributionthroughout the entire reactor. This is done insuch a way that indirect water cooling is appliedin a co-current direction to syngas flow. To attainefficient heat removal, the water evaporatesalmost throughout the entire reactor and getsslightly superheated at the end of the reactor. It ispresumed that the WGSR will be most intensive atthe beginning of the reactor thus, most of the heatwill be released in the first part of the reactor. Thesweeping N 2 gas enters the reactor in a countercurrentway. The reason for that is to keep the H 2partial pressure difference reasonably high in allparts of the reactor in order to achieve better fluxthrough the reactor’s membrane.3 RESULTS AND DISCUSSION3.1 Calculations in MathematicaIn the subchapters bellow the WGSRkinetics are discussed and calculations for the basecase model are presented. A sensitivity analysis ofthe model is made by varying different parameterslike the membrane’s permeance, length (indirectlythe surface area) of the reactor and the molarfraction of H 2 in the permeate stream.3.1.1 WGSR KineticsThere is some discrepancy between theuncatalysed WGSR kinetic data available fromliterature. For this purpose, three different studieswere compared all using the Bradford mechanism[4] to describe the WGSR. Table 2 presentsactivation energies and pre-exponential factorsobtained from these studies.The rate coefficients for forward andbackward reaction were calculated according toEq. (3). As shown in Table 2, the rate coefficientscalculated with values obtained from Bustamante[10] are one order smaller than those obtainedwith values from Graven and Long [9]. Eventhough Bustamante’s research [10] was conductedat elevated pressures (16.21 bar), and Graven andLong’s [9] only at atmospheric pressure, the resultsfrom Graven and Long’s study [9] are in betteragreement with Culbertson [8] who conducted hisstudy at even higher pressures and temperatures(196.5 to 496.4 bar and 1200 to 2100 K).The calculations showed that the reactionrate according to Bustamante [10] is one ordersmaller than the one predicted from Graven andLong [9] (see Fig. 7). This has also been confirmedin the study from Culbertson [8], therefore thedecision was made that the coefficients deducedfrom Graven and Long [9] will be used in theWGSR kinetic study.3.1.2 Base Case StudiesOne of the purposes of this study was todetermine if the permeation through the membraneis sufficient or if there is a build-up of H 2 on theretentate side. First, the comparison was made byusing the molar flows of both processes calculatedby Eqs. (26) and (27).Only in the first two sections the reactionrate is slightly faster than the permeation (on Fig.a) Bustamante’s model b) Graven & Long’s modelFig. 7. Rate of reaction based on different modelsSimulation of Water-Gas Shift Membrane Reactor for Integrated Gasification Combined Cycle Plantwith CO 2 Capture919
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