Water gas shift equilibria using NIST Webbook and Matlab

Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMUPage 1 of 7 Matlab in ChemE@CMU Matlab in ChemE@CMU Water gas shift equilibria via the NIST Webbook Posted on December 12, 2011 PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> Water gas shift equilibria via the NIST Webbook John Kitchin The NIST webbook provides parameterized models of the enthalpy, entropy and heat capacity of many molecules. In this example, we will examine how to use these to compute the equilibrium constant for the water gas shift reaction range of 500K to 1000K. Parameters are provided for: in the temperature Contents ■ Setup equations for each species ■ Hydrogen ■ H2O ■ CO ■ CO2 ■ Standard state heat of reaction ■ Correcting ■ Plot how the $\Delta G$ and $\Delta G$ varies with temperature ■ Equilibrium constant calculation ■ Equilibrium yield of WGS ■ Compute gas phase pressures of each species ■ Compare the equilibrium constants ■ Summary Cp = heat capacity (J/mol*K) H° = standard enthalpy (kJ/mol) S° = standard entropy (J/mol*K) with models in the form: http://matlab.cheme.cmu.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 % 500-1700 K valid temperature range A = B = C = D = E = F = G = H = 30. B = -11. http://matlab.707974. S_H2 = (A*log(t) + B*t + C*t. First. we have heats of formation at standard state for each compound.082139. 223. 6.68.cmu.772874.^2) + G). E = -0. Hf_29815_H2O = -241. and is the temperature in Kelvin.534480. as well as at other temperatures. -241. but we do not consider them here. dH_H2O = A*t + B*t.^2/2 + D*t. as well as the absolute entropy. we have an expression for the change in enthalpy from standard state as defined above.^2/2 + C*t.^3/3 + D*t.980797.158558. D = -2.1000). H2O link Note these parameters limit the temperature range we can examine. Then. G = H = 172.83.H. and for non-elements. clc. free energy and equilibrium constant from 500K to 1000K.E.432816.363417.^2/2 + D*t. From these we can derive the reaction enthalpy. T = linspace(500. % J/mol/K dH_H2 = A*t + B*t. Hf_29815_H2 = 0. We can use this data to calculate equilibrium constants in the following manner. % kJ/mol S_29815_H2 = 130. and finally compute the equilibrium composition of a gas feed containing 5 atm of CO and H2 at 1000K.^2) + G).Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU Page 2 of 7 where . 6./(2*t.E.cheme. S_29815_H2O = 188. We will examine the water gas shift enthalpy.^3/3 . 0. F = -9.832514.H.0. -250. S_H2O = (A*log(t) + B*t + C*t.066178. Setup equations for each species First we enter in the parameters and compute the enthalpy and entropy for each species.8264. C = 11./(2*t. free energy and entropy at standard state. these are zero by definition./t + F .^3/3 + D*t.84. %this is Hf. -2. as these parameters are not valid below 500K.E.0.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 . There are also values for the absolute entropy at standard state.^4/4 . % degrees K t = T/1000.E. for elements.^2/2 + C*t.8810. clear all.^4/4 .^3/3 .09200. Hydrogen link % T = 298-1000K valid temperature range A = 33. 0. close all. There is another set of parameters for lower temperatures. they have values available from the NIST webbook.793435.3967./t + F . -33.^2/2 + D*t. CO2 link % 298. -2. -403. 228. -0. 7. 227.5271. %this is Hf.cheme.E.131021. S_29815_CO2 = 213.054656. 4. B = C = D = E = F = G = H = 55. 6.2f'. .096130.298.S_29815_H2O.^4/4 .53.Hrxn_29815) sprintf('deltaG = %1.15 K for the following reaction . -393. Standard state heat of reaction We compute the enthalpy and free energy of reaction at 298.79.E.136638./t + F ./t + F . . %this is Hf kJ/mol.E. Srxn_29815 = S_29815_CO2 + S_29815_H2 .69137.E.3665.56759.^2/2 + C*t.18696.2431.66.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 .Hf_29815_H2O.99735. 0.H.0089.Grxn_29815) ans = deltaH = -41.1200. dH_CO = A*t + B*t.62 http://matlab.^2/2 + C*t. dH_CO2 = A*t + B*t.15*(Srxn_29815)/1000. S_CO = (A*log(t) + B*t + C*t.^2) + G).2f'.51.Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU CO link Page 3 of 7 % 298.15 ans = deltaG = -28.^2) + G).^3/3 + D*t.5224.^2/2 + D*t. Hf_29815_CO = -110.S_29815_CO ./(2*t.948387. sprintf('deltaH = %1.H. Hrxn_29815 = Hf_29815_CO2 + Hf_29815_H2 .6075. H = -110.^3/3 + D*t.^3/3 ./(2*t.K valid temperature range A = 24.cmu.^4/4 .^3/3 .1300K valid temperature range A = B = C = D = E = F = G = 25. S_29815_CO = 197.671301. S_CO2 = (A*log(t) + B*t + C*t.Hf_29815_CO . -118. Hf_29815_CO2 = -393. Grxn_29815 = Hrxn_29815 . 314e-3. %kJ/mol/K K = exp(-Grxn/R.Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU Correcting and Page 4 of 7 we have to correct for temperature change away from standard state. hold all plot(T. strongly favoring the formation of products. http://matlab.cmu. Grxn = Hrxn . figure. but drops very quicky with increasing temperature. The entropy is on an absolute scale.Grxn) plot(T. with appropriate sign for reactants and products.dH_CO .T.Hrxn) xlabel('Temperature (K)') ylabel('(kJ/mol)') legend('\Delta G_{rxn}'.cheme.*(S_CO2 + S_H2 . Recall that H is in kJ/mol and S is in J/mol/K. Plot how the varies with temperature over this temperature range the reaction is exothermic./T). We only correct the enthalpy for this temperature change.'best') Equilibrium constant calculation Note the equilibrium constant starts out high. so we divide S by 1000 to make the units match. although near 1000K it is just barely exothermic. i.dH_H2O.S_CO .e. R = 8. so we directly calculate entropy at each temperature.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 . At higher temperatures we expect the reaction to become endothermic. '\Delta H_{rxn}'. The correction looks like this: Where are the stoichiometric coefficients of each species.S_H2O)/1000. and is precisely what is calculated for each species with the equations Hrxn = Hrxn_29815 + dH_CO2 + dH_H2 . 'location'. [1e-3 0.999]). For reactants. What is the equilibrium yield of H2? Let be the extent of reaction. which finally % reduces to $0 = K(T) . % pressure in atm % we can estimate the equilibrium like this. K_Temperature = interp1(T.K) xlim([500 1000]) xlabel('Temperature (K)') ylabel('Equilibrium constant') Page 5 of 7 Equilibrium yield of WGS Now let’s suppose we have a reactor with a feed of H2O and CO at 10atm at 1000K. Above % we simple computed a vector of enthalpies. Pc0 = 0. A = CO B = H2O C = H2 D = CO2 Pa0 = 5. We have to solve for the extent of reaction that satisfies the equilibrium condition.cheme. so that .Xeq) http://matlab. Pd0 = 0. etc. % If we let X be fractional conversion then we have $C_A = C_{A0}(1-X)$.cmu. We also have $K(T) = (C_C C_D)/(C_A C_B)$. sprintf('The equilibrium conversion for these feed conditions is: %1.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 . R = 0. is negative.082. f = @(X) K_Temperature .Temperature).2f'.K.X^2/(1-X)^2. but we would have to evaluate each term. % $C_B = C_{B0}-C_{A0}X$.Xeq^2/(1-Xeq)^2$ under these conditions. Xeq = fzero(f. Pb0 = 5. and for products.. is positive.. Temperature = 1000. and $C_D = % C_{D0}+C_{A0}X$. We could also calculate it % using the equations above. entropies. $C_C = C_{C0}+C_{A0}X$.Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU figure plot(T. 4 atm due to a much higher equilibrium conversion of 0.4352 Summary The NIST Webbook provides a plethora of data for computing thermodynamic properties.2748 P_H2O = 2. P_CO = Pa0*(1-Xeq) P_H2O = Pa0*(1-Xeq) P_H2 = Pa0*Xeq P_CO2 = Pa0*Xeq P_CO = 2.4352 ans = 1.88.cmu. we can directly calculation the pressures from the equilibrium conversion and the initial pressure of gases.Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU ans = The equilibrium conversion for these feed conditions is: 0. Luckily.cheme. For example. It is a little tedious to enter it all into Matlab. A limitation of the Webbook is that it does not tell you have the thermodynamic properties change with pressure.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 .2748 P_H2 = 2.55 Page 6 of 7 Compute gas phase pressures of each species Since there is no change in moles for this reaction. and a little tricky to use the data to estimate temperature dependent reaction energies.7252 P_CO2 = 2. At a lower temperature there would be a much higher yield of the products. They should be the same! K_Temperature (P_CO2*P_H2)/(P_CO*P_H2O) K_Temperature = 1. http://matlab.44 at 1000K.7252 Compare the equilibrium constants We can compare the equilibrium constant from the Gibbs free energy and the one from the ratio of pressures. at 550K the equilibrium constant is about 58. and the pressure of H2 is 4. consistent with the equilibrium constant of about 1. those changes tend to be small. you can see there is a slightly higher pressure of H2 and CO2 than the reactants. Share! Related posts: 1. thermodynamics by John Kitchin. Constrained minimization to find equilibrium compositions 2.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/] .12 Be Sociable. nonlinear algebra % tags: thermodynamics.edu/2011/12/12/water-gas-shift-equilibria-via-the-nist-webbook/ 08/02/2013 .cheme.cmu.cheme. Nonlinear algebra and tagged reaction engineering. ONE THOUGHT ON “WATER GAS SHIFT EQUILIBRIA VIA THE NIST WEBBOOK” Pingback: Gibbs energy minimization and the NIST webbook | Matlab in ChemE@CMU http://matlab.Water gas shift equilibria via the NIST Webbook | Matlab in ChemE@CMU % categories: Miscellaneous. Numerically calculating an effectiveness factor for a porous catalyst bead This entry was posted in Miscellaneous.cmu. reaction engineering Page 7 of 7 Published with MATLAB® 7. Bookmark the permalink [http://matlab.