"Thermodynamc Analyss of Processes for Hydrogen Generaton by Decomposton of Water" by John P. O'Connell Department of Chemcal Engneerng Unversty of Vrgna Charlottesvlle, VA 2294-4741 A Set of Energy Educaton Modules for Chemcal Engneerng Sponsored by The Center for Energy Intatves of The Amercan Insttute of Chemcal Engneers Insttute for Sustanablty Module 3: The Whole-Process Perspectve for Thermochemcal Hydrogen Introducton Module 1 of ths seres provdes the foundaton for thermodynamc analyss of processes for energy effects and process constrants. Module 2 provdes experence wth sngle-unt processes. The present Module treats processes for thermochemcal decomposton of water for hydrogen manufacture from an overall pont of vew. Module 4 does an analyss of a water decomposton process nvolvng 2 sectons that exchange methane and methanol as well as heat, whle Module 5 treats the 3-secton Sulfur-Iodne process. We frst repeat essental elements of Module 1. Fgure 3.1 llustrates the concept for a steady-flow system, wth nlet and outlet streams at specfed absolute temperatures, T, pressures, P, and sets of molar or mass amounts for the components, {N}, along wth energy that crosses the boundares as "shaft work", W s, and heat, Q. Note that f a stream has both vapor and lqud, ts specfcaton must nclude the amounts of components n the phases. For pure components, ths means specfyng ether T or P, the total flow, N, and the qualty or fracton of the system that s vapor, x. For mxtures, defnng the state s more elaborate. The balance equatons for steady flow processes are: Fgure 3.1. Steady Flow System for Applyng Materal, Energy, and Entropy Relatons, Eqs. (3.1) and (3.2). -1-
N h (T, P, x ) N o h o (T o, P o, x o ) s W s Q b Q e b Q N s (T, P, x ) N o s o (T o, P o, x o ) b b T b Q e S gen (3.1) (3.2) Here h s the molar enthalpy, s s the molar entropy, and {x} s the set of component mole fractons found from the set of numbers of moles of components, {N}, n a stream. Knetc and potental energy dfferences n the flowng streams have been gnored n Eq. (3.1). The summaton s over all nput streams,, and the summaton s over all output streams, o. Consequently, all molar flow numbers, {N} and {N} o, are postve. The summatons and are for the work and heat effects, respectvely, assocated wth external utltes. The speces amounts, {N} and {N} o are related by mass conservaton; moles are conserved only n nonreactng systems. These two relatons express the conservaton of energy among the forms generally treated n chemcal processes, Eq. (3.1), and the balance of entropy, Eq. (3.2), whch has entropy conservaton for reversble cases (s gen rev = ) and postve entropy generaton (s gen > ) n real systems. The heat effects, {Q b} and Q e, are defned to be postve when heat s put n; they cross the outsde of the system boundary (surroundngs) at temperatures T b and. A reversble process gves the absolute upper lmt, the best case, of the effcency of energy usage. That s, when s gen =, the soluton to Eqs. (3.1) and (3.2) wll gve the mnmum nput shaft work, hgh-temperature heat, or energy-carryng materal, to accomplsh a process that does not occur spontaneously. The two energy/entropy relatons force two unknown quanttes to be found from the known varable values, whle gvng consstency among molar flows for all chemcal reactons occurrng. Thus, many dfferent cases can be set up; Table 3.1 llustrates a few of these. Others are gven n Table 1.1 of Module 1. Table 3.1 Optons for Specfcatons and Soluton Varables for Eqs. (3.1) and (3.2). Case Specfcatons Soluton Varables A T, P, N, T o, P o, N o, W s, Q b, T b,, s gen Q e, Q bn D T, P, N, T o, P o, N o, W s, Q b, T b, Q e, s gen J T, P, N,, T o, P o, N o, W s, Q b, T b,, s gen Q e, N n * Includes all elements of set except n whch s solved for Note agan that 2-phase systems requre a specfcaton of the relatve amounts of the phases, such as by the qualty, x V, n a pure component system. Some generalzatons about effects of changng specfed varables can be made for closed and for sngle-unt open systems. For example, we can state the consequences of s gen >,.e., of puttng n rreversbltes whle keepng the same flow condtons. For work-absorbng devces, such as heat pumps, Eq. (3.2) shows entropy generaton means more heat must be removed (Q e real < Q e rev < ), so Eq. (3.1) gves more work nput (W s real > W s rev > ). For devces that produce work, such as heat engnes, real systems yeld less work (W s rev < W s real < ) and less heat s put n ( < Q b real < Q b rev). o s b -2-
Overall Analyss of Thermochemcal Hydrogen Systems The evaluatons of Modules 1 and 2 gve the fundamentals and llustrate applcaton of the energy/entropy analyss to sngle-unt systems. Ths Module begns the treatment of systems for thermochemcal decomposton of water to manufacture Hydrogen. Input hgh-temperature energy can be from ether a nuclear reactor or solar collector. The specfc mechansm can be ether as heat or by coolng a hgh pressure gas, whch has an nput and an output stream. The frst examples of Case III are those of Narkprasert [5] who appled Eqs. (3.1) and (3.2) to the whole process of H 2 O feed, H 2 and O 2 products, wth energy from drect heatng or from coolng hgh pressure Helum, and wth heat rejecton to the envronment. The energy requrements vary wth nlet and outlet condtons and entropy generaton. Case III Examples. Consder a process to decompose water to make Hydrogen and Oxygen usng hgh temperature heat wth no work effect. Fgure 3.1 llustrates the system. Fgure 3.1. Overall Schematc of Process to Thermochemcally Decompose Water. Problem 3.1 Comment on the smlartes and dfferences of Case III wth Case II of Module 2. Eqs. (3.1) and (3.2) become: (N W h W N H h H N O h O ) Q h Q e (N W s W N H s H N O s O ) Q h T h Q e N H s gen (3III.1) (3III.2) The bass for s gen s per kmol of Hydrogen produced. Wth a chemcal reacton nvolved, the analyss of the enthalpy and entropy dfferences becomes more complex. Typcally, the nformaton about property changes for reactons s compled n Gbbs energy and enthalpy changes of formaton of the speces n a standard state, wth the values of these standard state propertes for the atomc (or datomc gas) elements set to zero. Thus, Table -3-
3.1 gves the thermodynamc propertes of formng H 2 O from 1 mole of H 2 and 1/2 mol of O 2 for all speces as pure deal gases and for water as a pure lqud at T = 298.15 K and P = 1 bar [1]. These propertes satsfy the relaton G f H f T S f. The estmaton of energy effcences for Hydrogen manufacture depend on whether the water s gas or lqud; the enthalpy for the former s known as the "lower heatng value" whereas the latter s the "hgher heatng value". Table 3.1 Standard State Propertes of Formaton of Water at T = 298.15 K and P = 1 bar. Water Phase H Wf,MJkmol 1 G Wf,MJkmol 1 S Wf,MJkmol 1 K 1 Gas -241.83-298.13.18884 Lqud -285.83-36.69.6995 The property values for Eqs (3.1) and (3.2) are obtaned by addng the effects of changng the speces from ther standard states to the condtons of the process streams. The speces of a process to be analyzed are not normally deal gases. In the absence of tabulated nformaton such as steam tables, the effect of nondealty may be taken nto account by resdual propertes, h r and s r computed from an equaton of state sutable for the speces. One set of formal relatons for resdual propertes s: h r T, P ht, Ph g P T, P ( v T v T p)dp s r T, P st, Ps g T, P P ( R P v T P)dP For the system of Fgure 3.1, and usng the standard state propertes of the formaton (not decomposton) reacton and resduals, Eqs. (3.1) and (3.2) become: (3.3) (3.4) Q h Q e (N H h H r N O h O r N W h Wr ) N H h H g h H N O h O g h O N W h W g h W N H H r (3.5) Q h T h Q e N H s gen (N H s H r N O s O r N W s Wr ) N H s H g s H N O s O g s O N W s W g s W N H S r where the subscrpts are H for Hydrogen, O for Oxygen, and W for water. For pure nondeal-gas substances, such as steam and refrgerants, tables wth values of h(t, P, {x}) and s(t, P, {x}) for the nlet and outlet states are usually avalable. For deal gases, the fundamental relatons are: (3.6) h g h T cp g TdT T s g s T T cp g T T dt R ln P P (3.7a) (3.7b) Thus, the property dfferences h g H h H and s g H s H of Eqs. (3.5) and (3.6) can be found from Eqs. (3.7a) and (3.7b) wth T and P the standard state temperature and pressure, -4-
respectvely, and T the temperature of the stream. The reacton changes of a property,, where F H, G, ors, are gven by F r F. f If the thermodynamc propertes can be obtaned from tables or computaton, such as n flowsheetng software lke Aspen, the complextes of standard state and correctng for temperature and pressure effects are computed n the background, so these equatons become Q h Q e N H h H N O h O N W h W (3.8) N H s gen N H s H N O s O N W s W (3.9) Q h T h Q e Havng ths nformaton avalable wll be assumed here. Problem 3.2 A real process wll nvolve compressors and other work machnes. Why s there not an explct term of W s n the above relatons? It s common n energy scenaro calculatons to obtan an effcency whch s the rato of the amount of energy, actually enthalpy, obtaned from a process to the amount of enthalpy put n. Ths can be complcated when the energy values nvolve complex reactons, but for water to hydrogen to water, the rato s merely the standard enthalpy of hydrogen oxdaton to water, dvded by the heat put nto the process, Q h. Thus thermal effcency for ths process,, s F r H r /Q h 285.8/Q h (3.1) where Q h s n MJ kmol -1. Numercal Problems for Case III The propertes for the speces chosen for ths case are gven n Table 3.2. Here we wll consder Cases A, D, and J. Table 3.2 Propertes for Water Decomposton. Bold = Specfed; Italc = Solved. Speces N, kmol T, K P, MPa h*, MJ kmol -1 s*, MJ kmol -1 K -1 H 2 O (W) 1 275. (l).4-287.2 -.169 H 2 (H) 1 386.15 (g) 4. -7.32 -.23 O 2 (O).5 346.57 (g).4-25.99 -.7 *Reference [5]. The reference states for h =, s = here are dfferent from Table III.1. Case IIIA. For a specfed separaton and entropy generaton, what are the heat effects? Both real and reversble systems can be evaluated for ths case. Eqs. (3.7) and (3.8) can be combned and rearranged to fnd the desred varables, as for Eqs. (2.IIA1) and (2.IIA2) of Module 2: Q e N H (h HT h s H )N O h O T h s O N W h W T h s W T h N H s gen 1T h / Q h N H h H N O h O N W h W Q e (3.IIIA1) (3.IIIA2) -5-
Table 3.3 gves problems to evaluate heat effects when effcences from dfferent s gen values. Table 3.3 Specfc Problems for Case IIIA. Bold = Specfed; Italc = Solved. The temperatures for the heat exchanges are set at = 313K and T h = 942K Problem # s gen, MJ kmol -1 K -1 Q h, MJ Q e, MJ IIIA.1. 333-66 IIIA.2.25 IIIA.3.5 IIIA.4.75 For Problem IIIA.1, Eqs. (3.IIIA1) and (3.IIIA2) become Q e 17.32942.23.525.99942.71287.2942.1691942 1942/313 = -66 (3.IIIA1.1) Q h 17.32.525.991287.266333 (3.IIIA2.1) Problems 3.3 Complete Table 3.3 for problems #IIIA.2 - #IIIA.4. Plot the heat effects as a functon of s gen. The solutons to Problems IIIA.1- IIIA.4 show that as s gen s ncreased, the heat nput and output both ncrease n magntude, demonstratng that rreversbltes cause more energy to be requred for a process, wth the extra energy beng rejected to the envronment. The results are lnear n s gen. Table 3.4 gves problems to evaluate effcences from dfferent Helum condtons. Table 3.4 Specfc Problems for Effcences from Case IIIA wth Varyng Heat Exchange Temperatures. Bold = Specfed; Italc = Solved. Problem s gen, T h = 942 K T h = 1 K T h = 942 K T h = 1 K # MJ kmol -1 K -1 = 313 K = 313 K = 3 K = 3 K 86% 88% 87% 89% IIIA.5 IIIA.6 IIIA.7 IIIA.8.25.5.75 For Problem IIIA.5, Eq. (3.1) becomes 285.8/3331 86% (3.IIIA4.1) Input to these problems comes from the solutons to Problems IIIA.1 - IIA.4 and smlar ones. Problems 3.4 Complete Table 3.4 for problems #IIIA.6 - #IIIA.8. Comment on the effects of changng Helum condtons. -6-
Case IIID: For a specfed separaton and nput heat, what s the heat removal and the entropy generated? Only real systems, not reversble, can be evaluated for ths case. Eqs. (3.8) and (3.9) can be combned and rearranged to fnd the desred varables. Q e N H h H N O h O N W h W Q h s gen N H s H N O s O N W s W Q h T h Q e /N H (3.IIID1) (3.IIID2) Table 3.5 gves problems to evaluate the heat rejecton and entropy generated for dfferent heat nputs. Table 3.5 Specfc Problems for Case IIID. Bold = Specfed; Italc = Solved. The temperatures for the heat transfers are set at = 313K and T h = 942K Problem # Q h, MJ Q e, MJ s gen, MJ kmol -1 K -1 IIID.1 8-533 1. IIID.2 6 IIID.3 4 IIID.4 3-33 -.7 For problem #IIID.1, Eqs. (IIID.1) and (IIID.2) become Q e 17.32.525.991287.28 533 s gen [1.23.5.71.169( 8 942 533 )] 313 /1 1. (3.IIID1.1) (3.IIID2.1) Problem IIID.4 s evaluated smlarly. Problems 3.5 Complete Table 3.5 for problems #IIID.2 - #IIID.3. Note that s gen < for the smallest heat nput, Q h = 3, so the process s not feasble; there s not enough energy put nto the process. For Problems IIID.1 to IIID3, s gen >, so they are feasble. Case IIIJ. The energy for a thermochemcal process from a nuclear plant can be provded va pressurzed Helum that s cooled as ts energy s used for the decomposton. Thus, the block dagram s as n Fgure 3.2. The forms of Eqs. (3.1) and (3.2) become, for ths case wth the notaton of Fgure 3.2 and N N N o : N N Wh W s W N H h H s H N O h O s O N H s gen (3.11) c g g p (T o T ) c p lnto /T Q e (N H h H N O h O N W h W ) Ncp g (T o T ) (3.12) Helum can be consdered an deal gas under these condtons, so ts enthalpy and entropy dfferences can be computed wth Eqs. (3.7a) and (3.7b). Table 3.6 gves problems to evaluate the requred Helum flow and heat rejecton for dfferent entropy generaton values. -7-
N T N o T o T H, P H, N H T w, P w, N w T O, P O, N O Q e Fgure 3.2. Schematc for Thermochemcal Decomposton wth Energy Suppled By Hgh-Temperature Gas. Table 3.6 Specfc Problems for Case IIIJ. Bold = Specfed; Italc = Solved. The Helum states are set at T = 11 K, P = 4 bar, T o = 8K, P o = 38 bar along wth cp g T 5 2 R =.28 MJ kmol -1 K -1 and = 313 K. Problem # s gen, MJ kmol -1 K -1 N, kmol Q e, MJ IIIJ.1 53.4-66 IIIJ.2.25 IIIJ.3.5 IIIJ.4.75 For Problem IIIJ.1, Eqs. (3.11) and (3.12) become: N 1287.2313.16917.32313.23.525.99313.7313 53.4 kmol.28(811)313.28 ln8/11 Q e 17.32.525.991287.253.4.288 1166 MJ (3.IIIJ11.1) (3.IIIJ12.1) Problems 3.6 Complete Table 3.6 for problems #IIIJ.2 - #IIIJ.4. Note that the result for Q e for Problem #IIIJ.1 s the same as for Problem #IIIA.1 as t must. The moles of Helum, and therefore the heat rejected, rses dramatcally wth small amounts of rreversbltes. References [5] O'Connell, J.P., Narkprasert, P., Gorensek, M.B., Process model-free analyss for thermodynamc effcences of sulfur processes for thermochemcal water decomposton, Int. J. Hydrogen Energy, 29, 34, 433-44. [1] Lemmon, E.W., McLnden, M.O., Frend, D.G., "Thermophyscal Propertes of Flud Systems" n NIST Chemstry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Lnstrom and W.G. Mallard, Natonal Insttute of Standards and Technology, Gathersburg MD, 2899, http://webbook.nst.gov, (retreved July 12, 211). -8-