Work Flow In Reactive Processes

Transcription

1 UNIVERSIY OF HE WIWAERSRAND Wrk Flw In Reactive Prcesses Systematic apprach t Prcess Synthesis eta Bahunde Jhannesburg, 2014 A dissertatin submitted t the Faculty f Engineering and the Built Envirnment, University f the Witwatersrand, Jhannesburg, in fulfillment f the requirements fr the degree f Master f Science in Engineering. I

2 DECLARAION I declare that this dissertatin is my wn unaided wrk. It is being submitted t the Degree f Master f Science t the University f the Witwatersrand, Jhannesburg. It has nt been submitted befre fr any degree r examinatin t any ther University. eta Bahunde day f 2014 II

3 ABSRAC he industrial sectr s large energy use presents itself as a vast ptential fr energy saving and technlgy imprvements, making it an attractive target fr industrial sustainability thrugh increased energy efficiency. Prcess synthesis is a tl used early in the design stage f a prcess t generate flwsheets with ptimized efficiency, envirnmentally friendly and ecnmically viable. By understanding flwsheets design and parameters effects n the flw f heat and wrk thrugh a reactive prcess, ne is able t create prcesses capable f utilizing heat and wrk efficiently. Energy as heat and wrk is fundamental in the analysis f prcess perfrmance. his dissertatin therefre prpses tw case studies which reflect investigatins dne n the effect f temperature, cnversin and heat capacities n reactive prcesses. Findings shw that temperature, cnversin affect the heat and wrk use acrss the prcess in such a way that they can be adjusted t minimize heat and wrk lst acrss the prcess r a unit. Wrk lst minimizatin is an indicatin that heat and wrk supplied t the prcess is being utilized rendering the prcess efficient. Findings als shw that the larger the difference between the heat capacity at the stream ging int the prcess and the heat capacity at the stream ging ut f the prcess, the larger the required temperature and cnversin manipulatins t prduce an efficient prcess by minimizing wrk lst. III

4 ACKNOLEDGEMENS First and fremst, I wuld like t thank Gd fr being the cntinuus light and guidance in my life. Withut him, nne f this wuld be pssible. I thank my wnderful husband Clement fr his unwavering belief in me and fr his encuragement in this wrk. my children, this is fr yu. I thank my father Marcel M. Bahunde fr being the reference fr hard-wrk and perseverance. I als thank my mther Carmel G. Bahunde fr being a prf that curage is a driving frce fr success. I thank my brther and sisters with their families fr their lve and supprt. I sincerely thank Prfessr Diane Hildebrandt, Prfessr David Glasser and Dr. Celestin Baraka Sempuga fr their guidance and supprt thrughut the perid f my research. It has been a privilege fr me t cmplete this dissertatin under their supervisin. Last but nt least, I am very grateful t COMPS and the University f the Witwatersrand fr prviding a stimulating and serene envirnment t learn and grw. IV

5 able f Cntents List f Figures... VII List f ables... VIII 1 INRODUCION he Prcess Industry he Prcess Industry s place within a Sustainable Develpment mdel Gvernment - University - Industry link Scpe f the study AN INRODUCION O PROCESS SYNHESIS Intrductin Prcess synthesis methdlgy Prcess Synthesis ecnmic benefit HERMODYNAMIC ANALYSIS OF A PROCESS Wrk flw in reactive prcesses Energy and Entrpy balance acrss the prcess Energy and Entrpy Balance f the Heat Engine he Effect f Heat capacity (Cp) n prcess wrk flw Heat Capacity f the feed equal Heat Capacity f the prduct (Cp feed = Cp prduct ) Heat Capacity f feed different than Heat Capacity f prduct ( Cp feed Cp prduct ) Heat Exchanger energy and entrpy balance he Effect f Cnversin Heat and Wrk flw acrss the Reactr Reactin Equilibrium CASE SUDY I: BUANE ISOMERIZAION PROCESS emperature effect n the prcess emperature effect n Reactin s Equilibrium emperature effect n Wrk flw acrss the verall Prcess emperature effect n the Wrk flw at the Heat Exchanger emperature effect n the Separatr emperature effect n Wrk flw at the Reactr Wrk flws interactins within the prcess CASE SUDY II: REVERSE WAER-GAS SHIF (RWGS) REACION emperature effect n the prcess at cmplete cnversin in the reactr V

6 5.1.1 emperature effect n Wrk flw at the Heat exchanger emperature effect n Wrk flw at the Separatr and Mixer emperature effect n Wrk flw at the Reactr emperature effect n Wrk flw at the Prcess Wrk flws arund the prcess with incmplete cnversin in the reactr emperature effect n Reactin s equilibrium Cnversin effect n Wrk flw at the Prcess Wrk f separatin with incmplete cnversin in the reactr Wrk flws arund the prcess with incmplete cnversin in the reactr GENERAL CONCLUSIONS AND RECOMMENDAIONS REFERENCES APPENDIX A: List f ables APPENDIX B: Calculatins VI

7 List f Figures Figure 1-1. Graphical representatin f Sustainability (drv & Marinva, 2011)... 4 Figure 2-1. Onin mdel example applied t prcess synthesis Figure 2-2. Sample Hierarchical Decisin Prcedure Figure 3-1. Prcess setup as a Simple prcess where Figure 3-2. Simultaneus transfer f heat and wrk t a Simple prcess Figure 3-3. Wrk flw scenaris acrss the prcess where in (a) the prcess wrk requirement Figure 3-4. Basic equipments set-up fr the Simple prcess where Figure 3-5. Heat Exchanger setup within the prcess Figure 3-6. Basic equipment setup within a simple prcess which includes a separatr Figure 3-7: Supplying the wrk f separatin by directly Figure 3-8: Supplying wrk f separatin by adding heat Figure 3-9. Reactr unit setup within a Simple prcess Figure 4-1. Ismerizatin f is-butane (a) t n-butane (b) (Barrn, 2010) Figure 4-2. Basic equipments set-up fr the ismerizatin prcess f Butane Figure 4-3. gh-diagram subdivided in thermdynamic regins Figure 4-4. Butane ismerizatin prcess drawn in the gh-diagram Figure 4-5. emperature effect Equilibrium cnstant fr the ismerizatin reactin Figure 4-6. Change in Gibbs free energy acrss the reactr Figure Sgen curve as a functin f temperature fr Figure 4-8: Wrk required by separatr as a functin f reactr temperature, withut recycle Figure 4-9: Wrk required by separatr as a functin f reactr temperature, with recycle Figure 4-10: he wrk required by the reactr as a functin f Figure 4-11: Cmparisn f the wrk required by the reactr with Figure 4-12: emperature dependence f prcess parameters: Wrk f separatin, Figure 4-13: Wrk f separatin and wrk requirement f reactr Figure 4-14: Reactr reversible temperature as a functin f Figure 5-1: Setup f a RWGS prcess with cmplete cnversin in the reactr Figure 5-2. RWGS prcess drawn in the gh-diagram Figure 5-3: Wrk requirement at the heat exchanger as a functin Figure 5-4. emperature dependence f the wrk required by the reactr Figure 5-5. Wrk flws acrss the prcess as a functin f the temperature Figure 5-6: Setup f a RWGS prcess with incmplete cnversin in the reactr Figure 5-7. emperature effect n the RWGS reactin's equilibrium Figure 5-8. Change in Gibbs free energy acrss the reactr Figure Sgen term pltted as a functin f temperature fr the RWGS prcess Figure Change in Gibbs free energy acrss the prcess pltted as a functin f cnversin Figure 5-12: Wrk required fr separatin and equilibrium cnversin Figure 5-13:Wrk flws acrss the prcess as a functin f the temperature Figure 0-1. Flwsheet fr the Butane Ismerizatin Figure 0-2. Flwsheet fr the Reverse Water-Gas shift prcess VII

8 List f ables able 1. able f Cnstants able 2. able f Chemical Prperties (Yaws, 1999) VIII

9 1 INRODUCION 1.1 he Prcess Industry Fr centuries nw, fssil fuels (cal, il, r natural gas) have been a surce f energy as well as feedstck t industries. After the beginning f the eighteen hundreds, feedstck t relatively small cmmdity chemical industries cnsisted predminantly f cal. he intrductin f il and natural gas nly fllwed during the nineteenth century, triggering a strng dependency f glbal chemical enterprises t fssil fuels (Nardslawsky et al., 2006). As predicted by Rbert A. Linn (1984), tday s chemical industry which is f interest fr this study, is underging majr changes as the industry s members rethink the way they perate in rder t withstand severe cnstraints and cmplexities they face. Namely: - Fierce glbal cmpetitin ver the scarceness f the resurce. he diminished availability f fssil fuels is driving the chemical industry t think abut the way their businesses will functin in the future. Nardslawsky et al. (2006) have predicted a cnstant increase f crude il prices as the increase in demand can n lnger be ffset by increasing prductin. Cnsequently, fr its relatively glbal abundance, affrdability and reduced greenhuse gas emissins, natural gas is increasingly sught after as feedstck t chemical industries. - Envirnmental pllutin. here has been grwing envirnmental cncerns related t carbn prcessing industries. In additin t Carbn dixide (CO 2 ) emissins, pr management and dispsal f wastes are als affecting ur ecsystem. Fllwing a decade f research n this tpic, Steinberg (1994) believes that imprved energy 1

10 utilizatin efficiency is ne f the ways t cnsiderably reduce Carbn dixide emissins which make the largest part f greenhuse gas (GHG) emissins and is believed t be a majr cause f glbal warming. - Ecnmic perfrmance. he grwing scarcity and increasing demand f fssil fuels are reflected by the rising csts f fssil fuels explratin and explitatin ver the years. he diversificatin f energy surces by the inclusin f renewable surces (water, sun, wind, bimass, gethermal) t the energy mix culd be a slutin t meet the glbal energy demand and hinder envirnmental pllutin (Swift, 1999; Nel & Cper, 2009). A desirable energy mix wuld guarantee a steady, clean, and lw cst supply f energy which satisfies a balanced energy supply-demand mdel which is a fundamental part f the industrial develpment as well as a basis t ecnmic grwth. - Glbal ppulatin grwth. Glbal ppulatin and energy demand increase hand-in-hand (Abdelaziz et al., 2011). he frecast resulting frm glbal ppulatin grwth and increasingly scarce resurces predicts a cycle f cmplexities where sn enugh mre sil will be needed fr agriculture t feed the grwing ppulatin; fssil fuels demand will sar and as a result challenge the supply t energy prducers and industries. Integratin f renewable resurces t the energy mix culd be the key in vercming this challenge. - Geplitical frces disturbing the stability f the crude il and gas market. Steps tward the transfrmatin f industries in view t synthesize prcesses with enhanced prductivity, cnservatin f mass and energy, reduced GHG emissins, as well as reduced 2

11 perating and capital csts are evidently sme f the mst imprtant respnsibilities and challenges fr ur civilizatin. 1.2 he Prcess Industry s place within a Sustainable Develpment mdel he term Sustainable develpment has been defined by the Wrld Cmmissin n Envirnment and Develpment (WCED) as he develpment that meets the needs f the present withut cmprmising the ability f future generatins t meet their needs - (WCED, 1987). Its aim is t reach a balance between an ecnmic viability, scial equity, and envirnmental integrity such that ecnmic grwth ffers a desirable quality f life t the ppulatin withut damaging the envirnment. A graphical representatin f Sustainability is illustrated belw as a three circles mdel and shws its ecnmic, scial and envirnmental dimensins. 3

12 Figure 1-1. Graphical representatin f Sustainability (drv & Marinva, 2011) his mdel is als referred t as the Venn diagram r the three pillars mdel. It illustrates the relatinship between ecnmic, scial, and envirnmental develpment which cannt be addressed individually when sustainable develpment is desired, but in an integrated manner. Fr instance, ppulatin change, energy, water as well as fd demand are interlinked; finding a slutin fr ne aspect f the prblem culd help slving the thers. Energy is nt directly ne f the three sustainability cmpnents shwn in Figure 1-1, it is hwever linked t each as energy drives majrly -if nt mst f- the wrld s ecnmic activities; it is surced frm the envirnment and its related wastes are released t the envirnment; and services created frm the prductin and use f energy imprve living standards which ften supprt scial stability and prmte develpment. hus, since the prcess industry uses a large amunt f energy cnsuming abut 37% f the wrld s ttal delivered energy (Abdelaziz & al., 2011; Silveria & Luken, 2008), it presents itself as a significant parameter within the sustainable mdel fr imprvements in its 4

13 renewability, efficiency, accessibility, distributin, use as well as in lwering its envirnmental impact tailred based n lcal scial-ecnmic-envirnmental cnditins (Orecchini, 2011). As a respnse t the cnstant ppulatin grwth, fr instance, increasing energy supply t the prcess industry is nt the nly slutin t an unwavering energy future; reducing energy demand by imprving energy and equipments efficiency as well as industrial efficiency as a whle can als be a slutin. Anther slutin culd be t imprve energy supply management via the develpment f an effective energy planning, adptin f energy efficiency and waste minimizatin incentive plicies, as well as the adptin f GHG mitigatin plicies as ther channels t meet the same utcme. he develpment f a sustainable energy mdel that nt nly ensures steady lwest-priced and cnstant energy supply, but als avails necessary feedstck t the chemical industry is reinfrced under the verall sustainability mdel in Figure 1-1 thrugh the implementatin f energy management framewrks, energy technlgies, and tailred plicies aiming at regulating the prcess industry. Such framewrks are ften adapted in the frm f envirnment impact assessment, energy auditing, energy pricing, physical cntrl, Research & Develpment as well as educatinal methds (Munasinghe, 1983; Berrie, 1978). On the demand side, applicable plicies in aim t regulate the use f energy by the industry include GHG emissin taxes, cap and trade schemes, green technlgy tax reductins, preferential lans, as well as subsidy amng thers (anaka, 2011). 5

14 1.3 Gvernment - University - Industry link Knwledge in the frm f intellectual and human quality is a significant cntributr t ecnmic develpment. Similarly t the need fr balanced interactin between the three dimensins f Sustainability in Figure 1-1, it is imperative that the three majr entities playing a rle in ecnmic grwth: Gvernment-University-Industry, maintain a strng bnd. Fr many years nw, it is cmmn practice in develped cuntries as well as develping cuntries t have a dynamic transfer f knwledge frm University t Industry and viceversa. his flw f knwledge has an imprtant impact n ecnmic grwth and supplies the means t meet scial needs (Bekkers & Bdas-Freitas, 2008) by transfrming knwledge int labr, physical capital, prducts, as well as prcesses (Mueller, 2006). he University takes its place in the sciety in defining ne s pprtunity in reference t the quality f the educatin received, and in defining the level f peratin f the labr market. It can als be viewed as a plicy tl as it imprves scial mbility, adjusts the distributin f incme within a sciety, and als helps in channeling cmpatible skills with their respective fields fr ptimum utput t the industry and enhanced ecnmic perfrmance (Friedman, 2007). he term University is used here in its brader sense t refer t a higher level learning and research institutins with direct utput t the industry. A well crdinated relatinship between the university and the industry is critical, and s is the rle f the Gvernment in ensuring that the flw f knwledge between the University and the Industry thrugh the cmmercializatin f valuable ideas and skills is supprted by a favrable incentive structure which prmtes schemes such as spnsred researches and cnsulting agreements with research institutins, as well as supprt fr entrepreneurship 6

15 which in turn develps the industry by creating diversificatin and cmpetitiveness. Other frms f incentives fr innvatin culd als be applied t the inventr via cmpensatin, recgnitin, ryalties and equity. he flw f knwledge and skills between the University and the Industry thus ensures that innvatin is in cnstant expansin and the develpment f advanced technlgies as well as ideas frm bth the University and the Industry is cllective t imprve efficiency and t withstand glbal cmpetitiveness. 1.4 Scpe f the study he discussins cvered in this intrductry part f the dissertatin highlight the imprtance f aggregated energy efficiency at the industry level cmplemented by plicy regulatins capable f ffering a better quality f life, a sustainable ecnmy as well as a preserved envirnment t the sciety. Later chapters f this dissertatin elabrate n hw chemical prcesses are generated and hw specific thermdynamic parameters can be manipulated t reach ptimal energy efficiency hence imprving industrial perfrmance as a whle. Previus wrk by Patel et al. (2005, 2007) and Sempuga et al. (2010) have given methdlgies and tls t analyze and set targets fr verall prcesses using thermdynamics. his dissertatin ges a step further, where ne start putting pieces f equipment int the prcess and evaluate their effect n the thermdynamics f the verall prcess. We cnsider equipments such as the reactr, separatr and heat exchange and lk at hw certain parameters such as temperature and cnversin f these equipments will affect the target f the verall prcess. 7

16 Firstly, a basic prcess example where a specie (A) is transfrmed t prduce a specie (B) is used t cntextualize the theretical apprach used t understand the flw f wrk acrss a reactive chemical prcess. Secndly, a first case study n the ismerizatin f Butane fllwed by a secnd case study n the Reverse Water-Gas Shift (RWGS) prcess tgether illustrate hw thermdynamic assumptins such as temperature and cnversin under heat capacities (Cp) hypthesis affect the flw f wrk acrss chemical prcesses. In the first case study n the ismerizatin f Butane prcess, the effect f temperature and cnversin n the wrk flw acrss the prcess is evaluated as an example f a reactive prcess where the heat capacity (Cp) f the inlet stream t the prcess cntaining isbutane and the utlet stream f the prcess cntaining n-butane have almst the same values and cnsidered t be insignificant with 0.02 KJ/ml.K difference between the inlet and utlet streams f the prcess at 25 C (with KJ/ml.K at the feed stream and KJ/ml.K at the prduct stream). he secnd case study n the Reverse Water-Gas Shift (RWGS) prcess shws the effect f temperature and cnversin n the wrk flw acrss the prcess as an example f ne where the heat capacity (Cp) f the inlet streams t the prcess cntaining Carbn Dixide (CO 2 ) and Hydrgen (H 2 ) and the utlet streams f the prcess cntaining Carbn Mnxide (CO), Water in its gas phase (H 2 O), and any un-reacted feed as bi-prducts (CO 2 and H 2 ) have values that are significantly different frm each ther arund 5 KJ/ml. K average difference between the inlet and utlet streams f the prcess at 25 C (with 41.1 KJ/ml.K at the feed stream and 36.2 KJ/ml.K at the prduct stream). 8

17 Bth case studies n which this dissertatin is based evaluate the effect f temperature and cnversin n reactive prcesses at the difference that the inlet and utlet streams f bth prcesses represented have different magnitudes f heat capacity (Cp) between the inlet and utlet streams f the prcess. Cnclusins drawn frm this study will aim at prviding clarity and understanding n the effect f specific thermdynamic parameters (such as temperature, cnversin, and heat capacity) n reactive chemical prcesses and prevent further lss f resurces acrss the chemical industry. 9

18 2 AN INRODUCION O PROCESS SYNHESIS 2.1 Intrductin Prcess Synthesis is the develpment f prcess cnfiguratins that enables the cnversin f raw materials int prducts meeting the required specificatins in aim t imprve the verall prcess perfrmance. Prcess Synthesis results frm a series f decisins made during early stages f the prcess design and riginates frm a unit peratin cncept intrduced by Little in 1915 which relies n tw main dimensins f sustainability: Firstly whether the plant is fit-fr-purpse; and secndly whether financial returns are maximized. Prcess synthesis is als relying n unit peratins t satisfy tw ther dimensins f prcess sustainability: scial and envirnmental cnsideratins. Scial design cnsideratins ensuring that the health & safety factr, prvisins fr emplyment have been included as decisin features during the cnceptual phase f the prcess, while envirnmental design cnsideratins such as the minimizatin f emissins, envirnmental impact, as well as the amunt f feedstck have als been integrated during the prcess synthesis (Azapagic et al., 2004a). he mdern cncept f prcess synthesis is als based n unit peratins t develp ptimal prcesses which d nt necessarily result frm an arrangement f unit peratins set at their individual ptimal perfrmances, but rather result frm an verall prcess perfrmance cncept where ptimal equipment gemetry, prcess layuts, and perating cnditins are identified. he resulting flwsheet cnsist f intercnnectins and equipments rganized in their best arrangements with the aim f reducing csts (El-Halwagi, 2012), waste f raw material and energy as well as prevent GHG emissin and imprve efficiency, safety, and scale (Barnicki & Siirla, 2004). 10

19 It is imprtant t nte that in the past decades great prgress has been recrded in research in the field f prcess synthesis. he Center Of Material and Prcess Synthesis (COMPS) at the University f Witwatersrand is amng well knwn research grups wrldwide which has devted fr many years a cncrete fcus n the design f ptimal and feasible chemical prcesses. Innvative appraches by Patel et al. (2005, 2007) have prvided insightful methds t determine thermdynamic targets fr prcesses and have intrduced an analytical apprach t design ptimal flwsheets by ways f energy and mass balances. Several ther researchers including Sempuga et al. (2010) have brught mre light t the imprtance f the ntin f ptimizatin, mass and energy integratin in the cnceptual phase f a chemical prcess by illustrating pssible perfrmance adjustments that culd be applied t inefficient prcesses t vercme a histry f crippled chemical industry. 2.2 Prcess synthesis methdlgy he cnceptual phase f prcess synthesis cnsists f defining targets and analyzing their utcme and feasibility. Fr decades nw, varius appraches have been used in the industry t set targets amng which a cnceptual design practice knwn as System decmpsitin (Rudd, 1968) which splits the design int simpler sub-prblems t which slutins apply t the verall design. Fr this apprach t be efficient, the pint where the design splits int simpler sub-prblem must be identified, ecnmic evaluatin fr the incmplete design prblem must als be quantified. hese limitatins t the system decmpsitin apprach are reflected by its spare use during prcess synthesis. 11

20 Smith and Linnhff (1988) have intrduced an nin mdel which decmpses the chemical prcess int prcess design layers where the selectin f the inner-mst layer f the nin mdel, defines the requirements f the fllwing layers cnsecutively. Fr instance in Figure 2-1, the selectin f a reactr directly affects the ther layers f unit peratin namely the separatin system, recycle system, heat recvery, utilities, water and effluent. Figure 2-1. Onin mdel example applied t prcess synthesis prpsed by Zhan et al., 2013 A clsely related cncept knwn as the Hierarchical Decisin Prcedure (Duglas, 1985) prpses a design structure where the flwsheet is designed n a trial-and-errr basis fr decisins at varius assessment levels as shwn in Figure

21 Figure 2-2. Sample Hierarchical Decisin Prcedure fr prcess synthesis (Smith & Linnhff, 1988) Anther design practice knwn as Evlutinary mdificatin synthesis apprach (King et al, 1972) identifies pssible imprvements and alternatives befre mdifying the existing flwsheet. An additinal design practice knwn as Superstructure ptimizatin (Ichikawa et al, 1972) aims at imprving the perfrmance f the whle system by discarding f less advantageus ptins and remaining with the best ne. he superstructure ptimizatin is very similar t the Pinch analysis which suggests ways f setting practically achievable energy targets (Smith, 2000) fr the whle prcess since setting prcess equipments at their respective ptimal perfrmance wuld nt necessarily imprve the verall prcess perfrmance. Als, the Prperties hierarchy (Siirla & Rudd, 1971) which rganizes a series f prperties (mass, cncentratin, temperature, pressure, etc) and evaluates subsequently the effect f each n the prductin f the flwsheet s utput. 13

22 hese design appraches all revlve arund the same gals namely the minimizatin f energy and feedstck cnsumptin as well as preventin f GHG emissins which are amng the mst cmmn and imprtant basis fr setting targets. Fr this dissertatin, the apprach adpted in synthesizing an efficient prcess flwsheet is based n Prperties Hierarchy design methdlgy where the effects f assumptins such as temperature, cnversin, and thers are evaluated cnsecutively t identify their respective effects n the flw f wrk within reactive prcesses which in turn will identify prcesses energy efficiency and determine whether efficiency imprvement can be feasible. 2.3 Prcess Synthesis ecnmic benefit While early parts f this dissertatin discuss the place f energy within a sustainable develpment mdel, this part f the dissertatin fcuses n the ecnmic benefit assciated with Prcess synthesis. Prcess synthesis is a practice which desn t nly creates flwsheets n basis f feasible chemical, physical and unit peratin ptins, but als determines the ecnmic value f the verall chemical prcess based n prices and csts as it helps in identifying inferir design ptins and discard f prcesses with lw ecnmic perfrmance (Ichikawa et al, 1972). With the spread f glbalizatin, an increased pressure t decrease cst and increase prductivity has led the industry t justify the cst assciated t the cnstructin r mdificatin f an industrial plant by quantifying its benefits in ecnmic terms. Prcess 14

23 Synthesis is a fundamental tl used fr business decisins early in the design phase f the prject as it fixes 70 t 80% f the ttal cst f the prcess (Westerberg, 1989) while achieving an energy saving f 50% and a cst cutting f 35% (Siirla, 1996). he integratin f the thermdynamic feasibility tgether with business ratinal can lead t the creatin f ptimal industrial prcesses via the prmtin f systematic decisin framewrks in early cnceptual stages f the prcess. 15

24 3 HERMODYNAMIC ANALYSIS OF A PROCESS hermdynamics is a basic tl used during the design and analysis phase f a prcess t find ut whether a prcess is theretically pssible and realizable in practice. he first and secnd laws f thermdynamics prvide a fundatin t synthesize an energy efficient flwsheet using basic cncepts f energy (heat and wrk), equilibrium, and their relatinships t each ther as well as t temperature and cnversin. 3.1 Wrk flw in reactive prcesses Chemical prcesses are always accmpanied with a transfer f energy in r ut f the prcess. While heat is the mst cmmn and well understd frm f energy transfer, wrk is anther imprtant frm f energy that has a significant impact n energy efficiency and feasibility f the prcess; this wrk des nt refer t the mechanical wrk required t mve materials frm ne unit t anther acrss the prcess but rather refers t the wrk related t the chemical transfrmatin f the feed material int prducts. In this dissertatin, a methdlgy is prpsed t identify and analyze wrk flws acrss reactive prcesses. In rder t understand the cncept f wrk flw acrss a prcess, a basic example is used where a substance (A) is transfrmed int a substance (B) as represented belw: A B (3.1) his prcess has been chsen as an example fr its simple frm and t understand hw thermdynamic cnditins f reactive prcesses can influence the energy flw and, mre specifically fr this dissertatin, the flw f wrk within the prcess. 16

25 he prcess is assumed t be a steady-state simple prcess with inlet and utlet streams t the prcess at standard state (,P ) as illustrated belw: A Reactant (,P ) PROCESS B Prduct (,P ) Q H = ΔH Figure 3-1. Prcess setup as a Simple prcess where specie (A) reacts t frm specie (B) at standard state A Simple prcess as the ne shwn in Figure 3-1 is defined by Sempuga et al. (2010) as a prcess in which nly heat is exchanged with the surrundings at a single temperature and via a single pint (ften the reactr). his is nly pssible if we assume that the inlet and utlet streams t the prcess have the same heat capacities such that heat can be exchanged between them withut requiring extra cling r heating t bring the prduct t ambient temperature and/r t bring the feed t the reactr temperature. he effect f remving this assumptin is als part f this study and will be discussed as part f the secnd case study n the Reverse Water-Gas Shift (RWGS) prcess. Figure 3-1 is a representatin f the case where a prcess is endthermic and requires wrk in rder t perate. Many ther cases such as when heat and wrk are released, r when wrk is required t release heat, can als be explred. Evaluatins n which this dissertatin is based fcuses n the case where the prcess requires heat and wrk and assess hw the flw f wrk is affected by temperature and cnversin arund the reactr under the assumptin that the heat capacity f the feed (A) and that f the prduct (B) are equal. 17

26 Material streams in Figure 3-1 are represented by slid black lines carrying the feed (A) int the prcess and the prduct (B) ut f the prcess. he heat stream is represented by a dashed black line directed tward the prcess indicating that heat (Q H ) is supplied r needs t be supplied t the prcess. In rder fr any prcess t be feasible, bth the heat and wrk requirements f the prcess must be satisfied. Hwever fr the simple prcess shwn in Figure 3-1 and by definitin, must nly have ne pint f energy transfer in the frm f heat. hus, t satisfy the wrk requirement f the prcess, heat alne is used as the nly frm f energy transfer acrss the prcess. Heat by virtue f its temperature carries a specific amunt f wrk given by the Carnt engine equatin. hus when heat is transferred at a certain temperature t the prcess, it simultaneusly carries with it a certain amunt f wrk int the prcess. In rder t meet the wrk requirement f the prcess heat must be transferred at an apprpriate temperature specific t the prcess. his can be well understd by cnsidering the illustratin in Figure 3-2 belw: Reactants (, P ) PROCESS Prducts (, P ) Q H ( H ) HEng W s Q ( ) SURROUNDINGS Figure 3-2. Simultaneus transfer f heat and wrk t a Simple prcess via a heat engine cnfiguratin 18

27 Where the slid black lines in Figure 3-2 represent material streams fr the reactant ging in and prduct ging ut f the prcess fr which the mass balance is written in equatin (3.1); dashed lines represent energy streams supplied t the prcess as well as t the heat engine (HEng); and the intermittent dtted & dashed lines represent the verall system s bundary and the prcess bundary. he term Heat Engine in this dissertatin is used as a general term t refer t bth a heat engine (t cnvert heat t wrk) and a heat pump (t cnvert wrk t heat). he wrk carried int the prcess by the heat (Q H ) at a temperature H, can be understd as being supplied by a heat engine. he energy and entrpy balance fr bth the prcess and the heat engine system in Figure 3-2, will shw that the wrk required by the heat engine t supply the required amunt f heat at the required temperature is equivalent t the prcess change in Gibbs free energy between the inlet and utlet streams f the prcess Energy and Entrpy balance acrss the prcess ENERGY BALANCE An energy balance arund the prcess as shwn in Figure 3-2 maintaining the assumptins that the prcess is an pen steady-state prcess at cnstant temperature and pressure (,P ) is written as fllw: H Ek E p QH W (3.2) Where, (ΔH) is the change in enthalpy between the inlet and utlet streams f the prcess, Kinetic Energy (ΔE k ) as well as Ptential Energy (ΔE p ) will nt be accunted fr t simplify this study and are assumed t be negligible, (Q H ) is the heat supplied t the prcess, and where 19

28 the shaft wrk (W) is nil since n mechanical wrk is directly supplied t the prcess. he resulting energy balance frm equatin (3.2) becmes: H Q (3.3) ( ) hus in this case the amunt f heat supplied t the prcess (Q H ) via the heat engine setup is equivalent t the change in enthalpy (ΔH) between the inlet and utlet streams f the prcess. H ENROPY BALANCE An entrpy balance arund the prcess evaluates the quality f energy within the prcess by assessing the Entrpy generated (S gen ) als knwn as the cnversin f ptentially useful energy int useless thermal energy resulting in wrk that is irrecverably lst r Wrk Lst. he aim f evaluating the entrpy generated (S gen ) at the prcess referred t as (S gen(p) )- is t identify the maximum amunt f useful wrk which can be mved acrss the prcess and t minimize the amunt f irreversible wrk by manipulatin f thermdynamic parameters. An entrpy balance arund the pen steady-state prcess gives: Q S S (3.4) H ( ) gen( p) H Where, (S gen(p) ) is the entrpy generated at the prcess, (Q H ) is the heat requirement fr the prcess, and ( H ) is the temperature at which the heat (Q H ) is supplied t the prcess. Fr a thermdynamically reversible prcess as assumed fr this prcess, n entrpy will be generated (S gen(p) = 0), thus n wrk will be irreversibly lst. On the ther hand, fr an irreversible prcess where S gen(p) > 0, entrpy will be generated resulting in wrk that will be irrecverably lst (Wrk Lst). he Energy and entrpy balances are cmbined by eliminating Q H in bth equatin (3.3) and (3.4) t yield: 20

29 H S (3.5) ( ) ( ) Sgen( p) H he change in the Gibbs free energy acrss the prcess is given by: G H S (3.6) ( ) ( ) ( ) Eliminating S( ) between equatin (3.5) and (3.6) yields: G H 1 S ( ) ( ) gen( p) H (3.7) Fr a reversible prcess S gen(p) = 0 and thus equatin (3.7) becmes: G( ) H( ) 1 H (3.8) Energy and Entrpy Balance f the Heat Engine ENERGY BALANCE An energy balance arund the Heat engine is written as: U Ek E p Q Ws (3.9) Where, (Q) is the heat transferred frm the surrundings t the heat engine, (W s ) is the shaft wrk dne by the heat engine n its surrundings, Kinetic Energy (ΔE k ) and Ptential Energy (ΔE p ) will nt be accunted fr as they are assumed negligible, internal energy (ΔU) is nil since there is n change in vlume within the system. Simplifying equatin (3.9) gives: Ws Q QH Q (3.10) he shaft wrk (W s ) dne by the heat engine n its surrunding is equivalent t the difference between the heat supplied t the prcess (Q H ) and the heat supplied by the surrundings r cld reservir (Q ). ENROPY BALANCE 21

30 he Heat engine within the system in Figure 3-2 is assumed t be thermdynamically reversible where heat is used t carry the required amunt f wrk t the prcess by virtue f its temperature. his reversible Heat engine is als called Carnt Engine (Smith J.M. et al., 2005). An entrpy balance at the stream ging int the heat engine (S ) and the stream ging ut f the heat engine (S H ) is written as fllw: S H QH Q and S (3.11) H Because the heat engine is perated reversibly, n entrpy is generated, thus the ttal entrpy ging int the heat engine (S ) is equal t the entrpy ging ut f the heat engine (S H ) and as a result the change in entrpy (ΔS) arund the heat engine is nil as shwn in the relatinship belw: QH Q S SH S 0 (3.12) Where, (S H ) is the entrpy f the stream ging ut f the heat engine t the prcess r ht reservir, (S ) is the entrpy f the stream ging int the heat engine frm the surrundings r cld reservir. We cmbine the Energy and Entrpy balance by eliminating Q in equatin (3.10) and (3.12) t yield: H W s Q H 1 H (3.13) herefre, by lking at Figure 3-2 and equatins (3.3), (3.8) and (3.13) it can be cncluded that: G W (3.14) ( ) hat is, the change in Gibbs free energy acrss a simple prcess (a prcess with a single heat transfer at a single temperature) is equivalent t the amunt f wrk required by a heat engine, in rder t absrb heat frm the envirnment at ambient temperature and supply s 22

31 the required amunt f heat t the prcess at a required temperature. herefre the change in Gibbs free energy acrss the prcess at ambient cnditins is equivalent t the wrk requirement f the prcess. he temperature at which heat (Q H ) must be supplied t the prcess is referred t as the Carnt temperature ( Carnt ); it is the temperature at which the wrk carried by heat matches the wrk requirement f the prcess. G( ) H( ) 1 Carnt (3.15) Fr a simple prcess, when the prcess heat requirement ( H( )) is supplied at Carnt, n additinal wrk is required and n wrk will be lst and the prcess is reversible. Hwever if the prcess heat requirement is supplied at any ther temperature () than the Carnt temperature ( Carnt ), the prcess will either be wrk deficient r will lse wrk ptential depending n whether is abve r belw Carnt and the sign f H( ) and G( ) ; in this case the prcess will be irreversible and will generate entrpy as described by the fllwing equatin: G( ) ( ) 1 H Sgen( p) (3.16) Where the term S gen( p) is the additinal wrk that needs t be supplied in rder t meet the wrk requirement ( G( ) ) f the prcess r the wrk surplus carried in with heat and is lst. his term is generally referred t as the lst wrk ( W lst( p) ). hus: W S (3.17) lst ( p) gen( p) he Wrk lst term written as W lst(p) gives evidence f the irrecverable wrk which the chemical engineer can manipulate thrugh mass and energy balance t minimize its quantity. his Wrk lst -in fact- plays a majr rle in reducing energy waste acrss the prcess industry. As the aim nwadays is t save as much energy as pssible, the ideal target fr a flwsheet design is t cme up with ne which des nt favr entrpy generatin s 23

32 that the Wrk lst (W lst(p) ) is minimized rendering the prcess thermdynamically reversible and in turn benefiting frm the ttal amunt f heat and wrk ptential f the prcess. Hwever, since such an ideal situatin cannt be reached, the aim fr the engineer is t design a prcess as clse as pssible t an ideal situatin f zer W lst(p). It is t nte that fr all psitive values f W lst(p), wrk will be irreversibly lst; and fr all negative values f W lst(p), the prcess will be wrk deficient and will require additinal wrk t be supplied by ther means in rder fr the prcess t be feasible. An alternative equatin used t evaluate the Wrk lst (W lst(p) ) at the prcess at varius temperatures is given by the relatinship belw: 1 1 Wlst H p ( ) Carnt (3.18) Where when = Carnt, the Wrk lst term (W lst(p) ) ges t zer and n wrk is irreversibly lst. At any ther temperature abve r belw the Carnt temperature respectively, the prcess is either cnsuming mre wrk than needed (wrk lst) r is supplied with less wrk than required (wrk deficient). As a result wrk will either be irreversibly lst (W lst(p) > 0, S gen(p) > 0) r infeasible (W lst(p) < 0, S gen(p) < 0). he wrk lst at the prcess (W lst(p) ) written as per equatin (3.18) results frm a subtractin f equatin (3.16) frm equatin (3.15). herefre fr a prcess that requires heat and wrk t be supplied ( H( ) 0 and G( ) 0 ) wrk scenaris fr equatin (3.16) as interpreted abve can be illustrated as shwn belw: 24

33 (a) (b) (c) Additinal wrk W lst > 0 W Carnt ΔG W Carnt ΔG ΔG W Carnt Figure 3-3. Wrk flw scenaris acrss the prcess where in (a) the prcess wrk requirement is met thrugh heat, (b) the prcess wrk requirement is nt met thrugh heat alne, (c) the prcess wrk requirement is met with excess wrk Where in scenari (a) the prcess meets its exact wrk requirement by wrk supply thrugh heat alne, that is when = Carnt. In scenari (b) the prcess des nt meet its wrk requirement thrugh heat alne, the prcess is wrk deficient and infeasible as a simple prcess, additinal wrk must be added fr the prcess t be peratinal, that is when < Carnt and W lst < 0. In scenari (c) the prcess receives mre wrk than required and unless this wrk is recver it will be irreversibly lst t the surrundings, that is when > Carnt, W lst > 0, and a simple prcess is feasible. 3.2 he Effect f Heat capacity (Cp) n prcess wrk flw Heat Capacity f the feed equal Heat Capacity f the prduct (Cp feed = Cp prduct) S far we have lked at wrk flws arund a simple prcess, where it has been assumed that materials ging in and ut f the prcess have equal heat capacities (Cp) such that heat culd be exchanged between the tw streams t bring the inlet stream frm ambient temperature t the reactr temperature withut requiring external heating and t bring the exit stream frm the reactr temperature back t ambient temperature withut requiring external cling as shwn in Figure 3-4 belw: 25

34 HEA EXCHANGER WORK FLOW IN REACIVE PROCESSES A 1 2 REACOR B 4 3 Qr() Figure 3-4. Basic equipments set-up fr the Simple prcess where specie (A) reacts t prduce specie (B) nly If we cnsider the prcess in Figure 3-4 as being a simple prcess described by the hypthetical mass balance in equatin (3.1), then the feed material (specie A) is fed t verall prcess at ambient temperature and cnstant pressure (, P ) then ges thrugh a heat exchanger t step up the perating temperature frm ( ) t the reactr s temperature () befre prceeding thrugh the reactr where the reactin takes place at an assumed cmplete cnversin (x = 1). he prduct material (specie B) exits the reactr at temperature () then ges thrugh a heat exchanger nce again t step-dwn the stream s temperature frm reactr s temperature () t ambient temperature ( ) then prceeds t exiting the prcess at temperature ( ). here are n recycle/reflux streams r byprduct at this pint while feed and prduct materials enter and leave the prcess as pure cmpnents. Because the heat capacities f the streams in and ut f the prcess are assumed t be equal and n external heating is required, the change in enthalpy acrss the prcess is therefre equivalent t the change in enthalpy acrss the reactr and the change in Gibbs 26

35 free energy acrss the prcess is equivalent t the change in Gibbs free energy acrss the reactr. hus fr Cp in = Cp ut : H ( ) H ( ) ih ( ) ih ( ) Pr cess Reactr fi fi i p r ducts i r eac tants G ( ) G ( ) ig ( ) ig ( ) Pr cess Re actr fi fi i p r ducts i r eac tan ts (3.19) Where, ( HPr ( )) and ( GPr ( )) are the change in enthalpy between the inlet cess cess and utlet streams f the prcess and the change in Gibbs free energy between the inlet and utlet streams f the prcess at standard state (,P ) respectively, where ( H ( ) ) Reactr and ( G ( ) ) are the change in enthalpy f reactin and the change in Gibbs free Reactr energy f reactin at standard pressure (P ) and at the reactr temperature () respectively, (υi) is the stichimetric cefficient fr specie (i), where ( H ( )) and ( G ( )) are the change in enthalpy and Gibbs free energy f frmatins at standard cnditins (,P ) respectively. fi fi We therefre see that there are n wrk flws assciated with the heat exchanger with its surrundings since n external heat is added r remved frm the heat exchanger as a result frm all the wrk frm the ht stream (alng with its heat) being transferred t the cld stream f the heat exchanger; s in this case the prcess has nly ne pint f heat transfer which is at the reactr and thus nly ne pint f wrk transfer acrss the prcess Heat Capacity f feed different than Heat Capacity f prduct ( Cp feed Cp prduct) In the case where the heat capacity f the feed is nt equal t that f the prduct, the equatins in (3.19) will n lnger apply. In this case ne wuld need t evaluate the heat 27

36 capacity f each specie in rder t calculate the enthalpy and Gibbs free energy change acrss the reactr at the reactr temperature (). - his case needs t be cnsidered because the inlet and utlet streams nt having the same Cp will affect the wrk flw acrss the prcess since it implies that external heating r cling will be required t bring either the feed t the required reactr temperature r t cl dwn the prduct stream t ambient temperature; thus, the prcess will n lnger have a single pint f heat transfer but multiple pints f heat transfers which must be taken int accunt when analyzing wrk flws acrss the prcess. Additinally, the change in enthalpy (ΔH reactin ) and the change in Gibbs free energy (ΔG reactin ) acrss the reactr unit will als differ frm the change in enthalpy (ΔH prcess ) and the change in Gibbs free energy (ΔG prcess ) acrss the prcess. hus fr Cp in Cp ut : H ( ) H ( ) Pr cess Re actr G ( ) G ( ) Pr cess Re actr (3.20) he assumptin that heat capacities between inlet and utlet streams f the prcess r unit are far different applies t the secnd case study dne in this dissertatin n the Reverse Water-Gas Shift (RWGS) prcess where mre than a single heat surce will have t be supplied t the prcess fr it t prceed. he change in enthalpy (ΔH) between the inlet and utlet streams f the prcess r unit at temperature in this instance is given by the fllwing equatin: H( ) H( ) Cpd (3.21) 28

37 Where (ΔH ) is the change in enthalpy between the inlet and utlet streams f the prcess r unit at temperature, the term Cpd accunts fr the heat capacity change as a functin f temperature between the inlet and utlet streams f the prcess r unit. Nte that the heat capacity at cnstant pressure (Cp) f a cmpnent can be evaluated as a functin f temperature using the fllwing temperature dependent pwer series: Cp A B C D E i (3.22) Where the subscript (p) refers t the cnstant pressure heat capacity (Cp), where the subscript (ί) represents a specific specie, and where values fr cefficients A,B,C,D,E (3.22) are frm able 2 (APPENDIX A: List f ables ) f this dissertatin. he integratin using the Cp expressin in (3.22) in its expanded frm is written as: B 2 2 C 3 3 D 4 4 E 5 5 Cpd A (3.23) Under the same assumptin that heat capacities between inlet and utlet streams f the prcess are nt equal and calculating fr the change in entrpy (ΔS) acrss the prcess r unit is given by the equatin belw: S( ) S( ) Cp d (3.24) Where (ΔS ) is the change in entrpy between the inlet and utlet streams f the prcess r unit at temperature, the term d Cp accunts fr the heat capacity change as a functin f temperature between the inlet and utlet streams f the prcess r unit. he integratin in equatin (3.24) in its expanded frm is written as: 29

38 d C 2 2 D 3 3 E 4 4 Cp Aln B (3.25) he utcme frm bth assumptins: that the inlet and utlet streams f the prcess have equal heat capacities (Cp in = Cp ut ) r des nt have equal heat capacities (Cp in Cp ut ), is explained in subsequent parts f this dissertatin thrugh tw case studies n Butane ismerizatin and Reverse Water-Gas Shift (RWGS) prcess respectively. Fr simplicity Cp can be cnsidered t be independent f temperature and in that case the change in enthalpy (ΔH) acrss a particular unit at temperatures ther than the reference temperature ( ) can be estimated as fllws: ( ) ( ) H H Cp (3.26) Similarly, the change in entrpy (ΔS) between the inlet and utlet streams f prcess r unit at temperature can als be estimated as fllws: S( ) S( ) Cp ln (3.27) Where (ΔS ) is the change in entrpy between the inlet and utlet streams f the prcess r unit at temperature. he change in Gibbs free energy can then be calculated using (3.26) and (3.27) as fllws: G H S (3.28) ( ) ( ) ( ) Heat Exchanger energy and entrpy balance Here we are lking at the Heat Exchanger in Figure 3-4 fr the case where Cp feed Cp prduct. In this case the heat exchanger is nt able t either step up the temperature f the stream ging int the prcess carrying specie (A) (when Cp A > Cp B ) frm ( ) t the reactr s temperature () and thus wuld require additinal heat t be supplied externally in rder t 30

39 HEA EXCHANGER WORK FLOW IN REACIVE PROCESSES reach the reactr temperature, r t step-dwn the stream exiting the reactr carrying specie (B) (Cp A < Cp B ) frm reactr s temperature () t ambient temperature ( ) befre exiting the prcess and thus wuld require mre heat t be remved frm the prcess in rder t reach ambient temperature. he energy and entrpy balance arund the heat exchanger will reveal the wrk flw assciated with the additinal heat transfer at the heat exchanger. Let us explre this by cnsidering the Heat Exchanger setup as fllws: Q Hex A 1 2 B 4 3 Figure 3-5. Heat Exchanger setup within the prcess Where the slid lines in Figure 3-5 represent material streams ging in and ut f the Heat exchanger and where the dtted line represent the heat stream als carrying the wrk (W hex ) assciated with this heat. ENERGY BALANCE An energy balance arund the heat exchanger unit where Cp in Cp ut gives: H H Q H H 1 3 hex 2 4 H Q hex (3.29) 31

40 Where the subscripted numbers (1,2,3, and 4) refer t the streams in and ut f the heat exchanger as labeled in Figure 3-5, and where the change f enthalpy acrss the Heat exchanger is equivalent t the heat supplied t the Heat exchanger. ENROPY BALANCE An entrpy balance arund the heat exchanger where Cp in Cp ut gives: Q S S S S hex hex Q S hex hex (3.30) Where the subscripted numbers (1,2,3, and 4) refer t the streams in and ut f the heat exchanger as labeled in Figure 3-5, where (S) is the Entrpy f respective streams ging in and ut f the heat exchanger, where hex is the temperature at which the heat Q hex is supplied t the Heat exchanger. In a similar way as was dne in Sectin 3.1, the wrk assciated with external heat (Q hex ) transferred at the heat exchanger is equivalent t the mechanical wrk that a heat engine wuld require t absrb heat at ambient temperature and prvide a quantity f heat Q hex at temperature hex. hat is: W hex Q hex 1 hex (3.31) Als in the similar analysis as in Sectin 3.1, it can be shwn that this wrk is equivalent t the change in Exergy (ΔB) between the streams cming in and the streams cming ut f the heat exchanger. It is imprtant t nte that, the change in Gibbs free energy is equivalent t the wrk requirement nly if all the streams arund the prcess r unit are at ambient cnditins, 32

41 and P. When all the streams are nt at ambient cnditins, then the wrk requirement is equivalent t the change in exergy arund the prcess r the unit. he Exergy (B) f a stream at temperature and pressure P is defined as: B H S (3.32) (, P) (, P) (, P) hus by cmbining the energy and entrpy balance arund the heat exchanger (equatins (3.29) and (3.30)) and eliminating the entrpy terms by using equatin (3.32), we btain the fllws equatin fr a reversible heat exchanger: Whex Bhex H hex 1 revhex (3.33) We can als shw that in the case where the heat exchanger is nt reversible, that is when there is entrpy generatin equatin (3.33) becmes: W B H S hex hex hex 1 gen( hex) hex (3.34) Where S gen( hex) is the entrpy generated due t irreversibility cming frm transferring heat at a temperature, different frm the reversible temperature rev(hex). he change in exergy arund the heat exchanger in Figure 3-5 is calculated by expanding equatin (3.32) t give: d B Cp d Cp d Cp Cp hex A B A B d (3.35) Where, (W Hex ) is the wrk requirement at the heat exchanger, subscripts (A) and (B) refer t the species invlved in this prcess as shwn in Figure 3-4, (Cp) is the heat capacity term, is the temperature at which the feed stream is raised, and is the ambient temperature at which the prduct stream is cled. A psitive W Hex fr instance wuld mean that wrk is dne by the surrundings n the heat exchanger. 33

42 HEA EXCHANGER WORK FLOW IN REACIVE PROCESSES 3.3 he Effect f Cnversin S far we have lked at cases where there is cmplete cnversin f feed material t prduct in the reactr. In this part we explre the energy and wrk flw arund an additinal unit in the prcess, the separatr. he need fr a separatr ccurs when the prcess shwn in the mass balance in equatin (3.1) takes place at partial cnversin. Fr this example where specie (A) reacts t frm specie (B) at cmplete cnversin, there is n need fr a Separatr unit since the stream cming ut f the reactr nly cntains specie (B). If fr instance specie (A) reacted t frm specie (B) at partial cnversin and the resulting prducts -specie (A) and (B)- needed t be separated, a Separatr unit will be required at the exit f the reactr t direct the prducts in their respective streams as shwn in the figure belw. A (1ml) A (1+recycle) A (1+recycle) A (recycle) REACOR (X A = 1 ml) B (1 ml) SEP A (1+recycle-X A ) B (X A = 1ml) A (1+recycle-X A ) B (X A = 1ml) Wsep Qr() (W r ) Figure 3-6. Basic equipment setup within a simple prcess which includes a separatr t divide specie (A) frm specie (B) In Figure 3-6, fr 1 mle f specie (A) fed t the prcess t prduce specie (B) at partial cnversin (x), at the exit f the reactr: there will be an amunt f specie (A) exiting the 34

43 reactr equivalent t (1-x A ) and an amunt f specie (B) exiting the reactr equivalent t (x B ). Heat is exchanged between the streams cming in and ut f the reactr as was described previusly and then the prduct stream ges int a separatr as shwn in Figure 3-7. he separatr unit is designed as a reversible unit t prevent any additinal wrk requirement t perate the unit r any wrk lss t the surrundings. As a result, the heat lad at the separatr (Q Sep ) is nil and the wrk f separatin (W Sep ) is equivalent t the wrk f mixing at the reactr (W Reactr ) since: at the reactr, specie (B) is prduced and mixed with any un-reacted amunt f specie (A); and at the Separatr, the mixed species f (A) and (B) are un-mixed t their respective frms. he wrk f mixing generated at the reactr is virtually supplied t the separatr t meet its wrk requirement as shwn in the relatinship belw: W G nr xi ln xi (3.36) Sep mix(re actr ) Where, (W Sep ) is the wrk f separatin at the Separatr unit, (ΔG mix ) is the wrk f mixing at the reactr, (n) is the ttal number f mles present in the unit, (R) is the universal cnstant with its values available frm thermdynamic tables (see able 1 in APPENDIX A: List f ables), ( ) is the ambient temperature, and (x i ) is the mlar rati f a particular specie (i) ver the ttal mlar amunt. ENERGY BALANCE Cnsider the separatr depicted in Figure 3-7, the streams are assumed t cme in and ut f the separatr at ambient temperature and thus their enthalpies are given by: 35

44 H H H H H H 4( ) A( ) B( ) mixab( ) H 5( ) A( ) H 6( ) B( ) (3.37) herefre the change in enthalpy arund the separatr is: H H H H sep 5( ) 6( ) 4( ) herefre H sep H mixab( ) (3.38) he enthalpy change f mixing fr mst ideal mixtures is negligible. hus, if we assume ideal mixing then the energy balance arund the Separatr gives: 0 (3.39) H sep ENROPY BALANCE Similarly, the entrpy f the streams arund the separatr in Figure 3-7 is: S S S S S S 4( ) A( ) B( ) mixab( ) S 5( ) A( ) S 6( ) B( ) (3.40) herefre the change in entrpy arund the separatr is: S S S S sep 5( ) 6( ) 4( ) herefre S sep S mixab( ) (3.41) Unlike the enthalpy f mixing, the entrpy f mixing is nt negligible and is given by: S nr xi ln xi (3.42) mix Where n is the ttal number f mles f the mixtures, R is the ideal gas cnstant (refer t APPENDIX A: List f ables), and x i is the mle fractin f cmpnent i in the mixture. hus fr the mixture f A and B, the entrpy f mixing is: SmixA, B R( na nb)( xa ln xa xb ln xb) (3.43) he change in Gibbs free energy acrss the separatr is given by: 36

45 G H S (3.44) sep( ) sep( ) sep( ) Frm equatin (3.39) H sep 0 therefre: G S S G (3.45) sep( ) sep( ) mixa, B( ) mixa, B( ) We previusly shwed that the change in Gibbs free energy between the streams cming in and ut f a prcess r unit at ambient cnditins and P is equivalent t the wrk requirement f the prcess f the unit. herefre frm equatin (3.45) we see that the separatr requires wrk, equivalent t the Gibbs free energy f mixing, t be supplied, that is: WSep GmixA, B( ) R ( na nb)( xa ln xa xb ln xb) (3.46) We therefre see that althugh the energy balance suggests that n energy is required fr separatin, the entrpy balance shws that wrk (wrk ptential) must be supplied fr the separatin t take place. he minimum amunt f wrk required is equal t the wrk ptential that exist when mixing A and B, this wrk ptential is the Gibbs free energy f mixing. he wrk f separatin (W sep ) can be supplied t the separatr in tw ways: (1) By directly supplying mechanical wrk (W Shaft ). Fr example via pressure in membrane separatin) as shwn in Figure 3-7. A Wshaft B 5 6 SEP Wsep Qshaft (c) 4 A+B Figure 3-7: Supplying the wrk f separatin by directly adding mechanical wrk (shaft wrk) t the Separatr Energy in the frm f shaft wrk (W Shaft ) is added t the separatr and the same amunt f energy is remved frm the separatr in the frm f heat (Q Shaft ) at a temperature C, in this 37

46 way there is n net energy added r remved frm the separatr accrding t equatin (3.39), hwever the entrpy balance cmbined with the energy balance arund the separatr will shw that the wrk f separatin, W Sep is left behind in the separatr and is given by: W Sep WShaft C (3.47) W Sep can be thught f as virtual wrk r wrk ptential (because it des appear in the energy balance arund the separatr) needed t d separatin. We see frm equatin (3.47) that the higher C is the larger the amunt f shaft wrk is needed fr a fixed amunt f wrk separatin required. hus minimum shaft wrk is needed when heat (Q Shaft ) is remved at ambient temperature. (2) he wrk f separatin can als be supplied by adding and remving the same amunt f heat at different temperatures as shwn in Figure 3-8. A typical example f this is a distillatin clumn. A Wsep ( H ) B 5 6 SEP Wsep Qsep(c) 4 A+B Figure 3-8: Supplying wrk f separatin by adding heat at high temperature and remving heat at lw temperature A quantity f heat, Q Sep at a high temperature H is added t the separatr and the same quantity f heat is remved frm the separatr at a temperature C lwer than H. In this way there is n net energy added r remved frm the separatr accrding t equatin (3.39), hwever, in the similar way as with the previus case in (1), the entrpy balance in 38

47 cmbinatin with the energy balance will shw that wrk f separatin W sep is left behind in the separatr and is given by: 1 1 WSep QSep C H (3.48) 3.4 Heat and Wrk flw acrss the Reactr Fllwing evaluatins f heat and wrk flws at the prcess, a centered attentin is placed n the evaluatin f heat and wrk flw within the reactr. he reactr is the central unit within the prcess as shwn in Figure 3-9belw. he inlet stream t the reactr is at the required reactr temperature, after having been raised frm ambient temperature by the heat exchanger. he reactr is kept at the same temperature and thus the utlet stream frm the reactr is als at. In this discussin the reactr, as well as the ther units in the prcess, is kept at ambient pressure (P ). Heat (Q r ) at a the reactr, is added t supply the reactr with its energy requirements. he reactr is setup within the prcess as shwn in the figure belw: 39

48 HEA EXCHANGER WORK FLOW IN REACIVE PROCESSES A x A 1 2 x A B A Wsep 5 6 x B SEP 1-x A Qsep x A x B REACOR Qr() Figure 3-9. Reactr unit setup within a Simple prcess An energy balance arund the reactr will give the fllwing result: H E E Q W (3.49) r( ) k( ) p( ) r s Where, (ΔH r ) is the change in enthalpy between the inlet and utlet streams at the reactr at temperature Kinetic Energy (ΔE k ) as well as Ptential Energy (ΔE p ) will nt be accunted fr as they are assumed t be negligible, (Q r ) is the heat supplied t the reactr, and the shaft wrk (W s ) is nil since n mechanical wrk is directly supplied t the reactr. he resulting energy balance frm equatin (3.49) becmes: H Q (3.50) r( ) r Where, the subscript (r) refers t the reactr unit. An entrpy balance arund the reactr gives the fllwing relatinship: Qr Sr( ) Srut ( ) Srin( ) Sgen( r) (3.51) Where (S gen(r) ) is the entrpy generated at the reactr, and (S mix ) is the entrpy f mixing f specie (A) and (B) at the stream exiting the reactr at temperature. 40

49 We have previusly shwn that the wrk requirement (r wrk ptential) acrss a unit r a prcess, where the streams cming in and ut are nt bth at ambient cnditins, is given by the change in Exergy (ΔB) between the streams; thus by cmbining the energy and entrpy balance arund the reactr and knwing that B( ) H( ) S( ) we btain: B H S r( ) r( ) 1 gen( r) (3.52) Where, (ΔB r ) is the change in Exergy between the inlet and utlet streams f the reactr at temperature, (ΔH r ) is the change in enthalpy between the inlet and utlet streams f the reactr at temperature, ( ) is the temperature f the surrundings, and (ΔS r ) is the change in entrpy between the inlet and utlet streams f the reactr at temperature. Fr a reversible reactr, the change in Exergy (ΔB r ) between the inlet and utlet streams f the reactr at temperature can be written as: Br ( ) Hr( ) 1 Rev (3.53) Where, Rev is the reactr s reversible temperature. It is the temperature at which the heat requirement f the reactr ( H r ( )) must be supplied in rder t meet the wrk requirement f the reactr ( B r ( )). Rev can be evaluated by rearranging equatin (3.53) t give: Rev B 1 H r ( ) r ( ) (3.54) When the heat requirement is supplied at a temperature, ther than the reversible temperature Rev, the reactr wrk requirement will be described by equatin (3.52), where the term S gen( r) represent the wrk lst due t irreversibility. And thus the reactr will either be wrk deficient r will lse wrk depending n the sign f the heat and wrk 41

50 requirement as well as whether is abve r belw Rev. he lst wrk at the reactr can be evaluated by subtractin equatin(3.52) frm (3.53) t yield: 1 1 Wlst H r r( ) Rev (3.55) It is t nte that the change in Exergy (ΔB) at temperature and the change in Gibbs free energy (ΔG) at temperature are the same and bth refer t the wrk requirement f a prcess r a unit at temperature as shwn by the relatinship belw: B G H S (3.56) (, P) (, P) ( ) ( ) Where, (ΔB) at temperature is the change in Exergy, (ΔG) at temperature is the change in Gibbs free energy, (ΔH) is the change in enthalpy between the inlet and utlet streams f a unit r a system at temperature, ( ) is the temperature f the surrundings, and (ΔS) is the change in entrpy between the inlet and utlet streams f a unit r a system at temperature. 3.5 Reactin Equilibrium Fllwing the Secnd Law f thermdynamics, the ttal entrpy (r level f disrder) has a natural tendency t increase until it reaches its maximum at equilibrium state. Practically speaking, fr a chemical prcess where a reactin takes place in bth frward and reverse directin, the feed reacts t frm prducts in prprtins which will increase until the reactin reaches a state where the reactants and prducts cncentratin ratis n lnger change with time and where it is said t have reached the equilibrium state. he magnitude f the equilibrium cnstant (K) is an indicatin f hw far the reactin prceeds tward the prduct befre reaching equilibrium at a specific temperature. A small 42

51 value f (K) is an indicatin that the reactin prceeds very little tward the prduct, that is the prduct will in a smaller amunt at equilibrium r that there is almst n reactin taking place. A large value f (K) is an indicatin that the reactin prceeds almst cmpletely tward the prduct when it reaches equilibrium. Alternatively, when (K) has an intermediate value, the reactant and prduct are present in significant amunt at equilibrium. he relatinship between the Equilibrium cnstant (K) and temperature is shwn in the relatinship belw: dln K d H( ) (3.57) 2 R Where ( H( )) is the standard (at P ) change in Enthalpy f reactin, (R) is the Universal cnstant, the value f which is available frm thermdynamic tables (see able 1 in APPENDIX A: List f ables), () is the reactin temperature, and (K) is the Equilibrium cnstant. It fllws frm equatin (3.57) that fr an endthermic reactin with a psitive change in enthalpy ( H( ) ) f reactin, the equilibrium cnstant will increase as a functin f temperature. Inversely fr an exthermic reactin with a negative change in enthalpy f reactin, the equilibrium cnstant will decrease as a functin f temperature. he Equilibrium Cnstant (K) at temperature is ften estimated n the basis f the equilibrium cnstant at (written K ) using the Van t Hff equatin. his equatin assumes that the change in enthalpy ( H( )) f reactin is independent f temperature. he Van t Hff equatin is written as fllw: K H( ) 1 1 ln K R (3.58) 43

52 Where (K) is the equilibrium cnstant at a temperature, (R) is the Universal cnstant frm thermdynamic tables (see able 1 in APPENDIX A: List f ables), H( ) is the standard change in Enthalpy f reactin at ambient temperature, and (K ) is the Equilibrium cnstant at ambient temperature ( ) calculated frm the equatin belw: G( ) R ln K (3.59) Where ( G( )) is the change in Gibbs free energy f reactin standard temperature and pressure (,P ), and (R) is the universal gas cnstant. Bth ( G( )) and (R) values are available frm thermdynamic tables (see APPENDIX A: List f ables) and K given by: K G ( ) R e (3.60) he Van t Hff equatin is ften used as it gives a gd apprximatin n the equilibrium cnstant (K) at temperature which is an indicatin f the directin f the reactin withut perfrming lengthy calculatins fr the change in Gibbs free energy (ΔG) at temperature invlving heat capacity calculatins. he relatinship between the change in Gibbs free energy at temperature and reactin s equilibrium is well represented in the equatin belw: G R K (3.61) ( ) ln Where (K) is the Equilibrium cnstant at temperature, (R) is the Universal gas cnstant (see able 1 in APPENDIX A: List f ables), and (ΔG) is the change in Gibbs free energy between the inlet and utlet streams f the reactr at temperature als evaluated frm the fllwing relatinship: G H S (3.62) ( ) ( ) ( ) Where (ΔH) is the change in enthalpy between the inlet and utlet streams f the reactr at a temperature evaluated frm the relatinship in equatins (3.26) r invlving heat capacities calculatins, () is the temperature at which the heat is supplied, and (ΔS) is the 44

53 change in entrpy between the inlet and utlet streams f the reactr at a temperature evaluated frm the relatinship in equatin (3.27) als invlving heat capacities calculatins. Cmbining the energy balance and entrpy balances in equatins (3.50) and (3.51) respectively, and cmbining them with equatin (3.62) abve, t slve fr the change in Gibbs free energy acrss the reactr at temperature gives: G S (3.63) ( ) gen( r) In reference t equatin (3.63), fr a change in Gibbs free energy at a temperature equal t zer (ΔG = 0), he reactin is said t be reversible. Hwever equilibrium is reached at minimum ΔG. Perfrming a Gibbs free energy balance acrss the reactr where specie (A) enters the reactr at temperature and prduces specie (B) and un-reacted amunts f specie (A) in prprtins relative t cnversin (x) will give: H f Cp B Bd H f Cp A Ad G( ) Sgen ( x) S d d S f Cp B B S f Cp A A mix( AB, ) (3.64) Where subscripts (A) and (B) refer t the reactant and the prduct respectively; where (ΔG) at temperature is the change in Gibbs free energy between the inlet and the utlet streams f the reactr at a reactr s cnversin (x) t prduces the prduct; where (S mixa,b ) is the wrk f mixing at the stream exiting the reactr as evaluated belw: mix( AB, ) mix(3) S R (1 x)ln(1 x) ( x)ln( x) G R (1 x)ln(1 x) ( x)ln( x) S G mix( AB, ) mix(3) (3.65) 45

54 Where (G mix3 ) is the wrk f mixing at the stream ging ut f the reactr inversely equivalent t (S mixa,b ). he term -S gen(r) being a functin f reactin s equilibrium autmatically cnfirms that the wrk f mixing (G mix3 ) at the stream exiting the reactr is als a functin f equilibrium. w cnsecutive case studies n the ismerizatin f Butane fllwed by the Reverse Water-Gas Shift (RWGS) reactin are used t assess and cnfirm these relatinships. 46

55 4 CASE SUDY I: BUANE ISOMERIZAION PROCESS better illustrate the cncept f wrk flw in reactive prcesses, the ismerizatin f Butane is used as an example. his particular ismerizatin case study has been chsen fr its similarity t ur baseline assumptins where the prcess is an pen steady-state prcess at cnstant pressure which transfrms specie (A) t prduce specie (B) with the heat capacity f the inlet stream f the prcess being equal t the heat capacity f the prcess utlet stream. his example n the Butane ismerizatin prcess have almst equal heat capacities at the inlet and utlet streams f the prcess at temperature with Heat capacities values f KJ/ml.K at the inlet stream and KJ/ml.K at the utlet stream. Fr this case study the streams ging in and ut f the prcess are assumed t be equal because their difference is insignificant and thus is befitting t be cnsidered as a simple prcess. A cmparative evaluatin where heat capacities f the streams in and ut f the prcess have a large difference will fllw in later chapters f this dissertatin. his case study discusses the ismerizatin f Butane where is-butane als called i-butane; trimethylmethane; 1,1-dimethylethane; 2-methylprpane (Gas Encyclpedia, 2009) ismerizes t prduce n-butane as illustrated belw: Is-butane n-butane C H C H (4.1) Figure 4-1. Ismerizatin f is-butane (a) t n-butane (b) (Barrn, 2010) 47

56 HEA EXCHANGER WORK FLOW IN REACIVE PROCESSES Figure 4-1 shws the spatial cnfiguratins f is-butane (a) and n-butane (b) where bth Is-butane as well as n-butane have fur atms f carbn (in black) and ten atms f hydrgen (in white). Bth is-butane and n-butane are ismers f Butane with the mlecular frmula C 4 H 10, same empirical frmula, same bnd structure but different spatial arrangements. Fr this case study, ne mle f is-butane is fed as a pure substance t the prcess t prduce n-butane in quantities respective t cnversin. he amunt f feed t the verall prcess will remain ne mle fr the curse f this study while temperature and cnversin will vary cnsecutively t illustrate their respective effects n the wrk flw within the prcess. he ismerizatin prcess f Butane is graphically shwn in the figure belw: is-butane 1 2 REACOR x=100% n-butane 4 3 Qr() Figure 4-2. Basic equipments set-up fr the ismerizatin prcess f Butane at cmplete cnversin in the reactr Figure 4-2 shws the main equipments and streams invlved in the Butane ismerizatin prcess which is an in-depth reflectin f Figure 3-4 and where the feed material t the verall prcess (is-butane) at ambient temperature and pressure (, P ) ges thrugh a 48

57 heat exchanger t step-up the perating temperature frm ( ) t the reactr s temperature () then prceeds thrugh the reactr where the ismerizatin reactin takes place at cmplete cnversin. he feed and exit streams at the reactr exchange heat and reach their respective temperatures withut the need fr external heating r cling since the heat capacities f butane and is-butane are almst equal. he prduct material (n-butane) exits the reactr at temperature () befre ging thrugh a heat exchanger nce mre t step-dwn the stream s temperature frm reactr s temperature () t reference temperature ( ) and prceeds t exiting the prcess at temperature ( ) as a pure substance. here are n recycle/reflux streams fr this flwsheet r byprduct at this stage. he slid black lines in and ut f the prcess in Figure 4-2 represent material streams while the dashed line represents the energy stream, and intermittent dtted & dashed lines represent bundaries f energy balances perfrmed. Lking at the prcess as a whle and in rder fr this prcess t be peratinal, energy requirements in the frm f Heat (change in Enthalpy, ΔH at,p ) and Wrk (change in Gibbs free energy, ΔG at,p ) acrss the prcess must be met. What Sempuga et al. (2010) calls the ΔG-ΔH diagram (r gh-diagram) can be used t establish whether the ismerizatin prcess can be feasible and perated as a reversible simple prcess. he gh-diagram is shwn belw: 49

58 Figure 4-3. gh-diagram subdivided in thermdynamic regins (Sempuga et al, 2010) he gh-diagram is a graphical tl used t analyze the feasibility f chemical prcesses in term f heat and wrk lad as well as t establish the mst apprpriate methd f supplying r extracting wrk. he change in enthalpy acrss prcesses lies n the x-axis f the ghdiagram while the change in Gibbs free energy acrss prcesses lies n the y-axis f the ghdiagram. In Figure 4-3, the change in enthalpy (ΔH) and the change in Gibbs free energy (ΔG) are extensive prperties that are linked t the mass balance and nt directly t each ther. he fur main regins (1, 2, 3, and 4) f the gh-diagram shw whether the prcess heat and wrk is t be supplied r rejected and they are each subdivided in tw regins: Regins 1A- 4A and Regins 1B-4B as shwn in Figure 4-3. In Regins 1A, 2A, 2B, and 3A f the ghdiagram, it is pssible t run chemical prcesses reversibly as simple prcesses; while in Regins 1B, 3B, 4A and 4B, chemical prcesses cannt be run reversibly as simple prcesses 50

59 due t their unfeasible Carnt temperatures. he Butane Ismerizatin prcess lies in the gh-diagram as shwn belw: Figure 4-4. Butane ismerizatin prcess drawn in the gh-diagram he ismerizatin prcess f Butane is an endthermic prcess requiring 8.4 KJ f heat and 3.7 KJ f wrk in rder t prceed at cmplete cnversin. he amunt f heat requirement being greater than the amunt f wrk requirement fr this prcess is an indicatin that the prcess is feasible. Inputting the heat and wrk requirement values int Figure 4-4 shws that the prcess lies in regin 1A characterized by a psitive change in enthalpy as well as a psitive change in Gibbs free energy acrss the prcess represented n the gh-diagram. hus in principle supplying heat alne at an apprpriate temperature t the prcess shuld be sufficient t meet bth its heat and wrk requirement. Heat by virtue f the temperature will carry with it the wrk t the prcess as shwn in the heat engine cnfiguratin in Figure 51

60 3-2. In rder t meet the wrk requirement f the prcess via heat alne, heat must be supplied at least at the prcess Carnt temperature (538K) calculated frm equatin (3.15). 4.1 emperature effect n the prcess he apprach adpted in synthesizing an efficient prcess flwsheet fr the Butane ismerizatin prcess discussed in this dissertatin is based n prperties hierarchy design methdlgy where the effects f assumptins such as temperature and cnversin are evaluated cnsecutively t identify their respective effects n the flw f wrk acrss a prcess which in turn will identify the prcess verall energy efficiency and feasible efficiency imprvements. Based n targets and assumptins fr the synthesis f n-butane frm is-butane, it has been asserted that perating at the prcess reversible temperature (r Carnt temperature) wuld be mst beneficial since at the Carnt temperature heat is capable f carrying the minimum wrk requirement t the prcess thus the prcess wuld nt lse wrk nr will it be wrk deficient. emperature being an influential parameter t the verall prcess perfrmance as seen in the previus example where specie (A) reacts t frm specie (B), at Carnt temperature it has been recrded that the wrk requirement at the prcess culd be achieved. In this example n the Butane ismerizatin prcess, the flw f wrk acrss the prcess will be evaluated at the Carnt temperature where the prcess reversibility and equilibrium will be achieved as well as at different temperatures (between 300K and 1000K) and cnversins 52

61 (frm almst n cnversin t cmplete cnversin) t assess their respective effect n the flw f wrk acrss the prcess emperature effect n Reactin s Equilibrium Fllwing the Secnd Law f thermdynamics, the ttal entrpy (r level f disrder) has a natural tendency t increase until it reaches its maximum at equilibrium state. Practically speaking, fr a chemical prcess such as the ismerizatin f Butane where a reactin takes place in bth frward and reverse directin, the feed (is-butane) reacts t frm the prduct (n-butane) in prprtins which will increase until the reactin reaches a state where the reactants and prducts cncentratin ratis n lnger change with time where it is said t have reached equilibrium state. he relatinship between reactin s equilibrium and temperature has been established in a few equatins seen in previus chapters f this dissertatin. Applied t the ismerizatin f Butane reactin, the effect f temperature n the equilibrium cnstant (K) is pltted belw: 53

62 Figure 4-5. emperature effect Equilibrium cnstant fr the ismerizatin reactin Figure 4-5 shws that fr the endthermic ismerizatin reactin, the equilibrium cnstant (K) increases as a functin f temperature, thus encuraging the reactin t prceed frward (tward the prduct). At every pint n this increasing line in Figure 4-5, reactin equilibrium is reached. We ntice in Figure 4-5 that at the pint where = Carnt (538K), K =1, this can als be shwn using equatin (3.58). We als see that fr this case when K = 1, the equilibrium cnversin is 50% which means that the wrk f separatin wuld need t be supplied in rder t have pure prduct cming ut f the prcess, and a recycle will be needed t achieve the required prductin rate. We als knw that fr a simple prcess, where heat is added at the reactr nly and where it is assumed cmplete cnversin, when heat is transferred at = Carnt, the prcess as a whle is reversible. Hwever in this case, because f the limitatins 54

63 due t equilibrium cnversin, the prcess wuld nt be reversible since the prcess wuld require additinal wrk, in rder t separate the reactants frm the prduct. At temperatures abve the Carnt temperature, the reactin s equilibrium cnstant (K) is greater than ne, therefre the mixture cntains mre prduct than reactant and the wrk f separatin decreases, hwever frm the verall prcess pint f view wrk is lst, which can be evaluated frm equatin (3.18). At temperatures belw the Carnt temperature, the reactin equilibrium (K) is less than ne and the wrk lst at the prcess will be negative as evaluated frm equatin (3.18). hus fr this example fr K < 1, less prduct will be made and this might require larger recycle stream in rder t achieve the required prductin rate, thus the prcess might require a large amunt f wrk f separatin. Frm the prcess pint f view the ismerizatin prcess will be wrk deficient r infeasible as is; hwever if recvered, the large wrk f separatin may serve t cmpensate fr the wrk deficiency at the reactr. While the relatinship between temperature and reactin equilibrium has been established, the relatinship between the change in Gibbs free energy between the inlet and utlet streams f the reactr at temperature and the reactin equilibrium is assessed belw. he change in Gibbs free energy between the streams in and ut f the reactr at temperature, (ΔG ), is an indicatin f the directin f the reactin equilibrium as defined by the relatinship in equatin (3.61). Pltting the change in Gibbs free energy (ΔG ) acrss the reactr as a functin f temperature gives: 55

64 Figure 4-6. Change in Gibbs free energy acrss the reactr at temperature pltted as a functin f temperature Figure 4-6 shws a decreasing trend f the Gibbs free energy curve as a functin f temperature where the change in Gibbs free energy acrss the reactr at temperature curve crsses the x-axis at the reactr s reversible temperature (572K) evaluated as the temperature at which the difference between the Gibbs free energy at the stream entering the reactr and the Gibbs free energy at the stream exiting the reactr is nil because at this temperature the Gibbs free energy at the streams ging in and ut f the reactr are the same. Fr a negative (ΔG ), the Gibbs free energy at the stream ging int the reactr is greater than the Gibbs free energy at the stream ging ut f the reactr and -as per equatin (3.61), the crrespnding equilibrium cnstant (K) is greater than ne, thus the reactin is prceeding tward the prducts. Fr a psitive (ΔG ), the Gibbs free energy at the stream 56

65 ging ut f the reactr is greater than the Gibbs free energy at the stream ging int the reactr and -as per equatin (3.61), the crrespnding equilibrium cnstant (K) is less than ne, thus the reactin will nt prceed frward. he clse relatinship between the change in Gibbs free energy at temperature (ΔG ) and the -S gen term established in equatin (3.63) is an indicatin n the directin f the reactin s equilibrium. Pltting the -S gen term as a functin f temperature gives: Figure Sgen curve as a functin f temperature fr the Butane ismerizatin reactin he -S gen curve is a decreasing curve crssing the x-axis at the reactr reversible temperature (572K) because at this temperature the Gibbs free energy at the inlet stream f the reactr and the Gibbs free energy at the utlet stream f the reactr are equal. 57

66 Cnsequently, fr a psitive -S gen term, the prcess is prceeding tward the reactant (isbutane), and fr a negative -S gen term, the prcess is prceeding tward the prduct (nbutane). On these findings alne, in rder fr this prcess t meet its target and prduce n- butane, the change in Gibbs free energy between the inlet and utlet streams f the reactr at temperature will have t be nil r negative, and cnsequently the -S gen term will als be nil r negative. Based n the results n the effect f temperature n the ismerizatin reactin s equilibrium, additinal parameters will have t be included t these findings t make cmprehensive decisins. At the prcess level it is desirable t transfer heat t the prcess at the Carnt temperature where the prcess is reversible, while at the reactr level it is desirable t transfer heat t the reactr at the reactr s reversible temperature (572K) where the reactr is reversible and n waste f energy takes place. A dilemma arises when perating at the prcess reversible temperature, there are irreversibilities at the reactr and vice versa. But since when the prcess is perating at the reactr s reversible temperature (572K) irreversibilities ccur at the prcess level, it is preferable t supply heat t the prcess at its reversible temperature (Carnt temperature, 538K) where there are n irreversibilities ccurring at the prcess and maximize heat and wrk utilizatin within the prcess. Further investigatins n the wrk flw acrss the ismerizatin prcess will assess hw temperature affects the perfrmance f the Butane ismerizatin prcess which in turn will prvide basis fr decisin-making during the early stages f its prcess synthesis. 58

67 4.1.2 emperature effect n Wrk flw acrss the verall Prcess he flwsheet illustrated in Figure 4-2 shws majr equipments invlved in the ismerizatin prcess f Butane. he temperature f the streams cming in and ut f the verall prcess is intended nt t vary and remains at standard temperature and pressure thrughut these evaluatins, while the temperature at which heat is supplied t the reactr is varied (between K) t investigate its effect n the verall wrk flw acrss the prcess at its Carnt temperature (538K) as well as at ther temperatures. he change in Gibbs free energy (ΔG) at ambient temperature and pressure (,P ) acrss the prcess als called Ideal wrk is the minimum amunt f wrk required at the prcess and is given by the equatin belw: G H S (4.2) ( ) ( ) ( ) Where ( ) refers t the standard temperature, (ΔG) at temperature is the change in Gibbs free energy acrss the prcess als equivalent t the change in exergy (ΔB) at temperature as shwn in equatin (3.56), (ΔH) at temperature is the change in enthalpy acrss the prcess evaluated as per equatin(3.19), and (ΔS) at temperature is the change in entrpy acrss the prcess (refer t APPENDIX B: Calculatins). he change in Gibbs free energy between the inlet and the utlet streams f the prcess at temperature which is the wrk requirement fr the prcess des nt vary as a functin f temperature since the streams in and ut f the prcess are kept at ambient cnditins (,P ) irrespective f what ccurs within the prcess. Graphically, the change in Gibbs free energy (ΔG) between the inlet and utlet streams f the prcess at ambient temperature and pressure (,P ) is a cnstant linear curve at ΔG = 4.0 KJ and represents the amunt f wrk required by the ismerizatin prcess t prduce n-butane frm is-butane at 59

68 cmplete cnversin. It will be preferable t supply this amunt f wrk t the prcess reversibly thrugh a heat engine setup as shwn in Figure 3-2. We therefre see that the wrk requirement f the prcess remains the same irrespective f the temperature at which heat is supplied t the prcess, hwever there is nly ne temperature ( Carnt ) at which the wrk supplied with the heat matches the wrk requirement f the prcess, thus abve Carnt, mre wrk than required by the prcess is supplied with the heat this wrk will be lst if nt recvered; belw the Carnt less wrk than required by the prcess is supplied with heat, and thus the prcess wuld be wrk deficient unless additinal external wrk is supplied t the prcess emperature effect n the Wrk flw at the Heat Exchanger Evaluating the effect f temperature n the wrk flw at the heat exchanger will give an indicatin n whether wrk is absrbed, rejected, r nil at the heat exchanger. Fr this case f butane ismerizatin, it is clear that because the heat capacities f the streams in and ut f the prcess are very clse and almst equal, we have assumed them t be equal and therefre there is n need fr external heat transfer at the heat exchanger in rder t achieve the needed temperatures f the streams ging ut f the heat exchanger and thus there will be n wrk assciated with the heat exchanger. Fr the secnd case study n the Reverse Water-Gas Shift (RWGS) reactin where heat capacities at the streams ging in and cming ut f the prcess are significantly different, the heat and wrk evaluatins at the heat exchanger will be f relevance as it will affect the wrk flw within the prcess. 60

69 4.1.4 emperature effect n the Separatr Fr a simple prcess, it is assumed cmplete cnversin in the reactr and thus n wrk flw will be assciated with the separatr. Hwever even thugh we have used Butane ismerizatin prcess t demnstrate a simple prcess, we see that the cmplete cnversin assumptin will nt hld, because fr this prcess cnversin is limited by equilibrium in the reactr even when heat is supplied at Carnt, the prcess reversible temperature. herefre the prcess deviates frm being a simple prcess because f the wrk f separatin and a recycle that are required in rder t achieve a cmplete cnversin verall. he wrk f separatin can be calculated using equatin (4.3) Wsep is maximum at =rev = K 1.7 Wsep [kj] K [K] Figure 4-8: Wrk required by separatr as a functin f reactr temperature, withut recycle Figure 4-8 shws hw the temperature f the reactr affects the wrk required at the separatr when nly ne pass is cnsidered, that is n recycle. In this case the verall 61

70 prcess has incmplete cnversin that is the prduct (n-butane) prductin is less than 1 mle. W S W G (4.3) sep mix mix( reactr ) mix3 Where W sep is the wrk requirement at the Separatr, S mix is a mathematical equivalent t the wrk requirement at the Separatr, W mix(reactr) is the wrk f mixing at the reactr where the feed and the prduct generated are mixed, and G mix3 is the wrk f mixing at the stream exiting the reactr. he negative sign preceding the W mix(reactr) term in equatin (4.3) indicates that the wrk f mixing at the reactr is rejected. With an equal amunt f wrk requirement at the separatr, it appears as if the wrk f mixing is rejected at the reactr and absrbed at the separatr t split the mixed material in the reactr int separate streams. Frm Figure 4-8 we see that maximum wrk f separatin is required at = Rev = Carnt withut a recycle stream. Hwever the recycle stream needs t be added in rder t achieve cmplete cnversin fr the verall prcess, that is t be able t prduce 1 mle f n- butane frm 1 mle f is-butane; in this case the wrk required at the separatr as a functin f temperature is as fllws: 62

71 Wsep [kj] [K] Figure 4-9: Wrk required by separatr as a functin f reactr temperature, with recycle Frm Figure 4-9, we see that the wrk f separatin in this case decreases with increasing reactr temperature and this is because the size f the recycle als decreases as the cnversin increases with the reactr temperature. We will see what this means frm the pint f view f wrk flws arund the verall prcess in subsequent sectins emperature effect n Wrk flw at the Reactr Fr a simple prcess where it is assumed cmplete cnversin in the reactr, bth the stream cming in and that cming ut f the reactr are pure substances and thus n wrk f mixing is invlved. Fr this case, keeping in mind that the heat capacities are als equal, we can shw that the heat and the wrk requirement f the reactr are equal t the heat and wrk requirement f the entire prcess. hat is: W B G (4.4) r _ required ( ) r ( ) p 63

72 Where the wrk required (W r ) by the reactr, B( ) r is the change in Exergy acrss the reactr at the reactr temperature () and G( ) p is the change in Gibbs free energy acrss the prcess taken at ambient temperature. Fr the case f Butane ismerizatin, we saw that the cnversin at the reactr is limited by equilibrium and thus, the stream cming ut f the reactr is nt a pure substance but a mixture f reactant and prduct at a prprtins determined by the reactr temperature. Figure 4-10 is a plt f the wrk required by the reactr as a functin f reactr temperature at cmplete and incmplete cnversin. In bth cases the reactr prduces 1 mle f n- butane; hwever fr the incmplete cnversin case the amunt f is-butane in the feed t the reactr varies with temperature (i.e we allw fr recycle) in rder t achieve a prductin f 1 mle f n-butane fr all cnversin. 4 3 W r_required at cmplete cnversin at reactr 2 Wr_required [kj] 1 0 W r_required at incmplete cnversin at reactr [K] Figure 4-10: he wrk required by the reactr as a functin f reactr temperature at cmplete and incmplete cnversin 64

73 Figure 4-10 shws that when the cnversin at the reactr is cmplete the wrk requirement remain unchanged and is equal t that f the verall prcess at all temperatures. Hwever when the cnversin is incmplete the wrk requirement increases with increasing temperature but it is less than that f cmplete cnversin at all temperatures; the reasn fr that is because fr incmplete cnversin the wrk f mixing is included in the calculatin f the reactr wrk requirement, this implies that the wrk f mixing is used t supply fr sme f the reactr wrk requirement and thereby reducing the external wrk that needs t be supplied. In principle the wrk f mixing is nt recvered and is nt autmatically absrbed by the reactr, thus the plt in Figure 4-10 represents an ideal situatin where the wrk f mixing is recvered and absrbed by the reactr. We will cnsider that the wrk f mixing if nt recvered; it is simply lst and will be cnsidered as irreversibility in the reactr. HEA SUPPLIED O HE REACOR A DIFFEREN EMPERAURES Here we are cmparing the wrk that is supplied tgether with heat t the reactr at the reactr temperature versus the wrk requirement f the reactr. Remember that the wrk that is carried with heat at temperature is given by: W H r _ heat ( ) _ r 1 (4.5) Because the wrk f mixing is nt used by the reactr, it will nt be taken int accunt and therefre the wrk requirement f the reactr fr bth cmplete and incmplete cnversin will be the same. 65

74 7 6 W r_heat 5 4 Wr [kj] 3 W r_required 2 = rev W r_required = W r_heat = 537 [K] Figure 4-11: Cmparisn f the wrk required by the reactr with the wrk supplied with heat as a functin f temperature Figure 4-11 shws that when the heat supplied t the reactr is at temperature belw the Carnt, the wrk supplied with heat is less than what the reactr requires and thus the reactr wuld require additinal external wrk fr it t achieve the desired prductin rate. At Carnt, the wrk supplied with heat matches the wrk required by the reactr and thus in principle n additinal wrk is required at the reactr. Abve Carnt we see that heat carries mre wrk than required by the reactr and cnsequently the additinal wrk becmes irreversibility if it is nt recvered. he wrk deficiency r wrk lst at the reactr can be evaluated as a functin f temperature as fllws: 1 1 Wlst _ r H( ) _ r Carnt (4.6) 66

75 4.2 Wrk flws interactins within the prcess Previusly we have shwn wrk requirements and flws arund the majr equipments f the Butane ismerizatin prcess. Since the heat capacity f n-butane and that f is-butane are clse, we have assumed them t be equal and therefre we can ignre external energy transfers acrss the heat exchanger and nly fcus n the reactr and the separatr. We have shwn that if the reactr can achieve cmplete cnversin f is-butane t n- butane, there will be n need fr a separatr and that the reactr heat and wrk requirement will be the same as fr the entire prcess. In that case the prcess is a simple prcess which requires a single heat transfer at the Carnt in rder t satisfy the heat and the wrk requirement f the entire prcess. Hwever because the cnversin f reactin f is-butane t n-butane is limited by equilibrium, then there is need fr a separatr in rder and a recycle in rder t achieve the required butane prductin, that is 1 mle f butane frm 1 mle f is-butane. And therefre we see that there is an interactin between the reactr and the separatr and in this sectin we will explre this interactin. In Figure 4-12, we plt n the same figure the wrk required fr separatin, the wrk required at the reactr, the wrk supplied by heat at the reactr and cnversin as a functin f temperature, with cnversin axis n the right f the graph. 67

76 W Sep + W r_heat = Wrk supplied t prcess Wrk [kj] B A Cnversin Wr_heat = Wrk supplied via Wreactr = Wprcess = Wrk required by reactr/prcess Fractinal Cnversin 3 WSep = Wrk f separatin = 537 [K] Figure 4-12: emperature dependence f prcess parameters: Wrk f separatin, reactr wrk requirement, wrk supplied with heat and reactr cnversin In Figure 4-12 we see that equilibrium cnversin increases with increasing temperature but des nt reach a fractinal cnversin value f 1; each cnversin less than 1 crrespnds a certain amunt f wrk f separatin required. In fact we can see that even when heat is supplied at the reactr reversible temperature, cnversin is nly 50% (pint B) and thus the prcess still requires external wrk t be supplied fr separatin. We may recall that at the reversible temperature the heat added t the reactr carries with it wrk matching the wrk requirement f the prcess (shwn at pint A) and thus in principle n additinal external wrk is needed; hwever we can see frm Figure 4-12 that this is nt the case, ne still needs t supply the wrk f separatin due t cnversin limitatins at the reversible temperature. When < Carnt, the prcess is nrmally wrk deficient since the wrk supplied with heat at is less than what the prcess requires, but we see in Figure 4-13 that even at < Carnt, the prcess still receives mre wrk than required; this is because at these temperatures the 68

77 cnversin is lw and thus a large recycle is required in rder t maintain the prduct rate f 1 mle f n-butane per mle f is-butane, cnsequently the wrk f separatin is larger because f large amunt f material t separate. We therefre see that fr all temperatures at which the reactr perates at, the ttal wrk that ges t the prcess is mre than what is required and thus the prcess is irreversible, that is the ttal wrk supplied t the prcess is greater than the change in Gibbs free energy acrss the prcess: G H W ( ) ( ) 1 p r Sep Carnt (4.7) Where G( ) p is the wrk required by the prcess. he first term n the right hand side f the equatin represent the wrk supplied with heat at the reactr and the secnd term (W Sep ) is the wrk f separatin required given by equatin (3.46). We may als recall that fr a reversible prcess: G( ) _ ( ) _ 1 p H r Carnt (4.8) Fr the ismerizatin f butane ne can therefre cnclude that irreversibility in the prcess is : Caused by the lss f wrk f mixing in the reactr when the reactr is perated at Carnt. he wrk f mixing is caused by limitatins in cnversin due t equilibrium. A cmbinatin f the lss f wrk f mixing and irreversibility caused by supplying heat at any ther temperature than the Carnt. We therefre see that in rder t achieve a prductin f 1 mle f n-butane frm 1 mle f is-butane when the heat is supplied at the reversible temperature, we need t supply additinal wrk f separatin and thus this wrk becmes irreversibility t the prcess. 69

78 In rder t make the prcess reversible we must be able t recver the wrk f mixing frm the reactr and use it t supply fr the wrk required by the separatr. Alternatively if the reactr is able t use the wrk f mixing within itself then, in principle, its wrk requirement wuld be reduced by an amunt equivalent t the wrk f separatin and this will als make the prcess reversible. When the reactr uses the wrk f mixing then the wrk requirement f the reactr is given by: W B H S (4.9) reactr ( ) _ r ( ) _ r ( ) _ r Where the change in entrpy includes the entrpy f mixing as fllws: S S S S S (4.10) ut ut ut in ( ) _ r A( ) B( ) mix, A, B A( ) And when the reactr is reversible, heat must be supplied t the reactr at the reversible temperature ( Rev ). Rev here is nt the same as Carnt (the prcess reversible temperature) and Rev will nt necessarily match the current reactr temperature (). Rev is calculated frm the heat and wrk requirement acrss the reactr nly. hus fr a reversible reactr the heat and wrk requirement are related as fllws: B( ) _ r H( ) _ r 1 herefre Re v B 1 H ( ) _ r ( ) _ r Rev (4.11) 70

79 W sep + W reactr = W prcess 3 W sep = Wrk f separatin Wrk [kj] W reactr = Wrk supplied via rev [K] Figure 4-13: Wrk f separatin and wrk requirement f reactr when wrk f mixing is reintegrated in the reactr In Figure 4-13 the wrk requirement f the reactr (taking int accunt the wrk f mixing at the reactr s exit stream) and the wrk f separatin are pltted as a functin f the reactr temperature. We can see that the sum f these wrks matches the wrk requirement f the prcess and thus the prcess is reversible since the ttal wrk des nt exceed what the prcess requires. Hwever this requires that heat be added t the reactr at the reactr reversible temperature ( Rev ). Frm equatin (4.11) we can plt the reversible temperature f the reactr as a functin the actual reactr temperature as fllws: 71

80 rev [K] = the actual reactr temperature rev = temperature at which heat must be supplied t reactr [K] Figure 4-14: Reactr reversible temperature as a functin f the actual temperature in the reactr We may recall that the reactr reversible temperature ( Rev ) is the temperature at which heat must be supplied t the reactr in rder fr wrk within the heat t match the reactr s wrk requirement. We can see frm Figure 4-14 that Rev des nt match and is belw the actual reactr temperature (, the temperature which determines the wrk requirement f the reactr in equatin (4.9)) at all temperatures, and thus it may nt be pssible t transfer heat t the reactr while the heat surce is at a temperature lwer than that f the reactr. In cnclusin, the wrk flw analysis f the Butane ismerizatin case, indicates that the prcess can be run as a simple prcess nly if the reactr can achieve cmplete cnversin and if heat is supplied t the prcess at the Carnt temperature maximum energy efficiency can be achieved. Hwever because the cnversin f the Butane ismerizatin reactin is limited by equilibrium, the prcess cannt be run as a simple prcess since the energy fr 72

81 separatin needs t be added ver and abve the wrk requirement f the prcess and therefre the prcess is always irreversible even when heat is supplied at Carnt temperature. he surce f irreversibility is mainly due t the wrk f mixing being lst in the reactr. 73

82 5 CASE SUDY II: REVERSE WAER-GAS SHIF (RWGS) REACION he first case study n the ismerizatin f Butane has been used as an example t illustrate a simple prcess, and t analyze the effect f temperature n cnversin limitatins and wrk flw arund a prcess where the heat capacity f the streams ging int the prcess is very clse t the heat capacity f the streams cming ut f the prcess. hat is when ne can simply assume that the heat capacity f the feed material and that f the prduct material are equal. his assumptin has enabled us t simplify the prcess by eliminating wrk flw arund the Heat exchanger, and thus enabled us t cnsider the prcess as a simple prcess. Fr this secnd case study, the Reverse Water-Gas Shift (RWGS) reactin has be used as an example t illustrate the effect f temperature and cnversin n a prcess where the heat capacity f the stream ging int the prcess cntaining Carbn Dixide and Hydrgen is significantly different frm the heat capacity f the stream cming ut f the prcess cntaining Carbn Mnxide and Water steam. We will first start by assuming cmplete cnversin in the reactin in rder t be able t assess the effect f heat capacities f the feed and prduct stream n wrk flws arund the prcess; and then we will relax the assumptin f cmplete cnversin in rder t see the cumulative effect f cnversin limitatins as well as that f heat capacity differences between the feed and the prduct streams. he reverse reactin is called Water-Gas shift and is widely used in the gasificatin and refrming prcesses as well as petrchemical industry. he Reverse Water-Gas Shift prcess 74

83 is an endthermic prcess and is assumed t be an pen steady-state prcess with its mass balance written as shwn belw: Carbn Dixide + Hydrgen <=> Carbn Mnxide + Water Steam CO H CO H O (5.1) 2( g) 2( g) ( g) 2 ( g) Where Carbn Dixide (CO 2 ) and Hydrgen (H 2 ) in gas phase are fed t the prcess at ambient temperature and pressure (,P ) t prduce Carbn Mnxide (CO) and Water steam (H 2 O) as shwn in the flwsheet belw: Qad (ad) (Wad) CO2, P H2 1 2 MIXER 3, P 4 2nd Heat 5 x, P Exchanger, P, P HEA EXCHANGER REACOR x=100% CO H2O, P 8 9 SEP 7, P, P 6, P W Sep Qr () (Wr) Q H Figure 5-1: Setup f a RWGS prcess with cmplete cnversin in the reactr Fr this case study it is assumed that ne mle f Carbn Dixide and ne mle f Hydrgen are fed as pure substances t the RWGS prcess at ambient temperature and pressure (,P ) t prduce 1 mle Carbn Mnxide (CO) and 1 mle Water steam (H 2 O). he feed streams are first mixed, then fed t a Heat exchanger unit where heat is exchanged between the reactant and prduct streams. Hwever since the heat capacity f the reactant is greater than that f the prduct stream (Cp in >Cp ut ), then the reactant can nly be heated up frm 75

84 t a temperature f X lwer than the reactr temperature ; while the prduct stream can be cled frm t. herefre in rder fr the reactant stream t reach the reactr temperature, additinal heat Q ad must be supplied t a secnd Heat exchanger at ad t increase the stream temperature frm x t befre prceeding thrugh the reactr where the Reverse Water-Gas shift reactin takes place. he Prducts (Carbn Mnxide and Water steam) with byprduct (Carbn Dixide and Hydrgen) leave the reactr, ges thrugh a heat exchanger nce mre t step dwn the temperature frm t then ges thrugh a separatr unit t separate each prduct in their respective streams befre exiting the prcess at ambient temperature and pressure (,P ). Since it is assumed cmplete cnversin f the reactant int prduct; here is n recycle/reflux stream, hwever the prduct are cming ut the prcess as pure cmpnents, therefre there is need fr a separatr, t separate CO and H 2 O. he slid black lines in and ut f the prcess in Figure 5-1 represent materials streams while the dashed lines represent the energy streams, and intermittent dashed lines represent bundaries f energy balances perfrmed. he RWGS prcess is an endthermic prcess requiring 41KJ f heat and 28KJ f wrk t prceed at cmplete cnversin. he amunt f heat requirement being greater than the amunt f wrk requirement is an indicatin that the prcess is feasible. Inputting heat and wrk requirement values in the gh-diagram gives: 76

85 Figure 5-2. RWGS prcess drawn in the gh-diagram Figure 5-2 abve shws that the RWGS prcess lies in regin 1A f the gh-diagram meaning that the RWGS can be run reversibly as a Simple prcess if ne is able t meet the energy requirement f the prcess by supplying heat alne t the prcess at its reversible temperature (r Carnt temperature) t meet the prcess heat and wrk requirements. Given the change in Gibbs free energy and enthalpy acrss the prcess fr cmplete cnversin, the Carnt temperature fr this prcess can be calculated using equatin (3.15), and this gives Carnt = K. 5.1 emperature effect n the prcess at cmplete cnversin in the reactr 77

86 he Prperties Hierarchy design methdlgy is nce again used t evaluate the effect n temperature and cnversin n the flw f wrk acrss the RWGS prcess and assess the prcess verall energy efficiency in this case where the heat capacity f the inlet streams t the prcess is significantly different frm the heat capacity f the utlet streams t the prcess (~5KJ/ml.K difference). Fr this case study, the temperature, at which the reactr is perated, is varied and the effect n the wrk arund the prcess is analyzed emperature effect n Wrk flw at the Heat exchanger Because the difference in heat capacities at the streams in and ut f the RWGS prcess is significant, a certain amunt f additinal heat must be added r remved frm the heat exchanger in rder fr the streams cming ut f the heat exchanger t reach their desired temperatures, fr the reactant stream and fr the prduct stream. In this case the heat capacity f the reactant stream is greater than that f the prduct stream therefre an additinal amunt f heat Q ad must be added t the heat exchanger in rder t heat up the reactant stream t the reactr temperature, as shwn in Figure 5-1. he reactant stream is first heated frm t an intermediary temperature X by exchanging heat with the prduct stream while it cls frm t ; and then the stream ges int a secnd heat exchanger where external heat is added t heat it up frm X t. he additinal heat Q ad is given by the change in enthalpy acrss the heat exchanger; that is: Q H H (5.2) ad 5(, P ) 4( X, P ) If we assume that the secnd heat exchanger is reversible then we can calculate the wrk required by the heat exchanger in rder t raise the temperature f the stream frm X t. his wrk is given by the change in exergy acrss the secnd heat exchanger: W B B (5.3) ad 5(, P ) 4( X, P ) 78

87 hen we can calculate the temperature at which Q ad must be added in rder t meet the wrk requirement f the heat exchanger. Assuming that the heat exchanger is reversible ad is given by: ad W 1 Q ad ad (5.4) In principle heat is transferred in the heat exchanger at different temperatures, ad is then an average temperature between X and. In fact we can shw that ad is the lgarithmic mean temperature between X and, that is: ad X ln X (5.5) We therefre see that there is wrk flw assciated with the heat exchanger and since this wrk crsses the prcess bundary, it is necessary t evaluate the effect f the reactr temperature n the wrk flw at the heat exchanger. Pltting the wrk requirement at the Heat Exchanger as a functin f temperature gives: Wad [kj] [K] Figure 5-3: Wrk requirement at the heat exchanger as a functin f temperature fr the RWGS prcess 79

88 Figure 5-3 shws the increasing wrk requirement at the heat exchanger as a functin f temperature. Hwever ne can als see that the amunt f wrk transferred here is less than that f the reactr, thus the reactr will still have a greater influence n the wrk flw acrss the entire prcess. Further evaluatins f the wrk flw acrss the varius prcess equipments will prvide a clearer map fr the flw f wrk acrss the prcess emperature effect n Wrk flw at the Separatr and Mixer Althugh at this mment we assume cmplete cnversin in the reactr, tw different cmpnents are prduced and cme ut f the reactr as a mixture, therefre a separatr is required in rder t have pure cmpnents in the prduct streams, thus the need fr wrk f separatin. Cmplete cnversin means that the prductin rate f the prducts is cnstant and will nt depend n the reactr temperature. he wrk f separatin is given by the wrk f mixing in the prduct stream. On the ther hand the feed streams cme in the prcess as pure cmpnents and are mixed befre they enter the heat exchanger, thus there is wrk f mixing which can ptentially be recvered, hwever in this case this wrk is nt recvered and is cnsidered lst, therefre there is n wrk crssing the prcess bundary frm the mixer emperature effect n Wrk flw at the Reactr Wrk flw at the reactr is evaluated in rder t cnfirm whether the majr amunt f wrk is flwing thrugh the reactr; t assess hw this wrk varies with the temperature at which the reactr is perated; t investigate the cnditins at which the reactr can be run reversibly; and t capture hw these cnditins affect the prcess as a whle. Calculatins n the change in Exergy (ΔB) acrss the reactr will determine the amunt f wrk required 80

89 W r_required WORK FLOW IN REACIVE PROCESSES at the reactr (W r_required ) as per equatin (3.32). We can als evaluate the wrk that is supplied t the reactr via heat (W r_heat ) at the reactr perating temperature. he heat requirement f the reactr is given by the change in enthalpy between the reactants stream and the prduct stream. hus pltting bth wrks (W r_required and W r_heat ) as a functin f temperature gives: A Wreactr [kj] W r_heat Rev = 1077 [K] Figure 5-4. emperature dependence f the wrk required by the reactr at cmplete cnversin and that f the wrk supplied t the reactr via heat. he wrk required by the reactr (W r_required ) in Figure 5-4 decreases with increasing temperature, while the wrk supplied t the reactr via heat (W r_heat ) increases with temperature. he temperature at which W r_heat matches W r_required, pint A in Figure 5-4 is the reactr reversible temperature ( Rev ) here equal t 1077 K. When heat is supplied belw Rev, W r_heat is less than what the reactr requires fr cmplete cnversin, and as a cnsequence the reactr cnversin will be limited. he reactin will 81

90 prceed but the prductin rate f 1 mle f CO and 1 mle H 2 O per mle f H 2 and per mle f CO 2 will nt be achieved. On the ther hand when heat is supplied abve Rev, W r_heat is greater than W r_required, thus there will be wrk surplus in the reactr which will be lst if it is nt recvered and the reactr will be irreversible emperature effect n Wrk flw at the Prcess Understanding hw the flw f wrk is affected by temperature fr the RWGS prcess will give insights n the mst apprpriate temperature at which heat (ΔH () ) and wrk (ΔG ) shuld be supplied t the prcess. Heat t the prcess is supplied via the reactr and the secnd heat exchanger as shwn in Figure 5-1. here is n energy assciated with the separatr as explained in Figure 3-7 and Figure 3-8; therefre: H Q Q (5.6) ( ) p r( ) ad ( ad ) We nw see that in this case the heat requirement t the prcess is supplied at tw different pints and at tw different temperatures, thus the prcess is nt a simple prcess but a cmplex prcess. his means that, even if the prcess has a Carnt temperature ( Carnt = 969 K), the wrk requirement cannt be satisfied by simply adding heat at a single pint at Carnt as wuld be pssible in a simple prcess. In this case wrk must be added at different pint f the prcess, which are the heat exchanger, the reactr and the separatr. herefre: W G P _ required ( ) p W W W W P _ s upplied ad r Sep (5.7) Where W P_required, is the wrk that the prcess requires in rder t transfrm the feed material t the prduct material at the required prductin rate (fr this case 100% cnversin verall), W P_supplied is the ttal wrk supplied t the prcess, and W ad, W r, W Sep are 82

91 the wrks supplied t the prcess at the heat exchanger, the reactr, and the separatr respectively. he prcess is reversible when W P_supplied = W P_required W P_supplied 30 B W P_required 25 A Wrk [kj] 20 W r_heat W r_required W Sep W ad rev_p = 764 carnt = 969 Rev = 1077 [K] Figure 5-5. Wrk flws acrss the prcess as a functin f the temperature at which the reactr is perated with cmplete cnversin Figure 5-5 puts tgether the variatins f all the wrk flws and wrk requirements as a functin f, the temperature at which the reactr is perated. We can see frm Figure 5-5 that: When the reactr is perated at 764 K, the wrk supplied t the prcess via its equipments (W P_supplied ) matches the wrk required by the prcess (W P_required ) as shwn at pint B. he prcess at this pint is reversible there will be n wrk lss. We refer t this temperature as the prcess reversible temperature ( rev_p ), this is the temperature at which heat is supplied t the reactr t make the prcess as a whle reversible. It is different frm the Carnt temperature ( Carnt ) and frm the reactr reversible temperature ( Rev ). Remember that all ther variables f heat, 83

92 wrk and temperatures arund the prcess depend n the temperature f the reactr. Hwever we can als see that at rev_p, the wrk supplied t the reactr via heat (W r_heat ) is less than the wrk required by the reactr fr cmplete cnversin (W r_required ) thus at this pint the reactr is wrk deficient. he reactin will prceed but will nly reach a limited cnversin and therefre the prcess as a whle will nt achieve the required prduct rate unless additinal wrk is supplied. his can be dne by adding a recycle stream which will increase the wrk f separatin. When the reactr is perated at the Carnt temperature ( Carnt ), we can see that a surplus f wrk is supplied t the prcess (W P_supplied > W P_required ) which will be lst if nt recvered. Hwever at this pint the reactr is wrk deficient (W r_heat < W r_required ) thus cmplete cnversin cannt be achieved. Hwever if the wrk surplus f the prcess is recvered, it can be used t cmpensate fr the wrk deficiency at the reactr. At the reactr reversible temperature ( Rev ), the wrk supplied t the reactr via heat matches the wrk required by the reactr (W r_heat = W r_required ) as shwn at pint A, thus the wrk f the reactr is satisfied and the reactr is reversible; hwever the prcess as a whle has a surplus f wrk which will be lst if it is nt recvered. he additinal wrk (W ad ) that is required at the secnd heat exchanger des nt increase much with increasing temperature and is much less cmpared t that f the reactr. hus the reactr is the part f the prcess where much energy is supplied. We therefre see that, in this case where the heat capacity f the feed materials is nt equal t that f the prducts, running the equipments (mainly the reactr) reversibly des nt necessarily make the prcess reversible as a whle, and we als see that cnditins that are 84

93 required fr a reversible prcess may nt be ideal fr equipments. S, ne needs t find cnditins that will at least minimize wrk lsses fr the verall prcess. 5.2 Wrk flws arund the prcess with incmplete cnversin in the reactr In the previus case, we lk at the wrk flws arund the reactr assuming cmplete cnversin in the reactr. his enabled us t simplify the prcess by eliminating the need t separate the unused reactants frm the prducts and thereby eliminate the wrk f separatin. Althugh ne still has t separate the prduct cmpnents, the wrk f separatin required is fixed and des vary with the reactr temperature. herefre this allws us t assess the effect f the additinal pint f heat transfer t the prcess, which is required due t the difference in heat capacities between the feed and prduct materials. Here we relax the cmplete cnversin assumptin in the reactr and analyze the cmbined effect f cnversin limitatins as well as heat capacity differences. Since the reactin des nt g t cmpletin, the unreacted feed material needs t be separated and recycled back t the reactr in rder t achieve the required prductin rate. hus the prcess will be depicted as fllws: 85

94 Qad (ad) (Wad) CO2, P H2 1 2 MIXER 3, P 4 2nd Heat 5 x, P Exchanger, P, P CO2 H2 HEA EXCHANGER REACOR x<100% CO H2O, P 9 8 SEP 7, P, P 6, P W S Qr () (Wr) Q H Figure 5-6: Setup f a RWGS prcess with incmplete cnversin in the reactr w separate feed streams, ne cntaining Carbn Dixide as a pure substance and the ther cntaining Hydrgen als as a pure substance enter the pen steady-state prcess at ambient temperature and pressure (,P ), then ges thrugh a mixer unit t mix bth materials int ne as well as cmbine with the recycle streams materials befre ging thrugh a heat exchanger which steps up the stream s temperature frm t an intermediary temperature X then ges int a secnd heat exchanger where external heat is supplied t raise the stream temperature frm x t the reactr s temperature. he material leaving the heat exchanger enters the reactr (at temperature and ambient pressure P ) where the Reverse Water-Gas Shift (RWGS) reactin takes place. Frm the reactr, the material ges thrugh a heat exchanger t step dwn the stream s temperature t ambient temperature ( ) and prceed thrugh a separatr which separates the reactants (Carbn Dixide and Hydrgen) frm the prducts (Carbn Mnxide and Water steam). he prducts leave the separatr as pure cmpnents. 86

95 5.2.1 emperature effect n Reactin s equilibrium Fr the RWGS reactin, the feeds (Carbn Dixide and Hydrgen) react t frm the desired prducts (Carbn Mnxide and Water steam) in increasing prprtins until the reactin reaches a state where the reactants and the prducts cncentratin ratis n lnger change with time and where, it is said t have reached equilibrium state. Pltting the equilibrium cnstant as a functin f temperature gives: Figure 5-7. emperature effect n the RWGS reactin's equilibrium Figure 5-7 shws that the equilibrium cnstant (K) increases as a functin f temperature. he equilibrium cnstant curve ges frm clse-t-zer change in cncentratins f reactants t frm prducts t increasingly higher prprtins f reactants frming prducts. Nte that at the reactr reversible temperature Rev (1077 K) as well as n every pint n the 87

96 equilibrium cnstant curve, equilibrium is reached and it is at Rev that the equilibrium cnstant is equal t 1 (K = 1). Fllwing the findings n the effect f temperature n reactin s equilibrium, the subsequent evaluatin is n the effect n temperature n the change in Gibbs free energy acrss the reactr at temperature, (ΔG ) which is an indicatin n the directin f the reactin and cnsequently n the equilibrium state as expressed by the relatinship in equatin (3.61). he change in Gibbs free energy between the inlet and utlet streams f the reactr pltted as a functin f temperature gives: Figure 5-8. Change in Gibbs free energy acrss the reactr pltted as a functin f temperature Figure 5-8 shws that the change in Gibbs free energy evaluated at temperature is a decreasing curve crssing the x-axis at the reactr s reversible temperature (1077K) where 88

97 the difference between the Gibbs free energy at the inlet stream f the reactr and the Gibbs free energy at the utlet stream f the reactr is nil. Fr a negative change in Gibbs free energy between the inlet and utlet streams f the reactr (ΔG < 0) which crrespnds t an equilibrium cnstant greater than 1 (K > 1), the reactin will prceed tward the prducts; while fr a psitive change in Gibbs free energy between the inlet and utlet streams f the reactr (ΔG > 0), the equilibrium cnstant is less than 1 (K < 1), thus the reactin will prceed tward the reactants. he -S gen term as shwn in equatin (3.63) has als been established as an indicatin n the directin f the reactin s equilibrium. Shwn belw is the -S gen term pltted as a functin f temperature. Figure Sgen term pltted as a functin f temperature fr the RWGS prcess 89

98 he -S gen curve is a decreasing curve crssing the x-axis at the reactr s reversible temperature (1077K) where the difference between the Gibbs free energy at the inlet and that f the utlet streams f the reactr is nil. Fr a psitive -S gen term, the reactin is prceeding tward the reactants (Carbn Dixide and Hydrgen), and fr a negative -S gen term, the reactin is prceeding tward the prducts (Carbn Mnxide, Water steam and perhaps byprducts). In rder fr this prcess t meet its target and prduce Carbn Mnxide and Water steam, the -S gen term will have t be negative (-S gen < 0). 90

99 5.2.2 Cnversin effect n Wrk flw at the Prcess As seen in the first case study n Butane ismerizatin, and fr this case study as well, the wrk requirement acrss the prcess r change in Gibbs free energy at temperature is evaluated as a functin f cnversin and gives an indicatin n whether the flw f wrk acrss the prcess is affected by a change in cnversin. he change in Gibbs free energy acrss the RWGS prcess at temperature is pltted belw as a functin f cnversin: Figure Change in Gibbs free energy acrss the prcess pltted as a functin f cnversin he general trend f the change in Gibbs free energy acrss the prcess at temperature at varius cnversins which represents the wrk requirement at the RWGS prcess evaluated at varius cnversins are superpsed increasing linear curves. his is an indicatin that the change in Gibbs free energy acrss the RWGS prcess at temperature des nt varies as a functin f temperature but varies as a functin f cnversin which depends n 91

100 temperature and which influences the change in Gibbs free energy at temperature (ΔG ) such that ΔG will increase prprtinally with cnversin: the higher the cnversin, the higher the wrk requirement by the RWGS prcess Wrk f separatin with incmplete cnversin in the reactr In the previus case, cmplete cnversin is assumed and therefre the wrk f separatin is nly that required t separate the prducts int pure cmpnents and thus des nt vary with the reactr temperature. Nw we lk at the case where cnversin is incmplete and thus the wrk f separatin required includes that f separating the prduct streams frm the unreacted reactants Equilibrium cnversin Wsep [kj] Fractinal Cnversin Wrk f separatin [K] Figure 5-11: Wrk required fr separatin and equilibrium cnversin as a functin f reactr temperature Figure 5-11 shws the variatin f cnversin and that f the wrk f separatin with temperature. We can see that the wrk requirement fr separatin is much higher at lw 92

101 temperatures; this is due t the lw cnversins at lw temperatures which lead t large recycles in rder t achieve the required prductin rate. he wrk f separatin increases as the amunt f unreacted reactants increases Wrk flws arund the prcess with incmplete cnversin in the reactr In the previus case (sectin 5.1) we lked at the effect f heat capacities f the reactant and prduct streams n wrk flws arund the prcess at cmplete cnversin, nw here we nw lk at the effect f heat capacities f the reactant and prduct streams n wrk flws arund the prcess at incmplete cnversin in the reactr, which makes the wrk f separatin mre significant. he cmbined effect f all the wrks arund the prcess is depicted as shwn in Figure W P_supplied W P_required Wrk [kj] W r_heat A W r_required 15 W Sep 10 5 W ad Rev = 1077 [K] Figure 5-12: Wrk flws acrss the prcess as a functin f the temperature at which the reactr is perated with incmplete cnversin 93

102 In Figure 5-12 the effect f the wrk f separatin is nw mre significant at lw temperatures (because f lw cnversin) in the same rder as that f the reactr is at high temperature. he additinal wrk (W ad ) required at the heat exchanger is still much less ver the whle range f temperatures cmpared t that f the reactr and separatr. he mst significant effect f the cmbinatin f all these wrks is that the prcess is supplied with a surplus f wrk (W P_supplied > W P_required ) ver the range f temperatures chsen fr the reactr. his means that the prcess will be irreversible at all temperature unless there is a way f recvering the wrk surplus. We als see that W P_supplied des nt change much with temperature, and this means that the reactr temperature des nt have much effect n the irreversibility f the prcess, cntrary t what we see in Figure 5-3. herefre even when the reactr is run at its reversible temperature it will have n verall effect n the prcess. hus ne wuld want t run the reactr at as high temperature as pssible in rder t reduce the capital cst f the prcess; a high temperature in the reactr will lead t high cnversin, and therefre will reduce the wrk f separatin and the size f the recycle as well as that f the streams in the prcess; thereby reducing the size f equipments in the prcess. 94

103 6 GENERAL CONCLUSIONS AND RECOMMENDAIONS Reducing the amunt f energy cnsumptin in the chemical industry is ne f the elements tward sustainable develpment. In this dissertatin we present a methd f analyzing wrk flws arund a prcess using fundamental thermdynamic cncepts. We analyze the wrk flws arund a simplified chemical prcess in rder understand where majr wrk lsses ccur and hw they can be minimized, by using fundamental thermdynamic cncepts. he cncepts f Gibbs free energy, energy balance and entrpy balance as well as temperature and pressure, are clsely related with the basic design f a prcess. Analyzing the effect f temperature at which the reactr and the majr equipment in the prcess are perated, n the wrk flw in reactive prcesses have given insights n pssible design decisins that the chemical engineer can apply in aim t prduce ptimal flwsheets. Heat capacity difference f the material ging in and ut f the prcess has als been identified as a parameter affecting the flw f wrk acrss a reactive prcess. hrughut this dissertatin, the effect f temperature and that f heat capacities f feed and prduct material n the flw f wrk has been evaluated by first lking at a hypthetical prcess where specie A is cnverted t B and then lking at tw study cases, ne where the effect f heat capacities difference between the feed stream and the prduct stream f the prcess is ignred and the ther where this effect is taken int accunt. he fllwing cnclusin culd be drawn: - he case where specie A reacts t frm specie B. his case was a simple representatin f a basic evaluatin f wrk n a reactive prcess. his example has shwn hw the 95

104 majr pieces f equipments acrss a reactive prcess interact with each ther and gave the basic flw f wrk netwrk fr the prcess. In particular this case enabled us t define what we call a simple prcess which is a prcess where heat is supplied at a single pint and at a single temperature. In a simple prcess it is assumed that the heat capacity f the feed stream is equal t that f the prduct stream; in this way heat can be exchanged between these streams withut the need f additinal external heat t reach their required temperature. We were able t shw that, a single heat supply t a simple prcess allws t meet bth the energy requirement (given by the change in enthalpy acrss the prcess) and the wrk requirement (given by the change in Gibbs free energy acrss the prcess) simultaneusly when it is supplied at the Carnt temperature making the prcess reversible. - he case study n the Butane ismerizatin where is-butane reacts t prduce n- butane was used t crrbrate the findings f the hypthetical simple prcess. his case was used t shw the effect f temperature and cnversin n the Butane ismerizatin prcess where the difference between the heat capacities at the stream ging in the prcess and the stream ging ut f the prcess is insignificant, their heat capacity was cnsidered t be the same t enable us t cnsider the prcess t be a simple prcess. It was shwn that fr such steady-state endthermic reactive prcesses, it is nly when the cnversin in the reactr is cmplete that the prcess can be perated reversibly as a Simple prcess by supplying the prcess with its heat requirement at the Carnt temperature. It fllws that since the reactin is cmplete n separatr is required and since the heat capacity f the feed stream and that f the prduct stream are equal, n external energy is required at the heat exchanger, and thus all the wrk requirement f the prcess can nly be taken in by the reactr; therefre the reversible temperature at the prcess (Carnt temperature) is almst equal t the reversible temperature at the reactr. Hwever when the cnversin in the 96

105 reactr is nt cmplete due t equilibrium limitatins, it was shwn that the prcess wuld require additinal wrk fr separatin which decreases with increasing temperature. he prcess nw has tw pints where wrk is added and can n lnger be run as a simple prcess. It was als shwn that the prcess will have a wrk surplus at all temperatures and will be irreversible unless this wrk can be recvered. - he case study n the Reverse Water Gas Shift (RWGS) prcess where Carbn Dixide and Hydrgen react t prduce Carbn Mnxide and Water steam was used t shw the effect f temperature and cnversin n a prcess where there is a cnsiderable difference between the heat capacities f the streams ging in the prcess and the streams ging ut f the prcess. Fr such steady-state endthermic reactive prcesses, perating the prcess reversibly as a Simple prcess is nt pssible by supplying the prcess with heat required alne at the Carnt temperature because f the additinal external heat that is required at the heat exchanger. he prcess has tw pints f heat transfer at tw different temperatures. he heat requirement and the reversible temperature f the prcess are nt the same as thse f the reactr. It was shwn that if the cnversin in the reactr is cmplete there is a temperature at which the reactr can be perated which results in the ttal wrk supplied t the prcess (via the reactr and the heat exchanger) matching the wrk requirement f the prcess. his means that there is n wrk surplus r deficiency and therefre the prcess is reversible as a whle at a temperature called the reversible temperature f the prcess which is nt t be cnfused with the Carnt temperature. Hwever it was als shwn that at the prcess reversible temperature, the reactr was wrk deficient and cnsequently culd nt achieve cmplete cnversin and thus the prcess needed sme wrk f separatin in rder t achieve the required prductin rate. When the cnversin is nt cmplete, it was shwn that at all temperatures at which the reactr is perated, the ttal wrk supplied t the prcess (a cmbinatin f the 97

106 wrk at the reactr, at the heat exchanger and at the separatr) is greater than what the prcess requires, and thus the prcess always has wrk surplus. It was als shwn that fr the RWGS prcess the wrk surplus (r irreversibility) des nt change much with temperature and therefre in this case temperature has n effect n reducing fundamental inefficiencies in the prcess. Fr this case it is therefre recmmended that the reactr be run at as high temperature as pssible in rder t achieve a high cnversin which will then reduce the wrk f separatin required as well as reduce the size f the recycle and ptentially reduce the capital and perating cst f the prcess. Findings frm the abve evaluatins are cnclusive in a way that they prvide clear insights n hw and by hw much a reactive prcess can be imprved by adjusting the temperature which in turn refers t a specific cnversin f reactant int prduct. 98

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111 APPENDIX A: List f ables able 1. able f Cnstants Universal gas cnstant (R) R= 8.31 J/ml.K r KJ/ml.K able 2. able f Chemical Prperties (Yaws, 1999) HEA CAPACIY OF GAS Cp = A + B + C 2 + D 3 + E 4 [Cp- Jule/(ml K), - K ( K)] A B C D E Is-Butane e e e e -11 N-Butane e e e e -11 ENHALPY OF FORMAION OF GAS 500K Is-Butane N-Butane Hf = A + B + C 2 [Hf- KJule/ml, - K ( K)] A B C Is-Butane e e -05 N-Butane e e -05 GIBBS ENERGY OF FORMAION OF GAS 500K Is-Butane N-Butane Gf = A + B + C 2 [Gf- KJule/ml, - K ( K)] A B C Is-Butane e e-05 N-Butane e e-05 ENROPY OF FORMAION OF GAS jule/(ml K) Is-Butane N-Butane

112 APPENDIX B: Calculatins i. CALCULAION SHEE 1: BUANE ISOMERIZAION C H C H Is-butane n-butane A B Figure 0-1. Flwsheet fr the Butane Ismerizatin Butane ismerizatin prcess transfrms is-butane int n-butane. his example represents the case where the heat capacity difference between the streams in and ut f the prcess is significant (Cp in =Cp ut ). It is assumed that the reactant is fed t the prcess as a pure cmpnent at ambient temperature and pressure (,P ) and that the prducts are cming ut f the prcess as a pure cmpnent at ambient temperature and pressure (,P ). It is assumed that ΔH mix =0. 1. SREAMS H H H 1 f A (, P ) f A S S S 1 f A (, P ) f A G H S H H Cp d 2 fa S2 S f A CpA G H S A d 104