Thermodynamic Properties of CO 2 Mixtures and Their Applications in Advanced Power Cycles with CO 2 Capture Processes

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1 Thermodynamc Propertes of Mxtures and Ther Applcatons n Advanced Power Cycles wth Capture Processes Halong L Energy Processes Department of Chemcal Engneerng and Technology Royal Insttute of Technology Stockholm, Sweden

2 KTH, Royal Insttute of Technology School of Chemcal Scence and Engneerng Department of Chemcal Engneerng and Technology Dvson of Energy Processes SE Stockholm Sweden Copyrght Halong L, 2008 All rghts reserved TRITA-CHE Report 2008:58 ISSN ISBN

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5 Abstract: The thermodynamc propertes of mxtures are essental for the desgn and operaton of capture and storage (CCS) systems. A better understandng of the thermodynamc propertes of mxtures could provde a scentfc bass to defne a proper gudelne of purty and mpure components for the CCS processes accordng to techncal, safety, and envronmental requrements. However, the avalable accurate expermental data cannot cover the entre operaton condtons of the CCS processes. In order to overcome the shortage of expermental data, theoretcal modellng and estmaton are used as a supplemental approach. In ths thess, the avalable expermental data on the thermodynamc propertes of mxtures were frst collected; ther applcablty and gaps for theoretcal model verfcaton and calbraton were also determned accordng to the requred thermodynamc propertes and operaton condtons of CCS. Then, n order to provde recommendatons concernng calculaton methods for the engneerng desgn of CCS, a total of eght equatons of state (EOS) were evaluated for the calculatons concernng vapour lqud equlbrum (VLE) and volume of mxtures, ncludng N 2, O 2, SO 2, Ar, H 2 S, and CH 4. Wth the dentfed equatons of state, the prelmnary assessment of the mpact of mpurty was further conducted regardng the thermodynamc propertes of mxtures and the dfferent processes nvolved n the CCS system. Results show that the ncrement of the mole fracton of non-condensable gases would make purfcaton, compresson, and condensaton more dffcult. Comparatvely, N 2 can be separated more easly from the mxtures than O 2 and Ar. Moreover, a lower recovery rate s expected for the physcal separaton of /N 2 under the same separaton condtons. In addton, the evaluatons of the acceptable concentraton of non-condensable mpurtes show that the transport condtons n vessels are more senstve to the non-condensable mpurtes, thus, requrng very low concentraton of non-condensable mpurtes n order to avod two-phase problems. Meanwhle, the performances of evaporatve gas turbne ntegrated wth dfferent capture technologes were nvestgated from both techncal and economcal aspects. It s concluded that the evaporatve gas turbne (EvGT) cycle wth chemcal absorpton capture has a smaller penalty on electrcal effcency, but a lower capture rato than the EvGT cycle wth O 2 / recycle combuston capture. Therefore, although EvGT + chemcal absorpton has a hgher annual cost, t has a lower cost of electrcty because of ts hgher effcency. However, consderng ts lower capture rato, EvGT + chemcal absorpton has a hgher cost to capture 1 ton. In addton, the effcency of EvGT + chemcal absorpton can be ncreased by optmzng Water/Ar rato, ncreasng the operatng pressure of strpper, and addng a flue gas condenser condensng out the excessve water. Language: Englsh. Keywords: thermodynamc property, vapour lqud equlbrum, volume, equaton of state, nteracton parameter, mxtures, evaporatve gas turbne, chemcal absorpton, oxy-fuel combuston, cost evaluaton, capture and storage I

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7 Table of Contents Abstract... I Table of Contents... III Lst of Tables... V Lst of Fgures... VII Lst of Papers and Techncal Reports... IX Acronyms...XI 1 Introducton Global Warmng and Capture and Storage (CCS) Problems and Challenges Objectves Methodology Outlne of the Thess Part I: Thermodynamc Propertes of Mxtures Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Necessary Thermodynamc Propertes and Potental Operaton Condtons of CCS Avalable Expermental Data and Gaps Regardng and Mxtures Evaluaton of Calculaton Models on Thermodynamc Propertes of Mxtures Dscussons Impact of Impurty on Thermodynamc Propertes of Mxtures and Dfferent Processes Involved n the CCS Systems Impact of Impurty on Thermodynamc Propertes of Mxtures Impact of Impurty on the Dfferent Processes Involved n the CCS Systems Dscussons Part II: Evaporatve Gas Turbne Cycles Integrated wth Capture Evaporatve Gas Turbne Cycles Integrated wth Dfferent Capture Technologes System Confguratons Thermodynamc Performances of Varous Systems Economc Evaluaton on Varous Systems III

8 4.4 Investgaton of EvGT Integrated wth MEA Based Chemcal Absorpton Capture Regardng Electrcal Effcency Dscussons Conclusons Appendx References Acknowledgements IV

9 Lst of Tables Table 2.1 Major thermodynamc propertes of mxtures requred by the CCS system desgn and engneerng evaluaton Table 2.2 Estmated operaton condtons (P and T) of the CCS processes Table 2.3 Summary of the avalable expermental data for pure Table 2.4 Summary of the expermental data for bnary mxtures Table 2.5 Summary of TPxy ranges of the VLE expermental data for bnary mxtures Table 2.6 Summary of TPxy ranges of the volume expermental data for bnary mxtures Table 2.7 Summary of studed cubc EOS for VLE calculatons Table 2.8 Correlated k j for dfferent bnary mxtures based on VLE expermental data Table 2.9 AAD of EOS on the calculated VLE propertes of bnary mxtures Table 2.10 Supplement cubc EOS for volume calculatons Table 2.11 Correlated k j for dfferent bnary mxtures based on volume expermental data Table 2.12 AAD of EOS on both gas and lqud volumes of bnary mxtures (%) Table 2.13 Recommended equatons of state and ther correspondng accuraces for predctng VLE and volume of dfferent mxtures Table 3.1 Relatonshp between thermodynamc propertes and system parameters Table 3.2 Acceptable maxmum mole fracton of mpurtes at the gven temperatures and pressures Table 4.1 Input data and assumptons for the smulatons of gas turbne, compressors, chemcal absorpton and dehydraton Table 4.2 Compostons and propertes of feed streams and outlet streams Table 4.3 Comparson on electrcty generaton and nternal electrcty consumpton between combned cycle and EvGT cycle (n % of fuel LHV) Table 4.4 Assumptons made n the cost calculaton Table 4.5 Annual costs of dfferent systems V

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11 Lst of Fgures Fgure 1.1 Strategy to reduce global emssons Fgure 1.2 Basc prncples of three capture technologes for fossl fuel power generaton Fgure 1.3 Flow chart of ths study Fgure 2.1 Potental pressure and temperature wndows of the CCS systems Fgure 2.2 Relatonshp between calculaton accuracy and bnary nteracton parameter Fgure 2.3 AAD on P s, y s,co2, and P s +y s,co2 of /CH 4 at dfferent k j Fgure 2.4 AAD of PR EOS on P s, y s,co2, gas densty and lqud densty of /CH 4 at dfferent k j Fgure 3.1 Comparson of VLE characterstcs among the bnary mxtures contanng noncondensable mpurtes Fgure 3.2 VLE characterstcs of the mxtures contanng condensable mpurty SO Fgure 3.3 Heat capactes of dfferent components at dfferent temperatures Fgure 3.4 Enthalpy of dfferent gaseous mxtures Fgure 3.5 Volumes and denstes of mxtures at dfferent compostons Fgure 3.6 Smple process flow dagram of purfcaton Fgure 3.7 Relatve volatltes of the non-condensable components nvolved n mxtures Fgure 3.8 Energy consumpton of sothermal compresson work at dfferent compostons Fgure 3.9 Dschargng temperature and energy consumpton of sentropc compresson at dfferent CO compostons and pressures Fgure 3.10 Comparson on the compresson work of sothermal and sentropc processes Fgure 3.11 Energy consumpton of external refrgeraton requred by lquefacton at dfferent compostons and operaton condtons Fgure 3.12 Effectve volumes of dfferent mxtures at dfferent mole and mass concentratons Fgure 4.1 System sketch of System I (reference system): EvGT cycle wthout capture Fgure 4.2 System sketch of System II: EvGT cycle wth chemcal absorpton capture Fgure 4.3 System sketch of System III: EvGT cycle wth O 2 / recycle combuston capture Fgure 4.4 Breakdown of electrcty generaton and power consumpton (n % of fuel LHV) Fgure 4.5 Breakdown of the heat recovered for dstrct heatng and heat consumpton (n % of fuel LHV) Fgure 4.6 emssons per kwh produced electrcty and the capture rato Fgure 4.7 Comparson of capture cost of chemcal absorpton and O 2 / Fgure 4.8 Comparson of capture costs Fgure 4.9 Electrcal effcency of EvGT wthout/wth capture at dfferent Water/Ar rato Fgure 4.10 Specfc energy requrement and reboler temperature at dfferent strpper pressures Fgure 4.11 Confguraton of heat exchangers Fgure 4.12 Electrcal effcency at dfferent strpper pressures Fgure 4.13 Specfc reboler duty and electrcal effcency at dfferent condenser temperatures VII

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13 Lst of Papers and Techncal Reports Ths thess s based on the followng papers, referred to by the Roman numerals I- VIII, and techncal reports, referred to by the Roman numerals IX and X. Papers (appended): I. H. L, X. J, J. Yan. A new modfcaton on RK EOS for gaseous and gaseous mxtures of and H 2 O. Internatonal Journal of Energy Research, : II. III. IV. H. L, J. Yan. IMPACTS OF IMPURITIES IN -FLUIDS ON TRANSPORT PROCESS. In: Proceedngs of the ASME Turbo Expo 2006, Barcelona, Span May 8-11 th Paper No. GT H. L, J. Yan. PRELIMINARY STUDY ON PROCESSING IN CAPTURE FROM OXY-FEUL COMBUSTION. In: Proceedngs of the ASME Turbo Expo 2007, Montreal, Canada May th Paper No. GT H. L, J. Yan, J. Yan, M. Anheden. Impurty mpacts on the purfcaton process n oxyfuel combuston based capture and storage system. Appled Energy, 2008, In Press. V. H. L, J. Yan, Evaluatng cubc equatons of state for calculaton of vapour-lqud equlbrum of and mxtures for capture and storage processes. Appled Energy, 2008, In Press. VI. VII. VIII. H. L, J. Yan, PERFORMANCE COMPARISON ON THE EVAPORATIVE GAS TURBINE CYCLES COMBINED WITH DIFFERENT CAPTURE OPTIONS. Accepted by the Internatonal Green Energy Conference IV, Bejng, Chna H. L, S. Flores, J. Yan. Integratng Evaporatve Gas Turbne wth Chemcal Absorpton for Carbon Doxde Capture. Accepted by the Internatonal Green Energy Conference IV, Bejng, Chna H. L, J. Yan, Impacts of Equatons of State (EOS) and Impurtes on the Volume Calculaton of Mxtures n the Applcatons of Capture and Storage (CCS) Processes. Manuscrpt. Techncal Reports (not appended): I. H. L, J. Yan, J. Yan, M. Anheden. Evaluaton of Exstng Methods for the Thermodynamc Property Calculaton of mxture. KTH-Vattenfall, II. H. L, J. Yan, J. Yan, M. Anheden. Prelmnary Assessment of Impurty Impacts of mxture on Processng and Transport Process. KTH-Vattenfall, IX

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15 Acronyms Nomenclature: a, b Parameters n cubc equatons of state a 1, a 2 Parameters of modfed RK equaton C, c Heat capacty J/(mol K) c 1,, c 5 Constant to calculate heat capacty G Gas h Enthalpy kj/mol k j Bnary nteracton parameter L Lqud M General representatve of parameters n Mole number P Pressure MPa R Gas constant J/(mol K) T Temperature K V, v Molar volume mol/l u, w Parameters n 3P1T equaton of state x Mole fracton n lqud phase X Total mole fracton y Mole fracton n vapour phase Z Compressblty α Relatve volatlty ζ Bnary nteracton parameter of PT equaton of state Abbrevaton: AAD Absolute average devatons % ACCR Actual capture rato ASU Ar separaton unt Abs Absolute value BP Bubble pont BWR Benedct-Webb-Rubn CC Combned cycle CCR capture rato CCS capture and storage Comp Compressblty CS Carbon steel Dev Devaton DBDP Dfference between bubble pont and dew pont DP Dew pont ECV Effectve volume EOR Enhanced ol recovery EOS Equaton of state Equ. Equaton EvGT Evaporatve gas turbne FCT Flue gas condensng temperature FP Flat plate GHG Green house gases HAT Humd ar turbne IGCC Integrated gasfcaton combned cycle XI

16 IPCC ISRK LHV MEA MPR MSRK O&M PR PSRK PT PUR RK SRK SS STIG STP TEG TET TIT TRA T-S VLE W/A Intergovernmental Panel on Clmate Change Improved Soave-Redlch-Kwong Lower heatng value Mono-methyl ethanolamne Modfed Peng-Robnson Modfed Soave-Redlch-Kwong Operaton and mantenance Peng-Robnson Predctve- Redlch-Kwong-Soave Patel-Teja Purfcaton Redlch-Kwong Soave-Redlch-Kwong Stanless steel Steam njecton gas turbne Strpper pressure Trethylene glycol Turbne ext temperature Turbne nlet temperature Transport Tube-shell Vapour lqud equlbrum Water/Ar rato Subscrpt: c Crtcal cal Calculated exp Expermental g Gas, j Component labels l Lqud s Saturated 0 Reference status XII

17 1 Introducton 1 Introducton 1.1 Global Warmng and Capture and Storage (CCS) Emssons of greenhouse gases (GHG) have been assocated wth a rse n the global average temperature. The global average temperature has been ncreased by 0.74K snce the late 1800s and, accordng to the Intergovernmental Panel on Clmate Change (IPCC), s expected to further ncrease by another 1.1 to 6.4K by the end of 21 st century [1]. A global warmng may lead to serous consequences. For example, the average sea level has rsen by 10 to 20cm durng the past century, and an addtonal ncrease of 9 to 88cm s expected by the year 2100 [2]. Therefore, IPCC has stated that global GHG emssons should be reduced by 50 to 80 percent by the year 2050 [3]. The largest contrbutor amongst the greenhouse gases s carbon doxde ( ), whch s released by burnng such fossl fuels as coal, ol and natural gas, and by the burnng of forests. Carbon doxde capture and storage (CCS), whch nvolves the capture, transport and long-term storage of carbon doxde, s a techncally feasble method of makng substantal reductons of emssons. CCS s a crtcal technology amongst a portfolo of measures to lmt clmate change to a manageable level, along wth mprovng the effcency of energy converson and/or utlzaton, and swtchng to renewable energy resources. The mportance of CCS has been hghlghted n Fgure 1.1 as one of the key elements n the strategy of reducng greenhouse gas emssons [4]. At present, the man applcaton for CCS s n power generaton systems [5]. Fgure 1.1 Strategy to reduce global emssons [4] As shown n Fgure 1.2, there are three man technology optons for separaton from power plants: post-combuston capture, pre-combuston capture, and oxy-fuel combuston capture. Post-combuston capture means capturng from the flue gases produced by the combuston of fossl fuels and bomass n ar. It s a downstream process, n whch the n flue gas at near atmospherc pressure s typcally removed by a chemcal absorpton process usng absorbents such as alkanolamnes. Pre-combuston capture s to separate the fuel-bound carbon before the fuel s combusted. Ths nvolves a reacton between fuel and oxygen to prmarly gve a synthess gas or fuel gas, whch contans carbon monoxde and hydrogen. The carbon monoxde reacts wth steam n a catalytc reactor, called a shft converter, to gve and more hydrogen. s then separated, usually by a physcal or chemcal absorpton - 1 -

18 1 Introducton process. Oxy-fuel combuston capture means capturng from the flue gases produced n oxy-fuel combuston. The oxy-fuel combuston s the combuston takng place n a dentrogenaton envronment, resultng n a flue gas manly consstng of H 2 O and. The techncal-economc comparson of the three capture technologes s stll under way especally for large-scale ndustral applcatons. A preferable technology may hghly depend on ts further development and commercalzaton of the technologes. Fgure 1.2 Basc prncples of three capture technologes for fossl fuel power generaton 1.2 Problems and Challenges The thermodynamc propertes of mxtures are essental for the desgn and operaton of the CCS systems. How a specfc operaton parameter affects the performance and costs of the capture system hghly depends upon the knowledge of thermodynamc propertes of mxtures. For example, the vapour-lqud equlbrum (VLE) of mxtures s the basc parameters to desgn necessary purfcaton processes for mxtures captured from the flue gas of coal-fred power generaton. Meanwhle, for transportaton, t s preferable to transport n a hgh-densty state and avod the occurrence of two-phase flow n order to reduce the energy consumpton and nvestment costs, and to secure operaton safety. In order to guarantee the rght operaton condtons, the accurate thermodynamc propertes of mxtures are of great mportance to control and adjust parameters for the CCS system operaton. Therefore, a better understandng of the thermodynamc propertes of mxtures could provde a scentfc bass to defne a proper gudelne of purty and mpure components for the CCS processes accordng to techncal, safety and envronmental requrements. The more knowledge of the thermodynamc propertes, the more accurate, more economc, and safer gudelnes of purty could be defned. Moreover, new capture system development and techncal breakthrough wll also rely upon a deeper understandng of the thermodynamc propertes of mxtures and the related mpurtes. The exstence of mpurtes, however, makes t more dffcult

19 1 Introducton The most precse way to study the thermodynamc propertes of mxtures s va experments. However, there are some crtcal ssues regardng expermental data. Those CCS processes cover a large range of operaton condtons from normal atmosphere to supercrtcal state, and nvolve mult-component mxtures; therefore, the lmted expermental data cannot satsfy the requrements of the engneerng applcatons. In order to break the lmtatons of experments, theoretcal mathematc models are usually used to predct thermodynamc propertes. Due to the rapdly developng research on CCS, there has been an ncreasng nterest n fndng proper theoretcal models to predct the thermodynamc propertes of mxtures. So far, there are many avalable models of varous types. It has been proven that the relabltes of models vary for dfferent propertes, components and condtons [6-8]. However, only a lttle work has been done regardng several mxtures; and no comprehensve evaluatons and recommendatons are addressed concernng the applcatons n the CCS systems. For example, Carroll only studed Peng-Robnson (PR) [9] and Redlch- Kwong-Soave (SRK) equatons of state (EOS) [10] for the VLE calculatons of the bnary mxtures ncludng CH 4 and H 2 S [11-12]. 1.3 Objectves One of the man objectves of ths thess s to study the thermodynamc propertes of mxtures and analyze ther mpacts on the processes of CCS. In order to properly conduct the work, t s necessary to fnd or develop the proper models for the thermodynamc property calculaton. Another mportant objectve s to have an overvew of the advanced power cycles combned wth dfferent capture technologes, from both techncal and economc aspects, by applyng the results, obtaned from the property study, n the system smulatons. A novel gas turbne cycle, evaporatve gas turbne cycle (EvGT), was nvestgated as t s ntegrated wth chemcal absorpton capture and oxy-fuel combuston capture. 1.4 Methodology Fgure 1.3 llustrates the flow chart of ths study. The requred thermodynamc propertes and operaton condtons of CCS were frst dentfed n order to make the study more specfc; then the avalable expermental data on the thermodynamc propertes of mxtures were collected. Based upon the data, dfferent theoretcal models were evaluated and the recommendatons of calculaton methods were provded regardng the engneerng desgn of CCS systems. Wth the determned approprate methods, the mpacts of mpurtes upon the thermodynamc propertes of mxtures and the performances of dfferent processes nvolved n CCS were nvestgated. The results would be helpful to the desgn and optmzaton of the power cycles combned wth dfferent capture technologes. In ths study, our self-programmng codes are used to conduct the calculatons about the thermodynamc property and nvestgate the mpacts of mpurtes on some processes nvolved n CCS, such as compresson and flash purfcaton; whle the humd gas turbne cycles ntegrated wth capture are smulated wth Aspen Plus

20 1 Introducton Fgure 1.3 Flow chart of ths study 1.5 Outlne of the Thess The thess s a summary of eght scentfc papers, whch are appended, and two techncal reports. The research can be dvded nto two parts: Thermodynamc Propertes of Mxtures, whch ncludes Chapter 2 and 3; and Evaporatve Gas Turbne Cycles Integrated wth capture, whch ncludes Chapter 4. Chapter 2 nvestgates the calculaton methods about the thermodynamc propertes of mxtures. Secton 2.1 summarzes the requred thermodynamc propertes, the possble operaton condtons, such as temperature and pressure wndows for dfferent the CCS processes, and the potental mpurtes. In Secton 2.2, expermental data are collected concernng those requred propertes, and the expermental data gap s dentfed for the method evaluatons. In Secton 2.3, varous theoretcal models on the thermodynamc property calculaton are evaluated based upon the collected expermental data. Fnally suggestons on - 4 -

21 1 Introducton method selecton are provded n Secton 2.4. The presented materal s based upon Papers I, V and VIII and Report I Chapter 3 nvestgates the mpacts of mpurtes upon the thermodynamc propertes of mxtures and the dfferent processes nvolved n the CCS systems. It has been dentfed that mpurtes affect the CCS processes through ther mpacts upon the thermodynamc propertes of mxtures. The basc materal s taken from Papers II - IV and Report II. Chapter 4 addresses the study of the advanced power cycles combned wth capture processes. Secton 4.1 ntroduces three system confguratons ncludng EvGT, EvGT + Chemcal Absorpton Capture, and EvGT + Oxy-fuel Combuston. In Secton 4.2 and 4.3, those systems are analyzed from the vew ponts of both thermodynamc effcency and nvestment cost respectvely. In Secton 4.4, several ssues regardng the electrcal effcency are nvestgated. Results gven n ths chapter are based upon Paper VI and VII. Chapter 5 summarzes the conclusons found durng the course of ths research

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23 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Part I: Thermodynamc Propertes of Mxtures 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures 2.1 Necessary Thermodynamc Propertes and Potental Operaton Condtons of CCS Requred Thermodynamc Propertes and Ther Relaton to Engneerng Desgn The major thermodynamc propertes of mxtures requred by the desgn of the CCS systems have been dentfed based upon man processes and correspondng components as shown n Table 2.1 [13]. Meanwhle VLE and volume are the bass for other property calculatons. Therefore VLE and volume are consdered to be the most mportant propertes n ths study. Table 2.1 Major thermodynamc propertes of mxtures requred by the CCS system desgn and engneerng evaluaton Thermodynamc propertes Phase equlbrum Volume Enthalpy Entropy Capture Compresson Purfcaton Refrgeraton Transportaton Ppelne Small tanks Large tanks Storage Injecton Storage Operatng Wndows of the CCS Processes In order to determne the data needs for the evaluaton of thermodynamc propertes n the CCS processes, the operatng wndow should be defned wth the regons of phases and the CCS processes. The operaton condtons of the temperatures and pressures provde the bass upon whch to dentfy the relevant expermental data requrements and appled range, n whch property models should preferably be used to mnmze the uncertantes. A typcal CCS procedure from a fossl fuel power generaton normally conssts of four steps: capture from flue gas, processng (compresson, dehydraton, purfcaton/lquefacton, and further compresson/pumpng), transport and storage. The four steps make up a process chan for CCS. The operaton condtons of the CCS processes are estmated n terms of pressure and temperature n Table 2.2 [13]. Some subprocesses or optons for these CCS processes are ndcated n Table 2.2 as well. The P-T - 7 -

24 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures wndows are llustrated n Fgure 2.1, manly based on the estmated operaton condtons of the CCS processes. Table 2.2 Estmated operaton condtons (P and T) of the CCS processes CCS process P (MPa) T (K) compresson/purfcaton 0 to to Intal compresson 0 to to Dehydraton 2 to to Purfcaton 2 to to Further compresson/pumpng 5 to to transport 0.5 to to Ppelne 7.5 to to Small tanks 1.5 to to Large tanks 0.5 to to storage 0.1 to to Storage n Ocean Storage n Hydrocarbon Reservor Pressure (MPa) 10 1 Sold Dense Phase Lqud Lqud Trple Pont Transportaton n Ppelne Crtcal Pont Transportaton n Vessels Gas Compresson Process Temperature (K) Fgure 2.1 Potental pressure and temperature wndows of the CCS systems Impurtes n CO2 Mxtures Generally there are no strong techncal barrers to provde hgh purty of from the flue gas of fossl fuel fred power plants. However, hgh purty requrements are lkely to nduce addtonal costs and energy requrements resultng n a loss of power plant effcency. It s of mportance to fnd an optmal balance amongst the requrements from purfcaton, transport, storage, legal and envronmental aspects. The characterstcs of the streams captured from the power generaton may vary dependng on the capture technology used for CCS. The streams captured from post

25 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures combuston wth an amne soluton s relatvely clean. H 2 O s the man mpurty. However, relatve hgh levels of mpure components are expected n the captured streams from oxyfuel combuston, and a more complcated composton of the streams s found n the Integrated Gasfcaton Combned Cycle (IGCC) cases, manly ncludng dfferent hydrocarbons, such as CH 4. Based on the fuel converson processes for power generaton and the specaton of major mpurtes, the captured streams could be categorsed nto two types [14]: Oxdsng streams wth resdual O 2 and contamnated sulphur components manly wth SO 2 (e. g. captured from oxy-fuel and post combustons); and, Reducng streams wth almost no resdual O 2 and contamnated sulphur components manly wth H 2 S (e. g. captured from coal gasfcaton processes such as IGCC). The major dfferences of the two types of captured streams are the concentratons of noncondensable mpurtes such as N 2, Ar, and O 2 and types of mpurtes due to the dfferent redox condtons n the streams, for example the oxdsng sulphur speces SO 2 exstng n oxdsng streams whle the reducng speces H 2 S exstng n reducng streams. Therefore, the mpurtes, ncludng N 2, O 2, Ar, H 2 O, CH 4, SO 2, and H 2 S, are consdered for the study of the thermodynamc propertes of ther mxtures n ths research, whch may cover the most nterest non- components exstng n the captured streams. 2.2 Avalable Expermental Data and Gaps Regardng and Mxtures Accurate expermental data of both pure and mxtures ( + mpurtes) are requred to verfy the relabltes of calculaton models and calbrate parameters contaned n the models. Snce the 1980s, many experments wth hgher accuracy have been conducted for pure propertes. For the thermodynamc propertes of mxtures, nvestgatons were also carred out but focused manly on the mpurtes, such as water, hydrocarbons, ntrogen, and hydrogen sulphde due to ther mportance for producton and processng of natural gas resources and for usng the mxture for enhanced ol recovery (EOR) process. As a result, there are a lot of avalable expermental data about the mxtures of /H 2 O, /N 2, /CH 4, and /H 2 S, whch cover a wde range of temperature and pressure. However, the expermental data of the mxtures contanng O 2, Ar, and SO 2 are lmted, although such mpurtes n are mportant for the CCS processes, especally the oxy-fuel combuston technology. Avalable expermental data of pure are summarzed n Table 2.3. Dfferent knds of propertes ncludng volume, C p, VLE, and excess enthalpy are ncluded

26 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Table 2.3 Summary of the avalable expermental data for pure Source Year Type T (K) P (MPa) Uncertanty Holste et al [15] 1987 Volume P: ±0.01%; T: ±0.01K; Ernst et al [16] 1989 C p Duschek [17] 1990 VLE P: ±0.02%; T: ±0.003K a Glgen et al [18] 1992 Volume V:±(0.015~0.04)% Brachthuser [19] 1993 Volume V: ±(0.02~0.04)% Möller et al [20] 1993 Excess Enthalpy Fenghour [21] 1995 Volume P: ±0.02%; T: ±0.01K; Klmeck et al [22] 2001 Volume P: ±0.016% T: ±0.004K b ; Avalable expermental data of the mxtures contanng those mpurtes (N 2, O 2, Ar, SO 2, CH 4, H 2 O and H 2 S) are summarzed n Table 2.4. They are manly about the propertes of VLE and volume. Meanwhle almost all of them are about bnary mxtures. Table 2.4 Summary of the expermental data for bnary mxtures Source Year Type Mxture T (K) P (MPa) Uncertanty Caubet [23] 1901 TPVX /SO Reamer et al [24] 1944 TPxy /CH Steckel [25] 1945 PTxy /H 2 S Berlen et al [26] 1953 PTVX /H 2 S V: ±0.02% T: ±0.02K Donnelly et al [27] 1954 TPxy /CH Murbrook et al [28, 29] 1965 TPxy /O 2, /N 2, /N 2 /O Kestn et al [30] 1966 TPVX /Ar Greenwood [31] 1969 TPxy /H 2 O Up to 50 Fredenslund et al [32] 1970 TPxy /O Ara et al [33] 1971 PVTx /N 2, /CH Sarashna et al [34] 1971 PVTx /Ar Davalos et al [35] 1976 PTxy /CH Altunn et al [36] 1977 Comp /Ar Mraw et al [37] 1978 TPxy /CH Somat et al [38] 1978 TPxy /N Zawsza and Malesnska [39] 1981 TPVX /H 2 O Up to 3.3 Dorau et al [40] 1983 TPxy /N Patel and Eubank [41] 1988 TPVX /H 2 O Up to Esper et al [42] 1989 TPVX /N Sterner and Bodnar [43] 1991 TPVX /H 2 O Fenghour [44] 1994 TPVX /H 2 O Setz and Blencoe [45] 1999 TPVX /H 2 O * If partal pressure of was less than 5MPa, uncertanty was 1.5 percent. P: ±0.1% P: ±0.5% * T: ±1K P: ±0.5% T: ±0.02K P: ±0.01atm T: ±0.01K P: ±0.01atm T: ±0.01K P: ±0.015atm T: ±0.02K P: ±0.03% T: ±0.05K P: ±0.01%; T: ±0.01K P: ±0.015% T: ±0.01K P: ±1% T: ±1% o C P: ±0.02% T: ±0.01K P: ±0.01MPa T: ±0.01K

27 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Tables 2.5 and 2.6 summarzed the ranges of T, P, x and y of the expermental data on VLE and volume. There are stll some gaps between avalable expermental data and requrements of method for the evaluaton and calbraton. For example, there are few expermental data on VLE of /SO 2 at temperatures below 290K; there are few expermental data on VLE of /Ar, except at the temperature of K and pressure 5~10MPa; and there are no expermental data on volume of /O 2. Moreover only a few of the expermental data are avalable for mult-component mxtures such /N 2 /O 2. Table 2.5 Summary of TPxy ranges of the VLE expermental data for bnary mxtures T (K) P (MPa) x CO2 y CO2 No. of Exp. Pont /O /N /SO /H 2 S /Ar /CH /H 2 O Up to 310 0~0.99 0~0.99 >1000 Table 2.6 Summary of TPxy ranges of the volume expermental data for bnary mxtures Phase T (K) P (MPa) x CO2 y CO2 No. of Exp. Pont >1000 /O 2 V g NA V l NA /N 2 V g V l /SO 2 V g V l /H 2 S V g V l /Ar V g V l /CH 4 V g V l /H 2 O V g Up to >2000 V l > Evaluaton of Calculaton Models on Thermodynamc Propertes of Mxtures Introducton of the Calculaton Models The correlaton and predcton of mxture behavours are one of the central topcs n appled thermodynamcs. There are generally two types of thermodynamc methods for phase equlbrum calculatons: lqud actvty coeffcent based models and equaton-of-state based models. Actvty coeffcent models are the best way to represent hghly non-deal lqud mxtures at low pressures, and can be used to descrbe mxtures of any complexty. The equaton of state methods can be appled over wde ranges of temperature and pressure, ncludng sub-crtcal and super-crtcal regons. For deal or slghtly non-deal systems, the thermodynamc propertes for both the vapour and lqud phases can be computed wth a mnmum amount of component data. However, the EOS method has relatvely poor accuracy

28 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures for lqud phase calculatons. Consderng the wde range of operaton condtons of the CCS processes and many requred thermodynamc propertes, EOS may be more applcable than actvty coeffcent methods, because actvty coeffcent method can only be used n low pressure cases (usually those lower than 10atm) [47] and has more complcated procedure to calculate other thermodynamc propertes, such as volume, enthalpy, and entropy. A sem-emprcal EOS relates volume, pressure, temperature and composton of substances n mathematcal forms [46]. Any thermodynamc property can be obtaned from t by usng approprate thermodynamc relatons [48]. However, the development of such sem-emprcal equatons requres a great deal of expermental data on wde range to the correspondng substance. The shortage of those expermental data makes the progress slow and lmted to a few pure fluds nowadays. EOS can be dvded nto two categores: specalzed EOS, such as Span s EOS [49] for, and general EOS, such as van der Waals EOS [50]. Compared wth the latter, specalzed equatons have a better accuracy; however, ther applcatons are lmted to certan substances. For example, Span s EOS can only be appled to. Meanwhle the general equatons can be further dvded nto two types: equatons wth smple structures, such as Redlch-Kwong (RK) EOS [51]; and equatons wth complex structures, such as Benedct-Webb-Rubn (BWR) EOS [52]. Although the general equatons wth complex structure may gve better results, as they contan more parameters, ther calculaton procedures on the thermodynamc propertes are more complcated, especally when calculatng some derved propertes such as enthalpy and entropy. In addton, also due to the complcated calculaton procedure, t s more dffcult to ntegrate the general equatons wth complex structure nto some commercal software, such as Aspen Plus [47] and IPSpro [53], f they are not orgnally ncluded. Thus, from an engneerng standpont, a general EOS wth smple structure and reasonable accuracy s more preferable. Cubc equatons of state have very smple structures. Snce van der Waals proposed hs EOS n 1873, numerous modfed versons of cubc EOS wth two or more parameters have been developed to mprove predctons of volumetrc and phase equlbrum propertes of fluds. It has been well establshed that a cubc EOS can satsfactorly model phase equlbrum. In ths work, RK was modfed for gaseous and gaseous mxtures of /H 2 O; moreover the relabltes of cubc equatons of state were evaluated for predctng the thermodynamc propertes of mxtures A New Model for Gaseous CO2 and Gaseous Mxtures of CO2/H2O Snce the 1980s, new experments on gaseous and gaseous mxtures of /H 2 O have been conducted. However, lttle work on equaton of state has been done regardng the requrements of engneerng applcatons. Under such a stuaton, a new correlaton was developed wth the consderaton of new expermental data. It has been verfed that RK EOS [50] can represent vapour and lqud behavours effectvely. It was proposed n 1949 as: RT a P = (2.1) v b v 1/ 2 ( v + b) T Where a and b are parameters. Parameter a reflects ntermolecular attracton, and parameters b reflects molecular sze (repulsve forces). For smple non-polar gases, they can be calculated from crtcal data

29 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures R a = P RT b = P c c 2 T c 2.5 c Accordng to Bottnga s conclusons [54], f the parameters a and b were expressed by functons, RK EOS can descrbe propertes more accurately, even for polar gases. Therefore, n the current research, and based upon more precsely measured PVTs propertes, RK EOS wll be modfed for better precson for gaseous and for larger applcaton range for gaseous mxtures of and H 2 O. New descrpton of parameter a for gaseous s gven n Equ a = a 1 + a P a1 = 2 T a2 = 2 T RTc b = P 2 c T T T For gaseous /H 2 O, we modfed the mxng rules: T a = y y j aj (2.4) j b = y b (2.5) Wth 6 (2.2) (2.3) a j = a j = T T T T e (2.6) Compared wth expermental data, the absolute average devaton (AAD), whch s defned as: AAD = M cal M abs M exp N exp 100% of the new model s 1.68% for the volume of gaseous n the range K and MPa except for the crtcal regon ( K and MPa); and 0.93% for the volume of gaseous /H 2 O n the range K and MPa. Calculated results on other thermodynamc propertes, such as enthalpy and heat capacty, also ft the expermental data well. More detaled results were summarzed n Paper I. (2.7)

30 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Evaluatons of Cubc EOS for Predctng VLE and Volume of CO2 mxtures Predcton of VLE Fve cubc EOS wdely used n the petroleum and gas ndustres are evaluated for the calculaton on VLE propertes, ncludng Peng-Robnson (PR) [9], Patel-Teja (PT) [55], Redlch- Kwong (RK), Redlch-Kwong-Soave (SRK) [56], and 3P1T [57]. All studed equatons of state are summarzed n Table 2.7 wth the features as descrbed below: PR EOS s proposed based upon RK EOS. It s capable of predctng the lqud volume as well as vapour pressure n order to further mprove VLE predctons. It s recommended for hydrocarbon processng applcatons, such as gas processng, refnery, and petrochemcal processes. PT EOS has two substance dependent parameters whch are obtaned from the lqud volume and vapour pressure data, and correlated wth an acentrc factor. The 3-parameter PT equaton has been shown to gve satsfactory results for both vapour pressure and volume even for heavy and polar compounds. It s also recommended for hydrocarbon processng applcatons. RK EOS s the earlest modfcaton of van der Waals EOS; t mproved the ntermolecular attracton. It s more applcable for the system at low pressures. SKR EOS s another modfcaton of RK EOS by ntroducng a temperature-dependent functon to modfy the attracton parameter. It was one of the most popular EOS n the hydrocarbon ndustry. SRK s capable of predctng VLE for lqud mxtures; however, t s not very satsfactory for predctons of lqud compressblty. 3P1T EOS s an equaton of van der Waals type. It was prmarly developed for non-polar compounds, however, t was clamed to be able to be appled for polar substances as well [57]. The sem-emprcal equatons of state have been developed by usng pure component data. The applcaton of these equatons has been extended to a mult-component system by defnng mxng rules to evaluate the average parameters requred n the calculatons. In ths study, the conventonal random van der Waals mxng rules were employed for all of EOS. In the mxng rules, there s one very mportant parameter, bnary nteracton parameter k j, whch accounts for the attracton forces between pars of non-smlar molecules. Theoretcally, t s a modfcaton of ntermolecular attracton when calculatng thermodynamc propertes of mxtures. The value of k j s more senstve to dervatve or partal propertes such as fugacty coeffcents than to total propertes such as mxture molar volumes. For that reason, values of k j have most often been determned from VLE data. Snce the determnaton of k j requres a large amount of expermental data, the calbrated bnary nteracton parameters are not known for all the bnary systems and EOS. If the calbrated k j s unknown, for approxmate calculaton the dfference of attracton forces, whch are between non-smlar molecules and between smlar molecules, can be gnored, and dfferent molecules can be regarded as same. Thus, values of k j would be taken as zero (f (1-k j ) s used n the mxng rules, such as RK EOS) or unty (f (k j ) s used n the mxng rules, such as PT EOS)

31 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Table 2.7 Summary of studed cubc EOS for VLE calculatons EOS Functon Form Mxng Rule PR PT RK SRK RT P = V b V P = RT V b V RT P = V b V RT P = V + c b a ( V + b) + b( V b) a( T ) ( V + b) + c( V b) a T 0.5 ( V + b) a ( V + c)( V + b + c) RT a 3P1T P = 2 2 V b V + ubv + wb a = x x a a 1 j j 1/ 2 1/ 2 j ( k ) b = x b ; k j=k j ; a = x x a 1/ 2 a 1/ 2 ξ ; j j b = x b ; c = x c ; ξ j = ξ j a = x x a 1/ 2 a 1/ 2 1 k ; b a j = x b ; k j=k j = x x a 1/ 2 2 a 1/ 1 j j j j j j j j ( ) j ( k ) b = x b ; c = x c ; k j=k j a = x x a 1/ 2 a 1/ 2 1 k ; b = x b j j ; k j=k j j j ( ) However, an napproprate k j may cause a poor calculatng accuracy of an EOS. Fgure 2.2 shows the sum of average absolute devaton (AAD), on the saturated pressure and AAD on the saturated vapour fracton of (y s,co2 ) at dfferent bnary nteracton parameter k j, (to PT EOS, t s (1-k j )). It s clear that AAD changes wth the varaton of k j. j ; ; 40 AAD on P s + AAD on y s,co2 (%) VLE of /N 2 at 270K PR EOS PT EOS * RK EOS SRK EOS 3P1T EOS Absolute Average Devaton (%) VLE of /CH 4 PR EOS AAD on P s AAD on y s,co2 AAD on Ps + AAD on y s,co Value of k j Fgure 2.2 Relatonshp between calculaton accuracy and bnary nteracton parameter Value of k j Fgure 2.3 AAD on P s, y s,co2, and P s +y s,co2 of /CH 4 at dfferent k j In order to mprove the accuracy of cubc equatons and evaluate EOS precsely, the bnary nteracton parameters of varous bnary mxtures must frst be determned. Usually, the bnary nteracton parameter k j s consdered to be ndependent of temperature, composton, and volume [58]. However, there are also some dfferent conclusons that k j s temperature and composton dependent [59-61]. As k j s determned by matchng the predcted values wth expermental data, t should be consdered as a fttng parameter only and not a rgorous physcal parameter [7]. Hence, n ths study, the value of k j s stll regarded as a constant

32 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures The saturated pressures and saturated vapour compostons have been calculated from the known saturated temperatures (T s ) and saturated lqud compostons (x s ). Fgure 2.3 shows the AAD of PR EOS on P s, y s,co2, and P s +y s,co2 of /CH 4 at dfferent k j. Ths clearly dsplays that for varous propertes, the bnary nteracton parameter may be calbrated as dfferent values. Snce both saturated pressure and saturated vapour composton are mportant to the CCS processes, here k j s calbrated as the value that makes the sum of AAD on P s and y s,co2 mnmum (For /Ar and /SO 2. because x s and y s are not known at dew ponts and bubble ponts, respectvely, no AAD on y s,co2 /x s,co2 are calculated. In these cases, the value of k j that makes the AAD on P s mnmum s chosen.). The flow chart of the procedure for regressng k j s shown n Appendx A. Based upon the expermental data lsted n Table 2.4, k j was calbrated for each EOS concernng each bnary mxture. Snce /H 2 O has been examned ntensvely n prevous studes [62, 63], here H 2 O s excluded. Results are gven n Table 2.8. Table 2.8 Correlated k j for dfferent bnary mxtures based on VLE expermental data PR PT RK SRK 3P1T /CH /O /H 2 S /N /Ar /SO Wth the new calbrated k j, VLE of dfferent bnary mxtures were calculated usng dfferent EOS; and the calculated results were compared wth expermental data. Table 2.9 summarzes the absolute average devatons of EOS. All of the studed EOS have varous performances for varous mxtures; and comparatvely PR, PT and SRK are superor to RK and 3P1T for all of the studed mxtures. It should be stressed that although 3P1T s prmarly developed for non-polar compounds, t doesn t show any advantages n the VLE calculatons of /CH 4, /O 2, /N 2, and /Ar. For detaled analyss of these bnary mxtures, please refer to Paper V and Report VIII. Table 2.9 AAD of EOS on the calculated VLE propertes of bnary mxtures PR PT RK SRK 3P1T /CH 4 P s y s,co /O 2 s y s,co P /H 2 S s y s,co P /N 2 s y s,co P /Ar s y s,co P /SO 2 P s y s,co

33 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Predcton of Volume For the calculaton on volume, 3P1T was replaced by three other equatons due to ts poor performance on VLE. MSRK and MPR EOS nclude a translaton along the volume axs. Applcatons of ths mproved method to pure lqud, mxtures of lquds or gases, and petroleum fluds show that markedly superor volume estmatons are obtaned, except n the neghbourhood of the pure-component crtcal ponts; nonetheless, crtcal volumes for mxtures can be estmated correctly [64]. ISRK [65] EOS s another modfcaton of SRK, by ntroducng a temperature dependent volume correcton. ISRK can provde accurate volumes for polar and non-polar pure substances both near to and far from the crtcal pont. It can also be easly extended to mxtures, and the calculaton results show that t can shft the crtcal locus towards expermental values and gve good results for the lqud volumes of mxtures. Table 2.10 Supplement cubc EOS for volume calculatons EOS Functon Form Mxng Rule P = RT MPR V b ( V + c)( V + b + 2c) + ( b + c)( V b) MSRK ISRK RT P = V b RT P = V + c b a a ( V + c)( V + b + 2c) a( T ) ( V + c)( V + b + c) a = x x a a 1 j j 1/ 2 1/ 2 j ( k ) b = x b ; c = x c ; k j=k j a = x x a 1/ 2 a 1/ 2 1 k ; j j j j ( ) b = x b ; c = x c ; k j=k j a = x x a 1/ 2 a 1/ 2 1 k ; j j j j ( ) b + b jj b = xx j 1 j 2 c = x c ; k j =k j ; l j =l j j ; ( l ) It has been mentoned that the proper value of k j may be dfferent for dfferent propertes. Therefore, the k j calbrated from VLE data may not result n a hgh accuracy on the volume calculaton. Fgure 2-4 shows the AAD of PR EOS on the saturated pressure, the saturated vapour fracton of (y s,co2 ), the gas volume and lqud volume of /CH 4 at dfferent values of bnary nteracton parameter k j. It demonstrates that n order to pursue hgh calculaton accuracy on volume, k j should be calbrated separately for gas and lqud phases. Table 2.11 lsts the calbrated k j for volume calculatons on both vapour and lqud phases. j ;

34 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures 30 Absolute Average Devaton (%) /CH 4 PR EOS AAD on P s AAD on y s,co2 AAD on gas volume AAD on lqud volume 0 0,0 0,1 0,2 Value of k j Fgure 2.4 AAD of PR EOS on P s, y s,co2, gas volume and lqud volume of /CH 4 at dfferent k j Table 2.11 Correlated k j for dfferent bnary mxtures based on volume expermental data PR PT RK SRK MPR MSRK ISRK * G /0.189 /CH 4 L / G /0.125 /H 2 S L / G /0.099 /N 2 L /0.050 G /0.320 /Ar L /0.335 G / /SO 2 L / * k j /l j Tables 2.12 shows the absolute average devatons of equatons of state on the gas and lqud volumes of mxtures respectvely, whch were calculated wth dfferent values of k j. It s same to the calculatons on VLE propertes that the performances of EOS vary for varous mxtures. More concrete evaluatons are avalable n Paper VIII

35 2 Method Evaluatons for the Thermodynamc Property Calculatons of Mxtures Table 2.12 AAD of EOS on both gas and lqud volumes of bnary mxtures (%) PR PT RK SRK MPR MSRK ISRK /CH 4 V g V l /H 2 S g V l V /N 2 g V l V /Ar g V l V /SO 2 V g V l Dscussons Expermental Data Regardng the mxture, the TPX ranges of expermental data do not completely match the operaton condtons of the CCS processes. Ths wll result n poor evaluaton results of the theoretcal models because no suffcent expermental data are avalable for verfyng the models. For example, there are only 4 expermental results at the same temperature about VLE and lqud volume of /Ar. Based upon such expermental data, the verfed model may not be able to provde accurate results, when temperatures are beyond ths temperature. Moreover, the expermental data of /SO 2 mxtures are old. Updated expermental data are, therefore, needed to reduce the uncertanty of the evaluatons Calculaton Models To all cubc EOS consdered n ths study, k j has sgnfcant effects on the calculatng accuracy and the applcaton range of an EOS. Those equatons have better accuracy on VLE wth calbrated k j than wth the default value of k j. Therefore, f a new mpurty s ntroduced n mxtures, the calbrated k j of /new-mpurty should be obtaned n order to assure a hgh relablty. Moreover, as aforementoned, kj was calbrated as a constant n the calculatons of mxtures. To further mprove calculaton accuracy, there are two optons to handle k j. One way s that k j could be calbrated to a functon of temperature and pressure, perhaps even of composton, when suffcent expermental data are avalable. The other way s to calbrate k j n narrow T, P, x and y ranges, by whch the calculaton accuraces could be mproved for most nterested condtons. Ths, however, wll serously reduce the applcablty n extended ranges Suggestons Regardng Method Selectons Calculatng accuraces of dfferent EOS on VLE and volume are evaluated. Wth recommended EOS, the most of AAD on parameters of VLE are wthn 5%, whle AAD on volume are wthn 10% except those of /SO 2. Detaled results are summarzed n Table

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