A MODEL FOR THERMOPHYSICAL PROPERTIES OF CO 2 -BRINE MIXTURES AT ELEVATED TEMPERATURES AND PRESSURES

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1 PROCEEDINGS, Thirty-Sixth Wrkshp n Gethermal Reservir Engineering Stanfrd University, Stanfrd, Califrnia, January 31 - February 2, 211 SGP-TR-191 A MODEL FOR TERMOPYSICAL PROPERTIES OF CO 2 -BRINE MIXTURES AT ELEVATED TEMPERATURES AND PRESSURES Niclas Spycher and Karsten Pruess Lawrence Berkeley Natinal Labratry Earth Sciences Divisin, 1 Cycltrn Rad, Berkeley, CA 9472, USA nspycher@lbl.gv ABSTRACT A mutual CO 2-2 O slubility mdel was previusly reprted fr applicatin t CO 2 -enhanced gethermal systems. The ability f this mdel t predict PVT and calric prperties f the cmpressed gas phase is investigated. Cmpressibility factrs f pure CO 2 and CO 2-2 O mixtures can generally be predicted within a few percent f reference and experimental data. Calric data are als reasnably well reprduced fr CO 2-2 O gas mixtures at mderate water cntent. At elevated water cntents, mre significant deviatins are bserved between mdel results and published experimental enthalpies f mixing. wever, ttal enthalpies may still be predicted with reasnable accuracy fr applicatins t CO 2 -enhanced gethermal systems. Experimental data in the temperature and pressure range f mst interest t CO 2 -enhanced gethermal systems are scarce and wuld be needed fr further mdel validatin. BACKGROUND AND OBJECTIVES Recent theretical studies have stimulated interest in the ptential f using CO 2 instead f water as heat transfer fluid in enhanced gethermal systems (EGS) (Brwn, 2; Fuillac et al., 24; Pruess, 26, 28). Evaluating the develpment and peratin f an EGS with CO 2 as a wrking fluid requires a capability t accurately represent the thermphysical prperties f CO 2 -brine mixtures fr the entire range f fluid cmpsitins and thermdynamic cnditins, frm injectin t prductin. Furthermre, in rder t assess the behavir f CO 2 in natural subsurface envirnments, and t evaluate ptential leakage scenaris, thermphysical prperties need t be represented all the way t the land surface. We have previusly reprted n the develpment f a phase partitining mdel fr CO 2 -brine mixtures that is based n thermdynamic equilibrium principles and a cubic equatin f state (Spycher and Pruess, 21). Our mdel represents the mutual slubilities f CO 2 and NaCl brines largely within experimental uncertainties fr temperatures f 12 3 C, pressures f 1 6 bar and salinities frm t 6 mlal NaCl. ere, we investigate the applicatin f this mdel t the calculatin f pressure-vlume-temperature (PVT) data and calric prperties, with the bjective f applying this mdel t CO 2 -EGS studies. MODELING APPROAC AND TESTING Original Slubility Mdel The slubility mdel was described in detail by Spycher and Pruess (21) and references therein. Aspects f the mdel relevant t the present study are described here. Mutual slubilities are cmputed using a mdified Redlich-Kwng (RK) equatin f state (EOS) t cmpute the fugacity cefficients f CO 2 and 2 O in the cmpressed gas phase, cupled with equilibrium cnstants expressing the partitining f CO 2 in water. The effect f salts n CO 2 slubility in saline slutins is als accunted fr by a Pitzer activity cefficient mdel. The EOS parameters, equilibrium cnstants, and Pitzer interactin parameters were fitted t a large number f experimental mutual slubility data. Belw 1 C, the amunt f water partitining int cmpressed CO 2 is very small, which allws neglecting 2 O when cmputing prperties f the gas mixture. At temperatures abve 1 C, hwever, a significant amunt f water can vaprize in cmpressed CO 2, such that this amunt can n lnger be ignred when cmputing thermphysical prperties and phase equilibrium. In the present study, fcus is given t temperatures abve 1 C, as it is mst relevant t EGS with CO 2 as a wrking fluid. PVT and calric prperties predicted by the slubility mdel, withut any mdificatins f its riginal EOS parameters, are presented belw.

2 PVT Prperties Cmpressibility factrs (Z=PV/RT) f pure CO 2 and 2 O were fitted t reference data as part f the riginal slubility mdel. Fr CO 2, cmpressibility factrs frm Span and Wagner (1996) culd be reprduced with a rt mean square errr (RMSE) abut.5 % and n abslute deviatins > ~2%. Fr 2 O, cmpressibility factrs frm Wagner and Pruβ (22) fr the liquid phase culd be reprduced with an RMSE <.5% and n abslute deviatins > ~9%. wever, as wuld be expected with any cubic EOS, the vapr phase data alng the saturatin curve and the saturatin curve itself culd nt be accurately reprduced. Few PVT data have been reprted fr CO 2-2 O mixtures in the P-T range f interest t CO 2 -EGS (1 3 C and 1 6 bar). This is in part because, at these temperatures and pressures, CO 2-2 O mixtures frm tw immiscible phases ver mst f the mixture cmpsitinal range. In additin, the water cntent at the dew-pint f CO 2-2 O mixtures belw ~25 C and pressures abve 1 bar is typically limited. As a result, experimental PVT prperties are nt nly scarce, but als are mstly limited t pressures belw 1 bar. We previusly reprted a relatively gd agreement f mdel results with the cmpressed gas phase density data f Fenghur et al. (1996). Cmparisns f mdel results with experimental density values were since extended t include data frm Patel et al. (1987), Patel and Eubank (1988) and Zawisza and Maleslnska (1981). Cmputed cmpressibility factrs shw deviatins mstly within a few percent frm these experimental data sets (Figure 1). % Deviatin in Z Patel (1987, 1988): T = C y2o =.2.5 Zawisza (1981): T = 1 2 C y2o = Fenghur (1996): T = C y2o = Pressure (bar) Figure 1. Percent deviatin between cmputed cmpressibility factrs (Z = PV/RT) and experimental data frm the literature fr single-phase cmpressed CO 2-2 O gas mixtures ver a range f 2 O mle fractins (y 2O ) as shwn in the legend. Enthalpy The ttal specific enthalpy ( tt ) f a CO 2-2 O mixture, r f its pure cmpnents, is calculated frm the fllwing relatinship, tt = y O O + yco CO + (1) dep were y stands fr mle fractin, represents the specific mlar enthalpy f the pure cmpnents at zer pressure (i.e., in the ideal gas state) and dep is the departure enthalpy, which represents the difference between the ttal enthalpy at a given temperature and pressure, (T,P), and the ttal enthalpy at the same temperature and zer pressure, (T,P=). Values f are calculated frm heat capacity Maier- Kelley pwer functins f temperature, which are easily integrated analytically t yield as a functin f temperature. Parameters fr these functins were btained by fitting reference heat capacity data (C P) frm reference surces (Span and Wagner, 1996; Wagner and Pruβ, 22). The enthalpy departure, dep, is cmputed with a departure functin derived frm the mdel EOS. The departure functin includes derivatives f the EOS parameters as a functin f temperature (e.g., Jffe and Zudkevitch, 197; Rittman et al., 1982). These derivatives are calculated analytically frm the relatively simple functins f temperature given fr the parameters f the EOS and mixing rules (Spycher and Pruess, 21). Numerical derivatives were als tested, yielding gd results when centered, hwever highly inaccurate results when uncentered (i.e., when cmputatinally mre efficient frward numerical derivatives were used). Nte that fr clarity and cnsistent data cmparisns in this study, the specific enthalpies f bth CO 2 and 2 O are referred t zer fr the pure gases at the triple pint f water (at T =.1 C and P =.612 bar). Fr pure CO 2, specific enthalpies cmputed fllwing this apprach yield values typically within a few percent r less f reference data (Figure 2, tp), except near the critical pint were larger deviatins ccur because the cubic EOS cannt accurately predict the pint f the phase change. The average abslute deviatin fr pints shwn in Figure 2 abve the critical temperature (~3.4 C) is abut 1.7 kj/kg, with the largest deviatins ccurring belw 1 C. Fr pure water, belw 1 C, enthalpy predictins cannt be made because the mixing rules in the EOS assume infinite dilutin f 2 O in CO 2 (Spycher et al., 21). Abve 1 C, predicted liquid water enthalpies up t 3 C and 5 bar shw average abslute deviatins ~4 kj/kg frm reference data

3 (Figure 2, bttm). Because the EOS is nt intended fr pure water and cannt accurately predict the water saturatin pressure curve, significant deviatins frm reference data are bserved fr enthalpies f pure gaseus 2 O alng the saturatin curve (up t 17 kj/kg deviatins at 3 C). CO2 Enthalpy (kj/kg) 2O Enthalpy (kj/kg) X Enthalpy f pure CO 2 V L bar Psat 5 bar 1 bar 2 bar 5 bar Temperature ( C) Enthalpy f pure 2 O V bar Psat 5 bar 1 bar 2 bar 5 bar Temperature ( C) Figure 2. Cmparisn f cmputed specific enthalpies (lines) with reference data (symbls) frm Span and Wagner (1996) fr CO 2 (tp), and frm Wagner and Pruβ (22) fr 2 O (bttm). The same reference enthalpy is taken fr CO 2 and 2 O (zer fr the pure vaprs at.1 C and ~ bar). The nly data fund t evaluate mdel predictins with CO 2-2 O mixtures in ur P-T range f interest are ttal enthalpies reprted by Patel and Eubank (1988) (Figure 3). These data are limited t pressures mstly belw 1 bar and 2 O mle fractins n larger than.5. The average abslute deviatin f mdel predictins frm these data was fund t be reasnably small (1.9 kj/kg), althugh larger deviatins up t 13 kj/kg ccur at the higher end f investigated temperatures and 2 O mle fractins (Figure 3). Additinal experimental calric data were fund in the literature fr CO 2-2 O mixtures at 1 3 C, althugh in the frm f excess enthalpy. The excess L Enthalpy (kj/kg) Enthalpy (kj/kg) C 125 C 15 C y 2O = C Pressure (bar) 175 C 15 C 125 C 2 C 225 C Figure 3. Cmputed ttal specific enthalpies (lines) fr CO 2-2 O mixtures at varius 2 O mle fractins (y 2O ) cmpared with data reprted by Patel and Eubank (1988) (symbls). The same reference enthalpy is taken fr CO 2 and 2 O (zer fr the pure vaprs at.1 C and ~ bar). enthalpy ( E mix) can be related t the departure enthalpy as fllws (e.g., Ohta, 1993), ( y + y ) (2) E mix = dep 2O dep 2O CO2 depco C 2 C y 2O = Pressure (bar) where dep is the departure enthalpy f the mixture and dep are the departure enthalpies f the pure cmpnents. Enthalpies f mixing cmputed with Equatin (2), using dep frm the EOS and dep values frm reference data, were cmpared with experimental data frm the literature. The data f Bttini and Saville (1985), at C and up t 45 bar, were reprduced fairly well, with an average abslute deviatin f 2.4 kj/kg, but deviatins up t ~1 kj/kg at 2 O mle fractin abve.5. The data f Wrmald et al. (1986), at C and up t 73 bar, are primarily at a.5 2 O mle fractin. Cmparisn f mdel results with these data shw similar deviatins. The data frm bth studies unfrtunately cver a relatively lw pressure range. At these mderate pressures, the enthalpy f mixing cntributes t nly a small fractin f the ttal

4 enthalpy (< ~6%), such that the errr in ttal enthalpy remains less than a few percent (using the enthalpy reference pint adpted here). ENTALPY PREDICTIONS FOR CO 2 -EGS The mdel was used t predict enthalpies f CO 2-2 O mixtures at increasing 2 O mle fractins, and temperatures and pressures fixed at values relevant t CO 2 -EGS applicatins (Figure 4). Results were then cmpared with enthalpies calculated by linear (ideal) mixing f the pure cmpnents accrding t the relatinship tt = y 2O 2O + yco2 (3) CO2 where y, again, represents mle fractin and is the specific mlar enthalpy f the pure cmpnents (supercritical CO 2 and either liquid r gaseus 2 O). As previusly, these were taken frm Span and Wagner (1996) and Wagner and Pruβ (22), and referred t zer enthalpy at the water triple pint. At mderate pressures, it wuld be expected that water in the cmpressed gas mixture behaves mre like gaseus 2 O, thus giving preference t using the enthalpy f gaseus 2 O in Equatin (3) (vaprizatin mdel). On a mass basis, the specific enthalpy f gaseus 2 O (at saturatin) exceeds that f CO 2 in the pressure range f interest (Figure 2). Accrdingly, the mixture enthalpy predicted with Equatin (3) using gaseus 2 O increases with increasing 2 O cntent (Figure 4). It shuld be nted that n a mlar basis, the enthalpy change can be either psitive r negative, depending n pressure and temperature, because the specific mlar enthalpies f gaseus 2 O (at saturatin) and CO 2 verlap (Figure 5). Under increasing pressure, hwever, water in the mixture is expected t becme mre liquid-like. Because the specific enthalpy f liquid 2 O is much lwer than that f CO 2 (Figure 2), using this enthalpy in Equatin (3) expectedly results in a strng ttal enthalpy decrease as the water cntent f the gas mixture increases (Figure 4). As wuld be expected, enthalpies predicted by the mdel mstly fall between the values given by Equatin (3) with the specific enthalpy f either gaseus r liquid 2 O, and thus with mstly negative deviatins frm the vaprizatin mdel (Figure 4). wever, at pressures clse t the water saturatin pressure, slight psitive deviatins are predicted by the mdel (as the result f nn-ideal mixing). DISCUSSION AND CONCLUSIONS The mutual slubility mdel fr CO 2-2 O mixtures presented by Spycher and Pruess (21) appears t predict PVT and calric prperties with a reasnable level accuracy, except fr pure 2 O vapr at saturatin. The absence f experimental enthalpy data fr CO 2-2 O mixtures at pressures > 1 bar and temperatures < 3 C (mstly ver the tw-phase regin), tgether with bserved mdel deviatins frm available data at 2 O mle fractins >.5, 2 Mdel 1 CO2 + 2O(L) CO2 + 2O(V) T=15 C, P=1 bar T=15 C, P=5 bar T=2 C, P=1 bar T=2 C, P=5 bar T=25 C, P=1 bar T=25 C, P=5 bar Figure 4. Cmputed enthalpy change with increasing water cntent in CO 2-2 O mixtures at specified temperatures and pressures. Slid lines represent mdel predictins. The dashed and dtted lines represent apprximatins using Equatin (3) and enthalpies f pure cmpnents, using either gaseus r liquid 2 O (see text). At temperatures belw 25 C the curves extend t 2 O mle fractins crrespnding apprximately t the dew pint f the cmpressed gas mixture.

5 renders the predictin f mixing enthalpies quite uncertain fr P-T ranges typical f CO 2 -EGS. wever, in terms f ttal enthalpy, mdel predictins may have an accuracy acceptable fr mst practical CO 2 -EGS applicatins. The mdel is als expected t prvide mre realistic enthalpies than values apprximated assuming ideal mixing f pure CO 2 with either pure 2 O vapr r pure 2 O liquid. At fixed pressures arund 1 bar and temperatures C, additin f water t supercritical CO 2 is predicted (n a mass basis) t increase the mixture specific enthalpy (by ~ 6 kj/kg per mle % added 2 O). The reverse is predicted at 5 bar, with a cmputed drp in the mixture specific enthalpy (by ~ 1 2 kj/kg per mle % added 2 O). wever, this wuld need t be validated with experimental data. The paucity f PVT and calric data in the P-T range f mst interest t CO 2 -EGS warrants making the cllectin f such data a pririty. ACKNOWLEDGMENT This wrk was supprted by the Assistant Secretary fr Energy Efficiency and Renewable Energy, Office f Technlgy Develpment, Gethermal Technlgies Prgram, f the U.S. Department f Energy under Cntract N. DE-AC2-5C REFERENCES Bttini, S. B., and Saville, G. (1985), Excess enthalpies fr (water + nitrgen)(g) and (water + carbn dixide)(g) at 52 t 62 K and up t 4.5 MPa, J. Chem. Thermdynamics, 17, Brwn, D. W. (2), A t Dry Rck Gethermal Energy Cncept Utilizing Supercritical CO 2 Instead f Water, Prceedings f the Twenty- Fifth Wrkshp n Gethermal Reservir Engineering, pp , Stanfrd University, January Fenghur, A., and Wakeham, W. A. (1996), Densities f (water + carbn dixide) in the temperature range 415 K t 7 K and pressures up t 35 MPa, J. Chem. Thermdynamics, 28, Fuillac, C., Sanjuan, B., Gentier, S., and Czernichwski-Lauril, I. (24), Culd sequestratin f CO 2 be cmbined with the develpment f enhanced gethermal systems?, In: Paper presented at the Third Annual Cnference n Carbn Capture and Sequestratin, Alexandria, Virginia, May 3 6. Jffe, J. and Zudkevitch, G. (197), Predictin f liquid-phase enthalpies with the Redlich-Kwng equatin f state, Ind. Eng. Chem. Fundam., 9 (4), Enthalpy (kj/ml) Pure Gases CO2-5 bar CO2-1 bar CO2-2 bar CO2-5 bar 2O(V) - Psat Temperature ( C) Figure 5. Reference specific mlar enthalpies frm Span and Wagner (1996) fr CO 2 and frm Wagner and Pruβ (22) fr 2 O. The same reference enthalpy is taken fr CO 2 and 2 O (zer fr the pure vaprs at.1 C and ~ bar). Patel, M. R., lste, J. C., all, K. R., and Eubank, P.T. (1987), Thermphysical prperties f gaseus carbn dixide-water mixtures, Fluid Phase Equilibria, 36, Patel, M.R. and Eubank, P.T. (1988), Experimental densities and derived thermdynamic prperties fr carbn dixide-water mixtures, Jurnal f Chemical and Engineering Data, 33 (2), Pruess, K. (26), Enhanced gethermal systems (EGS) using CO 2 as wrking fluid A nvel apprach fr generating renewable energy with simultaneus sequestratin f carbn, Gethermics 35 (4), Pruess, K. (28), On prductin behavir f enhanced gethermal systems with CO 2 as wrking fluid, Energy Cnversin and Management, 49, Reid, R. C., Prausnitz, J. M., and Pling, B.E. (1987), The prperties f gases and liquids (4 th Editin), McGraw-ill Inc., New Yrk, 741 pp. Rittman, B., Knapp,., and Prausnitz, J. M. (1982), Enthalpy and dew-pint calculatins fr aqueus gas mixtures, Ind. Eng. Chem. Prcess Des. Dev., 21 (4), Span, R., and Wagner, W. (1996), A new equatin f state fr carbn dixide cvering the fluid regin frm the triple-pint temperature t 11K at pressures up t 8 MPa, J. Phys. Chem. Ref. Data, 25(6), Spycher, N., and Pruess, K., (21). A phasepartitining mdel fr CO 2 -brine mixtures at elevated temperatures and pressures: Applicatin t CO 2 -enhanced gethermal

6 systems, Transprt in Prus Media, 82, Wagner, W., and Pruβ, A. (22), The IAPW frmulatin 1995 fr the thermdynamic prperties f rdinary water substance fr general scientific use, Jur. Phys. Ref. Data, 31, Wrmald, C. J., Lancaster, N. M., Sellars, A. J. (1986), The excess mlar enthalpies f {x,o+(l -x)co}(g) and {x,o+(l -x)co,}(g) at high temperatures and pressures, J. Chem. Thermdynamics, 18, Zawisza, A., and Maleslnska, B. Y. (1981), Slubility f carbn dixide in liquid water and f water in gaseus carbn dixide in the range.2-5 MPa and at temperatures up t 473 K, Jurnal f Chemical and Engineering Data, 2 (4),