Pet.Sci.(014)11:569-577 DOI 10.1007/s118-014-0373-1 569 and modelling study of the solubility of in various CaCl s at different temperatures and pressures Alireza Bastami 1, Mohammad Allahgholi 1 and Peyman Pourafshary 1 Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran (Now with Department of Petroleum and Chemical Engineering, Sultan Qaboos University) China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg 014 Abstract: Study of the thermodynamic behaviour of CaCl -H O- systems is important in different H O- is a common system in also appears as the spent acid. Hence, study of the behaviour of this system and the solubility of in CaCl brine in different thermodynamic conditions is critical. In this study, solubility in 0, 1.90 and 4.80 mol/l CaCl s at 38.15 to 375.15 K and 68.9 to 06.8 bar were measured. These values are normal for oil reservoirs. A popular thermodynamic model is available in the literature for estimating the solubility in pure water and NaCl s. In as well. Based on the measured data, the component interaction parameters in the base model were adjusted for a CaCl -H O- system. The developed model could predict solubility in different conditions improvement is up to 65% better than in the base model. This model can be used in Darcy scale models Key words: Solubility of -CaCl solubility measurement 1 Introduction In recent years some researchers have been paying attention to environmental issues such as capture and geological storage in deep saline aquifers or depleted hydrocarbon reservoirs. Consequently, solubility in pure water and brine has been widely studied. A variety of of in brine, especially with NaCl, has been accomplished. Since the major salt in aquifers is NaCl, the -H O-NaCl a limited number of studies of the solubility of in other electrolyte s. A detailed description of the available in different electrolyte s is presented by Springer et al (01). The main purpose of these studies is the estimation of the soluble in pure or saline water. The CaCl -H O- system is a common compositional *Corresponding author. email: pourafshary@squ.edu.om Received January 3, 014 (HCl) is one of the most common acids used during carbonate, water and CaCl are produced from the reaction of HCl and calcite. HCl+CaCO 3 CaCl HO+CO Hence, the solubility of in CaCl s is carbonate formations. The produced may remain in the in a specific range of temperatures and pressures or may release and form a separate phase which affects can have some effects on the performance of wormholing during carbonate and calcite reaction and retard the reaction between acid and as a retarding agent. On the other hand, the formation of a separate phase can prevent the movement of the acid
570 of the relative permeability effect between fresh/spent acid and phases. Hence, formation of a separate phase can change wormholing performance and also the depth of penetration. There are several methods on different scales for study the mechanism of wormholing and the effect of different parameters on this complicated phenomenon. A comprehensive model is one which properly estimates the predicts the wormholing regime. Darcy models can be used equations of continuity, velocity, concentration and porosity simultaneously. They facilitate the design of an acid job. Nevertheless, the previous Darcy scale models proposed for can be applied together with the above-mentioned equations in acid jobs. Thus, it can be used to improve the accuracy important parameters of Darcy scale models. The systems containing CaCl studied as widely as NaCl-containing s. To calculate Pet.Sci.(014)11:569-577 the solubility of for this case, the models resulting from with some correction factors. The results of a study of solubility in different ranges of pressure and temperature was reported amount of much greater than the solubility of in spent acid in the operational ranges of temperature and pressure. In contrast to the attention paid to NaCl s, the number of publications on the CaCl -H O- system is very limited. This is readily apparent in Table 1, where the solubility in CaCl s by different authors are shown. Scharlin and Cargill (1996) and Springer et al (01) reviewed the few published studies of the CaCl -H O- (1877), Setchenow (189), Kobe and Williams (1935), (1993) are not particularly relevant as regards the reservoir conditions owing to low pressure and temperature values. The most significant paper published on solubility in CaCl s is that of Prutton and Savage (1945), since the range of temperatures, pressures and salt concentrations conditions. They measured the solubility in CaCl s at 348.65, 374.15, 394.15 K and pressures from 15. to 709.8 bar. Table 1 -H O- Reference Temperature range, K Pressure range, bar CaCl -1 81.15-303.15 1.01 0.4-1.7 Setchenow (189) 88.35 1.01 0.15-5 Kobe and Williams (1935) 98.15 1.01 6 Prutton and Savage (1945) 348.65-394.15 15.-709.8 1-3.9 473.15-63.15 101.33-395.17 1 Onda et al (1970) 98.15 1.01 0.-.3 98.15-348.15 47.6 0.-4.4 373.15-43.15 47.6 0.9-8.8 98.15-308.15 1.01 0.-5.3 Eremina et al (1989) 98.15-313.15 1.01-0.05 73.15-363.15 0.3-1.01 0.1-5 In this paper, the CaCl -H O- system at different ranges of pressure, temperature and CaCl molality, which are consistent with reservoir conditions, is studied to measure and model the solubility of models in Darcy scale. Experiments The purpose of t solubility in different CaCl s. The temperature and pressure ranges consi as the normal conditions of s.1 Materials The purity of was 99.99%. The anhydrous CaCl. Apparatus and procedures Fig. 1 shows a schematic of apparatus used in this study to estimate the solubility of in CaCl s. This
Pet.Sci.(014)11:569-577 571 apparatus is similar to the one used by Bando et al (003) and cm 3 /h in constant pressure mode, a high pressure cylinder with a volume of 500 cm 3 of 689 bar, a stainless steel pycnometer, high pressure transfer and 0.1 K precision, a pressure transducer for the 1-60 bar range with 0.007 bar precision, a densitometer, and a vacuum pump. An agitating pump system as shown in Fig. was designed to agitate the high pressure cylinder in the oven. The Fig. Agitating pump system First of all, the high pressure cylinder was opened and washed with distilled water and evacuated by a vacuum pump. CaCl and were then pumped into agitated at the desired temperature for 3 hours. The effects of agitating time were investigated for 1.9 mol/l CaCl at 137.9 bar and 351.65 K (Fig. 3). In this study, the soluble changed negligibly for data acquired in ensure equilibrium, the samples were agitated for 3 hours. As the pressure changed during the agitating period, the pressure was adjusted again. The concentration of the injected was more than its saturation concentration to ensure reaching the saturation concentration of in. Thus, there was a separate Fig. 3 The effect of agitating time on the of soluble (a at 351.65 K and 137.9 bar) supercritical phase in the high pressure cylinder after reaching equilibrium. Since the high pressure cylinder had was transferred gradually through lines to a pycnometer. W 1 ) at the final temperature and pressure. Knowing the weight of the evacuated pycnometer (W 0 ) and its volume means that we can determine the density. To determine the amount of dissolved in this, the pycnometer must be aged for 1 hour under room conditions to reach room temperature. Then, the pycnometer valve was opened and the gas was released slowly from the top of the pycnometer until no more gas was released and the weight of the cylinder did not
57 Pet.Sci.(014)11:569-577 change. Immediately, the pycnometer valve was closed to maintain the gas phase equilibrium. Finally, the pycnometer with the remaining was weighed (W ). All of the The total volume of soluble consisted of the released in the gas phase when the temperature and pressure (1) were reduced to atmospheric conditions ( V CO ), CO remaining in the gas phase in the pycnometer after its valve was opened () ( V ), and remaining in the liquid phase at atmospheric CO (3) pressure and room temperature ( V CO ). The difference between W 1 and W is the amount of in the gas phase which is released while the valve of the pycnometer is being opened. Hence, (1) CO 1 V 414 W W 44.0095 where,414 cm 3 is the volume of one mole of any gas at standard temperature and pressure (73.15 K and 1.01 bar (1. The in the gas phase which remained in the pycnometer after opening of the valve can be calculated through Eqs. ()-(4). W W V W () 0 CO, Troom brine 1 W W W V brine 0 CO cylinder CO brine (), Troom cylinder brine brine V V W (3) V V 73.15 T () () CO, Troom room where CO is the density, g/cm 3 brine is the CaCl brine density, g/cm 3 V cylinder is the volume of the pycnometer, cm 3. To estimate the solubility, it is required to estimate the amount of soluble in CaCl s at atmospheric pressure and room temperature. With reference to the method in aqueous electrolyte s can be estimated by the L L AC BC log 1 (5) L V V G 0 s s L V V L W W (3) CO L 0 brine where LL 0 is the Ostwald C s is the molar V is the volume of V L A and B are empirical constants dependent upon the particular solute present, as shown in Table, L/mol. These constants were different electrolyte s such as CaCl -H O using the method of least squares. (1) () (4) (6) (7) The absolute value of soluble volume in is then calculated from Eq. (8). (1) () (3) V V V V (8) CO CO CO CO The solubility in terms of molality is then given by byvco.414w water, in which W water can be calculated by W water W 1 1 1000 44.0095m 110.9840m brine CO CaCl (9) soluble in the can be calculated by Eq. (10): x m m CO CO CO 55.508 (10) where x is the total of CO m is the molality of in the liquid phase, mol/l. Table Parameters of Eq. (5) for solubility of 1979) Temperature, K A, L/mol B, L/mol 98.15 0.11 0.057 308.15 0.19 0.059.3 results pure water are listed in Table 3 and also depicted in Fig. 4. study at different temperatures. Koschel et al (006) measured the solubility in pure water at 33.15 K and 373.15 K not the same, this comparison confirms the accuracy of the Table 3 in pure water Temperature, K in water 38.15 348.15 351.65 368.15 68.9 0.0161 137.9 06.8 0.034 68.9 0.014 137.9 0.0183 68.9 0.0131 06.8 0.011 68.9 0.0119 06.8 375.15 137.9 0.0170
Pet.Sci.(014)11:569-577 573 0.05 0.00 study are listed in Tables 4 and 5. These data show the trend of changes in solubility in with changing pressure and temperature. Table 4 in 1.9 mol/l CaCl Temperature, K in water 38.15 348.15 68.9 0.0070 137.9 5 06.8 3 68.9 3 137.9 0.0088 06.8 9 351.65 137.9 0.0088 368.15 375.15 137.9 0.0083 06.8 6 68.9 8 06.8 6 Table 5 in 4.8 mol/l CaCl Temperature, K in water 38.15 348.15 351.65 368.15 68.9 137.9 0.0049 06.8 0 137.9 0.0041 06.8 0.0046 68.9 0 06.8 0.0045 68.9 137.9 9 06.8 0.0045 375.15 137.9 8 T=33.15 K T=38.15 K T=348.15 K T=351.65 K T=368.15 K T=375.15 K 5.0 75.0 15.0 175.0 5.0 Fig. 4 versus temperature in pure water These data indicate that at low pressures the solubility of in CaCl s increased directly with pressure. At high pressures, however, the effect of pressure on solubility faded and the rate of increase in solubility reduced with an increase in pressure. This observation was et al, 01). On the other hand, the temperature and CaCl concentrations had inverse effects on solubility. 3 Model development The solubility of in pure water and brine at reservoir for conditions up to 373.15 K and 1,000 bar, by Duan and Sun (003) for conditions up to 533.15 K and,000 bar and K and 600 bar. Duan and Sun (003) presented a popular thermodynamic model for the estimation of solubility in pure water and aqueous NaCl s. They stated, however, is possible to use it to predict solubility in other systems as well. The method of solubility estimation proposed by Duan and Sun (003) is based on the balance between chemical potentials between in liquid and gas phases. This balance results in Eq. (11). ln m ln y P RT l(0) CO CO CO CO m m m m CO -Na Na K Ca Mg m m m m m 0.07m -Na-Cl Cl Na K Mg Ca SO4 (11) where yco is the of CO P and R is the universal gas constant, 0.08314 bar L mol -1 K -1 T is the chemical potential and m SO is the molality of SO - 4 in 4 the liquid phase (if any), mol/l. - H O-NaCl system in the conditions of the study, it is assumed that the water vapor pressure of H to the pure water saturation pressure. Based on the study of Duan and Sun (003), this assumption may lead to errors l(0) (up to 5%) for CO RT. They stated that these errors have a negligible effect on the calculation of solubility. Thus, y P P P. Duan and y can be calculated by CO H O Sun suggested an empirical equation for calculating P as: 1.9 3 4 1 HO P PT c Tc c1 t ct c3t c4t c5t (1) where c is the critical pressure of water, P c T c is the critical temperature of water, T c P H O is the t T Tc Tc and the parameters of Eq. (1), c 1 -c 5, are listed in Table 6.
574 Pet.Sci.(014)11:569-577 Table 6 Parameters for Eq. (1) (after Duan and Sun, 003) Constant c 1 Value c 5.89484 c 3 59.876516 c 4 6.65467 c 5 10.637097 Duan et al (199) also developed an equation of state for supercritical, as in Eq. (13). Z PV T r r r 3 a1 a Tr a3 Tr V r 3 3 4 3 5 3 exp 1 a4 a5 Tr a6 Tr Vr a7 a8 Tr a9 Tr Vr a10 a11 Tr a1 Tr Vr a13 Tr V r a14 a15 V r a15 Vr (13) To calculate V r, the reduced temperature and pressure should be calculated and substituted in the EOS developed by Duan et al (199) as in Eq. (13). The parameters of Eq. (13) are listed in Table 7. Table 7 Parameters for Eq. (13) (after Duan and Sun, 003) Constant Value Constant Value a 1 8.9988497E-0 a 9 1.776511E-03 a a 10.51101973E-05 a 3 4.77945E-0 a 11 8.93353441E-05 a 4 1.03808883E-0 a 1 7.88998563E-05 a 5 a 13 a 6 9.49887563E-0 a 14 1.39800000E+00 a 7 5.0600880E-04 a 15.96000000E-0 a 8 They also deduced the formula to calculate the fugacity coefficient of, referring to this as EOS. The only interaction parameters are estimated by Eq. (14), with the constants listed in Table 8. 630 ln Par T, P c1 ct c3 T c4t c5 630T cpcplnt c PTc P 630 T (14) 6 7 8 9 c P T c T P 10 11 where Par is the interaction parameters. Interaction parameters are proposed for NaCl s. predicting the solubility in CaCl -H O system. They concluded that the model developed by the interaction parameters for NaCl s, can be applied for CaCl s as well. The parameters s and, s for Na + and Cl and also the standard chemical potential of in the liquid phase are essential to calculate the solubility as a function of temperature, pressure and salinity. On the other hand, measurements can only be made in electrically neutral arbitrarily. CO -Cl model. Table 8 Interaction parameters (after Duan and Sun, 003) Parameter CO l (0) RT CO -Na -Na-Cl c 1 8.9447706 33639 c 60763 c 3 97.5347708 c 4 1.0783E-05 c 5 33.816098 c 6 040371 c 7 c 8 0.00108 c 9 0.01706564 c 10 93713 c 11 1.41336E-05 and the data reported by Prutton and Savage (1945), the interaction parameters of Duan and Sun s solubility model are modified for CaCl s. The constants of Eq. (14) CO -Ca and CO -Ca-Cl, in comparison with the ones presented by Duan and Sun (003) for NaCl s, are shown (0) in Table 9. As can be seen from the table, l CO RT is not changed, because it is independent of the solvent in the. n t 1 1, t, t RMSE x x n (15)
Pet.Sci.(014)11:569-577 575 Parameter CO Table 9 Interaction parameters for NaCl and CaCl s l(0) RT CO -Na CO -Ca CO -Na-Cl -Ca-Cl c 1 8.9447706 33639 c 60763 60709 c 3 97.5347708 97.49964043 c 4 1.0783E-05 c 5 33.816098 c 6 040371 c 7 c 8 0.00108 18708 c 9 0.01706564 0.0084659 c 10 93713 c 11 1.41336E-05 1.41336E-05 4 Results and discussion The model proposed by Duan and Sun (003) overestimates the solubility in high molality s and also at high pressures as well. This observation was and Hilal, 010). A comparison between the solubility estimation by the base and modified models has been L CaCl s. The model is more accurate for higher concentration of CaCl and higher pressures as well. L s is reduced. Hence, the developed model is more accurate. The comparison between s is illustrated in Fig. 5. solubility estimations for the 1.90 mol/l CaCl seen in Fig. 5 for 4.80 mol/l CaCl s, however. This indicates that this improvement has more meaning for high concentrations of CaCl s. Prutton and Savage (1945) proves that predictions of the new as well. Fig. 6 shows a comparison between data estimated All plots of Fig. 6 show this improvement for different values of temperature, pressure and CaCl concentrations. solubility estimations are reduced by about 14%, 53% and 65% on the basis of the Prutton and Savage (1945) results for 1.01,.8 and 3.90 mol/l CaCl have been improved about 5% for 4.80 mol/l CaCl be concluded that the modified model shows a significant 0.011 0.008 0.007 0.004 (a) T=38.15 K 4.80 mol/l CaCl, 4.80 mol/l CaCl, modified 4.80 mol/l CaCl 1.90 mol/l CaCl, 1.90 mol/l CaCl, modified 1.90 mol/l CaCl 0.00 60 80 100 10 140 160 180 00 0 0.011 0.008 0.007 0.004 0.008 0.007 0.004 (b) T=348.15 K 4.80 mol/l CaCl, 4.80 mol/l CaCl, modified 4.80 mol/l CaCl 1.90 mol/l CaCl, 1.90 mol/l CaCl, modified 1.90 mol/l CaCl 60 80 100 10 140 160 180 00 0 (c) T= 368.15 K 4.80 mol/l CaCl, 4.80 mol/l CaCl, modified 4.80 mol/l CaCl 1.90 mol/l CaCl, 1.90 mol/l CaCl, modified 1.90 mol/l CaCl 0.00 60 80 100 10 140 160 180 00 0 Fig. 5 solubility in CaCl s at (a) 38.15 K, (b) 348.15K, and (c) 368.15 K
576 Pet.Sci.(014)11:569-577 T=348.15 K, 1.01 mol/l CaCl 0.05 0.00 Modified 0 100 00 300 400 500 600 700 0.00 T=373.15 K, 1.01 mol/l CaCl Modified 0 100 00 300 400 500 600 700 0.05 0.00 T=393.15 K, 1.01 mol/l CaCl Modified 0 100 00 300 400 500 600 700 800 T=348.15 K,.8 mol/l CaCl Modified 0 100 00 300 400 500 600 700 T=373.15 K,.8 mol/l CaCl Modified 0 100 00 300 400 500 600 700 T=393.15 K,.8 mol/l CaCl Modified 0 100 00 300 400 500 600 700 800 T=348.15 K, 3.90 mol/l CaCl Modified 0 100 00 300 400 500 600 700 T=373.15 K, 3.90 mol/l CaCl Modified 0 100 00 300 400 500 600 700 T=393.15 K, 3.90 mol/l CaCl Modified 0 100 00 300 400 500 600 700 800 Fig. 6 solubility based on data from Prutton and Savage (1945) improvement in estimations. The model presents better results for high concentration s. reduction, but that for the 1.90 mol/l is almost unchanged. in CaCl s in better agreement with increase with pressure, temperature and CaCl molality. Adding more CaCl to the results in decreasing solubility within the system. The base model cannot match RMSE 8.0E-04 6.0E-04 4.0E-04.0E-04 Modified 6.0E-04 Modified 0.0E+04 1.01 mol/l.8 mol/l 3.90 mol/l Total RMSE 4.0E-04.0E-04 0.0E+04 1.90 mol/l 4.80 mol/l Total Fig. 7 Fig. 8 this behaviour, but the new developed model can predict the behaviour of the system more precisely. This comparison solubility prediction in 3.90 mol/l CaCl s compared with the, as shown in Fig. 6. Since the range of CaCl concentrations in this study is improvement in estimating the soluble is noteworthy in wormhole propagation models. The original form of the overestimates solubility in spent
Pet.Sci.(014)11:569-577 577 presented in this study gives more reasonable estimates of solubility in spent acid. This solubility model can be used in an integrated study on wormhole propagation during 5 Conclusions 1) The solubility of in saline water is of particular importance regarding environmental issues such as capture and geological storage. Hence, the thermodynamic behavior of -H contrast, -H O-CaCl has only been studied to a limited in CaCl s. was prepared and the solubility of in 0, 1.90 and 4.80 mol/l CaCl s at 38.15 to 375.15 K and 68.9 to 06.8 that solubility decreases with increasing concentration, increasing temperature and decreasing pressure. The effect of pressure, however, diminishes at higher pressures. 3) A modified model was developed by refitting the interaction parameters to predict the solubility in CaCl s. The modified model can predict solubility better than the available Duan and Sun thermodynamic model. This improvement is up to 65% better than the Duan and Sun model. In addition, the modified model estimates the solubility in high concentration s and also high pressures with noticeable accuracy. Prediction by this model this study. 4) Darcy models on the basis of core scale predict In the course of reactions between acid and carbonates physically affect the performance of an acid job, it is of is not soluble in the (spent acid) and can form a separate study can be applied in Darcy scale wormhole propagation models to improve the accuracy of their predictions. References -H in aqueous Chemical & Engineering Data. 003. 48(3): 576-579 Dar wish N A and Hilal N. A simple model for the prediction of solubility in H O-NaCl system at geological sequestration conditions. Desalination. 010. 60(1-3): 114-118 4 - - H Dua n Z and Sun R. An improved model calculating solubility in pure water and aqueous NaCl s from 73 to 533 K and from model to capture wormhole formation during the dis of a -H O system and preliminary 005. Deliverable WP 4.1-3-05: 1-43 4 et Cosmochimica Acta. 1993. 57(15): 3533-3554 Engineering Science. 007. 6(4): 919-98 in water and NaCl(aq) at conditions of interest for geological sequestration. Fluid Phase Equilibria. 006. 47(1-): 107-10 in aqueous s of NaCl, KCl, CaCl pressures. The Journal of Supercritical Fluids. 011. 56(): 15-19 005. 51(1): 331-348 and acid-fracture conductivity. SPE Production & Operations. 013. 8(1): 46-54 (paper SPE 13617) Journal of the American Chemical Society. 1945. 67(9): 1550-1554 + H S 13-133 Sch arlin P and Cargill R W. Analytical Chemistry Division & International Union of Pure and Applied Chemistry. Commission on 1981. 33(7): 1196-10 (paper SPE 9388) H O-rich to the 151-171 Spy cher N and Pruess K. -H sequestration of 3309-330 Spy cher N, Pruess K and Ennis-King J. -H geological sequestration of. I. assessment and calculation of et Cosmochimica Acta. 003. 67(16): 3015-3031 solubility in NaCl brine and -saturated NaCl brine density. 1477 electrolyte s. Journal of Chemical & Engineering Data. 1979. 4(1): 11-14 (Edited by Sun Yanhua)