Extension of Vibrating-Wire Viscometry to Electrically Conducting

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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Extension of Vibrating-Wire Viscometry to Electrically Conducting Fluids and Measurements of Viscosity and Density of Brines with Dissolved CO2 at Reservoir Conditions Claudio Calabrese, Mark McBride-Wright, Geoffrey C. Maitland, and J. P. Martin Trusler*

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Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K. ABSTRACT: In order to design safe and effective storage of anthropological CO2 in deep saline aquifers, it is necessary to know the thermophysical properties of brine−CO2 solutions. In particular, density and viscosity are important in controlling convective flows of the CO2-rich brine. In this work, we have studied the effect of dissolved CO2 on the density and viscosity of NaCl and CaCl2 brines over a wide range of temperatures from 298 to 449 K, with pressures up to 100 MPa, and salinities up to 1 mol·kg−1. Additional density measurements were also made for both NaCl and CaCl2 brines with dissolved CO2 at salt molalities of 2.5 mol·kg−1 in the same temperature and pressure ranges. The viscosity was measured by means of a vibrating-wire viscometer, while the density was measured with a vibrating U-tube densimeter. To facilitate the present study, the theory of the vibrating-wire viscometer has been extended to account for the electrical conductivity of the fluid, thereby expanding the use of this technique to a whole new class of conductive fluids. Relative uncertainties were 0.07% for density and 3% for viscosity at 95% confidence. The results of the measurements show that both density and viscosity increase as a result of CO2 dissolution, confirming the expectation that CO2-rich brine solutions will sink in an aquifer. We also find that the effect of dissolved CO2 on both properties is sensibly independent of salt type and molality. and carbonate (CO32−). Although CO2 has a relatively low GWP, it is classified as a greenhouse gas because of the huge quantities emitted annually by human activities and it is one of the primary agents driving climate change.8 For this reason, large-scale CO2 capture combined with storage in geological formations is considered crucial for reducing atmospheric CO2 emissions. In this context, carbon capture and storage is an emerging technique capable of greatly reducing CO2 emissions from large-scale industrial combustion of fossil fuels. Depleted oil and gas reservoirs and deep saline aquifers are potential sinks to store large quantities of CO2 over a geological time scale. When injected into a geological storage formation, CO2 will contact the connate reservoir fluids, hydrocarbons and/or brines, present in the porous reservoir rocks. In order to design and operate safe and efficient carbon storage, it is therefore necessary to know the multiphase flow properties and the chemical and physical properties of mixtures of CO2 with reservoir fluids. The distribution of CO2 in the subsurface is a key element for successful carbon storage, and this is influenced by the relative permeability of the rock and the relation between saturation and capillary pressure.9 Another

1. INTRODUCTION This paper addresses the challenge of measuring the changes in viscosity and density of concentrated brine solutions caused by dissolution of CO2 under the extreme temperature and pressure conditions encountered in many industrial processes and in the subsurface storage of CO2 as a method to ameliorate anthropogenic climate change. This is achieved through extending the theory underpinning the vibrating-wire (VW) viscometer technique to enable this highly accurate method to be used not just for brines but for a wide range of conducting liquids. CO2 is a fluid widely employed in the petrochemical and chemical industries. Carbon dioxide in its supercritical (sc) state is commonly used in processes of purification and extraction;1 sc-CO2 is also employed in environmental engineering for treating industrial waste liquids.2 It plays an important role in petroleum engineering as a fluid for enhanced oil recovery (EOR) and enhanced coal bed methane recovery.3−7 It is also used as a refrigerant fluid instead of chlorofluorocarbons which have higher global warming potential (GWP) compared to CO2;8 for the same reason, in the near future, it could also replace other refrigerants such as hydrofluorocarbons. CO2 is a trace gas naturally present in the Earth’s atmosphere and it dissolves in the ocean where it forms carbonic acid (H2CO3), and the ions bicarbonate (HCO3−) © XXXX American Chemical Society

Received: March 20, 2019 Accepted: July 19, 2019

A

DOI: 10.1021/acs.jced.9b00248 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Available Experimental Data for Viscosity η and Density ρ of [xCO2 + (1 − x)NaCl(aq)], at Temperatures T, Pressures p, and Salt Molalities m, with Relative Uncertainty Ur references 14

Al Ghafri et al. Nighswander et al.15 Yan et al.16 Song et al.17 Kumagai and Yokoyama18 Bando et al.19 Fleury and Deschamps20 Kestin et al.21

property

T/K

p/MPa

x

m/(mol·kg−1)

Ur (%)

ρ ρ ρ ρ η η η η

298−473 353−473 323−413 333−413 273−278 303−333 308 293−423

0.9−68.4 2−10 5−40 10−18 0.1−30 10−20 8.5 0.1−35

0 ≤0.015 ≤0.022 ≤0.015 ≤0.0162 saturation ≤0.0176 0

1.06−6.00 0.173 1 and 5 1, 2, 3 and 4 0.34−0.86 0.00−0.53 0.34−3.15 0.00−6.00

0.05 0.65 0.1 0.02 0.8 2 ∼1.7 0.5

Table 2. Available Experimental Data for Viscosity η and Density ρ of [xCO2 + (1 − x)CaCl2(aq)], at Temperatures T, Pressures p, and Salt Molalities m, with Relative Uncertainty Ur references 14

Al Ghafri et al. Abdulagatov and Azizov23 Isono et al.24 Wahab and Mahiuddin25 Gonçalves and Kestin26 Zhang et al.27

property

T/K

p/MPa

x

m/(mol·kg−1)

Ur, %

ρ η ρ, η ρ, η η ρ, η

283−473 293−575 288−328 273−323 293−323 298

1.1−68.1 0.1−60 0.1 0.1 0.1 0.1

0 0 0 0 0 0

1.00−6.00 0.10−2.00 0.05−6.00 0.004−7.15 0.27−5.10 0.02−7.87

0.05 1.6 N/A 0.01, 0.5 0.3 0.01, 0.1

the data at high salt modalities appear to be oversaturated with CO2 and hence not representative of homogenous states. In the case of viscosity, Kumagai and Yokoyama,18 Bando et al.,19 and Fleury and Deschamps20 studied the effect of CO2 on the viscosity of NaCl(aq) at relatively low pressures and temperatures. The viscosity of CO2-free NaCl(aq) solutions has been studied by Kestin et al.21,22 over a temperature range from (293 to 423) K, pressures up to 35 MPa, and molalities up to 6 mol·kg−1; Kestin et al.21 also report a viscosity correlation in terms of temperature, pressure, and molality, with an uncertainty of 0.5%. No data are available for the [CO2 + CaCl2(aq)] systems but the viscosity of CO2-free CaCl2(aq) has been studied by Abdulagatov and Azizov,23 Isono,24 Wahab and Mahiuddin,25 Gonçalves and Kestin,26 and Zhang et al.27 Obtaining accurate values of fluid thermophysical properties at high temperature and pressure (HTHP) presents particular challenges. Vibrating tube (VT) and VW techniques are particularly suited to HTHP adaptation, and in particular, a VW viscometer is probably the most accurate device for measuring fluid viscosity under extreme conditions, giving uncertainties of ±0.1% in the most favorable circumstances (gases) and routinely ∼±1% for dense gases and liquids. However, in the case of conducting fluids, we have ascertained that using the existing theory for nonconducting fluids can lead to significant errors, sometimes in excess of ±5%. It is therefore necessary to develop more accurate working equations for conducting fluids to enable high precision viscosity data to be obtained for conducting fluids, especially ionic systems. Addressing this issue is necessary for this study, but also has much wider implications for enabling accurate (±1−2%) determination of viscosity for a wide range of conducting fluids, especially under extreme conditions where other (less accurate) methods such as capillary flow become more difficult to implement. In this paper, we present the improved working equation of the VW viscometer and report new viscosity and the density data for concentrated brines. The objectives of the work were fourfold: first, to develop a new working equation for the

important consideration is the injectivity of the wells through which the CO2 enters the storage formation, which must be sufficient to cope with the desired flow rate. Injectivity is also dependent upon both the absolute and relative permeabilities,10 and in turn, upon the thermophysical properties of the fluids and their mixtures. Finally, it is necessary to model the time scales of the different trapping mechanisms involved during geological carbon storage and these too are strongly influenced by thermophysical properties.11 The focus of the present work is on the viscosity and density of (CO2 + brine) systems under conditions encompassing those of CO2 storage in a deep saline aquifer. As shown by Pau et al.12 and confirmed in this work, the density of homogenous (CO2 + brine) solutions is higher than that of the original brine. As a consequence, once CO2 has dissolved in the brine, the resulting solution tends to be transported toward the bottom of the reservoir by means of natural convective flows with viscous fingering.13 The rate of this flow is strongly influenced by the density gradient and by the viscosity of the solution. This natural convection increases the rate of solubility trapping as fresh brine flows back to the top of the reservoir to contact undissolved CO2. For these reasons, knowing the viscosity and density of the (CO2 + brine) mixture as a function of temperature, pressure, and CO2 mole fraction is vital for characterizing the reservoir behavior and developing predictive tools to model the processes of injection and subsequent evolution of the CO2 plume. However, experimental data for the viscosity and density of (CO2 + brine) systems at reservoir conditions are presently few in the literature. Tables 1 and 2 summarize the existing literature data for the viscosity and density of NaCl and CaCl2 brine systems, with and without CO2 addition, under high pressure conditions. An extensive study has been made by Al Ghafri et al.14 of the density of CO2-free NaCl(aq) and CaCl2(aq) at temperatures between (283.15 and 473.15) K, pressures up 68.5 MPa, and various brine molalities. The effect of dissolved CO2 on the density has been studied by Nighswander et al.,15 Yan et al.16 and Song et al.17 The latter study has an estimated expanded relative uncertainty of only 0.02% and but many of B



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Table 3. Chemical Samples Description Where w is Mass Fraction, x is Mole Fraction, and ρe is Electrical Resistivity at T = 298.15 K chemical name

CAS number

source

purity

additional purification

calcium chloride dihydrate carbon dioxide sodium chloride water

10035-04-8 124-38-9 7647-14-5 7732-18-5

Sigma-Aldrich BOC Sigma-Aldrich Millipore Direct-Q UV3

w ≥ 0.990 x ≥ 0.99995 w ≥ 0.995 ρe > 18 MΩ·cm

none none none vacuum degassed

operation of a VW viscometer filled with a highly conductive solution; second, to study experimentally the effect of CO2 on the viscosity and density of NaCl(aq) and CaCl2(aq) solutions, over wide ranges of temperature and pressure, and at CO2 mole fractions close to saturation; third, to test the hypothesis that the effect of CO2 upon viscosity and density of a brine is independent of the salt type and molality; and finally, to provide an empirical model for both properties in terms of temperature, pressure, and CO2 mole fraction. Furthermore, the present study provides densities for the [CO2 + NaCl(aq)] and [CO2 + CaCl2(aq)] systems, in a range of conditions of interest for large-scale carbon storage and EOR processes. The viscosity measurements for [CO2 + NaCl(aq)] extend in temperature from (333 to 449) K and in pressure from (30 to 100) MPa, while the [CO2 + CaCl2(aq)] systems are studied for the very first time over wide ranges of temperature and pressure.

tensile strength, sufficient hardness, and resistance to corrosion. As a consequence, an alloy of platinum and iridium, containing 10 mass % Ir, was chosen for the wire. The density of the material at room temperature was ρw = 21560 kg·m−3,30 and the wire used was of 75 μm nominal radius. The density of the fluid was measured by means of a highpressure VT densimeter (Anton Paar DMA HPM) that was connected to an evaluation unit (mPDS 2000 V3) able to detect the period of oscillation with a resolution of 0.001 μs. The temperature was regulated by circulating silicone oil from a thermostat bath through a heat exchanger within the densimeter module and an external jacket around the viscometer. Temperatures were measured by means of platinum resistance thermometers (PRTs). One was inserted into a thermowell in VT densimeter and a second was inserted into a thermowell in the pressure vessel containing the VW viscometer. Fluid pressure was controlled by the high-pressure syringe pump. Temperature stability was within ±0.05 K and pressure stability was within ±0.02 MPa, both measured over a 1 h period. For all the other details regarding the viscosity sensor, the circulation pump, syringe pumps, and the other key components of the VW−VT apparatus, we refer the reader to a previous paper.28

2. MATERIALS AND METHOD 2.1. Chemicals. The chemicals used in this work are detailed in Table 3. Pure deionized water was used for preparing all solutions and the salts were dried in an oven. Brine solutions were degassed by agitation under vacuum immediately prior to injection into the system. 2.2. Apparatus. The apparatus was described in detail in a previous paper,28 and only a brief summary will be given here. In this work, the viscosity was measured with a VW viscometer, and the density was measured by means of a VT densimeter. Most of the wetted parts of the system were made of Hastelloy-C276 in order to avoid corrosion problems. The VW sensor was designed and built in-house in a configuration in which the VW was clamped at both ends. Figure 1 is a

3. NEW SEMI-EMPIRICAL WORKING EQUATION FOR HIGHLY CONDUCTIVE FLUIDS 3.1. Standard Equation for the VW Viscometer. The VW technique has been successfully employed in the past to study the viscosity of CO2 with hydrocarbons31 and with water.28 In the steady-state VW technique, a tensioned metallic wire is immersed in the fluid of interest and placed in a permanent magnetic field perpendicular to its axis. A sinusoidal current is passed through the wire creating a Lorentz force that sets the wire into transverse motion. According to Faraday’s law, this motion induces a voltage across the wire which can be measured.32 In this work, a lock-in amplifier was used to measure the complex voltage Φ as a function of the frequency f of the imposed current. The viscosity is obtained by analysis of the experimental resonance curve Φ(f) in terms of the following working equation

Figure 1. Simplified diagram of the VW−VT apparatus: (1) vacuum pumps, (2) aqueous brine solution, (3) CO2 gas cylinder, (4) syringe pump, (5) circulating pump, (6) VW viscometer, (7) VT densimeter, (8) waste bottle, (V1 to V3) valves.29

Φ=

Λif 2

2

f0 − f (1 + β) + if 2 (β′ + 2Δ0)

+ a + ib + icf (1)

Here, Λ is the amplitude, and f 0 and Δ0 are the resonance frequency and logarithmic decrement of the wire in vacuum; a, b, and c arise from the impedance of the stationary wire and any offsets in the lock-in amplifier (background term); finally, β and β′ are dimensionless parameters that account for the added mass and damping effect of the fluid surrounding the wire, respectively. These terms are given by33,34

simplified diagram of the VW−VT apparatus, identical to that shown previously.28 The viscometer and densimeter were connected with a circulation pump in a circuit that permitted mixtures to be homogenized in situ. The selection of the wire material was based on the following features: high density and melting temperature, adequate electrical conductivity and magnetic properties, high C


Journal of Chemical & Engineering Data ÄÅ ÉÑ ρ ÅÅÅÅ i + 4K1( iΩ ) ÑÑÑÑ (β + Iβ′) = ÅÅ Ñ ρs ÅÅÅÇ iΩ K 0( iΩ ) ÑÑÑÑÖ where

Ω=

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Φ = (Zw + Zm)[1 − G b(Zw + Zm)]I − Φoffset

Because the frequency range of the measurements is small, we assume that Zw and Gb are constants and, because Zw ≫ Zm, we approximate Gb(Zw + Zm) as GbZw to obtain

(2)

2πfρR2 , η

Φ = (Zw + Zm)(1 − G bZw )I − Φoffset (3)

Φ = ZmI(1 − G bZw ) − [Φoffset − ZwI(1 − G bZw )]

Φ=

Z = ( Z w + Z m ) [ 1 − G b( Z w + Z m ) ]

2

f0 − f (1 + β) + if 2 (β′ + 2Δ0)

+ a + ib (10)

Figure 3. Experimental resonance curve (components of the complex voltage Φ as a function of driving frequency f) in comparison with the standard and modified working equations: □, experimental in-phase voltage; ○, experimental quadrature voltage; green line, modified working equation; red line, standard working equation. Measurements carried out in NaCl(aq) at T = 448 K, p = 1.4 MPa, and m = 2.5 mol· kg−1.

(4)

If the admittance Gb is small, such that Gb(Zw + Zm) then eq 4 may be approximated as follows

Λ′if exp(Iθ ) 2

where Λ′ = AΛ is a real valued constant. According to this relation, the effect of the stray impedance is to modify the resonance term by a scale factor and to rotate its phase by angle θ. A constant background term with real and imaginary parts remains. If Gb and Zw were both real, then there would be no phase change. The main approximations made here are that all terms, except the resonance term, may be considered independent of frequency and that the product of the brine admittance and the impedance of the stationary wire is small compared with unity. The former is valid when the resonance data cover a narrow frequency band, that is, when the viscosity is small and the resonance curve is narrow. The latter is valid when Zb ≫ Zw. Both conditions appear to be satisfied experimentally. Figure 3 shows an experimental resonance curve measured in NaCl(aq) at T = 448 K, p = 1.4 MPa, and m = 2.5 mol·kg−1.

we seek to model, while Figure 2b is a simplified electrical equivalence circuit. Because the fluid surrounding the VW is conductive, it can be represented to a first approximation as additional impedance Zb (or admittance Gb = 1/Zb) in parallel with the VW. The electrical impedance of the VW itself may be written as the sum (Zw + Zm), where Zw is the electrical impedance of the stationary wire, and Zm is the additional impedance arising from damped motion of the wire in the presence of a magnetic field. The combined electrical impedance of this network is given by −1

(9)

The factor (1 − GbZw) is a complex constant which can be written in the form A·exp(iθ), where θ is a phase angle, and the term ZmI is the usual VW resonance term (see eq 1). Hence, absorbing the terms in the square brackets appearing in eq 9 into the background terms, a revised working equation can be obtained as follows

Figure 2. Simplified schematics of the VW sensor: (a) physical arrangement; (b) electrical equivalence circuit; OSC, sine-wave oscillator (0.05−5 V rms); Rs, series resistor (1 kΩ), I, electric current; Zw, electrical impedance of stationary wire; Zm, additional electrical impedance due to wire motion in the magnetic field; Zb, electrical impedance of brine; N and S, poles of the permanent magnet; A and B, differential signal terminals for connection to the lock-in amplifier.

Z = ( Z w + Z m ) [ 1 + G b( Z w + Z m ) ]

(8)

Equation 8 can be rewritten as

Kn is the modified Bessel function of the second kind of order n,35 ρ and η are the density and viscosity of the fluid, and ρs and R are the density and radius of the wire. The term icf in eq 1 is not always significant and can be neglected when, as in the present work, the viscosity is small and the resonance curve spans a narrow frequency range. 3.2. Revised Working Equation for Highly Conductive Fluids. The standard theory of the VW instrument does not account for the conductivity of the fluid surrounding the wire. Given the constraints upon the desired mechanical properties of the wire material, experiments with insulated wires have not been carried out and, instead, we aim to account for the electrical conductivity of the surrounding wire in the theory of the instrument. Figure 2a illustrates the physical situation that

−1

(7)

≪ 1, (5)

What is measured in an experiment is a voltage Φ given by Φ = ZI − Φoffset

This represents the most critical case considered in which we have the highest ratio of brine conductivity to viscosity. When the parameters of the standard working equation, eq 1, are fitted to these data significant discrepancies can be observed. However, eq 10 provides a high-quality fit. It is notable that, eqs 1 and 10 contain the same number of parameters, as we

(6)

where I is the current and Φoffset is a constant complex voltage offset set on the lock-in amplifier used to make the measurements. Accordingly, the recorded data are in the following form D



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have dropped the term icf in eq 10. Unfortunately, the analysis leading to eq 10 is still incomplete because it neglects the possibility of leakage currents flowing between the wire and the surrounding brine, which gives rise to additional damping. As a consequence, the viscosity obtained when eq 10 is fitted to the data is over-estimated, compared with the literature, by some 12%. Electrical damping of the wire resonance can occur because the voltage per unit length induced in the wire is proportional to the velocity amplitude of the wire, which varies greatly along the length of the wire from zero at each end to a maximum amplitude at the midpoint. Therefore, a distributed potential difference arises between the wire and the surrounding brine giving rise to a distributed leakage current that causes additional damping of the resonance. If this term is not recognized then the viscosity of the fluid will be overestimated, as in the example mentioned above because the leakagecurrent damping will be included with the viscous damping in the analysis. Therefore, to account for the additional damping mechanism, we must include a term β″ in addition to the viscous damping term β′ in the working equation as follows Φ=

Λ′if exp(iθ ) f0 2 − f 2 (1 + β) + if 2 (β′ + β″ + 2Δ0)

Figure 4. Additional damping β″ as a function of phase angle θ for NaCl(aq) with viscosity values constrained to literature data:21 □, m = 0.77 mol·kg−1; ○, m = 2.5 mol·kg−1; , quadratic correlation.

When the same resonance data were re-analysed with β″ replaced by the quadratic function of θ determined in Figure 4 and η treated as a free parameter, the resulting viscosities are found to be in close agreement with the correlation of Kestin et al.21 This comparison is illustrated in Figure 5. The absolute average relative deviation between our experimental data and the correlation was 0.3%, while the maximum absolute relative deviation was 0.9%.

+ a + ib (11)

Equation 11 is the revised working equation that we have employed in this study. 3.3. Determination of the Additional Damping Term. A quantitative analysis of the additional damping is complicated because, in general, neither the exact current paths nor the brine conductivity are known. Therefore, in this work, we propose a semi-empirical approach. We first observe that the phase angle θ is easily obtained when fitting the experimental resonance curves. Furthermore, both θ and β″ are functions of the brine conductivity for a VW sensor of fixed geometry but the latter is unknown. Therefore, we seek an empirical relation β″(θ) between the additional damping and the phase angle, eliminating the conductivity from the problem, and we parameterize that relationship by means of measurements carried out in concentrated NaCl brines of known viscosity and density. For these brines, we make use of the reference data of Kestin et al.21 for viscosity and Al Ghafri et al.14 for density. The correlation for viscosity is based on the experimental results obtained with an oscillating-disk viscometer.36 An overall uncertainty of 0.5% was attributed to the correlation based on a very detailed analysis of the experimental method.36,37 The correlation has been validated in a temperature range from (293.15 to 423.15) K, a pressure from (0.1 to 30) MPa, and NaCl(aq) molalities up to 5.4 mol· kg−1. Resonance-curve measurements were carried out for NaCl(aq) of molality m = (0.77 and 2.50) mol·kg−1 and the experimental resonance curve data were then analyzed in terms of eq 11 with β′ calculated from eqs 2 and 3 using reference values of viscosity and density. The parameters so determined from each resonance curve were Λ′, θ, f 0, β″, a, and b. The results of these measurements for the additional damping term β″, as a function of the phase angle θ, are shown in Figure 4. We also show a quadratic polynomial fitted to the data which we used in the subsequent measurements to compute β″(θ). When this model was fitted to the reference values of viscosity, the standard deviation of the correlation was found to be 0.2%.

Figure 5. Relative deviations Δη/η = (ηexp − ηcalc)/ηexp between experimental viscosities ηexp and calculated values ηcalc from the correlation of Kestin et al.21 for NaCl(aq) with molality m = 0.77 mol· kg−1: ▲ 1 MPa, ×,15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa.

The theory behind this approach is based on general physical−chemical principles. Both the phase angle θ and the additional damping β″ arise specifically from the conductivity of the fluid. For this reason, the modified working equation should be applicable to any highly conductive fluid provided that a correlation between the additional damping term and the phase angle is established in the entire range of conductivity investigated. However, it should be recognized that, this relationship is specific to a given sensor.

4. EXPERIMENTAL PROCEDURE 4.1. Mixture Preparation. Before starting a new set of measurements, the system was carefully washed with deionized water in order to remove brine residues from the previous experiment. The cleaning process employed one of the syringe pumps for the water injection, activation of the circulation pump to flush the entire loop, and discharge to the waste line. The VT densimeter allowed simultaneous density measurements of the fluid in the system, and during the cleaning E



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measured pressure with the reading given by a digital barometer in the same laboratory. Taking this drift into account, the standard uncertainty of the pressure was estimated to be 0.1 MPa. 5.3. System Volume. The volume of the system was calibrated with pure deionized water at T = 298.15 K and it was found to be 44.09 cm3, with an overall standard uncertainty of 0.09 cm3.28 5.4. CO2 Mole Fraction. Mixtures were prepared in situ as described below and the mole fraction x of CO2 in the final homogeneous solution was determined from the amounts nCO2 of CO2 and nb of brine injected nCO2 x= nCO2 + nb (12)

process, the density was observed to decrease over time toward that of water; at this point, the flushing process was stopped. The system was evacuated through valves V2 and V3 (see Figure 1). In order to ensure isothermal filling, the temperature of the densimeter and the viscometer was controlled at the temperature of the laboratory (T = 295.15 K). CO2(g) was admitted through valve V1 to an initial filling pressure calculated to give the desired mole fraction in the final aqueous solution. Knowing the system volume and the filling temperature and pressure, the amount of CO2 was computed from the equation of state of Span and Wagner.38 The initial pressure of CO2 in the system was selected based on the model by Duan et al.,39,40 which is able to predict the solubility of CO2 in aqueous NaCl and CaCl2 solutions. Next, degassed brine solution of molality m was injected quantitatively from one of the syringe pumps until the pressure reached about 15 MPa. During this operation, the temperature of the syringe pump was controlled at 295.15 K. Several strokes of the pump were required to fill the system but all pump displacements were measured with the brine in the syringe compressed to a pressure of 15 MPa. The precise amount of brine injected was determined from the total injected volume measured at a pressure of 15 MPa, the pump temperature, and the corresponding brine density calculated from the correlation of Al Ghafri et al.14 4.2. Measurement Sequence. The viscosity and density measurements were carried out in the pressure range from (1 to 100) MPa, at nominal temperatures of (275, 296, 323, 348, 373, 398, 423, and 449) K. Simultaneous density and viscosity measurements were carried out for brine molalities of 0.77 mol·kg−1 for NaCl(aq), and 1.00 mol·kg−1 for CaCl2(aq). Additionally, density measurements were made for both brine systems at m = 2.50 mol·kg−1 in the same temperature and pressure ranges. The mole fractions of CO2 in the NaCl(aq) system were x = (0, 0.0122, and 0.0159) at m = 0.77 mol·kg−1, and x = (0, 0.0044, 0.0081, 0.0119) at m = 2.50 mol·kg−1; at m = 0.77 mol·kg−1, density measurements were additionally made at x = 0.0078. For the CaCl2(aq), the mole fractions were x = (0, 0.0052, 0.0094, and 0.0137) at m = 1.00 mol·kg−1, and x = (0, and 0.0061) at m = 2.50 mol·kg−1. For each system, some combinations of salt-free mole fraction, pressure, and temperature were avoided to ensure that the mixtures remained in the homogeneous liquid region.

The standard uncertainty u(x) of the CO2 mole fraction depends upon the standard relative uncertainties ur(nCO2) of nCO2 and ur(nb) of nb as follows u 2(x) = [x(1 − x)]2 [ur 2(nCO2) + ur 2(nb)]

(13)

The individual standard relative uncertainties appearing in eq 13 have been discussed previously28 where it was shown that the uncertainty of the CO2 filling pressure was the dominant term such that u(x) ≈ xur(p). This leads to a final value u(x) = 0.0004 for all the mixtures investigated. 5.5. Density. The density ρ(T,p) of the (CO2 + brine) mixtures was determined from the period τ of the VT densimeter according to the simplified working equation ρ(T , p) = A(T , p)[τ 2 − τ0 2(T )]

(14)

where A(T, p) is a function of temperature and pressure, while τ0(T) is the temperature-dependent period of oscillation under vacuum. In order to determine A and τ0, the strategy of Comuñas et al.41 was employed with calibrations performed in pure deionized and degassed water at each nominal experimental pressure and temperature, and under vacuum conditions at each nominal experimental temperature. The quantity A(T,p) was then obtained from the following relation A (T , p) =

ρw (T , p) 2

τw (T , p) − τ0 2(T )

(15)

where subscripts “w” and “0” refer to water and vacuum conditions, respectively. The densities of water at each experimental temperature and pressure were obtained from the IAPWS-95 equation of state of Wagner and Pruss.42 Finally, the calibration functions were represented empirically as follows

5. CALIBRATION AND UNCERTAINTY ANALYSIS The calibration procedures for the VW−VT apparatus were described previously,28 and only a brief summary is given here. 5.1. Temperature. The temperatures of the VW viscometer and the VT densimeter were measured by means of two PRTs. The PRTs were calibrated against a standard PRT, which was in turn calibrated on ITS-90 with an expanded uncertainty of ≤0.015 K (k = 2). The calibration was carried out at temperatures from (273 to 473) K, in steps of 40 K; the Callendar−van Dusen equation was employed to represent the results. The standard uncertainty of the measured temperatures was 0.025 K. 5.2. Pressure. The pressure transducer (Honeywell TJE) was calibrated at pressures of (20, 40, 60, 80, and 100) MPa; the calibration was performed against a hydraulic pressure balance (DH Budenberg model 580 EHX) with an expanded relative uncertainty of 0.008% (k = 2). In order to correct for drift, the zero of the pressure sensor was re-adjusted periodically, by comparing (at atmospheric pressure) the

3

A=

1

∑ ∑ aij(T /K)i [p/(0.1 MPa)] j i=0 i=0

(16)

3

τ0 =

∑ ci(T /K)i i=0

(17)

The uncertainty analysis for density is exemplified in Table 4 for the [CO2 + NaCl(aq)] system at salt molality m = 0.77 mol·kg−1, and at the median temperature, pressure, and CO2 mole fraction. The overall expanded relative uncertainty of 0.07% was attributed to all density measurements reported in this paper because the uncertainties varied very little over the range of conditions investigated. F



Article

density and viscosity of the brine solutions can be expressed in a way that is independent of both salt type and molality. Accordingly, in the following analysis, the terms pertaining to the effects of dissolved CO2 will be identical with those determined earlier in connection with the (CO2 + H2O) system.28 We model the density according to the relation

Table 4. Uncertainty Analysis for the Density of CO2 Solutions in NaCl(aq) with Salt Molality m = 0.77 mol·kg−1 at the Median State Point in Terms of Standard Uncertainty u(X) of Dimensionless Parameters X and Arising Contribution ur(ρ) to the Overall Standard Relative Uncertainty of Density dimensionless parameter p/MPa T/K m/(mol·kg−1) x τ0/μs A/(kg·m−3·μs−2) τ/μs overall standard relative

X

u(X)

102ur(ρ)

50.22 373.24 0.77 0.0124 2580.53 2.4902 × 10−3 2658.00 uncertainty

0.1 0.025 0.0019 0.0004 0.003 1.6 × 10−7 0.020a

0.004 0.002 0.006 0.016 0.004 0.006 0.027 0.033

ρ=

Repeatability uncertainty.

5.6. Viscosity. The key calibration parameter in both the standard and revised working equations is the radius R of the VW which was determined previously by calibration in pure deionized water. The overall standard uncertainty of the viscosity is related to the standard uncertainties of temperature, pressure, CO2 mole fraction, density, logarithmic decrement in vacuum, additional damping term, wire radius, and thermal expansivity, and also the repeatability uncertainty. Table 5

p/MPa 50.22 T/K 373.24 m/(mol·kg−1) 0.77 x 0.0124 ρ/(kg·m−3) 1010.56 R/μm 73.20 106Δ0 29.9 αw/(10−6·K−1) 8.7 104β″ 1.64 η/(mPa·s) 0.3303 overall standard relative uncertainty

u(X)

102ur(η)

0.1 0.025 0.0019 0.0004 0.46 0.18 15 0.4 0.51 0.0045a

0.01 0.03 0.02 0.01 0.04 0.50 0.03 0.01 0.45 1.31 1.47

(18)

i=2 j=1

VCO2 /(cm 3·mol−1) =

∑ ∑ aij(T /K)i (p/MPa) j (19)

i=0 j=0 28

the coefficients aij are reproduced in Table 10. According to the hypothesis that we wish to test, the apparent molar volume CO2(aq), VCO2, is identical with that determined in the (CO2 + H2O) system as represented by eq 19 and the coefficients in Table 10. In order to model the brine viscosity under CO2 addition, we first require an accurate model for the viscosity of the CO2free brines as a function of temperature, pressure, and molality. To construct this, we first note the effect of pressure is generally very small for brine solutions and can be represented by a simple multiplicative factor such that

Table 5. Uncertainty Analysis for the Viscosity of CO2 Solutions in NaCl(aq) with Salt Molality m = 0.77 mol·kg−1 at the Median State Point in Terms of Standard Uncertainty u(X) of Dimensionless Parameters X and Arising Contribution ur(ρ) to the Overall Standard Relative Uncertainty of Density X

xVCO2 + (1 − x)Vb

where Mb = Mw(1 + mMs)/(1 + mMw) is the mean molar mass of the CO2-free brine solution, Mw is the molar mass of water, Ms is the molar mass of salt, Vb = Mb/ρb is the molar volume of the CO2-free brine, ρb is the brine density, MCO2 is the molar mass of CO2, and VCO2 is the apparent molar volume of CO2(aq). This last term was determined by McBride-Wright et al. for the (CO2 + H2O) system and correlated as a function of temperature and pressure as follows

a

dimensionless parameter

xMCO2 + (1 − x)Mb

η(T , p , m) = η0(T , m)[1 + κ(T , m)p]

(20)

where κ(T , m) = κ w(T ) + κ E(T , m)

(21)

Here, κw is the viscosity pressure coefficient of pure water, which we take from Kestin and Shankland,22 and κE is an excess pressure coefficient related to the salt type and molality, which we represent by the following three-parameter equation c 2m κ E(T , m) = c1m + (T /T0 − 1) (22)

a

Repeatability uncertainty.

We find that the Othmer model43 provides a very effective means of correlating η0(T,m). In this approach

shows the uncertainty analysis for the viscosity of the [CO2 + NaCl(aq)] system at molality m = 0.77 mol·kg−1 and at the median state point. Based on this, and the observation that the uncertainty varied only slightly over the range of conditions investigated, an expanded overall relative uncertainty of 3% was attributed to all viscosity measurements.

ln[η0(T , m)/ηw (T )] = A + B ·ln[ηw (T )/ηw (293.15 K)] (23)

where ηw(T) is the viscosity of pure saturated liquid water at temperature T, which we take from the IAPWS correlation.44,45 The parameters A and B are expressed as cubic functions of molality for each brine system as follows

6. RESULTS AND DISCUSSION 6.1. Experimental Results. The density results for the [xCO2 + (1 − x)NaCl(aq)] system and the [xCO2 + (1 − x)CaCl2(aq)] system, are reported in Tables 6 and 7, respectively, while the corresponding viscosity results are given in Table 8 and 9. 6.2. Hypotheses. In analyzing the results, we wish to test the hypothesis that the influence of dissolved CO2 on the

| o o o o i=1 o } o 3 o o io o B = ∑ Bj m o o o o i=1 ~

∑ Aimi oooo 3

A=

G

(24) DOI: 10.1021/acs.jced.9b00248 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 6. Experimental Densities ρ of [x CO2 + (1 − x) NaCl(aq)] at Temperatures T, Pressures p, and Salt Molalities ma p/MPa

ρ/(kg·m−3)

p/MPa

ρ/(kg·m−3)

ρ/(kg·m−3)

p/MPa

p/MPa

ρ/(kg·m−3)

−1

T = 274.83 K 1.31 15.21 30.12 49.95 69.81 99.82 T = 373.25 K 1.40 15.31 30.22 50.06 69.93 99.96 T = 274.93 K 15.20 30.11 49.98 69.86 99.90 T = 373.22 K 15.27 30.15 50.03 69.91 99.91 T = 274.99 K 15.26 30.15 50.04 69.90 99.95 T = 373.24 K 30.30 50.22 70.10 100.12

1033.05 1039.38 1045.95 1054.41 1062.53 1074.13 988.09 994.18 1000.44 1008.50 1016.20 1027.15

1042.10 1048.54 1056.88 1064.93 1076.47 995.79 1002.18 1010.37 1018.13 1029.24

1042.95 1049.29 1057.53 1065.51 1077.01 1002.42 1010.56 1018.40 1029.50

T = 296.22 K 1.38 15.22 30.11 49.93 69.81 99.84 T = 398.81 K 1.46 15.37 30.26 50.08 69.95 99.99 T = 296.22 K 15.21 30.09 49.94 69.82 99.84 T = 398.38 K 15.29 30.18 50.06 69.92 99.93 T = 296.20 K 15.26 30.13 50.01 69.88 99.94 T = 398.31 K 30.29 50.18 70.08 100.10

T = 274.98 K 15.23 30.17 50.06 69.94 99.99 T = 373.23 K 50.24 70.12 100.00

1013.07 1020.96 1032.18

T = 296.17 K 15.20 30.08 50.11 69.84 99.94 T = 398.29 K 50.25 70.11 99.99

T = 274.95 K 1.34 15.26 30.19 50.04 69.93 99.99

1098.36 1103.81 1109.50 1116.83 1123.92 1134.12

T = 296.19 K 1.33 15.24 30.16 50.02 69.88 99.98

1046.29 1052.59 1060.79 1068.70 1080.07

m = 0.77 mol·kg x = 0.0000 T = 323.33 1028.25 1.34 1034.12 15.26 1040.25 30.16 1048.04 49.98 1055.61 69.84 1066.51 99.89 T = 423.73 969.16 1.45 975.70 15.37 982.49 30.27 991.06 50.11 999.13 69.96 1010.69 100.00 x = 0.0078 T = 323.35 1036.82 15.23 1042.90 30.14 1050.70 50.01 1058.23 69.89 1069.13 99.87 T = 423.73 976.70 15.30 983.60 30.20 992.35 50.07 1000.65 69.94 1012.39 99.93 x = 0.0122 T = 323.34 1037.62 15.26 1043.57 30.17 1051.36 50.04 1058.94 69.92 1069.76 99.93 T = 423.62 983.55 30.29 992.36 50.17 1000.71 70.08 1012.48 100.03 x = 0.0159 T = 323.32 1040.88 30.18 1046.89 50.14 1054.61 69.97 1062.15 99.98 1072.95 T = 423.63 994.66 50.25 1003.10 70.11 1015.01 100.00 m = 2.50 mol·kg−1 x = 0.0000 T = 323.30 1090.47 1.38 1095.73 15.29 1101.16 30.22 1108.18 50.06 1115.02 69.95 1124.82 100.01 H

K 1017.80 1023.47 1029.36 1036.98 1044.30 1054.90 K 947.66 954.86 962.29 971.57 980.32 992.59 K 1025.97 1031.96 1039.57 1046.90 1057.49 K 955.13 962.72 972.37 981.27 993.88

T = 348.21 K 1.38 15.26 30.18 50.00 69.88 99.92 T = 448.97 K 1.46 15.38 30.29 50.12 69.98 100.00 T = 348.20 K 15.22 30.09 49.96 69.86 99.89 T = 448.95 K 15.30 30.21 50.08 69.94 99.94

1004.37 1010.15 1016.18 1023.83 1031.26 1041.89 923.83 932.02 940.31 950.53 960.05 973.43

1012.34 1018.37 1026.19 1033.63 1044.33 931.45 940.01 950.72 960.53 974.22

T = 348.19 K 30.23 50.08 69.94 99.98

1018.84 1026.61 1034.12 1044.82

T = 448.85 K 30.30 50.19 70.08 100.04

938.95 949.84 959.96 973.74

T = 348.21 K 50.24 70.10 99.99

1029.33 1036.87 1047.70

973.84 983.13 996.08

T = 448.83 K 50.25 70.14 100.00

951.41 961.71 975.91

1077.94 1083.20 1088.58 1095.53 1102.24 1111.99

T = 348.21 K 1.36 15.27 30.20 50.06 69.96 100.02

1064.12 1069.47 1075.01 1082.15 1089.02 1098.91

K 1026.65 1032.56 1040.12 1047.45 1058.01 K 962.25 971.93 981.10 993.79 K 1035.45 1043.09 1050.47 1061.04 K

K



Article

Table 6. continued p/MPa T = 373.22 K 1.38 15.31 30.23 50.09 69.96 100.04 T = 274.88 K 15.21 30.11 49.99 69.85 99.91 T = 373.22 K 15.28 30.18 50.07 69.95 99.95 T = 274.82 K 15.23 30.12 49.99 69.87 99.89 T = 373.21 K 30.24 50.09 69.96 99.92 T = 274.81 K 15.21 30.10 49.97 69.82 99.78 T = 373.21 K 50.20 70.00 99.85

ρ/(kg·m−3)

1047.69 1053.49 1059.36 1066.79 1073.94 1084.13

1105.65 1111.39 1118.74 1125.78 1135.93 1053.33 1059.51 1067.45 1074.88 1085.53

1107.67 1113.28 1120.56 1127.55 1137.66 1061.87 1069.52 1076.78 1087.06

1109.04 1114.75 1121.91 1128.98 1139.04 1070.48 1077.82 1088.58

p/MPa T = 398.29 K 1.39 15.30 30.23 50.08 69.98 100.05 T = 296.17 K 15.22 30.17 50.02 69.90 99.94 T = 398.27 K 15.30 30.20 50.08 69.96 99.97 T = 296.17 K 15.22 30.14 49.99 69.85 99.88 T = 398.27 K 30.23 50.11 69.97 99.91 T = 296.16 K 15.19 30.07 49.99 69.78 99.78 T = 398.26 K 50.18 70.03 99.87

ρ/(kg·m−3)

1029.58 1035.58 1041.92 1049.89 1057.41 1068.15

1097.40 1102.57 1109.85 1116.68 1126.53 1035.12 1041.53 1050.02 1057.85 1068.97

1099.22 1104.51 1111.65 1118.42 1128.22 1043.86 1052.07 1059.94 1070.72

1100.61 1106.11 1113.09 1119.81 1129.64

ρ/(kg·m−3)

p/MPa

x = 0.0000 T = 423.62 1.41 15.33 30.25 50.10 69.99 100.05 x = 0.0044 T = 323.30 15.24 30.15 50.02 69.91 99.91 T = 423.61 15.31 30.25 50.10 69.97 99.97 x = 0.0081 T = 323.33 15.23 30.15 50.02 69.90 99.90 T = 423.60 30.24 50.11 69.99 99.90 x = 0.0119 T = 323.26 50.05 69.85 99.82

K 1009.24 1015.81 1022.75 1031.25 1039.38 1050.77 K 1084.14 1090.05 1097.17 1104.02 1113.77 K 1015.02 1021.92 1030.95 1039.25 1051.18

T = 448.85 K 1.41 15.33 30.26 50.11 69.99 100.05 T = 348.19 K 15.26 30.17 50.04 69.93 99.95 T = 448.84 K 30.28 50.14 70.02 99.97

ρ/(kg·m−3)

987.39 994.66 1002.41 1011.56 1020.26 1032.59

1069.95 1075.82 1083.40 1090.55 1100.56 1000.99 1010.75 1020.09 1032.73

1024.02 1032.84 1041.28 1052.86

T = 348.19 K 15.25 30.21 50.05 69.92 99.93 T = 448.85 K 30.24 50.10 69.97 99.90

1003.16 1012.72 1021.84 1034.31

1105.08 1106.92 1116.77

T = 348.18 K 50.12 69.97 99.87

1086.39 1093.31 1103.30

1033.70 1042.15 1053.83

T = 448.82 K 50.17 70.02 99.85

1013.13 1022.50 1035.18

K 1086.41 1091.83 1098.77 1105.56 1115.24 K

K

T = 423.59 K 50.17 70.03 99.87

1052.89 1060.74 1071.64

p/MPa

1072.35 1077.96 1085.14 1092.02 1101.93

a

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the density is u(ρ) = 0.00033·ρ.

and Mahiuddin25 were found to be inconsistent with the other sources and were not used). Table 11 gives the parameters obtained for the two brine systems, together with the values of e1 and e2 determined previously. The correlations are valid for m ≤ 6 mol·kg−1. The goodness of fit may be summarized by the average absolute relative deviation, defined as follows

Finally, the viscosity of the CO2-containing solution is given by ln[η(T , p , m , x)] = ln[η(T , p , m)] + e1 exp[ − e 2(T /T0 − 1)]x

(25)

where the parameters e1 and e2 are identical to those determined previously for the (CO2 + H2O) system.28 The nine parameters (A1, A2, A3, B1, B2, B3, c1, c2, and T0) were determined by regression against the available literature data for the viscosity of NaCl and CaCl2 brines. For NaCl, the parameters were fitted to the data of Kestin et al.,21,22 while for CaCl2, we used the data of Abdulagatov and Azizov,23 Isono,24 Gonçalves and Kestin,26 and Zhang et al.27 (the data of Wahab

ΔAARD =

N i |η j i ,exp − ηi ,calc| yzz 1 zz ∑ jjjjj zz ηi ,exp N i=1 j z k {

(26)

where N is the total number of data points, ηi,exp is an experimental datum, and ηi,calc is the viscosity calculated from the model at the same state point. For the NaCl brines, N = I



Article

Table 7. Experimental Densities ρ of [xCO2 + (1 − x)CaCl2(aq)] at Temperatures T, Pressures p, and Salt Molalities ma p/MPa

ρ/(kg·m−3)

p/MPa

ρ/(kg·m−3)

ρ/(kg·m−3)

p/MPa

p/MPa

ρ/(kg·m−3)

−1

T = 274.87 K 1.27 15.18 30.07 49.88 69.75 99.73 T = 373.22 K 1.32 15.23 30.13 49.94 69.79 99.79 T = 274.93 K 15.23 30.10 49.96 69.81 99.77 T = 373.22 K 15.27 30.16 49.99 69.85 99.81 T = 275.00 K 15.24 30.13 49.98 69.82 99.79 T = 373.22 K 15.31 30.20 50.04 69.88 99.81

1088.12 1094.18 1100.27 1108.27 1115.89 1126.88 1042.78 1048.82 1054.88 1062.61 1070.00 1080.38

1095.95 1102.20 1110.12 1117.84 1128.61 1049.19 1055.45 1063.39 1070.85 1081.45

1097.91 1104.28 1111.83 1119.49 1130.36 1051.15 1057.23 1064.97 1072.37 1083.00

T = 296.18 K 1.28 15.17 30.07 49.90 69.75 99.73 T = 398.28 K 1.32 15.23 30.12 49.94 69.78 99.79 T = 296.18 K 15.22 30.11 49.95 69.79 99.79 T = 398.23 K 15.29 30.18 50.02 69.88 99.81 T = 296.22 K 15.25 30.08 49.92 69.77 99.79 T = 398.24 K 15.31 30.20 50.04 69.88 99.82

T = 274.93 K 15.17 30.07 49.90 69.74 99.68 T = 373.20 K 50.08 69.91 99.71

1066.09 1073.59 1084.28

T = 296.21 K 15.23 30.05 49.97 69.73 99.71 T = 398.21 K 50.09 69.91 99.73

T = 274.98 K 1.31 15.21 30.10 49.93 69.77

1201.94 1207.74 1212.77 1219.37 1225.90

T = 296.22 K 1.31 15.24 30.13 49.96 69.78

1099.49 1105.75 1113.62 1121.01 1131.95

m = 1.00 mol·kg x = 0.0000 T = 323.31 1082.39 1.24 1087.93 15.19 1093.68 30.07 1101.19 49.88 1108.40 69.76 1118.84 99.75 T = 423.60 1024.80 1.34 1031.20 15.25 1037.76 30.15 1045.99 49.95 1053.70 69.82 1064.71 99.81 x = 0.0052 T = 323.30 1089.50 15.25 1095.40 30.14 1102.90 49.98 1110.07 69.83 1120.45 99.77 T = 423.58 1031.24 15.29 1037.93 30.19 1046.43 50.03 1054.29 69.86 1065.50 99.81 x = 0.0094 T = 323.31 1091.33 15.26 1097.05 30.15 1104.48 50.01 1111.60 69.86 1122.03 99.83 T = 423.59 1033.21 15.32 1039.69 30.21 1048.04 50.05 1055.85 69.88 1066.96 99.82 x = 0.0137 T = 323.27 1092.96 30.06 1098.64 49.99 1105.96 69.77 1113.19 99.68 1123.55 T = 423.57 1048.79 50.10 1056.81 69.93 1067.97 99.73 m = 2.50 mol·kg−1 x = 0.0000 T = 323.23 1192.77 1.28 1197.73 15.18 1202.82 30.06 1209.46 49.91 1215.91 69.77 J

K 1071.60 1077.19 1082.81 1090.06 1097.04 1107.20 K 1004.42 1011.30 1018.56 1027.46 1035.71 1047.43 K 1078.28 1084.08 1091.43 1098.43 1108.64 K 1011.17 1018.37 1027.67 1036.13 1048.13

T = 348.20 K 1.30 15.22 30.10 49.93 69.79 99.77 T = 448.84 K 1.36 15.27 30.16 49.98 69.83 99.81 T = 348.17 K 15.27 30.15 50.00 69.83 99.78 T = 448.84 K 15.31 30.19 50.03 69.89 99.83

1058.82 1064.57 1070.33 1077.65 1084.72 1094.89 982.19 989.78 997.78 1007.39 1016.54 1029.19

1065.06 1071.00 1078.60 1085.75 1096.01 989.26 997.10 1007.25 1016.39 1029.42

T = 348.17 K 15.29 30.17 50.02 69.87 99.82 T = 448.85 K 15.31 30.21 50.04 69.88 99.82

991.10 998.83 1008.86 1017.95 1030.76

T = 348.15 K 50.03 69.89 99.71

1081.44 1088.69 1099.04

1029.65 1038.30 1050.48

T = 448.80 K 50.11 69.95 99.76

1009.00 1018.34 1031.47

1179.30 1184.63 1189.89 1196.52 1202.94

T = 348.19 K 1.32 15.22 30.11 49.95 69.79

1165.84 1170.56 1175.97 1182.84 1189.55

K 1080.19 1085.85 1093.16 1100.23 1110.37 K 1013.15 1020.20 1029.25 1037.70 1049.43 K 1087.27 1094.54 1101.66 1111.85 K

K

1067.02 1072.80 1080.25 1087.40 1097.65



Article

Table 7. continued p/MPa

ρ/(kg·m−3)

p/MPa

ρ/(kg·m−3)

p/MPa

ρ/(kg·m−3)

p/MPa

ρ/(kg·m−3)

x = 0.0000 99.75 T = 373.20 K 1.35 15.25 30.14 49.96 69.82 99.78 T = 275.25 K 15.24 30.11 49.95 69.79 99.77 T = 373.21 K 15.27 30.16 50.01 69.86 99.82

1235.53 1151.73 1156.76 1161.97 1168.74 1175.25 1184.69

1208.37 1213.62 1220.48 1227.11 1236.71 1157.31 1162.72 1169.65 1176.32 1185.83

99.74 T = 398.26 K 1.36 15.27 30.16 49.97 69.82 99.80 T = 296.22 K 15.21 30.09 49.94 69.79 99.79 T = 398.23 K 15.28 30.17 50.02 69.86 99.80

1225.32

99.73 T = 423.60 K 1134.93 1.36 1140.45 15.26 1146.01 30.15 1153.12 49.98 1159.89 69.81 1169.63 99.79 x = 0.0061 T = 323.28 K 1198.87 15.24 1204.08 30.10 1210.33 49.96 1216.84 69.83 1226.16 99.80 T = 423.56 K 1140.85 15.28 1146.52 30.19 1153.84 50.03 1160.68 69.86 1170.61 99.81

1212.15 1116.33 1122.22 1128.37 1136.00 1143.19 1153.51

1185.89 1190.97 1197.57 1203.93 1213.12 1122.76 1128.81 1136.63 1144.01 1154.33

99.79 T = 448.83 K 1.36 15.25 30.15 49.97 69.82 99.83 T = 348.12 K 15.26 30.17 50.01 69.87 99.79 T = 448.84 K 15.30 30.18 50.03 69.86 99.82

1199.01 1096.34 1102.89 1109.65 1117.84 1125.62 1136.51

1172.50 1177.70 1184.37 1190.88 1200.11 1103.38 1109.76 1118.26 1126.13 1137.12

a Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the density is u(ρ) = 0.00033·ρ.

experimental data upon which it was based to within ±0.25 kg· m−3. Figures 8 and 9 show the comparisons of our experimental data with the model for the [xCO2 + (1 − x)NaCl(aq)] and [xCO2 + (1 − x)CaCl2(aq)] systems, respectively. These figures also include the densities at m = 0 reported previously.28 Unsurprisingly, the model is in excellent agreement with the data at m = 0 because eq 19 was developed to fit those data. At finite salt molalities, there are small deviations within approximately ±2kg·m−3 with absolute average relative deviations of 0.07% for the NaCl(aq) systems and 0.05% for the CaCl2(aq) systems. From these comparisons, we conclude that the hypothesis that VCO2 is independent of salt type and molality is adequately confirmed. In Figure 10, we have shown the density of [xCO2 + (1 − x)NaCl(aq)] reported by Yan et al.16 and Song et al.17 as deviations from our model as function of temperature, CO2 mole fraction, and pressure. The results of Song et al. are plotted only for those states which, according to the solubility model of Spycher and Pruess,46 are undersaturated with respect to CO2. The literature data at NaCl molalities of (1 and 3) mol·kg−3 mostly agree with our model to within ±1kg· m−3 over all states, while those at molalities of 4 and 5 mol· kg−1 tend to fall between (2 and 4) kg·m−3 above the prediction of the model, although the data of Song et al. at m = 4 mol·kg−1 only deviate by more than 1 kg·m−3 at T = (393 and 413) K. It is notable that the deviations for each literature source and NaCl molality do not depend systematically upon either x or p. Yan et al.16 calibrated their densimeter at each salt molality against the data of Rowe and Chou47 and the observed deviations from our model at m = 5 mol·kg−1 simply reflect the differences between the brine densities of Rowe and Chou and those of Al Ghafri et al.14 used in this work. Overall, the agreement with the current model is quite satisfactory. The data of Nighswander et al. show much larger deviation from

415 and ΔAARD = 0.85% while, for CaCl2 brines, N = 437 and ΔAARD = 1.05%. The models presented for both density and viscosity are fully parameterized on the basis of independent data sources and are compared below with the present experimental data without further adjustment. 6.3. Density. Figure 6 shows the density as a function of mole fraction at constant pressure for the [xCO2 + (1 − x)NaCl(aq)] system at a molality of 2.50 mol·kg−1 and both the lowest and the highest temperatures investigated. Similarly, Figure 7 shows ρ(x) at constant p for the [xCO2 + (1 − x)CaCl2(aq)] system at m = 1.00 mol·kg−1 for the lowest and highest temperatures. In these examples, and all other cases investigated, the density increases linearly with the mole fraction of CO2. Plots of the molar volume Vm = M/ρ against x at constant T and p are also found to be linear functions of x such that Vm = Ax + B

(27)

where A = Vb and B = (VCO2 − Vb). The linearity of these plots also implies that the apparent molar volume of CO2(aq) is independent of x and, for practical purposes, practically identical with the partial molar volume at infinite dilution. In testing the hypothesis that the apparent molar volume of CO2(aq) is independent of salt type and molality, we have evaluated the molar volume Vb of the CO2-free brine from the correlation of Al Ghafri et al.14 so that no parameters were fitted to the present data and a direct comparison was made between the experimental results and eq 18 with independent inputs for both Vb and VCO2. The correlation of Al Ghafri et al.14 is strictly valid in the temperature range from (283 to 473) K at pressures up to 69 MPa and brine molalities up to 6.00 mol·kg−1. However, for present purposes, we have extrapolated in temperature down to T = 275 K, and in pressure up to p = 100 MPa. The model represents the original K



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Table 8. Experimental Viscosities η of [xCO2 + (1 − x)NaCl(aq)] at Temperatures T, Pressures p, and Salt Molality m = 0.77 mol·kg−1a p/MPa

η/(mPa·s)

T = 274.65 1.4 15.3 30.2 50.1

K 1.748 1.718 1.704 1.700

T = 398.18 1.4 15.3 30.2 50.1 70.0 100.0

K 0.247 0.251 0.256 0.260 0.265 0.273

T = 274.64 15.2 30.2 69.9 99.9 T = 398.24 30.3 50.2 70.1

K 1.899 1.882 1.843 1.813 K 0.260 0.265 0.269

T = 274.63 15.2 30.2 100.0 T = 423.28 50.2 70.1 100.0

K 1.961 1.942 1.872 K 0.222 0.227 0.235

p/MPa

η/(mPa·s)

x = 0.0000 T = 348.34 K 1.4 0.412 15.3 0.416 30.2 0.421 50.0 0.429 69.9 0.433 T = 423.31 K 15.3 0.206 30.2 0.212 50.1 0.216 70.0 0.220 100.0 0.228 x = 0.0122 T = 348.36 K 30.2 0.431 50.1 0.436 69.9 0.442 T = 423.37 K 30.3 0.213 50.2 0.219 70.1 0.224 100.0 0.232 x = 0.0159 T = 348.34 K 50.2 0.443 70.1 0.449 T = 448.23 K 50.3 70.1 100.0

p/MPa T = 373.31 K 1.4 30.2 50.0 69.9 100.0 T = 448.27 K 30.3 50.1 70.0 100.0

Table 9. Experimental Viscosities η of [xCO2 + (1 − x)CaCl2(aq)] at Temperatures T, Pressures p, and Salt Molality m = 1.00 mol·kg−1a

η/(mPa·s)

p/MPa

T = 274.75 1.3 49.9 99.7

0.310 0.318 0.323 0.329 0.338

T = 373.45 30.1 49.9

0.181 0.185 0.190 0.197

T = 373.34 K 30.3 50.2 70.1 100.1 T = 448.33 K 30.3 50.2 70.1 100.0

0.183 0.187 0.193 0.200

T = 373.29 K 50.2 70.1 100.0

0.335 0.341 0.351

η/(mPa·s)

T = 448.43 1.4 69.8 T = 274.87 15.2

0.325 0.330 0.336 0.346

T = 373.36 15.3 30.2 50.0 T = 448.43 15.3 30.2 69.9 T = 296.24 15.2 30.1

0.190 0.195 0.202

T = 398.28 15.3 30.2 50.0 69.9

a

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the viscosity is u(η) = 0.015·η

T = 274.93 15.2 30.1 69.7 T = 373.03 50.1

our model of between (4 and −27) kg·m−3 and are not shown in Figure 10. 6.4. Viscosity. Figures 11 and 12 illustrate the dependence of viscosity upon the mole fraction of dissolved CO2 under conditions of constant temperature and pressure. The viscosity increases linearly and the slope is more pronounced at low temperature, as shown in Figure 11 where data for [xCO2 + (1 − x)NaCl(aq)] are shown for the lowest and highest temperatures investigated. At the lowest temperature, addition of CO2 to near saturation increases the viscosity of the mixture by just over 12%, whereas, at the highest temperature studied, the relative increment is just below 3%. Similar results are found for the viscosity of CaCl2(aq) with molality of 1.00 mol· kg−1. The hypothesis that we set out to investigate is that these slopes are the same as found in the (CO2 + H2O) system. To test this, we plot in Figure 13 the partial derivatives (∂ln η/∂x) determined in the (CO2 + H2O) system determined previously,28 as well as the values determined from the present data at all states where three or more compositions were studied. Also shown is the same derivative according to eq 25:

T = 448.36 50.1 69.9 99.8

p/MPa

η/(mPa·s)

η/(mPa·s)

p/MPa

x = 0.0000 K T = 296.21 K T = 323.40 2.142 30.1 1.224 1.3 2.117 99.7 1.237 15.2 2.096 30.1 49.9 69.8 K T = 398.33 K T = 423.46 0.393 15.2 0.310 1.4 0.399 30.1 0.315 50.0 49.9 0.321 69.8 K 0.226 0.235 x = 0.0052 K T = 296.20 K T = 323.30 2.194 15.2 1.264 30.1 99.8 1.269 99.8 K T = 398.29 K T = 423.45 0.391 15.3 0.316 15.3 0.403 30.2 0.321 50.0 0.410 69.9 0.334 69.9 K 0.223 0.230 0.249 x = 0.0094 K T = 323.26 K T = 373.23 1.277 15.3 0.737 30.2 1.281 50.0 0.757 50.0 69.9 0.776 99.8 0.793 K T = 423.42 K T = 448.39 0.324 15.3 0.266 30.2 0.326 30.2 0.268 50.0 0.331 69.9 0.280 69.9 0.335 99.8 0.288 x = 0.0137 K T = 296.25 K T = 323.21 2.298 30.0 1.297 30.1 2.293 99.7 1.327 49.9 2.275 99.7 K T = 398.28 K T = 423.44 0.426 69.9 0.340 69.9 99.7 0.371 99.7 K 0.238 0.242 0.251

K 0.736 0.734 0.732 0.728 0.725 K 0.255 0.266 0.272

K 0.732 0.773 K 0.260 0.269 0.273

K 0.410 0.419

K 0.233 0.237 0.240

K 0.759 0.771 0.804 K 0.278 0.292

a

Standard uncertainties are u(T) = 0.025 K, u(p) = 0.1 MPa, u(m) = 0.0025·m, and u(x) = 0.0004. The overall standard uncertainty of the viscosity is u(η) = 0.015·η

(∂ln η/∂x) = e1 exp[−e2(T/T0 − 1)] with the parameters from Table 11. The data for (CO2 + H2O) were of course used to fit the parameters of the model and they follow eq 25 closely. The data for the two brine systems are more scattered and are generally larger than predicted by eq 25. The increased scatter L



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Table 10. Coefficients of Eq 19 for the Apparent Molar Volume of CO2 in Aqueous Solution a0,0

a1,0

a2,0

a0,1

a1,1

a2,1

51.19

−0.15575

3.2955 × 10−4

−6.0708 × 10−2

5.5026 × 10−4

−1.2114 × 10−6

Table 11. Parameters in 20 for the Viscosity of CO2−Brine Solutions A1 A2 A3 B1 B2 B3 c1 c2 T0/K e1 e2

NaCl

CaCl2

8.6075 × 10−2 2.3522 × 10−3 3.5710 × 10−4 −3.5198 × 10−2 5.4401 × 10−3 −4.2694 × 10−5 −0.3974 0.6125 142 65.560 2.468

2.6672 × 10−1 1.1635 × 10−2 5.7087 × 10−4 −7.2543 × 10−2 2.0379 × 10−2 −7.8848 × 10−4 −0.5511 0.8314

Figure 7. Densities ρ of [xCO2 + (1 − x)CaCl2(aq)] with m = 1.00 mol·kg−1 as a function of CO2 mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

Figure 6. Densities ρ of [xCO2 + (1 − x)NaCl(aq)] m = 2.50 mol· kg−1 as a function of CO2 mole fraction x at (a) T = 275 K and (b) T = 449 K: ×, 15 MPa; ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

reflects both the difficulty in measuring the viscosity of the brine solutions and the fact that the salting-out effect limits the amount of CO2 that can be dissolved and hence restrict the precision with which the partial derivative (∂ln η/∂x) can be determined. The error bars show two standard deviations based on the linear regression statistics. From this graph, we conclude that the data do not strongly confirm our hypothesis. It is also notable that the viscosity increases linearly with increasing pressure at constant composition and temperature, except at T = 275 K where a linear decrease is observed. Figure 14 illustrates this decrement in the viscosity for the [xCO2 + (1 − x)NaCl(aq)] system at T = 275 K. Similar behavior is observed for pure water.45 In Figure 15, we show the deviations of the present experimental viscosity results and of the literature data from eq 20 for the [xCO2 + (1 − x)NaCl(aq)] system. Overall, the deviations of our data from the model are mostly within ±2% and we find ΔAARD = 0.9%. Figure 15b shows that the deviations are essentially independent of x. Thus, while the individual slopes (∂ln η/∂x) at different state points do not

Figure 8. Deviations Δρ = (ρexp − ρcalc) between experimental densities ρexp of [xCO2 + (1 − x)NaCl(aq)], and densities ρcalc calculated from eqs 18 and 19 with brine densities from ref 14 as a function of CO2 mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg−1; orange, m = 0.77 mol·kg−1; green, m = 2.50 mol·kg−1.

conform very closely to eq 25, the overall prediction of viscosity in the CO2−brine solutions is of good accuracy under our hypothesis. The dependence of viscosity upon the CO2 mole fraction has also been reported in the literature for this system by Fleury and Deschamps,20 Bando et al.,19 and Kumagai and Yokoyama.18 Fleury and Deschamps20 studied the effect of dissolved CO2 on the viscosity of three NaCl(aq) M



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Figure 11. Viscosities η of [xCO2 + (1 − x)NaCl(aq)] with m = 0.77 mol·kg−1 as a function of CO2 mole fraction x at (a) T = 275 K and (b) T = 449 K: ●, 30 MPa; ▲, 50 MPa; ■, 70 MPa; ◆, 100 MPa. Solid lines are linear regression lines.

Figure 9. Deviations Δρ = (ρexp − ρcalc) between experimental densities ρexp of [xCO2 + (1 − x)CaCl2 (aq)], and densities ρcalc calculated from eqs 18 and 19 with brine densities from ref 14 as a function of CO2 mole fraction x at (a) T = 275 K, (b) T = 373 K, and (c) T = 449 K. Symbols: ○, 30 MPa; □, 70 MPa; ◇, 100 MPa. Colors: black, m = 0.00 mol·kg−1; orange, m = 0.77 mol·kg−1; green, m = 2.50 mol·kg−1.

Figure 12. Viscosities η of [xCO2 + (1 − x)CaCl2(aq)] with m = 1.00 mol·kg−1 as a function of CO2 mole fraction x at T = 373 K: ●, 30 MPa; ▲, 50 MPa. Solid lines are linear regression lines.

Figure 10. Deviations Δρ = (ρexp − ρcalc) between experimental literature densities ρexp of [xCO2 + (1 − x)NaCl(aq)], and densities ρcalc calculated from eqs 18 and 19 with brine densities from ref 14 as a function of (a) temperature T, (b) CO2 mole fraction x, and (c) pressure p: □, Yan et al.;16 ○, Song at al.17 Colors indicate NaCl molality: red = 1 mol·kg−1; green = 2 mol·kg−1; blue = 3 mol·kg−1; purple = 4 mol·kg−1; orange = 5 mol·kg−1.

Figure 13. Partial derivative (∂ln η/∂x) of the natural logarithm of the viscosity η with respect to the mole fraction x of dissolved CO2 as a function of temperature T: ●, CO2 + H2O;28 ▲, CO2 + NaCl(aq); ■, CO2 + CaCl2(aq). Solid line based on eq 25. Error bars show two standard deviations.

systems, with salinities of (20, 80, and 160) g·L−1, at T = 308.15 K and p = 8.5 MPa. Bando et al.19 measured the viscosity of three different NaCl brines of mass fractions (0, 1, and 3) %, with dissolved CO2 in a temperature range from

(303.15 to 333.15) K and at pressures from (10 to 20) MPa. Kumagai and Yokoyama18 measured the viscosity at temperatures between (273 and 278) K, and pressures up to 30 MPa, with CO2 mole fractions up to 0.015. The results of Fleury and N



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Figure 14. Viscosities η of [xCO2 + (1 − x)NaCl(aq)] with m = 0.77 mol·kg−1 as a function of pressure p at T = 275 K: ×, x = 0.000; ●, x = 0.0124; ▲, x = 0.0161. Solid lines are linear regression lines.

Figure 16. Relative deviations Δη/η = (ηexp − ηcalc)/ηexp between experimental viscosities ηexp of [xCO2 + (1 − x)CaCl2(aq)], and viscosities ηcalc calculated from eq 21 as a function of (a) temperature T, (b) CO2 mole fraction x, and (c) pressure p: ▲, this work; ▲, Isono;24 ●, Wahab and Mahiuddin;25 ◆, Gonçalves and Kestin;26 *, Zhang et al.;27 +, Abdulagatov and Azizov.23

been reported by Abdulagatov and Azizov,23 Isono,24 Wahab and Mahiuddin,25 Gonçalves and Kestin,26 and Zhang et al.27 The study of Abdulagatov and Azizov23 pertains to a molality of 2.00 mol·kg−1 and is the only one that extends to high pressures (up to 60 MPa). In the case of Isono,24 the measurements were made at atmospheric pressure, temperatures from (288.15 to 323.15) K, and molalities up to 6.00 mol·kg−1. Wahab and Mahiuddin25 studied the viscosity of pure CaCl2(aq) at atmospheric pressure, temperatures from (273.15 to 323.15) K, and molalities up to 7.15 mol·kg−1. Gonçalves and Kestin26 covered a temperature range from (293.15 to 323.15) K, molalities up to 6.00 mol·kg−1, and atmospheric pressure. Zhang et al.27 performed measurements at the single temperature of 298.15 K and a pressure of 0.1 MPa with molalities up 7.88 mol·kg−1. The viscosities measured by Abdulagatov and Azizov,23 Isono,24,25 Gonçalves and Kestin,26 and Zhang et al.27 are mostly represented by eq 21 to within ±2%, while those of Wahab and Mahiuddin25 exhibit deviations that increase with temperature to around 4%. Overall, the observed agreement with the model is good.

Figure 15. Relative deviations Δη/η = (ηexp − ηcalc)/ηexp between experimental viscosities ηexp of [xCO2 + (1 − x)NaCl(aq)], and viscosities ηcalc calculated from eq 21 as a function of (a) temperature T, (b) CO2 mole fraction x, and (c) pressure p: ▲, this work; ◆, Kumagai and Yokoyama;18 ●, Fleury and Deschamps;20 *, Bando et al.19

Deschamps20 and Bando et al.19 are in good agreement with eq 20, with most of the data within ±2% of the correlation. On the other hand, the data of Kumagai and Yokoyama18 deviate increasingly with increasing CO2 mole fraction and the absolute relative deviations reach about 6.5% at the highest values of x and p. Figure 16 shows the deviations of the present experimental viscosity results and of data from the literature from 20 for the [xCO2 + (1 − x)CaCl2(aq)] system. Overall, our data fall slightly below the model but the deviations, characterized by ΔAARD = 2.3%, do not depend significantly on temperature, pressure, or the mole fraction of dissolved CO2. Figure 16b, in particular, shows that in this system also the viscosity of the CO2−brine solution is predicted adequately by the model. For this system, there are no published data for the brine viscosity with dissolved CO2 and the comparison with literature is confined to x = 0. Viscosity data for CaCl2(aq) solutions have

7. CONCLUSIONS A new semi-empirical working equation has been developed and validated for determining the viscosity of highly conductive fluids using the VW technique. This equation accounts for the conductivity of the fluid, and we note that large errors result if this factor is ignored. Viscosity and density measurements are reported for compositionally characterized homogeneous aqueous solutions of CO2 and either NaCl or CaCl2 at temperatures from (275 to 449) K, pressures up to 100 MPa, and salt molalities of 0.77 and 1.00 mol·kg−1 for NaCl and CaCl2, respectively. Additional density measurements were also made for both brines with dissolved CO2 at salt molalities of m = 2.50 mol·kg−1 in the same temperature O



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Waste Water of Yulania Liliiflora. J. Chem. Technol. Biotechnol. 2016, 91, 1896−1904. (3) Arif, M.; Barifcani, A.; Lebedev, M.; Iglauer, S. CO2-Wettability of Low to High Rank Coal Seams: Implications for Carbon Sequestration and Enhanced Methane Recovery. Fuel 2016, 181, 680−689. (4) Elsharkawy, A. M.; Poettmann, F. H.; Christiansen, R. L. Measuring Minimum Miscibility Pressure: Slim-Tube or RisingBubble Method?. SPE/DOE Enhanced Oil Recovery Symposium, 1992 Copyright 1992; Soc Petrol Eng Inc.: Tulsa, Oklahoma, 1992. (5) Jaubert, J.-N.; Avaullee, L.; Pierre, C. Is It Still Necessary to Measure the Minimum Miscibility Pressure? Ind. Eng. Chem. Res. 2002, 41, 303−310. (6) Neau, E.; Avaullée, L.; Jaubert, J. N. A New Algorithm for Enhanced Oil Recovery Calculations. Fluid Phase Equilib. 1996, 117, 265−272. (7) Koottungal, L. General Interest: 2012 Worldwide EOR Survey. Oil Gas J. 2012, 110, 57−69. (8) Houghton, J. T.; Ding, Y.; Griggs, D. J.; Noguer, M.; Linden, P. J. v. d.; Dai, X.; Maskell, K.; Johnson, C. A. Climate Change 2001: The Scientific Basis; Cambridge University Press: Cambridge, 2001. (9) Saadatpoor, E.; Bryant, S. L.; Sepehrnoori, K. New Trapping Mechanism in Carbon Sequestration. Transp. Porous Media 2010, 82, 3−17. (10) Burton, M.; Kumar, N.; Bryant, S. L. CO2 Injectivity into Brine Aquifers: Why Relative Permeability Matters as Much as Absolute Permeability. Energy Procedia 2009, 1, 3091−3098. (11) Benson, S. M.; Cole, D. R. CO2 Sequestration in Deep Sedimentary Formations. Elements 2008, 4, 325−331. (12) Pau, G. S. H.; Bell, J. B.; Pruess, K.; Almgren, A. S.; Lijewski, M. J.; Zhang, K. High-Resolution Simulation and Characterization of Density-Driven Flow in CO2 Storage in Saline Aquifers. Adv. Water Resour. 2010, 33, 443−455. (13) Homsy, G. M. Viscous Fingering in Porous Media. Annual Review; Fluid Mechanics: Stanford, 1987; pp 271−311. (14) Al Ghafri, S.; Maitland, G. C.; Trusler, J. P. M. Densities of Aqueous MgCl2(Aq), CaCl2(Aq), KI(Aq), NaCl(Aq), KCl(Aq), AlCl3(Aq), and (0.864 NaCl + 0.136 KCl)(Aq) at Temperatures between (283 and 472) K, Pressures up to 68.5 MPa, and Molalities up to 6 mol.kg‑1. J. Chem. Eng. Data 2012, 57, 1288−1304. (15) Nighswander, J. A.; Kalogerakis, N.; Mehrotra, A. K. Solubilities of Carbon Dioxide in Water and 1 Wt. % Sodium Chloride Solution at Pressures up to 10 MPa and Temperatures from 80 to 200 °C. J. Chem. Eng. Data 1989, 34, 355−360. (16) Yan, W.; Huang, S.; Stenby, E. H. Measurement and Modeling of CO2 Solubility in NaCl Brine and CO2-Saturated NaCl Brine Density. Int. J. Greenhouse Gas Control 2011, 5, 1460−1477. (17) Song, Y.; Zhan, Y.; Zhang, Y.; Liu, S.; Jian, W.; Liu, Y.; Wang, D. Measurements of CO2-H2O-NaCl Solution Densities over a Wide Range of Temperatures, Pressures, and NaCl Concentrations. J. Chem. Eng. Data 2013, 58, 3342−3350. (18) Kumagai, A.; Yokoyama, C. Viscosities of Aqueous NaCl Solutions Containing CO2 at High Pressures. J. Chem. Eng. Data 1999, 44, 227−229. (19) Bando, S.; Takemura, F.; Nishio, M.; Hihara, E.; Akai, M. Viscosity of Aqueous NaCl Solutions with Dissolved CO2 at (30 to 60) °C and (10 to 20) MPa. J. Chem. Eng. Data 2004, 49, 1328− 1332. (20) Fleury, M.; Deschamps, H. Electrical Conductivity and Viscosity of Aqueous NaCl Solutions with Dissolved CO2. J. Chem. Eng. Data 2008, 53, 2505−2509. (21) Kestin, J.; Khalifa, H. E.; Correia, R. J. Tables of the Dynamic and Kinematic Viscosity of Aqueous NaCl Solutions in the Temperature Range 20−150°C and the Pressure Range 0.1−35 MPa. J. Phys. Chem. Ref. Data 1981, 10, 71−88. (22) Kestin, J.; Shankland, I. R. Viscosity of Aqueous NaCl Solutions in the Temperature Range 25−200 °C and in the Pressure Range 0.1−30 MPa. Int. J. Thermophys. 1984, 5, 241−263.

and pressure ranges. The expanded relative uncertainties at 95% confidence are 0.07% for density, and 3% for viscosity. These data were used to test the hypothesis that the influences of dissolved CO2 is sensibly independent of salt type and molality. The density data were found to support this hypothesis clearly. For viscosity, the situation is less clear but, overall, the viscosity data could be represented well as a function of temperature, pressure, and CO2 mole fraction by a correlation based on literature data for CO2-free brines and a term to account for dissolved CO2 developed previously for the (CO2 + H2O) system. This correlation is able to represent our experimental data with average absolute relative deviations of 0.9% for [CO2 + NaCl(aq)] and 2.3% for [CO2 + CaCl2(aq)]. Satisfactory agreement was also observed with the available literature data. For modeling the density of the (CO2 + brine) systems, an equation based on the partial molar volume of CO2 has been used. The latter has been correlated in terms of temperature and pressure, from the bubble pressure up to 100 MPa, and from (275 to 449) K. This equation was able to represent the experimental densities for the [CO2 + NaCl(aq)] systems with an absolute average relative deviation of 0.07%, while the maximum absolute relative deviation was 0.31%; the corresponding figures for the [CO2 + CaCl2(aq)] systems were 0.05 and 0.30%, respectively. The experimental densities of the CO2-free brine solutions were in good agreement with the current available literature data. The equations given in this paper, along with a model for the solubility of CO2, can be used to obtain both the viscosity and density of aqueous solutions containing both CO2 and either NaCl or CaCl2 over the ranges of temperature and pressure investigated, up to the CO2 saturation limit. The model is also expected to be reliable for higher salt molalities but the saltingout effect means that the amount of CO2 that can be dissolved in highly concentrated brines is very small, so that the effect of CO2 saturation will diminish rapidly with increasing salinity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

J. P. Martin Trusler: 0000-0002-6403-2488 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out as part of the Qatar Carbonates and Carbon Storage Research Centre (QCCSRC). We gratefully acknowledge the funding of QCCSRC provided jointly by Qatar Petroleum, Shell, and the Qatar Science & Technology Park, and for supporting the present project, and the permission to publish this research.

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REFERENCES

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