Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX-XXX
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Heat Transport Properties of CO2‑Expanded Liquids: n‑Hexane, n‑Decane, and n‑Tetradecane Kourosh Kian and Aaron M. Scurto* Department of Chemical & Petroleum Engineering and Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66045, United States ABSTRACT: A number of processes involve liquids saturated with significant quantities of gases at elevated pressures, e.g., processes in gasor CO2-expanded liquids (GXLs, CXLs), particle formation from gas or supercritical antisolvent methods (GAS, SAS, etc.), CO2 capture and sequestration, and enhanced oil recovery (EOR). In order to engineer these systems, the thermodynamic and transport properties are required. This contribution is one of the first reports for the heat transport properties of gas-expanded liquids at elevated pressures. The thermal conductivity, thermal diffusivity, and heat capacity are presented for binary systems of CO2 and the n-alkanes, n-hexane, n-decane, or ntetradecane, at 25, 40, and 55 °C and pressures up to 106 bar. Equation of state modeling of literature vapor−liquid equilibrium data was used to determine the compositions at the conditions of the experimental heat transport measurements. All measured properties decrease with increasing composition of CO2 (pressure) in a relatively linear manner until a CO2 composition of approximately 70 mol %. The Prandtl number, Pr, is calculated and decreases with increased CO2 composition for all systems. However, as the fluid viscosity decreases with increased CO2, the heat transfer coefficient, h, in pipe flow would actually increase in a turbulent flow regime.
1. INTRODUCTION Numerous applications in chemistry and engineering involve liquid phases containing significant quantities of dissolved gases. As more of the gaseous component dissolves, the liquid phase can develop different properties over the pure liquid. These changes in properties may be tuned or exploited for different applications. “Gas-expanded liquids” (GXLs) is a term for a mixture of a liquid solvent (usually organic, ionic liquid, or mixed aqueous solvent) with significant quantities of a compressible gas (such as CO2 and ethane).1 CO2-expanded liquids (CXLs) are the most common type of GXLs due to the usually high liquid solubility, safety (fire suppression, etc.), and economic advantages of CO2. CXLs have properties that range between the pure organic liquid and supercritical CO2. For instance, the viscosity of the liquid phase decreases with increasing gas composition,2,3 the solubility of other gases can increase in the expanded liquid phase,4 and the mass transfer rate of other reaction gases into the liquid increases.5 While not completely eliminating the use of organic solvents, the needed volume of solvent for a GXL significantly decreases. CXLs can be utilized for the preparation of uniform, fine particles, especially for pharmaceutical compounds. The gas antisolvent technique (GAS) sprays a liquid mixture containing the target solvent into compressed CO2. As the CO2 dissolves in the liquid droplet, it expands and decreases the solubility of the solute (i.e., acts as an antisolvent) leading to the formation of particles.6 Supercritical carbon dioxide can also be used as an antisolvent in a mechanism known as supercritical antisolvent (SAS) precipitation. © XXXX American Chemical Society
Other examples of liquids with large quantities of dissolved gas are found in CO2 capture and sequestration including enhanced oil recovery. Some types of CO2 capture occur at elevated pressures in both physically and chemically absorbing solvents, e.g., the Rectisol, monoethanolamine (MEA) solutions.7 The properties of the solvent change as larger amounts of CO2 are absorbed. These processes undergo thermal cycling as heat and lower pressures are used to desorb the dissolved CO2. Recently in a new application, a suspension of solid particles of n-tetradecane in water were used to enhance CO2 capture by hydrate formation by using the particles to absorb the enthalpy of hydration leading to the melting of the particles into a liquid−liquid suspension.8 CO2expanded liquids are also exploited in enhanced oil recovery (EOR) and geologic CO2 sequestration.9 Compressed CO2 is injected into a depleted petroleum reservoir to increase the amount of crude oil that can be produced and provide a disposal area for CO2.10 We have recently investigated the viscosity of several n-alkanes saturated with CO2.3 The viscosity dramatically decreases with high quantities of CO2. For development of any of these applications both thermodynamic and transport properties are needed. Phase equilibrium thermodynamic data are most often studied for these systems. However, experimental data of the transport properties (viscosity, thermal conductivity, and diffusivity) are Received: Revised: Accepted: Published: A
August 24, 2017 September 29, 2017 September 29, 2017 September 29, 2017 DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
house using 316 stainless steel and sapphire windows with appropriate O-ring seals. It has a 165 mL internal volume. Temperature is controlled via a heat jacket connected to a circulation heater with an integrated pump, which transfers the heating material to the heat exchanger and back to the heating unit. In order to make sure CO2 is well mixed in the solvent, agitation is performed via a stirbar within the cell and a magnetic stirring plate (Ika Werke, GmbH, Germany), PN RET Basic C). The unit is placed on a heavy bench with low vibrations (to prevent convection during measurement). Pressure for the CO2 is provided by an ISCO 250-D syringe pump (Teledyne-Isco, Inc., USA). A high precision digital pressure gauge, Omega DPG7000, with an error band of ±0.05% of full scale (FS = 3000 psi; ±0.1 bar), is utilized to accurately measure the pressure values. The LAMBDA instrument works on a transient hot-wire method standardized to ASTM D2717. A long cylindrical source of heat (platinum filament with radius r0) introduces a heat flux, q [mW/m], at a given time into the fluid sample. The heat flux will generate a temperature profile inside the fluid which is a function of time, t, and radial distance from the source of heat, r. By using the energy balance for a Newtonian fluid with constant density and applying appropriate initial and boundary conditions, thermal conductivity, λ, can be related to the temperature change by an analytical solution:
often significantly lacking. For instance, the authors are not aware of any study measuring the thermal transport properties of any liquid system with dissolved compressed gas despite the numerous applications where temperature needs to be known, controlled, or predicted with different heat transfer scenarios. In this study, the thermal conductivity (λ), thermal diffusivity (αT), and heat capacity (Cp) are measured for three binary alkane mixtures of n-hexane, n-decane, or n-tetradecane saturated with CO2, at three different isotherms (25, 40, and 55 °C) and pressures to 106 bar. In order to determine the composition of the mixtures at the various temperatures and pressures, equation-of-state modeling of phase equilibrium data has been performed. These properties allow various dimensionless groups used for thermal engineering, such as the Prandtl number, to be determined. These properties can have positive implications for the thermal engineering of CXLs for various applications.
2. EXPERIMENTAL SECTION 2.1. Measurement and Calculation of Thermal Conductivity, Thermal Diffusivity, and Heat Capacity. The thermal conductivity, thermal diffusivity, and heat capacity were measured using a Flucon Fluid Control GmbH (Germany) LAMBDA cell with a modified high-pressure equilibrium cell. A schematic picture of the probe and equilibrium cell is depicted in Figure 1. The measuring head
T (r , t ) − T0 = −
q ⎛ r2 ⎞ Ei⎜ − ⎟ 4πλ ⎝ 4αT t ⎠
where λ is the thermal conductivity and αT is the thermal diffusivity. The Ei(−x) function is called the exponential integral function and is defined as follows: −Ei( −x) =
∫x
∞
exp( −u) du u
The exponential integral function can be expanded as a Taylor series: −Ei( −x) = −γ − ln(x) +
x x2 x3 − + − ... 1·1! 2·2! 3·3!
where γ is the Euler constant and is equal to 0.5772. At relatively long times, one can use the following approximation to calculate the temperature profile at different points: t≫
r2 4αT
T (r , t ) − T0 = −
⎤ ⎡ r2 q + 0.5772⎥ ln⎢ 4πλ ⎣ 4αT t ⎦ (1)
λ=
⎛t ⎞ ln⎜ 2 ⎟ 8π (T2 − T1) ⎝ t1 ⎠ q1 + q2
(2)
From measurements at two different times, the value of thermal conductivity is independent of the wire diameter. The thermal diffusivity can be obtained by solving for eqs 1 and 2 as follows:
Figure 1. (a) Thermal conductivity probe and (b) windowed highpressure equilibrium vessel with water jacket.
contains a cylindrical shape platinum wire with small dimensions: diameter d = 0.1 mm and length L = 35 mm. The platinum wire is welded to platinum lead terminals. The lead terminals are supported by a circular Teflon plate, which has a diameter of 24 mm and a thickness of 5 mm. The probe has a built-in temperature Pt-1000 RTD probe as seen next to the wire in Figure 1. The equilibrium cell was constructed in-
a=
⎛ 4πλ ⎞ r0 2 exp⎜ T + 0.5772⎟ 4t ⎝ q ⎠
(3)
The heat capacity, Cp, requires knowledge of the fluid mass density (ρ) or molar volume (V) at any given temperature, pressure, and composition. For molar and specific heat capacity, respectively: B
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research Table 1. Equation of State Parameters and Mixing Rule Interaction Parameters from Ref 3 CO2 n-hexane n-decane n-tetradecane
CAS No.
Tc [K]
Pc [bar]
ω
k(1) ij
k(2) ij
l(1) ij
l(1) ij
124-38-9 110-54-3 124-18-5 629-59-4
304.21 507.60 617.70 693.00
73.83 30.25 21.10 15.70
0.223621 0.301261 0.492328 0.643017
− 0.0046 −0.7354 −0.1806
− 0.0003 0.0013 0.0011
− −0.6463 −1.3106 −3.5176
− 0.0020 0.0022 0.0129
Table 2. Comparison of Ambient Pressure Thermal Conductivity and Heat Capacity Data of the n-Alkanes: This Study vs Literature a
n-hexane
n-decanea
n-tetradecaneb
a
T [°C]
λexpt [mW/m·K]
λlit. [mW/m·K]
% diff
Cpexpt [J/mol·K]
Cplit. [J/mol·K]
% diff
25 40 55 25 40 55 25 40 55
126.51 121.57 116.43 130.10 127.88 124.81 140.67 137.19 134.27
126.18 121.18 116.34 129.48 125.62 121.83 141.90 137.90 134.20
0.26 0.33 0.07 0.48 1.80 2.45 0.87 0.51 0.05
195 193 190 297 298 296 424 421 419
194 200 206 312 320 328 419 401 383
0.58 3.70 7.81 4.79 6.99 9.73 1.20 5.02 9.53
Reference 12. bReference 13.
Cp =
V̲ λ α
Cp̂ =
λ ρα
reported values of thermal conductivity, diffusivity, and heat capacity are the averages of 10 data points. The standard deviation is reported as the precision of the measurement. The standard deviation of thermal conductivity values tend to be larger at higher temperatures and higher pressures, i.e., generally lower liquid density. Hence, one would expect to see the largest deviations at 55 °C and around the critical conditions. As density (molar volume) data is needed for the heat capacity calculation, interpolation errors propagate through these measurements. In this work we have assumed an average error of 5% in the values of interpolated molar volumes and, based on that, we have obtained the error propagation for heat capacity values. An average error of 5% in interpolated molar volumes will result in average standard deviations in the heat capacities equal to 12, 10, and 6 J/mol·K for n-tetradecane/CO2, n-decane/CO2, and n-hexane/CO2 mixtures, respectively. 2.4. Materials. Coleman Instrument grade carbon dioxide (99.999% purity) was obtained from Matheson Gas Products. n-Decane (CAS No. 124-18-5) 99+% was purchased from Acros, and n-tetradecane (CAS No. 629-59-4) 99+% was purchased from Alfa-Aesar. n-Hexane (CAS No. 110-54-3) 95+ % was purchased from Sigma-Aldrich. All materials were used without further purification.
(4)
2.2. Procedure. Approximately 5−40 cm3 of n-alkane (nhexane, n-decane, and n-tetradecane) is initially charged into the vessel, and enough time is given for the system to reach the preset equilibrium temperature (25, 40, and 55 °C). A constant pressure of CO2 is set and the liquid is stirred for about 15 min. The software then measures the thermal conductivity every 90 s to track the progress toward thermal and phase equilibria, which occur within 30 min for all systems studied. After an additional 15 min, 10 measurements are made and the average and standard deviation are reported. The stirrer is shut off for several minutes prior to measurement. Care must be taken to minimize vibrations and anything that could cause convection. Natural convection is minimized by allowing the liquid to come into thermal equilibrium with the equilibrium cell over appropriate times and the fact that the probe is at the centerline of the relatively wide vessel away from the walls where natural convection most often occurs. A new pressure is set for the CO2 and the procedure is repeated up to a maximum of 106 bar. It is important to know the volume expansion of the CO2-expanded mixture as the probe wire must be completely covered in the liquid phase, but the volume expansion should not encompass the entire volume of the cell. The windowed vessel allows general confirmation of the liquid level. As such, often several initial charges of the n-alkane are needed to measure the entire pressure range desired, i.e., smaller initial volumes of the n-alkane at the highest pressure (highest CO2 compositions due to the highest volume expansion), etc. Calibration is only required initially to set some of the internal parameters of the instrument. The calibration fluid is only required to be within an order of magnitude of the mixtures of interest. In order to calibrate the instrument, liquid n-hexane at 25 °C and atmospheric pressure is utilized. The reference density and thermal conductivity values are obtained from the NIST Standard Reference Database, REFPROP.11 2.3. Uncertainty in Measurements. The pressure gauge is accurate to ±0.1 bar and the RTD has an uncertainty of ±0.01 °C. Thermal control of the fluid is approximately ±0.1 °C. The
3. EQUATION OF STATE MODELING The direct measurements involve determining the liquid thermal conductivity at various temperatures and pressures. However, these conditions lead to different CO2 compositions in the liquid phase. In order to understand the composition effect on the thermal conductivity with CO2 in the alkane liquid, equation of state modeling is used to calculate the equilibrium compositions. The Peng−Robinson equation of state with van der Waals two-parameter mixing rules was used to predict the liquid compositions. The model was implemented in the ASPEN Plus V9 thermodynamics package. The physical properties of each component and the equation of state (EoS) parameters used in this study are shown in Table 1. In this study, the van der Waals two-parameter mixing rule, vdW2, was employed with two binary interaction parameters, kij C
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
possible.14−17 According to the classification scheme of Scott and van Konynenburg,17 the n-hexane/CO2 system has been characterized as a type I system, n-decane is a type II system, and n-tetradecane/CO2 is a type III system.15,16,18,19 This implies that the upper pressure limits to maintain two-phase vapor−liquid equilibrium for n-hexane at 25 °C will be the vapor pressure of pure CO2, beyond which will be miscible liquids. For the temperatures at 40 and 55 °C, the mixture critical pressure will be the maximum limit. For n-decane, the UCEP is at very low temperatures and, thus, VLE will terminate at the pure CO2 vapor pressure at 25 °C. For n-tetradecane, the VLLE pressure will be the maximum pressure for two-phase conditions; this is within a few bar from the vapor pressure of pure CO2. At 40 and 55 °C for both n-decane and ntetradecane, the mixture critical point will be the maximum pressure possible. Without knowledge of the general phase behavior and the use of view cells for the pressurized system, incorrect or mislabeled results could occur for the measurement of transport properties. For the n-alkane systems with CO2, a large number of literature reports exist for the vapor−liquid equilibrium at various isotherms.20−28 Few of these studies were measured at the exact temperatures and pressures of the thermal conductivity data discussed below. For several systems, interpolations of reliable data at the same isotherm would have been possible. However, as the majority of the data were at different conditions, it was decided to use equation of state modeling to predict the compositions at the conditions of interest for all of the thermal conductivity studies. Here only experimental vapor−liquid equilibrium (VLE) data was used and no data involving VLLE, LLE, etc. The Peng−Robinson equation of state with van der Waals two-parameter mixing rules (PR-vdW2) was used with temperature dependent interaction parameters as shown in eqs 5 and 6. The linear model was found to have a very good correlation with the fewest number of parameters yielding an average absolute relative deviation (%AARD) in the liquid composition data for all isotherms of 1.2% with a maximum of 1.9%. The model was then used to predict the liquid CO2 compositions for each of the three n-alkanes and three temperatures. Figure 2 illustrates the CO2 solubility in n-hexane, n-decane, and n-tetradecane at 55 °C. At any given temperature and pressure, the CO2 solubility is highest in n-hexane/CO2 and lowest in ntetradecane/CO2 mixtures. As expected, the CO2 solubility decreases with increasing temperatures (not shown).
and lij, for the attractive parameter (am) and covolume parameter (bm), respectively. These parameters are generally a function of temperature to have a quantitative fit with experimental data. In our previous study,3 we have used a linear temperature model which produces the best fit with the lowest number of fitted parameters: kij = kij(1) + kij(2)T
lij = lij(1) + lij(2)T
kij = kji
lij = l ji
(5) (6)
The fitted parameters are reported in Table 1.
4. RESULTS AND DISCUSSION In this work, we have measured the thermal conductivity, thermal diffusivity, and heat capacity values for binary mixtures of n-hexane/CO2, n-decane/CO2, and n-tetradecane/CO2 at three isotherms (25, 40, and 55 °C) and at different pressures. Using literature data, we have correlated the solubilities of CO2 in the n-alkanes to determine the corresponding composition for the thermal conductivity data. The phase behavior was previously investigated and confirmed for these systems. 4.1. Pure n-Alkane Thermal Conductivity Measurements and Literature Comparison. Thermal conductivity values of all pure n-alkanes under investigation in this study are first measured at ambient pressure and at the temperatures of interest. The experimental results are compared with the reported data in the literature, and the deviations are shown in Table 2. It should be noted that n-hexane was used as a calibration fluid for the instrument’s internal calculation method of thermal conductivity. Thus, a run-to-run uncertainty for the instrument is on average ±0.22% based on at least three measurements. As demonstrated, a very good agreement exists with the literature thermal conductivity data. The percent average absolute relative deviation from all of the data is 0.76% with the largest error of 2.45%. The heat capacity measurements contained higher deviations, 5.5% on average. As these measurements are calculated from both thermal conductivity measurements and density/molar volume interpolated from literature data, they are sensitive to error propagation especially in the molar volume. As the molar volumes (density) are interpolated, we assume a nominal 5% error in these quantities, which we believe to be highly conservative. A high-precision, high-pressure calorimeter would be able to obtain better precision and accuracy. However, we believe that reporting these values for systems that currently do not have any heat capacity data will be helpful for both their qualitative trends and at least an accuracy of ∼6% but believed to be better. 4.2. Phase Behavior, Equilibrium, and Equation of State Modeling. The goal of the investigation was to measure thermal conductivity in the CO2-saturated liquid phase. However, n-alkane systems with CO2 and other compressed gases are known to have multiple liquid phase and single-phase equilibrium behavior at various temperatures and pressures. We have recently investigated the phase behavior and vapor−liquid equilibrium for the systems investigated and give an overview here.3 Understanding the conditions of these transitions are required for proper experimental measurement; e.g., two liquid phases in contact with the thermal conductivity probe would yield erroneous results. Regions of vapor−liquid−liquid equilibrium (VLLE), liquid−liquid equilibrium (LLE), and mixture critical points (V = L, L = L, upper critical end point (UCEP), lower critical end point (LCEP)) are also
Figure 2. Vapor−liquid equilibrium prediction from EoS model CO2/ n-hexane, CO2/n-decane, and CO2/n-tetradecane at 55 °C. D
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
measured data point of approximately 95% CO2 to 100%. This may indicate that the liquid structure and mechanism of thermal conductivity is governed mostly by n-hexane with CO2 filling mostly free volume. This also indicates that simple “mixing rules” to predict mixture thermal conductivity based on pure component values, such as a mole/mass fraction average of conductivities of pure liquid alkane and pure liquid CO2, etc., would not be accurate or appropriate especially for the highCO2 liquid compositions. 4.4. Thermal Conductivities of CO2/n-Decane and CO2/n-Tetradecane. The liquid thermal conductivities of binary mixtures of n-decane and n-tetradecane saturated with CO2 were measured at 25, 40, and 55 °C and are listed in Tables 4 and 5, respectively. As shown in Figure 5a, increasing pressure/composition of CO2 decreases the liquid thermal conductivities of n-decane and n-tetradecane mixtures. The compositions were computed using the modeling results described above at each temperature and pressure point of the thermal conductivity measurements. With an increase in CO2 composition, the liquid thermal conductivity decreases in a generally linear manner until a very high composition of CO2. A comparison of the thermal conductivities of the three different n-alkanes saturated with CO2 is shown in Figure 6. In general, there is a relatively linear decrease in the thermal conductivity with increased composition of CO2. By increasing the CO2 composition in liquid phase, thermal conductivity increases in the order n-hexane, n-decane, and n-tetradecane. The only noticeable difference in the slope occurs at higher compositions of CO2 at conditions that are approaching phase transitions, such as VLLE transitions, near the vapor pressure of CO2 itself, etc. Both n-decane and n-tetradecane transition from VLE to VLLE and as shown in the plot have similar qualitative curvatures at the higher compositions. However, n-hexane becomes miscible with CO2 at the vapor pressure at 25 °C and seems to continue on a more linear trend. Similar trends are observed in the thermal diffusivity (a measure of thermal “inertia”) versus composition of CO2 as demonstrated in Figure 7. 4.5. Heat Capacities of Binary CO2/n-Alkane Systems. The heat capacities are calculated from the experimental thermal conductivity and diffusivity values and values for the mixture molar volume (density). In order to calculate the heat capacity, one needs to know the value of the density (molar volume) of the mixture. In this work, the molar volume values are interpolated from experimental data in the literature. The calculated results for all systems are reported in Tables 3−5. A comparison of the heat capacities of the three different nalkanes saturated with CO2 is shown in Figure 7 at 25 °C. In general, there is a relatively linear decrease in the heat capacity with increased composition of CO2. As can be seen in Figure 7, as the composition of CO2 in the liquid phase approaches unity, the heat capacities of the binary mixtures converge. 4.6. Heat Transfer Properties and Implications. The thermal conductivity/thermal diffusivity and heat capacity (along with density and viscosity) are required for a number of heat transfer characterizations and calculations. These are often accomplished through dimensionless groups. One of the most important is the Prandtl number (Pr), which is defined as
As discussed in the Experimental Section, the heat capacity is a calculation from our direct measurement of the thermal conductivity and thermal diffusivity, and the molar volume of the liquid mixture. Molar volume and related volume expansion were not directly measured in these studies. However, ample density data (molar volume data) are available for each of the systems in the literature at either the exact temperatures and pressure range or temperatures that bracket those used in these studies.29−34 Interpolation is used to determine the molar volume at each temperature, pressure, and composition. Figure 3 illustrates the change in molar volume of n-hexane with the
Figure 3. Molar volume of CO2/n-hexane versus pressure at various temperatures interpolated from ref 30.
increase in CO2 pressure and composition. For this system, the molar volume decreases rather linearly with CO2 composition. As the composition of CO2 in the liquid phase increases, the density (g/cm3) of the mixture slightly increases due to the increase in solubility being slightly larger than the increase in volume expansion (not shown). These interpolated molar volume values at the pressures of the heat transport measurements are found in Tables 3−5. The systems with ndecane and n-tetradecane behave qualitatively similarly. 4.3. Thermal Conductivity of CO2/n-Hexane. The liquid thermal conductivity of n-hexane saturated with CO2 was measured at 25, 40, and 55 °C until approximately the vapor pressure or mixture critical points and listed in Table 3. As shown in Figure 4a, increasing pressure of CO2 decreases the liquid thermal conductivity at each temperature. At 25 °C, the thermal conductivity decreases by about 12.9% between ambient pressure and 60 bar (at 25 °C, Pvap = 64.3 bar12). Again, this decrease is not a hydrostatic pressure effect but a composition effect. Using the modeling results described above, the compositions were predicted at each temperature and pressure point. Figure 4b now illustrates the thermal conductivity with composition of CO2. With an increase in CO2 composition, the liquid thermal conductivity decreases in a generally linear manner. Thermal diffusivities have similar trends. However, despite these decreases in thermal transport properties in CO2-expanded liquids, the actual heat transfer rates may increase as will be discussed below. The thermal conductivity of pure saturated liquid CO2 at 25 °C (and at the vapor pressure of 64.3 bar) is 80.8 mW/m·K.12 Outside of the measured data there would be a substantial decrease in thermal conductivity as the composition of CO2 goes from the last
Pr = E
η/ρ ηV̲ ν = = αT λ /(Cpρ) αT
(7) DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
Table 3. Experimental Thermal Conductivity (λ) and Thermal Diffusivity (α) of CO2-Saturated Liquid n-Hexane at Various Pressures with Predicted Compositions (xCO2), Molar Volume (VL), and Calculated Heat Capacity (Cp) P [bar]
xCO2a
VLb [cm3/mol]
ηc [mPa·s]
λ [mW/m·K]
− 11.0 20.9 31.4 40.6 51.8 60.4
0.000 0.147 0.287 0.435 0.573 0.793 0.963
131.6 120.1 109.2 97.4 86.1 70.2 59.9
0.298 0.279 0.250 0.217 0.189 0.166 0.158
126.5 124.7 120.6 118.2 115.7 112.0 110.2
− 10.7 20.9 30.5 41.4 50.1 61.3 70.5
0.000 0.119 0.234 0.343 0.466 0.571 0.723 0.876
134.5 122.5 113.4 104.8 95.1 86.7 75.5 65.9
0.259 0.242 0.226 0.194 0.167 0.152 0.144 0.131
121.6 119.7 117.7 114.8 112.2 109.2 105.3 101.7
− 11.7 20.5 31.0 41.1 50.8 60.0 69.9 80.4
0.000 0.111 0.195 0.293 0.387 0.479 0.570 0.676 0.803
137.5 120.8 114.1 106.9 100.0 93.1 86.5 78.5 68.4
0.227 0.209 0.198 0.178 0.151 0.137 0.128 0.119 0.104
116.4 113.4 111.6 108.6 107.4 103.7 99.9 97.8 92.7
±λ 25 °C 0.6 0.7 0.8 0.7 0.9 1.0 1.0 40 °C 0.7 1.1 0.9 1.3 1.5 1.3 1.6 1.7 55 °C 0.9 0.8 1.0 1.3 1.9 2.0 2.0 2.0 1.8
αT × 104 [cm2/s]
±αT × 104
Cpd [J/mol·K]
±Cpe
Pr
8.538 8.520 8.482 8.460 8.436 8.402 8.387
0.003 0.001 0.001 0.002 0.001 0.001 0.001
195 176 155 136 118 94 79
1 9 8 7 6 5 4
5.3 4.9 4.4 3.7 3.1 2.6 2.5
8.491 8.474 8.455 8.428 8.404 8.378 8.341 8.308
0.003 0.001 0.002 0.002 0.002 0.003 0.002 0.002
193 173 158 143 127 113 95 81
7 9 8 7 7 6 5 4
4.8 4.3 4.0 3.4 2.8 2.5 2.3 2.1
8.444 8.415 8.399 8.371 8.361 8.326 8.292 8.272 8.227
0.002 0.003 0.002 0.002 0.003 0.001 0.002 0.002 0.003
190 163 152 139 128 116 104 93 77
16 8 8 7 7 6 6 5 4
4.3 3.7 3.5 3.1 2.6 2.3 2.1 2.0 1.7
From PR-vdW2 prediction. bMixture value interpolated from literature data.30 cInterpolated from ref 3. dComputed from α, λ, and predicted VL. From error propagation assuming the error in molar volume is approximately 5%.
a e
Figure 4. Thermal conductivity of CO2/n-hexane (a) versus pressure and (b) versus composition.
where η is the dynamic viscosity and ν is the kinematic viscosity. Pr is the ratio of the viscous diffusion rate versus the thermal diffusion rate. The Prandtl number is related to the relative thickness of the momentum and thermal boundary layers. When Pr is much less than 1 (e.g., many types of gases, liquid mercury), the heat will diffuse (conduct) quickly compared to the velocity or momentum mechanism for heat transfer. The Nusselt number for heat transfer, Nu, is the ratio of convective to conductive heat transfer and is defined as
Nu =
hL λ
(8)
where h is the heat transfer coefficient (in units of power per area per degree of temperature), L is the characteristic length scale (e.g., L = pipe diameter for developed flow in a pipe). A related dimensionless group is the Biot number, Bi, which is identical to the Nusselt number except that the thermal conductivity is that of the solid body in contact with a fluid. Bi is used to determine whether the temperature inside a solid body will vary to any large extent over time. F
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
Table 4. Experimental Thermal Conductivity (λ) and Thermal Diffusivity (α) of CO2-Saturated Liquid n-Decane at Various Pressures with Predicted Compositions (xCO2), Molar Volume (VL), and Calculated Heat Capacity (Cp) P [bar]
xCO2a
VLb [cm3/mol]
ηc [mPa·s]
λ [mW/m·K]
− 11.3 21.4 30.8 40.4 50.0 60.3
0.000 0.136 0.250 0.350 0.451 0.554 0.686
195.7 175.3 158.7 144.3 130.1 115.6 97.4
0.874 0.793 0.691 0.606 0.516 0.440 0.354
130.1 129.1 128.1 126.2 123.0 119.8 117.6
− 9.5 20.3 30.9 40.9 51.3 60.6 70.7
0.000 0.097 0.200 0.295 0.377 0.463 0.535 0.615
199.0 184.5 169.0 155.0 143.0 130.5 119.8 108.4
0.699 0.610 0.550 0.474 0.383 0.307 0.289 0.237
127.9 125.8 124.5 121.3 119.5 117.5 115.5 114.8
− 10.5 22.0 31.9 40.6 50.5 60.8 71.4 81.8 90.8 100.1
0.000 0.092 0.187 0.263 0.325 0.393 0.460 0.526 0.588 0.638 0.684
202.4 188.7 174.3 162.8 153.5 143.3 133.2 123.4 114.3 107.0 100.3
0.583 0.512 0.430 0.358 0.295 0.235 0.208 0.177 0.159 0.148 0.141
124.8 122.6 120.1 118.4 116.3 114.7 112.4 111.4 107.1 105.3 104.3
±λ 25 °C 0.6 0.7 0.8 0.9 1.0 0.9 1.0 40 °C 0.8 0.7 1.1 0.9 1.1 1.3 1.5 1.9 55 °C 1.0 1.0 1.1 1.2 1.3 1.2 1.5 1.7 1.7 1.9 2.2
αT × 104 [cm2/s]
±αT × 104
Cpd [J/mol·K]
±Cpe
Pr
8.571 8.562 8.553 8.535 8.504 8.475 8.454
0.001 0.007 0.001 0.001 0.000 0.001 0.002
297 264 238 213 188 163 136
15 13 12 11 10 8 7
14.0 12.6 10.9 9.5 8.1 6.8 5.4
8.550 8.531 8.518 8.489 8.472 8.453 8.435 8.428
0.006 0.001 0.001 0.002 0.002 0.003 0.002 0.003
298 272 247 222 202 181 164 148
22 14 13 11 10 9 8 8
11.4 9.9 8.9 7.6 6.1 4.9 4.6 3.7
8.521 8.501 8.477 8.462 8.443 8.428 8.407 8.397 8.358 8.341 8.332
0.004 0.002 0.002 0.002 0.001 0.002 0.001 0.009 0.002 0.001 0.002
296 272 247 228 212 195 178 164 147 135 125
32 14 13 12 11 10 9 9 8 7 7
9.7 8.5 7.1 5.9 4.9 3.9 3.4 2.9 2.6 2.4 2.3
a From PR-vdW2 prediction. bMixture value interpolated from literature data.29,31,33−35 cInterpolated from ref 3. dComputed from α, λ, and predicted VL. eFrom error propagation assuming the error in molar volume is approximately 5%.
the conditions for the measurements in this contribution by interpolating the data of our previous viscosity study at similar conditions. As seen in Tables 3−5, the Prandtl numbers for all the binary mixtures at all isotherms decrease as the concentrations of CO2 in the mixtures increase. Figure 8a illustrates the relatively linear decrease in Prandtl numbers with CO2 composition for CO2/n-hexane mixtures. Similar trends are observed for each of the n-alkanes at 25 °C in Figure 8b and similarly at the other temperatures. Above about a CO2 solubility of approximately 0.7 mole fraction, the rate of decrease becomes smaller. It is worth noting that the decrease in Prandtl number for CO2/n-tetradecane mixtures is the greatest (on an absolute and percentage basis) while this drop is the least for CO2/n-hexane systems. In all these cases, the Prandtl number values are greater than 1.0 which means, in all binary mixtures, the momentum diffusivity dominates the heat transfer mechanism compared to the thermal diffusivity. By increasing the concentration of CO2 in the mixtures and by increasing the equilibrium temperature, the Pr decreases significantly. From our calculations, it can also be concluded that, for each binary mixture, the percentage of drop in Prandtl number increases at elevated temperatures. For instance, for CO2/n-tetradecane systems, the decreases in Prandtl numbers at 25, 40, and 55 °C are 67, 76, and 87%, respectively. These changes in the Prandtl number can have real practical implications for the equipment design of any gas-expanded-
The heat transfer coefficient between two phases (usually to/ from fluid and metal wall) is often the most important parameter to determine heat transfer rates and design a number of different process equipment, such as heat exchangers and reactors. The heat transfer coefficient is obtained through the Nusselt number which is a function of the Prandtl number, and the Reynolds number (or Rayleigh number for natural convection) and sometimes with additional parameters. The functional form of the Nusselt number depends on the flow regime, flow geometry, aspect ratio, etc. For fully developed laminar flow in a pipe, the Nusselt number is a constant. If the surface has constant heat, then Nu = 4.36; if it has a constant temperature, then Nu = 3.66. Thus, the Reynolds and Prandtl numbers have no bearing on the heat transfer coefficient for this flow regime. However, for turbulent flow in a pipe, the Dittus−Boelter correlation for the heating of a fluid in the turbulent flow regime within a tube (and Pr > 0.7) is given as Nu =
hD = 0.023Re 0.8Pr 0.4 λ
(9)
where D is the pipe diameter. Thus, the Prandtl number is needed to properly quantify the heat transfer rate in a pipe. For the systems of CO2/n-alkanes investigated here, the fluid viscosity is needed to calculate the Prandtl number. We have recently measured the viscosity for these CO2/n-alkane systems at similar isotherms.3 In Tables 3−5, the viscosity is reported at G
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Table 5. Experimental Thermal Conductivity (λ) and Thermal Diffusivity (α) of CO2-Saturated Liquid n-Tetradecane at Various Pressures with Predicted Compositions (xCO2), Molar Volume (VL), and Calculated Heat Capacity (Cp) P [bar]
xCO2a
VLb [cm3/mol]
ηc [mPa·s]
λ [mW/m·K]
− 11.8 21.9 31.6 40.1 50.9 60.7
0.000 0.127 0.225 0.310 0.381 0.465 0.541
261.1 233.6 209.8 193.1 175.4 159.1 144.4
2.150 1.943 1.649 1.417 1.263 0.976 0.732
140.7 138.7 137.3 133.1 130.9 128.4 123.7
− 11.4 20.4 31.5 41.1 50.0 61.5 71.2 80.2
0.000 0.103 0.177 0.261 0.326 0.382 0.449 0.500 0.540
265.0 242.3 225.1 207.3 191.7 180.4 166.2 154.9 145.9
1.612 1.499 1.313 1.139 0.889 0.713 0.654 0.472 0.397
137.2 136.6 135.0 129.3 126.4 124.9 122.4 120.5 118.0
− 10.2 21.4 31.2 41.6 50.8 61.7 69.4 80.6 91.2 101.1 105.5
0.000 0.079 0.160 0.223 0.285 0.336 0.390 0.425 0.472 0.512 0.543 0.554
268.9 252.6 234.6 220.6 206.5 195.3 183.3 175.5 164.9 156.1 149.2 146.6
1.264 1.194 1.025 0.920 0.701 0.588 0.481 0.407 0.300 0.222 0.195 0.170
134.3 131.6 129.2 125.3 124.2 122.6 121.3 119.7 116.5 113.2 111.6 110.5
±λ 25 °C 0.8 1.0 0.8 1.0 1.1 1.2 1.1 40 °C 0.7 1.0 0.9 1.0 1.4 1.1 1.2 1.3 1.8 55 °C 1.3 1.5 1.6 1.4 1.3 1.4 1.2 2.0 1.8 1.8 2.0 2.1
αT × 104 [cm2/s]
±αT × 104
Cpd [J/mol·K]
±Cpe
Pr
8.671 8.652 8.639 8.599 8.579 8.555 8.511
0.001 0.001 0.001 0.001 0.002 0.001 0.001
424 374 334 299 268 239 210
5 19 17 15 14 12 11
32.6 29.3 24.5 21.1 18.5 14.3 10.8
8.638 8.632 8.617 8.564 8.536 8.522 8.499 8.481 8.458
0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001
421 384 353 313 284 264 239 220 204
20 19 18 16 15 13 12 11 11
24.9 23.1 20.1 17.4 13.5 10.8 9.9 7.1 6.0
8.610 8.585 8.563 8.526 8.516 8.501 8.488 8.474 8.444 8.414 8.399 8.389
0.001 0.001 0.001 0.001 0.003 0.001 0.002 0.002 0.001 0.001 0.001 0.001
419 387 354 324 301 282 262 248 227 210 198 193
36 20 18 17 15 14 13 13 12 11 11 10
19.9 18.9 16.2 14.5 11.0 9.2 7.5 6.3 4.7 3.4 3.0 2.6
From PR-vdW2 prediction. bMixture value interpolated from literature data.31−33 cInterpolated from ref 3. dComputed from α, λ, and predicted VL. From error propagation assuming the error in molar volume is approximately 5%.
a e
Figure 5. Thermal conductivity versus composition of (a) CO2/n-decane and (b) CO2/n-tetradecane.
liquid system. For laminar flow in a tube of diameter D, the heat transfer coefficient, h, will be directly proportional to the thermal conductivity. Figure 9 illustrates the percent change of h at constant flow velocity and pipe diameter with various compositions of CO2 for n-decane at 25 °C. As shown, the heat transfer coefficient, h, decreases over pure n-decane by approximately 10% at a CO2 composition of ∼70%. For turbulent flow, the heat transfer coefficient, h, in a pipe could be
calculated from eq 7 as Pr is greater than 0.7 at all CO2 compositions and conditions investigated. For constant pipe diameter and flow velocity, the percentage change in the heat transfer coefficient between the pure n-alkane and the CO2/ alkane mixture can be determined. These calculations use the actual Re and Pr numbers at the indicated compositions of CO2. As seen in Figure 9, the heat transfer coefficients can increase up to 35% over the pure n-alkane at these conditions using the H
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 6. Comparison of thermal conductivities (a) and thermal diffusivities (b) of CO2/n-alkane mixtures at 25 °C.
Figure 7. Comparison of heat capacities of the liquid phase for alkane/ CO2 mixtures at 25 °C.
Figure 9. Percent change of the heat transfer coefficient, h, for CO2/ndecane for laminar and turbulent flow in a pipe at the same flow velocity and pipe diameter using eq 9 at 25 °C.
same fluid velocity and pipe diameter for n-decane at 25 °C. This is despite the fact that the thermal conductivity decreases and the Prandtl number decreases in the mixture with CO2 over the pure n-alkane value. Similar trends are seen at the other temperatures and the other n-alkanes. What is responsible for the increase in heat transfer rate despite slower conductivity is the increase in the Reynolds number. The Reynolds number increases as the dynamic and kinematic viscosities decrease with increasing composition of CO2. While this trend is for a specific heat transfer scenario and in the turbulent regime, this
qualitative trend of increase heat transfer rates for CXLs will hold for other correlations where the exponent of the Reynolds number is generally greater than that for the Prandtl number. For heat exchanger design especially determining the required surface area, knowledge of the pipe/tube and the heat transfer medium (steam, water, heat transfer fluids, etc.) is required. However, the surface area required for any application of a CXL with n-alkanes will be slightly larger in the laminar regime and markedly lower in the turbulent regime. However, it should be noted that the moderate pressure of CXLs would generally
Figure 8. Prandtl number with CO2 composition of (a) n-hexane at 25, 40, and 55 °C and (b) each n-alkane at 25 °C. I
DOI: 10.1021/acs.iecr.7b03513 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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(7) Sreedhar, I.; Nahar, T.; Venugopal, A.; Srinivas, B. Carbon capture by absorption − path covered and ahead. Renewable Sustainable Energy Rev. 2017, 76, 1080−1107. (8) Chen, B.; Xin, F.; Song, X.; Li, X.; Azam, M. Z. Kinetics of carbon dioxide hydration enhanced with a phase-change slurry of ntetradecane. Energy Fuels 2017, 31 (4), 4245−4254. (9) Uemura, S.; Tsushima, S.; Hirai, S. In Use of Carbon Dioxide in Enhanced Oil Recovery and Carbon Capture and Sequestration; John Wiley & Sons, Inc.: 2014; pp 287−300. (10) Kuuskraa, V. A.; Van Leeuwen, T.; Wallace, M.; DiPietro, P. Improving Domestic Energy Security and Lowering CO2 Emissions with “Next Generation” CO2-Enhanced Oil Recovery (CO2-EOR); National Energy Technology Laboratory: Pittsburgh, PA, 2011. (11) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Reference Fluid Thermodynamic and Transport Properties - REFPROP version 8.0; National Institute of Standards and Technology: Gaithersburg, MD, 2007. (12) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23. NIST Reference Fluid Thermodynamic and Transport Properties - REFPROP version 9; National Institute of Standards and Technology: Gaithersburg, MD, 2010; p 55. (13) Kroenlein, K.; Muzny, C.; Kazakov, A.; Diky, V.; Chirico, R.; Magee, J.; Abdulagatov, I.; Frenkel, M. NIST/TRC Web Thermo Tables (WTT), NIST Standard Reference Subscription Database 3Professional Edition, version 2-2012-1-Pro; Thermodynamics Research Center (TRC), National Institute of Standards and Technology: Boulder, CO, 2011. (14) Bolz, A.; Deiters, U. K.; Peters, C. J.; De Loos, T. W. Nomenclature for phase diagrams with particular reference to vapourliquid and liquid-liquid equilibria. Pure Appl. Chem. 1998, 70 (11), 2233−2257. (15) Galindo, A.; Blas, F. J. Theoretical examination of the global fluid phase behavior and critical phenomena in carbon dioxide + nalkane binary mixtures. J. Phys. Chem. B 2002, 106 (17), 4503−4515. (16) Hottovy, J. D.; Luks, K. D.; Kohn, J. P. Three-phase liquidliquid-vapor equilibriums behavior of certain binary carbon dioxide-nparaffin systems. J. Chem. Eng. Data 1981, 26 (3), 256−258. (17) Van Konynenburg, P. H.; Scott, R. L. Critical lines and phase equilibria in binary van der waals mixtures. Philos. Trans. R. Soc., A 1980, 298 (1442), 495−540. (18) Scheidgen, A. L.; Schneider, G. M. Fluid phase equilibria of (carbon dioxide + a 1-alkanol + an alkane) up to 100 MPa andt = 393 k: Cosolvency effect, miscibility windows, and holes in the critical surface. J. Chem. Thermodyn. 2000, 32 (9), 1183−1201. (19) van der Steen, J.; de Loos, T. W.; de Swaan Arons, J. The volumetric analysis and prediction of liquid-liquid-vapor equilibria in certain carbon dioxide + n-alkane systems. Fluid Phase Equilib. 1989, 51, 353−367. (20) Chen, D.; Chen, W. Phase equilibria of n-hexane and n-octane in critical carbon dioxide. Huaxue Gongcheng 1992, 20, 66−69. (21) Lay, E. N.; Taghikhani, V.; Ghotbi, C. Measurement and correlation of CO2 solubility in the systems of CO2+ toluene, CO2+ benzene, and CO2+ n-hexane at near-critical and supercritical conditions. J. Chem. Eng. Data 2006, 51 (6), 2197−2200. (22) Li, Y. H.; Dillard, K. H.; Robinson, R. L., Jr Vapor-liquid phase equilibrium for carbon dioxide-n-hexane at 40, 80, and 120/sup 0/c. J. Chem. Eng. Data 1981, 26 (1), 53−55. (23) Ohgaki, K.; Katayama, T. Isothermal vapor-liquid equilibrium data for binary systems containing carbon dioxide at high pressures: Methanol-carbon dioxide, n-hexane-carbon dioxide, and benzenecarbon dioxide systems. J. Chem. Eng. Data 1976, 21 (1), 53−55. (24) Wagner, Z.; Wichterle, I. High-pressure vapourliquid equilibrium in systems containing carbon dioxide, 1-hexene, and nhexane. Fluid Phase Equilib. 1987, 33 (1), 109−123. (25) Jiménez-Gallegos, R.; Galicia-Luna, L. A.; Elizalde-Solis, O. Experimental vapor−liquid equilibria for the carbon dioxide + octane and carbon dioxide + decane systems. J. Chem. Eng. Data 2006, 51 (5), 1624−1628.
increase the required wall thickness, although to a much lower extent than supercritical fluid processes (i.e., 100−300 bar).
5. CONCLUSIONS The thermal conductivity, thermal diffusivity, and heat capacity were measured for binary systems of CO2-saturated n-alkanes (n-hexane, n-decane, or n-tetradecane) at 25, 40, and 55 °C and pressures up to 106 bar. Phase behavior and equilibrium are discussed to determine the appropriate areas of study to maintain vapor−liquid conditions and for determining needed properties such as CO2 solubility and liquid molar volume/ density. Equation of state modeling of literature vapor−liquid equilibrium data was used to determine the compositions at the conditions of the heat transport measurements. Increasing pressure (i.e., increasing composition) of CO2 results in a relatively linear decrease in the liquid thermal conductivity, thermal diffusivity, and heat capacity of the binary mixtures. The Prandtl numbers are calculated and used to estimate the change in heat transfer coefficients. The required heat transfer areas would decrease with mixtures of CO2 systems over the pure n-alkane for turbulent flows and slightly increase for laminar flow.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: (785) 864-4947. Fax: (785) 864-4967. E-mail ascurto@ ku.edu. ORCID
Aaron M. Scurto: 0000-0001-7214-1871 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the U.S. National Science Foundation (CBET-0731244), the DOT:KU Transportation Research Institute (TRI) (DOT No. DT0S59-06-G-00047), and the KU General Research Fund. We would like to thank Anas Alanqar for some initial scouting work in VLE modeling.
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REFERENCES
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