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Automated in situ Measurement of Gas Solubility in Liquids with a Simple Tube-in-Tube Reactor Jiisong Zhang, Andrew R. Teixeira, Haomiao Zhang, and Klavs F. Jensen Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02264 • Publication Date (Web): 24 Jul 2017 Downloaded from http://pubs.acs.org on July 29, 2017
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Analytical Chemistry
Automated in situ Measurement of Gas Solubility in Liquids with a Simple Tube-in-Tube Reactor Jisong Zhang, Andrew R. Teixeira, Haomiao Zhang and Klavs F. Jensen* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, United States ABSTRACT: Gas solubility data in liquids are foundational for assessing a variety of multiphase separations and gas-liquid reactions. Taking advantage of the Tube-in-Tube reactor design built with the semi-permeable Teflon AF-2400 tubes, the liquids are rapidly saturated without direct contacting of gas and liquid. The gas solubility can be determined by performing a steady-state flux balance of both gas and liquid flowing into the reactor system. With this reactor, a fully automated strategy is developed for fast in situ measurement of gas solubility in liquids. This developed strategy enables precise gas solubility data measurement within 2-5 minutes compared with 5-48 hours using conventional methods. This technique is extended to the discrete multi-point steady-state and continuous ramped-multi-point data acquisition methods. The accuracy of this method is validated against several gas-liquid systems showing less than 2% deviation from known values. Finally, this strategy is extended to measure the temperature dependence of gas solubility in situ and estimate the local enthalpy of dissolution across a defined temperature range.
Gas solubility in a particular solvent describes the maximum amount of gas that can be dissolved into that solvent. The solubility data of gases in liquids are very important in assessing a large range of chemical processes. 1,2 For example, it is highly needed to screen CO2 solubility in solvent mixtures of continuous compositions as a selective and fast absorbing solvent plays a core role in developing an efficient CO2 capture processes.3,4 In many gasliquid reactions, gas solubility data are also required to incorporate into the reaction kinetics for a reliable design, optimization and control of chemical reactions.5 Building upon this, the infinite number of potential gas/solvent environments makes direct tabulation of solubility data challenging with standard slow methods. For this reason, it is desired to develop a rapid and automated approach to directly measure gas solubility for a system under process conditions (liquid-phase composition, temperature, pressure, etc.). There are various classical methods available to measure solubility of gases in liquids,6 such as pressure decay method,7-9 gravimetric microbalance method10, quartz crystal microbalance11 and synthetic (bubble point) method.12 Among those, the pressure decay method seems to be most frequently used. As depicted in Figure 1 (a), a known amount of gas contacts with the degassed liquid in a cell with fixed volume at constant temperature. By recording the pressure decay with the time within the welldefined geometry, both the gas solubility and diffusivity can be determined experimentally. This method is rather simple and can be used across a wide temperature and pressure range. However, the long experimental times of 4 ~ 5 h required for obtaining a single gas solubility data point is a major disadvantage of this method. The other
methods are much faster (2~5 min), but require complex systems and operations.10-12
Figure 1. Schematic illustration of two methods to determine the gas solubility. (a) Classical pressure decay method whereby gas is slowly diffused into a liquid at autogenous pressures; (b) Tube-in-Tube reactor where rapid transport leads to nearly instantaneous equilibration of the two phases at user-defined pressures.
Multiphase microfluidic approaches have been used to study the gas-liquid dissolution processes.13-15 For example, gas-liquid slug flow generated in the microchannels can be monitored by high-speed CCD camera on microscope to monitor bubble size with residence time. By recording the
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Figure 2. Schematic of the automated flow platform based on Tube-in-Tube reactor for in situ measurement of gas solubility in liquids.
volume reduction process of gas slugs, gas solubility,16 diffusivity in liquids17 and even the kinetics of fast gasliquid reactions18 can be determined. Owing to the small dimensions at microscale, this method has the advantages of faster equilibrium time and safer operation. Only 5 min are required for a solubility data at a specific temperature and pressure. However, this approach still requires a specific microscope with high-speed CCD camera and corresponding image analysis. When compared to the classical pressure decay method, it is substantially more complex and, thus limiting its broad adaptation into general lab use. Recently a “Tube-in-Tube” reactor integrating gas and liquid phases has attracted attention.19-26 It is composed of an inner semipermeable membrane tubing (Teflon AF2400) and an outer impermeable PTFE or steel tubing. The Teflon AF-2400 tubing is highly permeable to gas but non-permeable to liquid. With utilizing this material as a separation membrane in the radial direction, gas can be continuously delivered into the liquid stream without directly contacting the gas and liquid (Figure 1 (b)). Additionally, the small lengthscales (inner diameter = 0.6 mm) result in rapid transport times, leading to saturation times of only 10~30 seconds.20,25 Dasgupta et al27 first reported a high-sensitivity gas sensor using ultra-thin Teflon AF tubes in a annular geometry and absorbance detection. Ley et al20 used this reactor to measure H2 saturation concentration in dichloromethane with a digital 'bubble counting' technique and in-line FTIR was also incorporated to measure CO concentration in flow stream28. Several reports establishing potential applications of this system in gas-liquid reactions were also reported, such as ozonolysis (O3),19 hydrogenation (H2)20 and oxidation (O2)21. In addition, this reactor has the advantages of easy
fabrication and excellent compatibility with a wide range of gases and liquids due to the characteristics of the fluoropolymer. As a result, the Tube-in-Tube reactor is a highly promising alternative to study gas-liquid processes and may provide a fast, simple and general approach to measure the solubility of gases in liquids. Herein, we present a fully automated strategy based on the Tube-in-Tube reactor geometry for fast in situ measurement of gas solubility in liquids. Saturation time for several gas-liquid systems are tested ranging from 10 s to 40 s. To increase the measurement accuracy, two strategies of steady-state stepping and ramping have been proposed. Finally, this technique has been extended to automated screening of gas solubilities as a function of temperature, which can also allow the ready estimation of the enthalpy of dissolution at a limited temperature range.
Experimental Section Hydrogen (99.999%, pure), nitrogen (99.999%, pure), oxygen (99.99%, pure) and carbon dioxide (99.99%, pure) were all supplied by Airgas (Salem, NH, USA). Methanol, methylstyrene and heptane were all obtained from SigmaAldrich with the purity of 99.9%, 99% and 99+%, respectively. De-ionized water was obtained from VWR meeting ASTM type II specifications. A schematic overview of the automated flow platform is shown in Figure 2. The configuration and fabrication details of the Tube-in-Tube reactor have been described extensively in literature.19,20,29 The key considerations s of the system here are: 1) an integrated gas-phase flow meter is installed on the gas inlet; 2) in-line pressure monitoring of both gas/liquid inlets; 3) the downstream gas outlet is sealed to prevent gas-flow out of the system, causing the gas phase pressure to be controlled by the inlet pressure
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Analytical Chemistry
regulator while most reactor designs have a back-pressure regulator on the gas effluent. These design considerations bring two advantages. First, there is no gas vent at the gas outlet to avoid the gas waste into the environment and improve the safety especially when involving with dangerous gases such as hydrogen and oxygen. Second, the gas flow rate passing through the membrane into the liquids can be monitored by the gas flow meter at the gas inlet of the reactor, hence enabling the direct measure of gas dissolution, and forming the basis of gas solubility measurement in our paper. Before the experiments, liquid was degassed by pulling a vacuum on the headspace of the pure solvent for at least 1 h.30 The liquid was saturated with the analysis gas by bubbling pure gas at atmospheric pressure in a small tank with a gas vent port. With this method, the liquid can be continuously recycled/re-saturated during the course of the experiment, thus requiring only a small amount of liquid (less than 10 mL) even for long experimental times. During the experiments, liquid was delivered by a continuous pump (Valco Instruments, M50) into the inner Teflon AF-2400 tube (O.D. 0.8 mm, I.D. 0.6 mm). Gas from the regulated cylinder was fed into the outer PTFE tube (O.D. 3.18 mm, I.D. 1.59 mm) through a thermal mass flow controller (Brooks Instruments, 5850i, 5 sccm N2), which could be used as a flow meter when it was completely open. The flow-meter was recalibrated for each gas by applying a correction factor obtained from the supplier or calibrated in-house with the pure gas. When handling hydrogen, stainless steel tubing was used instead of PTFE for the outer tube wall to prevent slight leakage by diffusion through the outer wall. The length for the inner and outer tubes are both 1 m. Two in-line pressure transducers (Omega PX409) were placed in the gas and liquid inlets of the reactor to allow for online monitoring of the pressure. The outlet of liquid flow was connected to a back pressure regulator to control the pressure in the liquid flow. The entire Tube-in-Tube reactor was immersed into a water bath with a PID temperature controller (Omega CN7800). LabVIEW software was used to achieve communication between the pump, flow meter, pressure transducers and temperature controller for automated control the process and data acquisition.
Results and Discussion Gas solubility in liquids is usually characterized by Henry’s law. There are several common expressions of Henry’s law, however in the scope of this work we will assume only the following dimensional form:
=
(1)
where, (mol/L) is the liquid-phase molar concentration of specie i; (bar) is the equilibrium partial pressure of specie i in the gas phase and (mol/(L·bar)) is Henry’s constant. When the liquid exiting the Tube-in-Tube reactor is fully saturated, the liquid-phase molar species concentration can be calculated from the steady state flux balance assuming no accumulation in each phase.
=
(2)
where, (sccm, standard mL/min at 0 °C and 1 atm) is the gas flow rate into the system measured by the gas thermal mass flow meter; (mL/min) is the liquid flow rate into /out of the system, user-defined by the pump and (22.414 L/mol, constant) is the volume occupied of 1 mole gas at standard condition. The partial pressure of species at equilibrium, , is assumed to be equal to the total pressure of the pure gas line ( ) as set by the cylinder pressure regulator and monitored with the in-line pressure transducer and corrected as described later in this section. The validity of this assumption is assessed in literature,20 and verified by experiments in Supporting Information (Figure S1). While maintaining the liquid pressure drop larger than gas pressure drop (avoiding formation of gas bubbles in the liquid20), the liquid-phase concentration of H2 demonstrated the expected linear dependence on the gas pressure but no dependence on liquid pressure, indicating that the equilibrium is well-described by the gas-phase pressure, irrespective of liquid phase pressure. For all experiments in this paper, the liquid-phase pressure is all kept slightly higher than the gas-phase pressure to ensure that this criterion is met. It is also important to note that by sealing the downstream gas effluent, accumulation of slow-diffusing solvents into the gas-side of the Teflon-AF is also expected. After sufficient time, the volatile liquid vapor saturates the gas phase, effectively decreasing the partial pressure of the gas. To account for this, is corrected as: = − , where is the vapor pressure of the liquid at this temperature. Substituting Equation 2 into Equation 1, Henry’s constant can be directly determined. It is also important to note that to accurately measure solubility the liquid exiting the reactor must be fully saturated. To meet this condition, the residence time of liquid in the reactor must be longer than the saturation time. As described in our previous work,22 the saturation time in a specific Tube-in-Tube reactor is determined by three factors: gas solubility, membrane permeability and gas diffusivity in the liquids. Ley’s work has provided H2 and O2 concentrations in liquid flow as a function of gas pressure and residence time, indicating a fast saturation time of 5~20 s owing to the high permeability of Teflon-AF and the small inner tube dimension.20,25 To experimentally assess the saturation time, a simple approach is proposed here. At a specific temperature and pressure, a steady state gas flow rate is obtained while the liquid flow rate is held constant. A step perturbation of the liquid flow rate is then induced at a certain time and the response by the gas flow rate is monitored. The time required for reachieving steady state in the gas flow rate is described as the saturation time for this gas-liquid system. Figure 3 shows the perturbation analysis to determine saturation time for several gas-liquid systems. For the gas-liquid systems containing H2, the saturation time is only around 12
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s since hydrogen has a fast diffusivity in most liquids. In contrast, the saturation time is about 30 s for gas-liquid systems containing N2 or O2. As a result, for most gasliquid systems, gas solubility can be safely be determined with residence times of 1 min.
Figure 3. Perturbation analysis to determine saturation time o for several gas-liquid systems. Temperature: 23 C; gas pressure: 4~4.4 bar (gauge pressure); liquid flow rate varied from 0.1 mL/min to 1 mL/min for H2 and N2, 0.1 mL/min to 0.4 mL/min for O2; , gas flow rate before step tion, , gas flow rate after reaching a new steady state.
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gases exists, particularly when handling small molecules such as H2. To increase accuracy in measurement, two methods are proposed to account for this effect: stepping and ramping. Stepping indicates that the liquid flow rates are increased discretely stepwise as shown in Figure 4 (a) and the ratio of / can be represented by ∆ /∆ . With this method, the error can be reduced to 2.7% of known solubility, even for low flow rate of H2. The second method is called ramping, which means the liquid flow rate is changed continuously at a certain rate of change and the corresponding response curve of gas flow rate is measured as shown in Figure 4 (b). After performing a linear fitting of gas flow rate versus liquid flow rate, the slope (S) represents the ratio of / . With this method, the error can be decreased to 0.5% for low flow rate of H2. As discussed earlier, when the liquid flow rate is varied, a saturation time ranging from 10 s to 30 s is required to reach a new steady state as shown in Figure 3. For this reason, it is important to consider the validity of the steady-state assumption used in the flux balance and applied to the ramping studies. To address this, the ramping time is varied from 10 min to 1 min. As shown in Figure 5, the slopes at different ramping times (S1~S4) are almost identical for each condition, indicating that the ramping rate has no effect on the measurement within this scope. This is indicative of a constant rate of change in the liquid flow corresponding to the same constant rate of change (molar basis) in the gas uptake response, as expected by the equilibrated/saturated system.
Figure 5. Robustness of solubility ramping measurement across wide variation of ramping time for H2-methanol system. Gas pressure: 3.8 bar (gauge pressure); temperature: 23 o C; ramping time: 10, 5, 2 and 1min; corresponding ramping 2 rate: 0.09, 0.18, 0.45 and 0.9 mL/min .
Figure 4. Two methods to determine gas solubility for H2methanol system. (a) Stepping, gas pressure: 5.9 bar (gauge pressure); (b) Ramping, gas pressure:3.8 bar(gauge pressure). o Temperature: 23 C.
During the measurement, fluctuations in measured gas flow rate increase measurement errors, especially at lower flow rates. Additionally, background leakage of measured
Table 1 summarizes the measured Henry’s constants of several gas-liquid systems. Each data point is acquired within 5 min. The accuracy of all measured data are within 2% of the reported values in literature. This method proves to be robust, working well with different gases (H2, N2, O2 and CO2) and liquids (methanol, heptane and methylstyrene). The Henry’s constants at different temperatures are also determined with a high accuracy, indicating this method is able to rapidly measure temperature
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Analytical Chemistry Table 1. Henry's constants of several gas-liquid systems KH (exp)
o
KH (lit)
Gas
Liquid
T/ C
H2
Methanol
23
3.83±0.02
3.88
H2
Methanol
40
4.24±0.02
4.26
H2
Methanol
60
4.70±0.02
4.62
H2
Heptane
3
3
(mol/m )/bar
23
(mol/m )/bar
4.51±0.02
32
1.3
32
0.5
32
1.7
33
2.0
4.60
34
1.9
35
2.0
36
1.6
37
1.1
H2
Methylstyrene
23
2.51±0.01
2.56
N2
Methanol
23
6.46±0.03
6.60
O2
Methanol
23
9.87±0.05
9.72
CO2
Methanol
23
99.8±0.5
dependencies of gas solubility. Considering the glass transition temperature of Teflon AF-2400 is 240 oC,31 this system is currently limited to gas solubility measurements below 240 oC. In the current study, the highest pressure was 15 bar, in which the reactor performed well. Because the differential pressure between gas and liquid pressures can be maintained low by increasing the liquid pressure, operation at higher pressure without mechanical strain on the polymer membrane is possible.
Temperature and Thermodynamics Because fast gas-liquid equilibrium (10~30 s) is achieved in the Tube-in-Tube reactor, it is possible to realize rapid screening of gas solubility as a function of temperature. To achieve this goal, ramping of temperature is performed by varying temperature continuously at a constant rate of change while maintaining the liquid flow rate constant as shown in Figure 6. The CO2-water system was chosen as the example case to validate this method. To avoid the erroneous effect of liquid vapor pressure, the system pressure is maintained at a relatively large value (6.5 bar) compared with the largest water vapor pressure at 55 oC (about 0.15 bar).
o
o
Figure 6. Temperature ramping from 20 C to 55 C for CO2water system. Gas pressure: 6.5 bar (gauge pressure); liquid flow rate: 0.15 mL/min.
Relative error (%)
98.7
rate is due to both the change in solubility (i.e. flux into liquid) and the isobaric decrease in the number of moles present at elevated temperatures (Equation 3).
=
(3)
=
(4)
where, n (mol) is the gas molecule number in the space between inner and outer tubes. The latter contribution to the molar flux balance is accounted for with a decreasing term within the gas-phase headspace between the tubes, and is described by the time-dependent ideal gas relationship.
=
where, is the volume between inner and outer tubes, m3; R is ideal gas constant, 8.314 J/(mol·K); is initial temperature, K; is the temperature ramping rate, K/min; t is the ramping time, min. The concentration difference in liquids (∆ ) brought by the variation of temperature is calculated as:
∆ =
1
=− !
(5)
After correction, the obtained temperature dependence of gas solubility for CO2-water is compared with literature38 as shown in Figure 7. The results show that the measured curves of gas solubility versus temperature fit well with the literature except for minor deviation in the range of 20-24 oC. In that range, the transient temperature-increase rate has not fully stabilized due to limitations of the temperature control system. The results demonstrate that ability of this simple automated platform to generate temperature-series data by continuously varying system temperature. The efficiency of safely obtaining temperature dependence of gas solubility is highly promoted here in contrast to conventional methods where more time-consuming and labor-intensive processes are typically required.
As represented in Figure 6, gaseous CO2 flow rate decreases with the increases in temperature, consistent with the decreases in solubility expected at equilibrium. Quantitatively, however, the measured change in gaseous flow
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separately as shown in Figure 8. The enthalpies of dissolution at the two ranges are determined as -18.71±0.12 kJ/mol and -15.38±0.13 kJ/mol, respectively. The two values fall into the range of enthalpy of dissolution from the literature40: -19.44~-17.25 kJ/mol (25~40 oC) and -17.25~14.92 kJ/mol (40~55 oC). Similarly, the experimental measurement for the H2-methanol system and corresponding temperature dependence are given in Supporting Information (Figure S2). The enthalpy of dissolution of H2 in methanol is estimated as 4.94±0.04 kJ/mol. As a result, this automated platform provide a fast and easy strategy to estimate the enthalpy of dissolution of gases.
Figure 7. Comparison of measured temperature dependence of gas solubility by temperature ramping with that from literature (CO2-water system).
Temperature dependence of the measured gas solubility can be described by van’t Hoff relationship (Equation 6) when the temperature range is limited and enthalpy of dissolution ∆ "# $ (kJ/mol) does not changed much with temperature.39
% ∆ "# $ =− 1/
(6)
Conclusions In conclusion, we have developed a fully automated strategy for in situ measurement of gas solubility in liquids taking advantage of the Tube-in-Tube reactor and high gas permeability of Teflon AF-2400. The gas solubility is determined by the steady state flux balance of gas into the liquid. Two strategies of stepping and ramping are described to improve the measurement accuracy of this membrane-based measurement. This strategy enables single gas solubility data point measurement within 2-5 min compared with 4-5 h by conventional methods. High accuracy (
