Technical Note pubs.acs.org/ac
Direct Measurement of the Fluid Phase Diagram Bo Bao, Jason Riordon, Yi Xu, Huawei Li, and David Sinton* Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, M5S3G8, Ontario, Canada S Supporting Information *
ABSTRACT: The thermodynamic phase of a fluid (liquid, vapor or supercritical) is fundamental to all chemical processes, and the critical point is particularly important for supercritical chemical extraction. Conventional phase measurement methods require hours to obtain a single datum on the pressure and temperature diagram. Here, we present the direct measurement of the full pressure−temperature phase diagram, with 10 000 microwells. Orthogonal, linear, pressure and temperature gradients are obtained with 100 parallel microchannels (spanning the pressure range), each with 100 microwells (spanning the temperature range). The phase-mapping approach is demonstrated with both a pure substance (CO2) and a mixture (95% CO2 + 5% N2). Liquid, vapor, and supercritical regions are clearly differentiated, and the critical pressure is measured at 1.2% error with respect to the NIST standard. This approach provides over 100-fold improvement in measurement speed over conventional methods.
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of water in CO2 and minimum miscibility pressure of CO2 in oil were both measured using a microfluidic approach.18,19 Pinho et al. and Mostowfi et al. demonstrated microfluidic techniques that rapidly measure multicomponent pressure− temperature phase properties within a single microchannel, including dew point and bubble point, faster than PVT.20,21 However, phase mapping within a continuous flow suffers from poor precision due to multiphase flow instabilities, high-speed imaging limitations, subjective operator assessment, and impurity accumulation at phase change interfaces. We here demonstrate direct measurement of the full fluid phase diagram, where a fluid’s physical state is observed within 10 000 individual microwells simultaneously, each at a distinct pressure and temperature. Microwells are positioned in a square grid, where orthogonal, linear, pressure, and temperature gradients are applied (Figure 1a). The phase-mapping device is made of glass-silicon to enable high pressures and temperatures, and the high thermal conductivity of the silicon (k ∼ 149 W·m−1·K−1) ensures local control of temperature. We characterize the device using both pure CO2 and a 95% CO2 + 5% N2 mixture and validate these results using NIST reference values. We obtain highly accurate critical points, with critical pressures at 1.2% of expected values. As opposed to traditional methods that require several days to complete, our phasemapping device exploits short length scales and generates the full phase diagram quickly within a single run.
major limitation of traditional phase measurement technologies is that only a single pressure−temperature condition can be measured at once. The most common configuration is the pressure−volume−temperature (PVT) cell, common in petrochemical and polymer processing applications.1,2 These cells typically vary in size between 100 mL and 1 L and reach pressures and temperatures of 60 MPa and 150 °C, respectively.1 Since thermal and chemical equilibrium within these large systems must be reached between measurements, obtaining a full map of fluid phase behavior can take months, at considerable expense. The size of the fluid volume also limits the temperature accuracy attainable to 0.5 °C.3 For extreme temperatures and pressures, high-pressure optical cells (HPOCs) are used.4 New methods have recently been introduced that seek to reduce measurement times, often by detecting physical properties instead of direct observation. These techniques include spectroscopy,5,6 dynamic light scattering,7 acoustics,8,9 microwave resonance,10 shear-mode quartz sensing,11 quartzcrystal microbalance,12 pressure-drop measurement,13 and optical fibers.14,15 While PVT cells suffer from long measurement times, these new techniques have yet to achieve their success and widespread commercial use. Microfluidic technologies have emerged as a powerful tool for rapid, parallel measurements, fully leveraging short microscale diffusion times. For example, Shim et al. demonstrated a PDMS microfluidic device that mapped the phase behavior of water/solute fluid mixtures.16 Silicon-glass microfluidics can convey many of the control and speed benefits associated with lab-on-a-chip applications, with solvent-, pressure-, and temperature-tolerance required of energy applications and process industries.17 The dew point © XXXX American Chemical Society
Received: May 2, 2016 Accepted: June 22, 2016
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DOI: 10.1021/acs.analchem.6b01725 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry
Figure 1. Schematic of the microfluidic fluid phase-mapping device. (a) Full device featuring a 2D array of microwells subject to a vertical pressure gradient and a horizontal temperature gradient. Only a few channels are displayed for clarity; the actual phase-mapping device contains 100 horizontal channels, each with 100 microwells. (b) Enlarged view of microwells.
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EXPERIMENTAL SECTION The device was first characterized using pure CO2. A linear pressure gradient (Plow = 5.5 MPa to Phigh = 8.0 MPa) was distributed across the network by maintaining a continuous vertical single-phase liquid flow through a serpentine resistor channel. The resistor channel cross-section area (A = 25 μm × 25 μm) was low enough to (i) provide an elevated hydraulic resistance to render out-of-chip resistances negligible, (ii) ensure a manageable flow rate (Q = 0.08 mL/min), and (iii) ensure a low Reynold’s number (Re = 520). One hundred deadend channels were positioned at intervals of 250 μm and run horizontally across the chip from the resistor channel. Each horizontal channel has one hundred orthogonally connected microwells (diameter d = 100 μm) at 200 μm intervals (Figure 1b), to allow direct observation of phase properties without magnification. Under normal operation, the pressure distributes linearly along liquid phase in the resistor channel (vertically), effectively assigning each horizontal channel (and all 100 corresponding microwells) an identical pressure. A temperature gradient (Tlow = 13.7 °C to Thigh = 37.8 °C) was applied horizontally using external cooler and heater blocks. Details of the experimental setup and temperature characterization are presented in Figures S1 and S2.
Figure 2. Measurement of the pressure−temperature phase diagram of pure CO2. (a) Phase-mapping device in operation, with liquid, vapor, and supercritical regions visualized. (b) Microscope image of a region of the phase-mapping device with the critical point. Inset images show enlarged views of three liquid−vapor interfaces. (c) Pixel intensity profile across corresponding liquid−vapor interfaces. The inset shows how the height-to-width ratio of the pulses changes near the critical point. (d) Pressure−temperature phase transition point measurements and validation with NIST reference points. Inset images (contrastenhanced, outside area removed) show typical fluid behavior within microwells at various pressure−temperature conditions. The error band includes uncertainties on the pressure (pump) and temperature (heater/chiller).
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RESULTS AND DISCUSSION Pressure−Temperature Phase Diagram of Pure CO2. Figure 2a is a consumer camera image (image size ∼1 in. × 1 in.) of the chip in operation for a preliminary run, which shows how the liquid, vapor, and supercritical states are clearly distinguishable by eye. A liquid−vapor saturation line traverses the chip and becomes increasingly blurred as it nears the critical point. For precise phase mapping, a separate run was performed where a microscope was used to identify microwells nearest the liquid−vapor interface position. Figure 2b shows a microscope
image of an area containing the critical point. The distinct liquid−vapor interface vanishes at Row 78. In Figure 2c, intensity profiles across the liquid−vapor interfaces are plotted for pressures approaching the critical point. A sharp pulse corresponds to sharp light-dark-light liquid−vapor transitions. B
DOI: 10.1021/acs.analchem.6b01725 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry Broader, shallower pulses are produced nearer the critical point. Through Gaussian fitting, the height and width of these pulses were extracted. The height-to-width ratio, an expression of peak quality, is plotted in the inset of Figure 2c as a function of position along the horizontal channels and fitted to a sigmoidal curve. This method of evaluating liquid−vapor interface quality provides a quantified method of establishing the critical point value, without relying on subjective operator assessment, typical of traditional methods. Here, the critical point was measured at 7.47 ± 0.07 MPa/31.7 ± 0.5 °C, which compares favorably to the NIST reported value of 7.38 MPa/31.1 °C, a 1.2% deviation in critical pressure. To compile the full phase diagram, the position of all liquid− vapor interfaces (for all horizontal channels) was measured. Figure 2d shows the measured saturation line and critical point plotted with the NIST reference data. For all phase transition measurements, the standard deviation between the measured and NIST values was 0.03 MPa. The maximum pressure difference with respect to NIST reference data was −0.07 MPa. Similarly for temperature, the standard deviation was 0.2 °C and the maximum temperature difference was 0.5 °C. The estimated error band based on the pressure (pump) and temperature (heater/chiller) uncertainties was ±0.07 MPa and ±0.5 °C, and all NIST data fall within this range. With regard to resolution, the discretization of the field into microwells corresponds to 0.025 MPa and 0.24 °C per microwell in this test. It is important to note that reducing both the temperature and pressure range across the chip would improve accuracy and resolution, effectively zooming in to a narrower range. The accuracy achieved for even the relatively large P−T range here (Figure 2) is on par with existing technologies, such as PVT cells.3 While each microwell could be considered a single “point” on the P−T phase diagram, there is in fact a small temperature gradient of 0.14 °C within each well, providing additional information on phase kinetics. Figure 2d shows three microscope images of microwells taken along the saturation line. The surface tension of CO2 changes significantly from Plow to the critical point, decreasing from 1.3 mN/m to zero. This marked difference in surface tension results in distinct bubbling kinetics at the interface at various pressures. At lower pressure and temperature, a high interfacial tension prevents the formation of bubbles: only a single liquid−vapor interface is observed (sharp, well-defined meniscus shown in Figure 2d, inset (i). At higher pressures and temperatures, interfacial tension decreases and rapid bubbling was observed, biased to the high-temperature right-hand side of the microwell (Figure 2d, insets (ii) and (iii). When the liquid−vapor interface in the horizontal channel was directly below a microwell, nucleation (boiling) occurred on the right “hot” sidewall, with bubbles growing and flowing out of the well before collapsing at a position directly above the interface. This sidewall boiling mechanism is inherent to microwells nearer the critical point, where interfacial tension, a barrier to bubble formation, is low. A video showing the bubbling phase dynamics in near-critical microwells is provided in Supporting Information Video 1. Phase Diagram of a Mixture. To demonstrate the applicability of our phase-mapping device to mixtures, the phase diagram of a binary 95% CO2 + 5% N2 mixture was measured. For this experiment, pressures were set at 8.5 and 6.0 MPa for the inlet and outlet, respectively, and the temperature gradient was the same as for the pure CO2 experiment. In contrast to pure substances that are characterized by a single
Figure 3. Measurement of the fluid phase diagram of a 95% CO2 + 5% N2 mixture and comparison to NIST reference. Inset images (contrast enhanced, outside area removed) show typical fluid behavior within microwells at various P−T conditions. The error band includes the uncertainties on the pressure (pump) and temperature (heater/ chiller).
saturation line, the phase diagram of a fluid mixture is characterized by a phase envelope, bounded by an upper bubble point line and a lower dew point line. Within this envelope, both liquid and gas phases coexist in varying proportions. Figure 3 shows the measured pressure−temperature diagram for the mixture, with the expected phase envelope (solid line, NIST reference). The single liquid− vapor saturation line observed was centered between the dew point line and bubble point line of the NIST reference (Figure 3). This effective averaging is due to the interconnected nature of the microwells and equilibration to a global state reminiscent of the fractional distillation process. Specifically, the lighter component (N2) vaporizes first and preferentially accumulates on the right end of horizontal channels, resulting in a single effective liquid−vapor saturation line leading to the critical point. Near the critical point, intense bubbling behavior is observed as shown inset in Figure 3. At the region just below the critical point, several unique bubbling phenomena were observed at the interface (see Figure 3 insets (i)−(iv)). The dynamic behavior of bubbles in the four insets was recorded in videos (see Supporting Information Video 2). While a traditional phase envelope was not produced, the system nonetheless led to a highly accurate critical point measurement, 8.05 ± 0.07 MPa/26.2 ± 0.5 °C, and compares favorably to the NIST reference critical point, 8.15 MPa/27.0 °C, predicted for this mixture: a 1.2% difference in critical pressure. Accuracy and Speed. Notably, the addition of 5% N2 to the CO2 sample caused a 10% increase in the critical point pressure, and the device was shown to be fully capable of measuring each of these critical pressures at 1.2% error with respect to NIST reference values. The ability of the phasemapping device to correctly measure the critical point over a wide range underscores the importance and effectiveness of the method at measuring the critical point. Regarding fundamental measurement time, two metrics are noteworthy, (i) equilibrium time and (ii) degree of multiplexing. The phase-mapping device has 10 000 microwells operating in parallel (2 × 10−4 μL per microwell, or 2 μL for the entire array) that equilibrate in seconds. The phaseC
DOI: 10.1021/acs.analchem.6b01725 Anal. Chem. XXXX, XXX, XXX−XXX
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mapping device required ∼20 s to re-equilibrate after a 0.1 MPa pressure change (see Figure S3 and Video 3 in the Supporting Information). In practice, the experiment with 10 000 microwell data points described in Figure 2d required 3 h to complete, including 1 h of preparation, 1 h of testing, and 1 h of temperature calibration and postprocessing. In contrast, a traditional PVT system typically takes 8 to 10 h for a single P− T data point.21 A minimum of 800 h (100 P−T data points) would be needed using a traditional PVT system to achieve similar resolution, an over 100-fold longer measurement time. Applicability to Other Fluids. The experiments with pure CO2 and binary 95% CO2 + 5% N2 mixtures provide proof of concept for direct measurement of fluid phase diagrams. The pressure and temperature ranges used here were sufficient to encompass the critical point of these test fluids (5.5−8.0 MPa, T = 13.7−37.8 °C). Silicon-glass microfluidic chips with similar geometries and somewhat smaller features have been successfully operated at pressures and temperatures up to 30 MPa and 400 °C.22,23 This wide range indicates potential applicability to many important solvents, including water (22.1 MPa, 374 °C), alkanes from ethane (4.9 MPa, 32.2 °C) to ndodecane (1.8 MPa, 385 °C),24 methanol (8.1 MPa, 239 °C), ethanol (6.2 MPa, 242 °C), 1-propanol (5.2 MPa, 264 °C), 1butanol (4.4 MPa, 290 °C), acetone (4.8 MPa, 235 °C), toluene (4.1 MPa, 319 °C), and mixtures thereof.25
CONCLUSIONS In conclusion, we demonstrated direct mapping of the P−T diagram, where 10 000 data points were measured simultaneously, fully leveraging rapid microscale equilibrium times for 100-fold improvement in P−T mapping speed over the conventional PVT method. The device provided accurate measurement of the critical point, demonstrating critical pressure measurements with 1.2% error with respect to NIST values for both the pure CO2 and a 95% CO2 + 5% N2 mixture. ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b01725. Experimental setup, temperature characterization, and dynamic response to pressure change (PDF) Video 1 showing the bubbling behavior of pure CO2 (AVI) Video 2 showing the bubbling behavior of the CO2 + N2 mixture (AVI) Video 3 showing the dynamic response to pressure adjustments during the pure CO2 experiment (AVI)
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Technical Note
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the support from the Natural Sciences and Engineering Council of Canada and the Canada Foundation for Innovation. In addition, the Canada Research Chair program is gratefully acknowledged. D
DOI: 10.1021/acs.analchem.6b01725 Anal. Chem. XXXX, XXX, XXX−XXX
