Measurements of Density and Sound Speed in Mixtures Relevant to Supercritical CO₂ Cycles

The supercritical carbon dioxide (sCO₂) cycles are a promising technology for the future power generation systems, and there has been increased efforts in the literature to realize this concept with a variety of energy sources [1–7]. Accurate modeling of thermal and transport properties is crucial in combustion simulation, along with chemical kinetics for direct-fired sCO₂ systems [8–16]. The molar concentrations, reaction rates, and specific properties are directly influenced by the accuracy of thermal property modeling, while diffusion is governed by the transport property modeling. For low-pressure conditions, well-established methodologies [17] are being used to model thermal properties. However, at high pressures, molecules may attract or repel based on the electron cloud and distance between them. These intermolecular forces cause a drastic variation of properties. Hence, they must be accounted for while modeling combustion under critical to supercritical pressures. A common practice for high-pressure combustion simulations is to use an empirical real gas equation-of-state (EOS) and departure functions to account for the non-ideal behavior of the molecules [18–20]. Generally, density and compressibility factors are estimated with the EOS, and the derivatives of the compressibility factors are used in estimating departure functions of various thermal properties. It is extremely crucial to choose an appropriate and accurate EOS because reaction rates and the heat release rate are significantly influenced by the choice of EOS.

To illustrate the influence of density, a simple numerical experiment is carried out with a constant volume reactor. A constant volume reactor model is considered in Chemkin-II, and the density in the solver is forced to underestimate and overestimate by 20%. Figure 1 shows the effect of density on the reaction rate of a very important chain branching reaction, e.g., H + O₂ ↔ OH + O. The figure shows that there is a significant difference in the temporal reaction rate profile when density is wrongly estimated. Figure 2 shows the effect of density on the heat release rate. The first peak of any curve in Fig. 1 is comparable with the peak of the heat release rate of Fig. 2. The sudden increase in the slope of the first peak of Fig. 1 illustrates that the rate at which the reactants are forming products in the reaction H + O₂ ↔ OH + O is crucial for the heat release rate. Overestimating the density by 20% could increase the crucial first peak of Fig. 2 by 200%.

Also, the absolute difference in the predicted ignition delay times (IDTs) with respect to experimental IDTs under supercritical pressures due to various empirical EOS has been shown in Fig. 3 [16,21]. Here, CO₂ is diluted heavily in the H₂/O₂ mixture at approximately 300 bar [16,22,23]. The uncertainty of the experiments shown in this plot is approximately 20%. Based on the choice of EOS, the deviation in the predicted IDTs could be two to three times of the experimental uncertainty. In this case, as the reactants are forming the products (H₂O), the effective reduced pressure (P_r) and reduced temperature (T_r) of the combustion mixture decrease. The empirical EOSs highly disagree in their prediction when P_r and T_r are closer to unity, as there are drastic gradients in this region. Therefore, the van der Waal type EOSs must be validated before using for a simulation. Numerous modifications have been made to these EOSs, such as Refs. [24,25] to reduce the deviation of these models with experimental data. There are no experimental thermal data pertaining to sCO₂ combustion available in the literature to validate or modify the existing EOS models. In the current report, density measurements of various high-pressure, high-CO₂ concentration mixtures are presented. Also, for thermal and transport properties, general practice is to add departure functions to the properties computed based on the ideal gas assumption [26]. There is no reference data available in the literature to validate these models.

Generally, NIST REFPROP [27] which uses GERG 2008 [28] is used to validate the mixture property models and GERG 2008 model is validated against a wide range of binary and ternary mixtures up to supercritical pressures but not for mixtures which are interested in sCO₂ combustion. Therefore, there is a great need of these experiments to increase the confidence of the property model implementation. This work reports density and sound speed measurements of mixtures relevant to sCO₂ cycles. The results can be used for the validation of real fluid properties calculated from EOS of the mixtures. Properties of a frozen mixture with major species comprising of CO₂, CH₄, O₂, and H₂O were measured for conditions corresponding to different combustion states or reaction progress variables (RPV = 0; inlet, RPV = 1; exit). Referring to Fig. 4, properties of representative sample compositions corresponding to inlet (RPV = 0), mid-combustion (RPV = 0.5), and exit (RPV = 1) were measured up to 150 bar with a temperature range of 310–450 K.

The density of various mixtures, including CO₂, O₂, CH₄, and H₂O was experimentally measured under different pressure and temperature conditions, and the measurements were compared with the NIST REFPROP database. Target compositions of three selected mixtures are shown in Table 1. These conditions were adapted from the proposed model combustor system in the previous work [29].

A temperature-controlled, portable high-pressure cell was used for density measurements. Figure 5 shows the schematic of the experimental setup. The cell can withstand pressures up to 4000 psi (276 bar) at maximum. The manifold connection can be removed after filling mixtures for accurate weight measurements. A precision weight scale was used to measure the weight of gas mixtures in the test cell. Pressure and temperature were monitored using a high-pressure gauge and type-T thermocouple probes attached to the outer wall of the test cell. The approximate internal volume of the cell was 80 ml. The volume was measured after each modification of the test cell by filling liquid water or pure CO₂ to the cell. Mixture compositions were selected to be close to frozen mixtures at the inlet, mid-combustion, and exhaust conditions of a model sCO₂ combustor in the previous numerical simulation work. Temperature and pressure conditions of experiments are 310–450 K and 0–150 bar.

The density of pure CO₂ was measured to show the feasibility of the measurement system. Initially, the test cell was filled with CO₂ to the maximum pressure of 150 bar. Measurements were performed after the mixture reached thermal equilibrium within the test cell. The cell pressure was lowered for the next pressure condition, and weight measurement was repeated. Figure 6 shows density measurements of pure CO₂ under four different temperatures. Solid lines show isothermal density curves from the NIST REFPROP database. The density of high-temperature mixture showed ideal gas-like behavior, whereas low-temperature mixtures demonstrate the strong effect of non-unity compressibility. For the low-pressure cases, a clear tendency was found that CO₂ is more compressed (showing reduced dp/dρ) at the pressure near critical condition.

The uncertainty of density measurements was demonstrated for a selected temperature. Two independent sets of measurements of pure CO₂ at 330 K (57 °C) are compared in Fig. 7. Error bars represent the overall uncertainty of density and pressure. The uncertainty from different sources was vector summed to calculate the overall uncertainty. The measurement uncertainties by sources are as follows: pressure measurement, 1.4%, weight measurement, 1.68 kg/m³, and temperature measurement, 2.2 K. The uncertainty was calculated at a near critical temperature, where the density variation is highly sensitive to the condition. The uncertainty of pressure measurement is proportional to the absolute value, whereas the temperature uncertainty in the range of the test condition is a constant value. This different nature was considered in the calculation of overall uncertainty. The uncertainty of temperature is from two factors, non-uniform spatial temperature distribution and the accuracy of thermocouple. Based on observations of thermocouple readings at different locations of the test cell, 2 K is assumed as the difference of highest and lowest locations of the entire test cell volume. The type-K thermocouple probe has an accuracy of 2.2 K from the specification by the manufacturer. Density gradient by temperature (∂ρ/∂T) is 7 kg/m² K with CO₂ at 330 K, 100 bar. Density measurement uncertainty corresponding to the temperature uncertainty is 7.62%. The measurement uncertainty of chamber volume is estimated as 1.53%. Contribution from weight measurement is 0.12%. Summation gives the overall uncertainty, 9.27% of the measured density. Volume expansion by temperature is neglected because the amount of expansion adds 52 × 10⁻⁶ K⁻¹ (using the coefficient of thermal expansion of 304 stainless steel, 17.3 × 10⁻⁶ K⁻¹).

The isothermal density of inlet ternary mixture (CH₄:O₂:CO₂ = 1:2:24) was measured at five temperature conditions. Figure 8 shows the density measurements of the inlet mixtures. The compressibility of CO₂ is highest near the critical point of CO₂. The density difference between measurement and REFPROP was within 10%. Measurements agree well with REFPROP at pressures below 100 bar, within the estimated measurement uncertainty. Higher deviation from REFPROP was found at high pressures. For example, 137 bar measurement at 450 K was different by 10.3%, which is the highest difference observed. As discussed during the uncertainty analysis, a temperature difference of 2 K is estimated at maximum, regarding the non-uniformity of temperature distribution across the test cell. Compared to low-temperature cases (310–390 K), the highest temperature case at 450 K shows larger difference. Non-uniformity of the temperature across the test cell might exceed the estimated non-uniformity due to higher heat loss, but the amount of such effect is difficult to compensate. Considering the fact that temperature is the most significant factor of uncertainty source, more uniform temperature needs to be secured to overcome the limitation of current experimental setup in the future research.

A binary mixture with CO₂ and H₂O was used as a simplified exit condition frozen mixture. Although adding water was the most challenging part during the mixture preparation, the actual amount of water added to the cell was measured accurately by monitoring the vapor pressure of water using the pressure gauge. CO₂ was filled to the manifold as buffer gas during the water vapor pressure measurement to minimize pressure fluctuation due to water condensation at the manifold. Figure 9 and Table 2 show density measurements of the binary mixtures. H₂O compositions were 0.70% for 420 K data and 1.47% for 450 K data. Figure 10 shows the measured density of mid-combustion mixture at 450 K in comparison with REFPROP. Because the end mixture included water vapor, temperatures significantly above 373 K were required. Maximum operation temperature of the piezoelectric sensor limited the upper range to 450 K.

For uniformity with the inlet mixture conditions, 420 and 450 K test conditions were selected for the mid-combustion and exit mixtures. Figure 9 shows good agreement between measurement and REFPROP. Measured densities are higher than the REFPROP simulation by 2.74–6.89% as shown in Table 2 . The difference is within the range of estimated measurement uncertainty. Similarly, less than 5.5% difference was observed with mid-combustion mixture shown in Fig. 10.

The speed of sound of the pre-combustion mixture was measured using a pressure transducer to track the resonant frequencies of the pressure chamber filled with the mixture. The process is based on previous studies on time of flight measurements using an ultrasonic cell and acoustic resonators [30–32]. Due to modifications required for the current system, frequency shift tracking was employed rather than direct time of flight measurement. Sound generation and pressure data acquisition system and the signal processing procedure are shown in Fig. 11. A function generator and an audio power amplifier generated a sine wave signal to drive a speaker. The speaker was a high-power tweeter with input impedance 4 ohm, and it excited the pressurized cylindrical test cell externally. A Kistler pressure transducer (603B) was installed on the pressurized cell to receive resonance signals from inside the cell. The sensitivity of the Kistler system was 0.2 mV/Pa. Since the signal level of the piezo transducer was much lower than regular microphones, the signal needed to be bandpass filtered with a sharp and narrow pass window.

The pressure of the mixture was varied along an isotherm, with the frequency sweep repeated at each pressure step. The resonant peak shifts were tracked, normalized to the low-pressure speed of sound for that isotherm, and compared to REFPROP’s identically normalized models for speed of sound. The low-pressure speed of sound was chosen as the normalization factor because near-ideal behavior can be assumed, creating a “known” speed of sound well within REFPROP’s confirmed validated range.

Figure 12 shows a sample of the post-filtered signals of the acoustic sweeps of one isotherm of pure CO₂. The shift of the peaks to higher frequencies at lower pressures demonstrates a decreasing speed of sound. Multiple peak shifts were tracked for each isotherm.

As can be seen in an example given in Fig. 13, there is good agreement with the reference peak shift trend of pure CO₂. The experimental procedure was validated for the tested pressure and temperature range using pure CO₂ and comparing to trends using REFPROP. Figure 14 shows normalized data of peak frequency and speed of sound of six isotherms of the inlet mixture condition. The measured trends track very well with REFPROP’s models, especially at higher temperatures. The location of significant divergence from REFPROP’s model is near the critical point, where the transition to the supercritical region causes a significant variation of physical properties across small pressure and temperature differences. Similarly, any temperature non-uniformity across the cell at lower temperatures can result in liquid CO₂ formation, greatly influencing the speed of sound of the mixture. The largest difference observed in 310 K near 74 bar can be explained by this high sensitivity of properties near the critical point.

We measured the density and sound speed of supercritical CO₂ cycle relevant mixtures along isothermal curves at different temperatures. We present the first measurements of these properties in mixtures relevant to the supercritical CO₂ power cycles. A temperature-controlled high-pressure test cell was used for the density measurements. Sound speed was measured by resonant frequency detection using an external speaker and a piezoelectric pressure sensor. Mixtures studied in this work include carbon dioxide, methane, oxygen, and water vapor. Properties of pure CO₂ were measured to show the validity of our technique. Compositions were selected to be close to frozen mixtures at the inlet, mid-progress, and exhaust conditions of a model sCO₂ combustor in the previous numerical simulation work. Corresponding RPVs were RPV = 0, 0.5, and 1. Temperature and pressure conditions of experiments are 310–450 K, and 0–150 bar. In our study, density and sound speed from the NIST REFPROP database agree with experimental measurements within the range of our measurement uncertainties. The measurement uncertainty is acceptable considering challenges in the extreme test conditions. Also, the methodology used in this work shows possibility of future work to aim more tests closer to the realistic conditions with improved accuracy. The measurements performed in this work can validate the accuracy of mixture property calculations and mixing models containing the major components in sCO₂ combustor flows. Effort is currently underway to extend these measurements to higher temperatures and pressures.

This material is mainly based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under award number DE-SC0019640. Partial financial support is acknowledged from the Office of Naval Research (ONR) under award number N00014-18-1-2362. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.