Utilization of a High-Pressure Vibrating Tube Densimeter for Liquids at Temperatures Down to 100 K

A high-pressure vibrating tube densimeter, specified by the manufacturer for temperatures from (263 to 473) K at pressures up to 140 MPa, was tested at temperatures down to 100 K and from vacuum to pressures up to 10 MPa. To verify the functionality and overall performance under these conditions, the densimeter was calibrated with measurements under vacuum as well as methane and propane as reference fluids. The calibration range is T = (120 to 200) K at pressures from (2.0 to 10.0) MPa. To evaluate the recorded data, two established calibration models were used to describe the dependence of the densimeter's oscillation period on the investigated reference fluids' temperature, pressure, and density. The experiments showed that the vibrating tube densimeter is operational even at temperatures down to 100 K, but exhibits a shift of its vacuum resonance when subjected to thermal cycling at temperatures below 180 K. Accordingly, the calibration models were modified with respect to how the vacuum resonance is considered. Then, the determined calibration parameters reproduce the densities of the reference fluids within ± 0.10 kg·m-3 for the calibration model that performed better for the present study. Measurements on pure ethane and argon validate the calibration of the densimeter. Here, the densities are within (- 0.47 to 0.16) kg·m-3 of values calculated with the respective reference equation of state. The estimated combined expanded uncertainty (k = 2) in density for the validation measurements ranges from (0.52 to 1.13) kg·m-3 or is less than 0.1 % for liquid densities.

Supplementary Information

The online version of this article (10.1007/s10765-024-03357-9) contains supplementary material, which is available to authorized users.

Modification of the van der Waals and Platteeuw model for gas hydrates considering multiple cage occupancy

This study reviews available van der Waals- and Platteeuw-based hydrate models considering multiple occupancy of cavities. Small guest molecules, such as hydrogen and nitrogen, are known to occupy lattice cavities multiple times. This phenomenon has a significant impact on hydrate stability and thermodynamic properties of the hydrate phase. The objective of this work is to provide a comprehensive overview and required correlations for the implementation of a computationally sufficient cluster model that considers up to five guest molecules per cavity. Two methodologies for cluster size estimation are evaluated by existing nitrogen hydrate models showing accurate results for phase equilibria calculations. Furthermore, a preliminary hydrogen hydrate model is introduced and compared with the results of other theoretical studies, indicating that double occupancy of small sII cavities is improbable and four-molecule clusters are predominant in large sII cavities for pressures above 300 MPa. This work lays the foundation for further exploration and optimization of hydrate-based technologies for small guest molecules, e.g., storage and transportation, emphasizing their role in the future landscape of sustainable energy solutions.

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λ_r-6) fluid with a repulsive exponent λ_r from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/T_c from 0.55 to 4.5 and for reduced pressures of up to p/p_c = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

Demand-oriented biogas production to cover residual load of an electricity self-sufficient community using a simple kinetic model

Flexible biogas production can enable demand-oriented energy supply without the need for expensive gas storage expansions, but poses challenges to the stability of the anaerobic digestion (AD) process. In this work, biogas production of laboratory-scale AD of maize silage and sugar beets was optimized to cover the residual load of an electricity self-sufficient community using a simple process model based on first-order kinetics. Experiments show a good agreement between biogas demand, predicted, and measured biogas production. By optimizing biogas conversion schedules based on the measured gas production, a gas storage capacity of 7-8 h was identified for maximum flexibility, which corresponds to typical gas storage sizes at industrial biogas plants in Germany. Various stability indicators were continuously monitored and proved resilient process conditions. These results demonstrate that demand-oriented biogas production using model predictive control is a promising approach to enable existing biogas plants to provide balancing energy.

Comparison of pyrochar, hydrochar and lignite as additive in anaerobic digestion and NH4+ adsorbent

The impact of pyrochar, hydrochar and lignite addition on anaerobic digestion of food waste was investigated with and without ammonia inhibition under batch conditions. Furthermore, ammonium adsorption capacities of the chars were investigated. To determine anaerobic degradation of char, reference samples containing inoculum and char were analyzed, indicating a significant degradation of hydrochar. Depending on the evaluation method, the increase in methane yield due to hydrochar addition varied between no statistically significant difference and +14 %. No significant impact due to the addition of 5 g/l pyrochar and lignite on AD was found. NH₄⁺ adsorption capacities showed a significantly higher net adsorption capacity of lignite (1.58mg_NH4⁺/g_L), compared to pyrochar (0.63mg_NH4⁺/g_PC). A negative NH₄⁺ adsorption capacity (-0.51 mg_NH4⁺/g_HC) was found for hydrochar. A high H/C-ratio, O/C-ratio and cation exchange capacity of hydrochar and lignite indicate many functional groups and low chemical stability, enabling an increased interaction between NH₄⁺ and char.

Influence of Mineral Composition of Chars Derived by Hydrothermal Carbonization on Sorption Behavior of CO2, CH4, and O2

The doping of SiO₂ and Fe₂O₃ into hydrochars that were produced by the hydrothermal carbonization of cellulose was studied with respect to its impact on the resulting surface characteristics and sorption behavior of CO₂, CH₄, and O₂. During pyrolysis, the structural order of the Fe-doped char changed, as the fraction of highly ordered domains increased, which was not observed for the undoped and Si-doped chars. The Si doping had no apparent influence on the oxidation temperature of the hydrochar in contrast to the Fe-doped char where the oxidation temperature was reduced because of the catalytic effect of Fe. Both dopants reduced the micro-, meso- and macroporous surface areas of the chars, although the Fe-doped chars had larger meso- and macroporosity than the Si-doped char. However, the increased degree in the structural order of the carbon matrix of the Fe-doped char reduced its microporosity relative to the Si-doped char. The adsorption of CO₂ and CH₄ on the chars at temperatures between 273.15 and 423.15 K and at pressures up to 115 kPa was slightly inhibited by the Si doping but strongly suppressed by the Fe doping. For O₂, however, the Si doping promoted the observed adsorption capacity, while Fe doping also showed an inhibiting effect.

Accurate High-Pressure Measurements of Carbon Monoxide's Electrical Properties

Accurate measurements of carbon monoxide's electrical properties were carried out at high pressure for the first time enabling stringent comparisons with theoretical values calculated ab initio. Dielectric permittivity measurements were conducted utilising a microwave re-entrant cavity resonator over the temperature range from (255 to 313) K and at pressures up to 8 MPa with a relative combined expanded uncertainty (k=2) less than or equal to 52 ppm. The new data enable carbon monoxide's molar polarizability to be correlated within 0.5 %, significantly improving upon existing literature data, which have a relative scatter of about 10 %. The measured molecular polarizability and electric dipole moment of carbon monoxide were determined to be 2.176×10^-40  C²  m²  J^-1 and 0.107 D. Literature values from ab initio calculations for these properties are within 0.28 % and 3.9 %, respectively, of the measured quantities. Moreover, our measurement of the electric dipole moment at finite temperature agrees within 2.2 % with the value derived from accurate spectroscopic measurements for the ground rovibrational state. The second dielectric virial coefficient of carbon monoxide was determined experimentally for the first time to be b_ϵ =(1.015±0.044) cm³  mol^-1 , which compares reasonably with ab initio estimates.

Speed-of-Sound Measurements in (Argon + Carbon Dioxide) over the Temperature Range from (275 to 500) K at Pressures up to 8 MPa

The speed of sound of two (argon + carbon dioxide) mixtures was measured over the temperature range from (275 to 500) K with pressures up to 8 MPa utilizing a spherical acoustic resonator. The compositions of the gravimetrically prepared mixtures were (0.50104 and 0.74981) mole fraction carbon dioxide. The vibrational relaxation of pure carbon dioxide led to high sound absorption, which significantly impeded the sound-speed measurements on carbon dioxide and its mixtures; pre-condensation may have also affected the results for some measurements near the dew line. Thus, in contrast to the standard operating procedure for speed-of-sound measurements with a spherical resonator, non-radial resonances at lower frequencies were taken into account. Still, the data show a comparatively large scatter, and the usual repeatability of this general type of instrument could not be realized with the present measurements. Nonetheless, the average relative combined expanded uncertainty (k = 2) in speed of sound ranged from (0.042 to 0.056)% for both mixtures, with individual state-point uncertainties increasing to 0.1%. These uncertainties are adequate for our intended purpose of evaluating thermodynamic models. The results are compared to a Helmholtz energy equation of state for carbon capture and storage applications; relative deviations of (-0.64 to 0.08)% for the (0.49896 argon + 0.50104 carbon dioxide) mixture, and of (-1.52 to 0.77)% for the (0.25019 argon + 0.74981 carbon dioxide) mixture were observed.

Anaerobic co-digestion of the marine microalga Nannochloropsis salina with energy crops

Anaerobic co-digestion of corn silage with the marine microalga Nannochloropsis salina was investigated under batch and semi-continuous conditions. Under batch conditions process stability and biogas yields significantly increased by microalgae addition. During semi-continuous long-term experiments anaerobic digestion was stable in corn silage mono- and co-digestion with the algal biomass for more than 200 days. At higher organic loading rates (4.7 kg volatile solids m(-3)d(-1)) inhibition and finally process failure occurred in corn silage mono-digestion, whereas acid and methane formation remained balanced in co-digestion. The positive influences in co-digestion can be attributed to an adjusted carbon to nitrogen ratio, enhanced alkalinity, essential trace elements and a balanced nutrient composition. The results suggest that N. salina biomass is a suitable feedstock for anaerobic co-digestion of energy crops, especially for regions with manure scarcity. Enhanced process stability may result in higher organic loading rates or lower digester volumes.

In situ gas analysis for high pressure applications using property measurements

As the production, distribution, and storage of renewable energy based fuels usually are performed under high pressures and as there is a lack of in situ high pressure gas analysis instruments on the market, the aim of this work was to develop a method for in situ high pressure gas analysis of biogas and hydrogen containing gas mixtures. The analysis is based on in situ measurements of optical, thermo physical, and electromagnetic properties in gas mixtures with newly developed high pressure sensors. This article depicts the calculation of compositions from the measured properties, which is carried out iteratively by using highly accurate equations of state for gas mixtures. The validation of the method consisted of the generation and measurement of several mixtures, of which three are presented herein: a first mixture of 64.9 mol. % methane, 17.1 mol. % carbon dioxide, 9 mol. % helium, and 9 mol. % ethane at 323 K and 423 K in a pressure range from 2.5 MPa to 17 MPa; a second mixture of 93.0 mol. % methane, 4.0 mol. % propane, 2.0 mol. % carbon dioxide, and 1.0 mol. % nitrogen at 303 K, 313 K, and 323 K in a pressure range from 1.2 MPa to 3 MPa; and a third mixture of 64.9 mol. % methane, 30.1 mol. % carbon dioxide, and 5.0 mol. % nitrogen at 303 K, 313 K, and 323 K in a pressure range from 2.5 MPa to 4 MPa. The analysis of the tested gas mixtures showed that with measured density, velocity of sound, and relative permittivity the composition can be determined with deviations below 1.9 mol. %, in most cases even below 1 mol. %. Comparing the calculated compositions with the generated gas mixture, the deviations were in the range of the combined uncertainty of measurement and property models.

Effects of thermal pretreatment on anaerobic digestion of Nannochloropsis salina biomass

The marine microalga Nannochloropsis salina was investigated as feedstock for anaerobic digestion under batch and semi-continuous conditions for the first time. Biodegradability and methane yield were low under both digestion conditions. Thermal pretreatment prior to anaerobic digestion significantly increased the methane yield from 0.2 to 0.57 m(3) kg VS(-1) under batch conditions and from 0.13 to 0.27 m(3) kg VS(-1) in semi-continuous digestion. Still, the methane yield was limited with semi-continuous feeding due to volatile fatty acid (VFA) accumulation in the digester caused by high ammonium and salt concentrations in the feedstock. Despite VFA accumulation adaption of the microorganisms to the changing conditions and high buffer capacity resulted in steady methane production. A first energy balance considering the required heat for thermal pretreatment revealed significant benefit from the pretreatment. Conversely, the high energy demand for dewatering algal cultures is one major bottleneck for industrial-scale processing of microalgae.