Thermodynamically consistent modeling of gas flow and adsorption in porous media

In modeling of gas flow through porous media width adsorption, the thermodynamic properties of the adsorbed phase are usually approximated by those of the bulk liquid. Using non-isothermal, gaseous transport of moist air through a porous insulation material as example, we show that this leads to violation of the second law of thermodynamics and a negative entropy production. To resolve this violation, we use information about the adsorption and thermodynamic properties of bulk fluids to derive consistent thermodynamic properties of the adsorbed phase, such as the chemical potential, enthalpy and entropy. The resulting chemical potential of the adsorbed phase is a starting point for rate-based models for adsorption based on non-equilibrium thermodynamics. Incorporating the consistent thermodynamic description into the energy, entropy and momentum balances restores agreement with the second law of thermodynamics. We show that the temperature evolution in the porous medium from the consistent description differs from the standard formulation only if the adsorption depends explicitly on temperature. This highlights the importance of characterizing the temperature dependence of the adsorption with experiments or molecular simulations for accurate non-isothermal modeling of porous media.publishedVersio

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

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Theory and simulation of shock waves: Entropyproduction and energy conversion

We have considered a shock wave as a surface of discontinuity and computed the entropy production using non-equilibrium thermodynamics for surfaces. The results from this method, which we call the "Gibbs excess method" (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock front region, but with different assumptions about local equilibrium. Non-equilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number $M \approx 2$ and a strong shock with $M \approx 6$ and with a Prandtl number of the gas $Pr \approx 1.4$ in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97 \% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.Comment: 27 pages, 16 figures, Supporting material, Symbol list

Evaluation of SPUNG* and Other Equations of State for Use in Carbon Capture and Storage Modelling

AbstractIn this work, Equations of State (EoS) relevant for carbon capture and storage modelling have been evaluated for pure CO2 and CO2-mixtures with particular focus on the extended corresponding state approach, SPUNG/SRK. Our work continues the search of an EoS which is accurate, consistent and computationally fast for CO2-mixtures. These EoS have been evaluated: Soave-Redlich-Kwong (SRK), SRK with Peneloux shift, Peng-Robinson, Lee-Kesler, SPUNG/SRK and the multi-parameter approach GERG-2004. The EoS were compared to the accurate reference EoS by Span and Wagner for pure CO2. Only SPUNG/SRK and GERG-2004 predicted the density accurately near the critical point (< 1.5% Absolute Average Deviation (AAD)). For binary mixtures, Lee-Kesler and SPUNG/SRK had similar accuracy in density predictions. SRK had a sufficient accuracy for the gas phase below the critical point (<2.5%), and Peng Robinson had a decent accuracy for liquid mixtures (<3%). GERG-2004 was the most accurate EoS for all the single phase density predictions. It was also the best EoS for all the VLE predictions except for mixtures containing CO2 and O2, where it had deviations in the bubble point predictions (∼20% AAD). Even though multi-parameter EoS such as GERG-2004 are state-of-the-art for high accuracy predictions, this work shows that extended corresponding state EoS may be an excellent compromise between computational speed and accuracy. The SPUNG approach combines high accuracy with a versatile and transparent methodology. New experimental data may easily be taken into account to improve the predictive abilities in the two phase region. The approach may be improved and extended to enable applications for more difficult systems, such as polar mixtures with CO2 and H2O

Estimating metastable thermodynamic properties by isochoric extrapolation from stable states

The description of metastable fluids, those in local but not global equilibrium, remains an important problem of thermodynamics, and it is crucial for many industrial applications and all first order phase transitions. One way to estimate their properties is by extrapolation from nearby stable states. This is often done isothermally, in terms of a virial expansion for gases or a Taylor expansion in density for liquids. This work presents evidence that an isochoric expansion of pressure at a given temperature is superior to an isothermal density expansion. Two different isochoric extrapolation strategies are evaluated, one best suited for vapors and one for liquids. Both are exact for important model systems, including the van der Waals equation of state. Moreover, we present a simple method to evaluate all the coefficients of the isochoric expansion directly from a simulation in the canonical ensemble. Using only the properties of stable states, the isochoric extrapolation methods reproduce simulation results with Lennard-Jones potentials, mostly within their uncertainties. The isochoric extrapolation methods are able to predict deeply metastable pressures accurately even from temperatures well above the critical. Isochoric extrapolation also predicts a mechanical stability limit, i.e., the thermodynamic spinodal. For water, the liquid spinodal pressure is predicted to be monotonically decreasing with decreasing temperature, in contrast to the re-entrant behavior predicted by the direct extension of the reference equation of state. © 2024 Author(s).Estimating metastable thermodynamic properties by isochoric extrapolation from stable statesacceptedVersio

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer shallow water equations. So far, it has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions for the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly captures the behaviour of shocks and contact discontinuities without any additional closure relations. The proof yields a novel formulation of an effective one-layer shallow water model. The result shows that simplification to an effective one-layer model is well justified mathematically and can be made without additional knowledge of the shock behaviour. The shock speed in the proposed model is consistent with empirical models and identical to the front conditions that have been found theoretically by e.g. von K\'arm\'an and by Benjamin. This suggests that the breakdown of the shallow-water equations in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the shallow water framework to shocks by studying shocks in one-dimensional lock-exchange/lock-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. We then solve the equations numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer shallow-water equations. We also compare numerical results using our model with results from dam break experiments. Predictions from the one-layer model are found to be in good agreement with experiments.Comment: 23 pages, 17 figure

Cryogenic CO2 condensation and membrane separation of syngas for large-scale LH2 production.

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Thermal modeling of the respiratory turbinates in arctic and subtropical seals

Mammals possess complex structures in their nasal cavities known as respiratory turbinate bones, which help the animal to conserve body heat and water during respiratory gas exchange. We considered the function of the maxilloturbinates of two species of seals, one arctic (Erignathus barbatus), one subtropical (Monachus monachus). By means of a thermo-hydrodynamic model that describes the heat and water exchange in the turbinate region we are able to reproduce the measured values of expired air temperatures in grey seals (Halichoerus grypus), a species for which experimental data are available. At the lowest environmental temperatures, however, this is only possible in the arctic seal, and only if we allow for the possibility of ice forming on the outermost turbinate region. At the same time the model predicts that for the arctic seals, the inhaled air is brought to deep body temperature and humidity conditions in passing the maxilloturbinates. The modeling shows that heat and water conservation go together in the sense that one effect implies the other, and that the conservation is most efficient and most flexible in the typical environment of both species. By controlling the blood flow through the turbinates the arctic seal is able to vary the heat and water conservation substantially at its average habitat temperatures, but not at temperatures around −40 °C. The subtropical species has simpler maxilloturbinates, and our model predicts that it is unable to bring inhaled air to deep body conditions, even in its natural environment, without some congestion of the vascular mucosa covering the maxilloturbinates. Physiological control of both blood flow rate and mucosal congestion is expected to have profound effects on the heat exchange function of the maxilloturbinates in seals