Mass Balance Relationships Research Articles

Truncation of a nanosecond CO2 laser pulse by following of the temporal characteristics of the plasma parameters in laser ablation model

The evolution of laser-induced plasma for an aluminum target in a helium ambient gas at different pressures of 100, 300, 500, 700, and 1000 mbar is numerically studied. A thermal model of laser ablation is utilized for calculation of plasma parameters which comprise heat conduction, Euler equations, Saha–Eggert equations, Knudsen layer boundary condition, mass and energy balance relations, and optical shielding effects. In addition, in order to determine the temporal parameters of aluminum's plasma, the hydrodynamic equations are computed for calculation of the plasma absorption due to inverse Bremsstrahlung and photoionization. A CO2 laser pulse at a wavelength of 10.6 μm with different pulse durations of 50 and 100 ns is irradiated on laser induced Al plasma for truncation of the transmitted CO2 laser pulse. The laser intensities irradiated on the Al sample for producing plasma and generation of a shortened pulse are considered as 1016, 1017, and 5 × 1017 W/m2. Furthermore, for validation of the theoretical calculations, some experimental results are presented. Results showed that higher helium gas pressures caused the critical density attained at earlier delay times which caused the CO2 laser beam became efficiently truncated. Moreover, it is concluded that pulse duration has an inverse relation with ambient gas pressure and laser intensity which means that the higher gas pressure or laser intensity induces less pulse duration.

Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming

Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated.

Effects of the wind–mass balance constraint on ensemble forecasts in the hybrid‐4DEnVar

Ensemble forecast covariance plays an important role in the hybridized background error covariance framework to improve the resultant analysis quality. However, a localization of ensemble samples is needed to fully take advantage of flow‐dependent error modes. In this regard, it is an interesting and practical issue as to which variables, composing the ensemble perturbation, the localization should be applied to. This study examines this issue in a boreal‐summer month by comparing two experimental sets: (a) a set of model variables, and (b) another set of model wind variables and unbalanced dry mass (temperature and surface pressure) used for the control variables. In the comparison, it is shown that imposing the wind–mass balance on the ensemble perturbation improves the Antarctic lower‐stratospheric temperature and tropical mid‐/lower‐tropospheric humidity. The nonlinear wind–mass balance relationship smooths an evolution of humidity forecast forced by the resultant analysis increments.

Relationship of nanostructure and thermo-chemical response/thermal ablation of carbon aerogels

ABSTRACTIn this work, the interfacial mass balance relations combined with the non-parametric kinetic (NPK) analysis results were used for evaluating the thermo-chemical ablation process and oxidation mechanism of carbon aerogels with various porous structure. It was found that the two-parameter model of Nomen–Sempereis was able to describe the kinetics of the oxidation reaction and to reveal the structure-dependent contribution of two main processes with chemical and physical nature. The porosity of the carbon aerogel, rather than the other microstructural features, was realized more effective on the rate of ablation.

A globally mass-conservative method for dual-continuum gas reservoir simulation

In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference methods. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

Porosity estimation in kerogen-bearing shale gas reservoirs

Porosity is a fundamental petrophysical parameter in shale gas reservoirs that governs the space for hydrocarbon storage, and directly determines the free gas amount and absorbed gas capability. Technically, in kerogen-bearing shales, well-log derived porosity may yield inaccurate results as the porosity tools in response to both the kerogen and the liquid-filled pore spaces that are often undifferentiated. In this paper, we propose a new method for porosity estimation in kerogen-bearing shales, where porosity is assumed to be composed of both matrix porosity and kerogen porosity. The kerogen responses of density, sonic and neutron logs are first calculated from experimental data to calibrate porosity logs with the kerogen volume. The matrix porosity is then computed using the improved Wyllie equation based on the calibrated logging data with the kerogen influence removed. The kerogen porosity is estimated by a mass-balance relation based on the original total organic carbon (TOCo) and kerogen maturity characterized by the percentage of convertible organic carbon (Cc) and the transformation ratio (TR). Application of the new method to a shale gas reservoir in the Ordos Basin, China shows that the estimated porosity matches the core derived porosity satisfactorily well. Furthermore, the results also indicate that the shale kerogen porosity is relatively higher than the shale matrix porosity when the kerogen amount and maturity are high. The results of the study lead to a better understanding of the shale formation and thus contribute towards the better evaluation of shale gas reservoirs.

A novel modeling approach for evaluating microbial mechanism and design of contact stabilization process

AbstractBACKGROUNDThe paper offers a novel interpretation of microbial mechanisms and evaluates the assets of contact stabilization (CS) using multi‐component modelling. A model structure re‐defining microbial processes is adopted, where the function of the contact tank was limited to the utilization of soluble substrate fractions and that of the stabilization tank essentially involved endogenous decay and removal of the adsorbed particulate substrate.RESULTSThe model was used to simulate the microbial behaviour and performance of CS in comparison with a conventional activated sludge system (CAS), at an SRT range between 6 and 15 d. The results were confirmed by a stoichiometric description of the process using relevant mass balance relationships, which identified the role of major parameters in system behaviour and performance. A rational process design procedure was proposed based on modelling and process stoichiometry.CONCLUSIONThe CS process achieved effective carbon removal with a much smaller footprint and/or aeration volume with respect to CAS, due to its ability to work at significantly higher volumetric organic loadings; its flexibility to be operated at much higher SRT compared with CAS with the same HRT, allowed minimizing sludge production and sustaining a microbial composition also supporting nitrification. However, process stoichiometry reflected that the CS process, despite its significant advantages, should not be considered a suitable candidate for maximizing sludge harvest and energy recovery. © 2017 Society of Chemical Industry

Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis

In this study, with a view of understanding the structure of high-dimensional geochemical data and discussing the chemical processes at work in the evolution of arc magmas, we employed principal component analysis (PCA) to evaluate the compositional variations of volcanic rocks from the Sengan volcanic cluster of the Northeastern Japan Arc. We analyzed the trace element compositions of various arc volcanic rocks, sampled from 17 different volcanoes in a volcanic cluster. The PCA results demonstrated that the first three principal components accounted for 86% of the geochemical variation in the magma of the Sengan region. Based on the relationships between the principal components and the major elements, the mass–balance relationships with respect to the contributions of minerals, the composition of plagioclase phenocrysts, geothermal gradient, and seismic velocity structure in the crust, the first, the second, and the third principal components appear to represent magma mixing, crystallizations of olivine/pyroxene, and crystallizations of plagioclase, respectively. These represented 59%, 20%, and 6%, respectively, of the variance in the entire compositional range, indicating that magma mixing accounted for the largest variance in the geochemical variation of the arc magma. Our result indicated that crustal processes dominate the geochemical variation of magma in the Sengan volcanic cluster.

Cyanobacterial carbon concentrating mechanisms facilitate sustained CO<sub>2</sub> depletion in eutrophic lakes

Abstract. Phytoplankton blooms are increasing in frequency, intensity, and duration in aquatic ecosystems worldwide. In many eutrophic lakes, these high levels of primary productivity correspond to periods of CO2 depletion in surface waters. Cyanobacteria and other groups of phytoplankton have the ability to actively transport bicarbonate (HCO3−) across their cell membrane when CO2 concentrations are limiting, possibly giving them a competitive advantage over algae not using carbon concentrating mechanisms (CCMs). To investigate whether CCMs can maintain phytoplankton bloom biomass under CO2 depletion, we measured the δ13C signatures of dissolved inorganic carbon (δ13CDIC) and phytoplankton particulate organic carbon (δ13Cphyto) in 16 mesotrophic to hypereutrophic lakes during the ice-free season of 2012. We used mass–balance relationships to determine the dominant inorganic carbon species used by phytoplankton under CO2 stress. We found a significant positive relationship between phytoplankton biomass and phytoplankton δ13C signatures as well as a significant nonlinear negative relationship between water column ρCO2 and isotopic composition of phytoplankton, indicating a shift from diffusive uptake to active uptake by phytoplankton of CO2 or HCO3− during blooms. Calculated photosynthetic fractionation factors indicated that this shift occurs specifically when surface water CO2 drops below atmospheric equilibrium. Our results indicate that active HCO3− uptake via CCMs may be an important mechanism in maintaining phytoplankton blooms when CO2 is depleted. Further increases in anthropogenic pressure, eutrophication, and cyanobacteria blooms are therefore expected to contribute to increased bicarbonate uptake to sustain primary production.

Chemometric classification and geochemistry of oils in the Iranian sector of the southern Persian Gulf Basin

Crude oil samples collected from several oilfields across the southern Persian Gulf Basin from Jurassic to Cretaceous reservoirs were chemometrically classified into two genetically distinct oil families. Family A oils, occurring in the western areas, are restricted to the Jurassic series. Family B oils, mostly occurring in the eastern areas, were generated from a younger, homogeneous marine carbonate source rock. An improved geochemical understanding of Family A oils is achieved in this study, and a refined paleo-depositional model for their source rock is presented. These high-maturity oils were generated from a Middle Jurassic carbonate source rock formed within a shallow, anoxic intra-shelf basin that was connected to the Neo-Tethys marine environment. An initial phase of biodegradation is suggested to have affected family A oils during their initial accumulation phases, but the imprint has likely been masked with mixing of multiple charges or phase fractionation. Similarly, Family B oils appear to be controlled by mixing of at least two separate charges or phase-fractionation processes, although the trap charging dynamics of the Cretaceous accumulations agrees with a stronger probability for secondary alteration processes. Based on these findings, we conclude that the present-day geochemistry of both oil families is the result of a complicated sequence of events, including mixing of at least two separate charges with varying maturities or phase separation. These new insights can have practical implications for assessing volumetric mass balance relationships in advanced hydrocarbon generation models, identifying low-risk plays, and ranking prospects.

Quality and Impact of Indian Doppler Weather Radar Wind Profiles: A Diagnostic Study

In the tropics, efficient weather forecasts require high-quality vertical profiles of winds to overcome improper coupling of mass and wind fields and balance relationships in the region. The India Meteorological Department (IMD) operates the network of Doppler Weather Radar (DWR) in microwave frequencies (S-band or C-band) at various locations in India. The National Centre for Medium Range Weather Forecasting (NCMRWF) receives the volume velocity processing (VVP) wind profiles from all DWRs through the Global Telecommunication System (GTS) network in near real time. The radar VVP wind is a mean horizontal wind derived at different heights from radial velocities suitable for numerical weather prediction applications. Three numerical experiments, CNTL (without VVP winds), 3DVAR and HYBRID with the assimilation of VVP winds by means of 3-dimensional variational (3dvar) and hybrid data assimilation systems were conducted using the NCMRWF Global Forecast System (NGFS) model. This study had two objectives: (1) quality assessment of VVP winds and (2) investigation of the impact of VVP wind profiles on NGFS model forecast. The quality of VVP wind profiles was assessed against the NGFS model background and radiosonde wind profiles. The absolute values of zonal and meridional wind observation minus background (O−B) increased with the pressure for all DWRs. All radars exhibited the accepted (rejected) ratio as a decreasing (increasing) function of pressure. The resemblance between the zonal and meridional O−B statistics for 3DVAR and HYBRID experiments is apparently remarkable. The accepted VVP winds and radiosonde winds in both experiments (3DVAR and HYBRID) were consistent. The correlation coefficient (R) was higher at Patna (Patiala) for zonal (meridional) winds in the 3DVAR experiment and at Patna (Jaipur) in the HYBRID experiment. At Chennai, the R value was lower in both the experiments for both wind components. However, because of the assimilation of VVP winds by means of 3dvar, the root-mean-square error (RMSE) of zonal and meridional winds improved by approximately 2–3% up to the day 5 forecast in the analysis performed below 700 hPa. Further improvement in RMSE by approximately 5% was observed in both the wind components because of the hybrid data assimilation. The zonal and meridional wind RMSEs in the HYBRID (3DVAR) experiment improved by ≈5 (3)% compared with the 3DVAR (CNTL) experiment.

Optimization for energy consumption in drying section of fluting paper machine

Non-linear programming optimization method was used to optimize total steam and air consumption in the dryer section of multi-cylinder fluting paper machine. Equality constraints of the optimization model were obtained from specified process blocks considering mass and energy balance relationships in drying and heat recovery sections. Inequality constraints correspond to process parameters such as production capacity, operating conditions, and other limitations. Using the simulation, the process parameters can be optimized to improve the energy efficiency and heat recovery performance. For a corrugating machine, optimized parameters show the total steam use can be reduced by about 11% due to improvement of the heat recovery performance and optimization of the operating conditions such as inlet web dryness, evaporation rate, and exhaust air humidity, accordingly total steam consumption can be decreased from about 1.71 to 1.53 tonnes steam per tonne paper production. The humidity of the exhaust air should be kept as high as possible to optimize the energy performance and avoid condensation in the pocket dryers and hood exhaust air. So the simulation shows the supply air should be increased by about 10% to achieve optimal humidity level which was determined about 0.152 kgH2O/(kg dry air).

Shiitake mushroom packages tuned in active CO2 and moisture absorption requirements

Abstract Active packages of shiitake mushrooms with CO 2 - and moisture-absorbing sachet or pad were designed and tested in their effectiveness in quality preservation for a given shelf life of 5 days at 10 °C. Sachets of sodium carbonate (SC) and mix of SC and calcium hydroxide (CH), and SC-impregnated cotton pad were characterized in their CO 2 and moisture absorption properties to calculate proper amounts of the active components capable of scavenging the required amounts of CO 2 and water vapour. The demands of CO 2 and water vapour absorptions to maintain the desired modified atmosphere (MA) and avoid moisture condensation inside the packages were determined from mass balance relationships comprising the mushroom respiration/transpiration and gas transmission through the package layer. Super-absorbent polymer (SAP) of polyacrylate was added as a supplement material to bring about the water vapour absorption required further to attain non-saturated humidity condition. Sachet combined of SC and SAP attached inside the package of 180 g mushrooms maintained its atmosphere of 10.7–11.6% O 2 and 7.1–8.9% CO 2 concentrations at steady state helping to preserve the quality best. Proper combination of CO 2 and moisture absorbers can be useful tool to create the desired MA and alleviate saturated humidity conditions in packages of the commodities sensitive to high CO 2 and moisture condensation.

An adaptively controlled modified atmosphere container system for fresh produce

Time-variable open/close cycles of a gas diffusion tube may serve as a means to supply the desired gas transfer to attain a beneficial modified atmosphere (MA) in fresh produce containers. Because the produce respiration contributing to the atmosphere modification changes over time, adoption of real-time respiration in the open/close control of the tube may be an innovative tool to maintain the container atmosphere. An adaptive control of the tube responding to the real-time respiration of fresh produce was developed based on a simplified O 2 mass balance to generate and maintain the desired MA for the fresh produce. Here, the O 2 concentration change in the initially closed container before reaching the target value was used to calculate the respiration rate to determine the starting value of the opening ratio of the cycle time and the average O 2 concentration of each cycle after reaching the target value once was used in the mass balance relationship to update the opening ratio for the next cycle. The developed MA container system could attain the targeted O 2 concentrations and the expected desirable CO 2 concentrations for blueberries and spinach at steady state, helping to preserve their quality.

A methodology for estimating the organic porosity of the source rocks at the mature stage: example from the marlstone in the Shulu Sag, Bohai Bay Basin

In recent years, organic-matter pores have been identified as an important storage space type in unconventional reservoirs. Accurate estimation of the organic porosity is critical for unconventional petroleum evaluation and exploration. Organic-matter pores account for an important proportion of the pore network in the Shulu organic matter-rich marlstone. This study determined the characteristics of organic pores in this tight reservoir and provided a method to restore the original hydrogen index (HIo) of samples within the oil window zone, based on the relationship between the hydrogen index (HI) and temperature of the maximum yield of pyrolysate (Tmax). The original total organic carbon (TOCo) and the organic porosity (Φo) were estimated based on data from the pyrolysis experiment using a mass-balance relation. The results show that the value of HIo is in the range of 64 to 1048 mg HC/g TOC, with an average of 605 mg HC/g TOC. The value of TOCo is between 0.12 and 9.7 %,with an average of 1.9 %. The value of Φo is mainly from 0 to 2.5 %, with an average of 0.67 %,which is approximately 16.8 % of the total porosity. The calculated value of Φo is consistent with that obtained by SEM image-based organic porosity measurements. The approach outlined in this article involves a relatively simple methodology for estimating the organic porosity of kerogen-rich source rocks within the oil window zone, which is useful in the exploration and development of unconventional petroleum resources.

Crystal/melt partitioning of water and other volatiles during the near-solidus melting of mantle peridotite: Comparisons with non-volatile incompatible elements and implications for the generation of intraplate magmatism

Concentrations of H 2 O, F, Cl, C, P, and S have been measured by secondary ion mass spectrometry (SIMS) in experimentally produced peridotite phases (including clinopyroxene, orthopyroxene, olivine, garnet, amphibole, and mica) and coexisting basanitic glasses. Because only two experiments produced glasses on quenching (with the melt phase in others reverting to felt-like crystallite masses) H 2 O concentrations in melts were also separately determined from mass-balance relationships and by assuming constant H 2 O/La in melts and starting materials. The resulting values were used to calculate mineral/melt partition coefficients ( D values) for H 2 O [where D H 2 O crystal/melt = (mass fraction of H 2 O in crystal)/(mass fraction of H 2 O in melt)] for conditions of 1025–1190 °C and 1.0–3.5 GPa. These gave 0.0064–0.0164 for clinopyroxene, 0.0046–0.0142 for orthopyroxene, 0.0015–0.0016 for olivine, and 0.0016–0.0022 for garnet. Although less information was obtained for the other volatiles, F was found to be significantly more compatible than H 2 O during peridotite melting, whereas Cl is significantly less compatible. S also has small but appreciable solubilities in amphiboles and micas, but not in pyroxenes or olivine. The solubility of C in silicate minerals appears to be negligible, although C was present in coexisting melts (~0.5 wt% as CO 2 ) and as residual graphite during experiments. The D values for H 2 O in clinopyroxene and orthopyroxene are positively correlated with iv Al but negatively correlated with the H 2 O concentrations of melts (when considered as wt%). These relationships are consistent with the broad trends of previously published partitioning data. Although some of the concentration dependence can be related to cross-correlation between iv Al in pyroxenes and H 2 O concentrations in melts (via the latter’s control of liquidus temperatures) this relationship is too inconsistent to be a complete explanation. A concentration dependence for D H 2 O mineral/melt can also be independently predicted from speciation models for H 2 O in silicate melts. Thus it is likely that D H 2 O pyx/melt is influenced by both iv Al and the absolute concentration of H 2 O in melts. D H 2 O / D Ce for clinopyroxene is inversely correlated with M2 site radii. Because the latter decrease with increasing pressure and temperature, relatively hot and/or deeply derived melts should be enriched in Ce relative to H 2 O when compared to melts from cooler and shallower mantle sources. Conversely, melts from H 2 O-rich settings (e.g., subduction zones) should have higher H 2 O/Ce than their source rocks. When combined with previously obtained partitioning data for non-volatile elements (from the same experiments), our data are consistent with the enrichment of intraplate basalt sources in both volatile and non-volatile incompatible elements by small-degree melts derived from local mid-ocean ridge basalt sources. In this way, volatiles can be seen to play an active role (via their promotion of partial-melting and metasomatic processes) in the auto-regulation of incompatible element concentrations in the depleted upper mantle.

Adsorption of Mixture of Two Dyes on Activated Carbon

Activated carbon is known as adsorbent to various contaminants from wastewater and air. The aim of work was to estimate sorptive capacity of activated carbon in the removal of dyes, which are contaminants from textile wastewaters. The mixture of two dyes, methyl blue and naphtol green B were chosen to study, and as adsorbent we have chosen the activated carbon WDex, virgin and regenerated. Dye concentration in both cases was 200 mg/dm. Sorption abilities of activated carbon were expressed by mass balance relationship in case of fresh activated carbon it was 60 mg/g, and after regeneration from 8 to 13 mg/g. The experimental data adsorption isotherms were defined and adsorption theoretical model such as Freundlich or Langmuir, was selected. The highest removal efficiency in case of methyl blue was 94% for virgin carbon, the lowest 75% (carbon after 4 regeneration). The highest removal efficiency in case of naphtol green B was 78% for carbon after IV regeneration, the lowest 55% (carbon after 1 regeneration). The experimental data shows that activated carbon can be used for the decontamination of dyes from textile wastewater. However, model tests need to be verified on real wastewater samples.

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

We present a hybrid scheme for the coupling of macro- and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-diffusion equation, subject to linear heterogeneous reactive boundary conditions. The multiscale finite volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or global degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro- and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\Omega^{hs}$. Continuity of fluxes is enforced by prolongating to microscopic resolution the macroscopic model fluxes across the boundary of $\Omega^{hs}$. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.

Estimation of Nucleation and Growth Kinetics of Benzoic Acid by Population Balance Modeling of a Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer

Nucleation and growth kinetics of benzoic acid crystallized by cooling from 1.5:1 (w/w) water/ethanol solutions were determined using a 500 mL continuous mixed suspension, mixed product removal (MSMPR) crystallizer and a mathematical model of the MSMPR process. The developed model solves the population, moment, and mass balance relationships with the kinetic expressions for the system and is coupled with a nonlinear optimization routine for kinetic parameter estimation. Comprehensive experimental data for model fitting and parameter estimation was obtained by varying crystallizer operating conditions to induce changes in the rate-affecting variables for growth and nucleation (temperature, supersaturation, and suspension density). The size distribution was monitored in real-time using focused beam reflectance measurement (FBRM) to identify steady-state and hence to enable on-demand adjustment of the operating conditions to transition multiple steady-states for rapid acquisition of kinetic data. A Malvern M...

Thermodynamically consistent description of mass transfer in porous media by a singular surface

AbstractPhase transition processes are important and ubiquitous physical phenomena. These processes are not limited to systems like batch reactors, but can also appear inside porous solids such as in the sequestration of CO2 or in the food industry. In these processes, mainly first‐order transitions between the liquid and the gaseous phases of a certain fluid occur and are characterised by a jump in density and the coexistence of both phases during phase change. This jump is numerically handled by introducing a singular surface, which allows for a thermodynamically consistent description of the mass transfer during phase transition. The mass transfer is driven by the change in internal energy and couples the two mass balance relations of the two fluid phases.The formulation of a model for a multiphasic porous aggregate in a non‐isothermal environment, while accounting for the thermodynamics of the fluids and the phase transition, requires a potent theory for its description. Here, the Theory of Porous Media (TPM) provides a well‐founded, continuum‐mechanical basis to model deformable, fluid‐saturated porous media. In this particular case, a three‐phasic model is proposed, consisting of the thermoelastic solid phase, which is percolated by the compressible gaseous and liquid fluid phases. The representation of the interface between the fluid phases by a singular surface results in additional terms in the balance relations. The evaluation of these terms leads to a consistent formulation of the mass transfer, which basically compares the energy added to the system with the latent heat of the phase transition. This mass‐transfer term is furthermore dependent on the interfacial area, a factor defined by porosity and saturation.Finally, the proposed model for phase transition inside a porous medium is based on the mixture momentum balance, the volume balances of the fluid phases and the energy balance. Consequently, the four primary variables are the solid deformation, the effective pore pressures of the two fluid phases and the temperature. The numerical simulation of condensation or evaporation of CO2 in a porous solid rock, which can be either caused by changes in temperature or in pressure, allows for the demonstration of possible application areas for the presented model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)