Transient Mass Balance Research Articles

A transient site balance model for atomic layer etching

We present a transient site balance model of plasma-assisted atomic layer etching of silicon (Si) with alternating exposure to chlorine gas (Cl2) and argon ions (Ar+). Molecular dynamics (MD) simulation results are used to provide parameters for the model. The model couples the dynamics of a top monolayer surface region (‘top layer’) and a perfectly mixed subsurface region (‘mixed layer’). The differential equations describing the rates of change of the Cl coverage in the two layers are transient mass balances. Model predictions include Cl coverages and rates of etching of various species from the surface as a function of Cl2 or Ar+ fluence. The simplified phenomenological model reproduces the MD simulation results well over a range of conditions. Comparing model predictions directly to experimental optical emission spectroscopy data, as reported in a previous paper (Vella et al 2023 J. Vac. Sci. Technol. A 41, 062602), provides further evidence of the accuracy of the model.

Stable isotope hydrology of a polymictic lake: Capturing transience of groundwater interactions

Although there have been many studies of groundwater inflow to small lakes, no systematic attention has been paid to the role of the time interval in the reliability of transient flow analysis. We addressed this issue in a two-year study of the isotope hydrology and water budget of a small lake in eastern Washington State (USA) that has been subject to limited management over several decades. The weighted local meteoric water line is δ2H = 7.14 δ18O – 5.22, reflecting the impact of convective recycling in this semi-arid region of inland northwestern North America. Groundwater inflow to the lake was quantified over two years using a short-interval isotopic transient mass balance approach. Calculated inflow was less than a fifth of the lake’s total water budget. Unrealistic temporal fluctuation of the calculated inflow was apparently correlated with fluctuation of the observed isotopic ratio of lake water (δL). We obtained realistic lake fluctuation and groundwater–lake exchange estimates by experimenting with the time interval of the isotope mass balance. It is crucial to acknowledge that each lake possesses unique characteristics that influence hydrologic and isotopic variations. Therefore, the optimal time interval for sampling and calculating mass balance may vary among different small lakes. Our findings have implications for long-term studies with frequent interval sampling.

Multizone representation of time-varying airflows in naturally ventilated dwellings: Occupant-generated CO2 approach

Accurate measurement of air exchange-rates (AERs) is crucial in naturally ventilated dwellings. AER calculations must take into account the multizone and time-varying aspects to avoid significant deviations from reality. To address the issues of invasiveness, high cost, and inability to track real-time changes in airflow and to represent real airflow patterns associated with the multiple tracer gas methods, this study proposes a practical and feasible approach, belonging to the occupant-generated CO2 methods, for the multizone representation of time-varying airflow in naturally ventilated dwellings. In this approach, the idea of state traversal is introduced to account for all possible airflow patterns. For each airflow pattern, the transient indoor CO2 mass balance equation associated with Kalman filter, and the dynamic simulation of indoor temperature are applied to successively determine the airflow pattern that is closest to the actual pattern. The approach's reliability for multizone representation of airflow is validated in controlled multizone environments, and its applicability to natural ventilation of real residential situations is also evaluated. This study further examines the zoning criterion and the approach's correction capability, while also providing a detailed analysis of its strengths and weaknesses.

Efficient modeling and simulation of gas separations applying Maxwell-Stefan approach and Ideal Adsorbed Solution Theory

We present an efficient way to incorporate the Maxwell-Stefan approach (Krishna, 1990) for modeling gas separation processes, i.e., adsorbent particles and membranes. Ideal Adsorbed Solution Theory (Myers and Prausnitz, 1965) is applied for the description of competitive equilibria. The proposed calculation method introduces analytical expressions for the partial derivatives of the loadings w.r.t. fluid-phase concentrations, developed by Rubiera Landa et al. (2013), in the calculation of the thermodynamic correction factors, as required by Maxwell-Stefan flux equations. These expressions are solved simultaneously with transient mass balances that describe the gas separation processes in a differential-algebraic equation formulation. Robustness and advantages of the proposed solution approach are demonstrated with several examples adapted from the literature.

Estimating the line packing time for pipelines transporting carbon dioxide

During the operation of pressurised pipelines transporting compressible fluids, line packing is employed as an effective method that uses the pipeline itself as a buffer storage, compensating for fluctuations in the fluid supply or demand. While in large-capacity natural gas transmission systems, reaching maximum operating pressures during line packing is usually not of practical concern, in small capacity pipelines transporting low-compressibility fluids, such as liquid or dense-phase CO2, line packing can occur quickly, and therefore, estimating the line packing times becomes important to ensure avoiding exceeding the pipeline maximum allowable operating pressure. In this study, a correlation for estimating the line packing time is derived from the transient mass balance in the pipeline. The proposed correlation accounts for the pipeline overall dimensions, operating pressure and temperature, and the fluid properties, namely density and the expansion coefficient. The correlation is also adopted for the calculation of pipeline unpacking times caused by unbalanced discharge from a pipeline. A verification study on line packing in a dense-phase CO2 pipeline shows that within the ranges tested, the proposed correlation estimates conservatively the line packing times with ca. 15 % deviation from the results of simulations obtained using a rigorous transient pipeline flow model. The proposed correlation is also verified against predictions obtained using a parabolic flow model and is recommended for estimating line packing times for both dense-phase and gas-phase CO2 at pressures and temperatures in the ranges 2 - 12 MPa and 280 – 330 K, respectively. The limitations of the proposed line packing time correlation are discussed.

Air change rates and infection risk in school environments: Monitoring naturally ventilated classrooms in a northern Italian urban context

The importance of building ventilation in avoiding long-distance airborne transmission has been highlighted with the advent of the COVID-19 pandemics. Among others, school environments, in particular classrooms, present criticalities in the implementation of ventilation strategies and their impact on indoor air quality and risk of contagion. In this work, three naturally ventilated school buildings located in northern Italy have undergone monitoring at the end of the heating season. Environmental parameters, such as CO2 concentration and indoor/outdoor air temperature, have been recorded together with the window opening configurations to develop a two-fold analysis: i) the estimation of real air change rates through the transient mass balance equation method, and ii) the individual infection risk via the Wells-Riley equation. A strong statistical correlation has been found between the air change rates and the windows opening configuration by means of a window-to-volume ratio between the total opening area and the volume of the classroom, which has been used to estimate the individual infection risk. Results show that the European Standard recommendation for air renewal could be achieved by a window opening area of at least 1.5 m2, in the most prevailing Italian classrooms. Furthermore, scenarios in which the infector agent is a teacher show higher individual infection risk than those in which the infector is a student. In addition, the outcomes serve school staff as a reference to ensure adequate ventilation in classrooms and keep the risk of infection under control based on the number of the students and the volume of the classroom.

Dynamic thermal analysis of a coupled solar water heaters-thermal storage tank for solar powered district heating networks

The integration of solar thermal and energy storage systems into district heating networks (DHNs) has been considered as one of the most advantageous solutions to reduce the use of fossil fuels and carbon emissions. In this context, this work deals with the numerical investigation of a coupled solar water heaters-thermal storage unit for urban heating networks. The studied system contains flat plate solar collectors (FPCs) for hot water production, a shell-and-tube thermal storage unit with phase change material (PCM) for latent storage or water for sensible storage, hydraulic pumps and a mass flow rate regulation system. The functioning of the coupled system is simulated using a detailed dynamic model based on transient energy and mass balances. The reliability of the developed model is verified through comparing numerical results with measurement data from the literature and a good agreement is obtained with a maximum relative error of about 4.5 %. The validated model is used to investigate the system thermal performance under the weather conditions of the city of Pau, France, and the effects of multiple parameters such as the FPC area, the DHN target thermal power, and the storage medium type (latent or sensible) during both charging and discharging processes are presented and analyzed. Results show that the use of FPCs is beneficial for DHNs during summer as they allow the production of thermal energy for both the DHN use and the storage process. It was also shown that increasing the DHN target thermal power from 30 kW to 50 kW leads to a reduction in the thermal storage process duration by up to 40 %. For both charging and discharging operations, the use of PCM (latent storage) as a storage medium is more suitable than water (sensible storage) as it leads to an increase in the storage density and extends the duration of hot water production with constant thermal power by about 65 %.

RESPONSE OF A FIRST-ORDER SERIES SYSTEM TO THE TRANSFER FUNCTION, THE LIQUID LEVEL OF TWO INTERACTING TANKS

This article presents the experimental and theoretical results of the discharge and filling of water between two torispherical tanks connected in series at different heights, the model that was used was developed with equations reported in the literature for geometries of torispherical tanks and it was necessary to develop two more equations in the laboratory to calculate the discharge and fill volumetric flows for the tanks used. The unloading and filling model was obtained with transitory mass balances resulting in two simultaneous linear differential equations where the unloading and filling heights are related as a function of the operation time. The model was solved numerically, and the experimental results were compared against those of the proposed model, finally the transfer function for this system of interacting tanks was found. KEYWORDS: Transient mass balances in two atmospheric interacting tanks at different heights and equal torispherical geometries. The discharge and fill model of two interacting tanks as a function of time. The volumes of partially filled torispherical tanks. The transfer function of a pulse in the discharge pipe that affects the volumetric flow within the discharge tank.

Associating occupants' interaction with windows with air change rate --One case study

Air change rate (ACR) significantly influences the indoor thermal environment and indoor air quality. Moreover, as a matter of fact, ACR varies with time during natural ventilation. However, to date only a few studies have accounted for the dynamic ACR for the actual in-use buildings. To address this issue, a field measurement of outdoor/indoor environments and the window state was conducted in a dormitory in Beijing in spring, summer, and autumn. Transient Mass Balance Equation (TMBE) method associated with the extended Kalman filter (Hereinafter referred to as Kalman filter method) was adopted to obtain the dynamic results of the ACR. Then the correlations of outdoor/indoor environments with the ACR and the probability of window opening were investigated. The results confirm the validity of Kalman filter method for tracking the dynamic nature of natural ventilation in residential units, and further demonstrate that occupants' interaction with windows does not simply refer to opening/closing windows, but also refer to adjusting the extent of the window being open in response to occupants' ventilation needs. Therefore, in addition to the probability of window opening, ventilation needs, i.e., the dynamic ACR, as the underlying trigger for window opening behavior, should be used as an indispensable part of describing occupants' interaction with windows. This study provides a complete framework to describe occupants’ interactions with windows by combining the dynamic ACR and the probability of window opening.

Release kinetics modeling and fungal control potential of encapsulated thyme (Thymus vulgaris) essential oil

The essential oils have antifungal properties and their volatilization can be controlled through encapsulation. The work aimed at controlling the release kinetics of thyme (Thymus vulgaris) essential oil through ionic gelation encapsulation to assess the potential of inhibiting the development of Penicillium spp. Thyme essential oil was encapsulated with sodium alginate (NaAlg; 0.5 and 1.0%), calcium chloride (CaCl2; 0.8 and 2.5%), and different residence times in the calcium solution (10, 20, 40, and 60 min). Batches of capsules were placed in closed containers and volatilization was monitored. Release kinetics were evaluated through transient regime mass balances. Capsules had diameter and thickness between 2.16-2.81 and 0.20-0.46 mm, respectively. The best systems used AlgNa/CaCl2-1.0/0.8%, with residence in the calcium solution of 10 and 20 min, obtaining encapsulation efficiencies of 94.0 and 90.1%, respectively. Penicillium digitatum was inhibited through the controlled release of the essential oil.

Study on the dynamic natural ventilation rates of occupied residence

The residential natural ventilation rates have a significant impact on indoor thermal comfort and air quality and building energy consumption. The characteristics of the indoor-outdoor temperature difference and wind pressure change over time, as well as the occupants' window opening behavior and the use of HVAC systems, resulting in the residential air change rate being dynamic with time. Many previous studies of residential ventilation measured the steady-state air change rates, which does not reflect the actual dynamic characteristics. In this study, a field measurement was conducted in a bedroom of one natural ventilation residential building in Beijing with continuously monitoring the CO2 concentration, indoor air temperature, and outdoor meteorological parameters for one year. Using the CO2 released by occupants as a tracer gas, the extended Kalman filter based on the Transient Mass Balance Equation (TMBE) was adopted to calculate the dynamic air change rate. This method can effectively filter the CO2 concentration measurement noise. The trend of air change rate with each influencing factor was analyzed. This study is expected to lay the foundation for future studies of dynamic air change rates in residential buildings.

An investigation on CO2 concentration based on field survey and simulation in naturally ventilated Nepalese school buildings during summer

Natural ventilation is usually adopted to provide required indoor air quality (IAQ) and thermal comfort. IAQ to be represented by CO2 concentration and ventilation is correlated with the academic performance of students. Most Nepalese school buildings are relying on natural ventilation through windows and have no glass sheets within them. This study is assessing the ventilation performance in those buildings that has not yet been known, through the measurement of CO2 concentration and questionnaire survey during the summer of 2019 in three schools located in the temperate climate of Nepal. The indoor CO2 concentration was much lower than the acceptable limit. Most students accepted the IAQ under such condition of classrooms. Based on the transient mass balance, a numerical simulation method was developed for estimating the number of air change per hour (ACH) and the indoor CO2 concentration. The estimated ACHs were found higher than 25 h−1 and thereby confirmed that ventilation was performed very well. The indoor CO2 concentrations simulated using the estimated ACHs were compared and found well fit with the measured CO2 concentration. The simulation of how the reduction of the ACH to a half or a quarter affects the indoor CO2 concentrations was conducted and found that the CO2 concentration would be still quite low in these schools. The findings in this study should be useful for assessing the ventilation performance after the installation of glass windows to be necessary at one of the highest priorities is made in the future.

Phosphorus mass balance and input load estimation from the wet and dry periods in tropical semiarid reservoirs.

The dynamics of total phosphorus (TP) in 18 strategic reservoirs of the high-density reservoir network of the Brazilian semiarid was evaluated during the wet and dry periods for the past 12 years. Seasonal overlying concentrations presented no significant differences for about 90% of the reservoirs (p>0.05). This was attributed to a trade-off between the hydrological/limnological processes occurring in the two seasons. Then, a transient complete-mix mass balance model was applied with particular adaptations for the tropical semiarid reservoirs to estimate the TP load for each season. Because of the relatively well-mixed conditions and high hypolimnetic dissolved oxygen concentrations during the wet season, the wet load was assumed to represent the external TP load. On the other hand, because of the absence of reservoir inflow during the dry season, phosphorus release under anoxic sediment conditions and wind-induced resuspension under shallow water depths, the dry load was assumed to reflect the internal TP load. The maximum external loads were related to peak inflows, notably after drought periods. Consistently, the largest internal loads were obtained during the drought periods, when the reservoirs were shallower and more prone to phosphorus release and resuspension. By comparing the impact of the two input load types, the wet period load was predominant in 72% of the reservoirs. The areal phosphorus loads ranged from 0.66 to 7.29 gP m2 year-1, which were consistent with the literature, despite the very high density of reservoirs. Finally, power-law curves including data for all studied reservoirs were adjusted between the dry period load and volume, dry and wet period loads, wet period load and inflow, and total load and catchment area, resulting in satisfactory R2 (0.84-0.98).

Quantifying floodwater impacts on a lake water budget via volume-dependent transient stable isotope mass balance

Abstract. Isotope mass balance models have undergone significant developments in the last decade, demonstrating their utility for assessing the spatial and temporal variability in hydrological processes and revealing significant value for baseline assessment in remote and/or flood-affected settings where direct measurement of surface water fluxes to lakes (i.e. stream gauging) are difficult to perform. In this study, we demonstrate that isotopic mass balance modelling can be used to provide evidence of the relative importance of direct floodwater inputs and temporary subsurface storage of floodwater at ungauged lake systems. A volume-dependent transient isotopic mass balance model was developed for an artificial lake (named lake A) in southern Quebec (Canada). This lake typically receives substantial floodwater inputs during the spring freshet period as an ephemeral hydraulic connection with a 150 000 km2 large watershed is established. First-order water flux estimates to lake A allow for impacts of floodwater inputs to be highlighted within the annual water budget. The isotopic mass balance model has revealed that groundwater and surface water inputs account for 60 %–71 % and 39 %–28 % of the total annual water inputs to lake A, respectively, which demonstrates an inherent dependence of the lake on groundwater. However, when considering the potential temporary subsurface storage of floodwater, the partitioning between groundwater and surface water inputs tends to equalize, and the lake A water budget is found to be more resilient to groundwater quantity and quality changes. Our findings suggest not only that floodwater fluxes to lake A have an impact on its dynamics during springtime but also significantly influence its long-term water balance and help to inform, understand, and predict future water quality variations. From a global perspective, this knowledge is useful for establishing regional-scale management strategies for maintaining water quality at flood-affected lakes, for predicting the response of artificial recharge systems in such settings, and for mitigating impacts due to land use and climate changes.

Pulsating diffusion flames fed with biomass particles in counter-flow arrangement: Zeldovich and Lewis numbers effects

Natural and forced instabilities have a significant influence on the performance and efficiency of biomass-fueled combustion systems, where oscillatory behaviors cannot be ignored. This work concentrated on the analytical modeling of pulsating biomass-fueled diffusion flames in the non-premixed counter-flow arrangement, accounting for the effects of Lewis and Zeldovich numbers. Preheating, post-vaporization, reaction, and oxidizer zones were considered in the model derivation. In order to model the oscillatory characteristics, oscillations were mathematically modeled using a sinusoidal function. Transient mass and energy balance equations were formulated and analytically solved considering different Lewis and Zeldovich numbers. To preserve continuity and obtain the flame front position, jump conditions were given. After validating the derived analytical model, transient characteristics of flame temperature and position and time-varying distributions of reactants temperature and mass fraction were presented under pulsating conditions. Results show that Lewis number is the main parameter controlling the oscillatory and pulsating behaviors of the flame. Furthermore, Zeldovich number seems to escalate the effects of Lewis number.

Tidal creeks as hot-spots for hydrological exchange in a coastal landscape

Coastal ecosystem health and sustainability is tightly coupled to submarine groundwater discharge (SGD) and associated nutrient, carbon and pollutant fluxes. However, there are few studies that systematically analyse the interaction between the terrestrial aquifer system, catchment morphology and coastal SGD. The objective of this study was to evaluate the role of catchment morphology and how this influences the spatial distribution, timing and volume of the SGD flux to a branched tidal creek system, on the barrier island Spiekeroog, Germany. The subsurface salinity was mapped using electrical resistivity tomography (ERT) and a hydrogeochemical survey of the shallow groundwater. Temporal and spatial analysis of geochemical tracers (radon-222, chloride) in the tidal creek water was integrated into a transient 222Rn mass balance model for quantification of SGD rates during two field campaigns that encompassed spring and neap tides. The ERT mapping indicated that fresh groundwater dominated under the dune ridges down to about 15 m depth, but became progressively more brackish seawards. This is likely due to frequent tidal and storm flooding of low-lying areas. The highest groundwater fluxes into the creek were indicated by high 222Rn activities (average 468 Bq m−3) towards the dune ridge. Chloride concentrations (up to 17.3 g L−1) increased seawards showing the progressive salinization of water in the creek. The freshwater component of SGD was highly variable in time but was highest at low tide, while the total SGD flux (saline + fresh) was highest when tides changed from inflow to outflow as the rapid pressure release on the local aquifer caused a large hydraulic gradient towards the creek. Comparing the freshwater component of mean daily SGD to the creek with estimated groundwater recharge rates in the catchment (665 m3 d−1) shows that the fresh groundwater discharge exceeds fresh recharge during spring tides (~120%) but is was lower than recharge during neap tides (~27%). In this study we show that tidal creeks and their relation to catchment morphology are relevant for understanding the spatial and temporal exchange of fresh and saline water between the catchment and coastal zone.

Computational modelling of non-dispersive solvent extraction of uranium in hollow fiber contactor operated in recycle mode

Extraction of uranium and acidity by using TBP (tri-n-butyl phosphate)-n-dodecane through hollow fiber contactor operated in the Non-Dispersive Solvent Extraction (NDSX) configuration with recycle mode is simulated by using a two-dimensional axisymmetric multi-component Computational Fluid Dynamics (CFD) model. This multi-component model solves continuity and momentum transport equations for the feed and shell sides and solute transport equation for the feed side, shell side as well as for the membrane phase. Complex boundary conditions of flux continuity and concentration jump are implemented in the model. Recycle mode of operation is simulated by solving the differential equations representing transient mass balance for feed and solvent reservoirs bottles simultaneously with the governing equations of the CFD model. Validation of the model has been done by comparing predicted and experimentally measured percentage extraction of uranium and nitric acid for different parametric conditions. The validated model has been used to have detailed insights into the spatial and temporal variation of concentration and flux profiles inside the contactor. The CFD model of hollow fiber contactor, which is widely accepted as a separation process intensification tool, will be useful for optimization of the design, operation and scale-up.

Two-phase multi-scale modeling of a tubular loop propylene polymerization reactor

In the present paper a new two-phase multi-scale mathematical model of a tubular loop reactor is presented to describe the bulk polymerization of propylene. The model comprises transient mass and energy balances for the liquid and solid phases and population balance equations to describe the spatio-temporal evolution of the particles size distributions. Particularly, the mathematical modeling approach presented here also takes into account inter-phase transport phenomena for the first time for this class of reactors. As shown through computational simulations, inter-phase mass and energy transport constraints can exert significant influence on the properties of the final product and should not be neglected a priori.

Mass balance of the tribofilm in lubricated systems

The efficiency of the lubrication systems varies during the time of use of each batch of lubricant, increasing wear and friction in the lubricated system. In this work, transient mass balances of the lubricant precursors that form the protective film in lubricated systems, the substances that constitute the deposited film, and the waste products that form when the protective film is removed from the surface are implemented to simulate the dynamic behavior of protective film thickness. These mass balances are supported experimentally with measurements of the rates of growing and removal of the protective film. Simultaneous solution of mass balances and the Archard's wear model allowed to calculate and to profile the wear rate, friction, and efficiency of lubrication system.

An experimentally validated heat and mass transfer model for wax deposition from flowing oil onto a cold surface

AbstractA transport model is proposed for wax deposition onto a cold finger from flowing wax‐containing oils. The model solves transient energy and mass balances simultaneously for a reversible first‐order kinetic rate for precipitation of pseudo‐single‐component wax, and the effects of yield stress using a critical solid wax concentration to withstand flow‐induced stress at the deposit‐fluid interface. The model can predict the time evolution of the deposit thickness, and the spatial and temporal evolution of temperature and wax concentration as validated using cold finger experiments. It was found that for high wax content oils, deposit thickness growth is dominated by heat transfer. For low wax content oils that are unable to gel, the thickness growth is slow and accompanied by occasional sloughing. Regardless of the mechanism controlling the growth, mass transfer cannot be neglected as wax diffusion into the deposit continues to take place after the deposit has stopped growing.