Moisture Balance Equations Research Articles

Research on Relative Humidity and Energy Savings for Air-Conditioned Spaces without Humidity Control When Adopting Air-to-Air Total Heat Exchangers in Winter

In view of the problem that the exchange effectiveness is calculated according to a fixed value or only considering the influence of outdoor air parameters when analyzing the suitability of total heat recovery for plate heat recovery equipment in air-conditioned spaces without humidity control, the indoor humidity calculation model and moisture balance equation were established in this research to predict relative indoor humidity. Moreover, the relationship between total heat recovery, effective heat recovery, and the reduction in outdoor air heating load was analyzed using a psychrometric chart of the outdoor air treatment process. Referring to the standard for weather data of building energy efficiency in the Ningbo region, 6 typical days were taken as the calculation conditions. The moisture balance differential equation was solved using MATLAB software to obtain numerical solutions for the hourly indoor air humidity ratio, relative humidity, exchange effectiveness, and effective heat recovery when adopting an air-to-air total heat exchanger in an air-conditioned room of an office, classroom, or commercial building in the winter. The results indicate that, under the calculation conditions, the relative indoor humidity of commercial buildings is relatively high, making it unsuitable for a total heat exchanger. The relative humidity of indoor air in offices and classrooms can be maintained above 30%, and the total exchange effectiveness of a total heat exchanger is between 45% and 100%. The effective total heat recovery was calculated as sensible heat recovery under most calculation conditions.

Understanding the role of moisture recovery in indoor humidity: An analytical study for a Norwegian single-family house during heating season

Providing a high-quality indoor environment with appropriate indoor humidity levels for residential buildings is essential for good physical and mental health, occupant comfort, and long-term building performance. The role of moisture recovery in indoor humidity levels in cold climates has long been the subject of controversy; scholars have debated whether it ameliorates the problem of "too dry" air or causes a new problem of "too humid" air. The current study examines a method using moisture balance equations integrated with moisture recovery to analyse moisture recovery's effect in cold climates.A virtual single-family house in Oslo, Norway, was used to demonstrate the impact of moisture recovery on humidity levels in the kitchen, bathroom, bedroom and living room. The results show that moisture recovery has varying influences on indoor humidity depending on the intensity of moisture recovery, moisture production and ventilation. The indoor moisture production and humidity levels were validated against large-scale field measurements in residential buildings. For the virtual single-family house, the optimal moisture recovery effectiveness is about 50–60% with a 2-min interval, as the "too dry" air (RH<20%) issue is eliminated while the risk of "too humid" air (RH>80%) is not exacerbated.This work also identifies the possibility of controlling or optimising indoor humidity by altering the energy recovery system's moisture recovery effectiveness. Furthermore, the study's findings can be used to optimise thermal comfort or assess epidemiological risk in terms of the impact of indoor humidity.

New numerical model of heat and moisture transfer in the wet brick

The subject of this study is numerical modelling of the fully coupled heat and moisture transfer in the building material, i.e., in a brick. The new mathematical model of equilibrium transport of heat and moisture in the form of continuous liquid medium (funicular region), discontinuous liquid medium (pendular region) and gaseous phase with dry air is proposed. As independent variables, the total mass moisture content and temperature are chosen. Both energy and moisture balance equations are mutually coupled. It is due to dependence of capillary and vapor pressures on the moisture content and temperature. Additionally, vaporization and condensation phenomena are also accounted for in the energy balance equation. Both transport equations are supplemented with boundary conditions expressing the coupled heat and moisture transfer at the dried wall or heat transfer at impermeable walls. Balance equations are discretized on the rectangular control volume grid in the framework of the in-house computational code. A grid-based method of generation of the control volume mesh is proposed, with ‘half’ control volumes related to boundary grid nodes created at domain walls. This approach enables deeper insight into implemented code as well as simplifies analysis of influence of selected terms in balance equations and implementation of complex hygro-thermal boundary conditions.

Dynamic model development of heat and mass transfer for a novel desiccant regeneration system in liquid desiccant dehumidification system

In this paper, from the control point of view, a simplified dynamic model of the Desiccant Regenerations System (DRS) is proposed. The DRS is a serial system of the heat pipe heat exchanger and regenerator whose models are developed by writing the thermal and moisture balance equations, and the heat and mass transfer rates of each subsystem are derived by using the effectiveness-NTU and hybrid modeling approach. The unknown Model parameters are identified through the nonlinear least squares method and unscented Kalman filter algorithm with commissioning information. The dynamic model of the whole system is obtained by integrating the subsystem models to predicts the system performance. Compared with the existing DRS models, the presented model not requires iterative computations and also can be easily transformed into a state-space model. The proposed model accurately reflects the transient and steady state performance of the DRS over the wide operating condition in the experimental validation and is expected to work well for intelligent dynamic control and optimization applications.

Global well-posedness for passively transported nonlinear moisture dynamics with phase changes

We study a moisture model for warm clouds that has been used by Klein and Majda (2006 Theor. Comput. Fluid Dyn. 20 525–551) as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the spirit of Kessler (1969 Meteorol. Monogr. 10 1–84) and Grabowski and Smolarkiewicz (1996 Mon. Weather Rev. 124 487–97), in which water is present in the gaseous state as water vapor and in the liquid phase as cloud water and rain water. It thereby contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. Phase changes are associated with enormous amounts of latent heat and therefore provide a strong coupling to the thermodynamic equation.In this work we assume the velocity field to be given and prove rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture model with viscosity, diffusion and heat conduction. To guarantee local well-posedness we first need to establish local existence results for linear parabolic equations, subject to the Robin boundary conditions on the cylindric type of domains under consideration. We then derive a priori estimates, for proving the maximum principle, using the Stampacchia method, as well as the iterative method by Alikakos (1979 J. Differ. Equ. 33 201–25) to obtain uniform boundedness. The evaporation term is of power law type, with an exponent in general less or equal to one and therefore making the proof of uniqueness more challenging. However, these difficulties can be circumvented by introducing new unknowns, which satisfy the required cancellation and monotonicity properties in the source terms.

Space-time modeling of soil moisture

Abstract A physically derived space-time mathematical representation of the soil moisture field is carried out via the soil moisture balance equation driven by stochastic rainfall forcing. The model incorporates spatial diffusion and in its original version, it is shown to be unable to reproduce the relative fast decay in the spatial correlation functions observed in empirical data. This decay resulting from variations in local topography as well as in local soil and vegetation conditions is well reproduced via a jitter process acting multiplicatively over the space-time soil moisture field. The jitter is a multiplicative noise acting on the soil moisture dynamics with the objective to deflate its correlation structure at small spatial scales which are not embedded in the probabilistic structure of the rainfall process that drives the dynamics. These scales of order of several meters to several hundred meters are of great importance in ecohydrologic dynamics. Properties of space-time correlation functions and spectral densities of the model with jitter are explored analytically, and the influence of the jitter parameters, reflecting variabilities of soil moisture at different spatial and temporal scales, is investigated. A case study fitting the derived model to a soil moisture dataset is presented in detail.

Heat and mass transfer in fixed bed drying of non-deformable porous particles

A drying model for non-deformable porous spherical particles in a fixed bed passed by a drying agent was developed. The model was based on coupled moisture and heat balance equations, where the moisture molar flux evaporated from a pore was estimated according to the diffusion through a stagnant gas layer. Model equations included various process factors, e.g., characteristic parameters of porous particle (diameter, porosity, and pore tortuosity), fixed bed particles (void fraction, height, initial moisture content, and initial temperature), and drying agent (superficial velocity, input humidity, and initial temperature). Particle porosity and pore tortuosity were selected as adjustable parameters. An experimental study on air drying of fixed bed activated carbon was conducted and the adjustable parameters were fitted based on experimental data. Values of 0.28±0.04m3/m3 for particle porosity and 1.25±0.15 for pore tortuosity were obtained under studied operating conditions. The drying was faster with an increase in air superficial velocity (0.04–0.42m/s) and initial air temperature (25–45°C). The model predicted accurately different experimental data and it could be used in designing and optimizing the convective drying of fixed bed porous particles.

Relationship between soil moisture deficit and productivity of paddy lands in a major irrigation system in Intermediate zone of Sri Lanka

This study is conducted to investigate the relationship between paddy productivity and soil moisture deficit in a selected irrigation scheme in the Intermediate zone of Sri Lanka. The availability of water for crop growth is estimated using a soil moisture balance equation using field data for a period from 2005 to 2014 to find the soil moisture deficit. A regression showed that relationship between paddy productivity and severity of soil moisture deficit in Yala season is not statistically significant. However, the decrease of paddy productivity during Maha season is influenced by both number of days of soil moisture stress and the total soil moisture stress and the results are found to be statistically significant. About 72% and 88% of the variation of paddy productivity can be explained by the total number of days with soil moisture stress and total soil moisture stress respectively.

The effect of a rotary heat exchanger in room-based ventilation on indoor humidity in existing apartments in temperate climates

The investigation constructed and simulated moisture balance equations for single-room ventilation with a non-hygroscopic rotary heat exchanger. Based on literature, the study assumed that all condensed moisture in the exhaust subsequently evaporated into the supply. Simulations evaluated the potential for moisture issues and compared results with recuperative heat recovery and whole-dwelling ventilation systems. To assess the sensitivity of results, the simulations used three moisture production schedules to represent possible conditions based on literature. The study also analyzed the sensitivity to influential parameters, such as infiltration rate, heat recovery, and indoor temperature. With a typical moisture production schedule, the rotary heat exchanger recovered excessive moisture from kitchens and bathrooms, which provided a mold risk. The rotary heat exchanger was only suitable for single-room ventilation of dry rooms, such as living rooms and bedrooms. The sensitivity analysis concluded that varying heat recovery or indoor temperature could limit indoor relative humidity in dry rooms when a moderate risk was present. The rotary heat exchanger also elevated the minimum relative humidity in each room, which could help to avoid negative health impacts. A discussion emphasized the potential benefits of selecting heat recovery to match the individual needs of each room.

Multiscale hydro-thermo-mechanical model for early-age and mature concrete structures

Temperature and early-age mechanical properties in hydrating concrete structures present a significant risk for cracking, having a major impact on concrete durability. In order to tackle these phenomena, a multiscale analysis is formulated. It accounts for a high variety of cement properties, concrete composition, structure geometry and boundary conditions.The analysis consists of two steps. The first step focuses on the evolution of moisture and temperature fields. An affinity hydration model accompanied with non-stationary heat and moisture balance equations are employed.The second step contains quasi-static creep, plasticity and damage models. It imports the previously calculated moisture and temperature fields into the mechanical problem in the form of a staggered solution. The whole model has been implemented in the ATENA software, including also the effect of early-age creep, autogenous and drying shrinkage.Validation on selected structures shows a good prediction of temperature fields during concrete hardening and a reasonable performance of the mechanical part.

Estimating the needed amount of desiccant, water or moistener to adjust the equilibrium water activity of dry powder mixtures

Prior to their mixing, further processing or packaging, industrial pharmaceutical and food powder formulations, or their individual components, are sometimes equilibrated under controlled humidity conditions in order to reach a water activity level deemed desirable and safe. Occasionally, there is a need to lower this water activity by adding a desiccant, or raise it through free moisture adsorption or adding a moistener. If the components do not interact chemically, the system is closed, the moisture in the free space negligible and the temperature practically constant, the amount of water gained or lost by the mixture's components is determined by a simple moisture balance equation, which can be used to translate the exchanged moisture into the mass of a given desiccant or moistener needed. To find this mass, one needs to know the mixture's initial composition, the ingredients' masses and moisture contents (in order to calculate their dry mass), and their moisture sorption isotherm equations. The latter can be of any kind, including polynomial, and there is no limit on the number of their coefficients. Knowledge of the desiccant's moisture content, if not zero, or moistener's initial moisture contents, or water activity, and its moisture sorption isotherm equation is also needed. The calculation of the overall amounts of water exchanged and corresponding amount of desiccator or moistener needed has been automated and can be performed with a Microsoft Excel® spreadsheet especially written for the purpose and posted as freeware on the Internet.

Integration model of hygrothermal analysis with decay process for durability assessment of building envelopes

In this study a numerical simulation model that integrates hygrothermal analysis with the decaying process of wood structures caused by moisture accumulation is presented. This simulation model can quantitatively predict both hygrothermal conditions within the building envelopes and the progress of decay in wood structures under variable conditions. The following are characteristics of the simulation model used in this study: (1) the development of wood decay represented by a differential equation with a variable of mass loss of wood substance and (2) the addition into moisture balance equations of biochemical reactions within wood decay. Hence, the simulation model enables assessment of the long-term performance of building envelopes with regard to both durability and drying potential. Rate constants of the wood decay and a coefficient of the moisture production for the model were determined by the mass loss data of small wood samples in decay tests using Fomitopsis palustris, a brown rot fungus. Additionally, numerical simulations using the model were implemented to understand both the decaying process and moisture accumulation within building envelopes. The results numerically demonstrated important phenomenon that the moisture production by biochemical reactions of wood decay helps to maintain the decaying process.

Stochastic modeling of soil salinity

A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long‐term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in long‐term soil salinization trends, with significant consequences e.g. for climate change impacts on rain‐fed agriculture.

Numerical simulation of rough rice drying in a deep-bed dryer using non-equilibrium model

In this study, a non-equilibrium model of the grain fixed deep-bed drying for rough rice has been presented. The model was developed by using mass and energy balance inside a control volume of the bed and a proper rate equation for the thin-layer drying. The control volume was composed of two thermodynamical systems: intergranular air and grains. In most of the models reported in the literature, authors simplified the physical description by neglecting the accumulation terms from the energy and moisture balance equations without a relevant justification. Accurate modeling of the drying process is an important factor from design point of view as well as optimizing the operation. In the proposed model, in this work the accumulation terms were kept in both energy and mass balance equations. The set of coupled partial differential equations derived from the model was solved simultaneously by using the backward implicit method. Based on the discrete set of equation, a computer program was developed and implemented in MATLAB environment to simulate the grain drying process. The technique was capable to predict correctly the temperature of the air and grains, the air humidity and moisture content of the grains at different locations of the dryer at any time. The results of simulation were also compared with the experimental data. The results clearly show that the proposed method can predict the characteristics of the deep-bed dryer with a very good degree of accuracy.

Geospatial estimation of soil moisture in rain-fed paddy fields using SCS-CN-based model

Paddy fields are characterized by standing water and saturation condition during the entire crop growth period. However, in sub-humid and semi-arid areas, scarce rainfall and intermittent dry spells often cause soil moisture depletion resulting in unsaturated condition in the fields. These distinctive characteristics of the paddy fields have significant influence on the runoff generation and soil moisture retention characteristics of the watershed. In this study, the objective is to extend the application of the Soil Conservation Services Curve Number (SCS-CN)-based models for the geospatial and temporal simulation of soil moisture to paddy field-dominated agricultural watersheds in the water scarce areas. Different SCS-CN-based models, integrated with the soil moisture balance equation, are used to estimate the surface runoff and soil moisture content wherein, the spatial variation in the soil hydraulic characteristics is used to calculate the geospatial variation in soil moisture content. Physical significance of the terms initial abstraction ( I a ) and potential maximum retention ( S) in these models and their influence on the estimation of runoff and soil moisture are analysed in detail. A new SCS-CN-based model for soil moisture simulation (SCS-CN-SMS), to improve the soil moisture estimation, is proposed in this paper. The proposed model is built up on the soil moisture balance equation to account for the effect of ponding condition and soil moisture variation between the dry and saturation condition. The method is tested with 3 years observed surface runoff data and crop production statistics from a part of the Gandeshwari sub-watershed in West Bengal, India. The entire study area is divided into cells of 20 m × 20 m. Various components of the soil moisture balance equation are estimated for each cell as a function of the soil moisture content. Remote Sensing Technique and Geographic Information System (GIS) are used to extract and integrate the spatially distributed land use and soil characteristics. The Hortonion overland flow concept adopted in the SCS-CN method is used to estimate the soil hydraulic characteristics of each cell in which the curve number is used to infer the spatial variation of the land use and soil characteristics. Even though the original SCS-CN method and the existing modified versions are efficient for runoff estimation, these models are found to be inappropriate for the estimation of soil moisture distribution. On the other hand, the proposed SCS-CN-SMS model gives better results for both runoff and soil moisture simulation and is, therefore, more suitable for the hydrological modeling of paddy field-dominated agricultural watersheds.

Modeling banded vegetation patterns in semiarid regions: Interdependence between biomass growth rate and relevant hydrological processes

Vegetation patterns, such as regular spots and bands, have been observed in arid and semiarid lands. One of the most common explanations for vegetation banding is that the homogeneous steady state solution of soil moisture and vegetation biomass density balance, expressed in the form of a bucket model, may be unstable under conditions of scarce mean annual rainfall. Even though the theory seems to support our intuitive explanation of the phenomenon, there are still unresolved questions concerning soil parameterization, relevant hydrological processes, and the way plant physiology should be modeled in arid and semiarid environments where vegetation patterns have been observed. This paper examines the interrelation between hydrological processes and plant physiology. The biomass growth rate resembles plant physiology within the bucket model and determines the survival plant strategy given a limited soil moisture availability. The fact that very different hypotheses concerning the biomass growth rate have been formulated has not yet been given the important consideration it deserves. Different models for vegetation banding will be considered here. They are formulated by introducing different growth rates within the same soil moisture and vegetation balance equations. Linear stability analysis and numerical integration of the different models showed some relevant interrelation between hydrological and physiological features. It was demonstrated that the relation between biomass growth rate and biomass density determines which hydrological process enables vegetation pattern initiation. The discussion of this result leads to a critical review of previously published hypotheses on plant physiology and hydrological processes inducing vegetation organization.

Comparison of two non-equilibrium models for static grain deep-bed drying by numerical simulations

Non-equilibrium models of the grain stationary deep-bed drying are derived from the theoretical analysis of the physics of the drying process and consist of a set of four nonlinear partial differential equations describing, respectively, the moisture balance, air energy balance, grain energy balance and thin-layer drying rate. In these models, many authors simplify the physical description by neglecting the accumulation terms from the energy and moisture balance equations without a relevant justification. This simplification may reduce the complexity and computational time but depending of drying conditions can also reduce models’ accuracy. Accurate modelling of the drying process is a determining factor both for designing the drier, and for optimising its operation. In this paper, we use two non-equilibrium models to design two grain deep-bed drying computer codes. In the first, model 1, derived by Bakker-Arkema et al. [Bakker-Arkema, F. W., Bickert, W. G., & Patterson, R. J. (1967). Simultaneous heat and mass transfer during the cooling of a deep-bed of biological products under varying inlet air conditions. Journal of Agricultural Engineering Research, 12, 297–307] and also presented by Brooker et al. [Brooker, D. B., Bakker-Arkema, F. W., & Hall, C. W. (1974). Drying cereal grains. Westport, CT: AVI], the accumulation terms are kept, in the second, model 2, as assumed by these authors, these terms are neglected. Both models are discretized by second order semi-implicit schemes. We use these codes to simulate wheat static bed drying and we compare their predictions. We show that the transfer time, defined as the ratio of the bed height and the drying air velocity, and inlet air temperature and humidity are the main parameters which affect the behaviour of the deviation between the predictions of these models. We investigate the conditions allowing one to neglect the accumulation terms as in the model 1.

Ventilation Flow in Pig Houses measured and calculated by Carbon Dioxide, Moisture and Heat Balance Equations

Ventilation flow in commercial livestock buildings can be estimated by means of relatively simple indirect methods based on carbon dioxide (CO2), moisture or heat balances. However, ventilation flow on an hourly basis for these balances needs adjustment for diurnal variation in animal CO2 and heat production. This work examines the agreement between ventilation flow measured in a pig house over a period of 41 days and that estimated from the three balances, on a 24 h and on an hourly basis. The study shows that, all three methods can give reasonably good estimations of the ventilation flow on an hourly basis. On average, the calculated ventilation flow was 8% lower than measured ventilation flow for the CO2 balance, and 9% lower for the moisture and heat balances. A good agreement between measured and calculated ventilation flow was obtained on a 24-h basis (coefficient of determination R2 between 0·92 and 0·97) and on an hourly basis (R2 between 0·83 and 0·92). The study indicates that the agreement between measured and estimated ventilation flow on an hourly basis can be improved by taking into account the diurnal variation in CO2, moisture and heat production.

Complex Model to Study Long Term Environmental Tritium Behavior

ABSTRACTTo assess long-term environmental safety of a tritium facility, prediction of consequences of potential tritium releases in the environment is needed both during routine operations and in case of accidents. Modeling is the only method to obtain such assessment without any environmental contamination.The current paper describes the TRIEF model designed to assess consequences of long-term atmospheric tritium emission for such environmental compartments as atmosphere, soil, plants; tritium contamination of ground and underground water is also included. The model takes into account tritium transport among all of the compartments. The model has been successfully validated in model-experiment intercomparison study in framework of the IAEA co-ordinated research programme “BIOMASS” on assessment of environmental contamination from the continuous source of atmospheric tritium release. The experimental data included tritium concentrations in the atmospheric moisture, vegetation, soil and the overlying snow cover. The modelling period was 20 years. Most of the predicted values agreed with observations within experimental uncertainties, which were a factor of 2.The TRIEF model is based on both HTO equilibrium and material balance approach in all the compartments. Average concentrations in atmosphere are calculated by using the Gauss-type model for primary and secondary source. HT and HTO behavior are modeled separately. Both wet and dry deposition of HTO is taken into account in case of HTO emission. HTO concentration in soil moisture is determined by the moisture balance equation. HTO concentration in plant tissue free water and organically bound tritium are estimated as a combination of HTO content in soil moisture and atmospheric humidity. HTO contamination of aquifer is modeled using available finite-differences codes within 12 hydro-geological strata.

An analysis of mean transition time between flood and drought in the large river basin

A soil moisture balance equation over large spatial regions is studied at seasonal and annual time scales for the Arkansas river basin. Interaction and feedback effects between land-surface and atmospheric moisture are studied in the parameterization for this basin. Due to the interaction between the land-surface and atmosphere at large scales, the surface hydrology of large land areas is susceptible to two distinct stable modes in the long-term probability density function: a dry and a wet state. In the soil moisture balance equation, stochastic fluctuations lead to separate preferred statistical stable states with transitions between these stable states induced by environmental fluctuations. On the basis of historical data, the soil moisture balance equation is calibrated for the Arkansas river basin. The transition times between the stable modes in the model are studied based on the stochastic representation of the physical processes and the calibrated model parameters. This study has implications for prediction of the transition times between stable modes or residence times, that is, the time the system spends in a given stable mode, since this would be equivalent to predicting the duration of droughts or wet conditions.