Filtration Model Research Articles

Implementation of numerical modeling algorithms to examine the filtration of multiphase flow through the gas hydrate stability zone in the Ross Sea.

Abstract In the Ross Sea region (Antarctica), evidence of warming, ice melt, and high levels of thermogenic gas hydrates indicate that deep-seated hydrocarbons significantly contribute to carbon cycles in the region. A fluid dynamics filtration model has been developed to describe the movement of liquid and gas in a porous medium containing gas hydrate inclusions, while considering phase transitions. The study investigates structural changes in the gas hydrate stability zone as methane moves from the hydrate-melt zone to the seabed. This is achieved through algorithms based on balances of gas and water masses, and total energy while considering Darcy's law. A numerical fluid dynamics model is employed to study the potential introduction of deep-seated carbon to the Ross Sea ice shelf region for the first time, considering a gas hydrate stability zone under local thermodynamic equilibrium. The calculation results support the phenomenon of free gas from deep sediments migrating to a shallow zone with gas hydrate stability conditions, partially converting into hydrate, while the remaining gas is capable of migrating higher into the water column. The process is accompanied by the formation of a three-phase (gas, hydrate, H2O) hydrate-equilibrium zone, replacing the initially two-phase (hydrate, H2O) gas hydrate stability zone. The modeling results explain the discrepancy between the radiocarbon dating of the core and the study of the history of the ice sheet in the region.

Seawater intrusion and infiltration modelling coupled to digital tools to avoid high saline concentrations in reclaimed water: application in coastal central Italy

ABSTRACT An industrial symbiosis approach was established between an industrial company and a water utility to prioritize the reuse of urban wastewater for industrial purposes. This requires low-salinity water, but this area is frequently affected by saline intrusion, thus creating water-related conflicts between the different economic activities. This study proposes a digital solution that combines a dynamic simulation model (that predicts seawater intrusion and runoff) with digital tools, i.e., smart-equalization (a control algorithm) and a matchmaking platform (a decision support system). The models aim to predict the periods where significant peaks of salinity occur, whereas the tools aim to distribute the wastewater and reclaimed water streams to diverse applications (industrial and agricultural) and/or treatments (conventional treatment and reverse osmosis) to maximize the amount of wastewater reused in an efficient and sustainable way. During the 2D simulated period, wastewater conductivity was in the range of 2,100–2,700 μS·cm−1. Although this conductivity was over the limit required for industrial reuse, the digital solution implemented in this study enabled a recovery of 71% of the total wastewater produced for industrial purposes and 10% for irrigation, only discharging 19% of the total. The approach implemented in this study would be very useful to be replicated in coastal areas where saline intrusion is relevant.

Characterization of Damage and Infiltration Modeling of Coal-Slurry Consolidation Mechanics Under Loaded Conditions

Coal seam gas drainage is a primary measure for mitigating coal and gas outburst hazards. Grouting sealing can form coal-slurry consolidated bodies, significantly improving the sealing quality of gas drainage boreholes and alleviating coal and gas outburst risks. Therefore, this study conducts triaxial loading and seepage experiments to analyze the mechanical failure characteristics and permeability variation of coal-slurry consolidated bodies under loading conditions following grouting sealing of gas drainage boreholes. Based on the “cube” model, a permeability model for the damaged coal-slurry consolidated body under loading conditions is established. The findings provide guidance for evaluating the leakage prevention performance of sealing materials in field engineering and optimizing the sealing efficiency of grouting materials. Future research may explore the damage and seepage evolution of coal-slurry consolidated bodies under various loading conditions and sealing material types.

Ultrafiltration membrane modelling: Comparing two mathematical models by sensitivity and uncertainty analysis for Palermo and Corleone (Italy) water reuse case studies.

The new EU Urban Wastewater Treatment Directive requires stricter limits introducing quaternary treatments and poses significant challenges to achieving a sustainable environment. Advanced membrane-based treatment processes combined with mathematical models can be a good solution for facing the challenges above. Most existing literature on membrane filtration models primarily focuses on membrane bioreactors, lacking mechanistic models on ultrafiltration (UF) membranes. This study presents two new UF mechanistic models: a tailored GPS-X module (Model 1), and a custom-made mathematical model (Model 2). The two models were compared using sensitivity, uncertainty, and calibration analysis in two case studies. Results showed a higher capability of Model 2 to simulate membrane fouling and water quality. Model 1 failed in predicting transmembrane pressure and showed a longer simulation time. Both models provided acceptable uncertainty in predicting permeate concentrations.

Infiltration Model of Rheological Bentonite Slurry through Sands

Infiltration Model of Rheological Bentonite Slurry through Sands

Modelling district heating demand: A synthetic dataset for two residential neighbourhoods.

The extensive artificial datasets developed in this study capture the energy demands of two districts and, with reasonable constraints, emulate monitoring campaigns typically conducted on-site in inhabited houses. Generated datasets are the following, one 1) representing low-performing building stock from before the deployment of the Energy Performance of Buildings Directive (EPBD) (2006), and the other 2) reflecting high-performing stock constructed after 2006. The buildings in the datasets were simulated representing single-family homes, typical of neighbourhoods in Flanders, Belgium. The datasets were generated using Dymola and the IDEAS package integrated with TEASER. Each simulated house differs in geometry, size, envelope characteristics, occupancy patterns, and installed gas heating systems. Envelope characteristics for older houses were derived from Energy Performance Certificate (EPC) data, and categorized into four construction periods, while newer houses were based on Energy Performance of Buildings (EPB) reports, both evaluated in Flanders. The datasets feature only heavy-weight houses in terraced, semi-detached or detached configurations, modelled as either single- or two-zone buildings, depending on their number of storeys. The simulations incorporate a natural infiltration model and a stochastic occupant behaviour model that sets the temperature requirements and accounts for heat gains from occupants and appliances. Due to the computational effort of large-scale simulations, heating system performance was postprocessed using a data-driven approach assuming gas-fired heating systems. Six heating system configurations were allocated, including condensing and non-condensing boilers, each combined with one of three domestic hot water (DHW) setups: no integrated DHW, direct DHW, and DHW with a storage tank. For all system designs, production efficiency varied with the load ratio. Urban-scale simulations were carried out at 10-minute frequency using weather data for Heverlee, Belgium, from the year 2016. The primary objective of this dataset was to support the development of statistical tools for characterizing the heat transfer coefficient of building envelopes. However, the generated artificial datasets offer a wide range of typically hard-to-measure inputs, making them ideal for evaluating the impact of simulated components on the overall energy balance. While the initial focus was on the behaviour of individual buildings, these datasets are also valuable for urban-scale analyses, particularly in energy planning contexts.

Computer simulation of the soil water regime under an apple orchard in a mountainous area (using the example of the leached chernozem of the experimental agricultural station Gorno-Altaiskoe)

Relevance. Progressive degradation of farmland soils – erosion, salinization, desertification. Aim. To establish features of water-physical properties of leached chernozem under an apple orchard and associated patterns of soil profile moisture distribution in summer period when precipitation deficiency observed. Methods. Moisture content in soil horizons was determined by the gravimetric method. To determine the granulometric composition of soils, the pipette method was used. The soil bulk density was determined by the cutting ring method. For solid phase density determination the pycnometric method was used. The method of graphic interpolation was used for transition the soil texture classification from Russian to international one. Water infiltration modeling into the soil profile was carried out using the HYDRUS-1D program. The parameters of approximating of the water retention curve of soils by the Van Genuchten equation were obtained by the calculation method of pedotransfer functions «Rosetta Lite» of the RETC program, using data on soil density and soil texture. Results. It has been established that the upper well-structured horizons of leached chernozem under an apple orchard have a greater water-holding capacity; their water-retention curves are more flattened. The water retention curve of the more structureless B2k horizon, the soil texture of which is dominated by sandy fractions, is shifted towards lower humidity. During hot and dry summer period the moisture deficiency in the soil was noted only in the upper twenty-centimeter soil column (14 mm). The moisture of the lower horizons, where the bulk of tree roots are concentrated, is satisfactory. The model demonstrates the smallest discrepancies with the moisture values measured during the soil reclamation experiment one day after the start. The downward moisture penetration into the lower soil layers is prevented by low pressure in the clayey A and AB horizons. Selection of input parameters and debugging of the model based on experimental data allows it to be used to simulate further processes occurring in the soil. It was revealed that the formation of positive (upward) water flows, which ensure the “pull-up” of salts and substances from the lower part of the profile to the upper layers during dry periods of the year, has a significant impact on moisture distribution in the chernozem under the apple orchard.

3D modelling and simulation of thermal effects and dispersion of particles carrying infectious respiratory agents in a railway transport coach

Even though the COVID-19 pandemic now belongs to the long history of infectious diseases that have struck humanity, pathogenic biological agents continue to pose a recurring threat in private places, but also and mainly in places where the public congregates. In our recent research published in this journal in 2022 and 2023, we considered the illustrative example of a commuter train coach in which a symptomatic or asymptomatic passenger, assumed to be infected with a respiratory disease, sits among other travellers. The passenger emits liquid particles containing, for example, COVID-19 virions or any other pathogen. The size spectrum of particles varies depending on whether they are produced during breathing, speaking, coughing or sneezing. More specifically, droplets associated with breathing are in the range of 1–10 µm in aerodynamic diameter, while at the other end of the spectrum, drops associated with coughing can reach 100–1000 µm. In the first part of our research, we used Computational Fluid Dynamics (CFD) to model and simulate in 3D the transport and dispersion of particles from 1 µm to 1 mm in the turbulent flow generated by the ventilation of the railway coach. We used both the Eulerian approach and the Lagrangian approach and showed that the results were strictly similar and illustrated the very distinct aerodynamics, on one hand, of the aerosol of droplets suspended in the air and, on the other hand, of the drops falling or behaving like projectiles depending on their initial speed. In the second part of our research, we developed a model of filtration through a typical surgical mask and possible leaks around the mask if it is poorly adjusted. We resumed the twin experiment of the railway coach and compared the distribution of droplets depending on whether the passengers (including the infected one) wear masks or not and whether the masks are perfectly fitted or worn loosely. Our method made it possible to quantify the particles suspended in the air of the railway coach depending on whether the infected passenger wore their mask more or less well. In this third article, we specifically explore how thermal effects due to the presence of passengers influence the spatio-temporal distribution in the railway coach of aerosols produced by the breathing infected person. We demonstrate that the influence of thermal effects on aerodynamics is very significant and can be very favourable for air decontamination if the ventilation system is judiciously configured. Beyond its application to a commuter train, our work confirms the value of validated CFD tools for describing the airflow and dispersion of particles in complex spaces that do not always allow experimentation. The models that we have developed are applicable to any other semi-confined, ventilated public place, such as a classroom, a hospital room or a performance hall, and they enable the objective assessment of whether the occupation of these spaces could be critical with regard to infectious contamination and of how to limit this ubiquitous risk.

Establishment of a Basement Membrane-Related Prognosis Model and Characterization of Tumor Microenvironment Infiltration in Acute Myeloid Leukemia.

Background: Basement membrane is a special component of extracellular matrix of epithelial and endothelial tissues, which can maintain their normal morphologies and functions. It can also participate in tumor progression and affect tumor treatment. However, the roles of basement membrane-related genes (BMGs) in acute myeloid leukemia (AML) remain unknown. Material and methods: We downloaded the data of AML and normal samples from TCGA, GTEx, and GEO. Then, we performed bioinformatics analysis to identify differential BMGs. We calculated the risk score of the training cohort and divided it into two risk groups. In addition, we also introduced external cohorts, serving as validation cohorts, to estimate the accuracy of risk score. A nomogram was established based on the risk score and clinicopathological characteristics to predict the prognosis. Based on BMGs, AML patients of TCGA were clustered into 2 subtypes. To investigate the biological features and the association between immune cells and TME, we utilized GSVA to assess pathway enrichment and ssGSEA to quantify the levels of immune cell infiltration across samples. Results: We obtained 3 differential BMGs between AML and normal samples. The training cohort was divided into high- and low-risk groups based on the risk score. The Kaplan-Meier survival analysis indicated that the two groups had significant differences. The nomogram could be used to predict the survival outcomes of AML patients. Based on the clustering result, we found significant differences between the two gene clusters. Sankey's diagram suggested that cluster B was associated with the high-risk group and poor prognosis. GSVA analysis showed that cluster B was also related to the upregulation of intercellular and intracellular signal transduction pathways. In TME, resting mast cells, follicular helper T cells, and plasma cells decreased while monocytes increased in the high-risk group. In addition, the high-risk group was more sensitive to BTK and AKT inhibitors. Conclusion: Our study indicated that the nomogram model of BMGs could predict the prognosis of AML patients. Meanwhile, BMGs were correlated with immune TME in AML. A correct and comprehensive assessment of the mechanisms of BMGs in individuals will help guide more effective treatment.

Modified Green-Ampt model for infiltration analysis in loess area and its parameter determination and verification

Water infiltration into soil is important in geotechnical engineering. The classical Green-Ampt (GA) infiltration model is widely used in soil infiltration due to its physical significance, but it ignores the actual unsaturated layer in the infiltration process and has some deficiencies. Thus, the present study established a modified GA infiltration model (MLGA model) using Darcy’s infiltration law and continuity equation to fully consider the variation characteristics of the soil water profile in the infiltration process. The Philip model and the GA model have the same physical basis. By combining the internal relationship between the infiltration rate and cumulative infiltration of the two models, the expression of matrix suction of the MLGA model was obtained. The existing measured data was used to verify the correctness and applicability of the MLGA model. Finally, the sensitivity analysis of the critical parameters of the model was performed. The results showed that the MLGA model is reliable and can be used for water infiltration analysis in loess sites. When the MLGA model is used to calculate the infiltration depth, the maximum relative error between the calculated value and the measured data is less than 10%, and the average relative error is 5.54%, which indicates that the model has a high calculation accuracy. The average error of the MLGA model is 24.47% of the Kostiakov model and 80.42% of the existing modified GA model (LGAM model). Sensitivity analysis of the saturated permeability coefficient, initial water content, saturated water content, and matrix suction was performed using the single-factor disturbance method. The influence of each parameter on infiltration depth was summarized, and the sensitivity of each parameter was quantitatively evaluated, which revealed that saturated water content is a highly sensitive parameter. When using the MLGA model to calculate infiltration depth, the accuracy of saturated water content should be ensured first. Finally, the difference between the MLGA model and the LGAM model in describing the whole process of water infiltration is discussed, and the influence mechanism of critical parameters on the water infiltration process is deeply analyzed. The established MLGA model provides theoretical support for further study of the loess water infiltration mechanism.

Quantifying Dynamic Linkages Between Precipitation, Groundwater Recharge, and Streamflow Using Ensemble Rainfall‐Runoff Analysis

AbstractUnderstanding streamflow generation at the catchment scale requires quantifying how different components of the system are linked, and how they respond to meteorological forcing. Here we present a proof‐of‐concept study characterizing and quantifying dynamic linkages between precipitation, groundwater recharge, and streamflow using a data‐driven nonlinear deconvolution and demixing approach, Ensemble Rainfall‐Runoff Analysis (ERRA). Streamflow in our mesoscale, intensively farmed test catchment is flashy, but occurs at time lags that are too long to be plausibly attributed to overland flow. Instead, ERRA's estimates of the impulse responses of groundwater recharge to precipitation, and of streamflow to groundwater recharge, imply that this intermittent streamflow is primarily driven by precipitation infiltrating to recharge groundwater, followed by discharge of groundwater to streamflow. ERRA reveals that streamflow increases nonlinearly with increasing precipitation intensity or groundwater recharge, and exhibits almost no response to precipitation or recharge rates of less than 10 mm d−1. Groundwater recharge is both nonlinear, increasing more‐than‐proportionally with precipitation intensity, and nonstationary, increasing with antecedent wetness. Simulations with the infiltration model Hydrus‐1D can reproduce the observed water table time series reasonably well (NSE = 0.70). However, ERRA shows that the model's impulse response is inconsistent with the real‐world impulse response estimated from measured precipitation and groundwater recharge, illustrating that conventional goodness‐of‐fit statistics can be weak tests of model realism. Thus, our proof‐of‐concept study demonstrates how impulse responses estimated by ERRA can help clarify linkages between precipitation and streamflow at the catchment scale, quantify nonlinearity and nonstationarity in hydrologic processes, and critically evaluate simulation models.

Advanced 1D model of deep filtration in a porous wall with complex morphology

Advanced 1D model of deep filtration in a porous wall with complex morphology

Snowmelt Infiltration and Runoff From Seasonally Frozen Hillslopes in a High Mountain Basin

ABSTRACTThere is relatively little research on infiltration into seasonally frozen soils on mountain hillslopes and few evaluations of infiltration model performance in this environment exist. As a result, the application of existing infiltration estimation methods developed in level environments is uncertain for estimating spring runoff in mountain basins. A field study was conducted in the Canadian Rockies using 8 years of snowpack, liquid soil moisture, and temperature profile observations from steep north‐facing and south‐facing slopes. Seasonal infiltration was calculated using soil freezing characteristic curves, timeseries of soil volumetric water content and temperature. Infiltration was found to primarily follow the limited case postulated by Popov (1972), with only 1 year at one site undergoing unlimited infiltration where nearly all meltwater infiltrated. Infiltration was estimated using an equation for the limited case developed from extensive observations of seasonal infiltration, initial soil saturation, and peak SWE in Canadian prairie agricultural fields. Whilst this equation accurately estimated infiltration depths on these mountain hillslope sites, it was unsuitable for application due to a statistical association between its driving variables. Initial soil saturation had no influence on infiltration depths at these sites and so a simpler single‐variable infiltration equation to estimate infiltration depths based on peak SWE was developed and found to have good predictive capability. Alternative approaches using modelled cumulative melt or infiltration opportunity time also had good predictability. Runoff depths estimated from a water balance, assuming negligible evaporation and sub‐surface drainage, were reliably predicted using peak SWE or cumulative melt depths by single‐variable infiltration equations in the absence of soil moisture, texture, aspect, or slope information. The results provide insights into estimating snowmelt runoff on hillslopes from snowpack accumulation that has been observed in cold region mountains, despite the complexity of hillslope hydrology and frozen soil infiltration processes.

Flooding system optimization: Advantages of a hybrid approach to developing neural network filtration models

Flooding system optimization: Advantages of a hybrid approach to developing neural network filtration models

Coupling Study of Fracture Propagation-Filtration-Seepage during Hydraulic Fracturing Assisted Oil Displacement in Offshore Low-Permeability Reservoirs.

Offshore low-permeability reservoirs are mainly composed of complex fault-block structures with poor physical properties, which makes establishing an effective displacement relationship particularly challenging. Hydraulic fracturing assisted oil displacement (HFAD) can effectively increase the oil production of a single well by creating fractures to replenish the producing energy. In this study, the Khristianovich-Geertsma-de Klerk (KGD) model is used to calculate the propagation of vertical fractures, and the flow tube method is used to calculate the two-phase oil-water flow in filtration and seepage. The semianalytical mathematical model for coupling fracture propagation, filtration, and seepage of the HFAD fluid is established, followed by conducting the sensitivity analysis and the main controlling factors analysis. In contrast to conventional methods, the filtration and seepage of the HFAD fluid during the fracturing process are taken into account. Based on actual well data, the fracture half-length and the wellhead pressure are verified. The mean calculation accuracy of the fracture half-length is 88.5%, and the mean calculation accuracy of the wellhead pressure is 90.7%. The research results indicate that the fracture propagation and the filtration and seepage of the HFAD fluid occur simultaneously, including rapid propagation in the early stage, discontinuous propagation in the middle stage, and only infiltration without propagation in the later stage. Infiltration is considered a key factor in the fracture propagation of HFAD, with a higher infiltration rate leading to weaker energy storage at the fracture tip. The viscosity of the HFAD fluid significantly impacts fracture half-length and vertical infiltration distance, contributing 35% and 27%, respectively. To increase fracture half-length, select a thinner reservoir, increase HFAD fluid viscosity, and boost the injection rate. To increase the vertical infiltration distance, choose higher permeability reservoirs, reduce HFAD fluid viscosity, and increase cumulative injection volume. The results of the research study provide a valuable basis for the design of an HFAD construction scheme for offshore low-permeability reservoirs.

Modeling and Application of the Hydrus-2D Model for Simulating Preferential Flow in Loess Soil Under Various Scenarios

Soil hydraulic properties are mainly governed by the soil’s heterogeneity, anisotropy, and discontinuous structural characteristics, primarily when connected soil macropores characterize the structures. Therefore, researchers must document reliable hydrological models to elucidate how the soil medium affects the movement of soil water. This study, utilizing a field-scale staining tracer test, distinguishes between matrix flow and preferential flow areas in the seepage field of Xi’an loess. The Xi’an loess’s soil water characteristic curve (SWCC) was explored through field investigations and laboratory analyses. A dual-permeability model that couples matrix and macropore flow was developed using the Hydrus-2D model, enabling simulations of water migration under varying initial soil water content, rainfall intensity, and crack width. The results showed that (1) The SWCC of macropores in the preferential flow area exhibits a bimodal distribution, and the Fredlund & Xing model is applied for sectional fitting to obtain the corresponding soil water characteristic parameters. (2) Initial soil water content and rainfall intensity significantly influence water distribution, while crack width has a relatively minor effect. (3) The cumulative flux under the preferential flow is significantly higher than in the matrix area, and the wetting front depth increases with higher initial water content and rainfall intensity. This study reveals the key characteristics of preferential flow and moisture migration in the matrix zone and their influencing factors in loess. It constructs a two-domain infiltration model by integrating loess’s diverse structural characteristics and pore morphology. This model provides a theoretical basis and technical support for simulating preferential flow and studying the moisture dynamics of loess profiles.

Study on the cumulative effect of drip irrigation on the stability of loess slopes

Infiltration of irrigation water is an important factor affecting the stability of loess slopes. In this study, based on the Green-Ampt infiltration model. We analysed the cumulative effect of drip irrigation on the stability of loess slope through an indoor cumulative drip-irrigation infiltration test with a single-point source, which was combined with the Geo-Studio finite-element software. Our results show that: (1) infiltration of drip irrigation in loess slopes has an obvious cumulative phenomenon. The depth of infiltration and volumetric water content of underlying soil increase with increasing cumulative number of drip irrigation; (2) the infiltration time calculated by the classical and improved Green-Ampt infiltration models is more in line with the experimental results, with errors ranging from 4 to 11%. (3) Short-term 3-day drip irrigation creates a layer of infiltration area on the slope surface. The safety coefficient of the slope body is reduced by 0.01, which has less impact on the slope. Long-term 3-year drip irrigation increased the volumetric water content of the entire slope, and decreased the safety coefficient by 0.91, which had a greater impact on the slope. Our results have important scientific significance slope-disaster warnings, and prevention in loess areas.

Unsaturated hydraulic properties of recycled concrete aggregates blended with autoclaved aerated concrete grains for unbound road base materials in Vietnam

AbstractUnderstanding of hydraulic properties is necessary to evaluate the water infiltration and balance in a road course. An easily available hydraulic model can contribute to the design of urban flooding countermeasures and mitigation of urban heat islands by covering roads with pavements. Many studies have evaluated saturated hydraulic conductivity, but few studies of measurements and modeling of unsaturated hydraulic properties such as water retention and unsaturated hydraulic conductivity for roadbase materials have been done. Therefore, this study measured the unsaturated hydraulic properties of typical roadbase materials of recycled concrete aggregates (RCA) using an evaporation method in the laboratory. To improve the water retention capacity, RCA blended with autoclaved aerated concrete (AAC) grains were also used. The results showed that the Gardner–Campbell (GC) model described the hydraulic properties of tested roadbed materials well, and the inclusion of AAC grains increased the water-holding capacity effectively. As a case study, the GC model was incorporated into the Green–Ampt infiltration model to simulate the change in the infiltration rate over time. The simulated results analyzed the water infiltration characteristics well, and this approach would be a good tool to make a quick assessment of the infiltration process of roadbed materials.

Spatial and temporal variability in infiltration and soil characterization using ERT

ABSTRACT Infiltration of the aquifer is one of the primary processes of the hydrological cycle. It plays a crucial role in the estimation of artificial groundwater recharge, surface runoff, and soil erosion. The electrical resistivity tomography (ERT) surveys were carried out to characterize the subsurface soil, and double-ring experiments were carried out at different locations in the study area. The results estimated from the double-ring infiltrometer data were compared with the infiltration rates obtained from various models such as Horton, Green-Ampt, Kostiakov, etc. The parameters are to be calibrated under the same hydrological site conditions, and these models’ water content and constants were estimated using the Graphical method. The best-fit models were estimated for each site, and the performance of the infiltration models was assessed based on the correlation coefficient, coefficient of determination, and root mean square error (RMSE). Horton model showed minimum RMSE, maximum correlation coefficient, and coefficient of determination, i.e. 5.24, 0.99, and 0.98, respectively, at most sites. The ERT data showed that sand is the predominant material available in the subsurface, and the saturated infiltration rate lies in the range of the sand. Nonlinear regression modeling was used to develop novel infiltration rate models from infiltration data.

Numerical Determination of a Time-Dependent Boundary Condition for a Pseudoparabolic Equation from Integral Observation

The third-order pseudoparabolic equations represent models of filtration, the movement of moisture and salts in soils, heat and mass transfer, etc. Such non-classical equations are often referred to as Sobolev-type equations. We consider an inverse problem for identifying an unknown time-dependent boundary condition in a two-dimensional linear pseudoparabolic equation from integral-type measured output data. Using the integral measurements, we reduce the two-dimensional inverse problem to a one-dimensional problem. Then, we apply appropriate substitution to overcome the non-local nature of the problem. The inverse ill-posed problem is reformulated as a direct well-posed problem. The well-posedness of the direct and inverse problems is established. We develop a computational approach for recovering the solution and unknown boundary function. The results from numerical experiments are presented and discussed.