Water Flow Model Research Articles

Cross-Scale Modeling of Shallow Water Flows in Coastal Areas with an Improved Local Time-Stepping Method

A shallow water equations-based model with an improved local time-stepping (LTS) scheme is developed for modeling coastal hydrodynamics across multiple scales, from large areas to detailed local regions. To enhance the stability of the shallow water model for long-duration simulations and at larger LTS gradings, a prediction-correction method using a single-layer interface that couples coarse and fine time discretizations is adopted. The proposed scheme improves computational efficiency with an acceptable additional computational burden and ensures accurate conservation of time truncation errors in a discrete sense. The model performance is verified with respect to conservation and computational efficiency through two idealized tests: the spreading of a drop of shallow water and a tidal flat/channel system. The results of both tests demonstrate that the improved LTS scheme maintains precision as the LTS grading increases, preserves conservation properties, and significantly improves computational efficiency with a speedup ratio of up to 2.615. Furthermore, we applied the LTS scheme to simulate tides at grid scales of 40,000 m to 200 m for a portion of the Northwest Pacific. The proposed model shows promise for modeling cross-scale hydrodynamics in complex coastal and ocean engineering problems.

Multi-parameter modeling for prediction of gas–water production in tight sandstone reservoirs

Tight sandstone reservoirs are significant sources of natural gas reserves. As traditional reserves become increasingly scarce and costly, optimizing the development of these reservoirs becomes crucial. This study introduces a novel two-phase gas–water flow model for single wells, incorporating both Darcy and non-Darcy flow equations. These equations are derived from mass conservation and momentum principles for both gas and water phases. Using data from a real tight gas well, our model, which includes stress-sensitive phases for gas and water, outperforms traditional Darcy flow models. Specifically, the average relative deviations in daily production rates were 0.1815% for gas and − 0.2677% for water, which are significantly smaller compared to traditional Darcy flow models. Further application of the non-Darcy flow model reveals strategies to enhance well performance. For example, mitigating liquid lock damage within a 2 m radius near the well could restore the permeability from 0.045 to 0.143 mD, thereby tripling the daily gas production. This non-Darcy flow model is easy to implement and shows significant potential in forecasting production yields in tight sandstone reservoirs, highlighting its importance in the petroleum and natural gas industry.

Exploring Advanced Analysis Technique for Shallow Water Flow Models with Diverse Applications

The present article focuses on the analytical approach using fractional orders and its applicationin the dynamics of physical processes. Fractional order models align better with experimental data compared tonon-fractional ones. This study primarily focuses on employing the new approximate analytical method to solveshallow water models with fractional orders. Numerical examples within the Caputo fractional derivative showcasethe method’s application. Results for both integer and fractional orders are graphically depicted, demonstrating thefractional solutions’ closeness to actual data. Analysis of 3D and 2D fractional order graphs reveals convergencetoward integer order graphs as fractional derivatives approach non-fractional ones. This method shows promise fordirect application in solving targeted problems and can be easily adapted for other fractional nature problems.

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

Quantification of the soil hydraulic conductivity is key to the study of water flow and solute transport in unsaturated soils. Rapid advances in measurement technology have provided a large number of observations at different scales, offering unprecedented opportunities and challenges for the estimation of hydraulic parameters. This paper proposes an inverse estimation method for downscaling of observations on coarse scales to estimate hydraulic parameters on high-resolution scales. Due to the significant spatial heterogeneity, the inversion faces the problems of dynamics-based integration of data at different scales, model uncertainty due to hundreds and thousands of parameters, and computational consumption due to the large number of forward simulations. To overcome these problems, this paper uses an efficient Bayesian optimization DREAM(ZS) as an inverse framework, and incorporates an analytical upscaling method and Karhunen–Loève (KL) expansion to infer finer-scale saturated hydraulic conductivity distribution conditioned on coarse-scale measurements. The efficient upscaling method is used to link measurements and hydraulic parameters at different scales, and Karhunen–Loève (KL) expansion is incorporated to greatly reduce the dimension of the parameter to be estimated. To further improve the efficiency of the inversion, a locally one-dimensional (LOD) algorithm is used to solve the multidimensional water flow model at coarse scales. The proposed inverse model is applied in a series of numerical experiments to demonstrate its applicability and effectiveness under different flow boundary conditions, different levels of ratio between coarse- and fine-scale grids, different densities of observation points, and different degrees of statistic heterogeneity of soil mediums.

Climate change impact on groundwater resources in sandbar aquifers in southern Baltic coast

Shallow coastal aquifers are vulnerable hydrosystems controlled by many factors, related to climate, seawater-freshwater interactions and human activity. Given on-going climate change, sea level rise and increasing human impact, it is especially true for groundwater resources situated in sandbars. We developed numerical models of unsaturated zone water flow for two sandbars in northern Poland: the Vistula Spit and the Hel Spit using HYDRUS-1D. The simulations were performed for three types of land use: pine forest, grass cover and bare soil, for 2024–2100 based on weather data and sea level rise forecasts for two emissions scenarios (RCP 4.5 and RCP 8.5). The results present prognosis of groundwater recharge, water table level and water content changeability in near-term (2023–2040), mid-term (2041–2060), and long-term period (2081–2100). Expected sea level rise and decreasing hydraulic gradient of the sandbar aquifers will probably cause in-land movement of the freshwater–saltwater interface, leading to significant decrease or complete salinization of groundwater resources. The study shows that holistic monitoring including groundwater level and salinization, sea level rise, and metheorological data (precipitation amount and variability, temperature) is crucial for sustainable management of vulnerable aquifers located in sandbars.

Inverse modeling of frequency domain-based one-dimensional soil water flow in layered soils

Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (Ks) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of Ks everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying Ks utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between Ks and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of Ks. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of Ks. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous Ks. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK Ks is very similar to that of the VG Ks, although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK Ks can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation.

A 2D shallow water flow model with 1D internal boundary condition for subgrid-scale topography

In this work, a dynamic internal boundary condition is used as subgrid model in a two-dimensional (2D) model based on the shallow water equations in order to model narrow regions in the domain. In this way, computational savings are sought, since it is not necessary to discretize these regions with cells of reduced size. The new internal boundary condition simplifies other works where 1D–2D coupled models were presented, since the 1D model is a subgrid for the 2D mesh, so the coupling between both models is simple and direct. The coupling is performed using mass conservation, simplifying the calculation in the transfer between both models. Test cases are studied to validate the implemented boundary condition, and a mountain catchment as a realistic case. The results obtained with a fully 2D mesh and a 2D mesh with rills in narrow regions are very similar, with a large reduction in computational cost when using rills, both in test cases and in the realistic case. Thus, the use of the implemented internal boundary condition is an effective tool to study regions with narrow regions by reducing the computational cost with little loss of accuracy in the results.

A Graph Theory Approach for Spatial Data-Based Surface Water Flow Modeling

This research proposes an innovative approach that combines graph theory with spatial data to model surface water flow with the Single Flow Direction (SFD) concept, also known as the D8 algorithm. The objective is to show the water flow from the ground surface to a lower place. The research methodology involves collecting spatial data from the Digital Elevation Model (DEMNAS) in raster data type format. Test results show that the effectiveness of the graph approach in modeling water flow can produce clear flow output. This happens because each pixel traversed by water is connected by a line that forms a well-defined water flow path. This study significantly stimulates the development of more sophisticated modeling tools and practical applications in the future. This can help in more efficient management of water resources or produce more accurate flow modeling, contributing to improved understanding and better management of the environment.

Oxidation of Phenol and Acetone in a Model Water Flow in Continuous Mode at High Pressure

The oxidation of the “water-phenol-acetone” system, simulating the organic component of the concentrated water runoff from the Bisphenol-A plant of PJSC Kazanorgsintez, was experimentally studied in the temperature range of 523÷873 K, pressure 25 MPa, duration 2÷4 min in continuous mode. Air oxygen taken with excess coefficients equal to 10÷30 was used as an oxidizing agent. The composition of the oxidation reaction product, the indicator of chemical oxygen demand, the pH of the initial sample and reaction products, and the conversion were determined. A decrease in the initial organic compounds in the model runoff has been established.

Multicomponent image-based modeling of water flow in heterogeneous wet shale nanopores

Shale contains abundant multicomponent nanopores with different wettability. Water flow in multicomponent nanoporous systems is still unclear due to the effects of mineral composition, complex pore-throat topology, and heterogeneous wettability. This work develops a contact angle-dependent numerical model for nanoconfined water flow considering heterogeneous wettability, slip effect, and effective viscosity. Water flow in single-component (i.e., clay, organic, inorganic) and multicomponent nanoporous media reconstructed utilizing image fusion techniques is systematically investigated. Results show that the enhancement factor increases exponentially, and the tortuosity increases with increasing contact angle. Water flow is inhibited under strongly hydrophilic conditions, with the enhancement factor linearly negatively correlated with specific surface area. Under hydrophobic conditions, the throat aspect ratio is inversely related to the enhancement factor, which is suppressed in quasi-circular pores. Water flow is restricted in clay pores and enhanced in organic pores due to the differences in pore-throat size and wettability. For the heterogeneous wetting system, the global flow is enhanced compared to no slip and homogeneous wetting conditions. Affected by clay and organic pores with different wettability, the velocity is non-uniformly enhanced, and the effect diminishes as water flows. This work provides a numerical perspective for water flow in heterogeneous wet nanoporous systems.

Mechanistically derived macroscopic root water uptake functions: The α and ω of root water uptake functions

AbstractWater uptake by plant roots is an important component of the soil water balance. Predicting to what extent potential transpiration from the canopy, that is, transpiration demand, can be met by supply of water from the soil through the root system is crucial to simulate the actual transpiration and assess vegetation water stress. In models that simulate the dynamics of vertical soil water content profiles as a function of water fluxes and soil water potential gradients, the root water uptake (RWU) distribution is represented by macroscopic sink terms. We present RWU functions that calculate sink terms based on a mechanistic model of water flow in the soil–root system. Based on soil–root hydraulics, we define α‐supply functions representing the maximal uptake by the root system from a certain soil depth when the root collar water potential equals the wilting point, ω‐supply factors representing the maximal supply from the entire root system, and a critical ωc factor representing the potential transpiration demand. These functions and factors are subsequently used to calculate RWU distributions directly from potential transpiration or demand and the soil water potentials. Unlike currently used approaches, which define α‐stress functions and ω factors representing ratios of actual uptake to uptake demand, the supply‐based formulations can be derived directly from soil and root hydraulic properties and can represent processes like root hydraulic redistribution and hydraulic lift.

Waterfront developments and engineered canals in the UAE

Engineered canals and waterfront developments as a means to revitalize aging riverfront and coastal areas, dominated until the mid-thirties by industrial buildings and warehouses, have been at the forefront of many American and European cities. Urban revitalization is accomplished after prolonged public participation and has succeeded to transform abandoned areas to healthy public spaces, renovating old warehouses and industrial buildings to apartments with water views, and keeping alive the historical memory of a city. In contrast, in the United Arab Emirates (UAE), most of these waterfront developments, such as Al-Qana, a recent project in Abu Dhabi promote forms of modern, spectacular architecture that project a sense of departure from tradition, local culture and architecture. This is also visible in the area around the Dubai canal, which has opted for a modern development on its banks, replacing parts of an existing open park. A project that diverges from such an approach is the two-decades old waterfront project in the city of Sharjah, UAE. Al-Qasba in Sharjah aimed for a more balanced approach, intertwining new architectural forms with hybridized Islamic ornaments. The current article analyzes these three UAE waterfront development projects, focusing on the one in Abu Dhabi. In order to assess the water quality in these engineered canals on the long term we created simulation waterflow models using 2D Finite Element Surface Water Modelling System (FESWMS). Our hydrodynamic modeling results indicate that water velocities in some canals was better than others. Furthermore, on the long-term Al-Qana may require mechanical means in order to maintain healthy waterflow conditions.

Modeling water flow and volumetric water content in a degraded peat comparing unimodal with bimodal porosity and flux with pressure head boundary condition

AbstractDegraded peatlands release large amounts of greenhouse gases. The development of effective mitigation and management measures requires an understanding of relevant site‐specific biogeochemical and hydraulic processes. However, the simulation of water fluxes and vadose zone state variables of degrading peatlands relies on proper process description, parameterization of hydraulic functions, and representation of the boundary conditions. The objective of this study was to analyze the effects of unimodal versus bimodal soil hydraulic functions and pressure head versus flux‐type lower boundary conditions (LBCs) on the calculated hydraulic characteristics of a degraded peat profile. HYDRUS‐1D was used to study the hydraulic flow dynamics parameterized with data from a weighable groundwater lysimeter for the period from May 1 to December 31, 2019. Simulations comparing uni‐ and bimodal hydraulic functions showed only minor differences. Simulations of soil water pressure at a depth of 30 cm using a flux‐type LBC (RMSE: 27 cm, where RMSE is root mean square error) performed better than simulations using a pressure head LBC (RMSE: 48 cm). The pressure head LBC performed better at simulating volumetric water contents in 30‐cm depth than the flux LBC variant (RMSE: 0.05 vs. 0.09 cm3 cm−3). For specific site conditions with a shallow, fluctuating groundwater table and temporary air entrapment, the choice of LBC was important for a more accurate simulation of soil water fluxes and volumetric water content.

Root hydraulic properties: An exploration of their variability across scales.

Root hydraulic properties are key physiological traits that determine the capacity of root systems to take up water, at a specific evaporative demand. They can strongly vary among species, cultivars or even within the same genotype, but a systematic analysis of their variation across plant functional types (PFTs) is still missing. Here, we reviewed published empirical studies on root hydraulic properties at the segment-, individual root-, or root system scale and determined its variability and the main factors contributing to it. This corresponded to a total of 241 published studies, comprising 213 species, including woody and herbaceous vegetation. We observed an extremely large range of variation (of orders of magnitude) in root hydraulic properties, but this was not caused by systematic differences among PFTs. Rather, the (combined) effect of factors such as root system age, driving force used for measurement, or stress treatments shaped the results. We found a significant decrease in root hydraulic properties under stress conditions (drought and aquaporin inhibition, p < .001) and a significant effect of the driving force used for measurement (hydrostatic or osmotic gradients, p < .001). Furthermore, whole root system conductance increased significantly with root system age across several crop species (p < .01), causing very large variation in the data (>2 orders of magnitude). Interestingly, this relationship showed an asymptotic shape, with a steep increase during the first days of growth and a flattening out at later stages of development. We confirmed this dynamic through simulations using a state-of-the-art computational model of water flow in the root system for a variety of crop species, suggesting common patterns across studies and species. These findings provide better understanding of the main causes of root hydraulic properties variations observed across empirical studies. They also open the door to better representation of hydraulic processes across multiple plant functional types and at large scales. All data collected in our analysis has been aggregated into an open access database (https://roothydraulic-properties.shinyapps.io/database/), fostering scientific exchange.

Numerical Study of Pore Water Pressure in Frozen Soils during Moisture Migration

Frost heaving in soils is a primary cause of engineering failures in cold regions. Although extensive experimental and numerical research has focused on the deformation caused by frost heaving, there is a notable lack of numerical investigations into the critical underlying factor: pore water pressure. This study aimed to experimentally determine changes in soil water content over time at various depths during unidirectional freezing and to model this process using a coupled hydrothermal approach. The agreement between experimental water content outcomes and numerical predictions validates the numerical method’s applicability. Furthermore, by applying the Gibbs free energy equation, we derived a novel equation for calculating the pore water pressure in saturated frozen soil. Utilizing this equation, we developed a numerical model to simulate pore water pressure and water movement in frozen soil, accounting for scenarios with and without ice lens formation and quantifying unfrozen water migration from unfrozen to frozen zones over time. Our findings reveal that pore water pressure decreases as freezing depth increases, reaching near zero at the freezing front. Notably, the presence of an ice lens significantly amplifies pore water pressure—approximately tenfold—compared to scenarios without an ice lens, aligning with existing experimental data. The model also indicates that the cold-end temperature sets the maximum pore water pressure value in freezing soil, with superior performance to Konrad’s model at lower temperatures in the absence of ice lenses. Additionally, as freezing progresses, the rate of water flow from the unfrozen region to the freezing fringe exhibits a fluctuating decline. This study successfully establishes a numerical model for pore water pressure and water flow in frozen soil, confirms its validity through experimental comparison, and introduces an improved formula for pore water pressure calculation, offering a more accurate reflection of the real-world phenomena than previous formulations.

The time validity of Philip's two‐term infiltration equation: An elusive theoretical quantity?

AbstractThe two‐term infiltration equation is commonly used to determine the sorptivity, , and product, , of the dimensionless multiple and saturated soil hydraulic conductivity from cumulative vertical infiltration measurements (L) at times (T). This reduced form of the quasi‐analytical power series solution of Richardson's equation of Philip enjoys a solid physical underpinning but at the expense of a limited time validity. Using simulated infiltration data, Jaiswal et al. have shown this time validity to equal about 2.5 cm of cumulative infiltration. The goals of this work are twofold. First, we investigate the extent to which cumulative infiltration measurements larger than 2.5 cm bias the estimates of and . Second, we investigate the impact of epistemic errors on the inferred time validities and parameters. Partial infiltration curves up to 2.5 cm of cumulative vertical infiltration improve substantially the agreement between actual and least squares estimates of and . But this only holds if the data generating infiltration process follows Richardson's equation and experimental conditions satisfy assumptions of soil homogeneity and a uniform initial water content. Otherwise, autocorrelated cumulative infiltration residuals will bias the least squares estimates of and . Our findings reiterate and reinvigorate earlier conclusions of Haverkamp et al. and show that epistemic errors deteriorate the physical significance of the coefficients of infiltration functions. As a result, the parameters of infiltration functions cannot simply be used in storm water and vadose zone flow models to forecast runoff and recharge at field and landscape scales unless these predictions are accompanied by realistic uncertainty bounds. We conclude that the time validity of Philip's two‐term equation is an elusive theoretical quantity with arbitrary physical meaning.

Physics-Informed Neural Networks for Modeling Water Flows in a River Channel

The impacts incurred by floods regularly affect the planet&#x0027;s population, inflicting social and economic problems. Optimal control strategies based on reservoir management may aid in controlling floods and mitigating the resulting damage. To this end, an accurate dynamic representation of water systems is needed. In practice, flood control strategies rely on hydrological forecasting models obtained from conceptual or data-driven methods. Encouraged by recent works, this research proposes a novel surrogate model for water flow in a river channel based on Physics-Informed Neural Networks (PINNs). This approach achieved promising results regarding the assimilation of real-data measurements and parameter identification of differential equations that govern the underlying dynamics. This work investigates PINN performance in a simulated environment built directly from a configuration of the Saint-Venant equations. The objective is to create a suitable model with high prediction accuracy and scientifically consistent behavior for use in real-time applications. The experiments revealed promising results for hydrological modeling and presented alternatives to solve the main challenges found in conventional methods while assisting in synthesizing real-world representations. <i>Impact Statement</i>&#x2014;The research seeks to contribute to the hydrological modeling area with a surrogate model based on Physics-Informed Neural Networks to water flow in a watershed. In practice, these models use conceptual or data-driven methods. Conceptual models to reach the precision provided by the methodology use large numbers of physical parameters. These parameters can demand deep knowledge about the environment and are possibly hard to identify in a complex basin. On the other hand, while data-driven methods do not require such knowledge about the dynamic system, they depend on a reliable and useful database to guarantee the accuracy of system behavior. We introduce PINNs as a viable solution for training neural networks with a few training data and estimating the PDE parameters that govern the underlying dynamics. In addition, we present a novel strategy for training PINNs inspired by Bayesian inference for parameter estimation problems. The research aims to bring forward opportunities to the nontrivial task of hydrological modeling and tools for balancing learning from both physics and data. Consequently, to develop concepts for real-time applications.

Energy stable and structure-preserving schemes for the stochastic Galerkin shallow water equations

The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges that motivate the central advances of this paper. Starting with a spatially one-dimensional hyperbolicity-preserving, positivity-preserving stochastic Galerkin formulation of the parametric/uncertain shallow water equations, we derive an entropy-entropy flux pair for the system. We exploit this entropy-entropy flux pair to construct structure-preserving second-order energy conservative, and first- and second-order energy stable finite volume schemes for the stochastic Galerkin shallow water system. The performance of the methods is illustrated on several numerical experiments.

Study on Numerical Simulation of Gas–Water Two-Phase Micro-Seepage Considering Fluid–Solid Coupling in the Cleats of Coal Rocks

The increasing demand for natural gas energy will promote unconventional natural gas, such as coal seam gas and shale gas, to play a key role in future energy development. The mechanical properties of coal seams are weaker compared with conventional natural gas reservoirs. The fluid–solid coupling phenomenon exists widely at the pore scale and macro scale of coal seams, and runs through the whole process of coalbed gas exploitation. The objective of this study is to establish a microscale gas–water flow model for coalbed methane considering fluid structure coupling. Frist, this study used scanning electron microscopy (SEM) to obtain microscopic pore images of coal rocks. Then, we constructed a numerical model to simulate the movement of coalbed methane and water within the scale of coal cleats based on the Navier–Stokes equation, phase field method, and solid mechanics theory. Finally, we analyzed the effects of injection pressure and wettability on the microscopic two-phase seepage characteristics and displacement efficiency of coal. Our research shows that when the injection pressure is increased from 60 kPa to 120 kPa, the displacement completion time is shortened from 1.3 × 10−4 s to 7 × 10−5 s, and the time is doubled, resulting in a final gas saturation of 98%. The contact angle increases from 45° to 120°, and the final gas saturation increases from 0.871 to 0.992, an increase of 12.2%.

Effects of geometry on the thermal-fluid dynamics of a transition water flow in a square heated asymmetric cavity channel

Cavity channels candidate as a promising passive cooling configuration in thermal management. The superior performance and the limited scientific investigation regarding cavity channels dictate the need for better understanding of the thermal-fluid dynamics. To the best knowledge of the authors, there are few works investigating the effect of the geometry on the thermal-fluid dynamics of cavity channels with no focus on thermal data and quantification of the recirculation effect which can depend on geometrical parameters. In this work, numerical RANS simulations were performed in ANSYS Fluent with the kT-kL-ω turbulence model for a transitional water flow in an asymmetric square cavity channel with different attachment angles in the range of 20°–90°. The optimal heat transfer performance in terms of uniform and high Nusselt numbers is provided by the configuration with an angle in the range of approximately 30°–40°. Recirculation plays an important role in enhancing heat transfer and its strength is associated with the penetration capacity in the boundary layer. Two regions of strong and weak recirculation are identified along the channel; when the recirculation is weak, other mechanisms such as the thinning of the thermal boundary layer play a more important role. By increasing the attachment angle it is shown the local thinning of the thermal boundary layer, an augmentation of the magnitude of the negative turbulent heat flux peak, and a similarity of the conductive sublayer thickness with the recirculation strength.