This study presents a detailed analysis of the morphological evolution of beaches in the Bocagrande sector of Cartagena de Indias, Colombia, over more than a decade, based on periodic monitoring of six beach profiles. The beaches in this area are in bays constrained by headlands and promontories located at both ends of each bay. Changes in shoreline position, dry beach widths, and the surf zone were evaluated using aerial photographs, orthophotos, satellite imagery, and field data, together with sediment size determined through granulometric analysis. The results indicate that the beaches exhibit characteristics of wave-dominated, exposed systems, with sediments classified as fine sand that tend to increase in grain size toward the northern sector of the bay. A cyclical variation in the shoreline was observed, with average retreats and advances ranging from 5 to 10 m, depending on the climatic season. Dry beach widths ranged from 10 to 90 m, decreasing toward the north. Differences in morphology between profiles and shoreline variation are attributed to the climatic season, profile location within the bay, and proximity to a coastal structure and its particular type. Beach profiles were fitted to conceptual equilibrium profile models using traditional equations, which yielded a coefficient of determination of 0.76; when machine learning algorithms were applied, this value improved to 0.99. This study provides an important baseline for future morphological assessments and coastal management efforts in the city and places with similar characteristics, particularly considering ongoing shoreline protection projects.
Studying sub-atmospheric pressure patterns in emptying pipeline systems is crucial because these processes could cause collapses depending on the installation conditions (the underground pipe covering height, type, fill, and pipeline stiffness class). Pipeline studies have focused more on filling than on emptying processes. This study presents an analysis of the following variables: air pocket pressure, water velocity, and water column length during the emptying of an irregular pipeline without an air valve by two-dimensional computational fluid dynamics (2D CFD) model simulation using the software OpenFOAM. The mathematical model predicts the experimental values of the study variables. Water velocity vectors are also analysed within the experimental facility, assessing the sensitivity of the drain valve to different openings and changes in water column length during the hydraulic phenomenon.
Methylene blue and safranin are dyes that may have harmful effects on both aquatic ecosystems and human health. This research aims to simulate an industrial-scale operational adsorption column for competitively removing these dyes from wastewater, employing Cedrela odorata L. as a bioadsorbent material. Aspen Adsorption (v.1) software simulated an industrial-scale packed-bed adsorption column under various configurations. Moreover, machine learning algorithms were applied to predict the results generated by Aspen, representing an advancement in the development of new strategies in this field. The kinetic model employed was the Linear Driving Force (LDF) model. Adsorption efficiencies of 96.1% were achieved for both methylene blue and safranin using the Langmuir–LDF model. The Freundlich–LDF model showed efficiencies of 94.8% for methylene blue and 96% for safranin. Meanwhile, the Langmuir–Freundlich–LDF model achieved up to 96.1% for methylene blue and 94.8% for safranin. This study demonstrated the feasibility of simulating the competitive adsorption of dyes in solution at an industrial scale using Cedrela odorata L. as a bioadsorbent. The application of LDF kinetic models and adsorption isotherms (Langmuir, Freundlich, and Langmuir–Freundlich) resulted in high adsorption efficiencies, highlighting the potential of this approach for the remediation of dye-contaminated effluents as a viable method for predicting the performance of full-scale packed columns. Machine learning algorithms were implemented in this research, obtaining R2 higher than 0.996 for validation and testing stages for the responses of the model.
The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases—water and air—typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system’s transient behaviour.
Recently, emptying processes have been studied in experimental facilities in pipelines, but there is a lack regarding applications in actual pipelines, which permits establishing the risk of collapse because of sub-atmospheric pressure occurrence. This research presents a mathematical model to simulate the emptying process of water supply networks, and the application to a water emptying pipeline with nominal diameter of 1000 mm and 578 m long which is located on the southern of Cartagena, Bolívar Deparment, Colombia. In the application, both pipes and the air valve data manufacturer were considered. The behavior of all hydraulic and thermodynamic variables is considered. Results show that is crucial to know sub-atmospheric pressure values to prevent the collapse of the pipeline. The application of the mathematical model confirms that the hydraulic system is well designed depending on air valve sizes and maneuvering of drain valve.
During the filling process in pressurized hydraulic systems, sudden pressure changes generated inside the pipes can cause significant damage. To avoid these excessive overpressures, air valves should be installed to allow air exchange between the inside and outside during the filling process. This study presents a mathematical model to analyse the hydraulic transients during filling processes. This model, which has already been validated in small laboratories, is now applied to real large-scale systems that consist of DN400 and DN600 pipelines from Empresa Mixta Metropolitana S.A (EMIMET – Group Global Omnium), which is the company that manages the water supply of the metropolitan area of Valencia (from the Drinking Water Treatment Station to the municipalities). The mathematical model for large pipes is validated by comparing the experimental measurements and the results of model.
An air pocket's behaviour inside of a pipeline during transient conditions is of great importance due to its effect on the safety of the hydraulic system and the complexity of modeling its behaviour. The emptying process from water pipelines needs more assessment because the generation of troughs of subatmospheric pressure may lead to serious damage. This research studies the air pocket parameters during an emptying process from a water pipeline. A well-equipped experimental facility was used to measure the pressure and the velocity change throughout the water emptying for different air pocket sizes and valve opening times. The phenomenon was simulated using a one-dimensional (1D) developed model based on the rigid formulation with a non-variable friction factor and a constant pipe diameter. The mathematical model shows good ability in predicting the trough of subatmospheric pressure value as the most important parameter which can affect the safety of hydraulic systems.
Over the past few years, there has been significant interest in the importance of reversible hydro-pumping systems due to their favorable flexibility and economic and environmental characteristics. When designing reversible lines, it is crucial to consider dynamic effects and corresponding extreme pressures that may occur during normal and emergency operating scenarios. This research describes essentially the turbine operation, although various boundary elements are mathematically formulated and presented to provide an understanding of the system complexity. Different numerical approaches are presented, based on the 1D method of characteristics (MOC) for the long hydraulic circuit, the dynamic turbine runner simulation technique for the behavior of the power station in turbine mode and the interaction with the fluid in the penstock, and a CFD model (2D and 3D) to analyze the flow behavior crossing the runner through the velocity fields and pressure contours. Additionally, the simulation results have been validated by experimental tests on different setups characterized by long conveyance systems, consisting of a small scale of pumps as turbines (at IST laboratory) and classical reaction turbines (at LNEC laboratory). Mathematical models, together with an intensive campaign of experiments, allow for the estimation of dynamic effects related to the extreme transient pressures, the fluid-structure interaction with rotational speed variation, and the change in the flow. In some cases, the runaway conditions can cause an overspeed of 2–2.5 of the rated rotational speed (NR) and an overpressure of 40–65% of the rated head (HR), showing significant impacts on the pressure wave propagation along the entire hydraulic circuit. Sensitivity analyses based on systematic numerical simulations of PATs (radial and axial types) and reaction turbines (Francis and Kaplan types) and comparisons with experiments are discussed. These evaluations demonstrate that the full-load rejection scenario can be dangerous for turbomachinery with low specific-speed (ns) values, in particular when associated with long penstocks and fast guide vane (or control valve) closing maneuver.
The probabilistic analysis of streamflow and drought event durations plays a crucial role in the efficient and sustainable management of existing water resources in the region. This approach involves the collection of historical hydrological data from river gauging stations, the use of statistical and probabilistic models, and the assessment of hydrological projections at different return periods to provide valuable information for society to understand the potential impacts of extreme events. The analysis is carried out on the Sinú River in Colombia, with consideration given to both the presence and absence of the Hydropower Plant Urrá I. The results reveal that, under natural conditions, a higher number of return periods correspond to less extreme drought flows and longer temporal durations. However, when the hydropower plant is operational, the occurrence and duration of drought are influenced by the regulations implemented during energy generation. The results of this analysis can guide water resource management policies, considering the operation of the hydroelectric plant, thereby enabling decisions that enhance the resilience and sustainability of the river’s hydrological conditions and communities that depend on it.
Air pockets generated during emptying operations in pressurized hydraulic systems cause significant pressure drops inside pipes. To avoid these sudden pressure changes, one of the most widely used methods involves the installation of air valves along the pipeline route. These elements allow air exchange between the exterior and the interior of the pipe, which alleviates the pressure drops produced and thus prevents possible breaks or failures in the structure of the installation. This study uses a mathematical model previously validated by the authors in smaller installations to simulate all hydraulic variables involved in emptying processes over time. The purpose of these simulations is the validation of the mathematical model in real large-scale installations, and to do this, the results obtained with the mathematical model are compared with actual measurements made by the partner company. The hydraulic system selected for the study is a pipeline with a nominal diameter of 400 mm and a total length of 1020 m. The results obtained from the mathematical model show great similarity with the experimental measurements, thus validating the model for emptying large pipes.
Emptying processes are typical maneuvers that should be performed by water distribution companies for operation purposes. These processes involve a complex numerical analysis, since a set of algebraic and ordinary differential equations needs to be solved for the intricacy of hydraulic and thermodynamic formulations for two analyzed phases (liquid and gas). This research provides an implicit equation to compute exactly the final conditions in water emptying operations in single pipelines without an air valve (or admitted air). The implicit expression was developed by considering that for all final conditions, the water velocity is null, and thus, the water column length and air pocket pressure can be computed. The friction factor, internal pipe diameter, and opening maneuvers of drain valves do not disturb the final conditions in draining processes. The developed implicit formulation was validated using experimental measurements in a pipeline with a total length of 4.36 m. The equation is of utmost importance, since it can be utilized for engineers to easily plan for future conditions in water distribution networks.
Emptying processes are operations frequently required in hydraulic installations by water utilities. These processes can result in drops to sub-atmospheric pressure pulses, which may lead to pipeline collapse depending on soil characteristics and the stiffness of a pipe class. One-dimensional mathematical models and 3D computational fluid dynamics (CFD) simulations have been employed to analyse the behaviour of the air–water interface during these events. The numerical resolution of these models is challenging, as 1D models necessitate solving a system of algebraic differential equations. At the same time, 3D CFD simulations can take months to complete depending on the characteristics of the pipeline. This presents a mathematical approach for directly solving air–water interactions in emptying processes involving entrapped air, providing a predictive tool for water utilities. The proposed mathematical approach enables water utilities to predict emptying operations in water pipelines without needing 2D/3D CFD simulations or the resolution of a differential algebraic equations system (1D model). A practical application is demonstrated in a case study of a 350 m long pipe with an internal diameter of 350 mm, investigating the influence of air pocket size, friction factor, polytropic coefficient, pipe diameter, resistance coefficient, and pipe slope. The mathematical approach is validated using an experimental facility that is 7.36 m long, comparing it with 1D mathematical models and 3D CFD simulations. The results confirm that the derived mathematical expression effectively predicts emptying operations in single water installations.
In Colombia, daily maximum multiannual series are one of the main inputs for design streamflow calculation, which requires performing a rainfall frequency analysis that involves several prior steps: (a) requesting the datasets, (b) waiting for the information, (c) reviewing the datasets received for missing or data different from the requested variable, and (d) requesting the information once again if it is not correct. To tackle these setbacks, 318 rain gauges located in the Colombian Caribbean region were used to first evaluate whether or not the Gumbel distribution was indeed the most suitable by performing frequency analyses using three different distributions (Gumbel, Generalized Extreme Value (GEV), and Log-Pearson 3 (LP3)); secondly, to generate daily maximum isohyetal maps for return periods of 2, 5, 10, 20, 25, 50, and 100 years; and, lastly, to evaluate which interpolation method (IDW, spline, and ordinary kriging) works best in areas with a varying density of data points. GEV was most suitable in 47.2% of the rain gauges, while Gumbel, in spite of being widely used in Colombia, was only suitable in 34.3% of the cases. Regarding the interpolation method, better isohyetals were obtained with the IDW method. In general, the areal maximum daily rainfall estimated showed good agreement when compared to the true values.
Water utilities frequently perform pipeline-emptying operations for maintenance, repair, and operational management. This process involves transient flow conditions with entrapped air. It must be carefully controlled, as the expansion of air pockets can generate sub-atmospheric pressures that may lead to pipeline collapse. The mathematical modelling of emptying processes with air valves has been extensively studied in recent years; however, such approaches typically rely on complex algebraic–differential equation systems. This study advances understanding of this phenomenon by proposing a novel procedure that uses a machine learning model to approximate system behaviour while avoiding fully coupled hydraulic formulations. An experimental facility consisting of a pipeline with an internal diameter of 0.042 m and a total length of 4.6 m was used, in conjunction with a complete regulation valve manoeuvre. The system was first calibrated using experimental data and subsequently employed in Monte Carlo simulations to generate a dataset for training the machine learning model. The results demonstrate that a Rational Quadratic Gaussian Process Regression model can accurately predict the minimum sub-atmospheric pressure, achieving a coefficient of determination greater than 0.999 during validation and testing. The proposed framework is presented as a proof-of-concept and has been validated only for the specific case study analysed. While the results highlight its potential to support planning for emptying operations under varying air-admission conditions and air-pocket sizes, further validation is required before generalising to real-world water distribution systems. For practical implementation, the model must be appropriately trained for each specific installation.
<p class="Resumen">El proceso de vaciado en conducciones de agua genera depresiones por la expansión del aire en el interior de las tuberías y esto podría causar el colapso del sistema dependiendo de las condiciones de instalación y de la rigidez de la conducción. En este artículo se presenta el análisis de sensibilidad del modelo matemático desarrollado por los autores, analizando los principales parámetros hidráulicos y termodinámicos que intervienen en este proceso tales como: diámetro interior de la tubería, factor de fricción, pendiente longitudinal de la tubería, coeficiente politrópico, diámetro de la ventosa, tamaño de la bolsa de aire y tiempo de apertura. Este análisis se realizó para dos casos posibles: Caso No. 1, tubería con el extremo aguas arriba cerrado; y Caso No. 2, tubería con una ventosa instalada en el extremo aguas arriba. Los resultados muestran que para el Caso No. 1 los parámetros que más inciden en las depresiones son la pendiente longitudinal de la tubería, el coeficiente politrópico y el tamaño de la bolsa de aire; mientras que para el Caso No. 2, la mayoría de los parámetros influyen significativamente durante el proceso de vaciado.</p>
Emptying pipelines can be critical in many water distribution networks because subatmospheric pressure troughs could cause considerable damage to the system due to the expansion of entrapped air. Researchers have given relatively little attention to emptying processes compared to filling processes. The intricacy of computations of this phenomenon makes it difficult to predict the behaviour during emptying, and there are only a few reliable models in the literature. In this work, a computational model for simulating the transient phenomena in single pipes is proposed, and was validated using experimental results. The proposed model is based on a rigid column to analyse water movement, the air–water interface, and air pocket equations. Two practical cases were used to validate the model: (1) a single pipe with the upstream end closed, and (2) a single pipe with an air valve installed on the upstream end. The results show how the model accurately predicts the experimental data, including the pressure oscillation patterns and subatmospheric pressure troughs.
