Numerical simulation of density-driven flow and heat transport processes in porous media using the network method

Density-driven flow and heat transport processes in 2-D porous media scenarios are governed by coupled, non-linear, partial differential equations that normally have to be solved numerically. In the present work, a model based on the network method simulation is designed and applied to simulate these processes, providing steady state patterns that demonstrate its computational power and reliability. The design is relatively simple and needs very few rules. Two applications in which heat is transported by natural convection in confined and saturated media are studied: slender boxes heated from below (a kind of Bénard problem) and partially heated horizontal plates in rectangular domains (the Elder problem). The streamfunction and temperature patterns show that the results are coherent with those of other authors: steady state patterns and heat transfer depend both on the Rayleigh number and on the characteristic Darcy velocity derived from the values of the hydrological, thermal and geometrical parameters of the problems.The first author acknowledges the support of the Universidad Politécnica de Cartagena through a pre-doctoral scholarship and the economic support of the Universidad Católica del Norte to cover the costs to publish in open access

Calculation of seepage surface and water flow on pumping wells for unconfined aquifers employing the network method

Water scarcity has led to its extraction from underground reserves or aquifers, for which pumping wells are built. For this reason, the phenomenon has been mathematically (and then, computationally) modelled for either confined or unconfined aquifers. As former theoretical approaches to the problem, solution for groundwater flow in unconfined aquifers did not consider vertical flow and variables such as seepage surface were not studied. The aim of this work is to provide a methodology to estimate both parameters using a computational model based on the network method. This methodology consists on the analogy between electrical quantities (voltage and intensity) and geotechnical variables (water potential and flow). The results obtained with this tool are compared to those from scale models.We would like to thank the SéNeCa Foundation for the support given to this research and for the scholarship awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

Numerical simulation of seepage maps under dams with sheet piles on their ends

Seepage maps formed by both stream and equipotential lines, emerging under dams with sheet piles on their ends, can be determined by simulating the Laplace conjugate equations using a numerical technique such as the network method. Based on these maps, engineers can immediately deduce the amount of water circulating under the structure and design the sheet piles depth to safe values that allow to limit risks such as siphoning or erosion of the base of the dam. For a fix depth of the upstream sheet pile, seepage maps are shown for different configurations of the downstream sheet pile, in a 2D scenario with finite depth and with large extensions both upstream and downstream of the dam.We would like to thank the Séneca Foundation for the support given to this research, thanks to the scholarship awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

Verification against failure by piping on retaining structures applying the network method

When designing retaining structures, different phenomena must be studied in order to classify them as safe from a geotechnical point of view. Among them is pipping, a physical process related to seepage under the structure which leads to an unstable situation and might finally cause failure. In order to quantify this risk, a comparison between the critical gradient and the estimated hydraulic gradient is usually accepted. The calculation depends on geometric parameters, geotechnical data and flow boundary conditions, as well as the designed structure. Nevertheless, most of the universal solutions, such as graphics, have not been developed considering an anisotropic medium as foundation soil, so no realistic results are obtained. The aim of this work is to provide a methodology to obtain an estimation of the average gradient using a computational model based on the network method. This consists on the analogy between electrical magnitudes, such as voltage and intensity, and geotechnical variables, which are groundwater head and flow. The safety factor is calculated whether the soil is anisotropic or not, and so, the structure can be classified from a safety point of view.We would like to thank the Séneca Foundation for the support given to this research and for the scholarship awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

The dimensional character of permeability. Dimensionless groups that govern Darcy’s flow in anisotropic porous media.

The dimensional character of permeability in anisotropic porous media, that is,its dimension or dimensional equation, is an information that allows setting thedimensionless groups that govern the solution of the flow equation in terms ofhydraulic potential patterns. However, employing the dimensional basis {L, M,T} (length, mass, time), the dimensionless groups containing the anisotropic per-meability do not behave as independent monomials that rule the solutions. Inthis work, the contributions appearing in the literature on the dimensional char-acter of permeability are discussed and a new approach based on discriminatedand general dimensional analysis is presented. This approach leads to the emer-gence of a new and accurate dimensionless group,kxkyl∗2yl∗2x, a ratio of permeabilitiescorrected by the squared value of an aspect factor, beingl∗xandl∗ytwo arbitrarylengths of the domain in the directions that are indicated in their subscripts. Spe-cific values of this lengths, which we name ‘hidden characteristic lengths’, arealso discussed in this article. To check the validity of this dimensionless group,numericalsimulationsoftwoillustrative2-Dseepagescenarioshavebeensolved.The authors would like to thank SéNeCa Foundation for the support given to this research and for the scholarships awarded to Martínez-Moreno E. to carry out her doctoral thesis

Network model for the numerical solution of groundwater flow. Application to partially penetrating retaining structures in geotechnical engineering

Based on the network simulation method, a precise numerical model is designed for the 2‐D groundwater flow in porous and isotropic aquifers. If a partially penetrating impervious barrier exists, groundwater will flow downstream circumventing the underground structure. The network model is solved free code. Thanks to the powerful mathematical calculation algorithms implemented in is this type of codes, the provided solutions are quite precise for a relatively small grid size, with practically negligible computing times. The proposed model is applied to illustrative problems, providing hydraulic isopotentials and stream lines, showing that as the dam penetration depth increases the hydraulic gradient downstream decreases, thus reducing the risk of hydraulic failure.We would like to thank the Séneca Foundation for the support given to this research and for the scholarships awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

Regional flow and vertical heat transport in groundwater. Numerical solution for the study of temperature profiles

In this work, temperature patterns and profiles have been obtained in large 2-D groundwater scenarios, with constant and horizontal regional flow and thermal conditions that reproduce approximately real cases, such as the daily or seasonal variation of the soil surface temperature. For this purpose, a numerical model based on the network simulation method has been designed and applied to real scenarios to determine the correlation between derived temperature profiles and groundwater flow. The results of this first work allow to see more closely the possibility of addressing a much more complex problem, such as the determination of the regional velocity field from temperature profiles read from in situ wells.We would like to thank the Séneca Foundation for the scholarship awarded to José Antonio Jiménez Valera, which will allow us to continue this investigatio

Simultaneous determination of the position, release time and mass release rate of an unknown gas emission source in short-term emissions by inverse problem

This article proposes a protocol for the simultaneous determination of the position, release time and mass release rate of an unknown gas emission source from experimental data in the form of an inverse problem, since these are the main variables in the short duration release of pollutants. Records of pollutant concentration and of measurement time (with their inherent errors) carried out at two measuring stations are the input data for the inverse problem. The actions of the protocol are divided into two well-differentiated stages. In the first, the simulations are started for each iteration, the functionals are calculated to program the next iteration, setting the new values of measurement time and the distance of the emission source in downwind direction with respect to the measuring stations by comparing the simulated and experimental values, and so on until reaching the final solution. In the second, an analogous procedure is followed until the mass rate and the emission source position is obtained. In addition, it has been necessary to define a new coefficient that relates the effect of dispersion in the measurement time, the distance in the downwind direction and the atmospheric stability categories. The reliability of the proposed protocol is checked by means of a problem whose parameters are known a priori. First, the direct problem is solved to obtain the values of contaminant concentration and the measurement time of the stations. These variables are then affected by random errors of up to 2% to provide the input data for the inverse problem. In all the examples shown in this work, solutions have been obtained that can be considered very successful in this field of engineering.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

SICOMED_3D : simulación y diseño de problemas de consolidación de suelos con mechas drenantes

Contiene la descripción del funcionamiento del programa SICOMED_3D (‘consolidación en suelos multicapa, de geometría rectangular 3-D, con mechas parcial o totalmente penetrantes’), incluyendo el diseño y estructura de los modelos en red, los fundamentos teóricos del problema de consolidación y las bases para una caracterización adimensional que proporcione resultados universales. Se describe la interfaz de comunicación (entrada de datos y presentación de resultados gráficos) con el usuario. Se presentan aplicaciones que ilustran la aplicación de SICOMED_3D en los campos docente, profesional y de investigación

Simulación numérica del modelo de consolidación no lineal de Davis y Raymond

Escuela Técnica Superior de Ingeniería de Telecomunicación (ETSIT), Escuela Técnica Superior de Ingeniería Agronómica (ETSIA), Escuela Técnica Superior de Ingeniería Industrial (ETSII), Escuela Técnica Superior de Arquitectura y Edificación (ETSAE), Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos y de Ingeniería de Minas (ETSICCPIM), Facultad de Ciencias de la Empresa (FCCE), Parque Tecnológico de Fuente Álamo (PTFA), Vicerrectorado de Estudiantes y Extensión de la UPCT, Vicerrectorado de Investigación e Innovación de la UPCT, y Vicerrectorado de Internacionalización y Cooperación al Desarrollo de la UPCT[SPA] La ecuación de gobierno que define el proceso de consolidación en suelos saturados viene regida por el coeficiente de consolidación cv, de manera que, a valores mayores del mismo, el proceso de consolidación por disipación del exceso de presiones intersticiales es más rápido. El modelo de consolidación no lineal de Davis y Raymond asume que el valor de este coeficiente permanece constante durante todo el proceso, pero no así las propiedades del suelo de las cuales depende su valor. Empleando el método de redes, se ha resuelto numéricamente este modelo, obteniéndose soluciones muy precisas, con tiempos de computación mínimos. [ENG] The governing equation that defines the consolidation process in saturated soils is governed by the coefficient of consolidation cv, so that, for higher values of this, the consolidation process by dissipation of the excess pore pressure is faster. The nonlinear model of consolidation by Davis and Raymond considers that the value of this coefficient remains constant throughout the whole process, but not the soil properties of which depends on its value. Using the network method, the model has been solved numerically, obtaining very accurate solutions, with very low computing times.[ENG] The governing equation that defines the consolidation process in saturated soils is governed by the coefficient of consolidation cv, so that, for higher values of this, the consolidation process by dissipation of the excess pore pressure is faster. The nonlinear model of consolidation by Davis and Raymond considers that the value of this coefficient remains constant throughout the whole process, but not the soil properties of which depends on its value. Using the network method, the model has been solved numerically, obtaining very accurate solutions, with very low computing times