Wettability has a dramatic impact on fluid displacement in porous media. The pore level physics of one liquid being displaced by another is a strong function of the wetting characteristics of the channel walls. However, the quantification of the effect is still not clear. Conflicting data have shown that in some oil displacement experiments in rocks, the volume of trapped oil falls as the porous media becomes less water-wet, while in some microfluidic experiments the volume of residual oil is higher in oil-wet media. The reasons for this discrepancy are not fully understood. In this study, we analyzed oil displacement by water injection in two microfluidic porous media with different wettability characteristics that had capillaries with constrictions. The resulting oil ganglia size distribution at the end of water injection was quantified by image processing. The results show that in the oil-wet porous media, the displacement front was more uniform and the final volume of remaining oil was smaller, with a much smaller number of large oil ganglia and a larger number of small oil ganglia, when compared to the water-wet media.

Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation.

In the present work, we evaluate the prediction capability of six pedotransfer functions (PTFs), reported in the literature, for the saturated hydraulic conductivity estimations (KS). We used a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. Additionally, six new PTFs were constructed for KS from clay percentage, bulk density, and saturation water content data. The results show, for the evaluated models, that one model presents an overestimation for KS > 0.5 cm h−1 values, three models have an underestimation for KS > 1.0 cm h−1, and two models have a good correlation (R2 > 0.98) but more than three parameters are necessary. Nevertheless, the last two models require 3–4 parameters in order to obtain optimization. On the other hand, the models proposed in this work have a similar correlation with fewer parameters. The fit is seen to be much better than using the existing ones, achieving a correlation of R2 = 0.9822 with only one variable and R2 = 0.9901 when we use two.

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0<β≤1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R2>0.999.

In the present work, we construct several artificial neural networks (varying the input data) to calculate the saturated hydraulic conductivity (KS) using a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. All of them were constructed using two hidden layers, a back-propagation algorithm for the learning process, and a logistic function as a nonlinear transfer function. In order to explore different arrays for neurons into hidden layers, we performed the bootstrap technique for each neural network and selected the one with the least Root Mean Square Error (RMSE) value. We also compared these results with pedotransfer functions and another neural networks from the literature. The results show that our artificial neural networks obtained from 0.0459 to 0.0413 in the RMSE measurement, and 0.9725 to 0.9780 for R2, which are in good agreement with other works. We also found that reducing the amount of the input data offered us better results.

In recent years, groundwater levels have been decreasing due to the demand in agricultural and industrial activities, as well as the population that has grown exponentially in cities. One method of controlling the progressive lowering of the water table is the artificial recharge of water through wells. With this practice, it is possible to control the amount of water that enters the aquifer through field measurements. However, the construction of these wells is costly in some areas, in addition to the fact that most models only simulate the well as if it were a homogeneous profile and the base equations are restricted. In this work, the amount of infiltrated water by a well is modeled using a stratified media of the porous media methodology. The results obtained can help decision-making by evaluating the cost benefit of the construction of wells to a certain location for the recharge of aquifers.

The infiltration phenomena has been studied by several authors for decades, and numerical and approximate results have been shown through the asymptotic solution in short and long times. In particular, it is worth highlighting the works of Philip and Parlange, who used time and volumetric content as independent variables and space as a dependent variable, and found the solution as a power series in t1/2 that is valid for short times. However, several studies show that these models are not applicable to anomalous flows, in which case the application of fractional calculus is needed. In this work, a fractional time derivative of a Caputo type is applied to model anomalous infiltration phenomena. Fractional horizontal infiltration phenomena are studied, and the fractional Boltzmann transform is defined. To study fractional vertical infiltration phenomena, the asymptotic behavior is described for short and long times considering an arbitrary diffusivity and hydraulic conductivity. Finally, considering a constant flux-dependent relation and a relation between diffusivity and hydraulic conductivity, a fractional cumulative infiltration model applicable to various types of soil is built; its solution is expressed as a power series in tν/2, where ν∈(0,2) is the order of the fractional derivative. The results show the effect of superdiffusive and subdiffusive flows in different types of soil.

The snap-off is an instability phenomenon that takes place during the immiscible two-phase flow in porous media due to competing forces acting on the fluid phases and at the interface between them. Different theoretical approaches have been proposed for the development of mathematical models that describe the dynamics of a fluid/fluid interface in order to analyze the snap-off mechanism. The models studied here are based on the “small-slope” approach and were derived from the mass conservation and other governing equations of two-phase flow at pore scale in circular capillaries for pure and complex interfaces. The models consist of evolution equations; highly nonlinear partial differential equations of fourth order in space and first order in time. Although the structure of the models for each type of interface is similar, different numerical techniques have been employed to solve them. Here, we propose a unifying numerical framework to solve the group of such models. Such a framework is based on the Fourier pseudo-spectral differentiation method which uses the Fast Fourier Transform (FFT) and the inverse FFT (IFFT) algorithms. We compared the solutions obtained with this method to the results reported in the literature in order to validate our framework. In general, acceptable agreements were obtained in the dynamics of the snap-off.