Solute transport in unsaturated porous media can be viewed as a coupled phenomenon with water and heat transport, together with mechanical behaviour of media. In this paper, solute transport is formulated mathematically considering heat and water flow in deformable porous media. Advection, dispersion and diffusion of chemical species in the liquid phase are considered. Convection and conduction for heat flow is taken into account. Water flow is considered in both vapour and liquid phases. Equilibrium equation, energy conservation, mass conservation and linear momentum for water, gas and solute are written and solved simultaneously using finite element method. The developed model is validated by solving some examples and comparing results with the results of experimental observation.

Large water distribution systems can be highly vulnerable to penetration of contaminant factors caused by different means including deliberate contamination injections. As contaminants quickly spread into a water distribution network, rapid characterization of the pollution source has a high measure of importance for early warning assessment and disaster management. In this paper, a methodology based on Probabilistic Support Vector Machines (PSVMs) is proposed for identifying the contamination source location in drinking water distribution systems. To obtain the required data for training the PSVMs, several computer simulations have been performed over multiple combinations of possible contamination source locations and initial mass injections for a conservative solute. Then the trained probabilistic SVMs have been effectively utilized to identify the upstream zones that are more likely to have the positive detection results. In addition, the results of this method were compared and contrasted with Bayesian Networks (BNs) and Probabilistic Neural Networks (PNNs). The efficiency and versatility of the proposed methodology were examined using the available data and information from water distribution network of the City of Arak in the western part of Iran.

River networks consist of many branches that connect at river confluences. Because pollutants usually enter the river in different situations from the upstream branches, it is essential to investigate the mixing process through the river network. Based on the cell concept and separation of advection and dispersion operations, this study developed a new analytical relationship through the confluences of rivers. A physical model of the Y-shaped junction was created in the laboratory, and four inlet flow discharges 25, 21, 12, and 9 l/s and three initial concentrations of sodium chloride solution 80, 160, and 200 g/L were selected as study parameters. Then, the concentration-time curves along the sub-branches, the intersection, and the downstream of the river's main channel were taken at 2-second intervals. In order to evaluate the efficiency of the analytical model, the parameters of the model were first calculated by coding based on its framework and using the least squares method. It was observed that the presented model could produce double-peaked curves and also cover experimental data series precisely. The dispersion coefficients and the related time parameter in the presented model (T) were found to increase by moving downstream of the river junction. It was also observed that the Peclet numbers 〖(P〗_e=xu/D) are increased like dispersion coefficients by increasing the distance downstream of the confluence. In addition, the research results showed that increasing the residence time parameter in dispersion cells (T) causes growth in the dispersion coefficient, despite increasing the residence time in advection cells (β).