Flow and Transport Phenomena through Heterogenous Media in Groundwater Systems

1. Introduction

Globally, groundwater is an indispensable and invaluable source for producing drinking water, agricultural irrigation [1], industrial processes [2], and related welfare decision making [3]. Particularly in arid and semi-arid regions with abundant surface water sources, groundwater often stands as the primary, and sometimes sole, drinking water resource. However, escalating human activities, driven by increasing livelihood and development needs, have contributed to the degradation of groundwater quality. Due to these factors, aquifer systems are displaced from their natural equilibrium, both quantitatively and qualitatively. Inadequate management and protection measures during the planning and execution of development projects in recharge areas result from negligent operations of groundwater resources. Overexploitation of aquifers leads to a decline in groundwater quality and nearly irreversible contamination of the aquifer system. Experience over recent decades has revealed that once groundwater is tainted by chemical, biological, or radiological agents, cleanup becomes exceedingly challenging, and remediation entails substantial costs [4]. Consequently, safeguarding groundwater against depletion and pollution is pivotal for sustainable water development.

Growing apprehension surrounding environmental protection issues, particularly pollution, and the substantial costs associated with remediation policies propels the advancement and implementation of groundwater management models. These models integrate optimization procedures with groundwater flow and transport models. In decision-making processes that necessitate a comprehension of the hydrogeological environment, a critical consideration is uncertainty, primarily arising from incomplete concepts or descriptions of processes and an inherent lack of information about the aquifer’s properties. Enhancing our understanding of the physical and chemical processes within aquifer systems facilitates more dependable decision making and mitigates the investments required for water management.

When dealing with groundwater flow and transport processes in heterogeneous aquifers, it is essential to account for associated features inherent in this environment.

Following continuum mechanics, a deterministic macroscopic framework can be established to analyze quantities, decomposing each into spatially averaged Representative Elementary Volume (REV). The deviation of these quantities from the average is significantly smaller than the typical length order of the REV. This averaging methodology is not applicable to Brownian motion distributions. It plays a crucial role in transport through advection–dispersion mechanisms characterized by the Péclet number. These mechanisms involve the usage of Darcy’s velocity and Fick’s hydrodynamic dispersion, often expressed in the conventional form of empirical or theoretical terms for diffusive fluxes. Nevertheless, the approach allows for implementing macroscopic (i.e., volume-averaged) conservation laws for extensive quantities, utilizing spatiotemporal derivatives that address the scale of the REV.

The influence of media heterogeneity on flow and transport equations (FE and TE, respectively) becomes apparent through a non-dimensional analysis of the corresponding macroscopic equations. These equations establish relationships involving the typical distance of the hydraulic head gradient, the slope/divergence of the permeability/dispersivity change, and their mean values. The theoretical analysis of deterministic FE can impact stochastic TE. Consequently, stochastic methods can be employed to simulate contaminant transport, and from the deterministic theoretical framework, one can derive stochastic transport properties. Furthermore, due to the volume-averaging procedure, the deterministic macroscopic extensive momentum balance equation can incorporate a momentum flux, indicating the dispersion of specific momentum (i.e., a macroscopic quantity derived from the product of density and velocity deviations).

The momentum components representing dispersion, advective, and diffusive fluxes are considerably smaller than the non-deviation quantities in the macroscopic balance momentum equation. The significant difference in orders of magnitude justifies separating two approximations for the momentum balance equation. The primary approximation operates on the REV scale, while the secondary one works at a smaller adjacent scale, such as the pore scale. The secondary approximation is a hyperbolic transient partial differential equation associated with the dispersion of a specific momentum rate and its advective and diffusive fluxes. During an abrupt pressure change (i.e., the impact of a pressure impulse), inertia may briefly dominate over drag, causing the momentum balance equation to conform to a wave equation. This latter can be represented either by a non-linear shockwave or a linear compaction wave equation. Such waves drive the displacement of fluids and solutes.

In addressing a coupled transport phenomenon, the phase energy balance becomes a focal point due to temperature-related constitutive relations. These include factors such as an isotropic elastic solid with a strain-dependent temperature associated with the momentum balance, solute mass transfer influenced by a change in phase temperature gradient (Soret number), and phase energy transfer affected by a change in solute concentration gradient (Dufour number). Consequently, abrupt changes in prime variables, such as pressure and temperature, are propagated throughout the phase mass-momentum-energy system.

Moreover, this coupled transport phenomenon necessitates informed decision making regarding the spatiotemporal utilization of water–energy–food (WEF), entwined with subjective considerations related to these WEF elements, directly impacting human welfare. Decision-making processes must consider causality-driven directed information involving extensive big data analysis, especially concerning designated units. This is essential for overcoming water production’s uncertainties in quantity and quality (e.g., chemical and microbiological effects).

All these factors underscore the inherent complexity of investigating flow and transport in heterogeneous aquifers.

The articles featured in this Special Issue encompass a broad spectrum of topics pertinent to groundwater dynamics. These include well hydraulics, protection from contamination, recharge, parameter estimation, integrated management, and environmental impact assessment. Additionally, the collection delves into exploring models and numerical solution methods, providing a comprehensive and diverse perspective on various facets of groundwater dynamics.

2. Special Issue Overview

This Special Issue, entitled “Flow and Transport Processes in Groundwater Systems,” contains five papers. In what follows, we briefly describe each study.

Chen et al. (contribution 1) investigated the influence of drainage on groundwater flow within the Hetaoyu coal field in the Longdong area. The research employed a coupled three-dimensional transient groundwater flow model and a one-dimensional fracture water flow model to simulate water flow processes in a multilayer aquifer. The findings highlight the substantial impact of mine construction on groundwater resources in the heterogeneous porous-fractured aquifer system. During the coal mining phase, the formation of new water-conducting fractures led to a significant increase in mine water inflow, resulting in a groundwater drawdown of up to 23 m and a descending funnel covering approximately 4.5 square kilometers. This drawdown surpassed the locally regulated limit value set by the Water Authority, indicating the necessity for corresponding actions to address the situation.

Mei et al. (contribution 2) introduced an innovative analytical approach for the quantitative estimation of groundwater seepage both through and beneath a fully penetrating cut-off wall. Given the intricate nature of the seepage problem arising from the interplay between these two paths, the authors devised a method to obtain analytical solutions for flow rates. This involved superimposing drawdowns from two distinct models: one considering only leakage through the wall body and the other focusing solely on seepage beneath the wall. The accuracy and applicability of the proposed method were then assessed through comparison with a numerical model. The findings underscore the substantial impact of wall penetration depth, permeability, and thickness on seepage flow. The method presents a straightforward yet efficient way of rapidly estimating aquitard seepage quantities.

Sbai and Larabi (contribution 3) developed an innovative approach employing a moving mesh for modeling unconfined groundwater flow, utilizing a mixed-hybrid finite element approximation. The methodology involves adjusting a layered mesh to conform to the water table interface, treated as a kinematic boundary condition. The validity of the approach was confirmed through both analytical and numerical solutions. The authors demonstrated that the mixed-hybrid finite element approximation is effective for highly heterogeneous and anisotropic aquifers, offering more accurate solutions even with coarser grids than conventional fixed-grid numerical methods. This makes it a suitable approximation technique, particularly before conducting advective particle tracking or simulations involving solute/heat transport. The simulated phreatic surface also lacks cellwise interpolation errors and remains independent of the vertical grid size, a notable advantage over fixed mesh methods.

Marwa et al. (contribution 4) explored the integrated management of sustainable groundwater exploitation in the Toshka District, Egypt, against a large-scale development initiative to mitigate overpopulation along the Nile River and address imminent food shortages. The study employed a coupled groundwater flow and solute transport model to assess the environmental impact in the region. Various pumping scenarios were simulated to evaluate their effects on groundwater depletion and water quality. The research also delved into the impacts of climate change and increased water requirements for crops. Significant water level fluctuations in the lake emerged as a crucial factor influencing aquifer hydraulics and flow direction. The solute transport model developed by the authors was applied to simulate the spatial distribution of salinity and the lateral movement of pollutants emanating from ongoing activities. The study’s findings are poised to assist decision-makers in formulating environmental impact assessment criteria for sustainable development in the area.

Groundwater recharge is an important parameter affecting the use of groundwater resources. Ponded infiltration tests are often conducted to investigate how land surface flooding events affect infiltration and groundwater recharge. Faybishenko (contribution 5) introduces the pioneering concept of fuzzy dual permeability for fractured porous media. This concept is rooted in a fuzzy systems analysis of ponded infiltration test results conducted in fractured basalt. The author systematically reexamined outcomes from tests conducted in various locations. Fuzzy clustering and fuzzy regression methods were then applied to elucidate the time-depth waterfront penetration, enabling the characterization of phenomena involving rapid flow through a predominantly fractured component and slow flow through a porous matrix component. The results indicate that integrating the fuzzy systems approach into hydrogeological analysis and modeling holds substantial promise for addressing challenges characterized by imprecise, vague, and ambiguous information. This innovative approach is envisioned to have applications in water resources management, decision-making processes, and risk analysis, particularly in characterizing uncertainties related to flow and transport phenomena in heterogeneous geological formations.

3. Conclusions

The primary aim of this Special Issue was to spotlight recent advancements in groundwater studies, focusing on fundamental inquiries into water flow, solute transport, and heat transfer. The exploration employed various tools, including experimental techniques, mathematical modeling of physical mechanisms, management strategies, and insights from case studies. The Special Issue comprised five high-quality papers that covered a spectrum of topics, including well hydraulics, groundwater contamination and protection, hydraulic parameter estimation, integrated management, environmental impact assessment, and numerical modeling techniques.

The compilation of papers in this Special Issue emphasizes the significance of fundamental research in comprehending the behavior of aquifers, many of which currently face stressful conditions. The findings from these studies directly contribute to developing an enhanced understanding of groundwater dynamics and efficient aquifer utilization. Future research endeavors should continue in the direction of integrative investigations, exploring the interactions of groundwater with other components of the hydrogeochemical cycle, such as the atmosphere, surface waters, soils, and lithosphere.