Groundwater Flow In Heterogeneous Aquifers Research Articles

Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources

<abstract> <p>In nature, aquifers are usually composed of distinct kinds of media, i.e., heterogeneous domains rather than homogeneous domains. Groundwater level and flow changes in such domains are more complicated than those in homogeneous domains; thus, building a mathematical model for addressing groundwater flow in heterogeneous aquifers is the present research goal. In conventional research on similar topics, many one-dimensional (1D) analytical models have been presented, but it is challenging to simulate real-world scenarios. This study develops a two-dimensional (2D) analytical model for modeling groundwater flow in a conceptual sloping heterogeneous domain imposed by variable recharge. This model can consider distinct slope angles, medium heterogeneity, and any type of lateral recharge for a semi-infinite domain. The results indicate that groundwater level and flow discharge are greatly affected by the abovementioned factors. The recharge intensity significantly affects the peak of the groundwater level. For example, when the recharge rate increases by 30%, the peak water level increases by 50% as the groundwater flows from the sandy loam zone to the loam zone. The loops delineating the relationship between discharge and groundwater level for different bottom slopes cannot become close for heterogeneous aquifers. The presented 2D analytical model can simulate and better predict results of groundwater changes than previous 1D analytical models. Further, this model can simultaneously consider the effect of varying recharge over time and space on groundwater level change.</p> </abstract>

Deep transfer learning for groundwater flow in heterogeneous aquifers using a simple analytical model

Deep learning models exhibit good interpolating ability, but their performance is often hindered by the scarcity of data in groundwater problems. Analytical models (solutions) provide a first-order physical principle for groundwater flow, but they are only applicable under specific conditions, such as when the aquifer is homogeneous. This study introduces a novel framework for deep transfer learning that integrates the strengths of both methods and overcomes their limitations. Specifically, we propose a deep learning model guided by a simple analytical model to predict groundwater flow in heterogeneous aquifers. It differs from previous deep learning model by incorporating the knowledge from the simple analytical model and utilizing transfer learning technique to improve the prediction in relatively complicated problems where the analytical model is not applicable. The model is tested against the traditional deep learning model Deep Back Propagation Neural Network (DBPNN) in the scenarios with unknown hydraulic conductivity fields. The results show that the proposed model significantly improve the accuracy of hydraulic head predictions by fusing analytical knowledge with neural networks. The hydraulic conductivity mainly affects the parameters of the shallow layers in the neural network, which enables the use of transfer learning techniques in more complex problems. In all test scenarios, the prediction errors of the proposed model are much smaller than those of the DBPNN. Additionally, the proposed model performs satisfactorily even with limited training data.

Influence of nonuniform recharge on groundwater flow in heterogeneous aquifers

<abstract><p>The composition of soils in aquifers is typically not homogeneous, and soil layers may be cracked or displaced due to geological activities. This heterogeneity in soil distribution within aquifers affects groundwater flow and water level variations. In the present study, we established a two-dimensional (2D) mathematical model that considers the influence of surface recharge on groundwater flow in heterogeneous sloping aquifers. By considering temporal variations in surface recharge, slope angle and aquifer heterogeneity, the simulated results are expected to better reflect real conditions in natural aquifers. The effects of aquifer heterogeneity on groundwater flow and water levels are particularly significant in sloping aquifers. The study's findings indicate that even when the soil composition remains constant, variations in groundwater level and flow may be considerable, depending on factors such as soil alignment, slope angle of the aquifer's base layer and the direction of water flow.</p></abstract>

Lagrangian Complexity Persists with Multimodal Flow Forcing in Compressible Porous Systems

We extend previous analyses of the origins of complex transport dynamics in poroelastic media to the case where the input transient signal at a boundary is generated by a multimodal spectrum. By adding harmonic and anharmonic modal frequencies as perturbations to a fundamental mode we examine how such multimodal signals affect the Lagrangian complexity of poroelastic flow. While the results apply to all poroelastic media (industrial, biological and geophysical), for concreteness we couch the discussion in terms of unpumped coastal groundwater systems having a discharge boundary forced by tides. Particular local regions of the conductivity field generate saddles that hold up and braid (mix) trajectories, resulting in unexpected behaviours of groundwater residence time distributions and topological mixing manifolds near the tidal boundary. While increasing spectral complexity can reduce the occurrence of periodic points, especially for anharmonic spectra with long characteristic periods, other signatures of Lagrangian complexity persist. The action of natural multimodal tidal signals on confined groundwater flow in heterogeneous aquifers can induce exotic flow topologies and mixing effects that are profoundly different to conventional concepts of groundwater discharge processes. Taken together, our results imply that increasing spectral complexity results in more complex Lagrangian structure in flows through poroelastic media.

Random walk evaluation of Green’s functions for groundwater flow in heterogeneous aquifers

The use of the Walk on Grid (WOG) approach for the reliable evaluation of the Green’s function associated with groundwater flow scenarios in heterogeneous geologic media is explored. The study rests on the observation that, while the Green’s function method (GFM) is one of the most significant and convenient approaches to tackle groundwater flow, Green’s function evaluation is fraught with remarkable difficulties in the presence of realistic groundwater settings taking place in complex heterogeneous geologic formations. Here WOG approach is used to simulate pressure dissipation by lattice random walk and establish a quantitative relationship between space-time distribution of random walkers and the Green’s function associated with the underlying flow problem. WOG-based Green’s function method is tested (a) in three scenarios where analytical formulations are available for the Green’s function and (b) in two groundwater flow systems with increased level of complexity. Our results show that WOG can (a) accurately evaluate the Green’s function, being highly efficient when the latter can be analytically expressed in terms of infinite series; and (b) accurately and efficiently evaluate temporal evolutions of hydraulic heads at target locations in the heterogeneous systems. As such, a WOG-based approach can be employed as an efficient surrogate model in scenarios involving groundwater flow in complex heterogeneous domains.

Improved Characterization of Groundwater Flow in Heterogeneous Aquifers Using Granular Polyacrylamide (PAM) Gel as Temporary Grout

AbstractThe range of options for investigation of hydraulic behavior of aquifers from boreholes has been limited to rigid, cumbersome packers, and inflatable sleeves. Here we show how a new temporary borehole sealing technique using soft grains of polyacrylamide (PAM) gel as a sealing material can be used to investigate natural groundwater flow dynamics and discuss other possible applications of the technology. If no compressive stress is applied, the gel packing, with a permeability similar to open gravel, suppresses free convection, allowing for local temperature measurements and chemical sampling through free‐flowing gel packing. Active heating laboratory and field experiments combined with temperature measurements along fiber optic cables were conducted in water‐filled boreholes and boreholes filled with soft grains of polyacrylamide gel. The gel packing is shown to minimize the effect of free convection within the well column and enable detection of thin zones of relatively high or low velocity in a highly transmissive alluvial aquifer, thus providing a significant improvement compared to temperature measurements in open boreholes. Laboratory experiments demonstrate that under modest compressive stress to the gel media the permeability transitions from highly permeable to nearly impermeable grouting. Under this configuration the gel packing could potentially allow for monitoring local response pressure from the formation with all other locations in the borehole hydraulically isolated.

Mixed finite element methods for groundwater flow in heterogeneous aquifers

This paper is concerned with a comparison of the performance and efficiency of mixed finite element methods for solving single phase fluid flow in porous media. Particular attention is given to the accurate determination of the groundwater fluxes. The linear systems generated by the mixed finite element method (MFEM) are indefinite. Symmetric positive definite linear systems are generated through the introduction of Lagrange multipliers giving rise to the mixed hybrid finite element method (MHFEM). The convergence behaviour of the numerical approximations is investigated over a range of conductivity coefficients from heterogeneous, isotropic and diagonal to discontinuous, anisotropic and full, on both triangular and quadrilateral, structured and distorted meshes. The robustness and efficiency of various preconditioned solvers is investigated in terms of optimality with respect to both mesh size and conductivity coefficient.

Adaptive-grid simulation of groundwater flow in heterogeneous aquifers

The prediction of contaminant transport in porous media requires the computation of the flow velocity. This work presents a methodology for high-accuracy computation of flow in a heterogeneous isotropic formation, employing a dual-flow formulation and adaptive gridding. The dual equations, describing the hydraulic head and the streamfunction, are numerically solved through finite element approximations. The application of classic finite-element methods requires a rather large number of nodes to represent suitably the flow in high-contrast formations. We present a mesh-adaptive approach that enhances the accuracy of the numerical flow solution for a given computational effort. We rely on an a posteriori error estimator to identify areas where refinements of the finite element mesh are needed or unrefinements are acceptable. We also demonstrate through numerical experiments that the developed methodology efficiently enhances accuracy through successive mesh adaptation.

Technical comment on: “On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers”, by M.L. Kavvas and A. Karakas (Journal of Hydrology Vol. 179 (1996) 321–351)

In this note, we demonstrate that statements made in a recent paper by Kavvas and Karakas (1996) (J. Hydrol., 179: 321–351), concerning the assumptions underlying the stochastic model of solute transport in spatially-heterogeneous aquifers developed by Kabala and Sposito (1991) (Water Resour. Res., 25: 341–350), are incorrect.

Response to comments of Z.J. Kabala and G. Sposito on the paper “On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers” by M.L. Kavvas and A. Karakas (Journal of Hydrology Vol. 179 (1996) 321–351)

It is shown that the comment of Kavvas and Karakas (J. Hydrol., 179: 321–351, 1996) concerning the inapplicability of Eqs. (A10) and (6) in Kabala and Sposito (Water Resour. Res., 27: 341–350, 1991) to transport by nonstationary flow is correct, and that Eqs. (A10), (6) and (7) of Kabala and Sposito (1991) are incorrect for the transport case treated in that paper. The correct expressions for Eqs. (A10) and (6) in Kabala and Sposito (1991) are provided. It is also shown that the claims of Kabala and Sposito (1998) concerning the theoretical developments in Kavvas and Karakas (1996) have no basis.

On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers

In this study the exact and approximate deterministic partial differential equations of the time-space evolution of mean solute concentration, of solute concentration two-point moment and of solute concentration n-point moment for conservative solute transport by unsteady and steady groundwater flow in a heterogeneous aquifer were developed in the real time-space domain under second-order cumulant expansion. These derivations were performed by means of the cumulant expansion method, combined with the calculus for the time-ordered exponential and with the calculus for Lie operator. The mean solute transport equations which describe the time-space evolution of mean conservative solute concentration under transport by unsteady and steady groundwater flows in a heterogeneous aquifer have convective-dispersive forms whose convective and dispersive coefficients are defined precisely in terms of the mean and covariance functions of the pore flow velocity random field. However, owing to the spatial nonuniformity of groundwater flow in heterogeneous porous media a new convective coefficient, besides the standard mean velocity vector, appeared in the derived mean solute transport equations in the case of steady flows. In the case of transport by unsteady groundwater flow in a heterogeneous aquifer, the new convective coefficient (besides the standard mean velocity vector) is due to the non-zero divergence of the pore flow velocity. The fundamental reason for the convective-dispersive form of the mean transport equations is the second-order truncation of the formal cumulant expansion. In the derived mean solute transport equations the macroscopic dispersion coefficient emerges as the time integral of the covariance function of the pore flow velocity. However, both in the case of transport by unsteady groundwater flow and in the case of transport by steady spatially nonstationary-nonuniform groundwater flow the macroscopic dispersion coefficients and convective coefficients vary with spatial locations within the porous medium. Only in the case of transport by steady spatially stationary-nonuniform flow are both the macroscopic dispersion coefficient and the convective coefficient constant with respect to spatial location within the heterogenous aquifer. Therefore, only in the case of conservative solute transport by steady spatially stationary-nonuniform groundwater flow in a heterogeneous aquifer does the mean transport equation apply to all spatial locations within the aquifer with the same parameter values at each time instant.

Continuous time stochastic analysis of groundwater flow in heterogeneous aquifers : M. M. Hantush & M. A. Marino, Water Resources Research, 31(3), 1995, pp 565–575

Continuous time stochastic analysis of groundwater flow in heterogeneous aquifers : M. M. Hantush & M. A. Marino, Water Resources Research, 31(3), 1995, pp 565–575

Continuous Time Stochastic Analysis of Groundwater Flow in Heterogeneous Aquifers

The problem of depth‐averaged groundwater flow in heterogeneous aquifers is looked at from a stochastic point of view. The Galerkin finite element version of the linearized stochastic equation governing the flow is solved analytically in time using an eigenvalue‐eigenvector technique. The stochastic solution, which is valid for small variance of aquifer log transmissivity, relates spatial and temporal variabilities of aquifer head to aquifer heterogeneity, stochastic recharge, and random initial head. The computational effort requires the evaluation of integrals of matrices whose elements are linear functions of the nodal mean heads. The solutions are obtained for the exact (i.e., continuous) and quasi‐steady approximation of the mean head. Aquifer‐head temporal covariances are evaluated using standard matrix operations once the storage matrix is inverted and the associated generalized eigenvalue problem is solved. Implication of the level of spatial discretization on the performance of the solution is examined, and the influence of aquifer heterogeneity on spatial and temporal variances of hydraulic heads is investigated in the presence of a semipervious boundary.

A perturbation boundary element code for steady state groundwater flow in heterogeneous aquifers

A boundary element code is developed for the steady state Darcy's flow in heterogeneous porous media. The solution is based on the expansion of the piezometric head into perturbation series. The governing equation is decomposed into a Laplace equation and a sequence of Poisson equations with known right‐hand sides. Regular boundary element procedure is applied for their solutions. Three numerical examples with moderate hydraulic conductivity variations are provided to demonstrate the applicability of the code. The convergence of the perturbation solution is discussed using a one‐dimensional problem.