Laboratory analog and numerical study of groundwater flow and solute transport in a karst aquifer with conduit and matrix domains

Statistical evidence of recharge and supply controlling nitrate variability at springs discharging from the upper Floridan Aquifer

Over the last several decades, rising nitrate concentrations in springs discharging from north Florida's karstic Upper Floridan Aquifer have coincided with proliferation of algae in Florida spring runs and subsequent ecosystem degradation. As agriculture and development are primary contributors to groundwater nitrate and are predicted to continue expanding, understanding unique contributions and transmission pathways of nitrate pollution is vital to restoring impaired spring ecosystems. In this study, we use statistics and signal processing to analyze continuous nitrate timeseries data collected over five years at four north Florida springs. We quantified a significant, low-frequency annual signal in nitrate concentrations superimposed on increasing nitrate trends. We show nitrate concentrations at springs increase during the rainy season, potentially in response to recharge and seasonal fertilizer application. Thus, we suggest seasonal fluctuations observed in nitrate concentrations are caused by increased recharge of nutrient-rich soil waters through fractures that deliver water on relatively short timescales to conduits during the rainy season. We further speculate the steady, monotonically increasing concentration is maintained by accumulation of Nitrogen as slow flow through matrix porosity through the remainder of the year. Seasonal nitrate concentrations resulting from flow through karst aquifers may thus be poorly simulated using equivalent porous media models that are increasingly being used for nutrient management, because they do not capture heterogenous flow and transport dynamics.

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

In this recent work, the continuous dependence of double diffusive convection was studied theoretically in a porous medium of the Forchheimer model along with a variable viscosity. The analysis depicts that the density of saturating fluid under consideration shows a linear relationship with its concentration and a cubic dependence on the temperature. In this model, the equations for convection fluid motion were examined when viscosity changed with temperature linearly. This problem allowed the possibility of resonance between internal layers in thermal convection. Furthermore, we investigated the continuous dependence of this solution based on the changes in viscosity. Throughout the paper, we found an “a priori estimate” with coefficients that relied only on initial values, boundary data, and the geometry of the problem that demonstrated the continuous dependence of the solution on changes in the viscosity, which also helped us to state the relationship between the continuous dependence of the solution and the changes in viscosity. Moreover, we deduced a convergence result based on the Forchheimer model at the stage when the variable viscosity trends toward a constant value by assuming a couple of solutions to the boundary-initial-value problems and defining a difference solution of variables that satisfy a given boundary-initial-value problem.

Review of Laboratory Scale Models of Karst Aquifers: Approaches, Similitude, and Requirements

This review focuses on investigations of groundwater flow and solute transport in karst aquifers through laboratory scale models (LSMs). In particular, LSMs have been used to generate new data under different hydraulic and contaminant transport conditions, testing of new approaches for site characterization, and providing new insights into flow and transport processes through complex karst aquifers. Due to the increasing need for LSMs to investigate a wide range of issues, associated with flow and solute migration karst aquifers this review attempts to classify, and introduce a framework for constructing a karst aquifer physical model that is more representative of field conditions. The LSMs are categorized into four groups: sand box, rock block, pipe/fracture network, and pipe-matrix coupling. These groups are compared and their advantages and disadvantages highlighted. The capabilities of such models have been extensively improved by new developments in experimental methods and measurement devices. Newer technologies such as 3D printing, computed tomography scanning, X-rays, nuclear magnetic resonance, novel geophysical techniques, and use of nanomaterials allow for greater flexibilities in conducting experiments. In order for LSMs to be representative of karst aquifers, a few requirements are introduced: (1) the ability to simulate heterogeneous distributions of karst hydraulic parameters, (2) establish Darcian and non-Darcian flow regimes and exchange between the matrix and conduits, (3) placement of adequate sampling points and intervals, and (4) achieving some degree of geometric, kinematic, and dynamic similitude to represent field conditions.

Modeling the Matrix-Conduit Exchanges in Both the Epikarst and the Transmission Zone of Karst Systems

Usual conceptual models of karst hydrodynamics highlight the important role of unsaturated subsystems in recharge repartition. However, few of them have been compared with scarce suitable physically-based numerical models. Hybrid models that couple single continuum medium with discrete features promise an improved consideration of karst specificities. Here we evaluate their capability to properly reproduce interactions between a vertical conduit and the surrounding unsaturated matrix. We simulate the response of such a configuration to a single recharge event for various sets of parameters. We show the ability of hybrid models to reproduce the most significant behaviors described in the literature, i.e., transient storage and distribution of recharge, flow concentration towards conduits in the epikarst, and matrix-conduit exchanges varying in time and space. In addition to the explicit conduits, simulating variably saturated flows with the Richards equation and distinguishing the epikarst and the transmission zone are key elements to reproduce most processes. The contrasts between subsystems necessary to observe desired behaviors have been quantified. They are reinforced by the varying matrix saturation that causes realistic competition between matrix and explicit conduits. The study also highlights the need to deepen knowledge of the scaled medium properties we need to know to apply such models to actual cases.

Assessment of groundwater quality and remediation in karst aquifers: A review

Karst aquifers, capable of storing and transmitting large amount of water, are the main source of drinking water in many regions worldwide. Their excessive permeability leads to an enhanced vulnerability to retain and spread the contamination accordingly. From sustainability perspective, the environmental, economic and social impacts of karst contamination on water resources management are gaining more attention. In this study, an overview of hydrogeological processes and concepts regarding groundwater flow and contaminant transport in karstic systems is presented, followed by a short discussion on surface water and groundwater interaction. Due to the complexity of karstic systems, different approaches have been developed by researchers for investigating and understanding hydrogeological processes and groundwater behavior in karst which are reviewed herein. Additionally, groundwater contamination issues and the most common and effective remediation techniques in karstic terrains are discussed. Lastly, modeling techniques and remote sensing methods, as beneficial and powerful tools for assessing groundwater flow and contaminant transport in karst terrains, are reviewed and evaluated. In each section, relevant research works conducted for Puerto Rico are discussed and some recommendations are presented to complement the ongoing hydrogeological investigations on this island.

Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

A novel numerical model for groundwater flow in karst aquifers is presented. A discrete-continuum (hybrid) approach, in which a three-dimensional matrix flow is coupled with a one-dimensional conduit flow, was used. The laminar flow in the karst matrix is described by a variably saturated flow equation to account for important hydrodynamic effects in both the saturated and unsaturated zones. Turbulent conduit flow for both free surface and pressurized flow conditions was captured via the noninertia wave equation, whereas the coupling of two flow domains was established through an exchange term proportional to head differences. The novel numerical approach based on Fup basis functions and control-volume formulation enabled us to obtain smooth and locally conservative numerical solutions. Due to its similarity to the isogeometric analysis concept (IGA), we labeled it as control-volume isogeometric analysis (CV-IGA). Since realistic verification of the karst flow models is an extremely difficult task, the particular contribution of this work is the construction of a specially designed 3D physical model ( dimensions: 5.66 × 2.95 × 2.00 m) in order to verify the developed numerical model under controlled laboratory conditions. Heterogeneous porous material was used to simulate the karst matrix, and perforated pipes were used as karst conduits. The model was able to capture many flow characteristics, such as the interaction between the matrix and conduit, rainfall infiltration through the unsaturated zone, direct recharge through sinkholes, and both free surface and pressurized flow in conduits. Two different flow experiments are presented, and comparison with numerical results confirmed the validity of the developed karst flow model under complex laboratory conditions.

Modeling solute reactivity in a phreatic solution conduit penetrating a karst aquifer

A two-dimensional model for solute migration, transformation, and deposition in a phreatic solution conduit penetrating a karst aquifer is presented in which the solute is anthropogenic to the natural system. Transformation of a reacting solute in a solution conduit has generally been accepted as likely occurring but actual physical measurements and mathematical analyses of the suspected process have been generally minimally investigated, primarily because of the logistical difficulties and complexities associated with solute transport through solution conduits. The model demonstrates how a reacting solute might decay or be transformed to a product solute some of which then migrates via radial dispersion to the conduit wall where it may become adsorbed. Model effects vary for laminar flow and turbulent flow in the axial direction. Dispersion in the radial direction also exhibits marked differences for both laminar flow and turbulent flow. Reaction zones may enhance subsequent reactions due to some overlap resulting from the longitudinal dispersion caused by flow in the axial direction. Simulations showed that varying the reaction rate coefficient strongly affects solute reactions, but that varying deposition coefficients had only minimal impacts. The model was applied to a well-known tracer test that used the tracer dye, Rhodamine WT, which readily converts to deaminoalkylated Rhodamine WT after release, to illustrate how the model may be used to suggest one possible cause, in addition to other possible causes, for less than 100 tracer-mass recovery. In terms of pollutants in a karst aquifer the model also suggests one possible mechanism for pollutant transformation in a solution conduit.

Characterizing flow pathways in a sandstone aquifer: Tectonic vs sedimentary heterogeneities

Sandstone aquifers are commonly assumed to represent porous media characterized by a permeable matrix. However, such aquifers may be heavy fractured when rock properties and timing of deformation favour brittle failure and crack opening. In many aquifer types, fractures associated with faults, bedding planes and stratabound joints represent preferential pathways for fluids and contaminants. In this paper, well test and outcrop-scale studies reveal how strongly lithified siliciclastic rocks may be entirely dominated by fracture flow at shallow depths (≤180m), similar to limestone and crystalline aquifers. However, sedimentary heterogeneities can primarily control fluid flow where fracture apertures are reduced by overburden pressures or mineral infills at greater depths. The Triassic St Bees Sandstone Formation (UK) of the East Irish Sea Basin represents an optimum example for study of the influence of both sedimentary and tectonic aquifer heterogeneities in a strongly lithified sandstone aquifer-type. This fluvial sedimentary succession accumulated in rapidly subsiding basins, which typically favours preservation of complete depositional cycles including fine grained layers (mudstone and silty sandstone) interbedded in sandstone fluvial channels. Additionally, vertical joints in the St Bees Sandstone Formation form a pervasive stratabound system whereby joints terminate at bedding discontinuities. Additionally, normal faults are present through the succession showing particular development of open-fractures. Here, the shallow aquifer (depth≤180m) was characterized using hydro-geophysics. Fluid temperature, conductivity and flow-velocity logs record inflows and outflows from normal faults, as well as from pervasive bed-parallel fractures. Quantitative flow logging analyses in boreholes that cut fault planes indicate that zones of fault-related open fractures characterize ~50% of water flow. The remaining flow component is dominated by bed-parallel fractures. However, such sub-horizontal fissures become the principal flow conduits in wells that penetrate the exterior parts of fault damage zones, as well as in non-faulted areas. The findings of this study have been compared with those of an earlier investigation of the deeper St Bees Sandstone aquifer (180 to 400m subsurface depth) undertaken as part of an investigation for a proposed nuclear waste repository. The deeper aquifer is characterized by significantly lower transmissivities. High overburden pressure and the presence of mineral infillings, have reduced the relative impact of tectonic heterogeneities on transmissivity here, thereby allowing matrix flow in the deeper part of the aquifer. The St Bees Sandstone aquifer contrasts the hydraulic behaviour of low-mechanically resistant sandstone rock-types. In fact, the UK Triassic Sandstone of the Cheshire Basin is low-mechanically resistant and flow is supported both by matrix and fracture. Additionally, faults in such weak-rocks are dominated by granulation seams representing flow-barriers which strongly compartmentalize the UK Triassic Sandstone in the Cheshire Basin.

Simulation of Regional Karst Aquifer System and Assessment of Groundwater Resources in Manatí-Vega Baja, Puerto Rico

The North Coast karst aquifer system of Puerto Rico, the most productive aquifer of the island, is a vital water source for drinking water and local ecosystems. High freshwater demands alter the coastal groundwater system that impacts both human populations and coastal ecosystems of the island. To predict how this system might respond to rainfall events and high pumping demands, we used the equivalent porous medium (EPM) technique to develop a three-dimensional ground-water flow model to estimate hydrogeological parameters and assess groundwater resources in the Manatí-Vega Baja karst aquifer. The approach is based on the hypothesis that the simplified EPM approach will reproduce groundwater hydrodynamics in this complex karst environment. The steady-state model was calibrated with trial and error and parameter estimation methods using an observed groundwater table of 1995 (r = 0.86, p < 0.0001, n = 39). The large-scale simulation suggested that groundwater flow roughly follows the elevation slope [i.e. south to north). Calibrated hydraulic conductivities range from 0.5 to 86 m/d, whereas the hydro-geologic data strongly suggest higher permeability in the middle karst section of the study area. The transient model adequately estimates the observed groundwater fluctuations in response to rainfall events from 1980 until 2014. The transient results indicate that the conceptual model accuracy is more acceptable with a mean error (ME) of −0.132 m, mean absolute error (MAE) of 0.542 m and root mean square (RMSE) error of 0.365 m. The results of water budget simulation show that the total recharge satisfies the total groundwater withdrawal rate in the past, but continuous closure of more contaminated wells causes groundwater levels to increase in the future. The results indicate that the assumption of applicability of EPM approach is sustained and supported by measured data in the study area. Taking future water demands into account, this model could be applied further to predict the changes of groundwater levels and mass balance under different exploitation scenarios.

Review: Groundwater flow and transport modeling of karst aquifers, with particular reference to the North Coast Limestone aquifer system of Puerto Rico

Karst systems have a high degree of heterogeneity and anisotropy, which makes them behave very differently from other aquifers. Slow seepage through the rock matrix and fast flow through conduits and fractures result in a high variation in spring response to precipitation events. Contaminant storage occurs in the rock matrix and epikarst, but contaminant transport occurs mostly along preferential pathways that are typically inaccessible locations, which makes modeling of karst systems challenging. Computer models for understanding and predicting hydraulics and contaminant transport in aquifers make assumptions about the distribution and hydraulic properties of geologic features that may not always apply to karst aquifers. This paper reviews the basic concepts, mathematical descriptions, and modeling approaches for karst systems. The North Coast Limestone aquifer system of Puerto Rico (USA) is introduced as a case study to illustrate and discuss the application of groundwater models in karst aquifer systems to evaluate aquifer contamination.