Constant Head Boundary Research Articles

A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers

In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer could be associated with various boundary conditions, such as the general Robin boundary conditions or even the mixed boundary conditions with no-flow boundary on one side and constant head boundary on the other side. The derived solution has analytical characteristics since it is obtained through the Green’s function method within the domain. Unlike traditional numerical methods, the proposed solution using the Laplace-transform boundary element method does not require discretization in spatial and temporal dimensions. In this study, boundary integral equation using Green's second theorem and the fundamental solution of Green function for dual-porosity models are given. A boundary element matrix in Laplace space is established, which allow us to consider irregularly shaped boundary. The drawdown and flux on the boundary can be obtained through solving the boundary element matrix by Gauss's elimination method. The final solution for wellbore drawdown is evaluated using numerical Laplace inversion algorithm of Stehfest (1970). Many previous solutions for transient flow in finite single-porosity aquifers with no-flow outer boundary condition are shown to be special cases of the present solution. Furthermore, the solution with a mixed outer boundary condition is used to investigate the effect of important parameters of aquifers on wellbore drawdown, including fracture storage coefficient, inter-porosity flow coefficient from matrix to fissures, boundary shape, boundary location, and interference of multiple wells.

Demystifying Fisher Information: What Observation Data Reveal about Our Models.

Information theory is the basis for understanding how information is transmitted as observations. Observation data can be used to compare uncertainty on parameter estimates and predictions between models. Jacobian Information (JI) is quantified as the determinant of the weighted Jacobian (sensitivity) matrix. Fisher Information (FI) is quantified as the determinant of the weighted FI matrix. FI measures the relative disorder of a model (entropy) in a set of models. One-dimensional models are used to demonstrate the relationship between JI and FI, and the resulting uncertainty on estimated parameter values and model predictions for increasing model complexity, different model structures, different boundary conditions, and over-fitted models. Greater model complexity results in increased JI accompanied by an increase in parameter and prediction uncertainty. FI generally increases with increasing model complexity unless model error is large. Models with lower FI have a higher level of disorder (increase in entropy) which results in greater uncertainty of parameter estimates and model predictions. A constant-head boundary constrains the heads in the area near the boundary, reducing sensitivity of simulated equivalents to estimated parameters. JI and FI are lower for this boundary condition as compared to a constant-outflow boundary in which the heads in the area of the boundary can adjust freely. Complex, over-fitted models, in which the structure of the model is not supported by the observation dataset, result in lower JI and FI because there is insufficient information to estimate all parameters in the model.

Meshfree Multiquadric Solution for Real Field Large Heterogeneous Aquifer System

Meshfree methods are often tested in literature for the rectangular domain with uniform aquifer properties (e.g. transmissivity or hydraulic conductivity) and constant groundwater head boundary conditions. In this paper, a multiquadric meshfree (Mfree) groundwater model is developed for a real field irregular domain aquifer system which is capable of incorporating variability like heterogeneity, temporally and spatially varied groundwater head and flow boundary conditions. The developed model is free from the inadequacy of meshing which eventually saves the time on computing resources by calculating the groundwater head-derivatives at different nodes sprinkled over the entire flow domain. Initially, two synthetic problems with pre- existing analytical and grid based results are tested against the presented model. Sensitivity analysis of different parameters like time step size, nodal density and support size of basis function are also investigated. Subsequently Mfree solutions are obtained for a large Mahi Right Bank Canal (MRBC) unconfined aquifer located in Gujarat India. The Mfree solution performance on two synthetic and one real field large aquifer problem revealed that the projected method is advantageous over other grid based simulator in terms of computational time consideration. Such a simulation is preferable in groundwater management models where flow models are coupled with the optimization problem.

Performance assessment of an underground gas storage cavern using water-shed scale groundwater flow modeling with large grid spacing

In this study, we simulated the water-shed scale groundwater flow near an underground LPG storage cavern system to assess its performance. To consider the effects of the storage cavern system on groundwater flow with large grid spacing, we proposed a mathematical model of a head-dependent flux boundary condition for a storage cavern system. Then, we examined its applicability by comparing the simulation results from assigning head-dependent flux boundary conditions, to those from assigning constant head boundary conditions for a hypothetical storage cavern system. Then, we applied this new simulation to the performance assessment of a real underground LPG storage cavern system. The results show that the influence of a storage cavern system on groundwater flow can be modeled in a 3-D water-shed scale with large cells by applying the proposed head-dependent flux boundary condition. The proposed model for a head-dependent flux boundary condition was used for performance assessment of the storage cavern systems and discussion of future works for their performance.

Intrawellbore kinematic and frictional losses in a horizontal well in a bounded confined aquifer

AbstractHorizontal drilling has become an appealing technology for water resource exploration or aquifer remediation in recent decades, due to decreasing operational cost and many technical advantages over vertical wells. However, many previous studies on flow into horizontal wells were based on the Uniform Flux Boundary Condition (UFBC), which does not reflect the physical processes of flow inside the well accurately. In this study, we investigated transient flow into a horizontal well in an anisotropic confined aquifer laterally bounded by two constant‐head boundaries. Three types of boundary conditions were employed to treat the horizontal well, including UFBC, Uniform‐Head Boundary Condition (UHBC), and Mixed‐Type Boundary Condition (MTBC). The MTBC model considered both kinematic and frictional effects inside the horizontal well, in which the kinematic effect referred to the accelerational and fluid‐inflow effects. A new solution of UFBC was derived by superimposing the point sink/source solutions along the axis of a horizontal well with a uniform flux distribution. New solutions of UHBC and MTBC were obtained by a hybrid analytical‐numerical method, and an iterative method was proposed to determine the well discretization required for achieving sufficiently accurate results. This study showed that the differences among the UFBC, UHBC, and MTBC solutions were obvious near the well screen, decreased with distance from the well, and became negligible near the constant‐head boundary. The relationship between the flow rate and the drawdown was nonlinear for the MTBC solution, while it was linear for the UFBC and UHBC solutions.

New Analytical Expressions for Two-Dimensional Aquifer Adjoining with Streams of Varying Water Level

This research presents new analytical expressions to analyze interactions between streams of varying water level and a confined aquifer. The stream water level is assumed to vary exponentially with time. The expressions are obtained by means of Laplace and Fourier transform methods and the results are verified with those obtained from MODFLOW. In fact, we derive a new analytical expression for predicting of the groundwater level and flow rate in a confined aquifer between two streams of varying water level at the north and the right boundaries and two constant head boundaries at the left and the south ends. Also, a numerical example is used to investigate about the aquifer response to stream water level changes. Therefore the effects of variation water level of each stream on the flow rate at the left and the south boundaries and also at four points of the aquifer are discussed. Finally, some other new analytical expressions are also deduced for other types of boundary conditions.

Evaluating Groundwater Interbasin Flow Using Multiple Models and Multiple Types of Data.

The groundwater interbasin flow, Qy , from the north of Yucca Flat into Yucca Flat simulated using the Death Valley Regional Flow System (DVRFS) model greatly exceeds assessments obtained using other approaches. This study aimed to understand the reasons for the overestimation and to examine whether the Qy estimate can be reduced. The two problems were tackled from the angle of model uncertainty by considering six models revised from the DVRFS model with different recharge components and hydrogeological frameworks. The two problems were also tackled from the angle of parametric uncertainty for each model by first conducting Morris sensitivity analysis to identify important parameters and then conducting Monte Carlo simulations for the important parameters. The uncertainty analysis is general and suitable for tackling similar problems; the Morris sensitivity analysis has been utilized to date in only a limited number of regional groundwater modeling. The simulated Qy values were evaluated by using three kinds of calibration data (i.e., hydraulic head observations, discharge estimates, and constant-head boundary flow estimates). The evaluation results indicate that, within the current DVRFS modeling framework, the Qy estimate can only be reduced to about half of the original estimate without severely deteriorating the goodness-of-fit to the calibration data. The evaluation results also indicate that it is necessary to develop a new hydrogeological framework to produce new flow patterns in the DVRFS model. The issues of hydrogeology and boundary flow are being addressed in a new version of the DVRFS model planned for release by the U.S. Geological Survey.

Estimate of river seepage by conditioning downward groundwater flow in the Toyohira River alluvial fan, Japan

ABSTRACTRiver seepage serves as the main source of groundwater in alluvial fans. However, reasonable estimates are rarely obtainable due to inaccuracy of vertical flows around the losing river. In the alluvial fan of the Toyohira River, Japan, to provide a straightforward description of vertical hydraulic gradient (VHG), this study demonstrates assignment of constant head boundary conditions on the shallowest aquitard instead of no-flow conditions on the basement. Initial constant heads and layer-scale anisotropy are calibrated in terms of hydraulic heads. As a result, the simulated river seepage is in reasonable agreement with previous discharge measurements, with net water loss determined to be approximately 1 m3/s. Although the simulation fails for water gain in the lower section, due to a lack of sporadic intercalations of fine deposits, the conditioned VHG modelling approach is found to be effective on a regional scale, especially when losing/gaining sections have not been identified in advance.EDITOR D. Koutsoyiannis ASSOCIATE EDITOR J. Ward

Slope stabilisation using EPS block geofoam with internal drainage system

Lightweight expanded polystyrene (EPS) geofoam (geofoam block) is used in slope remediation works as a soil substitute fill to reduce driving forces that can lead to global instability. On the other hand, the presence of seepage flow requires special attention because geofoam block slope systems are vulnerable to seepage-induced lateral forces. In this study, the effect of an internal drainage system on the alleviation of piezometric pressures within the back-slope of a geofoam block slope system was investigated. For this purpose, laboratory experiments were conducted using a small-scale lysimeter with dimensions of 60 cm height, 20 cm width, and 200 cm length. The slope was compacted with sand to obtain an overall dry unit weight of 14 kN/m3. The constant piezometric head boundary conditions of 25, 38 and 50 cm generated the necessary hydraulic energy gradient for the seepage flow directed from the water reservoir of the lysimeter to the 45° angle slope face. The slopes were remediated by using geofoam blocks assembled in an embankment-type configuration at the toe of the slope. The internal drainage system consisted of grooved geofoam blocks that formed the 10, 15 and 22.5 cm high embankments. Deep-seated failures of the non-remediated slope were prevented except for the experiments with 10 and 15 cm high embankments under 50 cm pressure head boundary conditions. In general, the internal drainage system alleviated the piezometric pressure conditions within the back-slope by lowering the phreatic surface using the active drainage channels observed during laboratory experiments. These drainage channels provided a convenient passageway for seepage flow. The coupled numerical variably saturated flow modelling and slope stability modelling predicted the factor of safety for global stability which confirmed the observed physical conditions in the laboratory. The use of the internal drainage system increased the factor of safety of the geofoam block slope system under seepage conditions.

Groundwater System Modeling for Simultaneous Identification of Pollution Sources and Parameters with Uncertainty Characterization

Contamination of groundwater poses serious threat to the human health and environment. It is difficult and expensive to clean up contaminated aquifers. Identification of unknown pollution sources is vital for adopting any remediation strategy. Groundwater flow and transport simulation model is used to generate necessary data for Artificial Neural Networks (ANN) model building processes. Breakthrough curves obtained for specified pollution scenario are characterized to reduce the inputs to ANN model. The characterized breakthrough curves parameters serve as inputs to ANN model. Unknown pollution source characteristics, flow parameters and transport parameters are outputs for ANN model. Identification of sources is performed with considerations of three cases—simultaneous estimation of unknown sources and flow parameter; simultaneous estimation of unknown sources, flow and transport parameters; and simultaneous estimation of unknown sources and boundary head. Characterization of uncertainty in source identification due to uncertainty in flow parameter, uncertainty in transport parameter and uncertainty in constant head boundary estimation is performed using fuzzy vertex alpha-cut techniques.

Estimation of Fluxes across Boundaries for Groundwater Flow Model Using GIS

The present study aims at using GIS hydrology tool for calculating inflow/outflow fluxes across the boundary of a study area in a situation where physical boundaries in the vicinity of the study area cannot be identified. This approach has an edge over the simplest approach of no flow or constant head boundaries alone, which may be far from reality. The reported methodology will improve groundwater modelling in the areas where the hydrological cycle is predicted because of climate change.

Determination of the location of the groundwater divide and nature of groundwater flow paths within a region of active stream capture; the New River watershed, Virginia, USA

The relatively rapid stream capture of the New River basin by the Roanoke River basin provides a unique example of topographic change within a tectonically inactive environment. A previous investigation of abandoned river deposits has shown the capture of ~225 km2 of New River basin area, which has caused approximately 250 m of incision by the Roanoke River. Difference in base level elevations between the lower Roanoke to the higher New River could be the source of potential energy driving rapid incision. Significant incongruities in base level elevations at the boundaries of an aquifer can steepen the gradient and shift the groundwater divide further toward the higher elevation. If a steep groundwater gradient and expanded groundwater basin exists beneath the Roanoke River tributaries, this would suggest a groundwater control on incision and capture. This investigation incorporates average total head, measured from 18 domestic wells, and constant-head river boundary conditions into numerical models to calculate water levels and gradients between the rivers. Thermal patterns and particle tracking of spring locations were utilized to better understand flow paths in the region. Our results show the groundwater divide is shifted toward the higher elevation boundary, indicating that the groundwater basin is captured prior to surface capture. Flow pathways utilized by groundwater capture can be either diffuse or conduits; however, further work should be done to better understand travel times and flow depths.

Evaluation of the effects of the radial constant-head boundary in slug tests

A semianalytical model of slug tests, conducted in a completely penetrating well within a radial constant-head boundary, was derived. The model, based on the Cooper et al. (1967) model, estimates the hydraulic conductivity and storage coefficient through the matching of type curves. Type curves of the semianalytical solution were plotted, and the effect of the distance of the radial constant-head boundary is discussed. For different storage coefficients, the critical distances of the effect of the constant-head boundary were determined. The effect of the storage coefficient on the response of the water head in slug tests with a radial constant-head boundary of a certain distance is also shown. To verify the model, laboratory slug-test experiments were carried out using a cylindrical test platform, in which an artificial confined coarse-sand aquifer was built. Pumping tests were also executed using the test platform. The Cooper et al. (1967) model and new semianalytical model were used to analyze measurements; the hydraulic conductivity and storage coefficient determined using the two methods were compared to demonstrate the importance of the radial constant-head boundary. A model considering the inertial effect was also used to analyze the slug-test measurements, and although the water head response did not oscillate greatly, the inertial effect affected the slug-test calculation result. The laboratory experiments indicate that the proposed semianalytical model is reasonable and reliable. Cooper HH, Bredehoeft JD, Papadopulos IS (1967) Response of a finite-diameter well to an instantaneous charge of water, Water Resour Res 3(1):263–269.

Effect of heterogeneity on spatiotemporal variations of groundwater level in a bounded unconfined aquifer

Spatiotemporal variations of groundwater level due to a white noise recharge time series and a random transmissivity field in a bounded unconfined aquifer was studied. The analytical solutions for the variance and covariance of groundwater level were derived with non-stationary spectral analyses and superposition principle. It was found that the fluctuations of groundwater level are spatially non-stationary due to a fixed head boundary condition and temporal non-stationary at early time but gradually became stationary as time progresses due to effect of the initial condition. The variation in groundwater level is mainly caused by the random source/sink in the case of temporally random recharge and spatially random transmissivity. The effect of heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The heterogeneity also enhances the correlation of groundwater level, especially at large time intervals and small spatial distances.

지하수 모델링 기법을 이용한 인공함양정 최적 위치 평가

A Fortran program was developed to determine the optimal locations of an artificial recharge well. Three objective functions were considered: (1) maximizing the recovery rates, (2) maximizing the injection rates, and (3) minimizing the coefficient of variation of the increased pumping rates. We also suggested a new aggregate objective function which combined the first and the third objective functions. The model results showed that locating the injection well inside the cluster of pumping wells was desirable if either the recovery or the injection rate was taken into account. However, the injection well located outside the cluster evenly increased the pumping rates in existing pumping wells. Therefore, for clustered pumping wells, installing an injection well at the center or the upstream of the pumping wells seems beneficial. For linear arrangement of pumping wells parallel to the constant head boundary, locating the injection well in the upstream was recommended. On the contrary, in case of the linear arrangement perpendicular to the constant head boundary, the injection well installed on both sides of the central part of the pumping wells was preferable.

Analytical solution for transient groundwater flow during slug test in vertical cutoff walls

SUMMARY An analysis method for transient groundwater flow during slug tests performed in vertical cutoff walls is presented. The analytical solution for evaluating hydraulic conductivity of vertical cutoff walls is derived by applying the method of images to the previously developed analytical solution that is exclusively applicable to an infinite aquifer. Two distinct boundary conditions are considered to account for the configuration of the vertical cutoff wall: the wall-soil formation interfaces with or without the existence of filter cakes, that is, constant-head boundary and no-flux boundary conditions. A series of type curves is constructed from the analytical solution and compared with those of a partially penetrated well within an aquifer. The constant-head boundary condition provides faster hydraulic head recovery than the aquifer case. On the other hand, the no-flux boundary condition leads to a delayed hydraulic head recovery. The greater the shape factor and well offset from the center of the cutoff wall, and the smaller the width of the cutoff wall, the greater the effect of the boundary condition observed in the type curves. This result shows the significance of considering proper boundary conditions at the vertical cutoff wall in analyzing slug tests. Copyright © 2014 John Wiley & Sons, Ltd.

General well function for soil vapor extraction

This paper develops a well function applicable to extraction of groundwater or soil vapor from a well under the most common field test conditions. The general well function (Perina and Lee, 2006) [12] is adapted to soil vapor extraction and constant head boundary at the top. For groundwater flow, the general well function now applies to an extraction well of finite diameter with uniform drawdown along the screen, finite-thickness skin, and partially penetrating an unconfined, confined, and leaky aquifer, or an aquifer underneath a reservoir. With a change of arguments, the model applies to soil vapor extraction from a vadose zone with no cover or with leaky cover at the ground surface. The extraction well can operate in specified drawdown (pressure for soil vapor) or specified flowrate mode. Frictional well loss is computed as flow-only dependent component of the drawdown inside the extraction well. In general case, the calculated flow distribution is not proportional to screen length for a multiscreen well.

Representation of water abstraction from a karst conduit with numerical discrete-continuum models

Abstract. Karst aquifers are characterized by highly conductive conduit flow paths embedded in a less conductive fissured and fractured matrix, resulting in strong permeability contrasts with structured heterogeneity and anisotropy. Groundwater storage occurs predominantly in the fissured matrix. Hence, most mathematical karst models assume quasi-steady-state flow in conduits neglecting conduit-associated drainable storage (CADS). The concept of CADS considers storage volumes, where karst water is not part of the active flow system but hydraulically connected to conduits (for example karstic voids and large fractures). The disregard of conduit storage can be inappropriate when direct water abstraction from karst conduits occurs, e.g., large-scale pumping. In such cases, CADS may be relevant. Furthermore, the typical fixed-head boundary condition at the karst outlet can be inadequate for water abstraction scenarios because unhampered water inflow is possible. The objective of this work is to analyze the significance of CADS and flow-limited boundary conditions on the hydraulic behavior of karst aquifers in water abstraction scenarios. To this end, the numerical discrete-continuum model MODFLOW-2005 Conduit Flow Process Mode 1 (CFPM1) is enhanced to account for CADS. Additionally, a fixed-head limited-flow (FHLQ) boundary condition is added that limits inflow from constant head boundaries to a user-defined threshold. The effects and the proper functioning of these modifications are demonstrated by simplified model studies. Both enhancements, CADS and FHLQ boundary, are shown to be useful for water abstraction scenarios within karst aquifers. An idealized representation of a large-scale pumping test in a karst conduit is used to demonstrate that the enhanced CFPM1 is able to adequately represent water abstraction processes in both the conduits and the matrix of real karst systems, as illustrated by its application to the Cent Fonts karst system.

Multi-scale Experimentation and Numerical Modeling for Process Understanding of CO2 Attenuation in the shallow subsurface

Abstract The goal of this study is to quantify the effects of geologic heterogeneity on the dynamic process of CO 2 attenuation in shallow aquifers through the use of multi-scale laboratory experimentation and numerical modelling. First, an experiment was conducted in an intermediate scale two-dimensional cell that was packed with water-saturated porous media in a simple heterogeneous configuration. Constant-head boundary conditions were applied to the system, and then CO 2 -saturated water was injected through it. As the CO 2 -saturated water migrated through the system, gas phase CO 2 evolved within the porous media, as observed by dielectric saturation sensors. The outflow of CO 2 gas from the top of the system was monitored by a gas flow meter, and the outflow of water from the side of the tank was monitored via collection into a container that was placed on a computer-interfaced scale. After the multiphase CO 2 evolution appeared to have reached steady state, clean water was injected through the cell until all of the CO 2 was expelled from the system. In addition to the experiments, numerical models were performed using the Finite Element Heat and Mass transfer (FEHM) code as a first step toward planning larger scale experiments. Results indicate that the presence of geologic heterogeneity, which is ubiquitous in natural environments, can significantly hinder the migration of CO 2 in the shallow subsurface.

Steady-state freshwater–seawater mixing zone in stratified coastal aquifers

Summary The mixing zone between freshwater and intruding seawater, which controls regional groundwater flow dynamics and reactive transport processes, is the most important component in coastal aquifers. Laboratory experiments and numerical simulations were conducted to investigate the effects of aquifer stratification on the thickness of a steady-state freshwater–seawater mixing zone. A series of experiments were implemented in a laboratory tank packed with three layers of coastal sands and manipulated by two flow cells for maintaining constant-head boundary conditions. Packed aquifers included a homogenous aquifer, a high hydraulic conductivity (K)–low K–high K stratified aquifer, and a low K–high K–low K stratified aquifer. Both tank-scale and field-scale density-dependent models were developed to simulate the laboratory experiments and to systematically investigate aquifer stratification effects on the thickness of a steady mixing zone with varying layer configurations. Results showed that when an aquifer layer with a low K overlies a layer with a relatively high K, slanting upward flow of diluted saltwater and re-circulated seawater flow are refracted at the interface between the two layers, resulting in streamline separation and a broad mixing zone in the low-K layer. By contrast, the mixing zone in a high-K layer is slightly narrowed when it overlies a layer with a relatively low K because flow refraction squeezes the streamlines within the mixing zone. The mixing-zone profile in head-controlled systems is a function of K contrast, but independent of the magnitude of K. Our results demonstrated the significant impact of aquifer stratification on controlling groundwater flow and solute transport in coastal subsurface environments and would have significant implications for studying physical, chemical and biological processes in coastal subsurface environments, as aquifer stratification is naturally prevalent.