Determination of Storage Coefficients During Pumping and Recovery

An aquifer test is used mostly to determine the storage coefficient and transmissivity. Although residual drawdown data are widely used in estimating the transmissivity of aquifers, the estimation of storage coefficients with recovery data is controversial. Some researchers have proposed methods to estimate storage coefficients with recovery data by assuming equality of storage coefficients for the recovery and pumping periods (S = S′). The aim of this study is to determine storage coefficients without such an assumption, that is, S≠S′. The method is a modified version of Banton‐Bangoy's method without considering drawdown data due to pumping. Drawdown is plotted vs. the logarithmic ratio (t′/t) or time since pumping stopped to the duration of pumping and the ratio of storage coefficient during recovery to the storage coefficient from the pumping period (S′/S). The method is verified with one case study and two synthetic examples. Thus, it is possible to determine storage coefficient of pumping period accurately without any data from pumping period by recovery data.     

Well storage effect during pumping tests in an aquifer of low permeability

Abstract

Well storage effect is generally considered while interpreting pumping test data from large diameter wells. However, in an aquifer of low permeability, the well storage is found to be significant during pumping tests conducted on bore wells. The interpretation of such data gives ambiguous results unless well storage effect is taken into account. A field example is presented to illustrate the difficulty in interpretation of the pumping test data. In order to take into account the well storage effect, a finite difference approach of interpreting pumping test data is suggested.     

Rainfall—runoff response,event-based runoff coefficients and hydrograph separation

Abstract

Event-based runoff coefficients can provide information on watershed response. They are useful for catchment comparison to understand how different landscapes “filter” rainfall into event-based runoff and to explain the observed differences with catchment characteristics and related runoff mechanisms. However, the big drawback of this important parameter is the lack of a standard hydrograph separation method preceding its calculation. Event-based runoff coefficients determined with four well-established separation methods, as well as a newly developed separation method, are compared and are shown to differ considerably. This signifies that runoff coefficients reported in the literature often convey less information than required to allow for catchment classification. The new separation technique (constant-k method) is based on the theory of linear storage. Its advantages are that it is theoretically based in determining the end point of an event and that it can also be applied to events with multiple peaks. Furthermore, it is shown that event-based runoff coefficients in combination with simple statistical models improve our understanding of rainfall—runoff response of catchments with sparse data.     

A single recovery type curve from Theis'' exact solution

The Theis type curve matching method and the Cooper-Jacob semilog method are commonly used for estimation of transmissivity and storage coefficient of infinite, homogeneous, isotropic, confined aquifers from drawdown data of a constant rate pumping test. Although these methods are based on drawdown data, they are often applied indiscriminately to analyze both drawdown and recovery data. Moreover, the limitations of drawdown type curve to analyze recovery data collected after short pumping times are not well understood by the practicing engineers. This often may result in an erroneous interpretation of such recovery data. In this paper, a novel but simple method is proposed to determine the storage coefficient as well as transmissivity from recovery data measured after the pumping period of an aquifer test. The method eliminates the dependence on pumping time effects and has the advantage of employing only one single recovery type curve. The method based on the conversion of residual drawdown to recovered drawdown (buildup) data plotted versus a new equivalent time (delta(t) x t(p)/t(p) + delta(t)). The method uses the recovery data in one observation point only, and does not need the initial water level h0, which may be unknown. The accuracy of the method is checked with three sets of field data. This method appears to be complementary to the Cooper-Jacob and Theis methods, as it provides values of both storage coefficient and transmissivity from recovery data, regardless of pumping duration.     

Improvement on the estimation of constant-rate drawdown in large-diameter wells

Abstract

Papadopulos and Cooper's (PC) solution can be used to describe the drawdown resulting from pumping with a constant rate at a large-diameter well. However, this solution is too complicated to be accurately evaluated due to the oscillatory nature of the Bessel functions. The PC approach resulted in tabulated values of dimensionless drawdown at the well with an accuracy of four or fewer digits for selected values of dimensionless storage coefficient versus dimensionless time. Some researchers have fitted the tabulated values with interpolation formulas that are easy to use in engineering applications. Those formulas may be more accurate if the tabulated values are computed with greater accuracy. In this study, we propose an efficient numerical procedure, including a root search scheme, to find the roots of the integrand, Gaussian quadrature for numerical integration, and Shanks transform to accelerate convergence of infinite series. The proposed procedure can evaluate the dimensionless drawdown with greater accuracy and is useful in practice if there is a need for high accuracy for the observation either at the well or in the aquifer at some distance from the pumping well

Editor D. Koutsoyiannis

Citation Chang, Y.C., Yeh, H.D., and Wang, C.T., 2013. Improvement on the estimation of constant-rate drawdown in large-diameter wells. Hydrological Sciences Journal, 58 (3), 716–727.     

An improved straight-line fitting method for analyzing pumping test recovery data

Theis (1935) derived an exact solution for the residual drawdown in a well after the cessation of a pumping test by summing two drawdowns: one (s1), caused by imaginary continuation of the original pumping and the other (s2), due to an imaginary injection at the same constant rate. We approximated the Theis solution to obtain a simple linear relation for determining the transmissivity and storage coefficient from recovery data. Unlike other existing straight-line fitting methods, in our method, we applied different approximations to the well functions in the solutions of s1 and s2. We used the well-known Cooper-Jacob approximation for s1, truncating the expansion of the well function in s2 to its first three terms. For the same level of truncation errors, while the Cooper-Jacob approximation requires the argument u1相似文献   

The Effect of Undetected Barriers on Groundwater Drawdown and Recovery

In large-scale pumping projects, such as mine dewatering, predictions are often made about the rate of groundwater level recovery after pumping has ceased. However, these predictions may be impacted by geological uncertainty—including the presence of undetected impermeable barriers. During pumping, an impermeable barrier may be undetected if it is located beyond the maximum extent of the cone of depression; yet it may still control drawdown during the recovery phase. This has implications for regional-scale modeling and monitoring of groundwater level recovery. In this article, non-dimensional solutions are developed to show the conditions under which a barrier may be undetected during pumping but still significantly impact groundwater level recovery. The magnitude of the impact from an undetected barrier will increase as the ratio of pumping rate to aquifer transmissivity increases. The results are exemplified for a hypothetical aquifer with an unknown barrier 3 km from a pumping well. The difference in drawdown between a model with and without a barrier may be <1 m in the 10 years while pumping is occurring, but up to 50 m after pumping has ceased.     

A theoretical assessment of casing storage effects when pump sampling a partially penetrating borehole

ABSTRACT

A borehole partially penetrating a confined aquifer and pumped at a constant rate is modelled, taking account of water stored within the casing of the borehole. A solution for drawdown in the Laplace transform domain is obtained. The proportion of aquifer water in well discharge is numerically evaluated, tabulated as a function of time and compared with results for a fully penetrating well. Modification of the fully penetrating well theory, for application to partially penetrating wells, was found to give comparable results to the more complete analysis for a partially penetrating well both at early and late times. A previous estimate of the time of pumping before sampling (t_s) to minimize casing storage effects, based on the fully penetrating well theory, was confirmed by the partially penetrating well analysis and in fact was shown to be a conservative estimate (or overestimate) of the pumping time required when sampling from a partially penetrating well.     

Simulating Head Recovery and Intermittent Discharge in Free Flowing Wells

Modeling of the head recovery (buildup) in and intermittent operation of flowing wells lacks rigorous analytical tools. Presently different methods are applied in discharging and recovery phases. The presented reliable approximate solution considers a continuous free flow process and time variant screen loss parameters. The latter are temporarily set to large value to prevent inflow into the well bore during the single recovery or in repeated shut down periods. This method is called as screen loss control or SLC technique and is verified by means of comparative analysis with the constant rate pumping‐recovery test simulated in leaky aquifer. The evaluation of the free flow and recovery test in the free flowing well 28 (Artesia Heights) concluded with calibrated parameters close to those obtained in the earlier analyses based on split well flow process. The simulation of intermittent flowing well operation also underwent successful validation resulting in reasonable values of the Q_w and s response functions.     

Integrated assessment of lateral flow, density effects and dispersion in aquifer storage and recovery

Aquifer storage and recovery (ASR) involves the injection of freshwater into an aquifer for later recovery and use. This paper investigates three major factors leading to reduction in performance of ASR systems in brackish or saline aquifers: lateral flow, density-driven flow and dispersive mixing. Previous analyses of aquifer storage and recovery (ASR) have considered at most two of the above processes, but never all three together, and none have considered lateral flow and density effects together. In this analysis, four dimensionless parameters are defined to give an approximate characterisation of lateral flow, dispersive mixing, mixed convection (density effects during pumping) and free convection (density effects during storage). An extensive set of numerical models spanning a wide parameter range is then used to develop a predictive framework using the dimensionless numbers. If the sum of the four dimensionless numbers (denoted R_ASR) exceeds 10, the ASR operation is likely to fail with no recoverable freshwater, while if R_ASR < 0.1, the ASR operation is likely to provide at least some recovery of freshwater. The predictive framework is tested using limited data available from ASR field sites, broadly lending support to the framework. This study has several important implications. Firstly, the lack of completeness of field data sets in the literature must be rectified if we are to properly characterise mixed-convective flow processes in ASR operations. Once data are available, the dimensionless numbers can be used to identify suitable ASR sites and the desirable operational conditions that maximise recovery efficiencies.     

Interpretation of the behaviour of agrowell systems in Sri Lanka using radial flow models

Abstract

This paper describes a study of the use of large diameter “agrowells” used for irrigation in Sri Lanka. Detailed field information for a single location is presented and a numerical radial flow model was used to interpret the field response. Initially the model was used to represent a pumping test in which the pumping and subsequent recovery were monitored. It was then used to investigate the operation of the well during a dry season. Satisfactory agreement could only be obtained when account was taken of the withdrawal of water from below the water table by trees. From the simulation it was possible to show that skilful farming practice could be used in steadily exploiting the resources for irrigation over the whole of the dry season.     

An analytical approach to capture zone delineation for a well near a stream with a leaky layer

Abstract

An analytical solution is developed to delineate the capture zone of a pumping well in an aquifer with a regional flow perpendicular to a stream, assuming a leaky layer between the stream and the aquifer. Three different scenarios are considered for different pumping rates. At low pumping rates, the capture zone boundary will be completely contained in the aquifer. At medium pumping rates, the tip of the capture zone boundary will intrude into the leaky layer. Under these two scenarios, all the pumped water is supplied from the regional groundwater flow in the aquifer. At high pumping rates, however, the capture zone boundary intersects the stream and pumped water is supplied from both the aquifer and the stream. The two critical pumping rates which separate these three scenarios, as well as the proportion of pumped water from the stream and the aquifer, are determined for different hydraulic settings.

Editor D. Koutsoyiannis; Associate editor A. Koussis

Citation Asadi-Aghbolaghi, M., Rakhshandehroo, G.R., and Kompani-Zare, M., 2013. An analytical approach to capture zone delineation for a well near a stream with a leaky layer. Hydrological Sciences Journal, 58 (8), 1813–1823.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

Solutions for Non‐Darcian Flow to an Extended Well in Fractured Rock

We have investigated non‐Darcian flow to a vertical fracture represented as an extended well using a linearization procedure and a finite difference method in this study. Approximate analytical solutions have been obtained with and without the consideration of fracture storage based on the linearization procedure. A numerical solution for such a non‐Darcian flow case has also been obtained with a finite difference method. We have compared the numerical solution with the approximate analytical solutions obtained by the linearization method and the Boltzmann transform. The results indicate that the linearized solution agrees generally well with the numerical solution at late times, and underestimates the dimensionless drawdown at early times, no matter if the fracture storage is considered or not. When the fracture storage is excluded, the Boltzmann transform solution overestimates the dimensionless drawdown during the entire pumping period. The dimensionless drawdowns in the fracture with fracture storage for different values of dimensionless non‐Darcian hydraulic conductivity β approach the same asymptotic value at early times. A larger β value results in a smaller dimensionless drawdown in both the fracture and the aquifer when the fracture storage is included. The dimensionless drawdown is approximately proportional to the square root of the dimensionless time at late times.     

Quantifying threats to groundwater resources in the Republic of Maldives Part II: Recovery from tsunami marine overwash events

Marine overwash events are among the most serious short‐term threats to groundwater supply of small coral islands. During such events, seawater can inundate small islands partially or completely, causing salinization of the aquifer. A comprehensive knowledge of freshwater lens recovery is essential for water planners on these islands. In this study, a numerical modelling approach is used to quantify recovery of the freshwater lens on 4 islands of the Maldives after a tsunami‐induced overwash event similar to that experienced from the Indian Ocean earthquake in December 2004. The islands vary in size (0.2 to 10.1 km²) and span the climatic regions of the Maldives. A tested 3‐dimensional SEAWAT groundwater model for each island is used to simulate the recovery process. Recharge rates from historical rainfall data and from global climate models are imposed on each island during the post‐overwash recovery period. The effect of groundwater pumping on lens recovery also is examined. Results show abrupt decrease in fresh groundwater volumes for each island, followed by recovery that is significantly influenced by island size and recharge patterns. Overall, salinization is more widespread on small islands (<1 km²), but recovery is more rapid than for large islands. Between 50% and 90% of lens recovery occurs after 2 years for small islands (<1 km²) whereas only 35% and 55% for large islands. Imposing pumping rates required to sustain the local population lengthened the recovery time between 5% and 15%, with smaller islands having the higher percentage. However, the governing factor on recovery time is the spatial extent of land surface inundation by the overwash event, with wave height and duration of the event having a negligible impact. A strong relationship exists between required recovery time and island surface area, thereby providing a method to determine recovery time for other atoll islands not investigated in this study with similar geologic structure. Our results can be used to aid in managing water resources during the post‐overwash period.     

An Approximation of Inner Boundary Conditions for Wells Intersecting Highly Conductive Structures

Inner boundary conditions describe the interaction of groundwater wells with the surrounding aquifer during pumping and are associated with well-skin damage that limits water production and water derived from wellbore storage. Pumping test evaluations of wells during immediate and early time flow require assignment of inner boundary conditions. Originally, these concepts were developed for vertical well screens, and later transferred to wellbores intersecting highly conductive structures, such as preferential flow zones in fractured and karstic systems. Conceptual models for pumping test analysis in complex bedrock geology are often simplified. Classic analytical solutions generally lump or ignore conditions that limit or enhance well productivity along the well screen at the onset of pumping. Numerical solutions can represent well drawdowns in complex geological settings, such as karst systems, more precisely than many analytical solutions by accounting for additional physical processes and avoiding assumptions and simplifications. Suitable numerical tools for flow simulations in karst are discrete pipe-continuum models that account for various physical processes such as the transient hydraulics of wellbores intersecting highly conductive structures during pumping.     

Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms

Abstract

A nonlinear, multi-objective optimization methodology is presented that seeks to maximize free product recovery of light non-aqueous phase liquids (LNAPLs) while minimizing operation cost, by introducing the novel concept of optimal alternating pumping and resting periods. This process allows more oil to flow towards the extraction wells, ensuring maximum free product removal at the end of the remediation period with minimum groundwater extraction. The methodology presented here combines FEHM (Finite Element Heat and Mass transfer code), a multiphase groundwater model that simulates LNAPL transport, with three evolutionary algorithms: the genetic algorithm (GA), the differential evolution (DE) algorithm and the particle swarm optimization (PSO) algorithm. The proposed optimal free-phase recovery strategy was tested using data from a field site, located near Athens, Greece. The PSO and DE solutions were very similar, while that provided by the GA was inferior, although the computation time was roughly the same for all algorithms. One of the most efficient algorithms (PSO) was chosen to approximate the optimal Pareto front, a method that provides multiple options to decision makers. When the optimal strategy is implemented, although a significant amount of LNAPL free product is captured, a spreading of the LNAPL plume occurs.

Editor Z.W. Kundzewicz; Associate editor L. See

Citation Dokou, Z. and Karatzas, G.P., 2013. Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms. Hydrological Sciences Journal, 58 (3), 671–685.     

Simulation and control of the linked systems of water quantity–water quality–socio-economics in the Huaihe River basin

Abstract

This work makes explicit an algebraic expression giving the matrix of transient influence coefficients associated with a one-dimensional semi-confined aquifer model. The domain studied is divided into a series of connected and completely mixed compartments over which the governing equation is discretized. The discrete equations obtained are solved for the compartmental hydraulic head and used to derive the algebraic expression in question. The basic properties of the so-called algebraic influence coefficients are investigated. In particular, their consistency with the exact Green function is highlighted. Finally, the newly derived influence coefficients are applied to a simplified aquifer system in order to formulate and solve the problem of identifying illegal groundwater pumping.     

An innovative method to estimate regional-scale hydraulic diffusivity using GRACE data

ABSTRACT

Estimation of hydraulic properties in the field is usually small-scale and not cost-effective. This paper proposes an innovative method for estimating hydraulic diffusivity at regional scale. Monthly groundwater storage change over the period from 2003 to 2013 is first estimated from GRACE-derived terrestrial water storage (TWS). Assuming that the aquifer system is unconfined and the hydraulic properties are uniform in a geographical cell, the water balance principle and Darcy’s law are used to establish a relation between groundwater storage and hydraulic diffusivity. The value of hydraulic diffusivity is then adjusted using the generalized least squares and linear correlation method. This GRACE-derived hydraulic diffusivity estimation method, or GHDE method for short, is first verified with a hypothetical case and then applied in the Beishan area with available field-measured hydraulic conductivity data. The hypothetical case study demonstrates that the method works perfectly if the TWS data are error free. The Beishan case study illustrates that the estimated hydraulic diffusivities using the GHDE method correlate reasonably well with field test results, suggesting that this method is applicable. The accuracy of this method is constrained by the resolution of the GRACE-derived TWS data and is most suitable for very large scale groundwater problems due to the current accuracy of the GRACE data.

EDITOR A. Castellarin ASSOCIATE EDITOR N. Verhoest