Drawdown Data Research Articles

Corroborating stable isotopic data with pumping test data to investigate recharge and groundwater flow processes in a fractured rock aquifer, Rivirivi Catchment, Malawi

Fractured rock aquifers continue to support millions of people in arid and semiarid regions. However, due to heterogeneous nature of their hydrogeology and comparative low yields, research in these formations is regarded expensive, and thus, very little is known about their dominant hydrological processes. In this study, we corroboratively used pumping test and stable isotopic data to understand groundwater recharge and flow processes in fractured hornblende-biotite-gneiss. It was established that rain is the main source of groundwater recharge. The groundwater system seems to retain the stable isotopic signatures of precipitation which has undergone evaporation before infiltration. Geochemical data also show that the groundwater system has not undergone pronounced geochemical evolution as evidenced by low total dissolved solids in both seasons. A combination of stable isotopic data and derivative plots of drawdown data helped identification of apparent recharge zones, no-flow boundaries and dominant flow types in the pumped wells with bilinear flow being the dominant type of flow in BP1 and BP2, while linear flow was dominant in BP3 and BP4. Geochemical, stable isotopic and hydraulic data further revealed hydraulic connection between two wells juxtaposed across Ntcheu Fault, indicating potential for groundwater flow across the fault and highlighting that the fault may be acting as a groundwater conduit across it. The established phenomena are important when considering groundwater development and sustainable management of the resource.

Three-dimensional imaging of aquifer and aquitard heterogeneity via transient hydraulic tomography at a highly heterogeneous field site

Previous studies have shown that geostatistics-based transient hydraulic tomography (THT) is robust for subsurface heterogeneity characterization through the joint inverse modeling of multiple pumping tests. However, the hydraulic conductivity (K) and specific storage (Ss) estimates can be smooth or even erroneous for areas where pumping/observation densities are low. This renders the imaging of interlayer and intralayer heterogeneity of highly contrasting materials including their unit boundaries difficult. In this study, we further test the performance of THT by utilizing existing and newly collected pumping test data of longer durations that showed drawdown responses in both aquifer and aquitard units at a field site underlain by a highly heterogeneous glaciofluvial deposit. The robust performance of the THT is highlighted through the comparison of different degrees of model parameterization including: (1) the effective parameter approach; (2) the geological zonation approach relying on borehole logs; and (3) the geostatistical inversion approach considering different prior information (with/without geological data). Results reveal that the simultaneous analysis of eight pumping tests with the geostatistical inverse model yields the best results in terms of model calibration and validation. We also find that the joint interpretation of long-term drawdown data from aquifer and aquitard units is necessary in mapping their full heterogeneous patterns including intralayer variabilities. Moreover, as geological data are included as prior information in the geostatistics-based THT analysis, the estimated K values increasingly reflect the vertical distribution patterns of permeameter-estimated K in both aquifer and aquitard units. Finally, the comparison of various THT approaches reveals that differences in the estimated K and Ss tomograms result in significantly different transient drawdown predictions at observation ports.

Slim hole drilling and testing strategies

The financial and geologic advantages of drilling slim holes instead of large production wells in the early stages of geothermal reservoir assessment has been understood for many years. However, the practice has not been fully embraced by geothermal developers. We believe that the reason for this is that there is a poor understanding of testing and reservoir analysis that can be conducted in slim holes. In addition to reservoir engineering information, coring through the cap rock and into the reservoir provides important data for designing subsequent production well drilling and completion. Core drilling requires significantly less mud volume than conventional rotary drilling, and it is typically not necessary to cure lost circulation zones (LCZ). LCZs should be tested by either production or injection methods as they are encountered. The testing methodologies are similar to those conducted on large-diameter wells; although produced and/or injected fluid volumes are much less. Pressure, temperature and spinner (PTS) surveys in slim holes under static conditions can used to characterize temperature and pressure distribution in the geothermal reservoir. In many cases it is possible to discharge slim holes and obtain fluid samples to delineate the geochemical properties of the reservoir fluid. Also in the latter case, drawdown and buildup data obtained using a downhole pressure tool can be employed to determine formation transmissivity and well properties. Even if it proves difficult to discharge a slim hole, an injection test can be performed to obtain formation transmissivity. Given the discharge (or injection) data from a slimhole, discharge properties of a large-diameter well can be inferred using wellbore modeling. Finally, slim hole data (pressure, temperature, transmissivity, fluid properties) together with reservoir simulation can help predict the ability of the geothermal reservoir to sustain power production.

Variability of the useful life of reservoirs in tropical locations: A case study from the Burdekin Falls Dam, Australia

Large dam construction for irrigation, hydropower, water supply, and flood control in tropical to sub-tropical areas increased markedly after 1950. Many of the dams built during this period have filled with sediment and no longer perform to their original design specifications; in many cases, forecast dam life was greatly overestimated. This study investigates the useful life of Burdekin Falls Dam (BFD), northeastern Australia and compares the findings with other tropical reservoirs. Using two independent methods it is estimated that between 61 and 65 million m3 of sediment has been deposited in the reservoir over the 24 years of operation through 2011. This sediment volume equates to an average of 0.15% of capacity lost per year since construction was completed. If current sediment loads/climate regimes persist, reservoir capacity will be reduced by 50% after 345 years. However, the useful life of the BFD reduces to just 276 years when drawdown data are considered; these data show reservoir use would be affected once 40% of storage was filled with sediment, with a 60% drawdown return period of 1 in 15 years. When compared to similar large tropical to sub-tropical reservoirs, the BFD has a slightly longer reservoir useful life than dams in India and a much longer half-life than for both similar-sized and larger dams in China, Brazil, and Iran. Properties of the BFD that promote a longer useful life include a lower trap efficiency, relatively low annual sediment load delivered to the reservoir, limited sediment deposition behind the dam wall (and uniform distribution of deposited sediment), and the export of highly turbid annual floodwaters before settling and deposition of any remaining sediment within the reservoir.

A stable computation of log‐derivatives from noisy drawdown data

AbstractPumping tests interpretation is an art that involves dealing with noise coming from multiple sources and conceptual model uncertainty. Interpretation is greatly helped by diagnostic plots, which include drawdown data and their derivative with respect to log‐time, called log‐derivative. Log‐derivatives are especially useful to complement geological understanding in helping to identify the underlying model of fluid flow because they are sensitive to subtle variations in the response to pumping of aquifers and oil reservoirs. The main problem with their use lies in the calculation of the log‐derivatives themselves, which may display fluctuations when data are noisy. To overcome this difficulty, we propose a variational regularization approach based on the minimization of a functional consisting of two terms: one ensuring that the computed log‐derivatives honor measurements and one that penalizes fluctuations. The minimization leads to a diffusion‐like differential equation in the log‐derivatives, and boundary conditions that are appropriate for well hydraulics (i.e., radial flow, wellbore storage, fractal behavior, etc.). We have solved this equation by finite differences. We tested the methodology on two synthetic examples showing that a robust solution is obtained. We also report the resulting log‐derivative for a real case.

Reliable yields of public water-supply wells in the fractured-rock aquifers of central Maryland, USA

Most studies of fractured-rock aquifers are about analytical models used for evaluating aquifer tests or numerical methods for describing groundwater flow, but there have been few investigations on how to estimate the reliable long-term drought yields of individual hard-rock wells. During the drought period of 1998 to 2002, many municipal water suppliers in the Piedmont/Blue Ridge areas of central Maryland (USA) had to institute water restrictions due to declining well yields. Previous estimates of the yields of those wells were commonly based on extrapolating drawdowns, measured during short-term single-well hydraulic pumping tests, to the first primary water-bearing fracture in a well. The extrapolations were often made from pseudo-equilibrium phases, frequently resulting in substantially over-estimated well yields. The methods developed in the present study to predict yields consist of extrapolating drawdown data from infinite acting radial flow periods or by fitting type curves of other conceptual models to the data, using diagnostic plots, inverse analysis and derivative analysis. Available drawdowns were determined by the positions of transition zones in crystalline rocks or thin-bedded consolidated sandstone/limestone layers (reservoir rocks). Aquifer dewatering effects were detected by type-curve matching of step-test data or by breaks in the drawdown curves constructed from hydraulic tests. Operational data were then used to confirm the predicted yields and compared to regional groundwater levels to determine seasonal variations in well yields. Such well yield estimates are needed by hydrogeologists and water engineers for the engineering design of water systems, but should be verified by the collection of long-term monitoring data.

An analytical model for flow induced by a constant-head pumping in a leaky unconfined aquifer system with considering unsaturated flow

A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang’s et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters.

Analysis of Sandface-Temperature-Transient Data for Slightly Compressible, Single-Phase Reservoirs

Summary This paper presents new semilog-straight-line and temperature-derivative methods for interpreting and analyzing sandface-temperature transient data from constant-rate drawdown and buildup tests conducted in infinite-acting reservoirs containing slightly compressible fluid of constant compressibility and viscosity. The procedures are dependent on the analytical solutions accounting for Joule-Thomson (J-T) heating/cooling, adiabatic-fluid expansion, and conduction and convection effects. The development of the analytical solutions is dependent on the fact that the effects of temperature changes on pressure-transient data can be neglected so that the pressure-diffusivity and thermal-energy-balance equations can be decoupled. The analytical solutions are verified by and are found in excellent agreement with the solutions of a commercial nonisothermal reservoir simulator. It is shown that drawdown and buildup sandface-temperature data may exhibit three infinite-acting radial-flow (IARF) periods (represented by semilog equations): one at early times reflecting the adiabatic expansion/compression effects, another at intermediate times reflecting the J-T expansion in the skin zone if skin exists, and the third at late times reflecting J-T expansion effects in the nonskin zone. Performing semilog analyses by use of these IARF regimes gives estimates of permeability of skin and nonskin zones as well as the radius of the skin zone, assuming that the J-T coefficient of the fluid and the viscosity are known. Parameters such as skin-zone permeability and radius are not readily accessible from conventional pressure-transient analysis (PTA) from which only the skin factor and nonskin-zone permeability can be obtained. The applicability of the proposed analysis procedure is demonstrated by considering synthetic and field-test data. The results indicate that the analysis procedure provides reliable estimates of skin-zone and nonskin-zone permeability and skin-zone radius from drawdown or buildup temperature data jointly with pressure data.

Bayesian estimation of the transmissivity spatial structure from pumping test data

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

Inverse modeling of interbed parameters and transmissivity using land subsidence and drawdown data

Accurate modeling of hydraulic properties such as transmissivity and interbed specific storages is significant for reliable predictions of land subsidence modeling. Calibration of land subsidence model is a challenge because of the strong non-linearity of groundwater flow equation especially when it accounting for the interbed drainage process. Pumping well drawdown and land subsidence data are very important signals for identification of aquifer hydraulic properties. In this work, it is proposed that the ensemble Kalman filter is used to calibrate the transmissivity and interbed elastic and inelastic specific storages using both drawdown and subsidence data for the first time. A synthetic example demonstrated that the characterization of transmissivity and specific storages is improved, and the uncertainties of predictions of both drawdown and subsidence are reduced, when additional dynamic observation data are used for inverse modeling. Issues such as how to account for interferometric synthetic aperture radar data, which may be encountered using the EnKF for real case studies, are discussed.

Application of the flow dimension concept for numerical drawdown data analyses in mixed-flow karst systems

A numerical discrete conduit-continuum model is employed to investigate large-scale groundwater abstraction in karst aquifers. The application of large-scale experiments is one approach to deal with the scale problem in hydraulic parameter assessment, caused by significant contrasts of hydraulic parameters in a karst aquifer. Here, conduit drawdown is evaluated by diagnostic plots and by considering the apparent flow dimension. These tools are frequently used for the interpretation of hydraulic borehole tests by analytical solutions. In contrast to existing analytical solutions, a numerical groundwater model allows the incorporation of the effect of complex parameter distributions. The objective is to demonstrate the application of diagnostic plots and flow dimension analysis for a systematic analysis of the effect of different boundary conditions as well as sink/source terms for idealized two-dimensional mixed karst aquifer systems, which ultimately extends existing analytical solutions and, therefore, contributes to the interpretation of measured field data. The analysis is focused on the apparent flow dimension and shows the extension of the cross-sectional flow area for selected models. The results are used to evaluate the large-scale pumping test of the karstified Cent Fonts catchment (Languedoc, France). The inverse calibration of two realistic, but still simplified, catchment models reveals that the apparent flow dimension supplies useful information about the general flow pattern during the Cent Fonts pumping test. The flow dimension after the end of the storage period can be explained by a large contribution of exchange flow resulting in a strong influence of radial flow on regional, i.e., kilometer scale.

Transient Pressure Behavior of a Well Located between a Constant Pressure Boundary and a Sealing Fault

Pressure transient analysis has been used to evaluate performance of a well located between one sealing fault and one constant pressure boundary. Type curves were generated by determining 1) dimensionless pressure and 2) rate of change of dimensionless pressure drop with respect to dimensionless time. When the well is located closer to the no flow boundary, both sets of type curves have three distinct slopes. These slopes characterize: 1) flow in an infinite reservoir, 2) presence of the no flow, and 3) the constant-pressure boundaries. When the well is closer to the constant pressure boundary, the type curves show two distinct slopes. These correspond to: 1) flow in an infinite reservoir, and 2) the presence of a constant pressure boundary. The type curves can be used to match actual pressure drawdown data and determine the drainage area and relative well location with respect to physical boundaries.

On the importance of geological data for hydraulic tomography analysis: Laboratory sandbox study

This paper investigates the importance of geological data in Hydraulic Tomography (HT) through sandbox experiments. In particular, four groundwater models with homogeneous geological units constructed with borehole data of varying accuracy are jointly calibrated with multiple pumping test data of two different pumping and observation densities. The results are compared to those from a geostatistical inverse model. Model calibration and validation performances are quantitatively assessed using drawdown scatterplots. We find that accurate and inaccurate geological models can be well calibrated, despite the estimated K values for the poor geological models being quite different from the actual values. Model validation results reveal that inaccurate geological models yield poor drawdown predictions, but using more calibration data improves its predictive capability. Moreover, model comparisons among a highly parameterized geostatistical and layer-based geological models show that, (1) as the number of pumping tests and monitoring locations are reduced, the performance gap between the approaches decreases, and (2) a simplified geological model with a fewer number of layers is more reliable than the one based on the wrong description of stratigraphy. Finally, using a geological model as prior information in geostatistical inverse models results in the preservation of geological features, especially in areas where drawdown data are not available. Overall, our sandbox results emphasize the importance of incorporating geological data in HT surveys when data from pumping tests is sparse. These findings have important implications for field applications of HT where well distances are large.

Transient temperature behavior and analysis of single-phase liquid-water geothermal reservoirs during drawdown and buildup tests: Part I. Theory, new analytical and approximate solutions

This work focuses on transient temperature responses of single-phase liquid-water geothermal reservoirs to constant-rate drawdown and buildup tests. New analytical and approximate solutions are presented for predicting drawdown and buildup sand-face transient temperature behaviors of a fully penetrating vertical well in an infinite-acting homogeneous reservoirs. The solutions account for the effects of Joule-Thomson (J-T) heating/cooling, transient adiabatic fluid expansion/compression, convection, and conduction. The solutions are compared and verified with the solutions from three different non-isothermal simulators that solve the mass and thermal energy balance equations rigorously and simultaneously. The impacts of various parameters such as wellbore storage, skin zone near the wellbore, thermal conductivity, and outer reservoir boundary conditions on the sand-face temperature responses are also investigated and discussed. Drawdown and buildup sand-face temperature data are shown to exhibit three infinite-acting radial flow (IARF) periods (represented by semi-log straight-line equations); early-time IARF reflecting the adiabatic expansion/compression effects in the skin zone if it exists, intermediate-time IARF reflecting the J-T effect in the skin zone, and late-time IARF reflecting the J-T effect in the non-skin zone. In an accompanying paper (Part II), we present an interpretation and analysis methodology based on the analytical solutions derived here for parameter estimation from temperature transient data jointly with pressure transient data.

Transient temperature behavior and analysis of single-phase liquid-water geothermal reservoirs during drawdown and buildup tests: Part II. Interpretation and analysis methodology with applications

In this work, we present new semi-log straight line and temperature-derivative methods for interpreting and analyzing temperature transient data acquired during drawdown and buildup tests in an infinite acting homogeneous, single-phase liquid-water geothermal reservoirs. The methods are based on the analytical solutions derived in our accompanied paper (Part I) accounting for the effects of Joule-Thomson (J-T) heating/cooling, transient adiabatic fluid expansion/compression, convection, and conduction. Drawdown and buildup sand-face temperature data are shown to exhibit three infinite-acting radial flow (IARF) periods; early-time IARF reflecting the adiabatic expansion/compression effects in the skin zone if it exists, intermediate-time IARF reflecting the J-T effects in the skin zone, and late-time IARF reflecting the J-T effect in the non-skin zone. Semi-log straight-line analyses based on the identified proper IARF regimes and their time intervals on a log-log diagnostic plot of the absolute value of temperature-derivative vs. elapsed time, jointly with conventional pressure transient analysis (PTA), provide estimates of porosity, J-T coefficient of fluid, mobility of skin and non-skin zones as well as radius of the skin zone, which are not readily accessible from PTA alone. The applicability of the proposed analysis methods is demonstrated by considering two synthetic test examples and one field test data set.

Extending Theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

AbstractA framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi‐Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log‐transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations.

Comprehensive Solution for Transient Flow in Heterogeneous Porous Media

Solutions of the hydraulic diffusivity equation are of utmost importance for many reservoir engineering problems. Despite all the efforts, there is still a need for the development of rigorous and comprehensive solutions for transient flow problems in heterogeneous oil reservoirs. This study demonstrates the use of an integral transform approach to obtain such a rigorous and comprehensive solution for the hydraulic diffusivity equation in heterogeneous porous domain. The reservoir heterogeneities can be approximated by any continuous differentiable function. The presented general solution and its derivation are valid for multi-dimensional problems in any orthogonal coordinate system. It has the advantage of rigorously solving the hydraulic diffusivity equation for transient, late-transient and steady-state (or pseudo-steady-state) flow regimes in a single formulation that allows the consideration of variable flowrates. In this work, applications of the general solution for one-dimensional problems in the Cartesian and radial coordinate systems are presented, showing comparisons of the results obtained with a finite difference numerical scheme. The solution presented can be used to analyze buildup, drawdown and interference test data, making it a useful tool for pressure transient analysis applied to reservoir engineering problems.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

Summary We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A . In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy’s law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg–Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

Forward Coupled Modeling and Assessment of Gravity Anomalies Caused by Pumping Tests in Unconfined Aquifers Under Unsteady-State Conditions

Analysis of drawdown data from pumping tests is the most common method for identification of aquifer properties and estimation of hydraulic parameters in hydrogeology. Limited hard hydraulic data from wells, expensive and intrusive, can be supplemented with geophysical spatially distributed information. Gravity, sensible to mass variations, can provide information about hydraulic parameters and storage coefficients of aquifers. A satisfactory use of gravity requires the computation of temporal evolution of gravity anomalies related with the dynamic hydraulic process. For simplified and ideal problems, the calculation can be accomplished with analytical solutions. However, the limitations of analytical solutions in capturing some relevant characteristics, like heterogeneities, that require the use of numerical models, are well known. This article shows how the time-dependent gravity anomaly caused by a pumping test can be calculated in a unique code, in a coupled manner and in a single run. The methodology avoids the use and transference of data between various codes and can be utilized in a coupled hydrogeophysical inversion procedure. Additionally, it is flexible enough to include a wide range of characteristics that can be encountered in any pumping test, and is an adequate framework for field survey planning via analysis and study of time-dependent gravity curves.

Finding the right balance between groundwater model complexity and experimental effort via Bayesian model selection

Summary Groundwater modelers face the challenge of how to assign representative parameter values to the studied aquifer. Several approaches are available to parameterize spatial heterogeneity in aquifer parameters. They differ in their conceptualization and complexity, ranging from homogeneous models to heterogeneous random fields. While it is common practice to invest more effort into data collection for models with a finer resolution of heterogeneities, there is a lack of advice which amount of data is required to justify a certain level of model complexity. In this study, we propose to use concepts related to Bayesian model selection to identify this balance. We demonstrate our approach on the characterization of a heterogeneous aquifer via hydraulic tomography in a sandbox experiment (Illman et al., 2010). We consider four increasingly complex parameterizations of hydraulic conductivity: (1) Effective homogeneous medium, (2) geology-based zonation, (3) interpolation by pilot points, and (4) geostatistical random fields. First, we investigate the shift in justified complexity with increasing amount of available data by constructing a model confusion matrix . This matrix indicates the maximum level of complexity that can be justified given a specific experimental setup. Second, we determine which parameterization is most adequate given the observed drawdown data. Third, we test how the different parameterizations perform in a validation setup. The results of our test case indicate that aquifer characterization via hydraulic tomography does not necessarily require (or justify) a geostatistical description. Instead, a zonation-based model might be a more robust choice, but only if the zonation is geologically adequate.