Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multi-method and multiscale validation of (original) (raw)
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Journal of Hydrology, 2007
Hydraulic tomography potentially is a viable technology that facilitates subsurface imaging of hydraulic heterogeneity. To date, a comprehensive validation of hydraulic tomography has not been done either at the laboratory or field scales. The main objective of this paper is to examine the accuracy of hydraulic conductivity (K) tomograms obtained from the steady-state hydraulic tomography algorithm of [Yeh, T.-C. J., Liu, S., 2000. Hydraulic tomography: development of a new aquifer test method. Water Resources Research 36, 2095-2105]. We first obtain a reference K tomogram through the inversion of synthetic cross-hole test data generated through numerical simulations. The purpose of reference K tomogram generation is to examine the ability of the algorithm to image the heterogeneity pattern under optimal conditions without experimental errors and with full control of forcing functions (initial and boundary conditions as well as source/sink terms). Parallel to the generation of synthetic data, we conduct hydraulic tests at multiple scales in a laboratory aquifer with deterministic heterogeneity to generate data that are used to validate K tomograms from hydraulic tomography. Measurements include multiple K estimates from core, slug, single-hole and cross-hole tests as well as several unidirectional, flow-through experiments conducted on the sandbox under steady-state conditions. Validation of K tomograms involved a multi-method and multiscale approach proposed herein which include: (1) visual comparisons of K tomograms to the true sand distributions and the reference K tomogram; (2) testing the ability of 0022-1694/$ -see front matter Published by Elsevier B.V. a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j h y d r o l
Water resources research, 2007
Hydraulic tomography is a promising approach for obtaining information on variations in hydraulic conductivity on the scale of relevance for contaminant transport investigations. This approach involves performing a series of pumping tests in a format similar to tomography. We present a field-scale assessment of hydraulic tomography in a porous aquifer, with an emphasis on the steady shape analysis methodology. The hydraulic conductivity (K) estimates from steady shape and transient analyses of the tomographic data compare well with those from a tracer test and direct-push permeameter tests, providing a field validation of the method. Zonations based on equal-thickness layers and cross-hole radar surveys are used to regularize the inverse problem. The results indicate that the radar surveys provide some useful information regarding the geometry of the K field. The steady shape analysis provides results similar to the transient analysis at a fraction of the computational burden. This study clearly demonstrates the advantages of hydraulic tomography over conventional pumping tests, which provide only large-scale averages, and small-scale hydraulic tests (e.g., slug tests), which cannot assess strata connectivity and may fail to sample the most important pathways or barriers to flow.
Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site
Groundwater, 2014
Over the past several decades, different groundwater modeling approaches of various complexities and data use have been developed. A recently developed approach for mapping hydraulic conductivity (K ) and specific storage (S s ) heterogeneity is hydraulic tomography, the performance of which has not been compared to other more ''traditional'' methods that have been utilized over the past several decades. In this study, we compare seven methods of modeling heterogeneity which are (1) kriging, (2) effective parameter models, (3) transition probability/Markov Chain geostatistics models, (4) geological models, (5) stochastic inverse models conditioned to local K data, (6) hydraulic tomography, and hydraulic tomography conditioned to local K data using data collected in five boreholes at a field site on the University of Waterloo (UW) campus, in Waterloo, Ontario, Canada. The performance of each heterogeneity model is first assessed during model calibration. In particular, the correspondence between simulated and observed drawdowns is assessed using the mean absolute error norm, (L 1 ), mean square error norm (L 2 ), and correlation coefficient (R) as well as through scatterplots. We also assess the various models on their ability to predict drawdown data not used in the calibration effort from nine pumping tests. Results reveal that hydraulic tomography is best able to reproduce these tests in terms of the smallest discrepancy and highest correlation between simulated and observed drawdowns. However, conditioning of hydraulic tomography results with permeameter K data caused a slight deterioration in accuracy of drawdown predictions which suggests that data integration may need to be conducted carefully.
Hydraulic Tomography: Continuity and Discontinuity of High- K and Low- K Zones
Groundwater, 2015
Hydraulic tomography is an emerging field and modeling method that provides a continuous hydraulic conductivity (K ) distribution for an investigated region. Characterization approaches that rely on interpolation between one-dimensional (1D) profiles have limited ability to accurately identify high-K channels, juxtapositions of lenses with high K contrast, and breaches in layers or channels between such profiles. However, locating these features is especially important for groundwater flow and transport modeling, and for design and operation of in situ remediation in complex hydrogeologic environments. We use transient hydraulic tomography to estimate 3D K in a volume of 15-m diameter by 20-m saturated thickness in a highly heterogeneous unconfined alluvial (clay to sand-and-gravel) aquifer with a K range of approximately seven orders of magnitude at an active industrial site in Assemini, Sardinia, Italy. A modified Levenberg-Marquardt algorithm was used for geostatistical inversion to deal with the nonlinear nature of the highly heterogeneous system. The imaging results are validated with pumping tests not used in the tomographic inversion. These tests were conducted from three of five clusters of continuous multichannel tubing (CMTs) installed for observation in the tomographic testing. Locations of high-K continuity and discontinuity, juxtaposition of very high-K and very low-K lenses, and low-K ''plugs'' are evident in regions of the investigated volume where they likely would not have been identified with interpolation from 1D profiles at the positions of the pumping well and five CMT clusters. Quality assessment methods identified a suspect high-K feature between the tested volume and a lateral boundary of the model.
Practical Issues in Imaging Hydraulic Conductivity through Hydraulic Tomography
Ground Water, 2007
Hydraulic tomography has been developed as an alternative to traditional geostatistical methods to delineate heterogeneity patterns in parameters such as hydraulic conductivity (K) and specific storage (Ss). During hydraulic tomography surveys, a large number of hydraulic head data are collected from a series of cross-hole tests in the subsurface. These head data are then used to interpret the spatial distribution of K and Ss using inverse modeling. Here, we use the Sequential Successive Linear Estimator (SSLE) of Yeh and Liu (2000) to interpret synthetic pumping test data created through numerical simulations and real data generated in a laboratory sandbox aquifer to obtain the K tomograms. Here, we define “K tomogram” as an image of K distribution of the subsurface (or the inverse results) obtained via hydraulic tomography. We examine the influence of signal-to-noise ratio and biases on results using inverse modeling of synthetic and real cross-hole pumping test data. To accomplish this, we first show that the pumping rate, which affects the signal-to-noise ratio, and the order of data included into the SSLE algorithm both have large impacts on the quality of the K tomograms. We then examine the role of conditioning on the K tomogram and find that conditioning can improve the quality of the K tomogram, but can also impair it, if the data are of poor quality and conditioning data have a larger support volume than the numerical grid used to conduct the inversion. Overall, these results show that the quality of the K tomogram depends on the design of pumping tests, their conduct, the order in which they are included in the inverse code, and the quality as well as the support volume of additional data that are used in its computation.
Field Study of Subsurface Heterogeneity with Steady-State Hydraulic Tomography
Ground Water, 2013
Remediation of subsurface contamination requires an understanding of the contaminant (history, source location, plume extent and concentration, etc.), and, knowledge of the spatial distribution of hydraulic conductivity (K ) that governs groundwater flow and solute transport. Many methods exist for characterizing K heterogeneity, but most if not all methods require the collection of a large number of small-scale data and its interpolation. In this study, we conduct a hydraulic tomography survey at a highly heterogeneous glaciofluvial deposit at the North Campus Research Site (NCRS) located at the University of Waterloo, Waterloo, Ontario, Canada to sequentially interpret four pumping tests using the steady-state form of the Sequential Successive Linear Estimator (SSLE) (Yeh and Liu 2000). The resulting three-dimensional (3D) K distribution (or K -tomogram) is compared against: (1) K distributions obtained through the inverse modeling of individual pumping tests using SSLE, and (2) effective hydraulic conductivity (K eff ) estimates obtained by automatically calibrating a groundwater flow model while treating the medium to be homogeneous. Such a K eff is often used for designing remediation operations, and thus is used as the basis for comparison with the K -tomogram. Our results clearly show that hydraulic tomography is superior to the inversions of single pumping tests or K eff estimates. This is particularly significant for contaminated sites where an accurate representation of the flow field is critical for simulating contaminant transport and injection of chemical and biological agents used for active remediation of contaminant source zones and plumes.
Hydraulic tomography: Development of a new aquifer test method
Water Resources Research, 2000
Hydraulic tomography (i.e., a sequential aquifer test) has recently been proposed as a method for characterizing aquifer heterogeneity. During a hydraulic tomography experiment, water is sequentially pumped from or injected into an aquifer at different vertical portions or intervals of the aquifer. During each pumping or injection, hydraulic head responses of the aquifer at other intervals are monitored, yielding a set of head/discharge (or recharge) data. By sequentially pumping (or injecting) water at one interval and monitoring the steady state head responses at others, many head/discharge (recharge) data sets are obtained. In this study a sequential inverse approach is developed to interpret results of hydraulic tomography. The approach uses an iterative geostatistical inverse method to yield the effective hydraulic conductivity of an aquifer, conditioned on each set of head/discharge data. To efficiently include all the head/discharge data sets, a sequential conditioning method is employed. It uses the estimated hydraulic conductivity field and covariances, conditioned on the previous head/discharge data set, as prior information for next estimations using a new set of pumping data. This inverse approach was first applied to hypothetical, two-dimensional, heterogeneous aquifers to investigate the optimal sampling scheme for the hydraulic tomography, i.e., the design of well spacing, pumping, and monitoring locations. The effects of measurement errors and uncertainties in statistical parameters required by the inverse model were also investigated. Finally, the robustness of this inverse approach was demonstrated through its application to a hypothetical, three-dimensional, heterogeneous aquifer.
Validation of hydraulic tomography in an unconfined aquifer: A controlled sandbox study
Water Resources Research, 2015
In this study, we demonstrate the effectiveness of hydraulic tomography (HT) that considers variably saturated flow processes in mapping the heterogeneity of both the saturated and unsaturated zones in a laboratory unconfined aquifer. The successive linear estimator (SLE) developed by for interpreting HT in unconfined aquifers is utilized to obtain tomograms of hydraulic conductivity (K), specific storage (S s ), and the unsaturated zone parameters (pore size parameter (a) and saturated water content (h s )) for the Gardner-Russo's model. The estimated tomograms are first evaluated by visually comparing them with stratigraphy visible in the sandbox. Results reveal that the HT analysis is able to accurately capture the location and extent of heterogeneity including high and low K layers within the saturated and unsaturated zones, as well as reasonable distribution patterns of a and h s for the Gardner-Russo's model. We then validate the estimated tomograms through predictions of drawdown responses of pumping tests not used during the inverse modeling effort. The strong agreement between simulated and observed drawdown curves obtained by pressure transducers and tensiometers demonstrates the robust performance of HT that considers variably saturated flow processes in unconfined aquifers and the unsaturated zone above it. In addition, compared to the case using the homogeneous assumption, HT results, as expected, yield significantly better predictions of drawdowns in both the saturated and unsaturated zones. This comparison further substantiates the unbiased and minimal variance of HT analysis with the SLE algorithm.
Laboratory sandbox validation of transient hydraulic tomography
Water Resources Research, 2007
Hydraulic tomography is a method that images the hydraulic heterogeneity of the subsurface through the inversion of multiple pumping or cross-hole hydraulic test data. Transient hydraulic tomography is different from steady state hydraulic tomography in that it utilizes transient hydraulic head records to yield the distribution of hydraulic conductivity (K) as well as specific storage (S s) of an aquifer. In this paper we demonstrate the robustness of transient hydraulic tomography through the use of hydraulic head data obtained from multiple cross-hole pumping tests conducted in a laboratory sandbox with deterministic heterogeneity. We utilize the algorithm developed by Zhu and Yeh (2005) to conduct the transient inversions and validate the K and S s tomograms using a multimethod and multiscale validation approach previously proposed by Illman et al. (2006). Validation data consist of cross-hole tests not used in the inversion as well as other hydraulic tests that provided local (core, single-hole tests) as well as large-scale (unidirectional flow-through tests) estimates of hydraulic parameters. Results show that the algorithm is able to yield consistent estimates that agree with independently collected local as well as large-scale hydraulic parameter data. In addition, we find that the transient hydraulic tomography requires a fewer number of pumping tests to estimate a similar quality K tomogram when compared with steady state hydraulic tomography, as the former approach utilizes more data from each pumping test. Overall, we find that transient hydraulic tomography is a robust subsurface characterization technique that can delineate the subsurface heterogeneity in both K and S s from multiple pumping or crosshole hydraulic tests.