Steady-state Hydraulic Tomography Research Articles

Identification of high-permeability and water-rich zones in a fractured karst water source area based on the hydraulic tomography method

Determining the spatial hydraulic parameters of aquifers is of paramount importance for the development and utilization of groundwater in water source areas. However, most methods are unable to accurately characterize the heterogeneity of aquifers because of the influences of complex geology, hydrogeology, structure and insufficient information. Hydraulic tomography (HT) is an effective and robust method for hydraulic parameter inversion to characterize heterogeneity. In this study, a two-dimensional HT model was established to simulate hydraulic parameter fields for a fractured karst aquifer in the Zhangji water source area (Xuzhou city, China). Steady-state hydraulic tomography (SSHT) and transient hydraulic tomography (THT) with different prior information conditions were applied to determine the high-permeability area and water-rich zones, and to infer possible locations of karst conduits and strong runoff paths in the water source area. The results indicate that: (1) THT can better reveal larger-scale heterogeneous characteristics of hydraulic properties compared to SSHT. The hydraulic conductivity distribution estimated by THT correlates well with the geological conditions of the area, especially in identifying water-rich zones formed by faults and other formations. (2) When combined with geological conditions, HT possesses the ability to identify strong runoff paths in fractured karst aquifers. (3) Accurate prior information, which is more relevant to the head response information, is conducive to obtaining more acceptable HT results. (4) THT can simultaneously identify high-permeability and high-storage zones, and the analysis of the overlap of these two regions has the potential to predict underground water reservoirs, which is of the utmost importance for the development and utilization of groundwater resources in water source areas.

A new attempt for the detection of potential water-bearing structures in tunnels via hydraulic tomography: The first numerical investigation

Water-bearing geological structures in front of the tunnel and underground engineering are prone to water inrush hazards, which seriously threaten construction safety. This study investigated the potential of hydraulic tomography (HT) in detecting water-bearing structures to prevent groundwater hazards in tunnels. We established two synthetic heterogeneous aquifers with two different water-bearing structures, fractures and cavern zones. A comprehensive HT inversion analysis was performed using hydraulic head records generated by forward hydraulic tests. The results show that 1) sufficient pumping and observation wells can assist in capturing water-bearing structures and hydraulic properties; 2) transient hydraulic tomography (THT) inversion has a better effect than steady-state hydraulic tomography (SSHT) inversion since the temporal variation of head records carries non-redundant characteristics and distribution information of water-bearing structures; 3) inverted hydraulic conductivity and specific storage fields are positively correlated with observed heads at the end and early stages of the pumping test, respectively; 4) taking geological information as a prior can greatly assist in mapping potential water-bearing structures. This study can provide valuable guidance for detecting water-bearing structures in tunnel and underground engineering and formulating effective control schemes for water inrush hazards.

Improved high-resolution characterization of hydraulic conductivity through inverse modeling of HPT profiles and steady-state hydraulic tomography: Field and synthetic studies

• Inverse modeling approach proposed to invert cm-scale K from HPT surveys. • Based on inverted K , a new power-law model was developed for HPT surveys at NCRS. • The site-specific model predicted K values that correspond well with permeameter K. • Integrating HPT-inverted K into SSHT better defined sharp boundaries of a K field. Direct-push based hydraulic profiling tool (HPT) and geostatistically-based hydraulic tomography (HT) are two promising techniques for the high-resolution estimation of hydraulic conductivity ( K ) for unconsolidated sediments. Although HPT surveys could be conducted rapidly, relating the 1.5-cm resolution injection logging profiles to K always involve the upscaling of centimeter-scale measurements to coarser intervals for the development of site-specific formulae. On the other hand, K fields reconstructed by HT could be smooth when pumping test data are sparse. In this study, an inverse modeling approach was firstly utilized to estimate K values directly from HPT survey data for the glaciofluvial deposits at the North Campus Research Site (NCRS) in Waterloo, Ontario, Canada. A site-specific power-law relationship was generated for the NCRS to relate HPT profiles to the vertical distributions of K . Then, the proposed inverse modeling approach was evaluated with a two-dimensional synthetic aquifer under controlled conditions, and the estimated K profiles from inverse analysis of synthetic HPT surveys were incorporated into the steady-state HT. Results of the field study showed that K estimates from the developed formula corresponded better with K values from permeameter tests, than those estimated from the empirical model of McCall and Christy (2010) for HPT surveys. Moreover, through synthetic experiments, we demonstrated that integration of K values inverted from HPT into steady-state HT analyses yielded K tomograms that were significantly better than the geostatistical inversion results relying on pumping test data alone. Overall, this study highlights the need in developing site-specific formulae for the HPT and the joint implementation of HPT and HT techniques for the more cost-effective high-resolution characterization of subsurface heterogeneity.

Numerical investigation of hydraulic tomography for mapping karst conduits and its connectivity

Hydraulic tomography (HT) is a well-established approach to successfully describe subsurface hydraulic heterogeneity. This work explored the potential of HT and the simultaneous successive linear estimator algorithm to map the distribution and connectivity of karst conduits and their hydraulic parameters at the engineering scale. Three generalized synthetic karst conduit models, auxiliary conduit, cave and waterfall, were established. A series of pumping tests were conducted at different locations as forward simulations to collect hydraulic head responses. These responses were then used for the HT inversion analysis to estimate hydraulic parameter fields of karst aquifers under steady-state and transient conditions. Our results show that high-density observation wells substantially assist with interpreting the reliable spatial distribution of hydraulic parameters. With the increase in the number of pumping wells in the HT inversion, the estimates of hydraulic conductivity and specific storage became more accurate for the auxiliary conduit model, but for the cave and waterfall models, there was no significant improvement. The hydraulic conductivity (K) tomograms from transient hydraulic tomography (THT) better indicated the heterogeneity of the three karst models than those from steady-state hydraulic tomography (SSHT) because a large number of hydraulic head records were introduced into the THT inversion process. Moreover, when reliable geological data are available, the accuracy of the estimated hydraulic parameter maps can be greatly improved even if only infrequent hydraulic head measurements can be obtained, implying that a priori geological information may be extremely valuable in mapping karst conduit heterogeneity. Finally, the robustness of HT in mapping karst conduits is verified through the simulation of independent cross-hole pumping tests. This study proved that hydraulic tomography utilizing groundwater responses from a series of cross-hole pumping tests is an efficient and cost-effective way and provided a feasible method for accurate identification of hydraulic heterogeneity of karst aquifers.

Use of steady-state hydraulic tomography to inform the selection of a chaotic advection system

The concept of chaotic advection is a novel approach that has the potential to overcome some of the challenges associated with mixing of reagents that commonly occur when injection based in situ treatment techniques are used. The rotated potential mixing (RPM) flow system is one configuration which has been theorized to achieve chaotic advection in porous media, and enhance reagent mixing by periodically re-oriented dipole pumping at a series of radial wells. Prior to field implementation of chaotic advection, the selection of an RPM flow protocol will likely require a numerical model that can adequately represent groundwater flow within the zone of interest. As expected, the hydraulic conductivity (K) field is the most critical input requirement for the selected groundwater flow model. Hydraulic tomography (HT) is an innovative characterization approach that has shown potential to provide information on a K field. In this investigation, we explored whether the same well system required to invoke chaotic advection can also be applied in a HT analysis, and evaluated the use of the generated K tomogram for the selection of RPM flow parameters that can enhance reagent mixing. A series of dipole pumping tests were conducted within an area of interest as defined by the limits of the circular network of eight injection/extraction wells used to invoke chaotic advection. Hydraulic head data collected from independent dipole pumping tests were used in an inverse model to perform steady-state hydraulic tomography (SSHT) analysis to generate a K tomogram. Both the K tomogram and an effective parameter approach (i.e., a single K value assigned across the entire spatial domain as determined by single well pumping and slug tests) produced estimates of hydraulic head that closely resembled those observed due to the relative homogeneous nature of the aquifer and the small spatial scale of the area of interest. In contrast, particle tracking results showed that incorporating a heterogeneous K field significantly enhanced the spatial distribution of particle trajectories indicative of reagent mixing. These findings support the hypothesis that the same well system used to invoke chaotic advection can be combined with SSHT analysis as a viable site characterization tool for delineating the spatial variability of K. Incorporating this K tomogram in a groundwater flow model with a particle tracking engine can be used as a design tool to aid in the selection of a site-specific RPM flow protocol to achieve enhanced reagent mixing.

On the importance of geological data for three-dimensional steady-state hydraulic tomography analysis at a highly heterogeneous aquifer-aquitard system

Hydraulic tomography (HT) has been shown to map subsurface heterogeneity accurately through the joint interpretation of multiple pumping tests. Previous research has shown that smooth hydraulic conductivity (K) estimates are obtained beyond where pumping/observation data are available using the geostatistical inversion approach, when the inversion begins with a homogeneous K and when data densities are not high. However, geological data are typically available through outcrops and borehole logs to provide geological variability. Therefore, we investigate the usefulness of geological data for HT analysis at a highly heterogeneous field site by: (1) comparing calibrated geological models of two different resolutions to two homogeneous and four highly parameterized geostatistical inverse models, in terms of both model calibration and validation performances as well as correspondence of estimated K values with permeameter-estimated K profiles along boreholes; and (2) using geological models as prior information for the geostatistical inversion approach. Results reveal that the simultaneous calibration of geological models to seven pumping test data yields K values that correctly reflect the general patterns of vertical distributions of permeameter-estimated K. We also find that the geostatistical inversion approach using a geological model as prior information performs better for both model calibration and validation than using a homogenous K as a prior, and more importantly, improves the correspondence of K estimates to permeameter test results along wells, as well as in preserving geological features where drawdown measurements are lacking. Overall, our results suggest the joint use of both geological and pumping test data for HT analysis when accurate geological data are available.

Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems

We consider the computational challenges associated with uncertainty quantification involved in parameter estimation such as seismic slowness and hydraulic transmissivity fields. The reconstruction of these parameters can be mathematically described as inverse problems which we tackle using the geostatistical approach. The quantification of uncertainty in the geostatistical approach involves computing the posterior covariance matrix which is prohibitively expensive to fully compute and store. We consider an efficient representation of the posterior covariance matrix at the maximum a posteriori (MAP) point as the sum of the prior covariance matrix and a low-rank update that contains information from the dominant generalized eigenmodes of the data misfit part of the Hessian and the inverse covariance matrix. The rank of the low-rank update is typically independent of the dimension of the unknown parameter. The cost of our method scales as O(mlogm) where m dimension of unknown parameter vector space. Furthermore, we show how to efficiently compute measures of uncertainty that are based on scalar functions of the posterior covariance matrix. The performance of our algorithms is demonstrated by application to model problems in synthetic travel-time tomography and steady-state hydraulic tomography. We explore the accuracy of the posterior covariance on different experimental parameters and show that the cost of approximating the posterior covariance matrix depends on the problem size and is not sensitive to other experimental parameters.

Image-guided inversion in steady-state hydraulic tomography

In steady-state hydraulic tomography, the head data recorded during a series of pumping or/and injection tests can be inverted to determine the transmissivity distributions of an aquifer. This inverse problem is usually under-determined and ill-posed. We propose to use structural information inferred from a guiding image to constrain the inversion process. The guiding image can be drawn from soft data sets such as seismic and ground penetrating radar sections or from geological cross-sections inferred from the wells and some geological expertise. The structural information is extracted from the guiding image through some digital image analysis techniques. Then, it is introduced into the inversion process of the head data as a weighted four direction smoothing matrix used in the regularizer. Such smoothing matrix allows applying the smoothing along the structural features. This helps preserving eventual drops in the hydraulic properties. In addition, we apply a procedure called image-guided interpolation. This technique starts with the tomogram obtained from the image-guided inversion and focus this tomogram. These new approaches are applied on four synthetic toy problems. The hydraulic distributions estimated from the image-guided inversion are closer to the true transmissivity model and have higher resolution than those computed from a classical Gauss–Newton method with uniform isotropic smoothing.

Field Study of Subsurface Heterogeneity with Steady‐State Hydraulic Tomography

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 using temporal moments of drawdown recovery data: A laboratory sandbox study

Hydraulic tomography (HT) is a new technology that images the hydraulic heterogeneity of the subsurface. Unlike steady state hydraulic tomography (SSHT), which provides a hydraulic conductivity (K) tomogram, transient hydraulic tomography (THT) provides reliable tomograms of both K and specific storage (Ss). Effective as it may be, THT is a computationally demanding technique. To ease the computational burden, a HT which utilizes zeroth and first temporal moments of transient drawdown recovery data (HT‐m) has been developed by Zhu and Yeh (2006). This procedure simplifies the governing equation from a single parabolic equation to two Poisson's equations for the zeroth moment and characteristic time defined as the ratio between the first and zeroth moments. The approach was previously tested using synthetic simulations. The numerical experiments tested the feasibility of HT‐m under ideal conditions, where measurements and model are assumed to be free of error. In this paper, we further evaluate the performance of HT‐m using cross‐hole pumping tests conducted in a heterogeneous, synthetic aquifer constructed in a laboratory sandbox in more realistic situations, where the data used in the inversion are not free of experimental errors. Unlike field tests, the laboratory tests were conducted in a synthetic aquifer created with a prescribed heterogeneity pattern and all forcing functions (initial and boundary conditions and source‐sink terms) controlled. Results from the HT‐m approach were compared to those from THT previously conducted by Liu et al. (2007). Our results show that the estimation of the K tomogram using the HT‐m approach is reasonable, but the estimation of the Ss tomogram is unreliable in comparison to the THT approach.

Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multi-method and multiscale validation of hydraulic conductivity tomograms

Summary 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 the K tomogram to predict the hydraulic head distribution of an independent cross-hole test not used in the computation of the K tomogram; (3) comparison of the conditional mean and variance of local K from the K tomograms to the sample mean and variance of results from other measurements; (4) comparison of local K values from K tomograms to those from the reference K tomogram; and (5) comparison of local K values from K tomograms to those obtained from cores and single-hole tests. The multi-method and multiscale validation approach proposed herein further illustrates the robustness of steady-state hydraulic tomography in subsurface heterogeneity delineation.

Laboratory sandbox validation of transient hydraulic tomography

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 (Ss) 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 Ss 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 Ss from multiple pumping or cross‐hole hydraulic tests.