Necessary conditions for inverse modeling of flow through variably saturated porous media

Wan

et al. 2013

Self Cite

[1] In this study, we developed a stochastic estimator for characterizing the hydraulic heterogeneity in both unsaturated and saturated zones of unconfined aquifers using transient drawdown data from sequential pumping tests. This estimator was built upon the successive linear estimator by Yeh et al. (1996), the simultaneous successive linear estimator by Xiang et al. (2009), and the 3-D finite element program for flow and transport through heterogeneous media by Srivastava and Yeh (1992). The estimator was tested afterward using simulated data sets of sequential pumping tests in a synthetic unconfined aquifer where saturated conductivity, specific storage, saturated water content, and pore-size distribution parameter vary spatially in three dimensions. Test results show that the estimator is able to produce parameter fields that capture the overall 3-D pattern of the true heterogeneous parameter fields. We subsequently validated the estimated parameter fields by assessing their ability to predict drawdowns during an independent pumping test, which was not used during the estimation phase. Results of the validation show that the predicted drawdowns based on the estimated heterogeneous parameter fields are in close agreement with the true drawdowns. In addition, predicted drawdowns based on the parameter fields from the joint interpretation are superior to those based on the parameters estimated from the homogeneous conceptual model. Lastly, while many field experiments are necessary to fully assess the robustness of this estimator and sequential pumping tests, results of this study suggest they are a promising characterization technique for unconfined aquifers.

Section: Equivalent Homogenous Conceptual Modelmentioning

confidence: 99%

Section: Highly Parameterized Heterogeneous Conceptual Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Joint interpretation of sequential pumping tests in unconfined aquifers

Mao

Wan

et al. 2013

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“…In order to provide a fair comparison, we simultaneously calibrated the 480 data selected from five pumping tests which are the same for SLE calibration. Such a large number of nonredundant data sets ensure the requirement of necessary conditions as outlined by Mao et al [2013a] for the inverse problem for homogeneous aquifers to be well defined. The effective parameters were estimated as K eff 5 1.47 3 10 22 cm/s and S seff 5 3.04 3 10 25 /cm for the saturated zone, and a eff 5 1.1 3 10 21 /cm, h seff 5 0.40 for unsaturated zone, while fixing the residual water content, h r 5 0.06.…”

Section: Comparison Of Ht Results With Homogeneous Model Resultsmentioning

confidence: 99%

“…A transient inverse model was first developed by Hughson and Yeh [2000] using successive linear estimator (SLE) for estimating hydraulic parameters under variably saturated flow. Mao et al [2013a] elucidated the necessary condition for inverse modeling of flow through variably saturated porous media to obtain a unique solution. Afterward, Mao et al [2013b] examined the cross correlation between the observed head during a pumping test in unconfined aquifers and variably saturated hydraulic parameters of the aquifers.…”

Section: Introductionmentioning

confidence: 99%

Validation of hydraulic tomography in an unconfined aquifer: A controlled sandbox study

Zhao

Illman

et al. 2015

Self Cite

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 Mao et al. (2013c) 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.

The relative importance of head, flux, and prior information in hydraulic tomography analysis

Tso

Wen

2016

Using cross-correlation analysis, we demonstrate that flux measurements at observation locations during hydraulic tomography (HT) surveys carry nonredundant information about heterogeneity that are complementary to head measurements at the same locations. We then hypothesize that a joint interpretation of head and flux data, even when the same observation network as head has been used, can enhance the resolution of HT estimates. Subsequently, we use numerical experiments to test this hypothesis and investigate the impact of flux conditioning and prior information (such as correlation lengths and initial mean models (i.e., uniform mean or distributed means)) on the HT estimates of a nonstationary, layered medium. We find that the addition of flux conditioning to HT analysis improves the estimates in all of the prior models tested. While prior information on geologic structures could be useful, its influence on the estimates reduces as more nonredundant data (i.e., flux) are used in the HT analysis. Lastly, recommendations for conducting HT surveys and analysis are presented.