Aquifer heterogeneity characterization with oscillatory pumping: Sensitivity analysis and imaging potential

Abstract

[1] Periodic pumping tests, in which a fluid is extracted during half a period, then reinjected, have been used historically to estimate effective aquifer properties. In this work, we suggest a modified approach to periodic pumping test analysis in which one uses several periodic pumping signals of different frequencies as stimulation, and responses are analyzed through inverse modeling using a ''steady-periodic'' model formulation. We refer to this strategy as multifrequency oscillatory hydraulic imaging. Oscillating pumping tests have several advantages that have been noted, including no net water extraction during testing and robust signal measurement through signal processing. Through numerical experiments, we demonstrate additional distinct advantages that multifrequency stimulations have, including: (1) drastically reduced computational cost through use of a steady-periodic numerical model and (2) full utilization of the aquifer heterogeneity information provided by responses at different frequencies. We first perform fully transient numerical modeling for heterogeneous aquifers and show that equivalent results are obtained using a faster steady-periodic heterogeneous numerical model of the wave phasor. The sensitivities of observed signal response to aquifer heterogeneities are derived using an adjoint state-based approach, which shows that different frequency stimulations provide complementary information. Finally, we present an example 2-D application in which sinusoidal signals at multiple frequencies are used as a data source and are inverted to obtain estimates of aquifer heterogeneity. These analyses show the different heterogeneity information that can be obtained from different stimulation frequencies, and that data from several sinusoidal pumping tests can be rapidly inverted using the steady-periodic framework.

What does hydraulic tomography tell us about fractured geological media? A field study and synthetic experiments

“…The Culebra is known as a laminated to thinly bedded argillaceous dolomite with abundant open and gypsum-filled fractures. Packers were placed in the seven boreholes for a series of sinusoidal pumping tests which were conducted at the upper and the lower zone of two boreholes, i.e., an oscillatory hydraulic tomographic survey (Cardiff et al, 2013). Lavenue and de Marsily (2001) then employed the pilot point inverse method and heterogeneous conceptual model to characterize the K field in the Culebra dolomite formation, using these data sets and available geologic facies data.…”

Strategies for avoiding errors and ambiguities in the analysis of oscillatory pumping tests

“…In a homogeneous aquifer, Rasmussen et al (2003) developed an integral expression describing the initial period of non-steady-periodic response, which can be evaluated numerically. Practically, Cardiff et al (2013) showed through numerical experiments that these conditions are often obtained within 5-10 periods of oscillation for reasonable aquifer conditions. Similarly, Zhou et al (2016) showed that in laboratory sandbox conditions, similarly quick attainment of steady-periodic conditions was observed.…”

“…While analytical processing techniques presented to-date generally use the amplitude and phase of the obtained head signal to produce aquifer parameter estimates, the Oscillatory Hydraulic Tomography (OHT) / Oscillatory Hydraulic Imaging (OHI) approach advocated by Cardiff et al (2013), which uses phasor coefficients instead of amplitude and phase as measurements, faces similar issues.…”

“…Alternatively, instead of performing standard one-at-a-time processing of pumping test data, the responses at 3 several observation wells (and, possibly, from multiple pumping tests) can be analyzed simultaneously using numerical, frequency-domain groundwater flow models. This process, dubbed Oscillatory Hydraulic Tomography or Oscillatory Hydraulic Imaging (Cardiff et al 2013, Zhou et al 2016 can take advantage of the differing sensitivities of tests performed across a range of pumping locations, observation locations, and frequencies in order to produce maps of heterogeneous aquifer properties. Blind application of either of these approaches, however, can lead to nonsensical results if "phase wrapping" occurs -i.e.…”

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

“…After the pioneering development of three dimensional HT models and simulations by Yeh and Liu [2000] and Zhu and Yeh [2005] and laboratory experiments by Liu et al [2002], numerous HT studies have been conducted using numerical models [Bohling et al, 2002;Xiang et al, 2009;Cardiff et al, 2009;Cardiff and Barrash, 2011;Liu and Kitanidis, 2011], controlled sandbox experiments Illman et al, 2007Illman et al, , 2008Illman et al, , 2010Yin and Illman, 2009;Berg and Illman, 2011a;Liu and Kitanidis, 2011], and field pumping tests [Bohling et al, 2007;Illman et al, 2009;Huang et al, 2011;Brauchler et al, 2011;Berg and Illman, 2011b, 2015Cardiff et al, 2009Cardiff et al, , 2012Cardiff et al, , 2013a. Among the various studies, steady state Cardiff et al, 2009], temporal moment Yin and Illman, 2009], transient Liu et al, 2007], travel time [Brauchler et al, 2011], and oscillatory pressure signal [Cardiff et al, 2013b] data have been inverted to map heterogeneity patterns. Compared to hydraulic parameters estimated via traditional approaches, such as kriging of local-scale data or effective parameters by treating the aquifer to be homogeneous, Illman et al [2010] and Illman [2011a, 2015] found that hydraulic parameters estimated through HT are significantly better in predicting drawdown responses.…”