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Author ORCID ID is 0000000262220530
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  1. The identification of sources of advection–diffusion transport is based usually on solving complex ill-posed inverse models against the available state-variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influences of the original sources. Importantly, the number of these original release sources is typically unknown, which hinders reliability of the classical inverse-model analyses. To address this challenge, we present a novel hybrid method for identification of the unknown number of release sources. Our hybrid method, called HNMF, couples unsupervised learning based on Non-negative Matrix Factorization (NMF) andmore » inverse-analysis Green’s functions method. HNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green’s function of advection–diffusion equation to identify their characteristics. In the paper, we introduce the method and demonstrate that it is capable of identifying the advection velocity and dispersivity of the medium as well as the unknown number, locations, and properties of various sets of synthetic release sources with different space and time dependencies, based only on the recorded data. HNMF can be applied directly to any problem controlled by a partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations.« less
  2. In this paper, we extended the analytical level set method [1, 2] for identifying a piece-wisely heterogeneous (zonation) binary system to the case with an arbitrary number of materials with unknown material properties. In the developed level set approach, starting from an initial guess, the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables (hydraulic head) is minimized. We derived an expression for the propagation velocity of the interface between any two materials, which is related to the permeability contrast between the materials on two sides of the interface, the sensitivity ofmore » the head to permeability, and the head residual. We also formulated an expression for updating the permeability of all materials, which is consistent with the steepest descent of the objective function. The developed approach has been demonstrated through many examples, ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the Los Alamos National Laboratory. These examples indicate that the level set method can successfully identify zonation structures, even if the number of materials in the model domain is not exactly known in advance. Although the evolution of the material zonation depends on the initial guess field, inverse modeling runs starting with different initial guesses fields may converge to the similar final zonation structure. These examples also suggest that identifying interfaces of spatially distributed heterogeneities is more important than estimating their permeability values.« less
  3. Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. Tomore » address this problem, here, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.« less
  4. In this paper, we present a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means ofmore » Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. Finally, it is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.« less
  5. Identification of the original groundwater types present in geochemical mixtures observed in an aquifer is a challenging but very important task. Frequently, some of the groundwater types are related to different infiltration and/or contamination sources associated with various geochemical signatures and origins. The characterization of groundwater mixing processes typically requires solving complex inverse models representing groundwater flow and geochemical transport in the aquifer, where the inverse analysis accounts for available site data. Usually, the model is calibrated against the available data characterizing the spatial and temporal distribution of the observed geochemical types. Numerous different geochemical constituents and processes may needmore » to be simulated in these models which further complicates the analyses. In this paper, we propose a new contaminant source identification approach that performs decomposition of the observation mixtures based on Non-negative Matrix Factorization (NMF) method for Blind Source Separation (BSS), coupled with a custom semi-supervised clustering algorithm. Our methodology, called NMFk, is capable of identifying (a) the unknown number of groundwater types and (b) the original geochemical concentration of the contaminant sources from measured geochemical mixtures with unknown mixing ratios without any additional site information. NMFk is tested on synthetic and real-world site data. Finally, the NMFk algorithm works with geochemical data represented in the form of concentrations, ratios (of two constituents; for example, isotope ratios), and delta notations (standard normalized stable isotope ratios).« less
  6. We present that in modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains themore » expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. Finally, we note that classic “LEA” (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium.« less
  7. In this study, we consider the late-time tailing in a tracer test performed with a push-drift methodology (i.e., quasi-radial injection followed by drift under natural gradient). Numerical simulations of such tests are performed on 1000 multi-Gaussian 2-D log-hydraulic conductivity field realizations of varying heterogeneity, each under eight distinct mean flow directions. The ensemble pdfs of solute return times are found to exhibit power law tails for each considered variance of the log-hydraulic conductivity field, σmore » $$2\atop{ln K}$$. The tail exponent is found to relate straightforwardly to σ$$2\atop{ln K}$$ and, within the parameter space we explored, to be independent of push-phase pumping rate, pumping duration, and local-scale dispersivity. We conjecture that individual push-drift tracer tests in wells with screened intervals much greater than the vertical correlation length of the aquifer will exhibit quasi-ergodicity and that their tail exponent may be used to infer σ$$2\atop{ln K}$$. Lastly, we calibrate a predictive relationship of this sort from our Monte Carlo study, and apply it to data from a push-drift test performed at a site of approximately known heterogeneity—closely matching the existing best estimate of heterogeneity.« less
  8. Groundwater contamination by heavy metals is a critical environmental problem for which in situ remediation is frequently the only viable treatment option. For such interventions, a three-dimensional reactive transport model of relevant biogeochemical processes is invaluable. To this end, we developed a model, CHROTRAN, for in situ treatment, which includes full dynamics for five species: a heavy metal to be remediated, an electron donor, biomass, a nontoxic conservative bio-inhibitor, and a biocide. Direct abiotic reduction by donor-metal interaction as well as donor-driven biomass growth and bio-reduction are modeled, along with crucial processes such as donor sorption, bio-fouling and biomass death.more » Our software implementation handles heterogeneous flow fields, arbitrarily many chemical species and amendment injection points, and features full coupling between flow and reactive transport. We describe installation and usage and present two example simulations demonstrating its unique capabilities. One simulation suggests an unorthodox approach to remediation of Cr(VI) contamination.« less
  9. Here, management of shale gas wastewater treatment, disposal, and reuse has become a significant environmental challenge, driven by an ongoing boom in development of U.S. shale gas reservoirs. Systems-analysis based decision support is helpful for effective management of wastewater, and provision of cost-effective decision alternatives from a whole-system perspective. Uncertainties are inherent in many modeling parameters, affecting the generated decisions. In order to effectively deal with the recourse issue in decision making, in this work a two-stage stochastic fracturing wastewater management model, named TSWM, is developed to provide decision support for wastewater management planning in shale plays. Using the TSWMmore » model, probabilistic and nonprobabilistic uncertainties are effectively handled. The TSWM model provides flexibility in generating shale gas wastewater management strategies, in which the first-stage decision predefined by decision makers before uncertainties are unfolded is corrected in the second stage to achieve the whole-system’s optimality. Application of the TSWM model to a comprehensive synthetic example demonstrates its practical applicability and feasibility. Optimal results are generated for allowable wastewater quantities, excess wastewater, and capacity expansions of hazardous wastewater treatment plants to achieve the minimized total system cost. The obtained interval solutions encompass both optimistic and conservative decisions. Trade-offs between economic and environmental objectives are made depending on decision makers’ knowledge and judgment, as well as site-specific information. In conclusion, the proposed model is helpful in forming informed decisions for wastewater management associated with shale gas development.« less

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