Jack C. Parker

CXTFIT/Excel-A modular adaptable code for parameter estimation, sensitivity analysis and uncertainty analysis for laboratory or field tracer experiments

We implemented the widely used CXTFIT code in Excel to provide flexibility and added sensitivity and uncertainty analysis functions to improve transport parameter estimation and to facilitate model discrimination for multi-tracer experiments on structured soils. Analytical solutions for one-dimensional equilibrium and nonequilibrium convection dispersion equations were coded as VBA functions so that they could be used as ordinary math functions in Excel for forward predictions. Macros with user-friendly interfaces were developed for optimization, sensitivity analysis, uncertainty analysis, error propagation, response surface calculation, and Monte Carlo analysis. As a result, any parameter with transformations (e.g., dimensionless, log-transformed, species-dependent reactions, etc.) could be estimated with uncertainty and sensitivity quantification for multiple tracer data at multiple locations and times. Prior information and observation errors could be incorporated into the weighted nonlinear least squares method with a penalty function. Users are able to change selected parameter values and view the results via embedded graphics, resulting in a flexible tool applicable to modeling transport processes and to teaching students about parameter estimation. The code was verified by comparing to a number of benchmarks with CXTFIT 2.0. It was applied to improve parameter estimation for four typical tracer experiment data sets in the literature using multi-model evaluation and comparison. Additional examples were included to illustrate the flexibilities and advantages of CXTFIT/Excel. The VBA macros were designed for general purpose and could be used for any parameter estimation/model calibration when the forward solution is implemented in Excel. A step-by-step tutorial, example Excel files and the code are provided as supplemental material.

Application of a hybrid MPI/OpenMP approach for parallel groundwater model calibration using multi-core computers

Calibration of groundwater models involves hundreds to thousands of forward solutions, each of which may solve many transient coupled nonlinear partial differential equations, resulting in a computationally intensive problem. We describe a hybrid MPI/OpenMP approach to exploit two levels of parallelisms in software and hardware to reduce calibration time on multi-core computers. HydroGeoChem 5.0 (HGC5) is parallelized using OpenMP for direct solutions for a reactive transport model application, and a field-scale coupled flow and transport model application. In the reactive transport model, a single parallelizable loop is identified to account for over 97% of the total computational time using GPROF. Addition of a few lines of OpenMP compiler directives to the loop yields a speedup of about 10 on a 16-core compute node. For the field-scale model, parallelizable loops in 14 of 174 HGC5 subroutines that require 99% of the execution time are identified. As these loops are parallelized incrementally, the scalability is found to be limited by a loop where Cray PAT detects over 90% cache missing rates. With this loop rewritten, similar speedup as the first application is achieved. The OpenMP-parallelized code can be run efficiently on multiple workstations in a network or multiple compute nodes on a cluster as slaves using parallel PEST to speedup model calibration. To run calibration on clusters as a single task, the Levenberg-Marquardt algorithm is added to HGC5 with the Jacobian calculation and lambda search parallelized using MPI. With this hybrid approach, 100-200 compute cores are used to reduce the calibration time from weeks to a few hours for these two applications. This approach is applicable to most of the existing groundwater model codes for many applications.

U(VI) bioreduction with emulsified vegetable oil as the electron donor-Model application to a field test

We amended a shallow fast-flowing uranium (U) contaminated aquifer with emulsified vegetable oil (EVO) and subsequently monitored the biogeochemical responses for over a year. Using a biogeochemical model developed in a companion article (Tang et al., Environ. Sci. Technol.2013, doi: 10.1021/es304641b) based on microcosm tests, we simulated geochemical and microbial dynamics in the field test during and after the 2-h EVO injection. When the lab-determined parameters were applied in the field-scale simulation, the estimated rate coefficient for EVO hydrolysis in the field was about 1 order of magnitude greater than that in the microcosms. Model results suggested that precipitation of long-chain fatty acids, produced from EVO hydrolysis, with Ca in the aquifer created a secondary long-term electron donor source. The model predicted substantial accumulation of denitrifying and sulfate-reducing bacteria, and U(IV) precipitates. The accumulation was greatest near the injection wells and along the lateral boundaries of the treatment zone where electron donors mixed with electron acceptors in the groundwater. While electron acceptors such as sulfate were generally considered to compete with U(VI) for electrons, this work highlighted their role in providing electron acceptors for microorganisms to degrade complex substrates thereby enhancing U(VI) reduction and immobilization.

Recovery of light, non-aqueous phase liquid from porous media: laboratory experiments and model validation

Abstract Laboratory experiments were conducted to measure flow of a light, non-aqueous phase liquid (LNAPL or simply “oil”) in porous media. The objective of these experiments was to measure oil recovery as influenced by hysteresis, the oil-water capillary fringe, and an oil seepage face. Oil was infiltrated and allowed to redistribute across the horizontal length of a two-dimensional tank filled with medium sand. The first experiment involved oil recovery without water pumping, while the second experiment involved oil recovery with water pumping to increase the gradient toward the recovery well. Observed oil recovery compared favorably with the predictions of a numerical model (ARMOS). A dual-energy gamma radiation attenuation system monitored oil and water saturations throughout the experiments, while hydrophobic tensiometers measured the location of the air-oil table (Zao). The experimental distribution of oil saturations suggested the need to incorporate an oil-water capillary fringe in the calculation of oil trapping in the saturated zone. Measurements of Zao indicated that hysteresis influenced the liquid saturation-pressure relationships. When the effects of hysteresis were incorporated into the model, predicted and measured values of Zao came into agreement, especially at early times during the recovery process. Experimental data also suggested the presence of an oil seepage face at the pumping well, but model results were not sensitive to this factor. Oil saturation measurements at later times suggested that the oil may have experienced delayed yield, an effect that was not modeled explicitly. A sensitivity analysis revealed that oil recovery predictions were most affected by horizontal hydraulic conductivity, fluid scaling parameters βao and βow, and van Genuchten α, n, and Sm. Overall, the numerical model appeared to match measured data for oil saturation, pressure, and recovery under two sets of boundary conditions.

Cost optimization of DNAPL source and plume remediation under uncertainty using a semi-analytic model

Dense non-aqueous phase liquid (DNAPL) spills represent a potential long-term source of aquifer contamination, and successful low-cost remediation may require a combination of both plume management and source treatment. In addition, substantial uncertainty exists in many of the parameters that control field-scale behavior of DNAPL sources and plumes. For these reasons, cost optimization of DNAPL cleanup needs to consider multiple treatment options and their associated costs while also gauging the influence of prediction uncertainty on expected costs. In this paper, we present a management methodology for field-scale DNAPL source and plume management under uncertainty. Using probabilistic methods, historical data and prior information are combined to produce a set of equally likely realizations of true field conditions (i.e., parameter sets). These parameter sets are then used in a simulation-optimization framework to produce DNAPL cleanup solutions that have the lowest possible expected net present value (ENPV) cost and that are suitably cautious in the presence of high uncertainty. For simulation, we utilize a fast-running semi-analytic field-scale model of DNAPL source and plume evolution that also approximates the effects of remedial actions. The degree of model prediction uncertainty is gauged using a restricted maximum likelihood method, which helps to produce suitably cautious remediation strategies. We test our methodology on a synthetic field-scale problem with multiple source architectures, for which source zone thermal treatment and electron donor injection are considered as remedial actions. The lowest cost solution found utilizes a combination of source and plume remediation methods, and is able to successfully meet remediation constraints for a majority of possible scenarios. Comparisons with deterministic optimization results show that not taking into account uncertainty can result in optimization strategies that are not aggressive enough and result in greater overall total cost.

U(VI) Bioreduction with Emulsified Vegetable Oil as the Electron Donor − Microcosm Tests and Model Development

We conducted microcosm tests and biogeochemical modeling to study U(VI) reduction in contaminated sediments amended with emulsified vegetable oil (EVO). Indigenous microorganisms in the sediments degraded EVO and stimulated Fe(III), U(VI), and sulfate reduction, and methanogenesis. Acetate concentration peaked in 100-120 days in the EVO microcosms versus 10-20 days in the oleate microcosms, suggesting that triglyceride hydrolysis was a rate-limiting step in EVO degradation and subsequent reactions. Acetate persisted 50 days longer in oleate- and EVO- than in ethanol-amended microcosms, indicating that acetate-utilizing methanogenesis was slower in the oleate and EVO than ethanol microcosms. We developed a comprehensive biogeochemical model to couple EVO hydrolysis, production, and oxidation of long-chain fatty acids (LCFA), glycerol, acetate, and hydrogen, reduction of Fe(III), U(VI) and sulfate, and methanogenesis with growth and decay of multiple functional microbial groups. By estimating EVO, LCFA, and glycerol degradation rate coefficients, and introducing a 100 day lag time for acetoclastic methanogenesis for oleate and EVO microcosms, the model approximately matched observed sulfate, U(VI), and acetate concentrations. Our results confirmed that EVO could stimulate U(VI) bioreduction in sediments and the slow EVO hydrolysis and acetate-utilizing methanogens growth could contribute to longer term bioreduction than simple substrates (e.g., ethanol, acetate, etc.) in the subsurface.

Dissolved plume attenuation with DNAPL source remediation, aqueous decay and volatilization — Analytical solution, model calibration and prediction uncertainty

A vertically-integrated analytical model for dissolved phase transport is described that considers a time-dependent DNAPL source based on the upscaled dissolution kinetics model of Parker and Park with extensions to consider time-dependent source zone biodecay, partial source mass reduction, and remediation-enhanced source dissolution kinetics. The model also considers spatial variability in aqueous plume decay, which is treated as the sum of aqueous biodecay and volatilization due to diffusive transport and barometric pumping through the unsaturated zone. The model is implemented in Excel/VBA coupled with (1) an inverse solution that utilizes prior information on model parameters and their uncertainty to condition the solution, and (2) an error analysis module that computes parameter covariances and total prediction uncertainty due to regression error and parameter uncertainty. A hypothetical case study is presented to evaluate the feasibility of calibrating the model from limited noisy field data. The results indicate that prediction uncertainty increases significantly over time following calibration, primarily due to propagation of parameter uncertainty. However, differences between the predicted performance of source zone partial mass reduction and the known true performance were reasonably small. Furthermore, a clear difference is observed between the predicted performance for the remedial action scenario versus that for a no-action scenario, which is consistent with the true system behavior. The results suggest that the model formulation can be effectively utilized to assess monitored natural attenuation and source remediation options if careful attention is given to model calibration and prediction uncertainty issues.

Kinetic analysis and modeling of oleate and ethanol stimulated uranium (VI) bio-reduction in contaminated sediments under sulfate reduction conditions

Microcosm tests with uranium contaminated sediments were performed to explore the feasibility of using oleate as a slow-release electron donor for U(VI) reduction in comparison to ethanol. Oleate degradation proceeded more slowly than ethanol with acetate produced as an intermediate for both electron donors under a range of initial sulfate concentrations. A kinetic microbial reduction model was developed and implemented to describe and compare the reduction of sulfate and U(VI) with oleate or ethanol. The reaction path model considers detailed oleate/ethanol degradation and the production and consumption of intermediates, acetate and hydrogen. Although significant assumptions are made, the model tracked the major trend of sulfate and U(VI) reduction and describes the successive production and consumption of acetate, concurrent with microbial reduction of aqueous sulfate and U(VI) species. The model results imply that the overall rate of U(VI) bioreduction is influenced by both the degradation rate of organic substrates and consumption rate of intermediate products.

Value of Information as a Context-Specific Measure of Uncertainty in Groundwater Remediation

The remediation of groundwater sites has been recognized as a difficult and expensive task for years. One of the challenges is that the success of remediation is usually contingent upon an appropriate level of characterization of the physical, chemical, and biological site properties. For example, thermal treatment cannot be economically applied if the location of a non-aqueous phase liquid (NAPL) source is unknown. Both characterization and remediation are expensive. Thus, efforts need to be prioritized and optimized taking effects of uncertainty into consideration. Traditional measures of uncertainty, such as variance and correlation coefficients, do not fully depict the significance of uncertainty. For example, a small error in a parameter to which performance is sensitive may affect the prospect for remediation success much more than a large error in a parameter that has minor influence. In this paper, we quantify uncertainty as the expected increase in the cost of achieving clean-up objectives that is associated with uncertainty in performance prediction models, i.e., the minimum expected cost attainable with the present state of uncertainty minus the expected cost achievable if uncertainty were fully or partially removed. This measure, a.k.a., the value of information (VOI), is context-specific, i.e., it is dependent on site conditions and remediation strategies as well as specific remediation objectives and unit costs. We consider clean-up objectives, cost formulations, and sensitivity of costs to uncertainty in parameters, measurements, and the model itself and seek to minimize expected cost under conditions of incomplete information. We present results from a synthetic case study of dense non-aqueous phase liquid (DNAPL) plume treatment. The results quantify the cost attributable to uncertainty, thus setting an upper limit on how much one should pay for characterization, and helping decision makers to decide whether the data should be collected or not.

Modeling uranium transport in acidic contaminated groundwater with base addition

This study investigates reactive transport modeling in a column of uranium(VI)-contaminated sediments with base additions in the circulating influent. The groundwater and sediment exhibit oxic conditions with low pH, high concentrations of NO(3)(-), SO(4)(2-), U and various metal cations. Preliminary batch experiments indicate that additions of strong base induce rapid immobilization of U for this material. In the column experiment that is the focus of the present study, effluent groundwater was titrated with NaOH solution in an inflow reservoir before reinjection to gradually increase the solution pH in the column. An equilibrium hydrolysis, precipitation and ion exchange reaction model developed through simulation of the preliminary batch titration experiments predicted faster reduction of aqueous Al than observed in the column experiment. The model was therefore modified to consider reaction kinetics for the precipitation and dissolution processes which are the major mechanism for Al immobilization. The combined kinetic and equilibrium reaction model adequately described variations in pH, aqueous concentrations of metal cations (Al, Ca, Mg, Sr, Mn, Ni, Co), sulfate and U(VI). The experimental and modeling results indicate that U(VI) can be effectively sequestered with controlled base addition due to sorption by slowly precipitated Al with pH-dependent surface charge. The model may prove useful to predict field-scale U(VI) sequestration and remediation effectiveness.