Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

LNAPL Volume Calculation: Parameter Estimation by Nonlinear Regression of Saturation Profiles

An estimation of the volume of light nonaqueous phase liquids (LNAPL) is often required during site assessment, remedial design, or litigation. LNAPL volume can be estimated by a strictly empirical approach whereby core samples, distributed throughout the vertical and lateral extent of LNAPL, are analyzed for LNAPL content, and these data are then integrated to compute a volume. Alternatively, if the LNAPL has obtained vertical equilibrium, the thickness of LNAPL in monitoring wells can be used to calculate of LNAPL in monitoring wells can be used to calculate LNAPL volume at the well locations if appropriate soil and LNAPL properties can be estimated.
A method is described for estimating key soil and LNAPL properties by nonlinear regression of vertical profiles of LNAPL saturation. The methods is relatively fast, cost effective, and amenable to quantitative analysis of uncertainty. Optionally, the method allows statistical determination of best-fit values for the Van Genuchten capillary parameters (n, α_oil-water and α_oil-air), residual water saturation and ANAPL density. The sensitivity of the method was investigated by fitting field LNAPL saturation profiles and then determining the variation in misfit (mean square residual) as a function of parameter value for each parameter. Using field data from a sandy aquifer, the fitting statistics were found to be highly sensitive to LNAPL density, α_oil-water and α_oil-air moderately sensitive to the Van Genuchten n value, and weakly sensitive to residual water saturation. The regression analysis also provides information that can be used to estimate uncertainty in the estimated parameters, which can then be used to estimate uncertainty in calculated values of specific volume.     

222Rn as Natural Tracer for LNAPL Recovery in a Crude Oil‐Contaminated Aquifer

The objective of this study was to investigate whether ²²²Rn in groundwater can be used as a tracer for light non‐aqueous phase liquid (LNAPL) quantification at a field site treated by dual‐phase LNAPL removal. After the break of a pipeline, 5 ha of soil in the nature reserve Coussouls de Crau in southern France was contaminated by 5100 m³ of crude oil. Part of this oil seeped into the underlying gravel aquifer and formed a floating oil body of about 3.9 ha. The remediation consists of plume management by hydraulic groundwater barriers and LNAPL extraction in the source zone. ²²²Rn measurements were performed in 21 wells in and outside the source zone during 15 months. In uncontaminated groundwater, the radon activity was relatively constant and remained always >11 Bq/L. The variability of radon activity measurements in wells affected by the pump‐and‐skim system was consistent with the measurements in wells that were not impacted by the system. The mean activities in wells in the source zone were, in general, significantly lower than in wells upgradient of the source zone, owing to partitioning of ²²²Rn into the oil phase. The lowest activities were found in zones with high non‐aqueous phase liquid (NAPL) recovery. LNAPL saturations around each recovery well were furthermore calculated during a period of high groundwater level, using a laboratory‐determined crude oil–water partitioning coefficient of 38.5 ± 2.9. This yielded an estimated volume of residual crude oil of 309 ± 93 m³ below the capillary fringe. We find that ²²²Rn is a useful and cheap groundwater tracer for finding zones of good LNAPL recovery in an aquifer treated by dual‐phase LNAPL removal, but that quantification of NAPL saturation using Rn is highly uncertain.     

Unifying NAPL Drawdown and Transmissivity Testing in Unconfined,Confined, Perched,and Fractured Settings using the Z-Factor and MH Principles

Light nonaqueous phase liquid (LNAPL) flow in in fractured rock is governed by the same physics as porous media, but LNAPL discharge to a well from fractured rock is subject to the unique geometry of the fractures within the rock and the degree of interconnectivity between the factures. Previous conceptualization and definition of drawdown of nonaqueous phase liquids (NAPL) has employed a single drawdown value to represent the entire vertical interval of mobile NAPL. Application of the single drawdown model may result in erroneous calculation of NAPL transmissivity in fractured rock settings. This work illustrates how drawdown in multiphase systems can be variable over the vertical interval of mobile NAPL. In settings with discrete fracture networks, it is clear that consistently applying a single drawdown value will not accurately represent the pressure gradients. This work presents the multiphase head (MH) model, which is proposed as a comprehensive methodology for evaluating NAPL drawdown in fractured rock, and unconsolidated porous media. The MH model utilizes fluid statics and physical principles to accurately represent pressure differences in the formation and convert those into NAPL drawdown for discrete elevations. This first principles approach to describing how drawdown varies with NAPL-production zone elevations and fluid levels, resulting in a more accurate representation of discharge vs. fluid elevation behavior. Application of the MH model to various scenarios has identified that dissimilar scenarios can represent similar behavior during recovery from a NAPL removal event or baildown test. The resulting understanding improves the selection of representative portions of baildown test data to use in NAPL transmissivity analysis. Proper conceptualization of drawdown in bedrock identifies an alternate analysis method, the Z-factor, to estimate NAPL transmissivity. The resulting drawdown calculations and transmissivity analysis method result in a comprehensive approach to calculating NAPL transmissivity in both bedrock and unconsolidated porous media.     

Characterization of groundwater contaminant source using Bayesian method

Contaminant source identification in groundwater system is critical for remediation strategy implementation, including gathering further samples and analysis, as well as implementing and evaluating different remediation plans. Such problem is usually solved with the aid of groundwater modeling with lots of uncertainty, e.g. existing uncertainty in hydraulic conductivity, measurement variance and the model structure error. Monte Carlo simulation of flow model allows the input uncertainty onto the model predictions of concentration measurements at monitoring sites. Bayesian approach provides the advantage to update estimation. This paper presents an application of a dynamic framework coupling with a three dimensional groundwater modeling scheme in contamination source identification of groundwater. Markov Chain Monte Carlo (MCMC) is being applied to infer the possible location and magnitude of contamination source. Uncertainty existing in heterogonous hydraulic conductivity field is explicitly considered in evaluating the likelihood function. Unlike other inverse-problem approaches to provide single but maybe untrue solution, the MCMC algorithm provides probability distributions over estimated parameters. Results from this algorithm offer a probabilistic inference of the location and concentration of released contamination. The convergence analysis of MCMC reveals the effectiveness of the proposed algorithm. Further investigation to extend this study is also discussed.     

A spatio-temporal climate-based model of early dengue fever warning in southern Taiwan

Dengue Fever (DF) has been identified by the World Health organization (WHO) as one of the most serious vector-borne infectious diseases in tropical and sub-tropical areas. During 2007, in particular, there were over 2,000 DF cases in Taiwan, which was the highest number of cases in the recorded history of Taiwan epidemics. Most DF studies have focused mainly on temporal DF patterns and its close association with climatic covariates, whereas they have understated spatial DF patterns (spatial dependence and clustering) and composite space–time effects. The present study proposes a spatio-temporal DF prediction approach based on stochastic Bayesian Maximum Entropy (BME) analysis. Core and site-specific knowledge bases are considered, including climate and health datasets under conditions of uncertainty, space–time dependence functions, and a Poisson regression model of climatic variables contributing to DF occurrences in southern Taiwan during 2007. The results show that the DF outbreaks in the study area are highly influenced by climatic conditions. Furthermore, the analysis can provide the required “one-week-ahead” outbreak warnings based on spatio-temporal predictions of DF distributions. Therefore, the proposed approach can provide the Taiwan Disease Control Agency with a valuable tool to timely identify, control, and even efficiently prevent DF spreading across space–time.     

Uncertainty assessment for watershed water quality modeling: A Probabilistic Collocation Method based approach

Watershed water quality models are increasingly used in management. However, simulations by such complex models often involve significant uncertainty, especially those for non-conventional pollutants which are often poorly monitored. This study first proposed an integrated framework for watershed water quality modeling. Within this framework, Probabilistic Collocation Method (PCM) was then applied to a WARMF model of diazinon pollution to assess the modeling uncertainty. Based on PCM, a global sensitivity analysis method named PCM-VD (VD stands for variance decomposition) was also developed, which quantifies variance contribution of all uncertain parameters. The study results validated the applicability of PCM and PCM-VD to the WARMF model. The PCM-based approach is much more efficient, regarding computational time, than conventional Monte Carlo methods. It has also been demonstrated that analysis using the PCM-based approach could provide insights into data collection, model structure improvement and management practices. It was concluded that the PCM-based approach could play an important role in watershed water quality modeling, as an alternative to conventional Monte Carlo methods to account for parametric uncertainty and uncertainty propagation.     

Probabilistic assessment of travel times in groundwater modeling

A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps.     

Probabilistic assessment of travel times in groundwater modeling

A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps.     

Stochastic forecasting of mine water inrushes

An event-based stochastic forecasting approach is used to model water inrushes into underground works under karstic water hazard. The stochastic properties of inrushes are related to the statistical properties of fissures in the karstic rock. The probability distributions (DF) of five random variables of interest in design are estimated; namely, inrush yield q, number N of inrushes per unit area, distance L between inrushes, maximum q_max in N events and total yield Q. The phenomenological hypotheses of log normal DF of q and Poisson DF of N are reinforced by observation data. On the basis of these DF, a Monte Carlo simulation of a spatial Poisson process of inrushes is run to estimate the DF of q_max and Q. The derivation of Bayesian DF to account for parameter uncertainty is discussed. The stochastic model is used for design and operation of minewater control facilities in the Transdanubian karstic region of Hungary.     

Partitioned multiobjective risk modeling of carcinogenic compounds in groundwater

Quantifying human cancer risk arising from exposure to contaminated groundwater is complicated by the many hydrogeological, environmental, and toxicological uncertainties involved. In this study, we used Monte Carlo simulation to estimate cancer risk associated with tetrachloroethene (PCE) dissolved in groundwater by linking three separate models for: (1) reactive contaminant transport; (2) human exposure pathways; and (3) the PCE cancer potency factor. The hydrogeologic model incorporates an analytical solution for a one-dimensional advective–dispersive–reactive transport equation to determine the PCE concentration in a water supply well located at a fixed distance from a continuous source. The pathway model incorporates PCE exposure through ingestion, inhalation, and dermal contact. The toxicological model combines epidemiological data from eight rodent bioassays of PCE exposure in the form of a composite cumulative distribution frequency curve for the human PCE cancer potency factor. We assessed the relative importance of individual model variables through their correlation with expected cancer risk calculated in an ensemble of Monte Carlo simulations with 20,000 trials. For the scenarios evaluated, three factors were most highly correlated with cancer risk: (1) the microbiological decay constant for PCE in groundwater, (2) the linear groundwater pore velocity, and (3) the cancer potency factor. We then extended our analysis beyond conventional expected value risk assessment using the partitioned multiobjective risk method (PMRM) to generate expected-value functions conditional to a 1 in 100,000 increased cancer risk threshold. This approach accounts for low probability/high impact outcomes separately from the conventional unconditional expected values. Thus, information on potential worst-case outcomes can be quantified for decision makers. Using PMRM, we evaluated the cost-benefit relationship of implementing several postulated risk management alternatives intended to mitigate the expected and conditional cancer risk. Our results emphasize the importance of hydrogeologic models in risk assessment, but also illustrate the importance of integrating environmental and toxicological uncertainty. When coupled with the PMRM, models integrating uncertainty in transport, exposure, and potency constitute an effective risk assessment tool for use within a risk-based corrective action (RBCA) framework.     

Estimating the role of a ditch network in groundwater recharge in a Mediterranean catchment using a water balance approach

Water balance variables were monitored in a farmed Mediterranean catchment characterized by a dense ditch network to allow for the separate estimation of the diffuse and concentrated recharge terms during flood events. The 27 ha central part of the catchment was equipped with (i) rain gauges, (ii) ditch gauge stations, (iii) piezometers, (iv) neutron probes, and (v) an eddy covariance mast including a 3D sonic anemometer and a fast hygrometer. The water balance was calculated for two autumnal rain and flood events. We also estimated the uncertainty of this approach with Monte Carlo simulations. Results show, that although ditch area represents only 6% of the total study area, concentrated recharge appeared to be the main source of groundwater recharge. Indeed, it was 40–50% of the total groundwater recharge for autumnal events, which are the major annual recharge events. This indicate that both, concentrated and diffuse recharge should be taken into account in any hydrological modeling approach for Mediterranean catchments. This also means that, since they collect overland flow that is often largely contaminated by chemicals, ditches may be a place where groundwater contamination is likely to occur. The uncertainty analysis indicates that recharge estimates based on water balance exhibit large uncertainty ranges. Nevertheless, Monte Carlo simulations showed that concentrated recharge was higher than expected based on their area.     

Stochastic analysis of estuarine hydraulics

A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit     

LNAPL Recovery Endpoints: Lessons Learnt Through Modeling,Experiments, and Field Trials

It is important to estimate what light nonaqueous phase liquid (LNAPL) recovery can be practicably achieved from subsurface environments. Over the last decade, research to address this included a broad field program, laboratory measurements and experimentation, and modeling approaches. Here, we consolidate key findings from the research in the context of current literature and understanding, with a focus on a well-validated, multiphase multicomponent modeling approach to achieve estimates of reasonable endpoints for LNAPL recovery. Simple analytical models can provide approximate saturation distributions and estimates of LNAPL recoverability via transmissivity approximation, but are insufficient to predict LNAPL saturation- and composition-based recovery endpoints for various recovery technologies. This is because they cannot account for multiphase, multicomponent fate and transport and key processes such as hysteresis. Recent advances to improve estimates of the fraction of recoverable LNAPL and its transmissivity are summarized. These advances include further development and application of a well-validated model to characterize active LNAPL recovery endpoints. We present key factors that affect the determination of LNAPL recovery endpoints, and outline how recovery endpoints are affected by natural source zone depletion (NSZD—currently gaining acceptance as a LNAPL remediation option). Major factors include geo-physical characteristics of the formation, magnitude of an LNAPL release and partitioning properties of the key LNAPL constituents of concern. Based on the capabilities of the validated model, the paper also provides a basis to optimize LNAPL recovery efforts.     

Joint Monte Carlo and possibilistic simulation for flood damage assessment

A joint Monte Carlo and fuzzy possibilistic simulation (MC-FPS) approach was proposed for flood risk assessment. Monte Carlo simulation was used to evaluate parameter uncertainties associated with inundation modeling, and fuzzy vertex analysis was applied for promulgating human-induced uncertainty in flood damage estimation. A study case was selected to show how to apply the proposed method. The results indicate that the outputs from MC-FPS would present as fuzzy flood damage estimate and probabilistic-possibilistic damage contour maps. The stochastic uncertainty in the flood inundation model and fuzziness in the depth-damage functions derivation would cause similar levels of influence on the final flood damage estimate. Under the worst scenario (i.e. a combined probabilistic and possibilistic uncertainty), the estimated flood damage could be 2.4 times higher than that computed from conventional deterministic approach; considering only the pure stochastic effect, the flood loss would be 1.4 times higher. It was also indicated that uncertainty in the flood inundation modeling has a major influence on the standard deviation of the simulated damage, and that in the damage-depth function has more notable impact on the mean of the fitted distributions. Through applying MC-FPS, rich information could be derived under various α-cut levels and cumulative probabilities, and it forms an important basis for supporting rational decision making for flood risk management under complex uncertainties.     

Parameter estimation in nonlinear environmental problems

Popular parameter estimation methods, including least squares, maximum likelihood, and maximum a posteriori (MAP), solve an optimization problem to obtain a central value (or best estimate) followed by an approximate evaluation of the spread (or covariance matrix). A different approach is the Monte Carlo (MC) method, and particularly Markov chain Monte Carlo (MCMC) methods, which allow sampling from the posterior distribution of the parameters. Though available for years, MC methods have only recently drawn wide attention as practical ways for solving challenging high-dimensional parameter estimation problems. They have a broader scope of applications than conventional methods and can be used to derive the full posterior pdf but can be computationally very intensive. This paper compares a number of different methods and presents improvements using as case study a nonlinear DNAPL source dissolution and solute transport model. This depth-integrated semi-analytical model approximates dissolution from the DNAPL source zone using nonlinear empirical equations with partially known parameters. It then calculates the DNAPL plume concentration in the aquifer by solving the advection-dispersion equation with a flux boundary. The comparison is among the classical MAP and some versions of computer-intensive Monte Carlo methods, including the Metropolis–Hastings (MH) method and the adaptive direction sampling (ADS) method.     

Geostatistical inversing for large-contrast transmissivity fields

The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements. The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance of the quasilinear approach when applied to strongly heterogeneous (or “high-contrast”) transmissivity fields and, when needed, to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss–Newton iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation, we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis–Hastings algorithm. Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear approach but at a considerably higher computational cost.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site

Today, in different countries, there exist sites with contaminated groundwater formed as a result of inappropriate handling or disposal of hazardous materials or wastes. Numerical modeling of such sites is an important tool for a correct prediction of contamination plume spreading and an assessment of environmental risks associated with the site. Many uncertainties are associated with a part of the parameters and the initial conditions of such environmental numerical models. Statistical techniques are useful to deal with these uncertainties. This paper describes the methods of uncertainty propagation and global sensitivity analysis that are applied to a numerical model of radionuclide migration in a sandy aquifer in the area of the RRC “Kurchatov Institute” radwaste disposal site in Moscow, Russia. We consider 20 uncertain input parameters of the model and 20 output variables (contaminant concentration in the observation wells predicted by the model for the end of 2010). Monte Carlo simulations allow calculating uncertainty in the output values and analyzing the linearity and the monotony of the relations between input and output variables. For the non monotonic relations, sensitivity analyses are classically done with the Sobol sensitivity indices. The originality of this study is the use of modern surrogate models (called response surfaces), the boosting regression trees, constructed for each output variable, to calculate the Sobol indices by the Monte Carlo method. It is thus shown that the most influential parameters of the model are distribution coefficients and infiltration rate in the zone of strong pipe leaks on the site. Improvement of these parameters would considerably reduce the model prediction uncertainty.