Extended Kalman Filtering to Improve the Accuracy of a Subsurface Contaminant Transport Model

Modeling the behavior of contaminants in a subsurface flow is important in predicting the fate of the pollutants, in risk assessment, and as a preliminary step of the mitigation process. A two-dimensional transport model with advection and dispersion is used as the deterministic model of a conservative contaminant transport in the subsurface. With the system model alone, it is very difficult to predict the true dynamic state of the pollutant. Therefore, observation data are needed to guide the deterministic system model to assimilate the true state of the contaminant. Extended Kalman Filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, is used in this study to predict the contaminant plume transport. A traditional root mean square error (RMSE) of pollutant concentrations is used to examine the effectiveness of the EKF in contaminant transport modeling. The result shows that EKF can reduce 74 to 91% of prediction errors compared to the numerical method while working with the full set of observation data and using the analytical solution as the true solution. It can reduce 24 to 90% of prediction errors while working with only 2.25% observation-site data and a simulated random true field.     

Identification of Geologic Fault Network Geometry by Using a Grid-Based Ensemble Kalman Filter

Discrete geologic features such as faults and highly permeable embedded channels can significantly affect subsurface flow and transport characteristics. Therefore, they must be properly identified, parameterized, and represented in subsurface simulation models. In this work, we use an improved ensemble Kalman filter (EnKF) for history-matching fault network geometry from production data. EnKF is a sequential Monte Carlo data assimilation method that simultaneously propagates and updates an ensemble of model states, resulting in a set of calibrated model realizations that can be readily used for model prediction and uncertainty analysis. A pattern-based stochastic simulation algorithm was used to generate fault network realizations based on a priori fault trace data. The classic EnKF algorithm was enhanced with a grid-based covariance localization scheme to better handle non-Gaussian permeability distributions resulting from the presence of faults. Numerical experiments indicate that the modified EnKF can be a promising method for uncovering unmapped faults by using production data.     

Probabilistic Forecasting of Project Duration Using Kalman Filter and the Earned Value Method

The earned value method (EVM) is recognized as a viable method for evaluating and forecasting project cost performance. However, its application to schedule performance forecasting has been limited due to poor accuracy in predicting project durations. Recently, several EVM-based schedule forecasting methods were introduced. However, these are still deterministic and have large prediction errors early in the project due to small sample size. In this paper, a new forecasting method is developed based on Kalman filter and the earned schedule method. The Kalman filter forecasting method (KFFM) provides probabilistic predictions of project duration at completion and can be used from the beginning of a project without significant loss of accuracy. KFFM has been programmed in an add-in for Microsoft Excel and it can be implemented on all kinds of projects monitored by EVM or any other S-curve approach. Applications on two real projects are presented here to demonstrate the advantages of KFFM in extracting additional information from data about the status, trend, and future project schedule performance and associated risks.     

Contaminant Transport Model for Unsaturated Soil Using Fuzzy Approach

Contaminant transport in the unsaturated zone is important for managing water resources and assessing the damage due to contamination in the field of irrigation, water management, wastewater management, and urban and agricultural drainage systems. Deterministic modeling which is widely used for contaminant transport is not adequate because it considers model input parameters as well-defined crisp values and hence does not account for uncertainties and imprecision. This paper presents a contaminant transport model based on fuzzy set theory to simulate water flow and contaminant transport in the unsaturated soil zone under surface ponding condition. Among all soil hydraulic parameters that have uncertainty associated with them, saturated hydraulic conductivity was found to be the most sensitive to model outputs. Trapezoidal fuzzy numbers were used to express the uncertainties associated with saturated hydraulic conductivity. The incorporation of uncertainties into contaminant transport model is useful in decision making, as it yields scientifically and practically based estimates of contaminant concentration.     

Effectiveness of Source-Zone Remediation of DNAPL-Contaminated Subsurface Systems

Concerted efforts to remediate subsurface systems contaminated with dense nonaqueous-phase liquids (DNAPLs) have met with limited success when measured by comparing solute concentrations to drinking water quality standards. One-dimensional and three-dimensional laboratory experiments and a field-scale experiment are used to investigate the effectiveness of source-zone remediation and to assess factors that contribute to the observed results. The three-dimensional laboratory experiment and the field-scale experiment used a surfactant flush followed by vapor extraction to reduce the DNAPL saturation, while vertical DNAPL mobilization was controlled using a brine barrier. DNAPL mobilization and recovery in the field-scale experiment was relatively ineffective due in part to the low saturation levels of the DNAPL. The results show essentially that complete removal of a DNAPL is required to reach typical cleanup standards and that details of the morphology and topology of a DNAPL distribution, in addition to the saturation, play an important role in determining the rate of mass transfer. The results are interpreted in terms of guidance for remediation approaches, realistic expectations for source-zone remediation, and elements needed for improved models of such systems.     

Improved Estimation of ADCP Apparent Bed-Load Velocity Using a Real-Time Kalman Filter

An estimate of apparent bed-load velocity (v) can be derived from the difference between differential global positioning system (DGPSs) and acoustic Doppler current profiler (ADCP) bottom track (BT) measurements when BT is biased by a moving bottom. A Kalman filter has been developed to integrate GPS and bottom track data to improve estimation of boat velocity during ADCP measurements under moving bed conditions (Rennie and Rainville, 2008, J. Hydraulic Eng., in review). The boat velocity estimated using the Kalman filter is superior to boat velocity from raw GPS data. In this paper we assess the improvement in estimation of v using the Kalman filter as opposed to raw GPS data. Specifically, a synthetic moving bed bias was generated for 22 repeat transects of the Gatineau River, Quebec. The synthetic moving bed bias had mean, variance, and distribution across the section as typically observed during bed-load transport conditions, and had the advantage that it was known explicitly. The errors in estimated apparent bed-load velocity derived using either raw DGPS data or the Kalman filter boat velocity were compared. It was found that the improved boat velocity from the Kalman filter yielded significantly (α = 0.05) better estimates of v, (e.g., 61% reduction in error when the Kalman filter boat velocity was used instead of wide area augmentation system GGA), because boat velocity errors were reduced. Tests with real moving bed data confirmed the Kalman filter was able to significantly reduce errors in bed load calculated with stand alone GPS.     

Improving Precision in the Reference Velocity of ADCP Measurements Using a Kalman Filter with GPS and Bottom Track

Global positioning system (GPS) data are used to measure boat velocity during acoustic Doppler current profiler (ADCP) discharge measurements, particularly when bottom tracking (BT) is biased by moving bed. A Kalman filter is developed to improve the velocity reference used by the ADCP under such conditions. Kalman filtering is a recursive statistical technique that estimates the current state of a process, given various inputs and their variance. In the case of data obtained by ADCP, the availability of two independent velocity measurements and a position measurement makes this method particularly attractive. The new Kalman filter combines raw inputs for GPS position (GGA) and Doppler velocity (VTG) with BT data in real time to produce best estimates of velocity. The technique is evaluated and calibrated using various accuracies of GPS data collected simultaneously along with unbiased BT data at two different sites. On the Gatineau River, real-time kinematic and wide area augmentation system corrections were used for this study. On the Saint Mary’s River, nondifferential GPS was collected. To examine the conditions under which such a system would be required, synthetic data for a moving bed contamination of BT were created. In all moving bed conditions evaluated, the Kalman filter estimates of reference velocity were superior to raw inputs.     

Improved Compartmental Modeling and Application to Three-Phase Contaminant Transport in Unsaturated Porous Media

The compartmental modeling approach has been widely used for simulating contaminant transport in porous media and surface waters. Yet a commonly used compartmental model that has only first-order accuracy may introduce considerable numerical errors under certain circumstances. Following a review of compartmental systems and compartmental modeling methodologies, performance and limitations of such a compartmental model are discussed. In particular, improvement approaches, including multipoint, high-order, linear, and nonlinear methods, are presented in detail. Finally, a number of testing problems are examined and various compartmental models that describe three-phase (dissolved, adsorbed, and vapor phases) contaminant transport in unsaturated porous media are compared with each other and also with standard numerical and analytical counterparts. The comparisons highlight the accuracy, applicability, and limitations of different compartmental models.     

Integrated Subsurface Modeling and Risk Assessment of Petroleum-Contaminated Sites in Western Canada

Soil and groundwater contamination can pose a variety of impacts and risks to communities. Identification of management schemes with sound environmental and socio-economic efficiencies is desired. Before any decisions regarding site remediation actions can be made, three major questions may have to be answered. They are namely “What happened underground?”, “What will happen in the future under the given remediation scenarios?”, and “Are there specific risks to the surrounding community?”. In this study, an integrated modeling and risk assessment method is developed for effectively managing petroleum-contaminated sites through technically answering the above questions. It presents an integral concept that integrates issues of multicontaminant transport simulation, biodegradation modeling, health risk assessment, and site remediation for real-world problems within a general decision support framework. The developed method is applied to a petroleum-contaminated groundwater system in western Canada for identifying cost-effective management schemes with improved environmental and socio-economic efficiencies. The research outputs are directly useful for the decision maker to gain insight into the site and to make remediation decisions.     

Using Complex Permittivity and Artificial Neural Networks for Contaminant Prediction

The use of the measured complex permittivity of electrolyte solutions for predicting ionic species and concentration is investigated. Four artificial neural networks (ANNs) are created using a database containing permittivities (at 1.0, 1.5, and 2.0 GHz) and loss factors (at 0.3, 1.5, and 3.0 GHz) of 12 aqueous salts at various concentrations. The first ANN correctly identifies cationic species in 83% of the samples and distinguishes between pure water and electrolyte solutions with 100% accuracy. The second ANN predicts cationic concentrations with a RMS error of 190 mg/L for the range of concentrations examined (0–3,910 mg/L) and explains 90% of the variability in these data. The third ANN correctly identifies 98% of the anionic species in samples and accurately distinguishes between pure water and anion-containing solutions. The last ANN predicts anionic concentrations with a RMS error of 164 mg/L for the range of concentrations examined (0–5,654 mg/L) with an r2 of nearly 98%.     

Strategic Filter Backwashing Techniques and Resulting Particle Passage

A new filter backwashing strategy, extended terminal subfluidization wash (ETSW), aimed at reducing particle passage into the filtered water during the initial filter ripening sequence immediately following backwashing has been evaluated on pilot-scale filters at a conventional water treatment plant using alum as the sole coagulant. Turbidities and particle counts were measured following backwashes extending across a range of ETSW flow rates. The ETSW procedure was effective in significantly reducing the passage of particles through filters that originated from the backwash remnant water flowing out of the filter during the first 20?min of the filter run. A secondary turbidity peak associated with the filter influent water leaving the filter was observed following all fluidization backwashes with or without the addition of air-scour or ETSW. The secondary peak was termed the “additional collector” peak and was attributed to cold-water impaired (CWI) alum coagulation at the plant. The secondary peak was not observed with the particle counter as it was with the turbidimeter, which indicates the particles passing were predominantly particles <2?μm in diameter. A backwash procedure consisting of only subfluidization water flow was evaluated because it was expected to leave significantly higher number of particles attached to the media grains to serve as “additional collectors.” The subfluidization wash procedure virtually eliminated all filter ripening peaks in spite of the CWI coagulation conditions.     

Contaminant Detection, Identification, and Quantification Using a Microchip Laser Fluorescence Sensor

This paper describes a series of laboratory tests conducted to assess the performance of a novel fluorescence-based in situ sensor for environmental contaminants. The sensor, which can be deployed downhole in a monitoring well, or incorporated into the shaft of a cone penetrometer, is less than 4?cm in diameter and uses a miniature microchip laser that produces ～ 200?ps pulses of ultraviolet radiation at a high repetition rate ( ～ 10?kHz) to excite fluorescence in a wide range of compounds. Results from laser induced fluorescence tests on single compound aqueous solutions of benzene, toluene, and o-xylene (BTX) demonstrate the sensor’s ability to perform contaminant analyses on compounds with fluorescence lifetimes on the order of 1?ns. A linear relationship between contaminant concentration and fluorescence intensity was observed for concentrations over several orders of magnitude from the sensor’s detection limit (<1?ppm for o-xylene) to solutions of pure BTX compounds at aqueous solubility. Owing to the microchip laser’s short pulse length, fluorescence lifetimes were obtained directly from measurements without the need for spectral deconvolution. Analysis of data from these tests highlights the importance of differentiating a sensor’s ability to detect, identify, and quantify compounds of interest—performance thresholds that ultimately define potential applications for the device.     

Impact of Chlorinated Water Exposure on Contaminant Transport and Surface and Bulk Properties of High-Density Polyethylene and Cross-Linked Polyethylene Potable Water Pipes

The aim of this work was to determine if the aging of polyethylene (HDPE, PEX-A and PEX-B) water pipes by exposure to chlorinated water altered polar and nonpolar contaminant diffusivity and solubility by analyzing new, laboratory-aged, and exhumed water-distribution system polyethylene (PE) pipes. After 141?days of aging in pH 6.5 water with 45??mg/L free chlorine, the surface chemistry and bulk properties of PEX-A pipe were unaffected. Carbonyl bonds (σ = 1,713??cm-1) were detected on the surfaces of HDPE and PEX-B pipe, and these oxygenated surfaces became more hydrophilic, resulting in statistically significant increases in diffusion rates. All 10 contaminant and four pipe material combinations had diffusivity increases on average of 50% for polar contaminants and 5% for nonpolar contaminants. Contaminant solubility was slightly increased for aged PEX-A and slightly decreased for PEX-B pipes. Toluene and trichloromethane diffusivity and solubility values for 7- to 25-year-old buried water utility pipes were similar to values for new and laboratory-aged HDPE-based materials. Because chlorinated water exposure alters how polar contaminants interact with aged PE pipes, results of this work should be considered in future health risk assessments, water quality modeling, pipe performance, and service-life considerations.     

Importance of Field Data in Stream Water Quality Modeling Using QUAL2E-UNCAS

The Stream Water Quality Model QUAL2E-UNCAS is widely used to simulate the dissolved oxygen of streams under steady flow conditions. It is the latest version of a series of water quality models that have a long history in systems analysis in water quality management, and has been applied to a number of streams and rivers around the world. This paper summarizes the conceptual representation of the computer model, briefly reviews a number of applications of the model that have been published in open literature, describes the included uncertainty analysis capability, and discusses the importance of field data in model predictions. Experience with the QUAL2E model has proven the importance of site-specific data to model predictions. An accurate representation of the properties of the system significantly contributes to simulation success.     

Simulation of Metals Total Maximum Daily Loads and Remediation in a Mining-Impacted Stream

Simulation of metals transport was performed to help develop metals total maximum daily loads (TMDLs) and evaluate remediation alternatives in a mountain stream in Montana impacted by hundreds of abandoned hardrock metal mines. These types of watersheds are widespread in Montana and many other areas of the western United States. Impacts from abandoned hardrock or metal mines include loadings of sediment, metals, and other pollutants causing impairment of multiple beneficial uses and exceedances of water quality standards. The United States Environmental Protection Agency (EPA) Water Quality Analysis Simulation Program (WASP) was used to model and evaluate TMDLs for several heavy metals in Tenmile Creek, a mountain stream supplying drinking water to the City of Helena, Mont. The model was calibrated for baseflow conditions and validated using data collected by the EPA and the United States Geological Survey, and used to assess existing metals loadings and losses, including interactions between metals in water and bed sediment, uncertainty, water quality standard exceedances, TMDLs, potential source areas, and required reductions in loadings. During baseflow conditions, adits and point sources contribute significant metals loadings to Tenmile Creek. Exceedances of standards are widespread throughout the stream under both baseflow and higher flow conditions. Adsorption and precipitation onto bed sediments play a primary role in losses from the water column in some areas. Modeling results indicate that some uncertainty exists in the metal partition coefficients associated with sediment, significance of precipitation reactions, and in locations of unidentified sources and losses of metals. TMDLs and loading reductions were calculated based on variations in flow, concentrations, loadings, and standards (which vary with hardness) along the mainstem. In most cases, considerable reductions in loadings are required to achieve TMDLs and water quality standards. Reductions in loadings from point sources, mine waste near watercourses, and streambed sediment can help improve water quality, but alteration of the water supply scheme and increasing baseflow will also be needed.     

Pollutant Transport and Mixing Zone Simulation of Sediment Density Currents

Prediction of water column concentrations of suspended sediment is often necessary for environmental impact assessment of point source industrial discharges. For example, in “flow lane” or “open water” disposal, suction dredges discharge large volumes of suspended sediment into shallow water disposal locations. A sediment density current mixing model is presented here as part of the D-CORMIX expert system for hydrodynamic simulation of mixing zone behavior. This density current model extends the CORMIX decision support system to simulate continuous negatively buoyant discharges with or without suspended sediment loads on a sloping bottom with loss of suspended particles by sedimentation. Sedimentation is modeled using Stokes settling for five particle size classes. Density current width and depth, trajectory, total solids, tracer concentration, dilution, and particle size concentration are predicted. In addition, location and widths of sediment deposits, accretion rates, including particle size fractions within the spoils deposit, are predicted. The model results are in good overall agreement with available field and laboratory data.