Geostatistical interpolation of chemical concentration

Measurements of contaminant concentration at a hazardous waste site typically vary over many orders of magnitude and have highly skewed distributions. This work presents a practical methodology for the estimation of solute concentration contour maps and volume averages (needed for mass calculations) from data obtained from the analysis of water and soil samples. The methodology, which is an extension of linear geostatistics, produces a point estimate, i.e., a representative value, as well as a confidence interval, which contains the true value with a given probability. The approach uses a parsimonious model that accounts for the skewness by adding only one parameter to those used in linear geostatistics (variograms or generalized covariances). The resulting nonlinear kriging method is not substantially more difficult to use than linear geostatistics. The methodology is most appropriate when concentration measurements are available on a reasonably dense grid and no additional information (based on modeling flow and transport) can be used. We present and illustrate through an application, a practical approach to estimate all the parameters needed and to select and test the model.     

Joint Estimation of Hydraulic and Poroelastic Parameters from a Pumping Test

The coupling of hydraulic and poroelastic processes is critical in predicting processes involving the deformation of the geologic medium in response to fluid extraction or injection. Numerical models that consider the coupling of hydraulic and poroelastic processes require the knowledge of relevant parameters for both aquifer and aquitard units. In this study, we jointly estimated hydraulic and poroelastic parameters from pumping test data exhibiting “reverse water level fluctuations,” known as the Noordbergum effect, in aquitards adjacent to a pumped aquifer. The joint estimation was performed by coupling BIOT2, a finite element, two‐dimensional, axisymmetric, groundwater model that considers poroelastic effects with the parameter estimation code PEST. We first tested our approach using a synthetic data set with known parameters. Results of the synthetic case showed that for a simple layered system, it was possible to reproduce accurately both the hydraulic and poroelastic properties for each layer. We next applied the approach to pumping test data collected at the North Campus Research Site (NCRS) on the University of Waterloo (UW) campus. Based on the detailed knowledge of stratigraphy, a five‐layer system was modeled. Parameter estimation was performed by: (1) matching drawdown data individually from each observation port and (2) matching drawdown data from all ports at a single well simultaneously. The estimated hydraulic parameters were compared to those obtained by other means at the site yielding good agreement. However, the estimated shear modulus was higher than the static shear modulus, but was within the range of dynamic shear modulus reported in the literature, potentially suggesting a loading rate effect.     

Estimation of the Change in Hydraulic Conductivity Above Mined Longwall Panels

The change in hydraulic conductivity (K) above subsided longwall panels at underground coal mines is determined using a data base of pre‐mining and post‐mining K measurements made at multiple locations down the depth profile at each of a number of sites worldwide. Results show that, following caving of roof strata, there is a clear difference in the magnitude of changes in K above and below the top of the collapsed zone. Within the collapsed zone, relative increases in K are larger, even when taking account of measurements made in potentially unsaturated strata. A generalized conceptual model is presented for K change above subsided longwall panels. These results form a third independent database supporting the height of desaturation reported in an earlier study.     

Geostatistical integration of near-surface geophysical data

Accurate statics calculation and near‐surface related noise removal require a detailed knowledge of the near‐surface velocity field. Conventional seismic surveys currently are not designed to provide this information, and 3D high‐resolution reflection/refraction acquisition is not feasible for large survey areas. Satellite images and vibrator plate attributes are dense low‐cost data, which can be used in spatially extrapolating velocities from sparse uphole data by geostatistics. We tested this approach in two different areas of Saudi Arabia and found that the optimal recipe depends on the local geology.     

Geostatistical sampling optimization of contaminated facilities

Geostatistics applied to radiological evaluation of nuclear premises provides methods to estimate radiological activities, together with their associated uncertainty. It enables a sophisticated sampling methodology combining radiation map and destructive samples. The radiological assessment is divided in two steps: first, a regular control of the surface activity is performed. Then, to assess the true contamination, concrete samples are collected and analyses are performed at several locations within the premises. These two types of measurement are first dealt separately, then cokriging techniques are applied to estimate the contamination over the premise, taking both information into account. This paper presents a methodological study of geostatistical and computational approaches to target suitable areas for additional radiological measures. In order to compare the proposed augmented sampling designs, several optimization criteria are taken into account. Their diversity ensures the coverage of a wide range of real problematics. Two algorithms (greedy algorithm and simulated annealing) are developed to optimize the chosen criterion value as a function of the location of the additional points. The sampling scenarios obtained with the different algorithms are compared in terms of optimization performance and computational efficiency.     

Simple Hydraulic Conductivity Estimation by the Kalman Filtered Double Constraint Method

This paper presents the Kalman Filtered Double Constraint Method (DCM‐KF) as a technique to estimate the hydraulic conductivities in the grid blocks of a groundwater flow model. The DCM is based on two forward runs with the same initial grid block conductivities, but with alternating flux‐head conditions specified on parts of the boundary and the wells. These two runs are defined as: (1) the flux run, with specified fluxes (recharge and well abstractions), and (2) the head run, with specified heads (measured in piezometers). Conductivities are then estimated as the initial conductivities multiplied by the fluxes obtained from the flux run and divided by the fluxes obtained from the head run. The DCM is easy to implement in combination with existing models (e.g., MODFLOW). Sufficiently accurate conductivities are obtained after a few iterations. Because of errors in the specified head‐flux couples, repeated estimation under varying hydrological conditions results in different conductivities. A time‐independent estimate of the conductivities and their inaccuracy can be obtained by a simple linear KF with modest computational requirements. For the Kleine Nete catchment, Belgium, the DCM‐KF yields sufficiently accurate calibrated conductivities. The method also results in distinguishing regions where the head‐flux observations influence the calibration from areas where it is not able to influence the hydraulic conductivity.