Bayesian estimation of the transmissivity spatial structure from pumping test data

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.Peer ReviewedPostprint (author's final draft

Inferring spatial distribution of the radially integrated transmissivity from pumping tests in heterogeneous confined aquifers

Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single estimates of representative flow parameters. However, natural subsurface formations are intrinsically heterogeneous, and hence, the flow parameters influencing the drawdown vary as the cone of depression expands in time. In this paper a novel procedure for the analysis of pumping tests in heterogeneous confined aquifers is developed. We assume that a given heterogeneous aquifer can be represented by a homogeneous system whose flow parameters evolve in time as the pumping test progresses. At any point in time, the interpreted flow parameters are estimated using the ratio of the drawdown and its derivative observed at that particular time. The procedure is repeated for all times, yielding time‐dependent estimates of transmissivity Ti(t) and storativity, Si(t). Based on the analysis of the sensitivity of drawdown to inhomogeneities in the T field, the time‐dependent interpreted transmissivity values are found to be a good estimate of Tg(r), the geometric mean of the transmissivity values encompassed within a progressively increasing radius r from the well. The procedure is illustrated for Gaussian heterogeneous fields with ln(T) variances up to a value of 2. The impact of the separation distance between the pumping well and observation point on data interpretation is discussed. The results show that information about the spatial variability of the transmissivity field can be inferred from time‐drawdown data collected at a single observation poin

Bayesian estimation of the transmissivity spatial structure from pumping test data

    Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests

A New Method for the Interpretation of Pumping Tests in Leaky Aquifers

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type‐curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume

Influence of heterogeneity on the interpretation of pumping test data in leaky aquifers

Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferre

Thermal based remediation technologies for soil and groundwater: a review

Thermal remediation technologies are fast and effective tools for the remediation of contaminated soils and sediments. Nevertheless, the high energy consumption and the effect of high temperature on the soil properties may hinder the wide applications of thermal remediation methods. This review highlights the recent studies focused on thermal remediation. Eight types of thermal remediation processes are discussed, including incineration, thermal desorption, stream enhanced extraction, electrical resistance heating, microwave heating, smoldering, vitrification, and pyrol-ysis. In addition, the combination of thermal remediation with other remediation technologies is presented. Finally, thermal remediation sustainability is evaluated in terms of energy efficiency and their impact on soil properties. The developments of the past decade show that thermal-based technologies are quite effective in terms of contaminant removal but that these technologies are associated with high energy use and costs and can has an adverse impact on soil properties. Nonetheless, it is anticipated that continued research on thermally based technologies can increase their sustainability and expand their applications. Low temperature thermal desorption is a prom-ising remediation technology in terms of land use and energy cost as it has no adverse effect on soil function after treatment and low temperature is required. Overall, selecting the sustainable remediation technology depends on the contaminant properties, soil properties and predicted risk level. © 2022 Desalination Publications. All rights reserved

Geophysical Imaging For Contaminated Site Characterization

The analysis and management of groundwater flow problems often involve the prediction of fluid flow and/or contaminant migration patterns. These phenomena, however, are strongly influenced by the heterogeneity of the hydrogeological properties of the soil. The purpose of this project is to derive joint geophysical-hydrogeological procedures for the characterization of subsurface flow parameters. The first part of this study presents a formal stochastic approach for the integration of surface seismic data and well data into the identification of the spatial arrangement- location, geometry, and interconnectedness of lithofacies. Towards this goal, the lithology of the subsurface is represented through a random indicator function whose spatial structure is identified from seismic reflection data and well logs. Seismic interval velocities and measures of their uncertainties are computed from normal moveout corrections to the seismic reflection data. Calibration curves constructed from the well logs transform these velocity estimates into a lithology indicator prior probability field. From the well data and the prior probability field, the indicator covariance function and its associated confidence limits are computed. Neighboring lithology logs and the indicator covariance function are then combined to update the indicator probability field. To illustrate the applicability of the proposed characterization procedure, a semi-synthetic case study- based on the Fremont study area near the city of Fremont, California- is performed.In the second part of this study, a Bayesian method is developed to estimate the spatial distribution of the permeability. In addition to sparsely sampled permeability and pressure data, the proposed approach incorporates densely sampled seismic velocity data along with semi-empirical relationships between seismic velocity, permeability and pressure. A hydrological inversion is first performed, based solely on the permeability and pressure data. In light of the available seismic data, the velocity-permeability-pressure relationships are then used to update, in a Bayesian sense, the image of the permeability field. To demonstrate the usefulness of this approach, synthetic case studies are performed. For further validation, the proposed methodology is applied to real data collected at Kesterson Reservoir, California. These studies demonstrate that by joining seismic data and hydrological data into a common inverse procedure, improved permeability images can be reproduced