High-Throughput Computing for the Analysis of Tracer Tests in Fractured Aquifers

Traditional approaches to characterization and modeling of fractured dolomite aquifers face many conceptual and technical challenges. One alternative strategy begins with the Generalized Radial Flow interpretation of hydraulic tests, which infers an additional parameter, the flow dimension, to describe the geometry of groundwater flow. This study examines the behavior and variability of the apparent flow dimension, n*, and advective transport for four stochastic models of heterogeneous transmissivity, T(x). This is accomplished through Monte Carlo analysis of numerical models simulating aquifer tests and converging flow tracer tests (CFTTs) in two-dimensional systems. For ln T(x) distributed as a multivariate Gaussian (mvG) variable of variance less than one, the apparent flow dimension of an aquifer test converges to n* = 2 if the scale of the test is large relative to the scale of correlation. The variability of the apparent flow dimension depends on the variance and integral scale of the transmissivity, suggesting that it may be possible to identify the variance and integral scale from a set of aquifer tests. For variances greater than one, the results suggest that the average of the apparent flow dimension is less than two initially, then converges to n* = 2, similar in some respects to a percolation network. The simulation of an uncorrelated log-Gaussian model suggests that the flow dimension of an aquifer test converges to n* = 2 even for large variances. For ln T(x) distributed as fractional Brownian motion (fBm), the apparent flow dimension averages to n* = 2 and its variability increases with time. An approximation of a percolation network model showed an average apparent flow dimension stabilizing between n* = 1.4 to 1.6, followed by an increasing trend. These characteristics apparently are functions of the transmissivity contrast between the percolating and nonpercolating fractions. In the low-variance mvG, uncorrelated log-Gaussian, and fBm models, CFTTs influenced by matrix diffusion showed late-time breakthrough curves (BTCs) with log-log slopes of -3/2, the characteristic behavior of matrix diffusion. In the percolation network model, a simulated CFTT influenced by matrix diffusion had late-time BTC with log-log slopes of -5/4, attributed to slow advection through low transmissivity regions. This indicates that some heterogeneity models can systematically affect the late-time behavior of a BTC for a CFTT. These results suggest that the flow dimension may be a useful diagnostic for selecting models of heterogeneity, and that flow dimensions n ≠ 2 may be associated with unique tracer behavior. Additional research is advocated to infer the general behavior of the flow dimension at various field sites, to assess a broader range of parameters, to examine other stochastic models, and to conduct a more detailed examination of transport behavior versus the flow dimension. Introduction The characterization and analysis of fluid flow and contaminant transport in fractured rocks is a common challenge faced by scientists and engineers worldwide. These rock formations form economically important aquifers and oil reservoirs throughout the world, ranging from the dolomite aquifers of Northeastern Illinois (NIPC, 2001); to carbonate oil reservoirs in South America, the North Sea, and the Mideast (Acuna and Yortsos, 1995; Raghavan, 2004; Sahimi and Mukhopadhyay, 1996); and to dolomite aquifers in the Southwestern United States that form pathways critical to the performance of nuclear waste disposal sites (Meigs and Beauheim, 2001). Despite their importance, the characterization and modeling of fluid flow and contaminant transport in fractured rocks continue to be a challenge because they tend to be highly heterogeneous. This heterogeneity concentrates flow into erratic channels that are not addressed by traditional analysis techniques. Responsible management requires reliable field characterization methods and modeling analyses to assess the impact of management options, yet currently available techniques are poorly suited to the analysis of flow and transport in fractured rocks (NRC, 1996). One such technique for field characterization is aquifer testing, where water level changes (drawdowns) are observed in the aquifer surrounding a pumped well. These drawdowns over time are interpreted by fitting a simple model of flow to a well, yielding estimates of hydraulic properties that are used in subsequent assessments of water resources. However, fractured rock aquifers often have complex flow geometries that are ignored by traditional interpretation approaches that assume radial (two-dimensional) flow. Figure 1 is a log-log diagnostic plot of the drawdown, s, and drawdown derivative ( ) t d ds s ln = ′ versus time. The plot compares a traditional model for interpreting an aquifer test with data from an aquifer test in a fractured dolomite aquifer in Kankakee County, in northeastern Illinois. The producing zone of this aquifer is a few meters thick, parallel to the plane of bedding, and laterally extensive. In this circumstance, the traditional approach to interpreting an aquifer test would fit the Theis model of radial flow in an infinite, two-dimensional domain (Theis, 1935). However, the slope of the Theis model fits the data poorly, as evidenced by the mismatch of the derivatives of the data and the model. Alternative combinations of hydraulic properties result in equally poor fits to the data, translating into unreliable parameter estimates and increased uncertainties in managing this water resource. The characterization of fractured rocks requires an approach that addresses the complex, often non-radial flow geometry experienced by aquifer tests in these systems. One starting point is the Generalized Radial Flow (GRF) model for interpreting aquifer tests in fractured rocks (Barker, 1988), which includes an additional parameter, n, called the flow dimension. In the GRF approach, the cross-sectional area of flow for an aquifer test is given by , so that the surface area of a unit sphere in n dimensions is 1 ) ( − = n nr r A α