Evaluating uncertainty in predicting spatially variable representative elementary scales in fractured aquifers, with application to Turkey Creek Basin, Colorado

Abstract

[1] Computational limitations and sparse field data often mandate use of continuum representation for modeling hydrologic processes in large-scale fractured aquifers. Selecting appropriate element size is of primary importance because continuum approximation is not valid for all scales. The traditional approach is to select elements by identifying a single representative elementary scale (RES) for the region of interest. Recent advances indicate RES may be spatially variable, prompting unanswered questions regarding the ability of sparse data to spatially resolve continuum equivalents in fractured aquifers. We address this uncertainty of estimating RES using two techniques. In one technique we employ data-conditioned realizations generated by sequential Gaussian simulation. For the other we develop a new approach using conditioned random walks and nonparametric bootstrapping (CRWN). We evaluate the effectiveness of each method under three fracture densities, three data sets, and two groups of RES analysis parameters. In sum, 18 separate RES analyses are evaluated, which indicate RES magnitudes may be reasonably bounded using uncertainty analysis, even for limited data sets and complex fracture structure. In addition, we conduct a field study to estimate RES magnitudes and resulting uncertainty for Turkey Creek Basin, a crystalline fractured rock aquifer located 30 km southwest of Denver, Colorado. Analyses indicate RES does not correlate to rock type or local relief in several instances but is generally lower within incised creek valleys and higher along mountain fronts. Results of this study suggest that (1) CRWN is an effective and computationally efficient method to estimate uncertainty, (2) RES predictions are well constrained using uncertainty analysis, and (3) for aquifers such as Turkey Creek Basin, spatial variability of RES is significant and complex.Citation: Wellman, T. P., and E. P. Poeter (2006), Evaluating uncertainty in predicting spatially variable representative elementary scales in fractured aquifers, with application to Turkey Creek Basin, Colorado, Water Resour. Res., 42, W08410,

Regional groundwater flow in mountainous terrain: Three‐dimensional simulations of topographic and hydrogeologic controls

“…Finally, the model is assumed to be an equivalent porous media under isothermal conditions. The assumption of an equivalent porous media is justified by the large scale of the model [ Wellman and Poeter , 2006] and by the generalized nature of both the model and our objectives. Anisotropy and heterogeneity of the hydraulic conductivity tensor, expected in mountain belts, is examined in the sensitivity analysis described below.…”

Estimation de la conductivité hydraulique des zones discrètes de réseaux de fractures à partir des charges hydrauliques : application au bassin versant du N’zo (ouest de la Côte d’Ivoire)

“…Par conséquent ces mailles ne peuvent plus représenter correctement le comportement discret des zones de perméabilité du réseau de fractures (BRACQ, 1994;HARDCASTLE, 1995). Le modèle de configuration spatiale des zones discrètes de perméabilités le plus représentatif de la région étudiée (maille de 4 km) doit être capable aussi de calculer les conductivités hydrauliques avec des incertitudes minimales (WELLMAN et POETER, 2006). Ainsi, les conductivités hydrauliques moyennes calculées dans les différentes zones de paramètres définies avec la maille de 4 km (K1, K2, K3 et K4), varient de 1,1 x 10 -6 à 2,4 x 10 -5 m•s -1 (Figure 13).…”

Effects of simplifying fracture network representation on inert chemical migration in fracture‐controlled aquifers

“…Dirichlet hydraulic boundary conditions are applied to the two opposing “Y”–“Z” peripheral faces of the model region such that a 0.05 hydraulic gradient is established collinear to the “X” coordinate axis. A hydraulic gradient of this magnitude falls between precipitous mountain watersheds with regional values of ∼0.10 [e.g., Wellman and Poeter , 2006] and those of flat lying topography, but the choice of gradient is considered arbitrary since dispersion scales to the flow velocity and no particular field site is considered. Along the four lateral model faces hydraulic head is linearly interpolated as a function of the “X” coordinate axis.…”

“…Synthetic studies of fracture networks, however, suggest that network connectivity may be nonasymptotic under certain circumstances [e.g., Bour and Davy , 1998]. Additional support for large scale influence is evident from the examination of scales for predicting bulk fluid flow in fractured aquifers applicable to evaluating water resources, which shows that basin scale consistency in fluid behavior is not reached until ∼100 m–1000 m [ Wellman and Poeter , 2005, 2006]. This implies that sufficient averaging of transport processes will occur at larger length scales given its greater dependence on flow path variability.…”