Generalized Radial Flow in Synthetic Flow Systems

Abstract

Traditional analysis methods used to determine hydraulic properties from pumping tests work well in many porous media aquifers, but they often do not work in heterogeneous and fractured-rock aquifers, producing non-plausible and erroneous results. The generalized radial flow model developed by Barker (1988) can reveal information about heterogeneity characteristics and aquifer geometry from pumping test data by way of a flow dimension parameter. The physical meaning of non-integer flow dimensions has long been a subject of debate and research. We focus on understanding and interpreting non-radial flow through high permeability conduits within fractured aquifers. We develop and simulate flow within idealized non-radial flow conduits and expand on this concept by simulating pumping in non-fractal random fields with specific properties that mimic persistent sub-radial flow responses. Our results demonstrate that non-integer flow dimensions can arise from non-fractal geometries within aquifers. We expand on these geometric concepts and successfully simulate pumping in random fields that mimic well-test responses seen in the Culebra Dolomite above the Waste Isolation Pilot Plant.

A B‐Spline Framework for Smooth Derivative Computation in Well Test Analysis Using Diagnostic Plots

“…Well test interpretation can be improved by analyzing the second drawdown derivative response over time, referred to as the flow dimension, n . This concept, introduced by Barker (), is related to the power by which the cross‐sectional flow change with distance from the borehole (Bowman et al ), and therefore is an additional tool to identify transient flow patterns during the test.…”

“…If a stable flow dimension exits, the second derivative will exhibit a constant value (preferably for one log cycle of time), equivalent to n ; otherwise, no stable flow dimensions occur, and no unique hydraulic properties can be inferred analytically from the test. The flow dimension is defined for values between zero to three, such as n = 0, for closed aquifers, n = 1 for linear flow, n = 2 for radial flow, n = 3, for spherical flow and values between these integer dimensions for highly heterogeneous media (Beauheim et al ; Giese et al ) or nonfractal geometries (Bowman et al ).…”

Flow-bearing structures of fractured rocks: Insights from hydraulic property scalings revealed by a pumping test

“…Translation of scalings in terms of generalized non-integral hydraulic dimensions has proven informative but challenging (e.g., Doe, 1991;Le Borgne et al, 2004;Bernard et al, 2006;Cello et al, 2009;Rafini and Larocque, 2009;Odling et al, 2013;Giese et al, 2017;Ferroud et al, 2018). Nonstandard pres-sure responses may be observed in complex reservoir geometries, which can be fractal-like structures (e.g., Chang and Yortsos, 1990;Acuna and Yortsos, 1995;Lods and Gouze, 2008) or non-fractal structures (e.g., Jourde et al, 2002b;Bowman II et al, 2013). Other studies have shown that fractional flow can be developed in some 2D heterogeneous transmissivity fields, such as long-range correlated media (e.g., Walker et al, 2006;de Dreuzy and Davy, 2007).…”