Well-Type Steady Flow in Strongly Heterogeneous Porous Media: An Experimental Study

Steady well-type flow was monitored in an aquifer that was artificially packed in order to reproduce a given, highly heterogeneous, statistical distribution of the log-conductivity Y. In particular, we focus on pumping tests carried out at 10 volumetric flow rates. The experimental arrangement was composed by a pumping well and several surrounding observation piezometers. The unique feature of this experimental study is that the high heterogeneity structure of Y is known fairly well. Thus, the study lends itself as a valuable tool to corroborate theoretical findings about flows driven by sources through porous formations, where the variance 2 (in the present study equal to 3.79) of Y is large. Besides discussing experimental findings, we tackle the crucial issue of upscaling the hydraulic conductivity in a well-flow configuration. In particular, we deal with the equivalent conductivity (EC) as that pertaining to a homogeneous (fictitious) medium which conveys the same volumetric flow rate of the real one, under the same boundary conditions. Hence, the EC can be identified straightforwardly by means of head measurements. Even if we show that the EC is a proper parameter to reproduce measurements, it is experimentally shown (in line with the theoretical results) to be position-dependent, and therefore, it cannot be regarded (unlike groundwater-type flow) as a formation’s property. This implies that the EC applies only to the configuration at stake. Then, we show that the EC, combined with a recent model of effective conductivity in well-flows through highly heterogeneous porous formation, leads to a reasonably reliable estimate of 2 , some limitations and approximations, notwithstanding. It is hoped that the present experimental study will be useful for other researchers who are engaged with similar research-topics.