Correlation Structure of Steady Well‐Type Flows Through Heterogeneous Porous Media: Results and Application.

Steady flow toward a fully penetrating well takes place in a natural porous formation, where the erratic spatial variations, and the raising uncertainty, of the hydraulic conductivity K are modeled within a stochastic framework which regards the log‐conductivity, ln K, as a Gaussian, stationary, random field. The study provides second order moments of the flow variables by regarding the variance of the log‐conductivity as a perturbation parameter. Unlike similar studies on the topic, moments are expressed in a quite general (valid for any autocorrelation function of ln K) and very simple (from the computational stand point) form. It is shown that the (cross)variances, unlike the case of mean uniform flows, are not anymore stationary due to the dependence of the mean velocity upon the distance from the well. In particular, they vanish at the well because of the condition of given head along the well's axis, whereas away from it they behave like those pertaining to a uniform flow. Then, theoretical results are applied to a couple (one serving for calibration and the other used for validation purposes) of pumping tests to illustrate how they can be used to determine the hydraulic properties of the aquifers. In particular, the concept of head‐factor is shown to be the key‐parameter to identify the statistical moments of the random field K. Plain Language Summary: Flow toward a single well takes place in a porous formation, where the hydraulic conductivity is regarded as a random space function to account for its irregular spatial variability. A simple solution to this difficult problem is achieved by adopting some simplifying assumptions which apply to numerous real settings. Theoretical results are applied to a series of pumping tests in order to demonstrate their utility in the identification of aquifers' hydraulic properties. Key Points: A simple, general formulation to compute second‐order moments is presentedThe head factor is introduced for a robust identification of aquifers' statistical parametersThe application to pumping tests is illustrated and discussed [ABSTRACT FROM AUTHOR]