Pumping tests in heterogeneous aquifers: An analytical study of what can be obtained from their interpretation using Jacob's Method

Abstract

Abstract. Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional methods of interpretation in real aquifers can be questioned, since the evaluation of the drawdown curves observed at different locations in a single test may not result in one consistent set of hydraulic parameters. Thus most hydrogeologists tend to look at estimated transmissivities (T) as some average property of the medium, while estimated storativities (S) are disregarded in some cases, particularly when they are obtained from data measured at the pumping well. An analytical study of drawdown under radially convergent flow toward a single point in heterogeneous aquifers shows that large time drawdown values form a straight line on a drawdown versus log time plot. Jacob's method consists of obtaining estimates for T and S from the slope and intercept of this line. We find that even in a heterogeneous field, these estimates provide valuable information about the aquifer. Estimated T values for different observation points tend to converge to a single value, which corresponds to the effective T derived under parallel flow conditions. Estimated storativities, however, display higher variability, but the geometric mean of the S es t values can be used as an unbiased estimator of the actual S. Thus it appears that although Jacob's method was originally derived for homogeneous media, it can provide valuable information in real aquifers. IntroductionThe analysis of constant-rate pumping tests is often carried out using Jacob's method [Cooper and Jacob, 1946]. It consists of plotting drawdown versus log time and fitting a straight line to late time data points. Estimates of the transmissivity (T) and storage coefficient (S) are obtained from the slope and intercept of this line. It is generally accepted that the estimated values (Test and Sest) derived from Jacob's method are representative values for the test area (some area surrounding the pumping and observation wells). In fact, Tes t values calculated from a single pumping test using drawdowns measured at different observation wells tend to be fairly constant. However, the corresponding S es t values display large variability. This seems to somewhat contradict the generally accepted belief that aquifer transmissivity is highly variable. Actually, Meier et al. [1998] and others have shown that these effects in Tes t and Sest are a consequence of the homogeneity assumption used in the interpretation. Thus, in pumping tests performed in heterogeneous media, the variability in the transmissivity field is apparent as a variability in the S estimates, while the estimated T values remain almost constant. In this paper we follow up the numerical work of Meier et al. [1998] with an analytical study. Relationship to Previous Work

Flow dimensions corresponding to hydrogeologic conditions

“…The parameter estimates of these tests are acknowledged to be spatial averages whose averaging scale depends on the test duration and the hydraulic properties of the formation. A number of authors have examined the spatial averaging of hydraulic tests and the relationship between the interpreted values and the moments of the heterogeneous formation [e.g., Butler, 1991;Meier et al, 1998;Sánchez-Vila et al, 1999]. In contrast, the flow dimension of a heterogeneous medium has received comparatively little attention.…”

Probabilistic human health risk assessment of degradation‐related chemical mixtures in heterogeneous aquifers: Risk statistics, hot spots, and preferential channels

“…Different metrics have been used to describe connectivity [Sanchez-Vila et al, 1999;Fernandez-Garcia et al, 2002;Carrera, 2005, 2006;Trinchero et al, 2008;Fernandez-Garcia et al, 2010]. In general, Renard and Allard [2013] distinguished two types of measures: Static connectivity metrics only depend on the spatial distribution of aquifer properties, and dynamic connectivity metrics depend on the flow and/or transport response to a given impulse.…”

Phase II Groundwater Flow Model of Corrective Action Unit 98: Frenchman Flat, Nevada Test Site, Nye County, Nevada, Rev. No.: 0

“…Sanchez-Vila et al (1999) also suggest that a good estimate of true storativity is rarely obtained in practice from pumping tests. It is possible that much of the apparent scatter in specific storage values is unrelated to the actual variability of storage properties.…”

“…However, it is not clear how representative the data are of the broader distribution over the entire NTS Investigation Area. Sanchez-Vila et al (1999) show that in the presence of heterogeneity, which always occurs in reality, storativity estimates will often vary strongly as a function of the relative transmissivity of the flow path between the pumping and observation well.…”