## Abstract

Specific capacity (${\displaystyle {\frac {Q}{s}}}$) data are usually much more abundant than transmissivity (${\displaystyle T}$) data. Theories which assume uniform transmissivity predict a nearly linear relationship between ${\displaystyle T}$ and ${\displaystyle {\frac {Q}{s}}}$. However, linear dependence is seldom observed in field studies. Since hydrogeologic studies usually require ${\displaystyle T}$ data, many hydrogeologists use linear regression analysis of ${\displaystyle T}$ versus ${\displaystyle {\frac {Q}{s}}}$ data to estimate ${\displaystyle T}$ values where only ${\displaystyle {\frac {Q}{s}}}$ data are available. In this paper we use numerical models to investigate the effects of aquifer heterogeneity on the relationship between ${\displaystyle {\frac {Q}{s}}}$ and ${\displaystyle T}$ estimates. The simulations of hydraulic tests in heterogeneous media show that estimates of ${\displaystyle T}$ derived using Jacob's method tend to their late‐time effective value much faster than ${\displaystyle {\frac {Q}{s}}}$ values. The latter are found to be more dependent upon local transmissivities near the well. This explains why the regression parameters for ${\displaystyle T}$ versus ${\displaystyle {\frac {Q}{s}}}$ data depend on heterogeneity and the‘lateness’of the test period analyzed. Since this effect is more marked in high ${\displaystyle T}$ zones than in low ${\displaystyle T}$ zones, we conclude that natural aquifer heterogeneity can explain the convex deviation from linearity often observed in the field. A further result is that the geometric mean of ${\displaystyle T}$ estimates, obtained from short and intermediate time pumping tests, seems to systematically underestimate effective ${\displaystyle T}$ (${\displaystyle T_{eff}}$) of heterogeneous aquifers. In the studied simulation cases, the median of the ${\displaystyle T}$ values or the arithmetic mean yield better estimates for ${\displaystyle T_{eff}}$.

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Published on 01/01/1999

DOI: 10.1111/j.1745-6584.1999.tb01149.x

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