A Numerical Study on the Relationship Between Transmissivity and Specific Capacity in Heterogeneous Aquifers

Abstract

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

Full Document