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

Specific capacity (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 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 Q/s data to estimate T values where only Q/s data are available. In this paper we use numerical models to investigate the effects of aquifer heterogeneity on the relationship between 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 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 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 (Teff) of heterogeneous aquifers. In the studied simulation cases, the median of the T values or the arithmetic mean yield better estimates for Teff.

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