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 transmissi vity (T) data. Theories which assume uniform transmissivity predict a nearl y linear relationship between T and Q/s, However, linear dependence is seld om 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 hydrau lic tests in heterogeneous media show that estimates of T derived using Jac ob's method tend to their late-time effective value much faster than Q/s va lues. The latter are found to be more dependent upon local transmissivities near the web, This explains why the regression parameters for T versus Q/s data depend on heterogeneity and the 'lateness' of the test period analyze d. 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 deviati on from Linearity often observed in the field, A further result is that the geometric mean of T estimates, obtained from short and intermediate time p umping 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.