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

== Abstract ==

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

==Full Document==

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