Discussion - Use Of An Analytical Solution For Preliminary Estimates Of Ground Water Flow To A Pit - Hanna, T. M., Azrag, E. A., Atkinson. L. C.

Discussion by Dan Plazak The authors are to be congratulated for presenting a simple and practical tool for quick estimates of ground water flow rates. At the risk of detracting from the simplicity of the method, I would like to suggest a slight refinement to the equation as presented. As the authors noted, the Jacob-Lohman equation (1952) assumes confined-aquifer conditions. To use confined-aquifer equations in water-table aquifers, Jacob (1963) presented a correction to convert water-table aquifer drawdowns [Ahw] to equivalent confined aquifer drawdowns [Ah,: 2] [Ah Ah = Ah - w(1) Cw 2H where: Ah, = Drawdown in confined aquifer: Ahw = Drawdown in water-table aquifer and H = Original saturated thickness of aquifer] Substituting the above in equation ( I) of Hanna. Azrag and Atkinson [4nT Ah - 2H ) Qj2.25 T t(2) 1 nr2 S W] Since the above expression predicts lower pump rates, it causes the Jacob-Lohman equation to agree more closely with appropriate analytical and numerical models. Figure 1, adapted from Fig. 5 of Hanna. Azrag and Atkinson, illustrates the closer agreement of the modified equation to their numerical model, as reflected in Qm/QJL ratios closer to unity. The agreement improves particularly as drawdown [Ah] becomes large in relation to aquifer thickness H. An additional advantage of the modified equation is that Hanna, Azrag and Atkinson's correction factor C is much more stable as pit depth increases. Assuming, as did Hanna, Azrag and Atkinson, that their numerical model is an accurate predictor, it is clear that the modification incorporated in equation (2) improves the accuracy of preliminary estimates of ground water flow to a pit.[ ] References Jacob, C.E and Lohman. S. W.. 1952, "Nonsteady flow to a well of constant drawdown in an extensive aquifer." Transactions, American Geophysical Union. Vol, 33, No. 4. pp. 559-569. Jacob. C. E.. 1963, `Determining the permeability of water-table aquifers,' USGS Water-Supply Paper 1536-1, pp. 245-271