FLOW TO A WELL IN MULTIPLE AQUIFER SYSTEM

Abstract

Water wells generally tap more than one aquifer. The mathematical solutions developed so far for determining drawdown and individual aquifer's contribution during the unsteady state flow to a multiaquifer well are intr actable. Therefore, only a few numerical results are available so far for a multiaquifer well system. In the present study using discrete kernel approach, complete analytic solutions have been developed for the following problems of unsteady flow to a multiaquifer well : a) Unsteady flow to a well tapping two confined aquifers separated by an aquiclude ; b) Unsteady flow to a well tapping more than two aquifers which are separated by aquicludes ; c) Unsteady flow to a well tapping two aquifers separated by an aquitard. For a well tapping two aquifers the studies have been extended when the top aquifer is unconfined and has delayed yield characteristics. The two aquifers may either be separated by an aquiclude or aquitard. Discrete kernel coefficients for drawdown in an unconfined aquifer have been evaluated using Boulton's solution. An efficient method has been found to compute 11 the discrete kernel coefficients for any value of tj, [t, =(0 +0y)/0 fwhere the storage coefficients 0and 0y correspond to early and later part of time drawdown curve of an unconfined aquifer]. With the method of analysis developed in the thesis, it is easy to find the discharge contributions of each of the aquifers when amultiaquifer well is pumped. When the well is tapping atwo aquifer system separated by an aquitard, the discharge contributions by each of the aquifers and the exchange of flow taking place bet ween the two aquifers through the intervening aquitard have been evaluated. The variations of each aquifer's contribution to well discharge with time have been prese- , . form nted in non dimensional/for various values of aquifer parameters. The following conclusions have been drawn from the present study. In amultiaquifer well when pumping is started, the aquifer with lowest hydraulic diffusivity contributes maximum to the discharge. However, as the pumping con tinues its contribution decreases with time. At nearly steady state condition i.e. after aprolonged constant pumping, contributions by each of the aquifers are pro portional to their respective transmissivity values. When the aquifers tapped have equal hydraulic Ill diffusivity values, their contributions to well discharge are independent of time and are proportional to their respective transmissivity values. It is true for both the cases of the aquifers separated by aquiclude or aquitard. In such a case when the two aquifers are sepa rated by aquitard no exchange of flow takes place through the aquitard irrespective of the magnitude of the leakage factor and the drawdown at any section in both the aquifers are same. by When the two aquifers are separated/an aquitard and the well taps both the aquifers ,the leakage factor may be defined as L = *f C where T is the mean value of the transmissivities. The mean transmissivities may either be harmonic, geometric or arithmetic mean value of the transmissivities of the two aquifers tapped. In case of two aquifers separated by aquitard, the near steady state conditions are attained comparatively at shorter time for lower values of leakage factor. NOTATIONS The following notations have been used in this thesis (except in chapter 2 which deals with review of literature, where original notations have been used) Notation Description B. c, Kl L M Thickness of the aquitard Hydraulic resistance of aquitard Time step Hydraulic conductivity of the aquitard Leakage factor (»T C) Total number of aquifers n] Time steps CL Constant well discharge Qx(n) Q2(n) Discharge contributions by individual aquifers at nth time step Dimension t -1 It iV1 1V1 Qr(i#j,n)Recharge taking place through the area of influence of node (i,i) at l3^1 nth time step QR(n) Total recharge taking place from one l3t~1 aquifer to the other iv Notation Description Dimension r Distance of observation well from 1 the pumped well rw Radius of well 1 s Drawdown at distance r from the 1 pumping well at time t after the onset of pumping T Transmissivity r^t*"1 T Harmonic mean transmissivity l2t""1 t,t time -j- ^X Grid size 1 x,y Cartesian coordinates i i JQ( ) Bessel function of first kind and zero order J±( ) Bessel function of first kind and first order a Reciprocal of Boulton's delay index t""1 p Hydraulic diffusivity (T/0) l2^1 0 Volume of water intantaneously released from aquifer storage per unit drawdown per unit horizontal area (storage coefficient) 0 Total volume of delayed yield from storage per -unit drawdovm per unit horizontal area which is commonly referred as specific yield d(n) Discrete kernel coefficient l/(l3/t)