STREAM AQUIFER WATER QUALITY INTERACTION

Abstract

The stream aquifer interaction problem has been examined in some detail in recent years. There are two main aspects of the interaction process: i) the flow from the stream to the aquifer during the periods of rising stream stage, and ii) the return flow from the aquifer to the stream consequent to decline in the stream stage. Another aspect of the problem, which needs attention, is the solute transport consequent to the exchange of flow between the stream and the aquifer. If the stream carries a solute, the aquifer will receive the solute during the rising flood and part of it will be returned to the stream after the flood recedes. If the aquifer is polluted then the solute shall be transferred from the aquifer to the stream during recession of flood. In the present analysis the following stream aquifer interaction and solute transport problems have been analysed: 1) the solute transport in a semi infinite aquifer due to change in stage in a fully penetrating stream, 2) the solute transport in a finite aquifer due to change in stage in a partially penetrating stream. Determination of the flow velocity distribution is a pre-requisite for solving a solute transport problem. The time variant flow at different sections In the aquifer due to varying stream stages has been found using discrete kernel coefficient. Starting from solution of Boussinesq's equation for one dimensional groundwater flow evolving due to a step rise in stream stage, the discrete kernel coefficients for flow at various sections for a fully penetrating stream have been derived analytically. The coefficients for a partially penetrating stream have been derived using solution of Boussinesq's equation for, onedimensional groundwater flow due to recharge from a strip source given by Polubarinova - Kochina. The flow in finite aquifer has been simulated using method of Images. Assuming that the flow from a partially penetrating stream hydraulically connected with an aquifer is linearly proportional to the potential difference between the stream and the aquifer in the vicinity of the stream, the time variant recharge from the stream for varying stage has been computed using the discrete kernel approach. Most of the experimental and theoretical works, which provide a basis for the study of real problems, deal with simple cases such as unidirectional flow, time invariant hydrodynamic boundary condition and concentration boundary condition. The advection dispersion equation has been solved either theoretically or by using numerical method. It is well known that the advectivedisperslve transport equation is more difficult to solve numerically than the flow equation. The problems are particularly j severe when advection dominates over dispersion. Numerical spatial oscillations are exhibited in numerical method. An alternate method of solving one-dimensional advection-dispersion transport equation, which does not suffer from oscillation is the cell model developed by Jacob Bear. In the present thesis, onedimensional advection-dispersion equation has been solved using a series of thoroughly mixed reservoir model which besides accounting for dispersion can consider the reversal of flow and its temporal and spatial variations. An explicit numerical scheme &as been developed for computing solute transport for varying (ii) stream stages. The following conclusions have been arrived at : a) Analytical expressions of discrete kernel coefficients for computation of flow rate and cumulative flow at any section have been derived for fully and partially penetrating streams and stream aquifer interaction during the passage of a flood wave has been quantified. It has been found that for a fully penetrating stream, the time of peak rate of groundwater recharge preceeds the time of peak flood stage. Also In the vicinity of the stream, the time of occurrence of peak flow at a section preceeds the time of occurrence of the maximum height of the flood wave. At distances far away from the stream, the time of occurrence of peak flow lags behind the peak stage of flood. b) For a partially penetrating stream, the time lag between occurrence of peak stage and occurrence of peak recharge rate diminishes. c) Consequent to recession of a flood wave, reversal of flow takes place. The reverse flow rate at any section attains maximum and then decreases. The decrease is monotonic at large time. It is found that in an aquifer of semi infinite areal extent the total volume of water which enters the aquifer during the rising flood does not come back to the stream after the stream stage comes back to the original level. For a flood wave, which attains a peak height of 3 m in 3 days after the onset of flood, continues to remain at the peak stage for 60 days and then comes back to the 3 original level in 17 days, 8.417 m of water enters the aquifer 2 whose transmissivity = 100 m /day, storage coefficient = 0. 1 and initial saturated thickness = 50 m, from unit length of the fully penetrating stream during the flood out of which 3.662 m3 of water comes back to the stream during recession. (iii) d) A second order polynomial approximation of an integrand F(t) in a strip t-At to t+At, leads to t+At J F(t) dt --±2 F(t-At) +|F(t) +?L F(t+At). In a solute mass balance for a period t to t+At, a second order polynomial approximation of the integrand (mass inflow rate or outflow rate) in the interval t-At to t+At, provides a more accurate result in comparison to that obtained by first order approximation of the integrand in the range t to t+At. e) The longitudinal dispersivity is confirmed to be approximately equal to half of the mixing length, Ax. In a thoroughly mixed reservoir, the strip length Ax in the direction of flow represents dispersion. Therefore if reservoir length Ax-* 0, the solute movement is similar to that of a piston. Also larger the mixing length, lengthier is the transition zone at any time. f) Under unsteady flow condition, the concentration C(x,t)/C at R a given time t and at a given distance x from the stream is nonlinearly dependent upon the step rise in stream stage. g) The variation of jc(x, tJ-CjW^Cj) with xat some specified time, for the specified flood and the aquifer parameters shows that the cleaning action of the stream is limited. The flood has no impact beyond 28 m from the stream. If the solute concentration in the stream water is zero, during the passage of flood, the solute in the aquifer in the vicinity of the stream is pushed into the aquifer, but with reversal of flow, the zone which was made free from the solute again gets polluted. If the stream is polluted and groundwater is free from it, for the above specified flood and aquifer parameters, the pollution will not travel beyond 28 m from the stream. h) Variation of cumulative quantity of solute entering the (iv) aquifer due to a flood wave whose duration is 20 days and which attains a peak height of 3 m in 3 days, shows that, if C = 0, 18 C enters into the aquifer out of which 10 C returns to the K R stream after the recession of the flood. If the stream water is free from solute, i.e. if C = 0, for R the flood having a duration of 20 days, 3.2 C is flushed out from the aquifer during the reversal of flow. 1) In case of a partially penetrating stream in a finite aquifer the peak flow from the stream to the aquifer is reduced considerably due to stream resistance. The peak recharge rate from a stream to the finite aquifer is not influenced by the aquifer boundary since maximum recharge occurs in the beginning. The recharge from the stream after attaining a maximum, decreases with time. As the time proceeds, the flow from the stream tends to zero, because of the limited lateral extent of the aquifer. For this reason, in case of partially penetrating stream in finite aquifer, solute movement during passage of a flood is restricted to small distance from the stream bank. s.