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f however,greatly affects L' and rhe:concenrration iR _ CL', occurring there. It is clear from these developments that the variable aquifer thickness H is the most significant parameter affecting dilution potential It is noted further that as the thickness of the plume at the waste boundary (L.1) approaches the aquifer thick- ness (H), the distance L' approaches zero and CL' Z tapproaches Co }VC Mixing with Continuous Recharge From Figure 2, the shaded area is assumed to be contaminated ground water moving with a }Q-' velocity Vc [equation (1)) , and is continuously Fig 2 Plume mixing with Continuous recharge ' replenished by a recharge rate R (a volume of water per unit area per unit time) Let m be the amount of mass of the pollutant in the shaded to some distance L is in the range of 10 years, region which has a volume V of z2"n, where z is an 100 years, 1000 years, then CL/Co = 0 91, 0 s, and average plume thickness, 2 is a unit distance, and 0 09, respectively Clearly, those contaminants n has already)jeen defined as the porosity The with long travel times (low flow velocities or large 1 change in concentration with nme is then distribution coefficients) undergo significant dC d(m/V) -m dV 1 dm --m dV --Cl dV dilution — dt dr + V dt m dt=— — = — — When applied to some alternative boundar} , - - V� dt V dt V� dt equation (1 1) is better expressed (9) 1 where dm/dr = 0 since dispersion and kinetic L - o 1 + (R/z)(L/V,) (1` effects are assumed to be absent The increase in -� fluid volume dVfdt is lust the recharge volume per where," is the Concentration as measured at the unit time. Hence, dV/dt = R22n if mixing of fresh waste boundary, and L is the distance to the water with the pollutant is 100% effective Subsn- alternative boundary where the concentration is tuting into equation (9) for dV/dt gives expected to be CL If the plume does not extend over the full thickness of the aquifer ' dC dt - 2 R£2n (10) with,n this region, z is taken as an average plume m thickness and R is modified to include only that part of the recharge rate that effectively mixes Integrating from zero to time t yields with the plume This latter value can only be a fiery 1 _rough estimate under the best of conditions C(t) = Co 1 + {R/z} t {11) Mixing with Streartis where Co is an initial concentration,z is an average Most ground water, by nature of its :not ement plume thickness,and R is the recharge rate that from topographically high areas to topographically effectively mixes with the plume over the thickness low areas will eventually discharge into streams or z rivers To compute a dilution factor for discharge _Equation (11) is best applied to that part of a of contaminated water into a flowing stream, as plume that occupies most of the thickness of an depicted by Figure 3, one must determine the aquifer For this case, Co is the concentration total contaminant added during some time period where the plume first assumes such a thickness, r, and the total volume of water in the stream that z = H is the aquifer thickness, and R is the recharge accepted this discharge during this time period Ur rate As an example, assume a conservative dilution J be the flux (average discharge per unit time per rate of 1%, i e , R/z equals 0 01 yr-' This means unit area) of the contaminant at the stream What C(t) equals C,,(I + 0 Olt) where Co is the boundary The flux J equals CLVL, where CL 1,111 oncentrarion where the plume first assumes the Vc are the concentration of the contaminant and full thickness of the aquifer If the transport time its velocity at the stream aquifer boundary, 307