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1 vslue problem creating this phenomenon It Co is spreading process Hence, considering lateral the masured concentration at the waste boundary ing to be insignificant, we are lett with and CL is rhe concentration of the ground water further downgradient at any point L (the alternative CO = 1 + 2L (DT/V, L)"1 boundary), then CL L, CL ' 1 _ 1 The interesting question regarding Verrical Co I + 2(L/L,)(DT/VcL)'" 1 + 2 [(DT 0"/L,] /Spreading is as tollows At what distance L' trod the solid waste boundary will the maximum _ (2) takejlace due to transverse spreading in a 4crt-r� where L is the distance to the alternative boundary, planes This will obviously occur where the cori;z=,- and L, is the horizontal width of the contaminant inant plume occupies most of the thickness of Uc ' stream at the waste boundary (Figure 1(a)] aquifer BearS1979, p 252) estimates this distarc: A more realistic assessment may be obtained to be about 10 to 15 times the aquifer thickness by-1 t7wo-dimensional front where there is transverse ItLthc general case of vertical spreading [Figure ' dispersion in two directions perpendicular to the 1(b)] , we expect the spreading thickness to be flow lines Hence, the front will not only spread approximated by L2 + (DT L/Vc)'" where L, laterally but vertically as well [Figures 1(a) and corresponds to the thickness-of the plume at ' 1(b)] If the transverse dispersion coefficient is the the waste boundary, andf`L`is any given distance same in both directions, the conservation of mass from the boundary As in all previous cases, the principle implies diffusio0_1 c .Dgti'(DT L/Vc)'5 is taken as an approxi- mate measure for the spread For the condition CO = [I + 2 (DTO [1 + - (DT t) ] (3) that L corresponds to the distance from the waste t � CL L, L, facility where the contaminant plume occupies ' or most of the aquifer thickness [L', Figure 1(c)] , the available spreading thickness equals the aquifer 2L 2L thickness"i�so that Co. _ [I + --' {DTNc!-)� � [1 + -- (D-r/Vc L)11] {4) CL L, L, H = L2 + (DT L'/bc)", (6) where the dimensions of the contaminant at the This gives l source are L,(horizontal) and(L2`(vcrtica.l), the - 1 latter being obtained from inventory wells a;_the' L' _ Vc (H — L )2 (7) waste boundary p 2 T As L, will in general be much larger than L2, The distance L',can be regarded as a "t-fixing leng h" the second bracketed quantity on the right-hand side of equation (4) will generally dominate the wherein the contaminant plume obtains maximum dilution due to vertical spreading From the conser- vation of mass statement Ct- where(C�ts the concentration at L' L, L Consider the following eYampie For Vc/DT so�, r- equals one (meter)", L, equals 2 meters, and an i sal tai aquifer thickness H of about 10 meters, L' is calcu- L' lated to be about 64 meters,and CL', equals 0 2 Co t 1 1 i f Hence, the limit to vertical spreading in this case 1 _ __ Wv4.Tchy_ _ _ _ __ _ occurs about 64 meters rrom the waste facilityL: H Transverse spreading throughout this distance will result in a lowering of the concentration to about 20 percent of the value observed at the waste Fig 1 Geometrical s reaaing of contaminant plume in a boundary ,fin increase in veloc.ty relative to trans- la) horizontal plane, b) vertical plane,and (c) vertical verse dispersion increases the distance L' but has no I Plane where the cont mant occupies the full aquifer effect on the dilution potential as erpiessed by thickness equation (8) An increase in aquifer thickness H, 306 -