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Groundwater Flow Modeling Study of the Love Canal Area, New York 8 INTRODUCTION The U.S. Environmental Protection Agency identified a need to assess the groundwater hydrology of the Love Canal area, Niagara Falls, New York. As part of this assessment, ground- water flow models were used to aid in data reduction and analysis and to attempt prediction of groundwater movement and contaminant migration. The modeling effort was started on August 20, 1980, and completed December 1, 1980. The objectives were to (1) devise a conceptual framework, (2) assist in data collection, (3) design and analyze aquifer tests, (4) predict system behavior, and (5) assess uncertainty. The technical approach involved the use of groundwater flow models, which were used to help interpret and predict the behavior of groundwater flow and convective transport at Love Canal. Since hydrodynamic dispersion is neglected, arrival times may be slightly underestimated. This chapter summarizes some of the work performed during 109 JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA GeoTrans, Inc. AB STRACT Increasing awareness of the problems presented by hazardous waste sites is leading toward an increased interest in, and application of, groundwater models. During the fall of 1980, a groundwater modeling study was conducted at the Love Canal area, Niagara Falls, New York. Flow models were used to aid in data reduction and analysis and to attempt prediction of groundwater movement. Both slug tests and aquifer tests were analyzed. The conceptual framework for the hydrogeologic units underlying Love Canal consists of a shallow water-table system of silts and fine sands and a deeper confined system in the Lockport Dolomite. The intervening confining layers consist of lacustrine and glacial clays. Modeling in the dolomite focused on characterizing the aquifer and assessing the potential for its contamination. Best judgment indicates that for the Lockport to be contaminated, the confining bed would have to be breached. Analysis of remedial action for the Lockport Dolomite indicates that three interceptor wells at the south end of the canal, pumped at only 32.3 mayday, would reverse the flow of groundwater to the river and provide an adequate halt to migration of potential contaminants to the river. this study. Results are presented for the aquifer test analysis and for modeling the Lockport Dolomite aquifer. The shallow system and remedial action modeling and analysis are pre- sented elsewhere (Mercer et al., 1981; Silka and Mercer, 19827. BAC KGROU N D The Love Canal site is located on the east side of Niagara Falls, New York. The landfill at Love Canal was operated for nearly 30 yr and occupied a surface area of approximately 16 acres with the south end 400 m from the upper Niagara River near Cayuga Island. The canal varies from about 3 to 11 m in depth with the original soil cover varying from 0 to 1.8 m in thickness (Leonard et al., 1977~. Figure 8.1 shows the typical strata at the Love Canal site. The soil layers are underlain by glacial till, which in turn is underlain by bedrock consisting of the Lockport Dolomite. In general terms, the groundwater hydrology includes (1) a shal-
110 DEPTH 1.8-2.5' (0.6-0.8 m) 4.0-5.5' (1.2-1.7 m) 7.5-8.5' (2.3 2.6 m) 10-5 11.5' (3.2 3.5 m/ 19.0 27.0' (5.8-8.2 m; 34.0-42.0' (10.4-12.8 m) DESCRIPTION Land Surface Clayey Silt Fill Silty Sand Soft Silty Clay Lockport Dolomite (Ranges in thickness from approximately 100 to 150 feet/ 30 to 46 meters) FIGURE 8.1 Typical strata in Love Canal landfill area (modified from Conestoga-Rovers & Associates, 1978). low system that is seasonally saturated and consists of the silt fill and silty sand and is underlain by (2) beds of confining material composed of clay and till that overlies (3) the Lockport Dolomite, which is underlain by the relatively impermeable (4) Rochester Shale. FIGURE 8.2 Generalized potentiometric surfaces for the Lockport Dolomite. JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA Lockport Dolomite The Lockport Dolomite is overlain by leaky confining beds and underlain by the relatively impermeable Rochester Shale Johnston, 1964) and is fairly continuous in the Niagara Falls area. Both artesian and water-table conditions occur in this fractured system, with the upper 3 to 4.6 m being the most permeable. Hydrogeologically, the dolomite in the Niagara Falls area probably is bounded on the south by the upper Niagara River (see Figure 8.2~. It is bounded toward the west by the lower Niagara River gorge. The dolomite thins north- ward, where it is bounded by its outcrops in the Niagara es- carpment. Under natural conditions, recharge occurs at the contact with the upper Niagara River near the falls and at an elevation high that is just south of the Niagara escarpment. Discharge occurs as seepage faces and springs at the lower Niagara River, along the Niagara escarpment, and along parts of the upper Niagara River away from the falls. A generalized potentiometric map developed from historic records for the Lockport Dolomite Johnston, 1964) is shown in Figure 8.2. The contours are highly idealized because the data were either (1) absent, (2) representative of several layers within the dolomite, or (3) collected over a two-year span dur- ing 1961-1962. A well hydrograph in the area indicates that flow is quasi- steady state. "Quasi" is used because seasonal variations of about +0.6 m are believed to be imposed on the steady-state condition in the upper part of the dolomite. Furthermore, since this study occurred in the fall, it is expected that the water levels represent seasonal lows. N _ SEA LEVEL DATUM N I AGARA ESCARPMENT ~ in AMER~ 4 ~ SITE Be< STUDY AREA ~ J 13 .' LOVE CANAL
Groundwater Flow Modeling Study Shallow System The shallow system at Love Canal is located in the upper units of silty sand and silt fill. It is probably bounded toward the north and west by creeks and toward the south by the Little Niagara River. Before remedial actions were taken, ground- water flow was probably toward the surface drainage, with the overall flow toward the south and the upper Niagara River. The soils in this area consist of the Canadaigua-Raynham- Rhinebeck association characterized by somewhat poorly drained to very poorly drained soils having a dominantly medium- to fine-texture subsoil (U.S. Department of Agriculture, 19721. These soils are silty loam to silty clay loam (ML to CL in the Unified Soil Classification). Previous work in the area has typ- ified the soils as shown in Figure 8.1 (Conestoga-Rovers & Associates, 1978~. Underlying the lacustrine sediments are gla- cial tills. The shallow system can be summarized as follows: 1. Silty sand and silt fill; approximately 3.7 m thick; hy- draulic conductivity is greater than or equal to 10- m/sec (Hart, 1978~. 2. Hard clay, transition clay, soft clay; 3.4 m thick; hydraulic conductivity is 10-l° to 10-il m/see (Leonard et al., 1977~. 3. Glacial till; 4.6 m thick; hydraulic conductivity is probably similar to that of clays (Glaubinger et al., 1979~. In addition to these units, storm-sewer and sanitary-sewer excavations as well as swales may act as conduits. Ebert (1979) describes the swales as old drainage ways up to 3 m deep and 12 m wide in their original state. Many of these old drainage ways have been filled with miscellaneous material. AQUIFER TESTING ANALYSIS Aquifer testing was designed, and subsequently modified, to characterize certain aspects of the groundwater system at the Love Canal site. These included the following: 1. Determination of the horizontal hydraulic conductivity and storage coefficient of unconsolidated glacial units and the Lockport Dolomite; 2. Determination of the variation of hydraulic conductivity with depth in the dolomite; 3. Determination of the hydraulic connection between the more permeable upper zones of the shallow system and the dolomite, that is, the vertical component of hydraulic conduc- tivity in the till and tight lacustrine sediments; and 4. Determination of the interconnection (vertical hydraulic conductivity) of permeable layers in the Lockport Dolomite. The tests used at the site included constant-pressure tests and constant-discharge tests in the Lockport Dolomite and a falling-head test in the overburden and till units. Except for the constant-discharge test, the results of the testing are dif- ficult to quantify. Therefore, only the constant-discharge test in the dolomite is described here and is presented for illustra- tive purposes. The basic solution used for the constant-discharge pumping 111 test is the Theis (1935) solution 4rrTJ: u (8.1) where s is the drawdown (L); r is the distance from pumped well to observation well (L>; Q is the discharge rate (Loft); t is the time after start of pumping; T is the transmissivity (L2lt); and S is the storage coefficient (dimensionless). Although the long-term pumping test in the dolomite at the site was designed to run at a constant-discharge rate, the actual pumping rate declined during the test. An approximate solution for these conditions can be obtained by using the principle of superposition in conjunction with the basic solution. The pro- cedure involves representing the variable pumping rate by a series of pumping periods having constant rates. The approx- imate solution is then given by 1 no s =~ (QjQ-1) W(u) (8.2) where j is the particular pumping period, m is the total number of pumping periods, W(u) is the exponential integral in Eq. cedure involves representing the variable pumping rate by a cedure is further detailed by Earlougher (1977~. Eqs. (8.1) and (8.2) provide forward solutions to the ground- water response. In this field test the inverse solution is re- quired; that is, from observed water-level changes, the hy- drologic parameters T and S need to be determined. In order to solve Eq. (8.2), a least-squares minimization technique is used. That is, to find T and S. n ~ [sO(ri, ti) sC(ri, ti>]2 (8. 3) i = 1 is minimized, where sO is the observed drawdown, sc is the calculated drawdown, i refers to a particular observation, and n is the total number of observations. Data were used from 12 observation wells and the pumping well. Measurements were continued at three observation wells for 2 h after the pump was shut down. With all of these data, there are several alternative ways to partition them for analysis. Two obvious ways are (1) match all the observations using one transmissivity value and one storage coefficient value (Case A), and (2) match the data for each well independently, calculating a separate T and S for each well (Case B). Both methods were used in this analysis. Comparing the results of both cases pro- vides a measure of validity in the analysis. The results of matching the data are presented in Table 8.1. Using all available data and matching all the wells with one T and S led to values of 0.0014 m2/sec and 1.49 x 1O-4, re- spectively. The mean deviation between observed values and calculated values using the above T and S was 0.12 m. Fitting the individual well data led to better matches of the data. For this case the transmissivity values were between 0.001 and 0.0035 m2/sec and the storage coefficient values were between 0.343 x 1O-4 and 3.12 x 1O-4. As noted, the matches on individual wells were better mean deviations for each well were between 0.010 and 0.064 m. Other results from aquifer testing are not presented but may be found in Mercer et al. (19817. The results of the aquifer
112 TABLE 8.1 Summary of Results of Pumping and Recovery Test Analysis JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA Matching Group Well T (m-/sec) S x 1O-4 Mean Deviation, m Case A (all wells together) 0.0014 1.490 0.119 Case B (individual wells) 38 0.0035 2.370 0.010 44 0.0031 1.650 0.014 48 0.0025 0.343 0.019 50 0.0018 0.483 0.032 56 0.0019 0.825 0.016 67 0.0017 1.750 0.025 68 0.0010 1.330 0.019 71 0.0019 1.500 0.020 79 0.0016 0.428 0.033 80 0.0014 1.290 0.025 86 0.0017 3.120 0.049 89 0.0010 2.000 0.064 Average 0.0020 1.420 testing partially fulfilled the original test objectives. The fol- lowing conclusions were drawn from the above analysis: 1. The 22-h discharge test in the Lockport Dolomite pro- vided an average field transmissivity of 0.0014 m2/sec and stor- age coefficient of 1.5 x 1O-4. These values are consistent with other values determined for the Lockport Dolomite in the Niagara vicinity. 2. Because many of the observation wells were completed only about 1 m into the dolomite, and because they responded quickly to the pumping from a well screened at a deeper level, the upper permeable zones of the dolomite appear to have significant vertical permeability. 3. The Lockport Dolomite is heterogeneous but less so than would normally be anticipated for carbonate aquifers. 4. The packer test results for the dolomite were inconclu- sive. Consequently, the regional observations of lohnston (1964) regarding the variation of hydraulic conductivity with depth are still assumed applicable to the site. Examination of the core description also supports lohnston's contention that the pri- mary water-bearing zones are located in the upper zones of the Lockport Dolomite. 5. The slug tests in the overburden wells provided an es- timate of the hydraulic conductivity of the lacustrine sediments and till. Both values are on the order of 3.04 x 10-~" m/see and indicate relatively impermeable material. 6. The shallow material tested at the slug test site was also relatively impermeable (on the order of 3 x 10-"' m/sec). However, this unit was quite clayey. Because the shallow silty- sandy units are highly variable, this one estimate is probably not representative of the shallow system at the site. 7. No estimates of storage properties for the overburden wells could be determined from the slug tests. LOCKPORT DOLOMITE MODEL the aquifer thickness. The boundary condition at the bottom is probably no-flow, since below the first 4.6 m parts of the Lockport Dolomite are relatively impermeable. At the top, the boundary condition is probably head-controlled flux repre- senting leakage through the confining beds. A groundwater flow model that handles these areal flow conditions is that presented by Trescott et al. (19767. Important assumptions include the following: 1. Groundwater flow and aquifer parameters in the Lock- port Dolomite are vertically averaged. 2. Q~asi-steady-state flow is assumed; that is, although there are seasonal variations, the system over an extended period of time does not change hydrologically from the seasonally av- eraged surface. This assumption is based on the few well hy- drographs available in the Niagara Falls area. 3. The aquifer in the Lockport Dolomite is assumed to be under leaky artesian conditions everywhere. 4. The aquifer transmissivity near the escarpment is as- sumed equal to 4.58 x 1O-5 m'/sec. Because of the analysis of tests at the Love Canal site, and because of the higher aquifer transmissivity near the river Johnston, 1964), a zone bordering the upper Niagara River was assumed to have a trans~nissivity of 4.58 x 10-4 m2/sec. This value is about one third the value obtained from the aquifer test analysis yet slightly greater than previously reported values. This value was selected because the aquifer test yielded a local value, whereas the lower value used in the model is more representative of a larger area. Transmissivity is assumed isotropic but nonhomogeneous. 5. Water moves vertically into or out of the Lockport Do- lomite through the confining layer. 6. The confining bed is assumed to be 7.6 m thick and is composed of clay and till. 7. The confining-bed hydraulic conductivity is assumed to be 10-~" m/see (Leonard et al., 1977~. Because of the better drained soils near the Niagara escarpment (U.S. Department of Agriculture, 1972>, this value was increased in that area to There are several numerical models that are appropriate for ~ ~^ ~~ ^ ^ ~ - ~ ~ simulating flow in the Lockport Dolomite. The approach taken was to vertically average the flow and aquifer parameters through ;~.25 x 1()-Y m/sec. (,ontining-bed hydraulic conductivity is also isotropic but nonhomogeneous. 8. There are not enough wells reported by Johnston (1964)
Groundwater Flow Modeling Study to construct a potentiometric surface for the silty sand and silt fill of the shallow system; wells that are in Johnston (1964) indicate that water levels are approximately 3 m below land surface; therefore, values determined from a topographic map were used and 3 m subtracted to produce a shallow-system potentiometric surface. In the Love Canal area, this resulted in heads that were 172 m above mean sea level. 9. The heads in the shallow system represent an average value and neglect seasonal variations or imposed stresses. 10. The rock underlying the permeable part of the dolomite is considered impermeable. 11. The scale of the Lockport Dolomite model is regional, covering most of the area in Figure 8.2. The area of interest was subdivided into rectangular blocks composing the finite-difference grid shown in Figure 8.3. The grid consists of 21 columns and 23 rows. The northern boundary is considered no-flow because it is located along the middle of a recharge area near the Niagara escarpment, i.e., a ground- water divide. Recharge is through the confining bed. The east- ern boundary is approximated as no-flow because it follows a flow line. The southern boundary is treated as constant head and corresponds approximately with the upper Niagara River. The western boundary follows approximately the covered con- duits of the pump-storage project and is considered constant head. Calibration Calibration of the Lockport Dolomite model consists of match- ing the observed steady-state potentiometric surface in Figure 1 - --- T--.- ~ - ~ I 173 ZERO TRANSMISSIVITY I E1 WELL BLOCK t N ~ 1 O lMILES 113 8.2. For steady-state flow conditions, the storage term can be eliminated during model calibration. Also, leakage through the confining bed is considered to be under steady-state conditions. The computed potentiometric surface is shown in Figure 8.4. As may be seen, the match is good on a regional scale, with the hydraulic gradient in the Love Canal area being toward the south and southwest. In terms of spatial distribution, leak- age into the Lockport occurred near the topographic high in the northern part of the study area. Leakage out occurred toward the escarpment and at lower elevations toward the up- per Niagara River. In the Love Canal area, leakage was gen- erally into the Lockport Dolomite. Thus, in the Love Canal area, the leakage is downward (annually averaged), using the value of 172 m for the head in the shallow system at the Love Canal site. The downward flow in the blocks representing the canal area, however, is very low, with rates ranging from 0.14 to 0.07 mm/yr. The head difference between the dolomite and shallow system is small, especially near the south end of the canal, and, as will be discussed later, the direction of leakage can be easily reversed. As for constant-head nodes, flow was into the dolomite at the pump-storage reservoir and, in general, was out through the western boundary. For the southern boundary, the upper Niagara River was gaining from the do- lomite near Love Canal and east; toward the west and near the pump-storage intake, the upper Niagara River was generally losing to the dolomite. Figure 8.5 shows a comparison of the hydraulic head com- puted from the steady-state match with the measured values, that is, in just the Love Canal area (section A-A' on Figure 8.4~. Even on a local scale, this match is good, with the com- FIGURE 8.3 Finite-difference grid for the Lockport Dolomite model.
114 FIGURE 8.4 Computed potentiometric sur- face for the Lockport Dolomite. GEOTRANS, INC. N COMPUTED STEADY STATE POTENT IOMETRIC SURFACE IN LOCKPORT DOLOMITE; FEET ABOVE MSL; CONTOUR INTERVAL = 10 FEET 111t'1 ~ O 1 mile puted values being slightly lower than the observed. This dif- ference may be the result of the head used in the shallow system as well as the constant-head value of 172 m that was used for the upper Niagara River near Love Canal. The observed profile near the river in Figure 8.5 is dashed, indicating that limited data were available there. This also indicates our uncertainty in using 172 m as the constant-head value. Sensitivity Analysis A detailed sensitivity analysis was performed on the Lockport Dolomite model. The following were considered: (1) the con- dition at the western boundary, (2) aquifer transmissivity, (3) confining-bed hydraulic conductivity, (4) river stage at the southern boundary, and (5) water level in the shallow system. 3 n - 72.5 - . J r =< 172.0 . in 171 .S . 171.0 - _ _56 6 O -56 - J 566 > At 565 tic 564 563 1 1 1 1 1 1 1 1 1 1 LOVE CANAL - LOCKPORT DOLOMITE LEGEND to RUN ONE · MEASURED 1 1 1 o.O 0.1 0.2 0.3 0.4 0.5 0.6 0 7 0.8 o.9 1.0 SOUTH - NORTH tM! LES FROM RIVER) ~T~ ~OTT 0.0 0.2 0.4 0.6 0.8 1.0 K I LOMETERS FROM R I VER 1.2 1.4 1 6 FIGURE 8.5 Magnification of mile O to 1.0 (O to 1.6 km) along section A-A'. JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA Pumped Storage Reservoi r B 1 oc ks A . ~ ~ LOVE CANAL : ~ A' Details are presented in Mercer et al. (1981~; only the results are presented in Table 8.2. Predictions Assuming Remedial Action Under natural conditions, flow in the Lockport Dolomite ap- pears to be at steady state. If remedial action for the dolomite is deemed necessary at some time in the future, the flow field will undoubtedly be disrupted. This will cause transient flow in the dolomite, which can also be simulated. The steady-state model described in the previous section was modified by varying values for the confining-bed specific storage and the aquifer storage coefficient. For the storage coefficient, a value of 1.5 x 1O-4 was used by Mercer et al. (1981) as determined from aquifer test analysis. A value of 2.6 x 10-3/m for plastic to stiff clay was estimated for the specific storage of the confining bed (Domenico, 19721. The computed steady-state hydraulic-head distribution in Figure 8.4 was used as the initial condition in the transient model. If remedial action is necessary for the Lockport Dolomite, installation of interceptor wells is a likely alternative to be considered. To evaluate the electiveness of this remedial op- tion, interceptor wells were incorporated into the Lockport Dolomite model at the south end of Love Canal. Three wells were placed at the southwest, southcentral, and southeast ends of the canal, since the flow gradient in the Lockport Dolomite is toward the south and southwest. Wells in these locations should intercept any solute that enters the dolomite beneath the canal. The pumping rates of the three wells were set at 7.6 L/min each. This amounts to a total withdrawal of 32.3 m3/day. The transient simulation lasted only 6.7 days, after which time the hydraulic heads in the dolomite came to a new steady state. These low pumpages are sufficient to cause a reversal in the hydraulic-head gradient. That is, the flow is no longer toward the upper Niagara River, which means the wells would
Groundwater Flow Modeling Study TABLE 8.2 Summary of Sensitivity Runs for Dolomite Run Description Effect 115 1 Lockport Dolomite steady state using constant-head boundary toward the "Best" comparison with observed data west and best estimate of parameters 2 Same as run 1 except with impermeable boundary toward the west Minor changes in heads at Love Canal site 3 Same as run 1 with aquifer trans~nissivity increased by 50% Slight increase in heads at Love Canal site 4 Same as run 1 with aquifer transmissivity decreased by 50% Slight decrease in heads at Love Canal site 5 Same as run 1 with confining-bed hydraulic conductivity increased by 50% Slight decrease in heads at Love Canal site 6 Same as run 1 with confining-bed hydraulic conductivity decreased by 50% Slight increase in heads at Love Canal site 7 Same as run 1 with river stage increased by 0.3 m About 1-ft decrease in heads at Love Canal site 8 Saline as run 1 with river stage decreased by 0.3 m About 1-ft decrease in heads at Love Canal site 9 Same as run 1 with heads in the shallow system in the Love Canal area Gradients through the confining bed were reversed; lowered by 0.3 m flow was out of the dolomite 10 Same as run 1 with confining-bed hydraulic conductivity increased to that Created groundwater mound in the dolomite of the dolomite in the grid block representing the south end of Love Canal a well radius of 7.6 cm) would be approximately 0.82 m, so that the assumptions of confined, artesian conditions in the dolomite are still valid. This new steady-state solution is dependent on the assump- tion of a constant-head boundary at the upper Niagara River. The hydraulic connection of the river and the Lockport Do- lomite is uncertain. If the connection is present to a lesser degree than assumed for the model, then the gradient would still be reversed by this pumpage; however, steady state may not be reached so quickly. Contamination Travel Times and Uncertainty Analysis If a contaminant is assumed to have entered the Lockport Dolomite, the travel time for the contaminant to reach the upper Niagara River can be computed. The uncertainty in travel time depends on the accuracy of our knowledge of the hydrogeologic system. The interstitial velocity of flowing groundwater can be writ- ten as vi = -, (8. 4) ~ as where vi is the interstitial velocity, K is the hydraulic conduc- tivity, ~ is the effective porosity, and ohms is the hydraulic gradient. Also note that for convenience the negative sign in Eq. (8.4) has been omitted. For steady uniform flow, travel time (t) is simply distance (L) divided by interstitial velocity. If all reactions between solute and the rock in which the groundwater is flowing are considered to be simple equilibrium linear sorption reactions, then the amount of solute present on the rock will be directly proportional to the amount of solute present in the fluid. This proportionality constant is the distribution coefficient, k`,, and from it one can calculate the rate of movement of solute in a flowing groundwater system relative to the rate of flow of the transporting water itself according to the expression water velocity = (1 + P kit), (8.5) solute velocity where p is the aquifer bulk density. Adjusting velocities and travel times for this retardation ef- fect results in the following expression for solute travel times: ( ) (8. 6) as Although this is a relatively simple equation, there are consid- erable uncertainties associated with ¢, K, and kit, which lead to uncertainties in the resulting calculated travel times. In this analysis, best estimated travel times to reach surface water for solute with various sorption properties are calculated. The un- certainty of this estimate is evaluated using Monte Carlo sim- ulation techniques. The Monte Carlo approach is used here even though for some of the extreme cases shown a direct analysis can be performed. The direct analysis is discussed later. Note that it is immaterial as to how the contaminant entered the groundwater in the Lockport Dolomite. The following best estimates are selected for evaluating Eq. (8. 61: L = 200 m, distance from the south end of Love Canal to the river; K = 3.0 x 1O-4 m/see (from aquifer test match, that is, 1.4 x 10-3 m2/sec/4.6 m, where a permeable thickness of 4.6 m is assumed>; dhlds = 1.52 x 1O-4 (from measured hydraulic head); p = 2.5 g/cm3, common limestone density (Clark, 19661; ~ = 0.02, effective porosity (estimated for fractured lime- stone from Winograd and Thordarson, 1975); kd = 0 to 10 mL/g (estimated from Apps et al., 1977). These values are best estimates from observed data, the aqui- fer-test analysis, and our hydrologic judgment. Eq. (8.6) gives a travel time for a perfect tracer (k`, = 0) or for the water itself of 1005 days. That is, if the clays were breached or if solute were transported through the clays, on entering the Lockport Dolomite, it is estimated to take 1005 days for the solute moving with the water to reach the river. In order to assess the statistical properties in the predicted results, it is first necessary to specify the statistical properties of the uncertain parameters. In this case the parameters in Eq.
116 (8.6) that have the greatest uncertainty are the hydraulic con- ductivity, the porosity, and the distribution coefficient. In the following analysis, ~ and K will be assumed to vary according to specified frequency distributions. Sensitivity analysis may be performed to evaluate the uncertainty in kit. There is also uncertainty in the simple uniform flow model and in the hydraulic gradient; however, this uncertainty will not be evaluated. Freeze (1975) presented a large body of both direct and indirect evidence that supports a log-normal frequency distri- bution for hydraulic conductivity. This distribution refers to the variance of hydraulic conductivity in space. The situation described by Eq. (8.6) is that of a constant, but uncertain, hydraulic conductivity. To evaluate this uncertainty, we as- sume the same distribution. If the hydraulic conductivity is log-normally distributed, a new parameter y = log K can be defined that is normally distributed and can be described by a mean value, ,uy, and a standard deviation, cry, that is, Nary, ayl. For this application, As = 1.9365 and cry = 0.5, that is, K = 0 3 x 10~93~ + 05> m/day (8.7) which is the value obtained from the aquifer-test analysis, with the standard deviation of one-half log unit. Freeze (1975) gives a range of hydraulic conductivity data for fractured rock with standard deviations ranging from 0.20 to 1.56, with a mean of 0.6785. These values of standard deviations indicate a larger spread of values for hydraulic conductivity than that deter- mined from the aquifer test. Because the values in Freeze (1975) are more comprehensive, our value of one-half log unit was estimated from his data. We use feet per day to compute travel times in terms of days. For the first simulation, Case 1, we estimated porosity to be 2 percent, that is ~ = 0.02. Although in theory a value for porosity may be calculated from the storage coefficient obtained from the aquifer tests, in this case it was not possible. The storage coefficient determined from the aquifer test indicates that the aquifer compressibility is more important than the water compressibility. Consequently, the storage coefficient is relatively insensitive to porosity and could not be determined. Values of K were chosen from a log-normal probability dis- tribution. This was done by recognizing that the values of Hi = log ~ come from a normal probability distribution. The normal distribution generator is y = crySn + lye (8. 8) where Sn is a random number taken from a normal distribution with a zero mean and a standard deviation of one, NfO,11. To obtain Sn, we use a random number, R*n' uniformly distributed on the interval (0,11. R*n is used to compute Sn (also called the random normal deviate, by Ralston and Wilf, 19671: So = ( - 2 in R*n):L'2 sin 2~rR*, ~ ~ (8.9) Using the value of y from Eq. (8.8), hydraulic conductivity is computed from K= 109 (8. 10) and used in Eq. (8.6) to compute the travel time to the upper Niagara River. To check convergence, we ran the Monte Carlo JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA simulations for 3200 and 6400 events. No significant difference appeared to exist, and the 6400-event distribution was used. A plot of the fraction of events in each interval versus the logarithm of travel time for a perfect tracer (k,` = 0) is shown in Figure 8.6. Case 1 refers to the case where the "best esti- mate" for porosity is used. Note that if porosity were decreased by an order of magnitude, the plot would shift one log unit to the left. The spread of the plotted travel times reflects the confidence with which we are able to specify them, given the precision of our estimate of the hydraulic conductivity, K. A range of 2 standard deviations on each side of the mean encompasses the 95 percent confidence interval. Based on the tabulated mean and standard deviation in Table 8.3, this means that there is a probability of less than 0.05 that the travel time of a tracer (nonretarded element) will be greater than 10,000 days or less than 100 days. In case 2, we analyze the uncertainty in both hydraulic con- ductivity and porosity, but assume they are uncorrelated. The same log-normal distribution for hydraulic conductivity is used, but porosity also is assumed log normally distributed with a standard deviation of 0.5 log unit. That is, x=log+, (8.11) where Nj,ux, (rXl and He = - 1.70 and ax = 0.5. This corre- sponds to a mean porosity of 0.02. The values of porosity are thus chosen from a log-normal probability distribution, rec- ognizing that the values of xi = log hi come from a normal probability distribution. The normal generator is X = (7xSn + ~ + ~X, (8. 12) where Sn+~ is a random number taken from NfO,11. Sn+~ is CASE 1 c Hi. ,\\4 . , . . . 1 , 1.0 2.0 3,0 4.0 5.0 6.0 LOG TRAVEL TIME (DAYS) r 10 1o2 103 104 105 1o6 TRAVEL T I ME ( DAYS ) FIGURE 8.6 Histogram of travel times in days of solute from the south end of Love Canal to the upper Niagara River through the Lockport Dolomite. Values are computed by Monte Carlo simulation for known porosity, uncertain hydraulic conductivity, and kit = 0.
Groundwater Flow Modeling Study 117 TABLE 8.3 Value of Log Mean and Log Standard Deviation of Travel Times in Days of Solute from the South End of Love Canal to the Upper Niagara River through the Lockport Dolomite for Several Values of Distribution Coefficients and Varying Uncertainty Assumptions about Hydrologic Parametersa Distribution Coefficient k,/ (mL/g) 0.0 Monte Carlo Case 1 Direct Analysis Case 2 Case 1 Case 2 0.0 0.1 .0 0.0 mean sigma mean sigma mean sigma mean sigma mean sigma 3.00 0.503 3.35 0.501 4.13 0.502 5.10 0.503 6.11 0.504 3.00 0.721 3.42 0.545 4.16 0.497 5.10 0.502 6.08 0.506 3.00 0.5 4.10 0.5 5.10 0.5 6.10 0.5 3.00 0.707 4.10 0.5 5.10 0.5 6.10 0.5 "Values determined by both Monte Carlo and direct analysis, as shown. cietermined from Ralston and Wilf (1967) as Sn + ~ = ~2 In R i'n)~'2 cos 21rR*n + i. (8. 13) Eqs. (8.9) and (8.13) provide a corresponding pair of random normal deviates with zero mean and unit variance for R*n and R*n+l Monte Carlo simulations for case 2 are not shown. The most probable travel time again is 3.00 log days, but the standard deviation now is 0.707 log unit. For this case, the probability is less than 0.05 that the travel time of a tracer will be greater than 25,942 days or less than 38 days. This broad spread in travel times in case 2 (~ = 10° 707) is a result of our assumption that porosity and hydraulic conductivity are completely un- correlated. There is unquestionably some correlation between porosity and conductivity. However, the amount of correlation is unknown; therefore, there exists uncertainty as to whether the standard deviation of the appropriate travel time is closer to 10°'5 or 10°7°7. We assume that the travel-time standard deviation is adequately represented by that resulting from un- certainty in the conductivity alone, i.e., 10° 5, since it is prob- able that porosity is highly correlated with hydraulic conduc- tivity. The preceding discussion and the results displayed in Figure 8.6 were restricted to solutes that are not retarded, i.e., to tracers. Such solutes have kit values of zero, so that the par- enthetic expression within Eq. (8.6) equals 1. Many solutes are likely to be retarded, having nonzero kit values. To account for retardation, additional sets of Monte Carlo simulations were made using Eq. (8.6) and k`' values of 0.01, 0.1, 1.0, and 10.0. Two runs were made for each kit value, corresponding to the conductivity and porosity choices of the two cases described above. The results of this sensitivity analy- sis are given in the form of tabulated log means and standard deviations of travel time in Table 8.3. The mean values of Table 8.3 show how retardation increases travel times for larger values of kit is the same and approximately equal to 10°5. This follows from direct analysis of the two extreme situations in which ~ >> kit and ~ << A,. For either extreme, Eq. (8.6) is linear in terms of logarithms. Because it is assumed that K and <h are both log normally distributed, the expected value and variance of log t can be calculated directly. Estimates of mean log and log standard deviation of travel time based on direct analysis are also shown in Table 8.3. Confining Bed The travel times from the bottom of the canal through the confining bed to the Lockport Dolomite are also of interest. In the calibration of the dolomite model, the leakage rate for a typical block representing the canal was approximately 1.1 X 10- i2 m/sec. This value can be used as a basis for estimating travel times through the confining bed by using the formula I'm' q~ t = - (8. 14) where b' is the thickness of the confining bed below the canal, +' is the confining-bed porosity, and q is the leakage rate given above. If it is assumed that the confining bed was not breached during excavation of the canal, there are two extreme possi- bilities for flow through the confining bed. In the first case, a thickness of 3.0 m for the confining material is assumed. This is less than the 7.6 m used in the dolomite model; however, because we are concerned with the area directly under the canal, it is anticipated that the thickness of the confining bed has been reduced somewhat by excavation. In addition, the confining bed is assumed to have an effective porosity of 0.1. Since we do not know what the effective porosity actually is, the effect of this parameter on the travel time will be dem- onstrated in the next case. Using these values and the above travel time from mean values of 103 °° (1000 days) for a tracer formula, the travel time for a tracer to reach the dolomite would to lOfi it (1,288,250 days) for a solute with kit = 10. Of particular be about 9000 yr. interest, though, is that the standard deviation associated with Although travel times on the order of thousands of years are
118 highly likely, a possibility that should not be overlooked is that fissured zones exist in the confining bed. Therefore, in the second case, we assume that the flow through the confining layer is mainly through fractures. This is a clear possibility because fissured clay in the upper shallow sediments in the Love Canal area were described by Owens (1979) and have been reported in other areas with similar geology (Freeze and Cherry, 1979~. If fissured, the clay would behave more like a fractured media, and an effective porosity of 0.0001 would be appropriate. Using this value and the 3.0-m thickness, the travel time for a tracer through the confining bed would be about 9 yr. Note that absorption would increase this value. Of these two extreme cases, the one leading to a longer travel time is more likely. This is because the sediments comprising the confining bed are generally observed to be very moist. The moisture is expected to cause the clay to swell, hence causing the fractures to heal or close. This is supported by Owens (1979), who observed that in the Love Canal area the fissured clays grade to soft moist clays at about 2.7- to 3.4-m depth. In addition, Freeze and Cherry (1979) point out that fracture zones in till and glacio-lacustrine clay tend to be less permeable with depth and that highly fractured zones usually occur only within several meters of the ground surface. The implication of an expected long travel time through the confining bed is significant. If contamination is found in the Lockport Dolomite, based on the above discussion, four pos- sible explanations, in order of plausibility, are the following: 1. The confining bed was breached during original construc- tion or during modification for disposal; 2. Contamination was caused by leakage from an upper zone because of a poorly sealed well; 3. The confining bed is significantly fractured; or 4. Solvents or some other free-phase organic may have sig- nificantly degraded the integrity of the confining bed. CONCLUSIONS In many modeling studies, a significant product is the increase in understanding of the hydrologic system. By setting up the model and conducting sensitivity analyses, the investigator gains insight into the behavior of the system and is enabled to make improved predictions of the system's response. This has oc- curred with the Love Canal study. As with any modeling study, the worth of the results is dependent on the input. Although there have been numerous studies conducted at Love Canal, the collection of hydrologic data at the canal has been accumulated over only a brief historic interval; therefore, many conclusions must be presented with a note of caution. Reliance on these predictions must be in accordance with the limiting assumptions used in the models. This is not to say that the results and predictions are mean- ingless. In addition to providing the only means in gaining any understanding of the hydrologic system, the results of modeling can be used to indicate additional data required to improve predictions or strengthen conclusions. The major conclusions from the Lockport modeling are a JAMES W. MERGER, CHARLES R. FAUST, and LYLE R. SILKA mixture of strong supportable conclusions and predictions that require additional data input to gain confidence. Of importance to the Love Canal problem is the potential for contamination of the Lockport Dolomite. This hinges on whether the confining clay beds have been breached under the canal. The vertical Darcian flow velocity through the confining bed is low, with rates on the order of 2.5 x 1O-5 m/yr. The direction of flow depends on the local gradient between the shallow system and the dolomite. It could be in either direction, and as the heads fluctuate seasonally, the gradient may reverse. Assuming a downward gradient through the confining bed, and that the confining bed was not breached and does not contain fracture zones, it would take a nonadsorbing solute on the order of hundreds to thousands of years to reach the dolomite. If ad- sorption occurs, travel times will be even longer. If contami- nants traceable to the chemicals disposed in the canal are found in the dolomite, the most likely explanation is that the confining layer was breached, given the long travel times calculated for the confining bed. If the confining beds were breached, down- ward flow could produce a groundwater high in the dolomite. Since the hydraulic heads in the two systems are nearly equal, however, it is not possible, based on hydrologic evidence alone, to determine whether the confining bed was breached. Thus, additional data would help to resolve this issue. Namely, chem- ical analyses of Lockport Dolomite groundwater should be ob- tained to determine if contaminants are present, and longer- term historical data on the head distributions in the shallow and Lockport systems are needed to better identify mounds and gradients between the two systems. If contaminants were to enter the Lockport Dolomite at the south end of Love Canal, and if there were no adsorption, the mean travel time to the upper Niagara River for the solute would be 1000 days. This is dependent on assumptions con- cerning the flow properties. Nevertheless, the gradient in the dolomite toward the river may be reversed by placing inter- ceptor wells near the south end of Love Canal. This can be accomplished with a total pumpage as low as 32.3 m3/day. ACKNOWLEDGMENT The work on which this Love Canal study is based was per- formed under Subcontract No. 1-619-026-222-003D to GCA/ Technology Division pursuant to U.S. Environmental Protec- tion Agency Contract No. 68-02-3168, Technical Service Area 3, Work Assignment No. 26. REFERENCES Apps, J. A., J. Lucas, A. K. Mathur, and L. Tsao (1977). Theoretical and Experimental Evaluation of Waste Transport in Selected Rocks: 1977 Annual Report of LBL Contract No. 45901 AK, Report LBL- 6022, Lawrence Berkeley Laboratory, Berkeley, Calif., 139 pp. Clark, S. P., Jr. (1966). Handbook of Physical Constants, revised edi- tion, Geol. Soc. Am. Mem. 97, 587 pp. Conestoga-Rovers & Associates (1978). Project Statement Love Canal Remedial Action Project, City of Niagara Falls.
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