GEOSTATISTICAL ASSESSMENT OF NUMERICALLY SIMULATED GROUNDWATER FLOW IN THE UPPER CHICOT AQUIFER NEAR PORT ARTHUR, TEXAS

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1 ModelCARE 90: Calibration and Reliability in Groundwater Modelling (Proceedings of the conference held in The Hague, September 1990). IAHS Publ. no. 195, GEOSTATISTICAL ASSESSMENT OF NUMERICALLY SIMULATED GROUNDWATER FLOW IN THE UPPER CHICOT AQUIFER NEAR PORT ARTHUR, TEXAS A. HAUG, R.H. PETRINI G.E. GRISAK INTERA Inc., 6850 Austin Center Boulevard, Austin, Texas 78731, USA K. KLAHSEN Chemical Waste Management, Inc., P.O. Box 2563, Port Arthur, Texas 77640, USA ABSTRACT A geostatistical analysis was performed to assess direction, magnitude and uncertainty of groundwater flow at a landfill facility near Port Arthur, Texas. The basis of the study was monthly water level data from the uppermost transmissive zone underlying the site. The monthly water levels were obtained over a period of more than five years from about 100 monitoring wells. Generalized kriging and jackknife tests were used to estimate the data uncertainty. Multiple sampling with replacement from the water-level data combined with the data uncertainty resulted in average groundwater velocity vectors for future time periods and in the corresponding confidence intervals. The results were compared to the result of a three-dimensional flow model of the site. In addition, the results were used to designate upgradient and downgradient monitoring wells for regulatory purposes. INTRODUCTION The primary objective of the geostatistical study presented in this paper was to assess direction, magnitude, and uncertainty of groundwater flow at the Chemical Waste Management Inc. Port Arthur (CWMI- PA) facility. The 175 hectare study area is located about 23 km north of the Gulf of Mexico coastline and about 13 km west of Port Arthur, Texas, on the Gulf Coastal Plain (Fig. 1). Geologically, the CWMI-PA facility is located in the Houston Embayment, a structural subdivision of the Gulf Coast Basin. This basin has been developing and receiving sediment from the North American landmass since Triassic time. The total sediment thickness probably exceeds 15 km. The upper 300 to 400 m of these sediments are usually referred to as the Chicot Aquifer (Wesselman & Aronow, 1971). At the CWMI-PA facility, the Chicot Aquifer consists, in general, of an upper sand and a lower sand, which are hydraulically separated by a continuous clay unit, the Basal Clay. The upper sand, also referred to as the Upper Chicot Aquifer, comprises about 55 m of finegrained, lithostratigraphically very complex, fluvial or deltaic sediments. During previous local studies, the Upper Chicot Aquifer has been subdivided into seven hydrostratigraphic units (Fig. 2). 427

2 A.Haug et al. CHEMICAL WASTE MANAGEMENT, INC. LANDFILL SITE (PORT ARTHUR, TEXAS) 01 SITE 02 SITE GROUNDWATER MONITORING WELL FIG. 1 CWMI-PA facility and well locations. 0 10O METERS DEPTH THICKNESS (m) SCHEMATIC GEOLOGIC LOG HYDROSTRATIGRAPHY AT PORT ARTHUR LANDFILL SITE SURFICIAL CLAY 6.1 UPPER TRANSMISSIVE ZONE ~5C m fhftj»^»g»»«i ' ^^^ "- -!." INTERVENING UNIT SAND S1a SAND S1b MIDDLE CLAY UPPER CHICOT AQUIFER 10.7 SAND S2 > 5.0 ^ M BASAL CLAY FIG. 2 Generalized hydrostratigraphy of the CWMI-PA facility. From a regulatory point of view, the upper transmissive zone (UTZ), which is the uppermost permeable stratigraphie unit at the site, has been defined as the appropriate hydrostratigraphic unit for detection and compliance monitoring. However, water levels measured on a monthly basis in about 100 monitoring wells in the UTZ indicate that there

3 Geostatistical assessment of simulated groundwater flow 429 o Monitoring Well Contour Interval: 0.1 m o Monitoring Well Contour Interval: 0.1 m FIG. 3 Piezometric Surface in the Upper Transmissive Zone (a) During May 1988 and (b) During August monitoring wells in the UTZ indicate that there is significant temporal variation in both the magnitude and the direction of groundwater flow in the UTZ. This variation is illustrated by the two water level maps in Figs 3.a and 3.b. A detailed analysis of the water level data led to the conclusion that the longterm mean water levels are superimposed by sitewide transients (recorded in all wells), by small scale transients (measured in several wells), by localized transients (identified in only one well, but during several monthly measurements) as well as by a random component. The first three types of variation are assumed to be hydraulically driven, whereas the fourth simply reflects the measurement error. These four transients result in a spatially and temporally very complex pattern for the groundwater flow in the UTZ. However, the hydraulic significance of the local-scale component cannot be assessed because its areal extent is unknown. Therefore, the local-scale component and the measurement errors are considered

4 430 A.Haug et al. in the following, the transients are considered to comprise three components: the sidewide transients, the small-scale transients and the data uncertainty. NUMERICAL SIMULATION OF GROUNDWATER PLOW In late 1988, a modelling study of groundwater flow and contaminant transport at the CWMI-PA facility was undertaken to develop a quantitative understanding of site hydrology. SWIFT II, a three-dimensional finite-difference flow and transport code (Reeves S Cranwell, 1981; Reeves et al., 1986a; Reeves et al., 1986b) was used to simulate the groundwater flow the CWMI-PA facility. The model area as well as the horizontal and vertical discretization are shown in Fig. 4. The horizontal model dimensions (2700 x 1200 m) were chosen to accommodate the dimensions of the entire CWMI- PA facility and also to allow for a buffer zone between the site and the model boundaries. The horizontal extent of the grid blocks is 100 x 100 m. In the vertical direction, the model comprises seven grid layers, one for each hydrostratigraphic unit of the Upper Chicot Aquifer (Fig. 2). The vertical extent of the grid blocks generally varies between 4.6 m (Intervening Unit) and 10.7 m (S2 Sand). The model thickness of the UTZ is constant over the entire site while the older hydrostratigraphic units become both slightly thicker and deeper west of the zero line (not shown in Fig. 4) in order to accommodate a general slope of of the Basal Clay. An average elevation of 1.2 m a.s.l. was assumed as base level for the ground FIG. 4 Model area and model discretization.

5 Geostatistical assessment of simulated groundwater flow 431 TABLE 1 Hydraulic conductivity values of model layers. Model Unit Hydraulic Conductivity K,, (m s" 1 ) K,, (m s" 1 ) Surficial Clay Upper Transmissive Zone Intervening Unit Sand Sla Sand Sib Middle Clay Sand S " " " " " " " " " " " " " " 5 surface. This elevation was locally adjusted in order to account for the site-specific topography. Hydraulic conductivity values (Table 1) consistent with field hydraulic testing results, laboratory permeability data, and with grain size analyses were selected for the different hydrostratigraphic units. A constant porosity of 0.3 was used for all model layers. The spatial and temporal variation of the water levels measured at the facility as well as the unknown magnitude of the data uncertainty make the definition of representative model boundary conditions very difficult. Consequently, no attempt was made to reproduce the transient behaviour of the hydrologie system. Also a detailed simulation of the spatial variation did not seem feasible. Therefore, the longterm mean water levels at the four model corners were estimated based on the monthly water level data. These values were used to linearly interpolate the water levels along the model boundaries. The interpolated water levels were then converted to pressures at the centers of the outer grid block boundaries assuming a zero vertical gradient. Finally, the pressures were implemented as prescribed pressure boundary conditions. The corresponding horizontal gradients between the assigned boundary conditions vary between and They are generally directed east to southeast. As such, they are in acceptable agreement with the regional estimate of (Wesselman & Aronow, 1971) and with gradients that can be estimated on the basis of monthly waterlevel contour maps (e.g., Fig. 3). Additional model features include a water-supply well located in the western half of the site and screened in the S2 Sand (production rate = s ), two groundwater recovery wells located in the eastern part of the site and screened in the UTZ (production rates = s ), and a storm water retention system located at the northeastern corner of the facility and implemented as prescribed pressure boundary to the corresponding grid blocks. The steady-state piezometric surface in the UTZ as calculated by the model described above is shown as a contour map in Fig. 5. The calculated gradients vary between and The corresponding flow velocities range from m s to m s. The effect of the water-supply well in the S2 Sand can be seen as a de-

6 A.Haug et al. o Monitoring Well Contour Interval: 0.05 m FIG. 5 Simulated steady-state piezometric surface in the upper transmissive zone. flection of the 0.65 m contour line in the western part of the site. The two groundwater recovery wells in the UTZ do not significantly influence the piezometric surface. The storm retention system causes a prominent low at the northeastern site boundary. In general, the simulated flow field in the UTZ appeared to be consistent with the long term averages of the measured water levels and with the regional flow field. Differences between the calculated and the measured data were interpreted to be either transient in nature or to be artifacts due to the data uncertainty. Thus, the simulated flow field was considered to be representative of the longterm average flow field in the UTZ at the CWMI-PA site. UNCERTAINTY OF THE WATER LEVEL MEASUREMENTS Several months after completion of the modelling study, it became necessary to designate some of the existing monitoring wells as hydraulically upgradient or downgradient in relation to the landfill facility. This designation was necessary within the context of designing a leak detection monitoring system. Therefore, the direction and the magnitude of groundwater flow in the UTZ was reevaluated in detail. As indicated above, some of the difficulties in determining the groundwater flow direction are related to the unknown magnitude of the data uncertainty. Therefore, a geostatistical analysis was performed to quantify the data uncertainty and to differentiate it from the other transient components which are assumed to be hydraulically significant. The evaluation of the data uncertainty comprised several steps. First, the constant component of the water-level data was removed from the water-level data base by subtracting the long-term wellspecific mean heads from the individual measurements. The resulting values are referred to in the following as reduced values. They represent the apparent and real water level fluctuations in the UTZ. These fluctuations are believed to be composed of the sitewide and

7 Geostatistical assessment of simulated groundwater flow 433 a Monitoring Well Contour Interval: 0.05 m FIG. 6 Well-specific data uncertainty. the small scale transients as well as the data uncertainty. The next step comprised the quantification of the site-wide and small-scale transients. Both transients are characterized by the fact that they can be identified in more than one well at a given point in time. Consequently, the spatial correlation between the reduced values can be used to quantify these transients. The spatial correlation between the reduced values was analyzed for each set of monthly water level data using generalized kriging techniques. The code employed for this analysis was a modified version of the generalized kriging code AKRIP (Kafritas & Bras, 1981). A generalized covariance function (GCF) for each of the monthly waterlevel data set resulted from this analysis. Systematic jackknife tests were then performed on all data sets. During these tests, the measured water level of one selected well was temporarily removed from the data set and the value was reestimated using the remaining data and the corresponding GCF. This procedure was repeated for all wells and all monthly data sets. The resulting rekriged water levels represent the component of the water level fluctuations that is supported by water level measurements in neighboring wells. Therefore, the rekriged water levels were interpreted as the site-wide and small-scale transient component of the transient water level fluctuations. The difference between the measured and the rekriged water levels represents the component of the transient fluctuations that is not supported by measurements in neighboring wells. This component represents the local-scale transient component and the measurement error of a given water level measurement. It is referred to as the residual. The standard deviation of all residuals at a given well can then be interpreted as the well-specific data uncertainty. The well-specific data uncertainty (one standard deviation), based on all measurements between 1983 and 1988, is shown as a contour map in Fig. 6. The values range from less than 1 to about 40 cm. Higher values are typically associated with increased distances between wells and/or a smaller number of measurements. The mean of all well-specific data uncertainties was calculated to be 5.6 cm.

8 434 A.Haug et al. ESTIMATION OF LONGTERM GROUNDWATER FLOW Having established the well-specific data uncertainty, the waterlevel data base can be used to predict the long-term average groundwater flow. For this prediction, the site was triangulated using selected monitoring wells as the corners of the triangles (Fig. 8). The longterm groundwater flow was then estimated for sash triangle using a simple bootstrapping technique (Efron, 1982). With each triangle, this approach comprised the following steps: First, a set of water-levels measured in the corner wells was randomly selected (sampling with replacement) from the historic water-level data base. Then, three random numbers were sampled (latin-hypercube sampling) from three normal distributions that represent the wellspecific data uncertainties at the corner wells. The random numbers were added to the selected historic data. The modified historic values were then used to calculate the corresponding gradient. Consistent with the one-month measurement frequency, such a gradient is considered to be one possible realization of the hydraulic situation during one month. Calculating the average of several gradients results in an average gradient that is one possible realization for the time period that corresponds to the number of individual gradients. This approach implicitly assumes that the historic water-level data are also representative of future groundwater flow. Consequently, the time period of the prediction should not substantially exceed the time period covered by the historic water-level record (i.e., five years). Therefore, during this study, 60 individual gradients were used to calculate an average gradient representative of five years. Such an average gradient can then be used to calculate the corresponding groundwater velocity vector. For this calculation, the mean hydraulic conductivity measured in the three corner wells and a porosity of 0.3 was used. The resulting velocity vector is one possible realization of the groundwater flow over a five year period. Repeating this procedure a large number of times (e.g., ) results in a large number of different flow vectors (Fig. 7). The - ^ ' " 0.0 \ Aj o a ~~" \ '\ o o -2.0 K * \f -V\ K.:. 1 \, ~ : "\ - -^ \ X :^<-,\ v 1 1 "- - / > / *r / / J 1 H \ / / -î n 1 1 \ 1 1 i 1 "o.o 1.0 V ~ _ VELOCITY X COMPONENT (m ysar" 1 )... Random Velocity Vectors Confidence Interval (0.95) y Mean Velocity Vector FIG. 7 Estimation of long-term groundwater flow (example triangle).

9 Geostatistical assessment of simulated groundwater flow 435 LINEAR VELOCITIES LIN. DISTANCES nm a"' m o Monitoring Wall FIG. 8 Predicted site-wide groundwater flow. mean of all these velocity vectors represents the best estimate of the average future groundwater flow at a given triangle. The distribution of the flow vectors can be used to calculate the confidence intervals (e.g., 95% level) of the direction and magnitude of the groundwater flow. These confidence intervals represent the uncertainty of the velocity vector due to the water level data uncertainty. Repeating the above procedure for all triangles results in best estimates of the future groundwater flow in all triangles and in the corresponding confidence limits (Fig. 8). Accordingly, no single major flow direction exists over the entire the CWMI-PA site. The groundwater flow appears to belong to several small scale flow regimes. This diversity can be caused by a number of different factors such as heterogeneities in the aquifer, localized recharge or other hydraulic disturbances outside the site boundary. Nevertheless, the wells located along the northern perimeter of the eastern part of the site appear to be consistently upgradient with respect to the landfill facility. ASSESSMENT OF THE SIMULATED FLOW FIELD The velocity vectors derived from the water-level evaluation (calculated velocities) can be compared to the flow velocities resulting from the modelling study (simulated velocities). Such a comparison (Fig. 9) reveals significant differences, primarily because the calculated flow field is substantially more complex. Taking into account the confidence limits of the calculated velocities, a comparison of the flow directions shows that they are consistent only in 10 of 35 triangles. As indicated in Fig.10, these triangles are located either on the northern or the southern site boundary in the eastern part of the site. Comparing the magnitudes of the flow velocity is more difficult because the hydraulic conductivities used during the water level evaluation were not identical to the ones used in the modelling studies.

10 436 A.Haug et al. GEOSTATISTICAL ANALYSIS: DASHED ARROWS GROUNDWATER MODEL SOLID ARROWS FIG. 9 Calculated and simulated groundwater velocities. AREA WITH CONSISTENT UN. DISTANCES FLOW DIRECTION 0 too m FIG. 10 Areas with consistent direction and magnitude of groundwater flow. Therefore, for the comparison shown in Fig. 9, the simulated velocities were adjusted for the hydraulic conductivities used during the water-level evaluation. A second difficulty is the fact that the uncertainties shown in Fig. 8 represent only the water-level uncertainty. Not considered are the uncertainty of the porosity and the hydraulic conductivity fields. Both parameters are usually assumed to be lognormally distributed. Based on the literature (e.g., Freeze & Cherry, 1979), the uncertainty (2 a) of the porosity was estimated to be a factor of ± 1.5. Based on the results of hydraulic fields tests, the uncertainty (2 a) of the hydraulic conductivity can be calculated to be a factor between ± 1.2 and ± 20.4, depending on the location. Assuming approximately lognormal distribution, those uncertainties

Geostatistical assessment of simulated groundwater flow 437 were superimposed on the head-related uncertainties using Gauss' error propagation.

11 Geostatistical assessment of simulated groundwater flow 437 were superimposed on the head-related uncertainties using Gauss' error propagation. The resulting total uncertainties were used to identify the areas where the calculated and the simulated flow magnitudes are consistent (Fig. 10). Accordingly, in 25 of 35 triangles the magnitude of flow can be considered to be consistent. The comparison of the calculated and the simulated flow field leads to the following conclusions: (i) the simulated flow field does not fully reflect the complexity of the real flow field; (ii) the simulated flow direction is representative only in some parts of the model area; (iii) the simulated flow velocities are generally too small; (iv) most of the simulated flow velocities have the right order of magnitude. Generally speaking, a substantially more complex numerical model which may have to feature complicated boundary conditions, localized recharge and heterogeneous aquifer parameters would be necessary to result in a substantially better representation of the hydrogeological system at the CWMI-PA landfill facility. REFERENCES Efron, B. (1982) The Jackknife, the Bootstrap and Other Resampling Plans. Society of Industrial and Applied Mathematics, Conference Board of the Mathematical Sciences, CBMS-NSF 38, Philadelphia, Pennsylvania. Freeze, R.A. & Cherry, J.A. (1979) Groundwater. Prentice Hall, Inc., Englewood Cliffs, New Jersey. Kafritas, J. & Bras, R. (1981) The Practice of Kriginq. M.I.T. Ralph Parson's Laboratory Report No. 263, Cambridge, MA. Reeves, M. & Cranwell, R.M. (1981) User's Manual for the Sandia Waste-Isolation Flow and Transport Model (SWIFT), Release Sandia National Laboratories, NUREG/CR-2324 and SAND Reeves, M., Ward, D.S., Johns, N.D. & Cranwell, R.M. (1986a) Theory and Implementation for SWIFT II, the Sandia Waste-Isolation Flow and Transport Model, Release Sandia National Laboratories, NUREG/CR-3328 and SAND Reeves, M., Ward, D.S., Johns, N.D. & Cranwell, R.M. (1986b) Data Input Guide for SWIFT II, the Sandia Waste-Isolation Flow and Transport Model for Fractured Media, Release Sandia National Laboratories, NUREG/CR-3162 and SAND Wesselman, J.B. Aronow, S. (1971) Groundwater Resources of Chamber and Jefferson Counties, Texas. Texas Water Development Board, Report 133.

Groundwater Flow Evaluation and Spatial Geochemical Analysis of the Queen City Aquifer, Texas

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