Manitoba's Mineral Resources
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Heterogeneous Transmissivity Fields for the Upper Carbonate and Winnipeg Formation Aquifers in the Winnipeg Region
by Dr. Allan Woodbury, P.Eng.
Introduction In southern Manitoba, there are two regional-scale bedrock aquifers that have been developed as a water resource. The “Carbonate Aquifer”, is a paleocarst aquifer that occurs in the upper 15 to 30 m of outcropping Devonian and Ordovician age carbonate rocks (Render, 1970). The rocks are highly fractured in this region resulting in a more permeable region. This aquifer is a primary source of groundwater in southeastern Manitoba and provides water for industrial, rural domestic, irrigation and agricultural purposes (Betcher et al., 1995). A second, less developed aquifer, is the “Sandstone Aquifer” located within the Ordovician aged Winnipeg Formation (McCabe, 1978). This formation consists of interbedded shales and sandstones with a persistent shale layer at the top of the unit. This shale layer provides a hydraulic boundary separating the Carbonate and Sandstone Aquifers. The Sandstone Aquifer is used primarily for rural domestic purposes (Betcher et al., 1995). |
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Transmissivity measurements were collected from several sources for both aquifers. A total of 2708 and 78 transmissivity values were collected for the Carbonate and Sandstone Aquifers, respectively. The measurements were of variable accuracy and quality, and were grouped into four categories based on the method in which the value of transmissivity was determined. The first was a pump test with at least one observation well other than the pumping well and this was deemed the most accurate of all methods and referred to as the “multiple-well drawdown test”. The second test type were “single-well drawdown tests”, in which the water levels are monitored within the same well that is being pumped. The third type, referred to as “specific capacity”, is transmissivity estimated from specific capacity, which will underestimate the value of the transmissivity (Domenico and Schwartz, 1990). This underdetermined value is a result of the analysis assuming a 100% efficient well. The last category was the transmissivity collected from sources where the test type was literally “unknown”.
As transmissivity was measured by various field tests, the result is a database of values determined at different scales. A large quantity of the measurements were estimated from specific capacity (2264 for the Carbonate Aquifer and 48 for the Sandstone Aquifer) or by single-well drawdown tests (68 for the Carbonate Aquifer), which can be considered point scale. This comprises 86% and 62% of the transmissivity database for the Carbonate and Sandstone Aquifers, respectively. The remaining measurements can be assumed point scale in comparison to the interpolation scale, which is 5,000 m. None of the pump tests were collected over such a large distance and are most likely less than 50 m in all cases. Therefore, the transmissivity measurements were all assumed to be point scale.
Discussion
These maps present the generation of heterogeneous transmissivity fields for the Carbonate and Sandstone Aquifers in southern Manitoba using Geostatistics and the Bayesian Updating method. Note that these maps are basically the “best estimate” of the transmissivity field in a mean-square sense. Substantial variability is possible within short distances. Please consult Kennedy and Woodbury (2002) and the brief descriptions below for more details.
Two different parameter estimation techniques in allocating heterogeneous properties have been found within the literature. One approach is to use that of zonation, where the study area is divided into a finite number of zones. The hydrogeological properties within each zone are maintained constant, i.e. homogeneous within each zone. The second approach is to consider the field of the hydrogeological property as random and assign a value to each finite element within the model, from the underlying field. This generally results in an underdetermined problem with a larger number of unknown values, due to the limited quantity of data available in form of measurements. This underdetermined problem can be solved by using a statistical method, in which the heterogeneous field is obtained from the uncertain data measurements and the probability distribution function (pdf) underlying the data. Kriging is one such interpolation method that is well known and uses the best linear unbiased estimation (BLUE) method of evaluating such a problem (Kitanidis, 1997). The problem is set up such that an interpolated point is a linear combination of the measurements, using a number of weights, λ, which must be determined. The solution is carried out by minimizing the objective function (mean square error), subject to a constraint equation that the λ sum to 1. This results in a constrained optimization problem that can be solved using Lagrange multipliers. A second interpolation method is that of Bayesian Updating (Bryson and Ho, 1969; Woodbury, 1989; and Woodbury and Ulrych, 2000). This method allows for uncertain data (measurements), “hard” information in the form of upper and lower bounds and “soft” geologic information.
Statistics
The statistics of the transmissivity database for both the Carbonate and Sandstone Aquifers found that the transmissivity followed a log normal distribution, agreeing with the literature (Hoeksema and Kitanidis, 1985; Domenico and Schwartz, 1990). For the correlation structure, the Moving Window semi-variance estimator of Li and Lake (1994) was found to give much better results of the Classical Estimator of Matheron (1962). This resulted in an extremely good variogram for the Carbonate Aquifer, which could easily be modeled. The widely used exponential model for log transmissivity variograms did not fit the data well as shown in the literature (Hoeksema and Kitanidis, 1985). A nested variogram with nugget, a spherical model and an exponential model was found to fit the variogram extremely well.
Due to a significantly smaller database of measured transmissivity in the Sandstone Aquifer, the variogram was not as high-quality as that for the Carbonate Aquifer. An exponential model was assumed to model the variogram. The best fit model had an integral scale of 16,828 m, a sill of 2.9 and nugget equal to 0.56. The integral scale and nugget value were within the range reported by Hoeksema and Kitanidis (1985), however the sill determined in this research was greater than the range of reported sills.
The variograms of the Carbonate Aquifer and Sandstone Aquifer did not exhibit fractal nature, as the semi-variance increased and leveled off at a sill. If fractal nature was observed, the pattern of semi-variance would be repeated at different scales and the semi-variance would grow indefinitely. This absence of fractal nature agrees with the results presented by Hoeksema and Kitanidis (1985).
- Transmissivity Map
- Carbonate Aquifer Transmissivity (MS Excel file, temporarily unavailable)
- Sandstone Aquifer Transmissivity (MS Excel file)
References
Betcher, R.N., G. Grove, and C. Pupp, Groundwater in Manitoba: Hydrogeology, Quality Concerns, Management, 47 pp., NHRI Contribution No. CS-93017, March 1995.
Bryson, A.E. and Y. Ho, Applied Optimal Control, Hemisphere Publishing, 1969.
D’Agnese, F.A., C.C. Faunt, M.C. Hill, and A.K. Turner, Death valley regional ground-water flow model calibration using optimal parameter estimation methods and geoscientific information systems, Advances in Water Resources, 22(8), 777-790, 1999.
Domenico, P.A. and F.W. Schwartz, Physical and Chemical Hydrogeology, 506pp., John Wiley & Sons, Inc., New York, 1990.
Hoeksema, R.J. and P.K. Kitanidis, Analysis of the Spatial Structure of Properties of Selected Aquifers, Water Resour. Res., 21(4), 563-572, 1985.
Kennedy, P.L. and A. D. Woodbury, Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada, Ground Water, 40(3), 273-283, 2002.
Kitanidis, P.K., Introduction to Geostatistics: Applications in Hydrogeology, Cambridge University Press, 249 pp, 1997.
Li, D and L.W. Lake, A moving window semivariance estimator, Water Resour. Res., 20(5), 1479-1489, 1994.
Matheron, G., Traite de geostatistique appliqueé, vol. I, Mem. BRGM, 14, 1962.
McCabe, H.R., Reservoir Potential of the Deadwood and Winnipeg Formations Southwestern Manitoba, 54 pp., Manitoba, Department of Mines, Resources and Environmental Management Mineral Resources Division. Geological Paper 78-3, 1978.
Render, F.W, Geohydrology of the Metropolitan Winnipeg Area as Related to Groundwater Supply and Construction, Canadian Geotechnical Journal, 7, 243-274, 1970.
Woodbury, A.D., Bayesian Updating Revisited, Mathematical Geology, 21(3), 285-308, 1989.
Woodbury, A.D. and T.J. Ulrych, A Full-Bayesian Approach to the Groundwater Inverse Problem for Steady State Flow, Water Resour. Res., 36(8): 2081-2093, 2000.
