Calibartion of a Groundwater Model Based on Pattern Search Method

Calibration of a Groundwater Model Based On a Pattern Search Method :

A Case Study

J.Z. Zou 1, S.T.S. Yuen 2, J. Schaeffer 1, J. Bradley 1 and J. Missen 3

1. Geo-Eng Group, Locked Bag 5, Morwell, Victoria 3840, AUSTRALIA

2. Departmental of Civil and Environmental Engineering, University of Melbourne, Parkville, Victoria 3052, AUSTRALIA

3. Loy Yang Power Ltd, PO Box 1799, Traralgon, Victoria 3844, AUSTRALIA

ABSTRACT : This paper presents a case study where a calibration program based on a Pattern Search Method was developed and applied to a quasi-3D 6-layer groundwater model for the simulation of an open-cut mine depressurisation system. The groundwater model was created for the Loy Yang Power Mine located in the Latrobe Valley, Australia, based on the Modular Three-Dimensional Finite Difference Groundwater Flow (MODFLOW) program. Modification was made to the MODFLOW program to take into consideration the time-dependent boundary conditions resulting from the regional groundwater level changes. A calibration program based on a Pattern Search Method was used to calibrate the model. The calibrated model was then run with different pumping options to identify the optimum depressurisation strategy.

KEYWORDS : MODFLOW, calibration, pattern search, time-dependent boundary conditions

1.INTRODUCTION

1.1Objective Of the Groundwater Modelling

The Loy Yang Power Mine is one of the three major brown coal open-cut mines located in the Latrobe Valley, Australia. The operation started in the early 1980’s. Over time, a large open pit has been created covering an area of approximately 480 hectares with a current depth of 100m. Water within the overburden layers, coal seams and interseams must be drained to ensure adequate stability of mining operations and to avoid flooding during the mining process. Pressure in deeper aquifers must be lowered to avoid floor heave and instability, and to maintain safe operating conditions as the mine develops in size and depth. Groundwater depressurisation is carried out using a network of 17 pumping wells located within and around the mine area.

The primary objective of establishing a groundwater model of the Loy Yang Power Mine area was to assist in the design and management of the aquifer depressurisation system. Prior to the development of the model, operational aquifer pressure levels were determined based on the weight balance and factor of safety approach which was inevitably conservative. A key part of the modelling work was to reduce the volume of groundwater needed to be extracted and hence the cost of pumping without compromising mine stability and safety.

The use of a numerical model helps to maximise the use of hydrologic data and enables the response of the aquifer system to different depressurisation scenarios to be readily simulated (Geo-Eng, 1996). A quasi-3D model using the Modular Three-Dimensional Finite Difference Groundwater Flow (MODFLOW) program (McDonald & Harbaugh, 1988) was established for the mine area to provide a detailed assessment of aquifer depressurisation. The model incorporates the major aquifer sequences encountered below the mine. It allows for the effects of pumping within different aquifers to be modelled, and the groundwater movement between layers to be assessed.

1.2Geology and Hydrogeology

In brief, the Loy Yang Power Mine is underlain by two major aquifer systems referred to as the Morwell Formation Aquifer System (MFAS) and Traralgon Formation Aquifer System (TFAS). The MFAS is shallower, and contains the M1A, M2A, M1B, M2B and M2C Aquifers. The shallower aquifers contain mostly clay in the mine area, and consequently only the M2B and M2C Aquifers are currently depressurised. The TFAS comprises a number of separate sand bodies, of which the Upper and Middle Aquifers are depressurised. There is no direct pumping from the Upper Aquifer and drawdown is the result of leakage through the intervening interseam sediments to the underlying Middle Aquifer from which direct pumping occurs.

2.MODEL DESCRIPTION

The model covers an rectangular area - 7000 m along the east-west direction and 5000 m along the north-south direction (Geo-Eng, 1997). The cell size is 100m X 100m which is compatible with the distribution of existing pump and observation bores. The grid orientation is north-south which matches the local north-south orientation of major faults and joint sets. The model area and model grid are shown in figure 1.

Figure 1 - Loy Yang Power Mine Groundwater Model Area and Grid

The model comprises 6 layers, with varying distances between layers to allow interaction between layers to be assessed by using the MODFLOW VCONT array which specifies the vertical leakance between layers. This is important for the simulation of groundwater movement between aquifers which are known to have a high degree of interconnection within the mine area.

The top and bottom elevations of each layer were imported from the project geological database and converted into a format readable by a MODFLOW pre-processor program. The six model layers, from top to bottom, represents in sequence the MFAS M2B Coal (1), M2B Aquifer (2), M2C Aquifer (3), the TFAS Upper (4), Middle (5) and Basal (6) Aquifers (Section 1.2 refers).

Historical water levels and pumping rates were obtained from the hydrogeological database. They were then averaged over a six monthly interval to be represented by a single stress period in the model calibration. A total of eight stress periods were used in the calibration which covered the time from December 1990 to December 1994.

Constant heads cells (Ibound = -1) were specified at the boundary of the MODFLOW model to provide the required recharge. The standard MODFLOW program does not allow any changes in the head of the constant head cells between stress periods. This constraint was unacceptable because water levels are declining beyond the boundary of the model due to the influence of other groundwater users. To account for the effect of declining water levels at the boundary of the model, a subroutine was added to the standard program to allow the constant head values at these constant head cells to change from one stress period to the next.

Head values for the changing boundary conditions were obtained by analysing regional groundwater observation data with a separate quasi-3D regional groundwater model that takes into consideration all other mines in the region.

To allow for any inaccuracies inherent in the above constant head values due to the relatively sparse data available for the regional model analysis, a "model couple zone" encompassing five cells from the model boundary was established. The calibration of the boundary was performed separately to allow for the relative uncertainty of the fixed head values used at the boundary (see also Section 3). If the boundary was not calibrated separately, uncertainties in boundary values would spill over to the more important central portion of the model.

Information obtained from the hydrogeological database was again used to define the hydrogeological model in terms of distribution of individual aquifers, their thickness, relative location beneath the mine and groundwater flow gradients. These data become sparse as the distance from the mine increases and this was taken into consideration when selecting the model boundaries.

For each layer, the hydraulic conductivity (K) and storativity (S) of the aquifer were required. These values were obtained from pumping tests conducted on bores within the mine area. Additional K values were obtained by applying Hazen’s method (1911) to grain size analyses obtained from bore samples.

3.Model CALIBration

The parameters calibrated in the Loy Yang Power Mine model were hydraulic conductivity, primary storage coefficient and vertical leakance.

The model was first used to calculate the drawdown in each observation bore in response to pumping. The predicted value was then compared with the observed value. If the two levels did not match within a specified tolerance, the program altered the hydraulic parameters until the modelled result improved and the changes were then accepted. The range of variability of hydraulic parameters was constrained so that the model could not provide values that were outside acceptable ranges. Calibration ended once the calculated water level matched the measured water level to within a specified tolerance in each observation bore.

The above calibration process can be performed manually using the standard MODFLOW package by changing the value of the hydraulic parameter to be calibrated and re-run the model for each trial. However, it could be tedious and time consuming as the number of variables increases. In the Loy Yang Power Mine study, a calibration subroutine was written to the standard MODFLOW program for a systematic calibration.

The calibration subroutine employs an optimisation technique based on the Pattern Search Method proposed by Hooke & Jeeves (1961). The method essentially involves local searches and moves for each variable (exploratory moves) to find the critical direction of movements, and a pattern move based on the optimum moves established from the previous local moves for individual variables. The process is repeated with pattern moves being successively applied if they give rise to a reduction in error, until no further error reduction is possible. In the calibration subroutine, slight modification was made so that multiplication factors were used for parameter adjustment rather than increments used in the original method, as factors are considered more appropriate for use in groundwater models.

The subroutine allows the calibration of hydraulic conductivity (transmissivity), vertical leakage (vertical hydraulic conductivity), aquifer geology (top/bottom), and storage coefficients. It uses numerous input/output files to record the changes in the properties, error at individual observation bore, mean error, and other information. The subroutine improves the efficiency of the calibration phase in both physical and computer time.

To facilitate the calibration, a map file was employed to delineate every cell in each layer the different zones (up to nine zones) of hydraulic values to be calibrated. A separate map file was used to calibrate the boundary of the model as discussed in Section 2.

4.calibration results

The calibration process indicates that alteration of hydraulic conductivity has the most significant impact on aquifer heads.

To measure the performance of the model, calibrated water levels were compared to observed water levels in all observation bores. Typical hydrographs showing observed and modelled aquifer heads for layer 2 to layer 6 are given in Figure 2. Across all layers of the model, the average error between the observed and modelled heads was 3.5 m. The errors were generally larger in the vicinity of pump bores due to the difficulty of modelling the steep drawdown near the bores. It is considered that the model error may be reduced by using shorter stress periods to allow for the rapid water level changes around pump bores.

5.CONCLUSIONS

The calibrated model is now being employed to test different depressurisation options to aid the siting and operation of pump bores in the strategic aquifers. It allows the drawdown from existing and proposed bores and their area of influence to be predicted. The most economical network of pump bores and the most efficient pumping operation can be established to maintain aquifer pressures at safe levels with substantial cost reduction. Future mine levels can be built into the model as required to allow assessment of new aquifer target levels.

Figure 2 - Examples of Observed and Modelled Aquifer Heads

REFERENCES

Geo-Eng (1996) Aquifer Depressurisation System Optimisation. Report No. 5407/4, Hazelwood Power Corporation Ltd. Hazelwood Mine.

Geo-Eng (1997) Review of Aquifer Depressurisation Strategy and Aquifer Target Levels. Report No. 1100/1205/14, Loy Yang Power, Loy Yang Mine.

Hazen, A. (1911). Discussion: Dams on Sand Foundations. Transactions, American Society of Civil Engineers, 73 (1911), 199.

Hooke, R., & Jeeves, T. A. (1961). "Direct Search" solution of numerical and statistical Problems. Journal of Association Computing Machinery, 8, 212-219.

McDonald, M. G., & Harbaugh, A. W. (1988). A modular three-dimensional finite-difference groundwater flow model (Technique of Water-Resources Investigation 06-A1). United States Geological Survey.

IAH International Groundwater Conference Melbourne February 1998