Using PEST for Drainage Optimization - page 01

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Fig01
Figure 1: An example of the correlation between the hydraulic head (h) and the pumping flow rate (Q) (after Ahlfeld and Mulligan (2000)).

 

Example

The proposed technique has been verified on a simple stationary unsaturated test model constructedusing FEFLOW software (Diersch (2006)). The model represents a hole in the ground and consists of 700 nodes in three FEM layers (see Fig. 2). Hydraulic conductivity K was set at 10-4m=s, storativity was set at 0:2, and the compressibility was set at 10-41=m. These material parameters were assumed to be uniform. Eight pumping wells were scattered randomly above the lowest layer, and nine observation points were scattered randomly on the surface within and around the hole. The dimensions of the model were 100 × 100 × 30 m3. Dirichlet boundary conditions were specified at the side boundaries. Pump flow rates could take values between zero and 2000 cubic meters per day.

The hydraulic head had to be at least 10 cm below the surface at each observation point. Weight w was one million. With smaller weights the convergence was slower, and the constraints to the hydraulic head were less well satisfied. The initial pumping rates were 1000 cubic meters per day, and the initial targeted hydraulic heads were set at 10 cm below the surface.

PEST practically converged after five iterations. The maximal relative input parameter change decreased to 1.8 · 10-6, the objective function declined from the initial 7.65 · 1014 to 9.98 · 107, and the minimal total pump flow rate was 8473.4m3/d. In the subsequent four iterations the maximal relative change was reduced to 4.8 · 10-8 and did not decline any further.

 

Fig02
Figure 2: Simple test model.