Using PEST for Drainage Optimization

 

Dragan Vidović1, Milan Dotlić1, Boris Pokorni1, Milenko Pušić2, and Milan Dimkić1

 

 

1 Jaroslav Černi Institute for the Development of Water Resources, Jaroslava Černog 80, 11226, Belgrade, Serbia, E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

2 University of Belgrade, Faculty of Mining and Geology, 11000 Belgrade, Serbia, E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

 

 

Abstract

A problem which often arises in drainage is to find the minimal total pump flow rate while satisfying the constraints placed on the hydraulic head and on pump flow rates. The freely available model-independent parameter optimization program, PEST, is probably the most popular optimization tool among groundwater modelers, but it solves minimization problems of a different form. In this paper we propose a conversion of this drainage optimization problem into a form that PEST can solve.

Keywords: PEST, drainage, dewatering, nonlinear optimization, FEFLOW

 

Introduction

 

Ground drainage using multiple pumps is often performed in engineering practice. Examples include mine dewatering and depressurization, drainage of construction sites, and remediation of contaminated aquifers. Such tasks may be subject to a number of constraints. The purpose of drainage is to reduce the hydraulic head at certain points below a set limit. On the other hand, a lower hydraulic head limit is required at pump locations to make pumping possible. It may also be necessary to keep the hydraulic head above a certain level in order to minimize the impact on the environment. Additionally, pumps have limited capacities. Finally, one would like to avoid unnecessary costs by minimizing the total pump flow rate.

A number of solutions to this problem have been reported in the literature. Linear programming techniques are proposed by Gorelick et al. (1984), Molz and Bell (1977), Willis (1979). The dependence of the hydraulic head on pump flow rates is generally non-linear, but as shown by Karterakisa et al. (2007) it is possible to use the classical linear simplex method by Dantzig (1963) with local linearization iteratively. Non-linear optimization techniques have also been proposed by Bear and Sun (1998), Gorelick et al. (1984). Finally, to combat the numerical difficulties arising from the complexity of a groundwater model, heuristic methods have been applied in Karterakisa et al. (2007), Mohan et al. (2007).

Probably the most popular optimization tool among groundwater modelers is the freely available model-independent parameter optimization program PEST (Doherty (2004)). This program is usually used for automatic model calibration, although its capabilities reach much further. It relies on a non-linear optimization technique described in Doherty (2004) and in papers referenced there. By varying specified parameters in the model input file, running the model, and analyzing the output file, PEST finds an approximate minimum of the Euclidean distance between a selected set of model output data and the prescribed (usually measured) values, while satisfying a set of linear constraints to the input parameters.

Drainage optimization is a problem of a different form: the objective function is the sum of model input parameters (pump rates) and linear constraints are imposed on the resulting hydraulic heads, while PEST minimizes a function of the model output and linear constraints are imposed on the input data.

In this paper we present a conversion of the drainage optimization problem into a form that PEST can solve.

The paper is organized as follows: the proposed conversion is presented in the following section. A minimization example is provided. Finally, conclusions are drawn.