SCHOOL OF DOCTORAL STUDIES IN ENVIRONMENTAL ENGINEERING

XX CYCLE

Research proposal

Doctoral student / Marta Castagna
Supervisor / Alberto Bellin
Main curriculum / Environmental engineering
Main research area / Subsurface hydrology

Project description

  1. Title

New fields tests for the estimation of hydraulic parameters of heterogeneous formations

  1. Status quo, context and motivations

Natural porous formations are heterogeneous and their hydraulic parameters vary widely in space. Hydraulic properties are traditionally obtained by comparing available analytical solutions for homogeneous formations with the measured drawdowns. But many problems of interest in applications, like certain pumping tests, flow around structures, transport processes, are of three dimensional nature and need a deeper knowledge of the 3-D heterogeneity of the media. In the seventies a great deal of interest roused around the stochastic approach, applied to groundwater flow problems, because it was found that the heterogeneity of the hydraulic properties can be represented by means of correlated random functions. Subsequently a great number of scientific articles were published for deriving the statistical moments of these quantities. Two main methods have been considered for calculating the statistical moments [Dagan, 1989]: the perturbation method, which provides simplified analytical solutions limited to weakly heterogeneous formations and regular domains, and the numerical techniques (Monte Carlo simulations) which allows for removing the most restrictive conditions adopted in the small perturbation method. Bayesian procedures are developed to take into account the available test information; Carle and Fogg [1999] developed also a method for including “soft” information such as the geological knowledge of the field into the geostatistical approach. However, these methodologies were applied mostly to natural head gradient cases with a steady state, or slowly varying, flow, while most of the techniques for aquifer’s characterization take advantage of forced flow configurations under unsteady state conditions.

Another technique that may be used to characterize the geostatistical models of variability is the tracer test. A controlled amount of a tracer is released and the concentration is measured a several monitoring wells. These data have been recently used in order to infer the geostatistical model of spatial variability (see e.g. A. Bellin and Y. Rubin [2004]). However, the inference of the geostatistical model often requires a large number of measurements at a prohibitive cost.

In these last years there has been a great development of the geophysical methods, like radar, seismic or electrical techniques. Once adequately interpreted they provide the spatial distribution of a geophysical parameter which is related to the spatial distribution of a related hydraulic parameter, for example the hydraulic conductivity. The main problem with these techniques is that the inferred parameter is not univocally related to the hydraulic parameter of interests such that the inversion is plagued by uncertainty and lack of unicity [Dietrich et al. 1998].

A new field method for the estimation of hydraulic property variations is the hydraulic tomography. This method essentially consists of a series of pulses of water discharge or pressure emitted from a well followed by monitoring of the hydraulic head in one or more monitoring wells. The procedure is similar to seismic tomography and for this reason it has been termed hydraulic [Peterson et al. 1985]. Following the approach used for interpreting seismic ray tomography, Vasco et al. [2000] derived a line integral relating the arrival time of a pressure signal to the reciprocal value of diffusivity (the ratio between S and K). Yie and Liu [2000] thought to use the hydraulic tomography as a way to obtain a large number of data set to apply to an iterative geostatistical inverse method. In any case these methodologies are affected by uncertainties and provide good solutions only under particular conditions.

  1. Objectives

During my doctoral programme I will try to develop new field methodologies in order to infer the hydraulic properties of an heterogeneous porous media. The analysis of the bibliography on this topic, highlights like the traditional field tests aren’t able to fully characterize the heterogeneity of an aquifer; for this reason it is worthwhile to discover new methodologies, searching new, low cost and easy field tests, importing tools usually used in other research fields and measuring new quantities connected to the hydraulic properties.

An important part of my research will also focus on new interpretation methodologies for traditional pumping tests, which are still widely used in field. This means a valuation of a combination of different field tests and their reliability.

  1. Development, timing and methodologies of the research

The activity will be organized according to the following work plane:

- Literature review, which I have just started studying this year (always)

- Analysis and modelling of the available field data sets, in order to improve the traditional way of interpreting pumping tests. This year I have analysed a data set of pumping test drawdown of an aquifer which shows some peculiarities which are not captured by the traditional methodologies of analysis. For this site a great number of stratigraphies and tracer tests are available. So it has been possible to employ a numerical model, taking into account the secondary information, to simulate the pumping test; only considering a 3D flow and the particular features of that site, a quite good approximation of the measured data has been achieved. This analysis has highlighted, also, some fenomena which can affect a pumping test, like the barometric effect. (up to now and for the next 6 months)

- Valuating the sensitivities of the methods of analysis in synthetic heterogeneous sites, through modelling. (II year)

- Monitoring of the tracer tests and improving the aquifer characterization through the use of geophysical surveys, in collaboration with the Department of Information technologies. (II year)

- Modelling water flows and tracer transport in synthetic sites to detect the critical factors. (III year)

- Modelling hydraulic tomography and other new techniques. (III year)

Bibliography

Books

  • Gedeon Dagan. Flow and Transport in Porous Formations. Speringer-Verlag, 1989.

Articles

  • Weissmann, G. S. ; Carle, S. F. ; Fogg, G. E. 1999. Three-dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics. Water Resour. Res. Vol. 35 , No. 6 , p. 1761.
  • A. Bellin and Y. Rubin. On the use of peak concentration arrival times for the inference of hydrogeological parameters. Water Resour. Res. Vol. 40 , 2004.
  • Dietrich, P., T. Fechner, J. Whittaker and G. Teutsch. An integrated hydrogeophysical approach to subsurface characterization. Groundwater quality: Remediation and protection, IAHS Publ., 250, 513-520, 1998.
  • Peterson , J.E., B.N.P. Paulsson, and T. V. McEvilly. Application of algebraic reconstraction techniques to crosshole seismic data. Geophysics, 50(10), 1566-1580, 1985.
  • D.W. Vasco, Henk Keers, and Kenzi Karasaki. Estimation of reservoirs properties using transient pressure data: An asymptotic approach. Water Resour. Res. Vol. 36 , No. 12 , p. 3447-3465, 2000.
  • T.C.Jim Yeh, Shuyun Liu. Hydraulic tomography: Development of a new aquifer test. Water Resour. Res. 36 (8): 2095-2105 Aug 2000.

Date,October 11th, 2005 / Signature Marta Castagna