R: Trieste Scientific news Digest

[ICTP info point]

Ph.D. Program in Environmental Fluid Mechanics
SEMINAR SERIES 2007

Friday April 27 14.30-16.30 , Lecture Room C , terrace level MB, ICTP
Prof. Alberto Guadagnini
Dipartimento Ingegneria Idraulica, Ambientale, Infrastrutture Viarie, 
Rilevamento (DIIAR). Politecnico di Milano, Piazza Leonardo da Vinci, 
32, 20133 Milano - Italy
1) Moment Equations for Prediction of Conditional Mean Flow in Randomly 
Heterogeneous Aquifers
We consider the effect of measuring randomly varying hydraulic 
conductivities K(x) on one’s ability to predict numerically steady 
state saturated flow in bounded domains driven by random source and 
boundary terms. The aim is to allow optimum unbiased prediction of 
hydraulic heads, h(x), and fluxes, q(x), by means of their ensemble 
moments, h(x)c and q(x)c, conditioned on measurements of K(x). 
These predictors have been shown to satisfy exactly an 
integro-differential conditional mean flow equation in which the flux 
predictor, q(x)c, is nonlocal and non-Darcian. Here, we show how to 
develop complementary integro-differential equations for second 
conditional moments of head and flux which serve as measures of 
predictive uncertainty; to obtain recursive closure approximations for 
both the first and second conditional moment equations through 
expansion in powers of a small parameter Y which represents the 
standard estimation error of ln K(x).It is then shown how to solve 
these equations to first order in σY2 by finite elements on a 
rectangular grid in two dimensions. In the special case where one 
treats K(x) as if it was locally homogeneous, and mean flow as if it 
was locally uniform, one obtains a localized Darcian approximation, 
q(x)c  Kc(x)h(x)c in which Kc(x) is a space-dependent 
conditional hydraulic conductivity tensor. This leads to the 
traditional deterministic, Darcian steady state flow equation which, 
however, acquires a non-traditional meaning in that its parameters and 
state variables are data-dependent and therefore inherently nonunique. 
A detailed comparison between finite element solutions of nonlocal and 
localized moment equations, and Monte Carlo simulations, under 
superimposed mean-uniform and convergent flow regimes in two dimensions 
is presented. An extension of the methodology to model (non-reactive) 
transport processes in heterogeneous groundwater systems is then 
presented.

2. Prediction of uncertainty associated with well capture regions in 
heterogeneous groundwater systems

The assessment of the distribution of solutes time-of-residence within 
an aquifer subject to pumping is of particular interest as extraction 
wells are commonly used both for drinking water supply and as 
remediation systems for contaminated aquifers. The delineation of 
pumping wells protection zones is usually performed by calculating the 
entire well catchment extent and specific time-related capture zones. 
The latter are, in turn, based on the concept of solute residence time. 
Early models which have been developed to delineate well catchments and 
time-related capture zones are based on the assumption that the aquifer 
can be modeled as a two-dimensional infinite homogeneous and isotropic 
porous medium. Even in the simplest scenario where one assumes that 
advection is the dominating process, an accurate knowledge of the 
hydraulic and hydrogeological properties of the aquifer is generally 
needed, together with (initial and) boundary conditions. Since a 
complete knowledge of aquifer properties is never achieved, it has then 
become common treating spatially varying subsurface flow parameters as 
auto-correlated random fields. This, together with uncertainty in 
forcing terms, renders the groundwater flow equations stochastic. The 
solution of such equations consists of the joint, multivariate 
probability distribution of dependent variables or, equivalently, the 
corresponding ensemble moments. The methodologies which are most 
commonly adopted to analyze the stochastic nature of solute residence 
times within extraction well fields are based either on numerical 
(unconditional or conditional on a variety of information) Monte Carlo 
simulations or on the (analytical and/or numerical) solution of 
approximate equations satisfied by the moments of the time taken by 
solute particles injected in the aquifer to be captured by a well. Here 
we discuss both methodologies and illustrate applications on synthetic 
and real world scenarios.

Vincenzo Armenio, Ph.D
Associate Professor of Environmental Hydraulics
http://www.dica.units.it/perspage/armenio/IEfluids.html#fluids
chair of the Ph.D Program in Environmental Fluid Mechanics
http://poseidon.ogs.trieste.it/phd/fluid/
Dipartimento di Ingegneria Civile ed Ambientale, Università di Trieste,
Piazzale Europa 1,
34127 Trieste, Italy
tel +39-040-558 3472
fax +39-040-572082
mobile +39-347-5846202