P1: OTA/XYZ P2: ABC
JWST061-12 JWST061-Caers March 29, 2011 12:43 Printer Name: Yet to Come
218 CH 12 EXAMPLE CASE STUDY
som
e
Earth
model geobodies
BA
BA
A
sand
geobody
a
clay
geobody
Figure 12.4 Definition of a geobody.
12.1.2 Contaminant Transport
In a detailed study a contaminant transport model would be run to predict for a given
Earth model whether or not the contaminant has reached the drinking well. In this study,
it will be assumed that the contaminant will travel to the drinking well if, and only if,
a geological connection exists between the point source and the drinking well. It will
be assumed that the clay is impermeable; hence, if the drinking well and point source
lie in the same sand body then the drinking well will get contaminated, otherwise no
contamination is going to take place. In order then to determine whether or not there is
a connection we calculate, for a given Earth model, the geobodies of that Earth model.
Figure 12.4 gives an example. When the Earth model consists of a binary system (just two
categories present, such as sand/shale), then a geobody consists of all cells belonging to
the same volume. In Figure 12.4, the locations A and B lie in the same “sand” geobody;
hence, if a contaminant is released from point A, then it is assumed, in this case study,
that it will eventually travel to point B.
12.1.3 Costs Involved
There are several costs related to the problem at hand, these cost are assumed to be deter-
ministic (which is doubtful for a lawsuit). The most relevant of these are the following:
Cost of cleaning up the contamination, $ 1 500 000
Cost of lawsuit in case of contamination, $ 5 000 000
Cost of geological study, $ 50 000
Cost of geophysical study, $: 100 000
12.2 Solution
12.2.1 Solving the Decision Problem
To solve the decision problem we refer to the decision tree in Chapter 4 (Figure 4.15).
Needed for the decision tree are the frequencies of “connection” in both channel/sand