ENVIRONMENTAL ENGINEERING - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 234

In principle, this solution represents a moving heat front in the reservoir at a
speed about two times slower than the true groundwater velocity (faster than the
Darcy velocity), since some energy is required to heat the solid matrix. Fig 14.6b
shows effects of conduction, dispersion and bleeding for a particular situation.
Equation (14.3a) can also be reformulated into

2

1 2 C C C

Bl C (14.5)

Pe ; ;

T T x tv vL 2 h ' L D '

0
T

with C , ; , , Pe , Bl (14.6)

T L L D vL

H

1 0

Two numbers characterise the heat transfer process. The Peclet number Pe gives
the ratio between convection and conduction in the reservoir. The thermal bleeding
number Bl gives the ratio between bleeding (conduction in the overburden) and
convection. For practical situations, Pe and Bl can be evaluated straightforwardly,
and they provide the reasoning when simplifying the transport equation by
eliminating partial processes of lesser importance. Fig 14.7 shows some numerical
examples of heat transport, radial flow from a well, plane flow, and the effect of
convection and conduction.

Figure 14.7 Numerical examples of heat transport (after Saeid); (upper left) radial
situation representing flow from a single well with a constant discharge; (upper right)
plane symmetric situation, approaching formula (14.4) with D T = 10D L ; (lower left) pure
conduction (no groundwater flow); (lower right) with convection and D T = D L .

Scaling the heat transport in porous media can be performed in a geocentrifuge
(see Chapter 9). The larger convection velocity v coincides with the equally smaller
spatial dimension L , while the similarity of each of physical numbers Pe and Bl is
preserved (see equation 14.6). However, the mechanical dispersion will not
maintain similarity, but its effect is minor for high Peclet numbers, which is the
case in many practical situations.