**Thermal and
Compositional Plumes in **

**Non-Reactive Porous
Media**

A numerical
model was used to predict the movement of fluids of varying temperatures and
concentrations, injected into a fluid saturated box of uniform and constant
porosity and permeability.

Some
important equations that are solved numerically by the model:

The stream
function is obtained by solving this Poisson type equation:

, where , ,

Conservation
of enthalpy equation is solved in order to update the temperature field with
each time step:

,
where , , ,

,

Conservation
of concentration equation is solved in order to update the concentration field
with each time step:

, where ,

In this model, was set at 0.60 and
ε was set to 0.1.

The
boundary conditions of the box do not allow for heat or mass flux through any
of the sides. The fluid initially
saturating the medium had a dimensionless temperature of 0.0 and a dimensionless
concentration of 0.0. By varying the
temperature and concentration of the injected fluid, the effects of density can
be observed. The injection of fluid is
simulated by setting different temperature and concentration values on a small
portion of the lower boundary.

As the
temperature is advected away from the source, both the matrix and the pore
fluid are heated. As the concentration
is advected away from the source, it
moves through the pore spaces only and does not interact with the matrix. Therefore, the concentration moves more
quickly through the medium than does the temperature.

Case
1: The concentration on the small
section of the lower boundary was set to a negative value and the temperature
was set so that it would not affect the buoyancy. This simulates the injection of a fluid with
a lighter concentration and the same temperature as the fluid already in the
box. The Rayleigh number was set to 10000. The result is a plume of fluid that rises
quickly to the top of the box with little lateral spreading.

A. Concentration field
B. Temperature field

Movies: Concentration, Temperature and
Stream Function, Stream Function

Case
2: The temperature on the small section
of the lower boundary was set to a positive value and the concentration was set
so that it would not affect buoyancy (thus, the concentration acts like a
passive tracer of the injected fluid).
This simulates the injection of a fluid with higher temperature and the
same concentration as the original pore fluid.
The Rayleigh number was set to 10000.
This results in the temperature field advecting more slowly than the
injected fluid, allowing the neutrally buoyant fluid to spread laterally as
well as upwards. The mushroom shape of
the fluid plume is due to the heating of the original pore fluid near to the
injection site, which then rises and becomes mixed in with the injected fluid.

A. Concentration field
B. Temperature field

Movies: Concentration, Temperature and
Stream Function, Stream Function

Case
3: The temperature and concentration on
the small section of the lower boundary were both set to positive values. The temperature is set to be three times more
buoyant than the concentration. This
simulates the injection of a fluid with both greater temperature and
concentration than the original pore fluid.
The Rayleigh number was set to 5000.
This results in the fluid initially rising upwards due to the high
temperature. As the injected fluid
begins to cool further away from the source, the high concentration then
creates a density contrast with the original pore fluid, and so the fluid
begins to move downwards.

A. Concentration field
B. Temperature field

Movies: Concentration,
Temperature and Stream Function, Stream Function

Some
practical uses:

Knowledge
of the movements of fluids of varying temperatures and concentrations through
porous media can be used:

1)
To
predict the movement of pollutants through aquifers.

2)
To
predict the precipitation pattern of economical minerals.

3)
To
determine whether the injection of fluid into a hydrocarbon reservoir will
enhance recovery.