IV1. ANDURIL DISPERSION SIMULATOR

IV. 1.1. Anduril software

Anduril is a software package for basic data treatment and preliminary interpretation based on the standard equations for convection-diffusion in porous media. Figure 95 shows the main window of the Anduril 2.3 software.

The main data (time, concentration and water flow rate in the producing well) is introduced in a grid manually or by a copy and paste operation from an ordinary spreadsheet. The information can also come from a pre-existing file. Water volume may be used as an independent variable instead of time. The software also needs the injected activity and the radioisotope (tritium is the default), the background concentration and the baseline expressed as a real constant multiplied by the background. Experimental concentration values below this line are not taken into account.

FIG 95. Anduril 2.3 main window.

• As a general rule for further calculations, the distance between wells, layer thickness, porosity and water saturation should be written, while the inclusion of some other parameters will depend on the selected model. Finally, any additional information may be included as a ‘commentary’ in an appropriate text box.

• Original concentrations are corrected for internal calculations or graphic operations both by background and by radioactive decay. However, the information remains unchanged in the main grid.

• The experimental data can be filtered in order to eliminate the quick and random alterations that could mask the true values. The fast Fourier transform is the mathematical tool used for the purpose of eliminating higher harmonics. The experimental curve can also be extrapolated.

• The software calculates and plots the tracer recovery as a function of time or volume. Tracer concentration is also plotted. The main statistic parameters are also evaluated.

• The response curve can be decomposed in several simple functions following the classical dispersion function. This operation can be performed manual or automatically. Error information is shown in both cases so as to enable the user to correct the ‘fit’ parameters in order to identify the best approach. Graphic representation of simple functions can be presented as well as numerical information on each curve.

• This software includes many other options, such as the calculation of sweep volume, breakthrough time, final time and mean residence time and a function to calculate the activity to be injected in future experiments.

A pattern of oil secondary recovery in which water is pumped into an injection well that is surrounded by several production wells can be modelled as a system ruled by radial flow. In such a case, the tracer concentration, as a function of time and space, can be analysed by means of the classical dispersion equation for one dimensional flow:

? 2C ЭС ЭС

D—-v — =

dx2 dx dt

the solution of which is:

(34)

where

C(xt) is the tracer concentration as a function of distance and time (Bq/m3); tN is the normalized time;

D1 is the coefficient of dispersion (m2/d); v is the tracer velocity (m/d); x is the distance from the injection point (m);

CREF is the reference tracer concentration (Bq/m3).

The normalized time is the ratio between the time and the mean residence time of the tracer, and:

	(35)

where

A is the injected activity (Bq);

h is the thickness of the layer (m);

ф is the average porosity;

Sw is the water saturation;

F is a constant.

The denominator represents the volume of free water in a cylinder whose radius is the distance between the injection and the production wells and whose height is the layer thickness.

Single response curves can be easily fitted by the model adopted by Anduril. However, in the case of complex response curves with multiple relative maxima, it is convenient and necessary to decompose them into simple functions in order to extract conclusions related with the behaviour of each of them.