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.

There are principally two different injection strategies:

(i) Pulse injection: The full tracer volume is injected within a time period which is short in relation to its movements between injector and producer. In practice, injection times of up to several tens of hours may be considered a pulse injection. Most oilfield reservoir tests utilize pulse injection. There are various pulse injection procedures.

(ii) Continuous injection: A diluted tracer volume is injected by pumping continuously over time. The pumping speed is preferably adjusted to the varying injection water flow rate in order to keep a constant tracer concentration in the injected water. Injection times may be as long as one year or more. By knowing the injected tracer concentration and by logging the tracer concentration in each production well, the fraction of injection waters in the produced water from each well can be derived directly. Only a small fraction of injections are performed in this way.

There is also another point to consider in the injection strategy, whether to emply topside or downhole injection. If the well construction and completion allows for downhole injection, it must be considered whether it is feasible (technically and economically) or desirable to inject separately in each reservoir section (for stratified reservoirs). This latter method requires that each reservoir section can be isolated during the injection.

Most tracer injections are carried out as integral topside injections; the water (and the tracer) injected at the well head will enter the formation through perforations in the various strata in an quantity which is approximately proportional to the water-relative permeability of the various zones.

The [Co(CN)6]3- complex is of interest as a basic carrier of the five different radionuclides 56Co, 57Co, 58Co, 60Co and 14C. The first four are gamma emitters while the latter is a pure beta emitter.

In actual field situations, [Co(CN)6]3- may be used in areas where 35SCN — or S14CN — have been applied simultaneously. Since the thiocyanate tracers have to be analysed by liquid scintillation counting the presence of [Co(CN)6]3-, regardless of the radiolabel, will disturb the counting of the thiocyanate. For gamma emitting labels, the analysis may be performed by gamma spectrometry, but if the label on the [Co(CN)6]3- is 14C, there will be a mutual disturbance of the two radiolabelled complexes. Therefore, there was a need to develop radiochemical procedures to separate cobalthexacyanide and thiocyanate at the tracer level in produced water and results of attempts at this separation have been reported.

A method was developed for quantitative analysis using 1000 mL of sea water (as a substitute for produced water) containing a mixture of SCN — and [Co(CN)6]3- produced by enrichment procedures and preconcentration into samples small enough to be measured by liquid scintillation counting. The sample volume for liquid scintillation counting should not exceed 8-10 mL, since this is normally the maximum water sample volume dissolved by modern scintillation cocktails (12 mL) for ordinary 22 mL scintillation vials.

The main hypothesis was to take advantage of the difference in anionic charges to obtain a separation. The test sequence involved the following:

• Screening tests used to find a selective separation procedure for [Co(CN)6]3- by the use of 60Co labelled complex as a tracer. The separation is based on either solvent extraction or ion exchange techniques.

• Testing of different stripping or elution agents in order to minimize the degree of quenching in the final counting samples.

• Checking the absorption and stripping/elution characteristics of SCN- in the [Co(CN)6]3- method.

• Performing separation experiments on an actual sample containing both tracers labelled with 60Co and 14C.

The screening experiments with 60Co were measured by gamma spectroscopy using a lead shielded, high resolution semiconductor detector and 14C was measured with a liquid scintillation counter.

Doses to humans during handling and injection of gamma emitting radiotracers may be reduced by passive shielding, e. g. lead. A narrow beam of monoenergetic photons with an incident intensity I0, penetrating a layer of material with mass thickness d and density p, emerges with intensity I given by the exponential attenuation law

1 = exp(- m m d) (28)

10 where /m = //p is the mass attenuation coefficient (cm2/g), / is the linear attenuation coefficient (cm-1) and p the material density (g/cm3). The mass thickness d = xp (g/cm2) where x is the distance or the linear thickness in the material (cm). Introducing the term d = xp into Eq. (28) and solving for x gives:

ln( / )

x = 10­

m m P

Mass attenuation coefficients for lead (p = 11.35 g/cm3) [23] have been reconstructed from the plot given for lead and used to calculate the linear attenuation coefficients for the main gamma energies of the various radionuclides used as radiolabels and treated below.

Once the daily fractional recovery curve has been drawn, then click on the Accumulated recovery button.

It is possible to copy or print an image of this window.

How to graph the streamlines?

To present a graph with the streamlines of the selected wells, click on the button Graph streamlines, as shown below.

Accumulated

recovery

Shows the picture

New, Open, Save, Save as, Print

PORO TracerSim allows the creation of new documents, saving and printing them, in the same way as many other programs that run with the same operative system. The files with which PORO TracerSim works have the extension ‘PORO’.