1.1.1.1. Maximum dilution method

If the reservoir is well known and a reliable model exists, the best estimate of the quantity of tracer required for an interwell study is obtained by numerical simulation of the various flow patterns involved. Then the quantity of tracer (mass or activity) needed for a specific experiment is calculated from the theoretical response and the detection limit. However, if the reservoir is well known, there is not much reason to perform a tracer test for reservoir evaluation purposes.

Most reservoirs, however, are poorly known, at least when it comes to the flow dynamics of reservoir fluids. Experience has shown that in this case some simple calculations may be equally trustworthy.

Owing to lack of better information, the quantity of tracer to be used can be based upon a purely geometrical consideration. Suppose that the reservoir is a homogeneous cylindrical volume around the injection well as shown in Fig. 2. Let the active pore volume be Vp, which may be calculated by Eq. (1):

Vp = n r2 h Ф Sw (1) where

h is the thickness of the tagged layer (m);

r is the distance between injection well and production well (m);

Ф is the porosity of the tagged layer (fraction, non-dimensional);

Sw is the water saturation (fraction, non-dimensional).

Assuming tracer dispersal is uniform in the available reservoir volume, then the expected output mean concentration is established by the detection limit (LD) of the tracer. In the case of a radiotracer, LD depends on the background, the counting geometry, internal counting efficiency, decay scheme characteristics and the measurement time. The activity (A0) to be injected to obtain a mean concentration equal to the detection limit is calculated by Eq. (2):

A0 = LdVp (2)

For a tracer pulse injection, which of course will not distribute tracer evenly throughout the whole reservoir section, tracer concentration in the response pulse at production wells will be considerably higher than the detection limit. However, this cannot always be guaranteed because of the possible existence of high permeability streaks, so-called ‘thief’ zones and adjacent water contacts where most of the injected tracer may disappear and never show up in production wells. Therefore, a safety factor F1 is normally introduced to Eq. (2). This factor may differ for various reservoir types and known reservoir heterogeneities, but Fj ~ 2-10 is common. Additionally, if the reservoir is known to be anisotropic and the flow known to have directional tendencies, a second factor, F2, may be introduced to account for this anisotropy. This factor, F2, may take values both below and above 1, i. e. wells along the prevailing flow direction have F2 > 1 while those lying in the flow shadow have F2 < 1.

Thus, the final simplified equation for the quantity of tracer to be injected is:

Ao = F1 F2 Ld n r2 h Ф Sw (3)

The required activity calculated by Eq. (3) only represents an approximation, but it is good enough as a reference value. The experience gained after having carried out a number of operations in different reservoirs is valuable in modifying the estimate values in order to determine the real quantity of tracer to use.