This method is based on an analytical model which was developed in a sequence of papers starting with Refs [33-36].

In the assumed model, the reservoir is considered a ‘layer cake’ of homogeneous, non-communicating layers. The injected tracer pulse is distributed among the layers in accordance with the flow conductivity (permeability and thickness) of each layer. The tracer material in a layer moves in the reservoir toward the producer wells and is broadened by longitudinal dispersion in the direction of movement. The combined tracer response from all the layers makes up the response curve of tracer concentration as a function of the cumulative volume of water injected or produced. The peak height, the breakthrough time and the shape of the produced tracer response curve can be computed from the quantity of tracer injected, the formation properties and the well pattern geometry.

The initial model was expanded by Abbaszadeh-Dehghani and Brigham, who presented analytical solutions of tracer breakthrough curves for a number of balanced patterns with a rigorous treatment of the effects of tracer dispersion [35].

The tracer response curves from all homogeneous and balanced patterns analysed by the authors can be correlated into a single curve using a dimensionless pore volume parameter (VpD) given by:

V Vp — VPBT

PD _ 1 — VpBT

Firstly, Abbaszadeh-Dehghani and Brigham found an analytical expression for the displacing fluid cut ‘fD’ for all the balanced patterns [35]:

When a ‘slug’ of tracer with a pore volume equal to VpT and an initial concentration of C0 is injected into a pattern, the effluent tracer concentration profile from the reservoir is the difference between two pattern breakthrough curves (in the absence of mixing or any other transport process). That is:

C

TT _ /d(f„)- /d([7]p — Vpt) (51)

C 0

The mixing of a tracer with reservoir fluid during its transport through a porous medium is due partially to molecular diffusion and partially to mechanical or hydrodynamic dispersion. On the basis of experimental results, the effect of molecular dispersion on mixing in field tracer tests can be neglected with a good approximation. Also, it is possible to neglect the transverse mixing. Furthermore, to simplify the derivation of tracer mixing expressions without losing too much accuracy, mixing is considered to be related in a linear fashion to the interstitial pore velocity, u, so that the dispersion coefficient is:

K = au (52)

Considering convection and hydrodynamic dispersion as the dominant transport processes, it is possible to write the tracer mass balance equation as:

d 2C _ ЭС ЭС

2 dx dt

For a small slug tracer injection, whose length is infinitesimal compared with the distance between wells and defining a coordinate, 5, along each streamline (5 replace x), the resulting solution is:

where As is the width of a stream tube occupied by an undiluted tracer slug at the distance, — and a is the variance of the tracer distribution profile that includes changes for mixing and the geometry of the stream tubes, where:

(55)

For a given pattern geometry the tracer response curve from a homogeneous layer is a function of the Peclet number, ala, where a is the distance between producers and a is the dispersivity of the formation. As an example, the concentration for a balanced five spot pattern is expressed by:

(56)

The Y(W) term is a hyperelliptical integral that results from the mixing integral and VpBT(F) is the pore volume injected at breakthrough of the streamline, W.

The Fr term is the tracer size expressed as a fraction of displaceable pattern pore volume: V

model [35, 36], it is possible to derive how far the true situation deviates from the ideal one. Nevertheless, some additional considerations may be easily included in the model. The effects of adsorption and radioactive decay were analysed by Abbaszadeh-Dehghani [37]. Tracer partition between the water and hydrocarbon phases was considered by Tang [38].

This method has been applied mainly for injected water. It is useful, especially where unsaturated water-wet rock may absorb short tracer pulses by water imbibition from the injected water front edge. Ideally, the method requires

continuous logging of the water injection rate and corresponding adjustment of the tracer dosage rate in order to maintain a constant concentration of tracer in the injected fluid. A simpler arrangement can be implemented if a constant water injection rate can be assured. An example of a tracer injection arrangement is shown in Fig. 14.

Typically, the tracer used is HTO and the concentration in the tracer container is 370 MBq/L. The tracer concentration in the injection water, and the corresponding rate of tracer dosage, depends on the detection limit in the analytical laboratory and on the expected fraction of traced injected water in the produced water. The design should be a tracer concentration at the top of the production curve (at ‘equilibrium’) corresponding to some 100-1000 Bq/L in the produced water.

There is an example of a field experiment with continuous injection of HTO tracer and a subsequent tracer pulse injection (125I). Such operations may be laborious and cumbersome, especially for offshore operations. They require access to tracer engineers on a semi-continuous basis; regular controls with the equipment and tracer solutions will have to be performed. In addition, long term storage and use of radioactive solutions give rise to some scepticism among petroleum rig personnel. This method should only be used if there are clear advantages over the pulse injection method.

In principle, this method may be used also for non-radioactive tracers, but the tracer reservoir volume has to be larger and the pump somewhat different from both that described in Fig. 12 (smaller than this) and that used in Fig. 14 (somewhat larger than this).

I.1. CASE 1: DIADEMA OILFIELD (ARGENTINA)

The study began in January 2006 when 740 GBq of HTO was injected into well I-103, 750 kg of ammonium thiocyanate into well I-124 and 40 L of uranine into well I-125, all of the wells belonging to the Diadema oilfield in the province of Chubut, Argentina. The patterns involved in the operation can be seen in Fig. 52.

The response curves are shown in Fig. 53 where the tracer concentrations are represented in a relative way (activity and mass). The ordinate scale is logarithmic.

О и із

Jgf of

G-119 G-116 G-141

©

G-122

© G-110

FIG. 52. Well pattern in the Diadema oilfield.

The tracers are moving mainly to the south, as can be seen in Fig. 54, where only those wells with a recovery mass or activity of more than 1% are reported.

Breakthrough times were in the range of 48-72 d for HTO, 11-34 d for ammonium thiocyanate and 8-83 d for uranine. Tracer recovery ranged around 0.2-10% for HTO, 15-48% for ammonium thiocyanate and 0.1-50% for uranine for those wells in which tracer was detected.

The area around the injection sites will be roped off and appropriate warning signs will be set up. Only personnel taking part in the injection work will be allowed to remain at the site. Water hoses that can deliver copious quantities of water should be placed at the injection site. Thus, any spill of tracers can be

washed away. In the case of onshore operation, the nearby surface area should be covered by plastic sheets with water absorbent tissue on top.

111.1.4.3. Personal protection equipment

The injection crew must carry visors and masks during the critical phases of the injection. Rainsuits or water repellent clothes should be worn in case of spillage of tracer solution.

The five spot set-up (Fig. 117) has been designed using a large rectangular vessel of 160 cm x 95 cm x 80 cm. It has been filled manually with sand with a density of 1.8 g/cm3 and an average granulometry of 0.75 mm (d10 = 0.5 mm, d50 = 0.75 mm, d90 = 0.90 mm). The size of the five spot is only 40 cm square to avoid boundary effects with 5 wells of 40 mm diameter.

It should be noted that the studied five spot used to analyse this effect is not symmetrical. The bed of sand is initially saturated with water.

Four experiments have been conducted, three experiments with stagnant water inside the bed and flow rates of 107 cm3/min (exp. 1), 107 cm3/min (exp. 2), 184 cm3/min (exp. 3) at the injected wells. The fourth experiment has been conducted with a linear velocity of the water table of 2 m/d. The experimental data treatment has been revised; curves have been time and area

FIG 117. Photo and scheme of the five spot set-up.

normalized in order to overcome the apparent discrepancy due to the non­homogenous radial injection. It should be noted that interpretation of tracer experiments in oilfields should take into account the near impossibility of having uniform radial distribution of the tracer injection. In some extreme cases, this may explain the low tracer recovery observed.

Figure 118 shows the superposition of the tracer responses at well 1 for the three static experiments and one of the curves obtained for well 4.

3×3” Nal(TI), Marinelli and cylindrical samples

A suitable procedure for dual label counting is normally supplied with the delivery of the liquid scintillation counting equipment.

(iii) Analysis of 60Co labelled water tracer by gamma spectrometry

The 60Co labelled water tracer is [60Co(CN)6]3-. The 60Co emits strong gamma radiation resulting in a simple gamma spectrum (main energies at 1173 and 1332 keV).

Thus, gamma spectrometry may be a useful analytical method, also when this radionuclide is in mixtures with tritium, 14C or 35S labelled compounds, since these are pure beta emitters. Analysis of this compound in water samples may be done in different ways:

I.6.1. Problem

A field tracer experiment was commenced by the Tuha Oil Company on 10 July 2005. The objectives of the experiment were:

— To validate 14C tagged KSCN and 60Co tagged K3[Co(CN)6] as interwell water tracers;

— To evaluate the water injection processes;

— To reveal the features of reservoir heterogeneity.

Figure 77 shows the well pattern and the tracer injection wells.

The analytical procedure is shown in Fig. 91.

111.3.3. Recommendations

It is recommended that a reference solution (sample with known tracer concentration in the brine of the target reservoir) should be prepared and applied in an actual scale test, in order to obtain very reliable results through the use of the above analytical procedures. The concentration of the tracer in the reference solution should be at a similar level to that in the samples collected from the field.

III.4. ANALYSIS OF RADIOLABELLED [Co(CN)6]3- IN SAMPLES OF PRODUCED WATER

There are several radioisotopes that can be used to label the [Co(CN)6]3- compound: 56Co, 57Co, 58Co, 60Co and 14C.

III.4.1. Method

Enrichment of radiolabelled [Co(CN)6]3- in reservoir brine is conducted by anion exchange column chromatography. The absorption efficiency of the

lOOOmLbrine

_____ 1 _________________

Filtration by 0.45 p m filter paper

I

Adjust pH to 5-6 by HCL and Na.^COj

_________________ 1 ‘ ___________________________________________

Loading to а Ф5.х100тт glass column with about 1g No. 717 resin (80-100 meshes)

—————————————— ———————————————————————

Seal the column

________________ 1 ___________________________

Gamma counting or spectral gamma analysis of the column
Well Type Detector

FIG. 92. Analytical procedure for analysis of radiolabelled [Co(CN) 6]3 in samples of produced water.

[Co(CN)6]3 to the resin is more than 99%. The analysis method consists of three steps:

(1) Sample purification by filtration;

(2) Use of No. 717 anion exchange resin column enrichment;

(3) Gamma counting or spectral gamma analysis.

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.

Experiments should be carried out to examine the potential for tracer distribution between the water and oil phases. Three different methods are:

(1) Static batch experiments, where phase mixing and separation takes place in a mixing apparatus and where samples can be extracted from each phase for analysis of tracer concentration. Equipment for this purpose ranges from the simplest, such as the separation funnel, to thermostatized equipment illustrated in Fig. 36 and to more complicated autoclaves where pressures can be applied if deemed necessary.

Thermostatized water і n

Magnetic stirrer

FIG. 36. Experimental set-up for studies of radiotracer partitioning between seawater and stock tank oil at temperatures <90 C and at ambient pressure.

(2) Dynamic experiments with continuous phase mixing followed by phase separation as exemplified by the flow injection apparatus shown in Figs 37 and 38.

(3) The dynamic or chromatographic method, where a small tracer pulse is forced through a porous medium with known oil saturation at moderate linear flow rates (25-50 cm/d) together with the standard reference non­partitioning tracer, HTO. Difference in tracer transportation time is a measure of the degree of partitioning. Various forms of flow rigs can be used for this purpose. One such piece of equipment is illustrated in Fig. 39.

Heating cabinet

FIG. 37. Flow equipment used for measurement of partition coefficients of tracers between water (brines) and oils at ambient pressure and moderate temperatures (<90 XI).

Method (1) will give the true equilibrium partition coefficient, as will method (2) if the length of the mixing coil is sufficient to ensure full equilibrium transfer. The mixing coil may be empty (capillary) or filled with a packing material (static mixer). Method (3) will give an ‘effective’ partition coefficient because it includes kinetic effects such as diffusion rates and rate of exchange between phases (across liquid boundaries) and diffusion into the bulk volume as

30 50 70

Temperature (°С)

the tracer pulse passes by. This latter may give values that are more representative for the situation in the reservoir where the tracer (in most examinations) is transported as a pulse through the porous medium. The best situation occurs when the results from both experiments match.

The degree of partitioning (partition coefficient) is expressed by:

C

K = -^ (16)

C

^tr, w

where Ctr, o and Ctr, w are concentration of the tracer in the oil phase (o) and the water phase (w), respectively.

This quantity is directly derived in method (1) above by the counting of water and oil samples. Since C is proportional to the disintegration rate:

Ctr, o = Ro /so (17)

and

Ctr, w Rw/sw

where є is the counting efficiency and R is the count rate in the oil and water phases. Thus,

In dynamic experiments, the practical partition coefficient K’ is derived on the basis of the recorded tracer production curve (or chromatogram). This curve is established by sampling the fluid effluent from the chromatographic column and counting by liquid scintillation counter and/or gamma spectroscopy. K’ can be calculated from Eq. (20):

K,=v; — Vw) ■ a — S0)

Vw ■ S o

where

Vtr is the retention volume of the tracer candidate, i. e. the volume from the

start injection to the peak maximum of the tracer production curve (which may be found by curve fitting);

Vw is the retention volume of the water represented by the non-partitioning

standard reference water tracer HTO;

So is the oil saturation or fraction of oil volume occupied by oil;

K « 0 for passive water tracers. Compounds with K > 0 are of interest for measurement of the remaining oil saturation.

A typical result for a passive water tracer is that the degree of partitioning into the oil phase is approximately 0, as illustrated for S14CN — with HTO as a control in Fig. 39.