Residual oil evaluation using single well chemical tracer test
The single-well chemical tracer (SWCT) test is an in-situ method for measuring fluid saturations in reservoirs. The most common use is the assessment of residual oil saturation (Sor) prior to improved oil recovery (IOR) operations (post-waterflooding).
Process for single well chemical testing
The SWCT test for Sor uses only one well and involves the injection and back production of water carrying chemical tracers. A typical target interval for SWCT testing is shown in Fig. 1. The candidate well should be completed only to the watered-out zone of interest (zone at Sor). The water used normally is from the formation to be tested, and often is collected during the initial setup for the test.
The injected volume is divided into two parts: the partitioning tracer bank, which carries a small concentration of tracer (usually some type of ester) dissolved in water, and the push volume of water, which pushes the partitioning tracer bank away from the wellbore 10 to 20 ft. A material-balance tracer (normally a water-soluble alcohol) is added to the entire injected volume to differentiate it from the formation water being displaced. This injection step is shown in Fig. 2.
The primary tracer is an alkyl ester. The esters used in SWCT testing usually are more soluble in oil than in water. This solubility preference is expressed quantitatively by the ester’s oil/water partition coefficient, Ke:
where Ceo = the concentration of ester in oil; Cew = the concentration of ester in water; Ceo and Cew are values at equilibrium.
For example, if the partition coefficient is four, the ester prefers the oil phase four times more than the water phase. For each tracer to be used in each test, the actual value of Ke must be measured in the laboratory at reservoir conditions. Oil and water samples are collected from the target formation for this purpose.
As the ester tracer enters the pore space containing the residual oil, it partitions between the oil and water phases. The ester maintains a local equilibrium concentration in the oil phase, controlled by the ester’s partition coefficient, even though the water is flowing.
Because the oil is stationary and the water is moving, the ester tracer moves more slowly through the reservoir pore space than does the water with which it was injected. The ester’s velocity thus is a function of the water velocity, the ester partition coefficient, and the Sor. Fig. 2 schematically shows the radial position of the injected ester and water. The material-balance tracer, normally an alcohol, is nearly insoluble in oil, so that it travels at approximately the same velocity as the water, reaching as far into the formation as the injected water.
For simplicity, Fig. 2 illustrates the no-dispersion case however, in all real reservoirs, the tracers disperse significantly, though this effect does not alter the basic mechanism of retardation of ester velocity by the residual oil.
After the ester and push injections are completed, the well is shut in for one to ten days, depending on the reactivity of the ester and the reservoir temperature. This shut-in period allows some of the ester to react with water in the reservoir, which forms a new tracer in situ, the secondary (or "product") tracer.
Reacting an alcohol and an organic acid makes an alkyl ester. At reservoir temperature, however, when dissolved in water, this ester slowly breaks down again into the alcohol and acid: Ester + H2O = Alcohol + Acid. The shut-in period must be long enough for measurable alcohol to form in situ by this reaction (Fig. 3).
It is the alcohol formed that makes the Sor measurement possible. The acid formed during the reaction is not observed because it is neutralized by the natural base components of the reservoir. The alcohol, however, is not in the original formation water, and can be detected at very low concentrations in the produced water, thus acting as a unique, secondary tracer.
At the end of the reaction period, the remaining ester and the product alcohol tracers are located together 10 to 20 ft from the wellbore. The tracers then are ready to be back produced to the wellbore and monitored at the surface in the produced water.
Fig. 4 shows the chromatographic separation of the product alcohol and ester tracers. This separation occurs because the product alcohol and water velocities are essentially the same, whereas the ester production velocity is slower because the ester must partition between the oil and water phases during production in the same manner described in the injection step.
Throughout the production period, samples of the produced water are collected frequently at the surface. Total produced volume is measured at the time each sample is taken. At a portable laboratory at the wellsite, the samples are analyzed immediately for product alcohol and remaining ester tracer concentrations. A plot of concentration of tracers vs. total volume produced is developed during the production, as the samples are analyzed.
Fig. 5 shows a hypothetical example of typical tracer concentration profiles. All three tracer profiles show the effects of dispersion, which always occurs during flow in porous formations. The unreacted ester, for example, was injected as a square wave and returns as a Gaussian peak.
Summary of SWCT test features
The important SWCT test features are summarized below:
- The Sor measurement is made in situ in the waterflooded layers of the target formation. The tracers can go only where the injected water goes.
- Compared to coring or logging method results, the Sor results are from a relatively large reservoir volume.
- The Sor measurement is carried out on an existing well, and usually in an existing completion, which can be perforated or openhole.
- Because the Sor measured actually is the volume fraction of oil in the pore space, the measurement is independent of porosity.
Calculating saturation quantitatively
Before discussing the design and interpretation of SWCT tests, we need to establish the quantitative relationship between tracer velocity, the tracer distribution coefficient, and Sor. Fig. 6 schematically shows a local population of ester tracer molecules in a control volume (Vc) of a pore. The tracer is assumed to be locally in equilibrium, even though the water phase is moving and the oil phase is fixed (residual oil conditions).
The number of ester molecules in the water (new) is given by
and the number of ester molecules in the oil (neo) is given by
where Cew and Ceo = the concentration of ester (molecules/unit volume) in water and oil, respectively; and Sw = saturation of water, in fraction of PV.
We determine the retardation factor for ester (βe) by dividing these two equations:
The larger βe is, the more the ester tracer is retarded by the residual oil. Substituting in Eqs. 2 and 3 and canceling Vc yields:
Because Ceo/Cew = Ke (see Eq. 1), the equilibrium distribution coefficient of ester between oil and water, and Sw = 1 – Sor, this becomes
The typical ester molecule spends a fraction of its time (ft) in water and the rest of its time (1 – ft) in oil. Elementary probability theory requires that
The probable behavior of each ester molecule is the same as the behavior of a large population of identical molecules. From Eq. 6, then:
Solving for ft:
The typical ester molecule will travel at the time-weighted average velocity:
where ve, vw, and vo = the time-weighted velocities of the tracer molecule, water, and oil, respectively. Because vo = 0 if oil is at residual saturation, the last two equations combine to give
Eq. 11 is the fundamental equation for tracer chromatography in a porous medium. Solving Eq. 11 for βe:
If we can develop a way to measure ve and vw using an in-situ test, then βe can be evaluated. We then can measure Ke in the laboratory (at reservoir conditions) and substitute it into Eq. 6 to solve for Sor:
Both the well-to-well flow of two tracers and the SWCT test are methods that have been used to measure ve and vw in the reservoir. Well-to-well was the first suggested of these and in it, tracers A and B are injected (dissolved in water) into Well 1, and water is produced from nearby Well 2 until the tracers arrive. Tracer A is a partitioning tracer, such as an ester, that has a partition coefficient ranging from 2 to 10. Tracer B is assumed to have an equilibrium distribution coefficient (KB) of zero (insoluble in oil), so that its time-weighted velocity (vB) = vw. Tracer B arrives first, after time tB, and tracer A later, after time tA. Because the two tracers travel the same distance,
where vA = the time-weighted velocity of tracer A. βA then is determined from Eq. 12. Once the equilibrium distribution coefficient of tracer A (KA) is measured, Sor follows from Eq. 13.
Often, the well-to-well method is impractical for determining Sor because well spacing is too large. At the velocities that can be achieved between such wells, tA is months, or even years. Also, where different permeability layers exist, the different travel time in each layer causes excessive dispersion of tracers traveling from Well 1 to Well 2.
|Ceo||=||concentration of ester in oil, mol/vol|
|Cew||=||concentration of ester in water, mol/vol|
|Ke||=||oil/water partition coefficient for ester|
|neo||=||number of ester molecules in oil|
|new||=||number of ester molecules in water|
|Sor||=||residual oil saturation, fraction of PV|
|Sw||=||saturation of water, fraction of PV|
|tA||=||arrival time of tracer A, day|
|tB||=||arrival time of tracer B, day|
|vA||=||average velocity of tracer chemical A, ft/D|
|ve||=||time-weighted velocity of ester|
|vo||=||time-weighted velocity of oil|
|vw||=||time-weighted velocity of water|
|Vc||=||control volume of a pore, bbl|
|βe||=||retardation factor for ester|
- Cooke, C.E. Jr. 1971. Method of determining Residual Oil Saturation in Reservoirs. US Patent No. 3,590,923.
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