You must log in to edit PetroWiki. Help with editing

Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information

PEH:The Single-Well Chemical Tracer Test - A Method For Measuring Reservoir Fluid Saturations In Situ

Jump to navigation Jump to search

Publication Information


Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 5 – The Single-Well Chemical Tracer Test-A Method For Measuring Reservoir Fluid Saturations in Situ

Harry Deans Charles Carlisle, Chemical Tracers, Inc.

Pgs. 615-649

ISBN 978-1-55563-120-8
Get permission for reuse

The single-well chemical tracer (SWCT) test is an in-situ method for measuring fluid saturations in reservoirs. Most often, residual oil saturation (Sor) is measured; less frequently, connate water saturation (Swc) is the objective. Either saturation is measured where one phase effectively is stationary in the pore space (i.e., is at residual saturation) and the other phase can flow to the wellbore. Recently, the SWCT method has been extended to measure oil/water fractional flow at measured fluid saturations in situations in which both oil and water phases are mobile.

The SWCT test is used primarily to quantify the target oil saturation before initiating improved oil recovery (IOR) operations, to measure the effectiveness of IOR agents in a single well pilot and to assess a field for bypassed oil targets. Secondarily, it is used to measure Swc accurately for better evaluation of original oil in place (OOIP). Fractional flow measurement provides realistic input for simulator models used to calculate expected waterflood performance.

This chapter familiarizes the reader with the SWCT method, and offers guidelines for selecting suitable test wells and for planning and executing the field operations on the target well. Test interpretation is also discussed and illustrated with typical examples.


The first SWCT test for Sor was run in the East Texas Field in 1968.[1] Patent rights were issued in 1971.[2] Since then, numerous oil companies have used the SWCT method.[3][4][5][6][7] More than 400 SWCT tests have been carried out, mainly to measure Sor after waterflooding.

The SWCT method has gained considerable recognition over the past few years because of increasing interest in the quantitative measurement of Sor. Some experts[8][9] consider the SWCT test to be the method of choice because of its demonstrated accuracy and reasonable cost.

Measuring Sor

Accurate Sor measurement is important because of a combination of basic problems in oil recovery. The industry still produces less than half the oil in the reservoirs discovered, and nearly all that oil is produced using traditional primary and secondary recovery methods.[10] Furthermore, as the cost of finding new reserves continues to increase, especially in the U.S.A., the oil remaining in old fields becomes a significant economic target for infill drilling and IOR projects. See Chaps. 12 through 17 in the Reservoir Engineering and Petrophysics volume of this Handbook for more detail on these methods.

In every target field, the quantity and location of the remaining oil must be determined. Fig. 5.1a illustrates the principle of material balance, as applied to an oil reservoir. The entire area of the graph represents the reservoir pore volume (Vp), which is known with varying degrees of uncertainty. The produced oil, corrected back to reservoir conditions, is the middle area; its accuracy, however, depends on how thoroughly the production records are kept.

The uppermost area is the connate water, which is known only as well as available methods and coverage of measurements allow. The lowermost area, the remaining oil, can be expressed as an average saturation of oil RTENOTITLE, if we accept the total pore volume Vp, produced oil, and Swc values as being accurate.

If a given field has been waterflooded, the fraction of the OOIP displaced by the water is a critical parameter. Testing for Sor in watered-out wells in the field can determine the maximum waterflood displacement efficiency. A significant difference between the material-balance So and the measured Sor would indicate the presence of bypassed oil. This would signify that parts of the reservoir had not been contacted by injected water, or had not received sufficient water throughput to reach Sor. This concept is shown in Fig. 5.1b.

A reliable in-situ measurement of Sor simultaneously defines the target for enhanced oil recovery (EOR) and allows estimation of the potential bypassed (mobile) oil in the field. This moveable oil is the target for infill drilling and/or flood sweep efficiency improvements.

Because Sor varies greatly with formation type, oil/water properties, and other variables that are not completely understood (e.g., wettability changes caused by water flood practices), Sor measurements range from < 10% to > 45%. There is no reliable way to predict Sor with acceptable accuracy for most reservoirs. Furthermore, measuring residual oil is not easy. Laboratory corefloods performed at other than native state wettability are unreliable.[11]

Well logs can give vertical profiles of Sor under optimal conditions, but their results are not absolute. Logs of all types require calibration by an independent method, which gives either a quantitative So at some point or an average So over some layer. Pressure cores or sponge cores can provide this calibration, but require a new well and are subject to saturation disturbances caused by mud filtrate invasion.

An advantage of the SWCT method is that it pushes tracers beyond damaged regions near the wellbore and into layers that are known to be at residual oil conditions. The tracers go where water is contacting the residual oil, as shown in Fig. 5.1b.

In an SWCT test, the formation volume sampled is large enough to be representative. A typical test quickly investigates hundreds of barrels of pore space in an existing watered-out well. The tracer-bearing fluids are produced back into the well without disturbing the formation, allowing further testing.

Measuring Swc

Connate water saturation is more variable (and less predictable) than Sor, with Swc measurements ranging from > 50% in certain rock types to < 5% in unusual reservoir situations. Large variations within the producing intervals of major reservoirs are well documented.[9]

As Figs. 5.1a and 5.1b show, estimates of recoverable oil depend fundamentally on knowing Swc. Oil-based coring can provide reliable results and is an effective choice if its expense can be justified at the time a well is drilled. Electric logs can give vertical profiles, but as with Sor, require calibration for quantitative Swc measurement.

Deans and Shallenberger[12] reported the first application of the SWCT method for measuring Swc. As in the case when measuring Sor, the reservoir volume sampled is large and the test is nondestructive, which is especially important for a producing oil well. The tracers used in measuring Swc are nonhazardous oxyhydrocarbons, so that no contaminated oil needs to be disposed of after the SWCT test. Most importantly, though, the test holds a high success rate—every known SWCT test for Swc has yielded quantitative results.

Measuring Sor

How the SWCT Test Works

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. 5.2. 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. 5.3.

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. 5.3 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. 5.3 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. 5.4).

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. 5.5 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. For an animation of the entire process, see [CD edition includes video ].

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. 5.6 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.

How the SWCT Test Works 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. 5.7 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. 5.2 and 5.3 and canceling Vc yields:


Because Ceo/Cew = Ke (see Eq. 5.1), 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. 5.6, 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. 5.11 is the fundamental equation for tracer chromatography in a porous medium. Solving Eq. 5.11 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. 5.6 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 v e and v w in the reservoir. Well-to-well was the first suggested of these[13] 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. 5.12. Once the equilibrium distribution coefficient of tracer A (KA) is measured, Sor follows from Eq. 5.13.

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.

Chap. 6 in this volume presents the technology of well-to-well tracer tests and discusses where they can be beneficial to the management of a reservoir.

The SWCT Test

Using the SWCT test avoids the problems of too-wide well spacing and excessive tracer dispersion caused by layering. In the SWCT test, the tracer-bearing fluid is injected into the formation through the test well and then produced back to the surface through the same well. The time required to produce the tracers back can be controlled by controlling the injected volume on the basis of available production flow rate from the test well.

In a single-well test, tracers injected into a higher-permeability layer will be pushed farther away from the well than those in a lower-permeability layer, as indicated in Fig. 5.8a; however, the tracers in the higher-permeability layer will have a longer distance to travel when flow is reversed. As the tracer profiles in Fig. 5.8b show, the tracers from different layers will return to the test well at the ame time, assuming that the flow is reversible in the various layers.

Flow reversibility in a single-well test is desirable for the reason just explained, but it complicates Sor measurement. The simple strategy of injecting two tracers with different partition coefficients does not work in this case. As Fig. 5.9 shows, tracers A and B separate during injection, just as in a well-to-well test, and at the end of injection, tracer B will be farther from the wellbore than tracer A because the presence of the residual oil retards A. During production, then, tracer B has farther to travel to return to the well. The separation achieved during injection is reversed during back production, so that A and B arrive back at the wellbore at the same time (if they were injected at the same time). No measurement of Sor is possible using Eqs. 5.12 and 5.13 because no information can be obtained about the ratio of velocities of A and B.

One possible way of avoiding this reversibility problem is to generate the second tracer in the formation instead of injecting it. The steps are: (1) Inject tracer A and push it into the target formation, as described above; (2) Stop flow to allow part of the injected A to react, forming tracer B in the same pore space where A is located, after the reaction time, A and B are together; (3) The fluid is then produced back into the test well; A and B must separate if their equilibrium distribution coefficients (KA and KB) are different and if residual oil is present. This concept is the basis for the SWCT test patent.[2]

The practicability of this method depends on finding suitable tracers. The demands on partitioning tracer A are especially severe: inexpensive, available in reasonable quantities at high purity, nontoxic, not present in the reservoir fluids, and easily measured at low concentrations in water. It must have an appropriate KA for the oil, water, and temperature of the target field, and, most importantly, it must react at a rate that allows formation of enough (but not too much) of a suitable tracer B. KB must be different from KA, and tracer B also must be measurable at low concentrations in the produced water, and not be present in the reservoir fluids.

A methyl, ethyl, or propyl ester of formic or acetic acid has proved suitable in every reservoir tested. These simple chemicals are sufficiently soluble in water, and have an appropriate range of K values and reaction rates. They are relatively inexpensive and nontoxic at the concentrations used, and they react with water to produce alcohols, which are not found in crude oils and can be detected readily in the produced fluid.

For best results,[3] choose an ester with a retardation factor (βe) in the optimum range (0.5 < βe < 1.5). This requires that Ke be in the range 0.5(1.0-Sor)/Sor<Ke<1.5(1.0-Sor)/Sor. Use the best available estimate of Sor to fix this range. Then choose the optimum ester using available correlations[14] for the dependence of Ke on temperature and water salinity.

In several past SWCT tests, two esters (e.g., methyl acetate and ethyl acetate) were used simultaneously to give two different depths of investigation for Sor in the same test. The multiple-ester test design has become increasingly popular in recent years.

Test Design

The design and implementation of a SWCT test for Sor is straightforward. Certain facts about the target formation are needed to begin test design. Some essential reservoir properties include oil cut of the test well; reservoir temperature; reservoir lithology; production rate; test interval size and average porosity; and formation water salinity.

Oil Cut of Test Well. Candidate wells for Sor measurement must be able to produce formation water to the surface. The produced fluid should be nearly all water to ensure that the test interval is at or near Sor. In cases where the test interval produces high oil cut, water can be injected into the test interval before testing to water-out the zone before tracers are injected.

Reservoir Temperature. Reservoir temperature dictates which esters are suitable for the SWCT test. The formate esters hydrolyze approximately 50 times faster than do the acetate esters, and are used in the reservoir temperature range of 70 to 135°F. The slower-reacting acetate esters generally are used in the 130 to 250°F range.

Reservoir Lithology. SWCT testing has been done in a variety of test conditions. In sandstone reservoirs, SWCT tests give satisfactory results for a wide range of test designs. Test timing, total injected volume, and the ester used can vary considerably for the same zone, with little effect on test interpretability.

However, SWCT tests in carbonate formations require much more precise design. In a given carbonate test zone, subtle changes in test design can cause significant variation in the tracer profile shapes. Each of our past carbonate test designs has required significant tailoring to overcome the dispersed nature of the production profiles generally present in carbonate test results.[15] The reason for this dispersed nature is that the assumption of local equilibrium is not always valid for carbonate reservoir tests. This problem is illustrated in Case 4 below.

Production Rate. The production rate of the candidate well controls the test size or volume to be injected. The amount of water that can be produced in one day is a normal test volume; two days’ production is a practical upper limit. In normal productivity reservoirs, the injection is sized to give a 15- to 20-ft depth of investigation into the formation. The injection rate of the SWCT test usually is approximately the same as the well’s production rate. Care must be exercised to avoid fracturing the formation during test injection.

Test-Interval Size and Average Porosity. SWCT test can be carried out on cased and openhole completions. Estimated interval size and porosity are used to calculate a theoretical radius of investigation for the design injection volume, although Sor results are not dependent on either. Interval sizes of from 1 to 100 ft have been tested with satisfactory results. Generally, testing on 10- to 50-ft zones generates more definitive results.

Formation-Water Salinity. Because it normally avoids chemical incompatibility, water that is produced from the test well generally is used to carry the chemical tracers into the reservoir. Because Ke depends on it, water salinity also is a factor in choosing the best ester for the SWCT test. To avoid difficulties during injection of the tracers, closely examine the water quality (especially suspended solids) and any precipitation tendencies.

Field Procedures

After selecting the ester and sizing the test volume, determine the field-test location, production method, and safety requirements. Then, schedule and implement the test.

Four lift methods have been used in SWCT testing. They are free flow, electric submersible pump, rod pump, and gas lift. These lift mechanisms are listed roughly in order of desirability, but all are satisfactory.

Before the field test, the candidate well should be produced long enough to establish the oil cut, measure the stabilized production rate, and clean up the tubular goods in the completion. Then accumulate produced water for the upcoming test in clean tanks near the well. Position the portable laboratory/pumping system near the test well.

Pure tracer chemicals usually are delivered to the wellsite in 55-U.S.-gal drums. The tracers either can be batch-mixed with formation water before injection, or continuously metered into the water during injection. Fig. 5.10 shows a schematic for a typical field setup for continuous metering of chemical in the injection water. For batch mixing, the tank can serve as the mixing vessels. With either batch-mixing or continuous metering, filter the water to one-micron or higher quality to prevent plugging when the fluids enter the reservoir.

After a short period for analytical equipment checkout, inject the chemical solution of ester and material-balance tracer and push it according to test design. Samples of the injection water should be analyzed periodically to verify tracer concentrations, and volume, rate, and pressure information should be monitored carefully throughout the injection. Be careful not to part the formation by exceeding the fracture gradient.

Once the injection is complete, the well is secured for the planned shut-in period. When the shut-in period is over, the well is placed on production. Fig. 5.11 shows a general schematic for the production phase of a SWCT test. The produced water flows through a portable separator (if necessary) to the storage tanks on location, where its volume is carefully measured. Production volume also can be measured using a field production test separator, if one is available.

During production, water samples should be taken near the wellhead and analyzed on location for tracer concentrations. On-site chemical analysis is necessary to gather data that are accurate for the time of production, whereas sending the samples to a service laboratory for analysis would allow additional hydrolysis of the ester to take place during transport. At the time each sample is taken, the total production volume is recorded and plots of tracer concentration vs. volume produced are generated. These tracer concentration profiles are the essential field data for the SWCT test.

Because of dispersion, the total produced volume required normally is two to three times the injected test volume. Injected volume usually is one day’s production, and two to three days normally are required for the back-production phase of an SWCT test.

Test Data Interpretation-Case[1]

Tomich et al.[1] report one of the earliest SWCT tests, which was performed on a Frio Sandstone reservoir on the Texas Gulf Coast. The results of this test are used here to demonstrate the details of SWCT test interpretation for an ideal situation.

The test well in the Tomich et al.[1] report was in a fault block that had been depleted for several years. Because of the natural water drive and high permeability of the sand, the formation was believed to be near true Sor. When the well was returned to production (gas lift), it produced 100% water at a rate of 1,000 BWPD.

On the basis of observed reservoir temperature (160°F) and brine salinity [100,000 ppm total dissolved solids (TDS)], ethyl acetate was chosen as the primary tracer. Formation oil and water samples were obtained for laboratory measurement of K at reservoir temperature conditions. The value of Ke measured for ethyl acetate was 6.5 at these conditions.

The test injection consisted of 1,000 bbl of formation water carrying ethyl acetate (13,000 ppm) and methyl alcohol (5,000 ppm), followed by a push bank of 1,000 bbl of formation water carrying methyl alcohol (5,000 ppm), injected over a period of two days. An eight-day shut-in period followed. During the production period, samples were collected regularly and analyzed on site using gas chromatography. The observed data are plotted as tracer concentration vs. produced volume in Fig. 5.12.

In ideal cases, when enough data have been gathered to define the tracer profiles, it is possible to use Eqs. 5.11 through 5.13 to approximate Sor in the field. If product tracer B and unreacted ester A begin together in the formation, the produced volume when A arrives back at the well (QpA) is related to the produced volume when B arrives (QpB) by the formula


where QpA and QpB are in bbl.

This suggests that if on the same graph we plot normalized concentration of A vs. volume produced (Qp) and normalized concentration of B vs. Qp(1 + βA), the two curves should coincide. Because we do not know βA, this must be done by trial and error (i.e., βA is adjusted until the best possible match of the two profiles is found).

Fig. 5.13 demonstrates this procedure. Profiles from the SWCT test (Fig. 5.12) first were normalized by dividing each observed concentration by the peak value measured for that tracer. βA then was varied to obtain the plot shown. The best-fit value for βA was 0.97.

Using Eq. 5.13, the Sor is approximated as


Agreement is only fair over the entire curve in Fig. 5.13; still, this result is quite close to the final interpreted result, obtained as described below under core/simulation. The approximated Sor depends on the validity of several idealized assumptions, which are rarely satisfied in practice:

  • That no B is present in the injected A, and that most of the hydrolysis reaction occurs during shut-in (no flow), so that B and unreacted A are exactly together before backflow begins. In reality, some reaction takes place during injection and production, and there always is some B present in the A as purchased. These two sources explain the high ethyl alcohol "tail" observed in Fig. 5.13.
  • That Sor is uniform throughout the formation tested. In practice, however, there often is evidence of several layers with different saturations in a given completion.
  • That the injected tracer-carrying fluids are stationary in the reservoir throughout the shut-in period. Actually, fluids sometimes relocate during the shut-in period, because of pressure gradients across the field or pressure differences within subzones of the test completion.
  • That the fluids inject uniformly into subzones and subsequently produce back to the test well reversibly. Total fluid flow reversibility is not observed in many tests.

Obtaining a more reliable answer for Sor requires a detailed simulation of the actual test procedure for a given SWCT test. Simulators are available to account for all the nonideal situations listed above. Simulation is time-consuming and is an added expense, but in our experience, it always is justifiable and its expense is small compared to that of field data acquisition.

Theory of Simulation. Mathematical modeling of the ideal SWCT test assumes that the carrier fluid flow is incompressible, pseudosteady state, single-phase, and radial only; that the formation is a homogeneous layer of thickness (h) and porosity (ϕ) extending from the wellbore radius (rw) to an external boundary radius (re), where reservoir pressure is constant.

With these assumptions, the interstitial fluid velocity (vfi) is given by


where r = radial position; q = fluid flow rate in the single well (q > 0 is injection and q < 0 is production); h = height of test zone; ϕ = porosity; and Sf = flowing fluid saturation, constant.

The additional assumptions regarding the tracers are:

  • That KA for tracer A is constant and that A is in local equilibrium between flowing fluid (saturation Sf) and residual fluid (saturation Sr). For Case 1, Sr = Sor and Sf = 1.0 – Sor.
  • That tracer A (primary) reacts in situ to form tracer B (product) at a rate given by


where RH = hydrolysis reaction rate, in moles of A per vol-day; CA = concentration of A, in mol/volume; and kH = hydrolysis rate constant (days–1) in the aqueous phase. Tracers are dispersed in the radial flow with an effective dispersion coefficient (Da), given by


where α = dispersivity (ft).

The material balance for tracer A is the partial differential equation:


Similar equations apply for product tracer B and the material-balance tracers.

SWCT test simulation requires the numerical solution of these equations for A, B, and the material-balance tracer. The equations first are converted to finite-differenced form, based on the perfectly mixed cell model.[16] The simulation program then solves the finite-differenced equations for the concentrations of the tracers in a radial series of cells over the test time interval.

Input to the simulation program consists of:

  • Known parameters, which are: q as a function of time (injection, shut-in, production), injected concentration of tracer A (CA) and concentration of tracer B (CB) as a function of time; rw, h, ϕ; KA and KB.
  • Unknown (estimated) parameters, which are: kH, Sor, and the radial dimension of the cells (ΔR). Note: according to the theory of the perfectly mixed cell model for small time intervals, ΔR = 2α.

Finding Best-Fit Parameters Using the Simulator-Case 1 Simulation

Simulation of a relatively ideal test now will be demonstrated using the tracer profiles of Case 1, shown in Fig. 5.12. The known parameters are input to the program, along with estimated values for ΔR, kH, and Sor.

First, several runs are made with different ΔR values, keeping all other parameters constant. The simulation predicts values for tracer concentrations vs. volume produced. Fig. 5.14 shows the CA results superimposed on the field data, for different values of ΔR. The best-fit value appears to be approximately 0.50 ft. (Further refinement, using least-squares criteria, yields a value of 0.52 ft.) Note that ΔR affects the shapes of the concentration peaks, not their average positions on the produced volume axis. The shapes of CA and CB peaks are similarly affected.

The next step is to find the best-fit value of kH, which determines how much product tracer B will form. In Fig. 5.15, the simulated profiles for CB are superimposed on the field data for CB, for a range of values of kH. Note that kH affects the height of the CB peak, but not its position. Because of the relatively small amount of hydrolysis in this case (less than 10% of the injected ester was hydrolyzed), the height of the simulated CA peak changes very little when kH is varied in this range of values.

Finally, the input value for Sor is varied. Minor adjustments are made in kH to keep the height of the CB peak constant. As Fig. 5.16 shows, changing the Sor moves the position of the product tracer peak on the "produced volume" axis. Changing the Sor does not affect the predicted position of the unreacted ester peak because of the reversibility effect that was discussed earlier.

The final best-fit simulation is shown with the field data in Fig. 5.16. The best-fit estimates of the unknown parameters for Case 1 are ΔR = 0.52 ft, kH = 0.011 days–1, and Sor = 0.13. To indicate the level of precision expected in the test, simulated CB peaks also are shown for Sor = 0.11 and Sor = 0.15. Sor = 0.13 ± 0.02 is the best estimate for Sor for this reservoir, using the SWCT method.

How to Simulate Nonideal SWCT Tests

The 400+ SWCT tests performed to date have demonstrated that most cases are not ideal. Some reservoir factors cause the produced concentration profiles to have irregular shapes. The challenge to the test interpreter in those cases is to deduce what has caused the irregularities and to modify the simulation to obtain a credible match to the field profiles.

The three major nonideal conditions observed in SWCT tests, in order of their potential encounter, include fluid movement in the formation at the test site; in carbonates, a lengthy time required for local equilibrium to be achieved by diffusion in liquids, as compared to test duration; and in sandstones, nonreversing flow behavior in formation layers.

Fluid Movement. In active parts of a reservoir (i.e., when other producers or water injectors are close to the test well), there might be fluid movement in the formation at the test site. This is known as fluid drift. The tracers injected with the SWCT test fluids are subjected to a flow field that is not radial and reversible, as is assumed by the simulation theory above. Such was the situation during the first SWCT test.[1] A specialized simulator was developed to interpret that test.

The simulation theory assumes that a linear flow field with a fixed drift velocity, vD, is superimposed on the radial flow at the test well. This requires the numerical solution of partial differential equations involving two space dimensions and time. Obtaining a best fit to field data involves varying drift velocity, vD, in addition to the unknowns ΔR, kH, and Sor. The drift velocity is caused by a regional pressure gradient in the formation, where as the radial component of velocity is caused by injection or production at the test well. The original simulator is furnished to licensed users of the SWCT method.

Local Equilibrium Time Length. The pore geometry of most carbonates is such that the basic assumption of local equilibrium of partitioning tracers is not valid. A significant fraction of the pore space is not directly in the flow paths, but is only in diffusional contact with these paths. Because the time required for local equilibrium to be achieved by diffusion in liquids can be long compared to the duration of the SWCT test, dual-porosity models must be used to simulate SWCT tests in carbonates. In addition to ΔR, kH, and Sor discussed earlier, several new unknown parameters must be added to the list:

  • The fraction of the total PV that appears to be poorly connected for flow (dead-end fraction).
  • The effective diffusion parameter for each tracer in the poorly connected fraction.
  • Sor in the poorly connected pores.

The dual-porosity simulator has been used to interpret more than 30 tests to date. Case 3 below uses the dual-porosity simulation model.

For a summary of SWCT test experience in carbonate formations, see Deans and Carlisle.[15]

Nonreversing Flow. Interpretation of SWCT tests in sandstone formations has revealed a very common nonideality. The formations tested appear to consist of two or more layers, as might be expected, but reversing behavior is not observed. One likely explanation is the existence of local pressure differences between the layers, caused by activity at other wells in the reservoir. Qualitatively, the effects of such pressure differences on the SWCT test results are:

  1. A layer at higher pressure accepts less fluid during injection and produces more fluid during production than a parallel layer at lower pressure. This results in a nonideal profile because the tracer bank from the higher-pressure layer will return earlier than it should and the tracer from the lower-pressure layer will be late.
  2. During the shut-in period for ester hydrolysis, fluid will flow through the wellbore from the higher-pressure layer to the lower-pressure layer. One tracer bank moves back toward the well and the other moves away during the shut-in period. This special flow condition, called crossflow, adds to the separation caused by effect 1.
  3. As mentioned earlier, apparent differences in Sor sometimes are observed in different layers in the same formation. Along with nonreversing flow, these differences require the use of a multilayer simulator program to interpret certain SWCT tests.

Once the specific nonideal conditions are recognized, the SWCT test simulation proceeds as before. The unknown parameter set now contains an estimate of the number of layers present, the fraction of total fluid injected/produced from each layer, the crossflow between layers, and the Sor for each layer. Because of the large number of adjustable parameters, semiautomated optimum-seeking subprograms have been developed help find the best fit. Seetharam and Deans[17] demonstrate that an accurate flow-weighted Sor is obtainable using such a multilayer simulator to match field data, even though the layering parameters are not unique. Case 2 (below) presents an example of a SWCT test in a layered sandstone formation.

In all SWCT test simulations, the objective is to find the simplest simulator model that adequately matches the observed tracer profiles. The same model must match all tracers used in a given test (ester, product alcohol, and material-balance tracers). In some tests, one or more additional tracers may be used in different injection patterns to identify wellbore and/or formation flow irregularities. The more tracers that are used, the more difficult it is for the simulator to find a reasonable model to fit all field-measured tracer profiles. Our experience suggests, however, that several models can adequately describe a given set of profiles, and that the least-sensitive parameter to changing models is the main target, Sor.

Simulation of SWCT Tests in Layered Formations-Case 2

The second field test example is from a candidate test zone with the following characteristics:

  • Produced water cut of 0% (100% oil).
  • Reservoir temperature of 234°F.
  • Lithology is sandstone.
  • Produced by gas lift.
  • Production rate of 500 B/D.
  • Perforated interval of 45 ft.
  • Average porosity of 22%.
  • Brine salinity of 43,000 ppm.

No well was available in this field that produced water only. In this case, the test well initially produced 100% oil. To generate residual oil saturation near the well, 6,500 bbl of filtered water first was injected into the test zone. The waterflood injection took eight days to complete, after which the well produced 100% water during a short test.

Samples of produced oil and water were collected for ester K value measurement. Ethyl acetate was selected as a suitable partitioning tracer. Its K value was 3.65, based on laboratory measurements at reservoir conditions. With an assumed Sor of 25%, the corresponding value of β is 0.94, which is close to the optimum value of 1.0.

For the test that followed the waterflood, 135 bbl of formation water was injected containing ethyl acetate (7,000 ppm), normal propyl alcohol (NPA) (3,900 ppm), and isopropyl alcohol (IPA) (12,700 ppm). This was followed by 550 bbl of formation water carrying only isopropyl alcohol (12,700 ppm). The injection rate was 650 B/D and wellhead pressure was 1,200 psia during injection. Wellhead pressure was monitored carefully during injection to avoid fracturing the test zone.

The SWCT test injection required 1.15 days. The well then was shut in for five days to allow hydrolysis of a fraction of the ethyl acetate tracer. After hydrolysis, the gas lift system was turned on and the well was produced through a separator at an average rate of 500 B/D, with a stable gas lift ratio of 620 scf/bbl.

The production period was 2.7 days, throughout which samples of the produced water were taken at 5- to 15-minute intervals and analyzed immediately at the wellsite for tracer content. Total produced volume was carefully recorded at the time of each sampling. Total produced volume was 1,350 bbl. No oil cut was observed in the produced fluids at the end of the 1,350-bbl production period.

The field data from this test are plotted in Figs. 5.17 and 5.18 as tracer concentration vs. total produced volume, along with simulation results. The best-fit simulation required four layers, with minor irreversible flow. The ethyl acetate contributions from the four layers are shown in Fig. 5.17, along with the composite concentration, which is the flow-weighted sum of the four layers. The two main layers accepted 73% of the injected tracer, and produced the same fraction. The early layer took 13% of the injection and gave back 19% of the production, and the late layer took 14% of the injected fluid, but only produced back 9%.

The predicted ethanol concentrations for the same four-layer model are shown in Fig. 5.18 . To obtain the ethanol best fit, only the Sor was varied for the four layers. The two main layers have an Sor ranging from 22 to 28%. A radial gradient of oil saturation caused by the waterflood performed before the SWCT test would produce a similar effect.

On the basis of this model, the tracer-injection average Sor is calculated to be 26 ± 2%. This is a permeability-thickness-weighted average for the PV accessed by the ethyl acetate, which is roughly the volume of a cylinder 8 ft in radius and 45 ft high.

Simulation of SWCT Tests in Dual-Porosity Media

Tracer test results from many carbonate formations seem far from ideal when compared to those from sandstone formations. One of the fundamental assumptions of the SWCT test—local equilibrium of tracer in all the available fluid—is invalid for carbonates. This also is the case with fractured sandstones.

Fig. 5.19 shows the assumed situation in these cases. Tracer material being transported through the well-connected pores can diffuse into the fluid in the dead-end pores. Depending on the geometry of the pore system and the flow rates, however, the tracer might not have enough time to approach equilibrium by diffusion during the test.

A dual-porosity simulator accounts for this effect.[15] First, a "source" term is added to each tracer material-balance equation, which now describes the flow of tracer in the well-connected pores. New material-balance equations then are written to describe the diffusion of each tracer in the local dead-end pores. The diffusion equations are connected to the flowing pore equations through the source term in the original material balances.

The new model introduces three new parameters:

  • The Sor in the dead-end pores, which is not necessarily the same as Sor for the well-connected pore space.
  • The fraction of total porosity that is in the dead-end pores.
  • A diffusion parameter that controls the rate at which tracers diffuse in the dead-end pores (this parameter is smaller for long, thin pores and larger for short, fat pores).

For details on the numerical solution of the dual-porosity model equations, consult Deans and Carlisle.[15]

Simulation of SWCT Tests in Carbonate Formations-Case 3

The field test example for Case 3 demonstrates the extreme nonidealities that are possible in carbonate formations. The test well in this case was completed in a carbonate reef structure in Alberta, Canada. Test well characteristics were:

  • Produced water cut of 99%.
  • Reservoir temperature of 133°F.
  • Lithology is vuggy carbonate.
  • Production rate of 320 B/D.
  • Perforated interval of 13 ft.
  • Average porosity of 12.8%.
  • Brine salinity of 113,000 ppm.
  • Sor (anticipated) of 20%.

Because of the low reservoir temperature and high brine salinity, ethyl formate was chosen as the partitioning tracer for this test. This was designed to be a relatively small-volume test because previous large-volume tests in the same formation had not produced definitive results and had taken many days to complete production. Because ethyl formate is highly reactive, a decision was made to try to complete the test in less than 5 days. At an injection rate of approximately 300 B/D, 20 bbl of formation water was injected carrying ethyl formate (10,800 ppm), IPA (cover tracer) (4,700 ppm), and NPA (material-balance tracer) (2,300 ppm). This bank was followed with a net push injection of 50 bbl of water containing NPA (2,300 ppm).

The well was shut in for 1.3 days to allow part of the ethyl formate to hydrolyze, producing the secondary tracer, ethyl alcohol. The well then was produced at a rate of 300 B/D for 3.0 days. Samples were taken at regular intervals and analyzed at the wellsite for ethyl formate, ethyl alcohol, NPA, and IPA. These data are plotted as concentration vs. produced volume in Figs. 5.20 through 5.24.

Fig. 5.20 shows the simulation of the NPA material-balance tracer profiles with an ideal model that assumes local equilibrium. Several features are obvious:

  • The ideal model is inadequate.
  • Although all the injected water contained 2,300 ppm of NPA, the first returns from the formation contain significantly lower concentrations.
  • The field data "tail" very badly—NPA is still being produced after 600 bbl, even though only 70 total bbl containing NPA were injected into the formation.

Figs. 5.21 through 5.24 show the dual-porosity test simulation results for each of the four tracers. The fraction of dead-end pores is 0.80 for all these simulated profiles. The Sor in both flowing and dead-end pores was 0.24. The dimensionless diffusion parameters ranged from 0.22 for ethyl formate to 0.28 for NPA and IPA.

Single-Well (One-Spot) Improved Oil Recovery (IOR) Pilot

The SWCT test can be used to evaluate an IOR process quickly and inexpensively. The one-spot procedure takes advantage of the nondestructive nature of the SWCT method.

The single-well (one-spot) pilot is carried out in three steps. First, Sor for the target interval is measured as described earlier. Then an appropriate volume of the IOR fluid is injected into the test interval and pushed away from the well with water. Finally, the SWCT test is repeated within the treated region. Typically, the entire process is completed in a few weeks, as compared to the much longer duration of pilot programs, even small-patterned ones.

The reduction in Sor observed in the postflood SWCT test is a measure of the IOR flood performance. By using several esters with different partition coefficients, it is possible to measure Sor as a function of radial position from the test well. This procedure also can be used to evaluate the stability of the IOR process because tracer test volume is increased relative to the IOR displaced volume.

  • The single-well IOR pilot concept has been applied in a number of different projects,[18][19][20][21] in the course of which the following IOR processes have been evaluated:
  • Surfactant, surfactant-polymer, and alkaline-surfactant-polymer (ASP).
  • CO2 miscible.
  • Caustic and caustic-polymer.
  • Hydrocarbon-miscible.

In every case, the process was evaluated successfully using the SWCT test. In most of these sequences, the IOR fluid injection and push steps were carried out by the SWCT test field group as a part of the field test program. A typical single-well pilot evaluation of an IOR process requires four to six weeks to complete.

SWCT Tests for In-Situ Evaluation of Hydrocarbon-Miscible IOR-Case 4

A series of SWCT tests was performed in the Aurora Field on the Alaska North Slope,[22] U.S.A., to provide an in-situ formation evaluation and to evaluate hydrocarbon-miscible IOR. The target well produced 100% oil.

The steps in the test sequence were:

  1. An SWCT test for Swc (see below under Other Field Measurements ).
  2. A multiple tracer test to determine oil/water fractional flow vs. saturation.
  3. A waterflood to reduce the near-wellbore oil saturation to near-residual conditions.
  4. An SWCT test for Sor.
  5. Injection of a bank of hydrocarbon-miscible solvent.
  6. A waterflood to displace the IOR bank away from the test well.
  7. A second SWCT test for Sor, to determine the post-IOR oil saturation in the flooded region.

Steps 4 through 7 constitute the "one-spot" pilot for the hydrocarbon-miscible IOR process.

The results of step 4 are shown in Fig. 5.25. The field data are plotted, along with the best-fit four-layer simulation model. Two nonideal effects are indicated by these data:

  • Nonreversing flow is evidenced by the early hump and the extended tail on the tracer profiles.
  • A radial gradient of oil saturation apparently was present in the formation because the waterflood of step 3 was not large enough to reduce the formation to true residual oil.

The four-layer model can account for both of these effects. The ester-weighted Sor measured in step 4 is 32 ± 3%.

The field data and best-fit simulation of the aftertest (step 7) are shown in Fig. 5.26. Again, two distinct nonideal effects are apparent:

  • Nonreversing flow again is a factor. An early hump and a tail indicate that small layers are needed to improve the fit of the simulation model.
  • In this case, the late layer, which produces the tail, also is anomalous regarding oil saturation. Whereas both of the other layers require an Sor of 6% to produce the best fit, the late layer appears to have an Sor of 26%. A likely explanation for this remarkable difference is gravity override by the miscible solvent bank. There appears to be a layer that was not contacted by the IOR bank.

Other Field Measurements

Connate Water Saturation Testing

In certain situations, it is necessary to obtain a reliable measurement for Swc in an oil reservoir. The SWCT method has been used successfully for this purpose in six reservoirs.[23] The SWCT test for Swc usually is carried out on wells that are essentially 100% oil producers. The procedure is analogous to the SWCT method for Sor, taking into account that oil is the mobile phase and water is stationary in the pore space.

Because oil is the mobile phase, it is used to carry the chemical tracers into and back out of the formation. The ester dissolved in oil is injected and then pushed away from the well. The first bank carries the ester plus material-balance tracer, as in the Sor test. The push bank contains only the material-balance tracer.

During the flow into the formation, the ester partitions between the oil and water phases. This partitioning slows the ester velocity only slightly because the ester is more soluble in the oil phase. After the push step, the ester bank is located 10 to 20 ft from the wellbore.

During the 2- to 10-day shut-in period, a portion of the ester hydrolyzes (reacts with the connate water) to form the alcohol product tracer. The product alcohol is much more soluble in the connate water than in the oil phase.

The well then is placed on production. Samples of the produced oil are taken frequently and analyzed for tracer content. The unreacted ester comes back first because it travels at nearly the same velocity as the carrier oil. The product alcohol is produced later because it travels more slowly than the oil. Because of its preferential solubility in the stationary water phase, the alcohol has a large β value compared to that of ester. The difference in arrival volumes between the ester and the delayed alcohol tracer thus is a function of Swc.

As in the SWCT test for Sor, β can be calculated directly from the concentration vs. produced volume profiles. Using the partition coefficients measured in the laboratory, Swc can then be calculated. However, the best-fit Swc result actually is determined by matching the field tracer profiles using our multilayer simulator program for the connate water test.

SWCT Test for Connate Water-Case 5

An example of a production profile from a SWCT test for connate water is shown in Fig. 5.27.[23] The target formation was in the Prudhoe Bay Field on the Alaska North Slope, U.S.A. The reactive ester injected was isopropyl acetate, which was dissolved in light diesel oil. The product tracer in this case was IPA.

The best-fit simulation model for this case used three layers, to account for the slightly nonreversing flow behavior. The injected ester-weighted average result was Swc = 0.15 ± 2%. This is in close agreement with the average Swc determined from oil-based cores on the same well.[23]

Gas-Saturation Testing

In formations where the pore space is occupied by a stationary gas phase and a mobile water phase, such as in a watered-out gas reservoir, the residual gas saturation (Sgr may need to be measured in situ. The Sgr also can be determined using a single-well injection/production test method.[24]

Sgr measurement involves injecting and immediately producing a suitable volume of water. The water used for injection typically is produced from the target well before the test and stored in tanks on the surface. During production, the amount of gas dissolved in the water (Rsw) that is produced from the formation is measured.

The injected water is essentially free of dissolved hydrocarbon gases (i.e., it is "dead"). As the injected water enters the formation that contains residual gas, the water dissolves the gas, becoming saturated at the temperature and pressure in the reservoir. A region of increasing radius around the wellbore is stripped of gas. Injection continues until a volume (VI) has entered the formation. A material-balance tracer such as methanol is added to all injected water.

At the end of the injection, the stripped region near the well is a volume of pore space that is filled with dead water (Vd). Just beyond this dead-water zone, the pore space contains the original gas saturation and gas-saturated injected water.

Immediately after injection, water is produced back from the formation through the well to the surface. The first volume of water produced is the Vd from the leached region, and so contains no dissolved gas. This dead water is followed by gas-saturated water from the region outside the stripped zone. The gas-saturated water is able to move through the stripped region without giving up its dissolved gas to reform the original gas saturation. This nonreversing behavior is the reason the method works in a single well.

After the volume of dead water is produced, the observed gas content of the produced water rises to the solubility Rsw (scf/bbl) of gas at reservoir conditions. The volume of gas-saturated water (VIVd) produced after the dead water contains the gas that was dissolved from the stripped zone. Thus, if Bg is the gas formation volume factor at reservoir conditions, the reservoir volume of gas dissolved in this fluid (Vg) is:


But this is just the volume of gas originally in the stripped zone, which is:


Equating the two and solving for Sgr:


Fig. 5.28 is a typical profile for gas content vs. produced water volume from a single-well injection test for Sgr. The volume required to produce the inflection point of the gas content profile is Vd. The final level of gas content is Rsw, the solubility of gas at reservoir conditions. These two values, along with the total injected volume VI, are the only field data required to calculate Sgr. The procedure for measuring Sgr is described in detail by Bragg and Shallenberger.[24]

Performing the Sgr test is relatively simple. The only operational requirements are that a method must be available to produce water from the formation in the test well and that there must be a way to measure the gas content of the water leaving the formation, with which the fluid lifting mechanism does not interfere. Because of the nonreversing feature, the test cannot be repeated in a given completion. The gas that is dissolved from the near-well pore space is not replaced during the production step.

This method can be used to measure either hydrocarbon gas or carbon dioxide (CO2) saturation after displacement by water, and in some cases where residual oil, residual gas, and mobile water all share the pore space (three-phase system), this test has been conducted in tandem with the SWCT test. The ester solution and push volume are added to the end of the dead-water injection. A shut-in period also is added. The Sor value measured by the SWCT test is for the two-phase (oil and dead water), gas-leached zone near the well. The Sgr obtained from the gas content profile represents the fraction of the near-well pore space filled with gas before the test injection.


This Handbook chapter has familiarized the reader with the SWCT method by presenting the essential details of its theory to establish its credibility. It also has covered the planning and execution of the field operations to show the practicality of the method, and has outlined the process of test data interpretation and applied it to real test data to demonstrate the SWCT method’s sensitivity and accuracy. High-quality fluid-saturation data always have been essential to the reservoir engineer, and in today’s challenging oil production operations, the information provided by SWCT testing methods is more important than ever before. In the coming years, this unique and intriguing method is likely to be used more widely in reservoir evaluation.


Bo = formation volume factor, oil, RB/STB
Bg = formation volume factor, gas, RB/Mscf
CA = concentration of tracer A, mol/vol
CAo = concentration of tracer A in oil
CAw = concentration of tracer A in water
CB = concentration of tracer B, mol/vol
CBo = concentration of tracer B in oil, mol/vol
CBw = concentration of tracer B in water, mol/vol
Ceo = concentration of ester in oil, mol/vol
Cew = concentration of ester in water, mol/vol
DE = effective dispersion coefficient, ft2/D
ft = fraction of time
h = thickness, ft
kH = hydrolysis rate constant (days–1) in the aqueous phase
K = equilibrium partition coefficient
KA = equilibrium partition coefficient for tracer A
KB = equilibrium partition coefficient for tracer B
Ke = oil/water partition coefficient for ester
neo = number of ester molecules in oil
new = number of ester molecules in water
q = fluid-flow rate in a single well, B/D
Qp = produced volume, bbl
QpA = volume required to produce tracer A, bbl
QpB = volume required to produce tracer B, bbl
r = radial position, ft
re = external boundary radius, ft
rw = wellbore radius, ft
RH = hydrolysis reaction rate, mol/vol-day
Rsw = gas solubility in produced water at reservoir conditions, scf/bbl
Sf = flowing fluid saturation, fraction of PV
Sgr = residual gas saturation, fraction of PV
So = oil saturation, fraction of PV
RTENOTITLE = average oil saturation in the reservoir, fraction of PV
Sor = residual oil saturation, fraction of PV
Sr = residual fluid saturation fraction of PV
Sw = saturation of water, fraction of PV
Swc = connate water saturation, fraction of PV
t = time, day
tA = arrival time of tracer A, day
tB = arrival time of tracer B, day
vA = average velocity of tracer chemical A, ft/D
vB = average velocity of tracer chemical B, ft/D
vD = fluid drift velocity in the formation, ft/D
ve = time-weighted velocity of ester
vfi = interstitial fluid velocity, ft/D
vo = time-weighted velocity of oil
vw = time-weighted velocity of water
Vc = control volume of a pore, bbl
Vd = volume of dead (gas-free) water produced, bbl
Vg = the reservoir volume of gas dissolved in gas-saturated water, scf/bbl
VI = volume of water injected, bbl
Vp = total pore volume, bbl
Vw = velocity of water
α = dispersivity
β = retardation factor
βA = retardation factor for tracer A
βe = retardation factor for ester
ΔR = radial dimension (ft) of a cell
ϕ = porosity


  1. 1.0 1.1 1.2 1.3 1.4 Tomich, J.F., Dalton, R.L.J., Deans, H.A. et al. 1973. Single-Well Tracer Method to Measure Residual Oil Saturation. J Pet Technol 25 (2): 211–218. SPE-3792-PA.
  2. 2.0 2.1 Deans, H.A. 1971. Method of Determining Fluid Saturations in Reservoirs. US Patent No. 3,623,842.
  3. 3.0 3.1 Deans, H.A. and Majoros, S. 1980. The Single-Well Chemical Tracer Method for Measuring Residual Oil Saturation, Final report, Contract No. DOE/BC20006-18. Washington, DC: US DOE.
  4. O'Brien, L.J., Cooke, R.S., and Willis, H.R. 1978. Oil Saturation Measurements at Brown and East Voss Tannehill Fields. J Pet Technol 30 (1): 17-25. SPE-6370-PA.
  5. Sheely, C.Q. 1978. Description of Field Tests To Determine Residual Oil Saturation by Single-Well Tracer Method. J Pet Technol 30 (2): 194-202. SPE-5840-PA.
  6. Thomas, E.C. and Ausburn, B.E. 1979. Determining Swept-Zone Residual Oil Saturation in a Slightly Consolidated Gulf Coast Sandstone Reservoir. J Pet Technol 31 (4): 513-524. SPE-5803-PA.
  7. Nute, A.J. 1983. Design and Evaluation of a Gravity-Stable, Miscible CO2-Solvent Flood, Bay St. Elaine Field. Presented at the Middle East Oil Technical Conference and Exhibition, Bahrain, 14-17 March 1983. SPE-11506-MS.
  8. Chang, M.M., Maerefat, N.L., Tomutsa, L. et al. 1988. Evaluation and Comparison of Residual Oil Saturation Determination Techniques. SPE Form Eval 3 (1): 251-262. SPE-14887-PA.
  9. 9.0 9.1 Donaldson, E.C. and Staub, H.L. 1981. Comparison of Methods for Measurement of Oil Saturation. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 4-7 October 1981. SPE-10298-MS.
  10. Energy Information Administration (EIA). 1980. Annual Report to Congress, Volume 3, DOE/EIA-0173(79)/3, Washington, DC (July 1979).
  11. Salathiel, R.A. 1973. Oil Recovery by Surface Film Drainage in Mixed-Wettability Rocks. J Pet Technol 25 (10): 1216–1224. SPE-4104-PA.
  12. Deans, H.A. and Shallenberger, L.K. 1974. Single-Well Chemical Tracer Method to Measure Connate Water Saturation. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 22-24 April 1974. SPE-4755-MS.
  13. Cooke, C.E. Jr. 1971. Method of determining Residual Oil Saturation in Reservoirs. US Patent No. 3,590,923.
  14. Carlisle, C.T. et al. 1982. Development of a Rapid and Accurate Method for Determining Partition Coefficients of Chemical Tracers Between Oils and Brines (for Single-Well Tracer Tests). Contract No. DOE/BC/10100-4, US DOE, Washington DC (December 1982).
  15. 15.0 15.1 15.2 15.3 Deans, H.A. and Carlisle, C.T. 1986. "Single-Well Tracer Test in Complex Pore Systems," paper SPE/DOE 14886 presented at the 1986 SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, 20–23 April.
  16. Deans, H.A. and Carlisle, C.T. 1986. Single-Well Tracer Test in Complex Pore Systems. Presented at the SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, 20-23 April 1986. SPE-14886-MS.
  17. Seetharam, R.V. and Deans, H.A. 1989. CASTEM - A New Automated Parameter-Estimation Algorithm for Single-Well Tracer Tests. SPE Res Eng 4 (1): 35-44. SPE-15435-PA.
  18. Sheely Jr., C.Q. and Baldwin Jr., D.E. 1982. Single-Well Tracer Tests for Evaluating Chemical Enhanced Oil Recovery Processes. J Pet Technol 34 (8): 1887-1896. SPE-8838-PA.
  19. Holland, K.M. and Porter, L.T. 1983. Single-Well Evaluation Program for Micellar/Polymer Recovery, Main and 99 West Pools, West Coyote Field, California. Presented at the SPE Annual Technical Conference and Exhibition, San Francisco, California, 5-8 October 1983. SPE-11990-MS.
  20. Edinga, K.J., McCaffery, F.G., and Wytrychowski, I.M. 1980. Cessford Basal Colorado A ReservoirCaustic Flood Evaluation. J Pet Technol 32 (12): 2103-2110. SPE-8199-PA.
  21. Cockin, A.P., Malcolm, L.T., McGuire, P.L. et al. 1998. Design, Implementation and Simulation Analysis of a Single-Well Chemical Tracer Test To Measure the Residual Oil Saturation to a Hydrocarbon Miscible Gas at Prudhoe Bay. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27–30 September. SPE-48951-MS.
  22. Carlisle, C.T. et al. 2002. Aurora Single Well Tracer Test (SWTT) Results. Poster presented at the SPE Western North American Region/Pacific Section AAPG Joint Meeting, Anchorage, 20–22 May.
  23. 23.0 23.1 23.2 Deans, H.A. and Mut, A.D. 1997. Chemical Tracer Studies To Determine Water Saturation at Prudhoe Bay. SPE Res Eng 12 (1): 52-57. SPE-28591-PA.
  24. 24.0 24.1 Bragg, J.R. and Shallenberger, L.K. 1976. In-Situ Determination of Residual Gas Saturation by Injection and Production of Brine. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6047-MS.

SI Metric Conversion Factors

bbl × 1.589 873 E − 01 = m3
°F (°F − 32)/1.8 = °C
ft × 3.048* E − 01 = m
ft3 × 2.831 685 E − 02 = m3
day × 1.0* E − 00 = d
lbm mol × 4.535 924 E − 01 = kmol
psia × 6.894 757 E − 00 = kPa
res bbl × 1.689 873 E − 01 = res m3


Conversion factor is exact.