SPE-172808-MS

Assessing EOR Potential from Partitioning Tracer Data

Olaf Huseby, Sven K. Hartvig, Kjersti Jevanord, and yvind Dugstad, Restrack AS, Instituttveien 18, NO-2027,Kjeller Norway

Copyright 2015, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Middle East Oil & Gas Show and Conference held in Manama, Bahrain, 811 March 2015.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright

Abstract

In development of mature oil fields using enhanced oil recovery (EOR) techniques, one of the challengesis to quantify remaining oil and to evaluate the potential gain of EOR in pilot studies. One of the proventechnologies to estimate remaining amounts of oil is the single-well chemical tracer test (SWCTT). Duringsuch push-and-pull tests, oil/water partitioning ester partially hydrolyses to a non-partitioning water tracer.A time-lag in back-production time between the injected ester and the alcohol generated in-situ yieldsremaining oil saturation (ROS) through a simple relation. A similar time-lag technique is used inpartitioning inter-well tracer tests (PITTs), where tracers are injected into injectors and sampled inproducers. New and stable, oil-water partitioning tracers suitable for oil reservoir PITTs have beenrecently developed and field tested (SPE164059), allowing measurement of remaining oil saturation ininter-well regions.

This paper reviews methodology to assess oil saturation in both near-well and inter-well regions of anoil reservoir, and highlights the differences and similarities of partitioning near-well and inter-well tracertests that can be used to evaluate the potential gain from an EOR-operation.

SWCTTs and PITTs target different scales of an oil field, as a SWCTT explores the near well zone,up to a few meters, and a PITT explore an inter-well region. In order to assess information on both thesescales we propose a systematic procedure for oil saturation measurement, using partitioning tracers. Theprocedure involves use of PITTs and systematic residence time distribution (RTD) interpretation of tracerproduction curves to extract information about remaining oil saturation and the distribution of thissaturation in an oil field. The procedure is validated using the tracer data recently reported by Viig et al.(SPE164059).

IntroductionTracers are chemical compounds that are used to label and track fluids. They can be used to monitor wells,production equipment, as well as fluid movement in the reservoir. In the reservoir, tracers can be used insingle well operations, e.g., to evaluate remaining oil in the near-well zone, or in inter-well tracer tests(IWTT), to evaluate fluid movement between injectors and producers. In the past, tracers applied in thepetroleum industry were usually radioactive, but with the development of chemical tracer technology thelast two decades, chemical tracers have largely replaced radioactive tracers. Typical chemical tracers are

fluorinated benzoic acids for water (Galdiga and Greibrokk, 1998), or perfluorocarbons for gas (Dugstadet al., 1992; Kleven et al., 1996). A general review of tracers applied in petroleum reservoirs is given byZemel (1994). A review of inter-well tracer testing is given by Dugstad (2007).

When qualifying tracers for oil or gas reservoirs several important parameters have to be fulfilled. Atracer has to be thermally stable at relevant reservoir temperatures, it has to be chemically and biologicallystable under reservoir conditions and sorption on rock surfaces should be negligible. In addition, suitedtracers must be stable during sample storage, have excellent analytical sensitivity, be environmentallyacceptable and be unique in the reservoir environment. The chemical tracers available today have beentested in a broad range of inter-well tracer testing (IWTT) applications and chemical tracer testing is nowestablished and proven as an efficient technology to obtain information on well-to-well communication,heterogeneities and fluid dynamics. During such tests, tracers are used to label water or gas from specificinjection wells. The tracers are then subsequently used to trace the fluids as they move through thereservoir together with the injection phase. Tracers are also important in development of mature oil-fieldsusing EOR-techniques, where one of the challenges is to quantify remaining oil (see e.g. Babadagli, 2007and Al-Mutairi et al., 2007 for recent reviews) and to evaluate the effect of EOR in pilot studies. Toestimate the amount of remaining oil, one of the proven technologies is the single-well chemical tracer test(SWCTT), pioneered in the US about 40 years ago by Esso (Deans, 1971). It exploits the difference intravel time between injected ester and alcohol generated in-situ by hydrolysis. SWCTTs have been usedto identify enhanced oil recovery (EOR) potential as well as to evaluate the effect of EOR in numerouson-shore fields (see Deans & Carlisle, 2007 for a recent review) and some off-shore locations (see e.g.Seccombe et al., 2008; Zainal et al. 2008; Jerauld et al., 2010; Skrettingland et al., 2011). SWCTTs havebeen used in relations to chemical EOR such as polymer, surfactant and alkaline-surfactant-polymer(ASP) floods (see e.g., Hernandez et al., 2002 ; Zainal et al., 2008; Oyemade et al., 2010; de Zwart et al.,2011). Recently there has been a growing interest in injection of low-salinity water to reduce remainingoil saturation and enhance oil production. Several pilot tests have been conducted and the SWCTT is usedin these projects to measure oil-saturation prior to and after the low-salinity water injection (see e.g.,McGuire et al., 2005; Seccombe et al., 2008; Jerauld et al., 2010; Skrettingland et al., 2011; Callegaro etal., 2014). An alternative to the SWCTT is the partitioning interwell tracer test (PITT), first proposed byCooke (1971). PITTs can be used to assess the remaining oil saturation in the interwell region from aninjector to a producer and are frequently used to investigate the presence and remediation of non-aqueousphase liquids in aquifers (see e.g Jin et al., 1995), where temperatures are moderate, compared to oilreservoirs. High temperatures greatly reduce the availability of stable and suitable partitioning tracers, andis one reason that PITTs have been rare in the oil industry (see e.g., Illiassov and Datta-Gupta for a notableexeption). In addition it has been difficult to find tracers that no not biodegrade (see e.g. Dugstad et al.,2013). Recently however, Viig et al. (2013) reported the discovery of a new class of partitioning tracersthat survive harsh petroleum reservoir conditions, that we believe is a significant breakthrough for PITTfor oil field applications.

Tracer test methodologies to assess remaining oil saturationTracer testing and tracer data qualityFor tracer testing to be useful, it is of course essential that the data are reliable. An absolute prerequisiteis that tracers are detected at the producer. The chemical water tracer used today have been extensivelytested in all kinds of reservoirs and should always be possible to detect, provided that they are injectedin sufficient amounts. In some cases (see e.g. Zaberi et al., 2013) very small tracer amounts are recovered.In fact, a low tracer recovery may suggests that water injection is effective and that injected water helpsto maintain pressure, without inducing significant water breakthrough at the producers. Working with lowconcentrations requires excellent detection limits, as measured concentrations may represent detection andquantification of concentrations down to 50 parts per trillion, i.e. 50 10-12 kg/l (Zaberi et al., 2013). This

2 SPE-172808-MS

is 1000 times lower than values reported by Cheng et al. (2012) and 10-20 times lower than valuesreported by Al-Kandari et al. (2012).

Specialized labs will typically be able to detect and quantify chemical tracers at concentrations of 50ppt or lower in most reservoirs chemical matrices. This reduces the required injected amounts (IA) andlowers material cost of tracer projects as the detection limit (DL) influence directly on injected amounts(if 100 kg tracer is sufficient at a 50 ppt detection limit, 10000 kg is required at 5 ppb to yield equivalentresults). The tracer study quality factor (TQF IA/DL) is related to the dilution volume in the tracer testand can be viewed as a measure for the risk of missing tracer detection. It is therefore an efficient mannerto compare and evaluate tracer designs. A lower TQF implies an inferior design and represents a risk thatinjected tracers are not detected (see also Figure 1a).

Another important aspect to consider for a successful tracer campaign is sufficient sampling and thatthe sampling is not ended prematurely. The data-set analyzed below contains about 60 water samples andis thus fairly robust. In general, 20-40 positive tracer data points should be sufficient to clearly define atracer curve. In the case reported by Viig et al. (2013) the sampling campaign had to be stopped somewhatprematurely. In general one should continue sampling at least until the peak of the tracer curve can beclearly identified.

Finally tracer data should always be carefully be investigated for potential contamination andre-injection. If re-injection of reservoir fluids is relevant, the re-injection contribution to the tracer signalcan be handled (see below), provided that the re-injection concentration is measured or can be estimatedfrom the tracer production curves.

Partitioning tracer conceptOrdinary water tracers are carefully designed to follow the water phase and should not interact with otherfluids or solids in the reservoir. However, in certain applications interaction with the oil in the form ofpartitioning between the oil and water phases can give information on the amount of oil remaining ina reservoir. To assess the amount of remaining oil from tracers, two tracers are used one ordinary idealwater tracer that follow the water phase, and one partitioning tracer that partitions between the oil phaseand the water phase. If water and oil moves with different velocity and if the partitioning behaviour is

Figure 1Illustration of the tracer study quality factor, TQF (left) and schematic overview of the wells (right) in the field reported by Viiget al. (2013) and summary of the main reservoir characteristics.

SPE-172808-MS 3

known, oil saturation can be inferred from the difference in arrival times of a partitioning and an idealtracer.

For negligible oil flow rates compared to the water flow-rates, the oil saturation is given by (Cooke1971)

(1)

where TR and TW are retention times for the partitioning and passive tracers, respectively, and K Co/Cw is the oil/water partition coefficient of the partitioning tracer.

Measurement of remaining oil saturation in a near well region, using a single-well chemical tracer test(SWCTT) was devised by Deans and co-workers in the 1970s (Deans, 1971; 1978), and has been morecommonly used than PITTs in the oil industry. The SWCTT exploits the same physical effect ofpartitioning as the PITT proposed by Cooke (1971). The main difference with the PITT is that thepartitioning tracer is injected from a single well and partially breaks down to an ideal tracer during ashut-in (soaking) period. The well is then produced back and difference in arrival times of the partitioningand ideal tracers used to assess So according to Eq. (1).

An important difference between the SWCTT and a PITT is the scale of the investigated region. Asillustrated in Figure 2 the SWCTT investigates a region close to the well (typically a few meters) whereasthe PITT can be used to assess saturation in a much larger region between the injector and the producer.The difference in scale is also reflected in the time scale of the tests. A SWCTT is typically performedin 1-2 weeks time whereas in a PITT results will not be available until the tracers have been producedat the producer well. Depending on the inter-well distance, this may take several weeks or months. On theother hand a PITT is carried out during normal operation of injectors and producers and does not requireany well operations except a simple injection at relevant injectors.

Figure 2Illustration of typical test zone sizes for the single well chemical tracer test (SWCTT) and partitioning inter-well tracer test(PITT).

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Partitioning inter-well tracer testIn the partitioning inter-well tracer test an ordinary, non-partitioning and a partitioning tracer are injectedsimultaneously in an ordinary injection well and then monitored at ordinary producers or observationwells. As explained above the partitioning tracer is delayed compared to the non-partitioning (or passive)tracer, as they are transported through the oil-reservoir. The time delay may be explained as analogouswith chromatographic separation between passive and partitioning tracers and is related to saturation ofa stagnant phase and the tracers partition coefficients between the flowing and stagnant phase for thetracers.

A convective dispersion equation describing the transport of a tracer in a porous media may be writtenformally as

(2)

if we assume that partitioning among the phases is an instantaneous process. Here, partitioning isdescribed by the coefficient , where is the concentration of q in phase i and Cq is theconcentration in a reference phase. For oil/water partitioning with water as the reference phase, this gives

and . Furthermore in Equation (2), is porosity, Si is phase saturation (So, Sgor Sw), vi is the velocity of phase i and is the dispersion in phase i.

If we assume a 1-D system of length L filled with oil and water, where the oil-phase is stagnant (So constant), the water flowing with a flow rate Q and negligible diffusion and dispersion Eq. (2) yields(Huseby et al., 2010)

Figure 3Illustration of the partitioning inter-well tracer test (PITT) concept. When an oil/water partitioning tracer, co-injected with anon-partitioning water tracer flows through an oil reservoir with remaining immobile oil, the partitioning tracer is delayed (a to c). Theconcentration in the produced water (d) increases first for the non-partitioning tracer, which is not delayed by immobile oil. The arrivaltime-difference is directly related to the amount of remaining oil.

SPE-172808-MS 5

(3)

Since So, Kw 1 and Ko K are assumed to be constant, we can define a constant vk Q/[(1 - So KSo)A] , and reduce the equation to a simple 1

st order wave equation with wave propagation velocityvK. If the initial concentration distribution is C0 C0(x.t0) the solution to the wave equation is C(x.t) C0(x - vKt). If we compare the solution for an ideal (K 0) to the solution for a partitioning (K 0) wefind that the partitioning tracer breakthrough time at x L(tK L/vK) is delayed compared to thenon-partitioning tracer breakthrough time (t0 L/v0) by

(4)

that we recognize as the expression given in Eq. (1). The 1-D solution is important as it supports therelation given by Eq. (1). Moreover, it can be generalized along 1-D streamlines in a reservoir and formsa theoretical basis to for Eq. (1) in a 3-D reservoir.

Single well chemical tracer testSingle-well chemical tracer tests exploit the same fundamental principle as PITTs, and uses the delay ofa partitioning tracer vs. an ideal one to assess oil saturation. SWCTTs are based on injection of an esterinto a watered out well (typically a producer that is pre-flushed with water). Some of the ester hydrolysesduring a shut-in period, and subsequent production of the ester and the alcohol produced during shut-inyield tracer production curves that can be used to find oil saturation. Commonly utilised esters in SWCTTsare propyl formate and ethyl acetate. Symbolically we can write the hydrolysis reaction as

(5)

For the specific example of ethyl acetate the relevant reaction is

(6)

i.e. a reaction where ethyl acetate (CH3COOCH2CH3) and water react and form ethanol (CH3CH2OH)and acetic acid (CH3COOH).

Simple analytical interpretation of SWCTT is possible if one assumes uniform oil saturation, negligiblehydrolysis during injection and production and assuming similar dispersion for all reservoir layers. Incomplex reservoir settings, including multilayer test zones, drift, cross-flow etc., reservoir simulation

Figure 4Illustration of the single-well chemical tracer test (SWCTT) principle. During a SWCTT, ester is injected into the formation.Parts of the ester react with water (hydrolyse) to form alcohol. During back-production (see illustration) the partitioning ester lagsbehind the alcohol and the time-difference is directly related to oil saturation in the formation.

6 SPE-172808-MS

tools, capable of handling the hydrolysis reaction is used (Jerauld et al., 2010; Skrettingland et al., 2011).In practice, coupled flow and chemical reaction simulators e.g. STARS (CMG, 2010) and UTCHEM(2000) are used.

Huseby et al. (2012) gave a simplified formulation of the relevant reaction-convective-dispersivetransport for SWCTT. This simplification assume the abundance of water and that the buffering capacityin the formations is large enough to neutralize the acid (R1COOH) effectively. The reaction can then beviewed as a decay of ester into alcohol:

(7)

with a constant reaction rate . This formulation, combined with an effective post-processingapproach to tracer simulation greatly reduces the simulation time for SWCTT and enables accuratesolutions with limited CPU-time available (Huseby et al., 2012).

Residence time distribution from tracer production curvesRTD is the distribution of times used by a population of tracer particles to travel through a medium. Thetracers represent elements of fluid that travel through different paths, and that therefore use differentamounts of time to pass through a medium. The distribution, E(t), of these times is called the exit agedistribution, or residence time distribution, of the fluid in the system. E(t) is defined from produced tracerconcentrations, C(t), production rate, Qp(t), and injected tracer amount, M, as

(8)

The unit of E is the inverse of the time unit. If a system has one injector and multiple producers j withproduction rates Qj, we can define residence time distributions between each injector and producer j as

(9)

In a closed system the normalization by injected tracer amount ensures that

(10)

where the sum is over all producers.Important information about the geometry and flow in a system can be obtained from the moments of

the residence time distribution, where the three first ones given as

(11)

The zero order moment (m0) represents the relative amount of tracer produced in production well j, thefirst order moment (m1) represents the average residence time for the tracers between the injection welland producer j and the second order moment (m2) is related to the dispersion of the tracers.

Shook (2003) and Shook and Forsmann (2005) introduced a method to characterize the flow andgeometry of a system using the residence time distribution. Briefly, two functions, the flow capacity F(t),and the storage capacity (t), can be defined as

(12)

and combined in a F - diagram to quantify a measure of the heterogeneity of the system. The sweptreservoir volume as function of time can be estimated from F(t). For a water tracer it is given as (Shooket al. 2009)

(13)

SPE-172808-MS 7

Correcting tracer data for reinjectionIn cases where produced fluid is re-injected, any contribution in tracer curves due to re-injection must beremoved. This can be done in a systematic and unambiguous manner, using de-convolution. The residencetime distribution at the outlet can be written as the convolution of the input signal and the injector-producer well-pairs residence time distribution function (see e.g. pp. 270-271 in Levenspiel, 1972)

(14)

If tracer is re-injected, with a normalized re-injection concentration denoted by Er(t), the function thatdescribes the total injected tracer is given by Ein (t) Er(t) for t 0, where the Dirac distributionrepresents the initial tracer pulse injection. Setting this into Eq. 14 and using the definition of the Diracdistribution and the commutative property of convolution integrals we find

(15)

This result states that at time t, the true tracer distribution from the delta pulse injection withoutre-injection, is given by the observed distribution Eout(t), subtracted the integral up to time t of the truedistribution and the known re-injection tracer distribution. We can thus calculate E(t) from knownquantities.

Field application of the partitioning interwell tracer testViig et al. (2013) demonstrated their PITT methodology in the Lagrave field, an onshore field located inthe South-West of France. In the following we will use the data from Viig et al. (2013) to demonstratean analytical solution approach to estimate oil saturation. During the field pilot reported by Viig et al., fourwells were operated, but here we will use results only for two of the wells (LAV-1 and LAV-2). Duringthe test all the produced water was re-injected into the reservoir and the injected water consisted entirelyof produced water, i.e. no external source of water was used for injection.

Viig et al. removed the re-injection background from their data and re-cast the tracer concentrations interms of a residence time distribution using Eq. (8) above. The effect of removing the re-injectionconcentration is significant, as can be seen in figure 8 of Viig et al.

Moment analysis of tracer curves requires normalization of residence time distributions that areintegrated to infinity. Because any tracer campaign must be ended at some finite time after injection,integration to infinity must be based on extrapolation of the tracer curves. Shook and Forsmann (2005),show that the function

(16)

is well suited to extrapolate tracer data for large times. In their case, Viig et al. found it difficult to applyan exponential fit to the data, the sampling was terminated somewhat early, and it was difficult to identifythe parameters a and b for some of the tracers in the producing wells. A different approach, based onfitting the type curve

(17)

with three parameters D0, t0, and M0, to the data, was therefore proposed and used for some of thetracers. The type function is based on solution of the tracer transport equation in simple geometries andfluid system (see e.g. Bear, 1972 and Welty & Gelhar, 1994).

Comparison of the two approaches show that they yield almost similar results and we therefore choseto use the type curve fit in the remaining of this paper. Examples of extrapolations are displayed for the

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ideal and one of the partitioning tracers in the well LAV-1 in Figure 5. The full distribution curves(including the extrapolations) are used to find the moments of the distributions in Eq. (11).

Recently, Sharma et al. (2014) developed an alternative to the exponential fitting of the tail, based ona log-normal distribution and illustrated its use based on simulated examples. It is likely that theirmethodology would also be suitable for the data reported by Viig et al.

Results from the RTD analysisRecovery of a tracer in a well is given by the zero moment (Eq. 11) of the residence time distribution. Fora given well, the recovery quantifies how much of the injected tracer is produced in that particular well.Average residence time for a tracer between the injector and a particular production well is given by thefirst moment of the residence time distribution, normalized by the zero moment .

The three first moments, the average residence time, Lorentz coefficient and swept volume for wellLAV-1 and LAV-2 are summarized in Table 1. As the extrapolation to infinity is different from that usedby Viig et al. for the 2-FBA tracer we do not find exactly the same results for the moments of thedistribution. The moments found by Viig et al. for LAV-2 were not consistent, as the residence time forthe partitioning tracers were in some cases smaller than for the ideal tracer, which is not consistent witha delay of the partitioning tracer. For the re-analysed results in Table 1 we note that this inconsistency isno longer present, as the average residence time is larger for the partitioning tracer, compared to the idealone in Table 1.

The flow capacity F(t), and the storage capacity (t), were estimated from the tracer data using Eq.(12). These functions can be summarized in F - plots (cf. Figure 6) and used to quantify the flow

Figure 5Corrected residence time distribution (filled circles) of the 2-FBA tracer (subfigure a) and the partitioning tracer (subfigureb) for well LAV-1. Real data are displayed together with the extrapolation (dashed line) of the data using the exponential fit in Eq. 16.The blue and red shaded areas illustrate the regions corresponding to real data and the extrapolation, respectively.

Table 1Summary of estimated quantities from the RTD analysis in LAV- and LAV-2.

Well Tracerm0

dimensionlessm1

dimensionlessm2

[ 104day2] [day]Lc

dimensionlessV5

[ 105 m3]

LAV-1 2-FBA 0.40 83.4 2.3 207 0.30 2.9

LAV-1 Partitioning 0.27 83.8 3.3 312 0.28 3.3

LAV-2 2-FBA 0.09 25.1 0.87 268 0.28 0.9

LAV-2 Partitioning 0.06 19.0 0.78 336 0.26 0.7

SPE-172808-MS 9

between an injector and producer. The storage capacity represents the volume accessible for flow andthe flow capacity F represents the flow.

The curves can thus be used to quantify how much of the flow occur in a certain part of the accessiblespace. This is a valuable approach to have an indication of the degree of heterogeneity of the reservoir.For a fractured rock, e.g. if large parts of the flow occur in a small fraction of the space, F would increasefast with increasing . The heterogeneity can be quantified by the Lorentz coefficient, defined by the areabetween the F - curve and the diagonal, normalised by 1/2, (see e.g. Shook et al., 2009):

(18)

Lc is zero for a completely homogeneous flow and 1 for completely heterogeneous flow (all flow ininfinitely narrow channel). Shook et al. (2009) reports Lc for a homogeneous 5-spot Lc 0.7 for thefractured Beowawe geothermal reservoir.

For the cases investigated here, all the tracers yield, Lc ~ 0.3 (cf. Table 1). This indicates that the sweptvolume between the injectors and producers is relatively heterogeneous. This corresponds well with thefact that the field is a carbonate reservoir with dominant flow channels.

Analytical solution of the tracer transportThe type curve fits given by Eq. (17) fit the data from Viig et al. (2013) very well as can be seen inFigure 5 above. The type curves are themselves based on the solution of the convection-dispersionequation in a 1-D system and it may seem somewhat surprising that the 1-D solution can be made to fitthe 3-D transport in the field. On the other hand, the relatively large Lorentz coefficient points to a fairlyheterogeneous transport, and the field is a carbonate field that may be expected to include narrow channelsor fractures that dominate transport.

To investigate further how well the transport can be described by 1-D solutions we will now considera simple 1-D system of length L with a constant oil saturation So. Assuming a constant water velocity vwa zero oil velocity vo 0, a constant dispersion Dw in the water phase and neglecting any diffusion ordispersion in the oil phase (Do 0), we can write the convention-dispersion equation (2) in the simplifiedform (cf. Maroongroge, 1994; Huseby et al., 2010)

Figure 6Flow capacity F vs. storage capacity based on the 2-FBA tracer data in LAV-1 and LAV-2. The heterogeneity can bequantified by the normalized area between the F - curve and the diagonal (Lorenz coefficient).

10 SPE-172808-MS

(19)

where v* vw(1 - So)/(KSo 1 - So) and D* (Dw(1 - So) DoKSo)/(KSo 1 - So) i.e. D* Dw(1- So)/(KSo 1 - So). With the initial and boundary conditions

(20)

this has the solution (Lenda and Zuber, 1995)

(21)

which gives concentration as function of time at the producer (x L) as

(22)

In terms of residence time distributions we thus find that

(23)

Eq. (23) is valid for both the ideal and the partitioning tracer. For the ideal water tracer, K 0, v* vw and D* Dw in Eq. (23), whereas for a partitioning tracer with partitioning coefficient K, v* vw(1- So)/(KSo 1 - So) and D* Dw(1 - So)/(KSo 1 -So). In Eq. (23) L is the distance from injector toproducer and vw and Dw can be estimated from the moments of the RTD from the measured water-tracerdata (Sahimi et al., 1986).

Solutions of the tracer transport problem, using Eq. (23) with v* and D* obtained from the momentsof the RTD, and using the known values for L (L 530 m for Lav-1 and L 1000 m for Lav-2) aredisplayed in Figure 7. The solutions for the ideal tracer is given directly from the moments of the RTDand the. For the partitioning tracer the solution must be tuned by varying the saturations until a satisfactorymatch is obtained. In Figure 7 the solution for the partitioning tracers corresponds to saturations So 0.23and S0 0.21 for Lav-1 and Lav-2, respectively. A few comments can be made to the results displayedin Figure 7. It is worth to note that the solutions are completely consistent with the model represented byEq. (19-20) and the solutions to this model given by Eq. (23). The parameters used for the partitioningtracer are found directly from the parameters estimated from the RTD of the ideal tracer, using therelations v* vw(1 - So)/(KSo 1 - So) and D* Dw(1 - So)/(KSo 1 - So). Hence the only free parameterin the solution is saturation So. This implies that the saturation can be estimated from the analyticalsolution by tuning So as the single parameter. The analytical model gives an excellent representation ofthe data, which shows that a 1-D model is sufficient to explain the flow of tracer in the field.

SPE-172808-MS 11

Finally, we note that an alternative approach to the analytical solution of the problem would be to fita curve to the ideal tracer data and estimate the values of vw and Dw. In this fit either the physics-based1-D solution represented by Eq. (23) could be used or a heuristic function such as the log-normalproposed by Sharma et al. (2014). The values for v* and D* can then be found by the relations above andused to fit a saturation.

Summary and conclusionWe have reviewed tracer test methodologies to estimate residual oil saturations focusing on thepartitioning interwell tracer test. This test was recently significantly improved by Viig et al. (2013), whointroduced several new partitioning tracers, stable and reliable at reservoir conditions.

RTD methodology is useful to interpret and quantify tracer data in petroleum reservoirs and was brieflyreviewed and re-applied to the ideal tracer and one of the partitioning tracer from the Lagrave case of Viiget al. (2013). RTD-analysis can be used to establish recovered mass and mean residence time as well asto quantify the heterogeneity of the investigated reservoir regions. One particularly appealing feature ofRTD analysis is ability for heterogeneity quantification using the flow capacity F vs. storage capacity .

The RTD-analysis was also used to assess the parameters vw and Dw from the ideal water tracer curvesin two of the wells described in Viig et al. (2013). The vw and Dw from the ideal tracer was subsequentlyused to solve the tracer transport problem for both the ideal and the partitioning tracer, using an analytical1-D model of the reservoir flow. The model matches the data very well and shows that the flow problemcan be viewed as a series of 1-D flows between the injector and the producers in the field, with close tostagnant oil. This view finds some support in the results from the heterogeneity evaluation based on theRTD, using Lorentz coefficients based on the F - curves. The heterogeneity evaluation yields Lc ~ 0.3for the wells, which represents a relatively heterogeneous system that could indicate flow along (closeto) 1-D conduits in the reservoir. The modelling yields saturations of 0.23 for LAV-1 and 0.20 for LAV-2,which is very close to the results obtained by Viig et al. (2013) using an alternative approach.

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Figure 7Solution to the tracer transport in wells LAV-1 and LAV-2. The solutions are obtained using an analytic 1-D model of the field,with stagnant oil at an oil saturation of 0.23 for LAV-1 and 0.20 for LAV-2.

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Assessing EOR Potential from Partitioning Tracer DataIntroductionTracer test methodologies to assess remaining oil saturationTracer testing and tracer data qualityPartitioning tracer conceptPartitioning inter-well tracer testSingle well chemical tracer testResidence time distribution from tracer production curvesCorrecting tracer data for reinjectionField application of the partitioning interwell tracer testResults from the RTD analysisAnalytical solution of the tracer transportSummary and conclusionReferences