Quantifying remaining oil saturation using time-lapse seismicamplitude changes at fluid contacts

Erick Alvarez1,2*, Colin MacBeth1 & Jonathan Brain21 Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK2 Shell UK Limited, 1 Altens Farm Road, Nigg, Aberdeen AB12 3FY, UK*Correspondence: erick.alvarez@shell.com

Abstract: Our study shows that time-lapse changes in the amplitude of the seismic reflection at an oil–water contact (OWC) and/or produced OWC can be used to estimate directly the displacement efficiency of water displacing oil, ED, without the need of arock and fluid physics model. From this value, it is possible to determine the remaining oil saturation if required. A preliminaryapplication is performed using several published literature examples, which are reinterpreted to assess the average ED and ensurethat the theory is consistent with expectations. Next, a North Sea field model with a known ED is used to create fluid-flowpredictions and the corresponding synthetic time-lapse seismic data. Application to these data again confirms the basic principlesof themethod and defines the accuracywhen applied to 4D seismic data. Finally, an observed 4D seismic dataset froma producingfield in the North Sea is analysed. The results suggest a displacement efficiency of between 21 and 65%with an accuracy of 3%due to data non-repeatability (with a NRMS of between 11 and 13%). Given an average irreducible water saturation of 0.32, thiscalculates the remaining oil saturations at between 24 and 53% for this field.A prerequisite for use of the proposedOWCapproachis that a discrete contact be interpreted on either the 3D or 4D seismic datasets. Therefore, successful application of this techniquerequires moderate- to high-quality seismic data and a fairly thick reservoir sequence without significant structural complexity.

Received 25 February 2016; revised 31 August 2016; accepted 1 September 2016

In this work, we consider the evaluation of the oil saturation leftbehind in a hydrocarbon reservoir after oil is displaced by water as aconsequence of natural drive oil production, or production supportedby water injection in the oil leg. This is an important objective forreservoir monitoring and surveillance, and understandably mucheffort has gone into the study of this topic in the published reservoirengineering literature over the past 50 years (Al-Harbi 2011).Remaining oil saturation (ROS) values impact our understanding ofthe reservoir’s recovery factor – a key parameter that defines thestrategy for production optimization. (Here we must distinguishbetween residual oil saturation and remaining oil saturation.Residualrelates to the end points of the relative permeability curves, whereasremaining includes all oil trapped in the reservoir heterogeneity at avariety of scales.) The distribution of ROS determines the sweepefficiency of the water displacement due to either edge or bottomwater mechanisms (Dake 2001). More generally, it identifiespossible zones of unswept, bypassed oil for future drilling, andalso the amount of oil left behind in the swept zone after production.The exact location and amount of ROS needs to be understood inorder to assess the feasibility of enhanced oil recovery (EOR)methods (such as miscible gas injection, water alternating gas,polymer flooding and surfactants) to further mobilize and extract theremaining oil. From a production perspective, knowledge of ROS isimportant for material balance, calculating production forecasts andis an essential input for the numerical simulation model.

There are many factors, acting at the microscopic (pore scale) andmesoscopic (outcrop) or macroscopic (reservoir/field) scale, thataffect the magnitude of ROS. At the smallest scale, residual oiltrapped within the pore space is immobilized by capillary forcesunder flow conditions (Fig. 1a). This residual oil saturation (Sorw)defines one of the end-points of the relative permeability of oil towater, and is the point at which oil no longer flows and oil is trappedby the invadingwater. This behaviour depends on a range of rock- andfluid-dependent factors, such as mineralogy, pore-size distributions,texture, geometry, roughness, clay content, and oil and formation

water composition. At this pore-scale, the wetting behaviour of therocks has also been identified to be of particular importance. Forexample, research by Skauge&Ottesen (2002) has shown that Sorw incore-flooding experiments decreases significantly when we movefrom awater-wet to an oil-wet reservoir (e.g. Sorw moves from 0.45 to0.04). ROS values at the mesoscopic or macroscopic scale areprincipally controlled by the geological heterogeneity (Fig. 1b), andhence are strongly related to the depositional environment. Clearly,ROS at the mesoscopic/macroscopic scale is greater than pore-scaleSorw in a fully swept region of the reservoir. Important factorscontrolling the value of ROS at mesoscopic/macroscopic scaleinclude the degree of diagenesis, cementation and trapping mechan-isms, such as laminae or cross-bedding (Pickup&Hern 2002). Faults,fractures and stratigraphic barriers also require consideration. Finally,at the field (macro)-scale (Fig. 2), zones of unswept (bypassed) oil canbe identified.Unswept zonesmayexist due to a diversionof thewater-displacement process, such as fingering and interbedding or diversionat a barrier or faulted structure. Such bypassed areas are still in theinitial oil saturation state and represent opportunities for improved oilrecovery (IOR) through infill drilling, better project management orby a change in the depletion strategy, such as production ratereductions. Such bypassed areas have been successfully identifiedfrom conventional application of techniques such as 4D seismic (seelater). Importantly, within the swept zone, there is oil not recovered bythe water-displacement mechanism and this represents a potentialEOR target, as discussed above. The focus of this current study is toextend the 4D seismic technique with the goal of identifyingremaining oil saturations in a practical manner that does not require adetailed rock and fluid physics study.

Measurement of ROS from engineering practice

Current methods to measure ROS range from laboratory experimentto open hole, and repeated cased-hole wireline or productionlogging. Teklu et al. (2013) provides a review of these methods.

© 2017 The Author(s). Published by The Geological Society of London for GSL and EAGE. All rights reserved. For permissions: http://www.geolsoc.org.uk/permissions. Publishing disclaimer: www.geolsoc.org.uk/pub_ethics

Research article Petroleum Geoscience

Published online November 1, 2016 https://doi.org/10.1144/petgeo2016-037 | Vol. 23 | 2017 | pp. 238–250

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Laboratory core-flooding tests are commonly used: where a rocksample in the shape of a cylinder is extracted from the reservoir,saturated with oil and then this is displaced by water or gas. Othertypes of measurement include centrifuge experiments, whichestablish the true residual oil saturation from the lowest achievablecapillary pressure when no further oil displacement is possibleunder capillary dominated flow conditions. Well measurements canalso be made using tools that measure oil saturation in reservoirzones that produce only water. However there is some uncertaintyassociated with these measurements. For example, resistivitytechniques are difficult to interpret in a mixed salinity (formation

and injected water) environment, or in mixed sand-shale lithologies.Single well chemical tracer tests can also provide a way ofestimating the concentrations of injected water, and hence residualoil values. Another, more recent development, is the use of porenetwork models, calibrated from digital CT images to numericallycompute the flow physics and hence relative permeabilities(Ryazanov 2012). Despite a range of methods available tomeasure ROS, it is observed that a generally accepted way topredict ROS across the field and between the wells does not exist, asit is difficult to capture the field variations with measurements basedat the wellbore (Pathak et al. 2012). No single measurementachieves a definitive result, and a combination in an integrated studyprovides the most satisfactory way of assessing the oil in place(Pathak et al. 2012). At the field scale, a whole reservoir averagemeasurement can be provided by material balance and productionanalysis (Sharma & Anil 1996). Finally, numerical simulationprovides the best current approach to capture areal and verticalvariations, and the field production-scale values (for example, Raoet al. 2013). However most approaches underestimate ROS as theydo not adequately capture heterogeneity and use conservative inputvalues of ROS (Valenti et al. 2002). Overall, values of ROS havebeen quoted as low as 0.04 and as high as 0.45, for both carbonateand clastic reservoirs (Skauge & Ottesen 2002; Vrachliotis 2012).

ROS determined from seismic data

The use of 3D seismic data for reservoir management is wellestablished, through the interpretation of reservoir structure (faultsand major bounding surfaces of the reservoir flow units) and fluidcontacts, which input directly into the determination of initial oilvolumes in the reservoir once saturations and porosities have beenassigned. The monitoring of reservoirs undergoing production andrecovery using repeated seismic surveying (the 4D, or time-lapse,seismic method) is now also firmly established by numerous casestudies over more than a decade (Jack 1998; Johnston 2013). Inparticular, it has been demonstrated that water-flooding, andassociated contact movements, are often visible in most 4Dseismic data despite the overlapping effects of pressure, temperature,salinity, geomechanical effects and acquisition non-repeatability.Indeed, water saturation changes have been detected in

Fig. 1. (a) Example of pore-scale trapping of oil due to viscous-dominated(fast) water displacement of oil. Average water saturation moves fromconnate water to predominantly water plus residual oil saturation.(b) Example of outcrop-scale trapping of oil in individual bed laminae aftera water flood (after Pickup & Hern 2002). (Saturation values are colourcoded in pdf as follows: green/yellow, oil; light and dark blue, water).

Fig. 2. Illustration of the field-scaleremaining oil saturation targeted in ourcurrent study. The water-flood (in blue onpdf) progresses from two injectors (I1 andI2) in the northern and southern downdipareas of the crestal structure, and bypassessome of the reservoir oil (zone A). Thetarget for our studies is not this unsweptoil, but the oil remaining in the zonesalready swept by water (zone B).(Figure adapted after Calvert 2005.)

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acquisition non-repeatability conditions, ranging from excellent topoor (a normalized root mean square metric of between 5 and 40%,respectively), both in onshore and offshore data, and for clastic(Marsh et al. 2003), chalk (Byerley et al. 2006) and hard rockcarbonate reservoirs (Al-Jenaibi et al. 2006). The principal use ofsuch information to date has been to identify economic infill targetscreated by bypassed pockets of mobile oil due to unexpected waterflow (Koster et al. 2000) or compartmentalization (Staples et al.2006). Other uses of 4D seismic data include evaluation of injectorperformance and subsequent intervention (Røste et al. 2009), andsimulation model updating (Gonzalez-Carballo et al. 2006; Oliveira2008). Less commonly mentioned is the need to estimate anaccurate value of ROS within the already water-swept zones(Johnston 2013; Alvarez & MacBeth 2014; Obiwulu & MacBeth2015) that impacts the economical evaluation of the displacementprocess and underpins future EOR strategies. A thoroughquantitative analysis of the 4D seismic data must draw a linkbetween the magnitude of the 4D seismic signature and theremaining oil saturations, and is the topic of this study.

The 4D seismic signature of an oil–water contactmovement during production

In this work, we attempt to estimate remaining oil saturation bymonitoring the original and produced OWCs from oil reservoirsdepleting with natural basal aquifer drive or with support fromwaterinjectors. We examine the steady upwards rise of a horizontal OWCthrough bottom water influx, and determine the magnitude of thefluid contact reflectivity before and after production using 4Dseismic data. The technique is suited to reservoirs in which the pre-and post-production fluid contacts are visible on the seismic data,and these contacts exhibit a detectable upwards movement. Selectedfield examples of such reservoirs in the published literature includeGannett C (Kloosterman et al. 2001), Nelson (McInally et al. 2001;MacBeth et al. 2005) and Alba (Tura et al. 2009), all of them fromthe North Sea. Seismic visibility of the contacts requires areasonably thick reservoir sequence, with good vertical connectivityand a mechanism for basal water drive.

The process of bottom water influx is simplified for ourcalculations as shown in Figure 3a, b. Here, we neglect thethickness of the transition zone between the oil leg (with irreduciblewater saturation) and the free water level (at 100% water saturation)relative to the vertical movement of the water contacts and overallthickness of the reservoir. We also collapse both the OWC and freewater level into one single discrete interface that we define

generically as the ‘oil–water contact’. Our simple ‘seismic’ modeltherefore assumes that the initial oil zone is saturated by water at theirreducible water saturation Swirr (the saturation below which watercannot flow), and ignores the fact that the initial water saturation ofthe undisturbed reservoir prior to production may contain formationwater that may also be produced with the oil. In this model, we alsoneglect the fluid pressure changes, as calculations show these are afactor of 10 smaller compared to the saturation changes (Alvarez &MacBeth 2014). The production state is represented by the creationof an additional ‘produced oil–water contact’. The assumptionsabove are all justifiable for seismic analysis purposes provided thatthe vertical permeability of the reservoir is relatively high (>100 mD), the API gravity of the oil (API > 30°) is also high and theseismic wavelength is long (larger than the transition zone).However, as in practice, transition zones can vary from a few metresto several hundred metres depending on the reservoir and thespecific capillary pressure curves (Ahmed 2006), the applicabilityof this model must be examined on a case-by-case basis. A finalassumption for our theoretical development is that both the originaland produced contacts are planar and horizontal, and therefore thatthe vertical connectivity is uniform – this is rarely the case for anactual reservoir owing to the hydrodynamic gradients andgeological heterogeneity. Furthermore, the seismic data couldexperience seismic travel-time variations that would prevent thecontacts from appearing flat in two-way time.

The original OWC is visible in the seismic data as a reflection in thebaseline (pre-production) data due to the fluid property contrastsbetween the oil leg (oil and irreduciblewater) and thewater leg (100%water saturation) (see Fig. 3a). This contrast may, or may not, be large,depending on the oil gravity – the lighter the oil, the stronger thecontrast. During production, as the OWC moves upwards it sweepsthrough the oil column (see Fig. 3b). The oil saturation remaining afterthis process will depend on the many factors outlined in the previoussection. There is now a seismic contrast between the unswept oil leg(oil and the irreducible water saturation) and the swept zone(remaining oil, invading water and irreducible water component),and also between the swept zone and the water leg with 100% water(MacBeth et al. 2005). These contrasts lead to seismic reflections atthe original and produced OWC (OOWC and POWC, respectively),the magnitudes of which vary according to the remaining oil. If thetwo-way time (TWT) difference is large enough to separate theseindividual reflections, then their amplitude can be used as ameasure ofthe remaining oil saturation as described below.

Reflectivity changes at the fluid contacts

For the model and assumptions defined in the previous subsection,the P–P wave reflection coefficients for the OOWC or POWCdepend predominantly on the saturation conditions above and belowthe contacts, provided that there are no significant facies changesacross the contact boundary. This condition has implications for thevariation of the reflection coefficient, R, with incidence angle, θ, ateach fluid–fluid interface within the same porous rock. Some ofthese characteristics have been explored by Wright (1986) in aprevious theoretical development based on the fluid substitutiontheory of Gassmann (1951) and the reflection coefficient approx-imations of Shuey (1985). This work showed that the P–P amplitudevariation with θ in the case of fluid–fluid contacts takes a simpleform. He concluded that reflection coefficients R(θ) at gas–brine,gas–oil or oil–brine contacts (that are all naturally positive at normalincidence) always increase monotonically with θ : that is, becomebrighter and more positive with angle/offset. To first-order inimpedance, and for small density contrasts (< 10%), this increase isfound to be independent of VP/VS and is given by:

R(u) ¼ R0(1þ sin2 u) (1)

Fig. 3. Schematic of the idealized ‘seismic model’ and associated fluidsaturations used in this work to compute fluid contact reflectivity. (a)Initial state of the reservoir prior to production. In the oil leg, Sw = Swirr,So = 1− Swirr; in the water leg Sw = 1. (b) After production, where the basewater has displaced the OWC upwards to a new location. In the sweptzone, Sw = 1−ROS, So = ROS. OOWC, original oil–water contact;POWC, produced oil–water contact.

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The reflectivity is thus controlled by the normal incidence reflectioncoefficient R0 scaled by an angle-dependent factor. This behaviouris also confirmed for our current study in Figure 4a, b, which plotsthe reflection coefficients for a range of fluid saturation jumps acrossthe OOWC and POWC against (1þ sin2 u) for angles up to 30°(seealso Table 1). Despite the exact reflection coefficients (solid curvesin Fig. 4) being calculated here using the plane-wave equations citedin Aki & Richards (1980) (also see Zoeppritz 1919), and not smallcontrast approximations as in Wright (1986), the trend identified is

still broadly valid (compare the dotted linear approximations anddashed quadratic approximations with the solid exact solutions inFigure 4). We also observe that the reflection coefficients for theOWCs are typically in the range 0.01 – 0.10. Such magnitudes arealso noted by Marsh et al. (2003) for a wide range of North Seafields. To develop these findings further for our desired objective ofestimating ROS, we first write the P-wave impedance as a functionof the water saturation, Sw, introduced into an initially oil-filledreference rock

I(Sw) ¼ I0(1þ aSw þ bS2w) (2)

where I0 is the impedance for the saturation state of Sw = Swirr, andthe terms in parentheses give the departure from this referencesaturation state. We approximate the impedance using a quadraticfunction, and find this to be reasonable for most fields analysed todate (Mavko et al. 1998; Alvarez 2014). The coefficients a and b aredetermined theoretically with a Gassmann fluid-substitutionexercise for a range of initial rock and fluid conditions. Thealternative to calibrating by regression to laboratory data wouldinvolve a representative sample initially saturated with oil, andtherefore would be difficult to obtain in practice. From the aboveand following Alvarez & MacBeth (2014), the angle-dependentreflection coefficient R(u) can be calculated to first order as:

R(u) � aDSw1

2sec2u

� �(3)

where ΔSw is the contrast in water saturation across the interface. Weneglect the higher-order terms in the saturation change for now, asthey contain complicated combinations of a, b, Swirr and ROS, anddo not lead to intuitive results that may be easily applied in practice.The full analytic expressions for the coefficient a are shown inAppendix A. Figure 4a, b shows that the linear approximation inequation (3) agrees with the full numerical computation from theZoeppritz result to a reasonable degree. For reference, the slightlymore accurate approximations with the quadratic ΔSw term are alsoshown. Importantly, equation (3) predicts a relatively uniformspacing of R(θ) with ΔSw for any fixed offset/incidence angle,which has implications for the practical understanding of the fluidcontact reflectivity, and we therefore continue with the seismic datadevelopment using this linear approximation.

In our model of contact movement, as the OWC moves upwardsthrough the oil column it leaves behind the remaining oil saturationROS in the water-swept zone. The seismic reflection from theoriginal OWC (OOWC) location still remains after this contactmovement, but will be diminished. The reduction is also related tothe emergence of the produced OWC (POWC). To quantify thisrelationship, equation (3) is applied to the angle-dependentreflection coefficients (or migrated amplitudes from angle stacks)prior to water sweep, giving:

RbeforeOOWC � a(1� Swirr) (4)

and

RbeforePOWC ¼ 0 (5)

where Swirr is the irreducible water saturation in the oil-saturatedportion of the reservoir, Rbefore

OOWC and RbeforePOWC are the reflection

coefficients of the OOWC and POWC contacts interpreted in thepre-production baseline. After movement of the OWC (monitor),the reflection coefficients are now:

RafterOOWC � aROS (6)

and

RafterPOWC � a0(1� ROS� Swirr) (7)

where a and a′ are defined in Appendix A (equations A8 and A9). In

Fig. 4. Variation of P-wave reflection coefficient (RPP) with 1 + sin2θ(where θ is the incidence angle), for (a) the OOWC and (b) the POWC.Curves represent different fluid saturation conditions at each contact, butthe same homogeneous rock. For each curve in (a), different fluidconditions lie over the water leg: (1) oil with Swirr = 20%; (2) swept zonewith Sorw = 60%; (3) swept zone with Sorw = 40%; and (4) swept zone withSorw = 20%. For each curve in (b), an oil leg with Swirr = 20% lies over thefollowing three scenarios: (1) a swept zone with Sorw = 20%; (2) a sweptzone with Sorw = 40%; and (3) a swept zone with Sorw = 60%. Colouredcurves represent the exact solution computed from Aki & Richards(1980), dotted lines represent the linear approximation and dashed linesare the quadratic approximations. Table 1 shows the seismic propertiesused for each of the saturation conditions above.

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these equations, we neglect the fluid pressure changes, as these aresmall compared to the saturation changes (Alvarez & MacBeth2014), which is a valid assumption when working above the oilbubble point pressure (as there is no liberated gas).

Inspection of these formulae reveals that if a baseline seismicdataset is acquired prior to contact movement, and a monitor datasetacquired after production-induced movement, then time-lapsechanges in the reflection coefficients for the OOWC and POWCare proportional to the maximum water saturation change(1� ROS� Swirr), but of opposite sign – this observation in itselfis a useful control when visually inspecting the seismic data forapplication of these equations. Furthermore, equation (6) indicatesthat the reflection coefficient at the OOWC after water sweep isdirectly proportional to ROS. Unfortunately, immediate practicaluse of the above equations as a direct indicator for ROS is maskedby lateral variations in the reservoir rocks and the initial fluidconditions, the imprint of which is carried into the reflectivity viathe spatially varying coefficients a and a′. In practice, waveletscaling must also be considered when interpreting the amplitudes inthe seismic volume. The scaling for each reflection coefficientcannot be independently determined using equations (2)–(5) as, ingeneral both ROS and Swirr are uncertain. One approach is to assessthe variability of a and a′ theoretically (e.g. see Alvarez 2014 andAppendix A of this paper). Alternatively, equations (5) and (6) doallow us to determine the much sought after mesoscopic/macroscopic displacement sweep efficiency, ED, defined by theratio of (1� Swirr � ROS) and (1� Swirr); this can be obtaineddirectly from the seismic data by taking a ratio of the reflectionamplitudes (on the assumption of adequately cross-equalizedseismic data):

ED ¼ RafterPOWC

RbeforeOOWC

� c1� Swirr � ROS

1� Swirr(8)

This requires the POWC on the monitor seismic data and theOOWC on the baseline seismic data to be picked, and theconstant c, which is a function of the fluid compressibilityand is typically a value between 0.85 and 0.95 (Appendix A),to be evaluated. Alternatively, only the OOWC may be picked,and the reflection amplitude before and after production usedto determine:

RafterOOWC

RbeforeOOWC

� ROS

1� Swirr(9)

or the sweep efficiency

ED ¼ RbeforeOOWC � Rafter

OOWC

RbeforeOOWC

� 1� Swirr � ROS

1� Swirr(10)

which requires only one contact on the seismic volume (the mostvisible) to be picked and is, therefore, less time-consuming.

The sweep displacement efficiency, ED, is a general qualityindicator for the water-flood progression, and is a useful metric toextract from the seismic data (Obiwulu & MacBeth 2015). Such

information is important when assessing a water injectionprogramme and remaining reserves, and for modifying thesupport strategy for sweep optimization. However, if it is necessaryto obtain an estimate of ROS directly from seismic data using theequations above, accurate knowledge of Swirr and its distributionacross the reservoir. Initial water saturation may be obtained fromthe analysis of resistivity logs, combined with estimates of porosityand capillary pressure curves from core flooding and othermeasurements that lead to saturation height functions. If there issufficient confidence in these estimates, then ROS can be obtainedfrom either equation (8) or equation (10). However, if Swirr is notknown with any more accuracy than ROS (as is the case when nocore measurements or water samples are available), one alternativeis to link both parameters together in a common estimate. This relieson the fact that the initial water-wet state is strongly influenced byrock texture, which in turn is controlled by the depositionalenvironment – suggesting a common origin for the rock and fluidphysics. Thus, fine-grained (lower-permeability) sediments usuallycharacteristic of low-energy depositional environments tend to havehigh Swirr, and coarse-grained (higher-permeability) sediments fromhigh-energy environments tend to have low Swirr. Complementarily,ROS is known (Humphry et al. 2013) to be a function of wettabilityrather than of pore structure, as the wettability influences how oil istrapped and controls the capillary forces required to remobilize theoil. In general, ROS is expected to be lower in strongly water-wetsystems (high Swi) and slightly higher in strongly oil-wet systems(low Swi). Note that the lowest ROS is found in mixed-wet rocks andlarge pores, whereas in small pores the above trends are generallyweak (Skauge & Ottesen 2002). In addition, there is some evidence(Maldal et al. 1998) that a linear relationship exists between theinitial oil saturation (hence, irreducible water saturation) and theremaining oil saturation in both clastic (Davies et al. 1993) andcarbonate (Verma et al. 1994; Masalmeh 2002) reservoirs. With alinear relationship between the two quantities defined from othercore or log data, it is then possible to use equations (9) and (10) todetermine Swirr and ROS together.

In cases where the first-order approximation for R0 as in equation(3) is not valid, such as in reservoirs close to the bubble point orwhen multiple fluid phases interact in reservoirs close to the seismictuning thickness, higher-order terms depend in a complicated wayon a, b, Swirr and ROS. Indeed, for our particular case study,Figure 4a, b shows a decrease in the separation of the R(θ) curveswith increasing water saturation. However, calculations by Alvarez(2014) show that this decrease in separation is easily predictable inpractice, and varies depending on the contrast between the oil andwater properties and on the stiffness of the rock matrix. Second-order terms contain differences and sums of the saturations, anddirect simplification is not easily obtained or not particularly useful.Instead, to increase accuracy by capturing the variability of ROS,the most direct approach is to calculate the reflectivity ratios inequations (9) and (10) as a function of 1− Swirr and ROS. Thisapproach will be used in the synthetic and observed examples in thefollowing subsections, which have been selected as they fall withinthe requirements of the assumptions of this study.

Table 1. Seismic properties used to calculate the reflection coefficients for the original and produced oil–water contacts (OOWC and POWC, respectively)shown in Figure 4

Oil leg Swept zone 1 Swept zone 2 Swept zone 3 Water leg

VP (km s–1) 2.563 2.583 2.626 2.699 2.834VS (km s–1) 1.382 1.378 1.375 1.372 1.368ρ (g cm–3) 2.053 2.066 2.076 2.086 2.096

These relate directly to the North Sea field example studied in this paper. Fluid properties are calculated using Han &Batzle (2004), and saturated rock properties via Gassmann (1951).Final values of the rock and fluid parameters are calibrated against wireline logs for the field. In these calculations, fluid pressure changes are ignored. The oil leg has a connate watersaturation of 12.8%. Swept zones 1, 2 and 3 have residual oil saturations of 60, 40 and 20%, respectively.

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Literature example 1

To illustrate use of the approach outlined above, we initiallyconsider two previously published examples. The first is from theGullfaks Field in the Northern North Sea. This field is structurallycomplex, and consists of early–middle Jurassic age reservoirs fromthe Brent sequence. Despite the field complexity, there is adetectable water sweep in response to production and waterinjection, and a uniform rise of the OWC in most reservoir units.As strong production effects are observed across the field, the 4Dseismic is widely used as part of an IOR programme to detectundepleted areas for infill drilling and to construct flooding maps(Talukdar & Instefjord 2008). Repeated saturation logs help tocalibrate the fluid movements and confirm the interpretations offluid contacts observed on the 4D seismic data (El Ouair & Stronen2006). Figure 5 shows the Top Tarbert Formation (top reservoir) andthe associated OOWC. The top reservoir dims significantly inresponse to increased water saturation, whilst the OWC also dimssubstantially and there is the appearance of a POWC. According toMaldal et al. (1998), the Tarbert reservoir rocks are mixed wet, withlow-viscosity oil in a thick oil zone, and good vertical communi-cation. These conditions allow gravity effects to play a role in therecovery process, leading to a high recovery and low residual oil.Indeed, laboratory measurements have determined ROS values aslow as 14% in the Tarbert and as low as 9% in the underlying Etivereservoir formation. Based on core-flooding tests, the followingrelationship exists for Gullfaks between the initial water saturation,Swi, and the residual oil saturation towater sweep, Sorw (Maldal et al.1998):

Sorw ¼ �1:6 Swi þ 0:7 (11)

This gives Swi = 0.35 for a residual oil saturation of 0.14. Applyingequation (10), this leads to a displacement sweep efficiency of 78%.The small amplitude observed at the OOWC is consistent with thisresult.

Literature example 2

The second example is from the Gannet-C Field in the Central NorthSea. This consists of a rim of Tertiary-aged turbidite reservoirs, dip-closed around a piercing salt diaper. The sands of the Forties andLower Tay Formation are high porosity (28%), relatively clean andwith a fraction of intra-reservoir shale stringers. There is a thick oilleg of 100 m overlain by a substantial gas cap (Kloosterman et al.2003). The oil is light, with an API of 38°. The seismic sections

shown in Figure 6 are pre-production (1993) and after several yearsof production (1998). The first 4D seismic monitor was acquired toidentify undrained or bypassed hydrocarbons in reservoir compart-ments, sealing and non-sealing faults, and the efficiency of the drivemechanisms and connected volumes to specific wells (Staples et al.2006). There is known to be good communication in the reservoirsands and reasonable aquifer support, leading to full-contact rise inboth the Forties and Lower Tay reservoirs. In addition, the seismicdata show clear and individual fluid-related reflections for the gas–oil contact (GOC) and the OWC before and after production(Fig. 6). Indeed, the fluid contacts are sufficiently clear for thecontact heights to be used directly to history match the simulationmodel (Staples et al. 2006). Figure 6 shows a weak POWC,moderate dimming of the OOWC and an upwards tilt of the GOC.The OOWC is visually estimated to dim by only 25%. Based on aconservative Swirr of 0.20, equations (4) and (6) therefore give aROS of 0.60, and equation (7) predicts that the POWC should be aquarter of the reflection strength of the OOWC before production(assuming a = a′). From equation (10), the overall sweep displace-ment efficiency would therefore be 25%. The ROS estimate is muchhigher than those quoted by Koster et al. (2000) for the entire field,but is consistent with the relative reflection strengths for the fluidcontacts in Figure 6. As Staples et al. (2006) mentioned thedisappearance of the OOWC after production on this field, there isthe suggestion that much lower ROS values exist elsewhere.

Synthetic example

To evaluate our approach further in an ideal situation where theanswer is already known and there is an absence of non-repeatabilitynoise, processing artefacts and significant heterogeneity, weconstruct a simulation model based loosely on the Gannett-CField example in the previous subsection. The reservoir modelparameters for this model are given in Tables 2 and 3. For thereservoir scenario we choose two dipping juxtaposed sandstonereservoir units with mean sand porosities of 27 and 29%, and net-to-gross ratios (NTG) of 0.70 and 0.90, respectively, lying against asalt dome. Both porosity and NTG are varied both vertically andlaterally within each unit, using a geo-statistical model, and theselead to corresponding variations in Sorw from 0.18 to 0.37 and Swirrfrom 0.12 to 0.15. In turn, this leads to an irregularly producedOWC and a variation in the displacement efficiency, ED, within andalong each unit. There are two producers in the field, and there areno injectors, The main production mechanism is edge aquifer drive,

Fig. 5. Example of contact movement fromthe literature. (a) Seismic data acquired in1985 prior to production, showing topreservoir reflection (red line on pdf) andthe OOWC (green horizontal line on pdf).(b) Seismic data in 1999 after productionand OWC movement, showing a vestige ofthe OOWC (black circled) and the POWC(green circle on pdf). (c) Illustration of theinterpreted fluid contact movement overthe 14 year period. Adapted from El Ouair& Stronen (2006) and El Ouair et al.(2007). (For the seismic traces on pdf: redand yellow, negative reflection coefficient,with yellow being the largest; blue andblack, positive reflection coefficient withblue being the largest.)

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and the wells receive good support from the aquifer. The resultantwater, oil and gas saturations for fluid-flow simulation before andafter 12 years of production are shown in Figure 7. Figure 8 givesthe resultant saturation changes, calculated displacement efficiencyand residual oil saturation for a section through the model, whichshould be compared with the estimates from the seismic data. Thereis a pressure change from 20 to 19 MPa during production, but thisdoes not affect our results significantly. The synthetic seismic dataare now created by applying the sequence of petroelastictransformation followed by convolutional modelling described inAmini et al. (2011). The seismic data are calculated at the samescale as the simulation model cell, resulting in a trace spacing of12.5 m. The corresponding synthetic seismic sections are shown inFigure 9a, b. Interestingly, although the top, base and intra-reservoirreflectors dominate the response, the flat spots associated with thecontacts can still be detected in the separate baseline and monitor

seismic sections. The anticipated dimming of the OOWC isapparent in the seismic data, together with the strong and obviousPOWC varying in elevation above the OOWC by up to 60 m withineach unit. The OOWC is picked on the baseline seismic data at afixed depth location, and the RMS amplitude for the contact isdetermined using a 10 ms symmetrical window. Equation (10) isthen applied to determine the displacement efficiency from theseismic data (Fig. 10b), and this is then compared with the modelresults in Figure 10a. The results estimated from the seismic dataagree fairly closely with the actual values, with an RMS error of 8%,but rising in some places to 20%. Small differences betweenthe seismic estimates and actual data arise from errors due to thedifferent way in which the model and the seismic sample thereservoir. The larger errors appear in regions where the reservoirthickness drops below tuning, and also where the NTG is low.

Field data example

The theory developed above is now applied to a Central North Seadataset that has readily identifiable OWCs in both the baseline andmonitor seismic data.

Background

The reservoirs in this field consist of a series of turbidite sandcomplexes deposited around a structural high associated with saltmovement at depth (Staples et al. 2007). The structure is dip closed,and characterized by crestal faults. There are three reservoirpackages, with the main Forties sandstone being the focus ofattention in our study. This is chosen because it is good-qualitysandstone with a high NTG of 90%, porosity of 26% and averagepermeability of 600 mD. Importantly, the Forties reservoirthickness (mean of 34 m) is significantly above the tuning thicknessacross most of the field. In addition, it is known from previous

Fig. 6. Time-lapse seismic data and theirinterpretation for the northern part of theGannet-C Field. (a) Seismic section priorto production in 1993 showing clear fluidcontacts – horizontal segments are inyellow. (b) Seismic section in 1998 afterproduction, with an additional producedoil–water contact (POWC). (c) & (d)Schematics illustrating the interpretation ofthe fluid contacts on the seismic data.Figures adapted after Kloosterman et al.(2003).

Table 2. Reservoir properties used for the synthetic model example inFigures 8–12. Main reservoir parameters for the model

Model dimensions 1.5 × 2 × 0.03 kmCell size 12.5 × 12.5 × 10 mOil gravity 37 ° APIInitial pressure 20 MPaFinal pressure 19 MPaUpper Tay mean porosity 29%Upper Tay mean NTG 90%Forties mean porosity 27%Forties mean NTG 87%Gas cap Swirr 15%Oil zone Swirr 15%Gas cap Sgro 25%Oil zone Sorw 30%

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studies that water sweep is clearly visible in the Forties sandstone,and that there is a good impedance contrast between the formationwater and the light 37° API oil. The 4D seismic data indicate that thefield is produced largely by bottom drive, with the west of the fieldbeing particularly strongly swept by the aquifer. The impact of waterreplacing oil on pressure is believed to be minimal owing to goodpressure support from regional aquifers (Lynn et al. 2014).However, pressure support in the reservoir as a whole is weak dueto shales and baffles, and the total depletion over 13 years asmeasured in the wells is about 3 MPa (450 psi). The reservoirpressure is still above the bubble point pressure. This leads to a slowupwards movement of the OWC over many years.

A pre-production baseline was shot in 1997, followed by monitorseismic surveys in 2006 and 2010: 9 and 13 years after production.The seismic data repeatability is excellent, with a normalized rootmean square metric (Kragh & Christie 2002) for the final migrated2006 – 2010 data of 11%, and 13% for 1996 – 2006. The field wasoriginally developed in 1997 with one vertical well (W1 in Fig. 11),which produced dry oil for nearly 1 year before starting to producewater, reaching up to 60% water cut by the time of the first monitor.

Table 3. Reservoir properties used for the synthetic model example inFigures 8–12. Seismic properties for the end-member saturation regimes*

Oil leg Water leg Gas legUpper TayVP (km s–1) 2.573 2.869 2.408VS (km s–1) 1.429 1.459 1.470ρ (g cm–3) 2.141 2.166 2.001FortiesVP (km s–1) 2.576 2.878 2.421VS (km s–1) 1.447 1.463 1.464ρ (g cm–3) 2.146 2.168 2.001ShalesVP (km s–1) 3.247VS (km s–1) 1.705ρ (g cm–3) 2.073

*Values range between these end-member values in the modelling exercise.

Fig. 7. Model structure and contacts for our synthetic example. Fluidsaturations are displayed with a ternary colour bar for the fluid saturations:(a) baseline condition; and (b) condition at the time of the first seismicmonitor survey. PGOC, produced gas–oil contact; OGOC, original gas–oilcontact – these particular contacts are not relevant to our current analysis.

Fig. 8. Results of fluid-flow simulation after 12 years of production: (a)water saturation changes; (b) the computed displacement efficiency forthis model; and (c) the known remaining oil saturation in this model.

Fig. 9. Time-lapse seismic data corresponding to our synthetic model,calculated using simulator to seismic modelling. (a) Seismic section priorto production showing the original gas–oil contact (OGOC) and theoriginal oil–water contact (OOWC). (b) Seismic section of the monitorsurvey data after 12 years of production, with an additional produced oil–water contact (POWC).

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A horizontal infill well (W2 in Fig. 11) was then drilled in theForties based on 4D seismic data (Staples et al. 2007). Surprisingly,W2 produced dry oil for about 3 years, much longer than W1, and

by the time of the second monitor it still showed a low water cut ofonly around 20%. Special core analysis tests were taken in well W1,providing core-scale values for the irreducible water saturation Swirrof 0.32 and a residual oil value Sorw of 0.22, or an ED of 68%. It isknown that as the Forties reservoir contains internal heterogeneitysuch as intra-reservoir shales, the field-scale measurement of ED

will be lower than this core-scale estimate.

Results of ROS calculation

Figure 11 shows seismic sections along a traverse through bothwells W1 and W2 for the baseline and monitor times. In the Fortiessandstone, the original fluid contact is clearly visible in the pre-production baseline seismic data (Fig. 11a), and this is confirmed bywell measurements. A clear dimming of the OOWC is observedover time, which becomes progressively dimmer whenmoving fromthe first to the second monitor survey. There is a significant

Fig. 10. Displacement efficiencies for thesynthetic example calculated: (a) directlyfrom the simulation model using ED = (1−Swirr− Sorw)/(1− Swirr) averaged over a10 m window about the known OOWC;and (b) from the seismic data usingequation (9) and applied to the RMSseismic amplitudes calculated in a 10 mssymmetric window about the pickedOOWC reflection. The dashed line A–A′corresponds to the seismic section inFigure 9. Note that the shapes are due toshales between the reservoir units (darkblue on pdf).

Fig. 11. Vertical sections along a traverse (A–A′ in Fig. 13) through thefield that intersects wells W1 and W2. (a) Baseline pre-production seismicdata in 1997 showing the position of the OOWC in time (light bluehorizon); (b) First monitor survey after 9 years of production in 2006showing the position of the POWC as interpreted from the 4D differencesection (Fig. 12). Well W2 was drilled after these results; (c) Secondmonitor in 2010 after 13 years of production and including productionfrom well W2. The new interpreted position of the POWC is marked by thedark (blue on pdf) horizon. All sections are drawn with the same amplitudescale. Well W2 is not present in (a) and (b) above, so is drawn as a thincurve for reference. Major timing lines are 100 ms two-way time apart.

Fig. 12. Vertical sections for the same traverse as shown in Figure 11. (a)Monitor 1 – base section (after 9 years of production) showing the positionof the OOWC and POWC1. W2 was drilled based on these results. (b)Monitor 2 – base section (after 13 years of production and includingproduction from W2), the new position POWC2 is marked by the dark(blue on pdf) horizon. Major timing lines are100 ms two-way time apart.

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dimming to almost zero to the west, but to the east the dimming isless pronounced and the contact movement is small. The POWCsfor monitor 1 and 2 are difficult to identify on the individualsections, but are quite clear on the difference sections (Fig. 12). Weuse the OOWC picked on the baseline seismic to measure themapped RMS amplitudes for the baseline, monitor 1 and monitor2. A 10 ms window was used after testing the window sizecompared to the reservoir thickness (Fig. 13). A displacementefficiency calculation was then performed for the picked OOWCusing the approximation in equation (10). Unlike our previoussynthetic data, this pick is not possible everywhere – Figure 13shows the limits at which the pick is no longer visible due to tuningwith the top reservoir. The resultant maps of displacementefficiency are shown in Figure 14 for each of the two monitors.Displacement efficiency for the first monitor period shows that oil isswept from the NW towards the well W1. The second monitorshows that after W2 was drilled, the eastern side of the field is alsobeing drained. The maximum efficiency is 65%, which is consistentwith the 62% from special core analysis (SCAL) measurements

(Alvarez 2014), indicating that water sweep of the light oil in thisreservoir is fairly efficient, although there is still oil remaining. Theresults show that there are some small areas of low efficiency insidethe confidence area (to the west and a small area in the NE) and alsoin the middle of the reservoir – based on well interference tests, it isbelieved the latter are related to small baffling faults. Such regionscould be potential targets for future EOR.

Discussion

Application of our theory to observed seismic data has highlightedseveral points to be considered for future implementation of thistechnique. First, the method for oil displacement efficiencydescribed in this work is limited to seismic data for which theOWC is clear and identifiable, and the contact movement can bereadily resolved either on 3D or 4D seismic data. The OWC isinterpreted on 3D seismic data as an approximately flat amplitudeevent (flat spot) that is unconformable with the adjacent reflectionsand extends over an area bounded by the structural contours.

Fig. 13. Map of the RMS amplitude extractions at the OOWC picked forthe baseline, and two monitor seismic surveys. The amplitudes of thepost-stack volumes are extracted within a 20 ms window around theinterpreted OOWC. A–A′ is the traverse considered in Figures 11 and 12.The dashed line boundary delineates the area within which the pick of theOOWC is reliable.

Fig. 14. Maps of displacement efficiency (ED) calculated from the RMSamplitude maps in Figure 13 using equation (9). The dashed lineboundary delineates the area within which the pick of the OOWC isreliable.

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However, as the reflection coefficient at the OWC is almost an orderof magnitude lower than the coefficients of the surroundinglithology contrasts (e.g. 0.02 as opposed to 0.2), it is often hard todistinguish fluid contrasts and fluid changes in the presence oflithology changes and noise. Nevertheless, fluid contact interpret-ation can always be supported by well logs from control wells andthen extrapolated across the field. The OWC is more visible on high-quality seismic data, and for thick reservoirs with good reservoirquality (i.e. high permeability, porosity and low shale or cementcontent, and younger sediments) and light oils with high API (30° –40°). A moderate dip of the reservoir structure also helps inidentifying the contact reflection. Factors that obscure detectioninclude irregular illumination, multiples, imaging uncertainties dueto velocity variations, lateral variations in facies or hydrodynamicgradients. Furthermore, fluid contacts are more likely to be visible inyounger shallow reservoirs than old highly compacted reservoirs:for instance, fields such as Alba in the North Sea with Tertiary-agesediments show a clear contact (Johnston 2013), whilst the JurassicGullfaks Field exhibits a discontinuous OWC (Landro & Stronen2003). Exceptions to the trend of geological age include theimpressive 9 km-long OWC observed in the Jurassic Troll Fieldreservoir using 2D data (Brown 2011). According to the manypublished case studies in the literature, OWC reflections aregenerally quite visible in seismic data from both clastics andcarbonates, and for a range of sediment age, although we must oftenwork hard to reveal their presence.

In 4D seismic data, changes in saturation are much more easilyobserved; as in order to observe distinct contact movement and theseparate appearance of the POWC there must be sufficient verticalmovement (and reservoir thickness) to produce distinct reflections.In practice, there is greater contact movement if the verticalpermeability is good, the reservoir volume is large and the aquiferconnectivity is high. An important observation is that even if fluidcontacts are not visible on the 3D seismic data, it is still possible toobserve and interpret them on the 4D difference data (Osdal et al.2006; Staples et al. 2006; Alvarez 2014). Indeed, water saturation-related changes are usually clearly observed in 4D seismic data,especially around water injectors or in areas of strong aquifer influx(e.g. Johann et al. 2009). The technique proposed in our study cantherefore also be used around water injectors (Obiwulu & MacBeth2015). For low-permeability reservoirs, such as chalks (Byerleyet al. 2006), the transition zone may be of significant thickness and,hence, Figure 3 is no longer appropriate. Of concern for the methodproposed in our study is a thin reservoir or small contact movement(i.e. < 10 m in our current work). An example of this would be theNelson Field, for which the seismic wavelets from the produced andoriginal contacts interfere at many locations (MacBeth et al. 2005).In the context of our study, the interpretation of interfering waveletsfrom each contact must attempt to unravel the composite effect ofROS on both amplitudes and time-shifts (Alvarez 2014). Such anapproach could be of benefit in refining vertical connectivity maps,such as those of MacLellan et al. (2006). The exact resolution willbe strongly case-dependent.

Finally, it should be noted that the GWC by comparison with theOWC is bright (much higher reflection coefficient) and flat, andmany clear case examples have been published, particularly fromthe Tertiary sediments of the Gulf of Mexico (Backus & Chen 1975;Brown 2011). Direct observation of hydrocarbon fluids from bright/flat spots is very well established in Tertiary clastic basins, of whichthe Gulf of Mexico is the most extensively studied, although thereare also a large number in older reservoirs. GWCs in thick reservoirsin offshore clastic therefore provide the easiest targets, whilst otherreservoirs represent a gradation of successively more elusive targets.OWC-related flat spots are much less commonly seen than brightspots, and the majority of flat spots are GWCs in gas reservoirs. Theabove suggests that further application for the technique proposed in

our work could be to a gas reservoir and analysis of the remaininggas saturation. For this, a relationship similar to in equation (6) mustbe established – in the case of a GWC or GOC, this is unlikely to belinear for the saturation change.

Conclusions

A method to obtain estimates of the efficiency of water displacingoil in the hydrocarbon reservoir from 4D seismic data is theoreticallydeveloped and tested in both synthetic and real data examples. Thismethod does not require an in-depth analysis of the rock and fluidphysics, therefore it is relatively simple and quick to apply on thedata, requiring only the additional picking of fluid contacts on thedatasets, and a calculation based on their amplitudes. The efficiencyfactor, ED, is linked to both the irreducible water saturation and theremaining oil saturation in the reservoir. The spatial distribution ofED is one of the key quantities for reservoir management purposesand, in particular, is required for enhanced oil recovery programmes.Themethod uses estimates of the reflected amplitude at the observedoil–water contacts and requires visible fluid contacts in the 3D or 4Dseismic data. Our approach extends the utility of 4D seismic databeyond the identification of bypassed oil to analyse the remainingoil in the already water-swept zones.

Acknowledgements and FundingWe thank the sponsors of the Edinburgh Time-Lapse Project, Phase V (BGGroup, BP, CGG, Chevron, ConocoPhillips, ENI, ExxonMobil, Hess, IkonScience, Landmark, Maersk, Nexen, Norsar, PGS, Petoro, Petrobras, RSI, Shell,Statoil, Suncor, Total and Taqa) for supporting this research. We thank ETLPgroup members David Yin, Veronica Omofoma and Hamed Amini for helpfuldiscussion and software support for this work. The authors also thank Shell UKLimited and Esso Exploration and Production UK Limited for permission to usetheir data.

Appendix A

To derive the seismic responses of the original and produced oil–water contacts (OOWC and POWC, respectively), we begin with theapproximation from Aki & Richards (1980) expressed in terms ofthe elastic moduli κ, μ, M and ρ (bulk modulus, shear modulus, Pmodulus and density, respectively) (Gray et al. 1999):

R(u) ¼ 1� 4

3

VS

VP

� �2" #

G1Dk

�kþ G2

Dr

�rþ VS

VP

� �2

G3Dm

�m(A1)

where

G1 ¼ 1

4sec2 u, G2 ¼ 1

2� 1

4sec2 u

and G3 ¼ 1

3sec2 u� 2 sin2 u

(A2)

In this case, the reflectivity associated with the OOWC and POWCis from the fluid contrast and Dm ¼ 0. Therefore:

R(u) ¼ G1Dk�M

þ G2Dr

�r(A3)

Following Alvarez (2014), we calculate the rock and fluid variationsin the bulk modulus and density across the interfacewithin the limitsof Sw ¼ 1 and Sw ¼ Swirr using the rock and fluid equations ofGassmann (1951) and Nur et al. (1995). Introducing the results into

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equation (A3), we obtain:

R(u)OOWC � �DS2w1

2

f

fC � f

� �kw � ko

kmin þ 4

3mmin

0B@

1CA

8><>:þDSw 5

f

1� f

� �rw � rormin

� ��sec2 u

þ Swirrf

1� f

� �rw � rormin

� �(A4)

and

R(u)POWC � DS2w1

2

f

fC � f

� �kw � ko

kmin þ 4

3mmin

0B@

1CA

8><>:

þDSw1

5

f

1� f

� �rw � rormin

� ��sec2 u

þ Swirrf

1� f

� �rw � rormin

� �(A5)

where φ is porosity and φC is the critical porosity as defined by Nuret al. (1995). Applying a first-order Taylor expansion and definingDSOOWC

w ¼ 1� Swirr and DSPOWCw ¼ 1� Soir � Swirr, equations

(A4) and (A5) reduce to:

R(u)OOWC � a(1� Swirr) (A6)

and

R(u)POWC � a0(1� ROS� Swirr) (A7)

where:

a ¼ 1

2

f

fC � f

� �kw � koMmin

� �þ f

1� f

� �rw � rormin

� �� �� sec2 u (A8)

and

a0 ¼ 1

2

f

fC � f

� �kw � koMmin

� �� f

1� f

� �rw � rormin

� �� �� sec2 u (A9)

Therefore, the ratio between the original and produced oil–watercontacts is given by:

R(u)aferPOOWC

R(u)beforeOOOWC

" #� c

(1� Swirr � ROS)

(1� Swirr)

� �(A10)

where:

c �(kw � ko)rw þ 3

4(rw � ro)kw

(kw � ko)rw � 3

4(rw � ro)kw

(A11)

Or, alternatively, using only the OOWC reflection:

R(u)beforeOOOWC � R(u)afterOOOWC

R(u)beforeOOOWC

" #� (1� Swirr � ROS)

(1� Swirr)

� �(A12)

From where the displacement efficiency, ED, can be calculated:

ED ¼ (1� Swirr � ROS)

(1� Swirr)

� �(A13)

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