tspecial section: monitoring reservoir and overburden ... · zhen yin 1, milana ayzenberg 2, colin...

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Enhancement of dynamic reservoir interpretation by correlating multiple 4D seismic monitors to well behavior Zhen Yin 1 , Milana Ayzenberg 2 , Colin MacBeth 1 , Tao Feng 2 , and Romain Chassagne 1 Abstract We have found that dynamic reservoir interpretation can be enhanced by directly correlating the seismic amplitudes from many repeated 4D seismic monitors to the field production and injection history from wells. This well2seiscrosscorrelation was achieved by defining a linear relationship between the 4D seismic signals and changes in the cumulative fluid volumes at the wells. We also found that the distribution of the well2seis correlation attribute can reveal key reservoir connectivity features, such as the seal of faults, fluid pathways, and communication between neighboring compartments. It can therefore enhance dynamic reservoir descrip- tion. Based on this enhanced interpretation, we have developed a workflow to close the loop between 4D seis- mic and reservoir engineering data. First, the reservoir model was directly updated using quantitative information extracted from multiple surveys, by positioning and placing known barriers or conduits to flow. After this process, a seismic-assisted history matching was applied using the well2seis attribute to honor data from the seismic and engineering domains, while remaining consistent with the fault interpretation. Compared to traditional history matching, that attempts to match individual seismic time-lapse amplitudes and production data, our approach used an attribute that condensed available data to effectively enhance the signal. In addition, the approach was observed to improve the history-matching efficiency as well as model predictability. The proposed methodology was applied to a North Sea-field, the production of which was controlled by fault com- partmentalization. It successfully detected the communication pathways and sealing property of key faults that are known to be major factors in influencing reservoir development. After history matching, the desired loops were closed by efficiently updating the reservoir simulation model, and this was indicated by a 90% reduction in the misfit errors and 89% lowering of the corresponding uncertainty bounds. Introduction With more than 20 years of application in industry, 4D seismic monitoring has been widely recognized as an effective technology for reservoir evaluation and management. It is proven that 4D seismic can detect changes in reservoir pressure and saturation, due to fluid displacements and distributions between wells and across the field. Normally, changes are revealed by subtracting the data from two seismic surveys ac- quired at different times, to reflect the corresponding dynamic changes during this particular time interval. From the engineering perspective, these 4D signals con- tain crucial information for updating reservoir models. A number of specialized techniques have been devel- oped to extract quantitative reservoir engineering infor- mation, especially pressure and saturation changes, from these 4D seismic signatures (Landrø, 2001; Mac- Beth et al., 2006; Falahat et al., 2013). After obtaining quantitative reservoir dynamic changes, workflows have also been proposed to close the loop between the observed and predicted 4D seismic and production history, to improve the reliability of reservoir simula- tion models for efficient well planning and production strategies (Staples et al., 2005; Landa and Kumar, 2011; Souza et al., 2011; Ayzenberg et al., 2013; Alerini et al., 2014; Ayzenberg and Liu, 2014; Tian et al., 2014). Addi- tionally, 4D seismic signatures can also assist in the di- rect estimation of reservoir model parameters. For example, Benguigui et al. (2014) show a method to cal- culate and update the fault transmissibility multipliers in the flow simulation model directly from mapped 4D seismic amplitudes, which was successfully applied to a fault-compartmentalized North Sea field. Multiple, repeated seismic monitors are now fairly common in offshore environments through the wide- spread application of towed-streamer technology. To further enhance data quality and seismic repeatability, seabed permanent reservoir monitoring (PRM) are used 1 Heriot-Watt University, Institute of Petroleum Engineering, Edinburgh, UK. E-mail: [email protected]; [email protected]; [email protected]. 2 Statoil ASA, Bergen, Norway. E-mail: [email protected]; [email protected]. Manuscript received by the Editor 2 September 2014; revised manuscript received 4 December 2014; published online 7 April 2015. This paper appears in Interpretation, Vol. 3, No. 2 (May 2015); p. SP35SP52, 13 FIGS. http://dx.doi.org/10.1190/INT-2014-0194.1. © 2015 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved. t Special section: Monitoring reservoir and overburden change Interpretation / May 2015 SP35 Interpretation / May 2015 SP35 Downloaded 04/20/15 to 137.195.73.49. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

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Page 1: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

Enhancement of dynamic reservoir interpretation by correlatingmultiple 4D seismic monitors to well behavior

Zhen Yin1, Milana Ayzenberg2, Colin MacBeth1, Tao Feng2, and Romain Chassagne1

Abstract

We have found that dynamic reservoir interpretation can be enhanced by directly correlating the seismicamplitudes from many repeated 4D seismic monitors to the field production and injection history from wells.This “well2seis” crosscorrelation was achieved by defining a linear relationship between the 4D seismic signalsand changes in the cumulative fluid volumes at the wells. We also found that the distribution of the well2seiscorrelation attribute can reveal key reservoir connectivity features, such as the seal of faults, fluid pathways,and communication between neighboring compartments. It can therefore enhance dynamic reservoir descrip-tion. Based on this enhanced interpretation, we have developed a workflow to close the loop between 4D seis-mic and reservoir engineering data. First, the reservoir model was directly updated using quantitativeinformation extracted from multiple surveys, by positioning and placing known barriers or conduits to flow.After this process, a seismic-assisted history matching was applied using the well2seis attribute to honor datafrom the seismic and engineering domains, while remaining consistent with the fault interpretation. Comparedto traditional history matching, that attempts to match individual seismic time-lapse amplitudes and productiondata, our approach used an attribute that condensed available data to effectively enhance the signal. In addition,the approach was observed to improve the history-matching efficiency as well as model predictability. Theproposed methodology was applied to a North Sea-field, the production of which was controlled by fault com-partmentalization. It successfully detected the communication pathways and sealing property of key faults thatare known to be major factors in influencing reservoir development. After history matching, the desired loopswere closed by efficiently updating the reservoir simulation model, and this was indicated by a 90% reduction inthe misfit errors and 89% lowering of the corresponding uncertainty bounds.

IntroductionWith more than 20 years of application in industry,

4D seismic monitoring has been widely recognized asan effective technology for reservoir evaluation andmanagement. It is proven that 4D seismic can detectchanges in reservoir pressure and saturation, due tofluid displacements and distributions between wellsand across the field. Normally, changes are revealedby subtracting the data from two seismic surveys ac-quired at different times, to reflect the correspondingdynamic changes during this particular time interval.From the engineering perspective, these 4D signals con-tain crucial information for updating reservoir models.A number of specialized techniques have been devel-oped to extract quantitative reservoir engineering infor-mation, especially pressure and saturation changes,from these 4D seismic signatures (Landrø, 2001; Mac-Beth et al., 2006; Falahat et al., 2013). After obtainingquantitative reservoir dynamic changes, workflows

have also been proposed to close the loop betweenthe observed and predicted 4D seismic and productionhistory, to improve the reliability of reservoir simula-tion models for efficient well planning and productionstrategies (Staples et al., 2005; Landa and Kumar, 2011;Souza et al., 2011; Ayzenberg et al., 2013; Alerini et al.,2014; Ayzenberg and Liu, 2014; Tian et al., 2014). Addi-tionally, 4D seismic signatures can also assist in the di-rect estimation of reservoir model parameters. Forexample, Benguigui et al. (2014) show a method to cal-culate and update the fault transmissibility multipliersin the flow simulation model directly from mapped4D seismic amplitudes, which was successfully appliedto a fault-compartmentalized North Sea field.

Multiple, repeated seismic monitors are now fairlycommon in offshore environments through the wide-spread application of towed-streamer technology. Tofurther enhance data quality and seismic repeatability,seabed permanent reservoir monitoring (PRM) are used

1Heriot-Watt University, Institute of Petroleum Engineering, Edinburgh, UK. E-mail: [email protected]; [email protected];[email protected].

2Statoil ASA, Bergen, Norway. E-mail: [email protected]; [email protected] received by the Editor 2 September 2014; revised manuscript received 4 December 2014; published online 7 April 2015. This paper

appears in Interpretation, Vol. 3, No. 2 (May 2015); p. SP35–SP52, 13 FIGS.http://dx.doi.org/10.1190/INT-2014-0194.1. © 2015 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

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Special section: Monitoring reservoir and overburden change

Interpretation / May 2015 SP35Interpretation / May 2015 SP35

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Page 2: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

to cover the life of the field and have been applied inmany fields throughout the world (Eriksrud, 2014).However, such frequently repeated 4D surveys will dra-matically increase the interpretation workload if analy-ses are based only on individual 4D differences betweentwo surveys. There are also other limitations whenworking with large numbers of 4D seismic surveys.For example, when using the 4D seismic to close theloop with production data, the workflow can be quitecomplex and nonunique, due to large amount of dataat hand. Meanwhile, it is known that the 4D seismic datacannot be unambiguously interpreted without a properunderstanding of the field development history (e.g., theproduction and injection history at each well). To re-solve this, Huang and MacBeth (2012) propose a cross-correlation method for reservoirs with 4D seismicsignatures predominantly controlled by pressurechanges. This “well2seis” approach unified multiple, re-peated seismic surveys with well behavior data. It wasshown that the method significantly eased the interpre-tation of dynamic reservoir connectivity in reservoirscontrolled by stratigraphic and structural features. Fol-lowing from this study, in this paper, the well2seistechnique is extended to reservoirs with 4D seismic sig-natures that can be influenced by pressure and watersaturation. Furthermore, the correlation properties aremeasured within a 3D volume rather than maps, to im-prove the volumetric understanding and apply themeasily to reservoir model updating. These improve-ments allow the development of a practical two-stepscheme to use multiple seismic surveys to update thereservoir model, at first manually and then with an as-sisted history match. It is observed that the combinationof well2seis derived by direct updating and assisted his-tory matching (AHM) improves the efficiency and speedof updating the static and dynamic reservoir models.The proposed scheme is therefore particularly usefulfor reservoirs with complex stratigraphic and/or struc-tural controls on the fluid flow. To exemplify the ap-proach, the workflow is applied to the North Seafield in which the 4D seismic signals are mainly influ-enced by pressure and water saturation changes.

MethodologiesThe well2seis technique

It is generally understood that 4D seismic signaturesare sensitive to changes of reservoir pressure, water,and gas saturation caused by fluid extraction or injec-tion from well behavior. Therefore, 4D seismic signalscannot be unambiguously interpreted without a clearunderstanding of the production and injection history.This statement leads to the understanding that 4D seis-mic changes at a specific location in the reservoir canbe connected to specific well behavior. To demonstratethis, here, we consider a noncompacting reservoir inwhich only oil and water phases are present, so thatthe time-lapse seismic difference will depend on pres-sure and water saturation changes in the reservoir. Ifmultiple, repeated seismic surveys are acquired at dif-

ferent times (i ¼ 1 to n), a total of N ¼ n × ðn − 1Þ∕2 4Dseismic differences will be generated for all the pairedcombinations of seismic vintages to form a sequencefΔA1;ΔA2; : : : ;ΔANg, where ΔA represents the differ-ence of a seismic attribute such as amplitude, impedance,or time shift. When working with amplitude cubes, 4Dseismic amplitude absolute differences are preferred tocompensate for wavelet polarity effects. For example,five repeated seismic surveys will create a 4D seismic se-quence with 10 differences fΔA1;ΔA2; : : : ;ΔA10g. Simi-larly, the reservoir fluid volume changes for the sametime intervals can be derived from the integration of wellproduction and injection data weighted by formation vol-ume factors. These constitute a well behavior time se-quence fΔV 1;ΔV2; : : : ;ΔVNg. When the 4D signatureis driven predominantly by pressure, Huang andMacBeth(2012) show that there is an approximate linear relation-ship between the 4D seismic amplitude and the netcumulative formation volume changes at each spatial lo-cation of the reservoir dynamically connected to the well.In practice, for an injector, around which a pressure-dominated 4D seismic signal is present, the injectedcumulative water ΔVwat can be correlated with the 4Dseismic attribute ΔA. Thus, a dimensionless normalizedcrosscorrelation factorW2SPres (W2S being the “well2seisattribute”) is then obtained to measure the similarity be-tween the 4D seismic sequence and the well activity se-quence as

W2SPres ¼P

Ni¼1ðΔAi −ΔAÞðΔVwat

i −ΔVwatÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1 ðΔAi−ΔAÞ2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1 ðΔVwat

i −ΔVwatÞ2q :

(1)

In this equation, the metric ranges from zero for no cor-relation (which means the well behavior is not respon-sible for the 4D seismic changes) to �1 for a perfectcorrelation. Either −1 or þ1 can be a perfect correlationdepending on the polarity of seismic attributes. Once thewell2seis attributeW2S is calculated for every seismic binwithin the reservoir, the distribution of W2S reflects theconnection between the 4D signals and the well behavior,which implicitly measures the degree of reservoir con-nectivity to the wells of interest. Compared to the originalseismic and well data alone, the well2seis attribute im-proves the spatial and temporal resolution. At the sametime, the signal-to-noise ratio improves because randomnoise cannot be correlated with well behavior, althoughthe correlation is still influenced by noise and errors in 4Dseismic and production data (see Appendix A).

Equation 1 can only be valid when the 4D signal ispressure dominant, which limits possible widespreaduse of the method. To circumvent this, we consider thesaturation-pressure change equation proposed by Mac-Beth et al. (2006) and Alvarez and MacBeth (2014) as

ΔA ¼ CSwΔSw − CPΔP; (2)

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Page 3: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

where Cp and CSware coefficients balancing the contri-

butions of the pressure change ΔP and water saturationchange ΔSw, and depending on the local geology, fluidproperties, rock physics, and reservoir boundaries.MacBeth et al. (2006) and Alvarez and MacBeth (2014)explain how these two coefficients can be evaluated.Now, for a producer or a group of producers, whenwater saturation change dominates the 4D signaturein the reservoir (which means the influence of pressureis suppressed relative to that of water saturation change[CSw

ΔSw ≫ CpΔPs]), CP will be small and equation 2becomes

ΔA ≈ CSwΔSw: (3)

For steady-state conditions, the water saturationchange in the reservoir is equal to the oil recovered be-tween the 4D time surveys in a reservoir undergoingwater flood (Welge, 1952; Dake, 2001):

ΔSw ¼ Bo × ΔVoil

PV; (4)

where PV is the reservoir pore volume (regarded as aconstant), ΔVoil is the cumulative oil production vol-ume during the 4D period, and Bo is the oil formationvolume factor. The combination of equations 3 and 4linearly relates 4D seismic signatures to cumulativeoil production volume from the wells as ΔA ∝ ΔVoil.When multiple repeated seismic surveys are available,the 4D seismic amplitude sequence ΔA can be directlycorrelated with the sequence of cumulative oil produc-tion volumes as

W2SSw ¼P

Ni¼1ðΔAi − ΔAÞðΔVoil

i − ΔVoilÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1ðΔAi − ΔAÞ2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1 ðΔVoil

i − ΔVoilÞ2q ;

(5)

where W2SSw is the correlation attribute for water-sat-uration-dominated 4D signals.

If the impact on the 4D seismic signature due to pres-sure and water saturation changes is similar in magni-tude, the individual contributions cannot be separated.However, a causative relationship still exists betweenthe 4D seismic signals and well historic data. For in-stance, even though the hardening signals due to pres-sure depletion and water displacement overlap in the4D seismic data, if they are both caused by the produc-tion/injection activities of the specific well/well group,the correlation attribute will reflect this relationshipand therefore indicate the connectivity. Differentiatingthe pressure and saturation effects is a general chal-lenge for most 4D seismic techniques, including thismethod, but it is not considered in our current work.

When a gas phase exists and affects the 4D seismic,the multilinear relationship proposed by Falahat et al.(2013) defines an approximate linear relationship be-tween 4D signatures and pore volume scaled gas satu-

ration changes. It is possible, in principle, to build thecorrelation between the 4D seismic signatures of gasand specific wells when the relationship between wellactivity and gas saturation changes is established. In acompartmentalized Norwegian Sea field in which threephases fluids (gas, oil, and water) are present, Yin andMacBeth (2014) achieve this by directly correlating cu-mulative gas production volumes from a specific wellgroup to gas-influenced 4D seismic signals. They suc-cessfully interpret reservoir connectivity in the gas-dominated 4D area using the correlation attributeand update the reservoir simulation model based onthe resultant interpretation.

Although the correlation attribute W2S does reveal aconnection between the 4D seismic signal and the wellbehavior, care must be taken regarding interpretationof this attribute. One consideration is the limited num-ber of 4D monitors and the existence of seismic noisebecause this can cause spurious correlations. In theory,the more 4D monitors with higher repeatability that areincluded, the more robust the correlation attribute.PRM such as life of field seismic and ocean bottom ca-ble will therefore enable the generation of the most sta-ble and reliable correlation properties. According tostudies over several fields from the North Sea (Huanget al., 2010, 2011; Huang and MacBeth, 2012; Yin andMacBeth, 2014), a minimum of five repeated seismicsurveys are required for the technique to work. To en-sure the robustness of the correlation product and re-duce ambiguities, a threshold value is required for theW2S attribute. Values below this threshold are inter-preted as having no correlation or spurious correlation,and these values cannot be used to interpret the reser-voir connectivity. Studies from these North Sea fieldsshow that a W2S value greater than 0.7 provides a99% confidence level when five repeated seismic sur-veys are used in the calculation. Finally, it should benoted that the well2seis formulation (equations 1 and5) is developed by assuming that there is an approxi-mate linear relationship between pressure/saturationchanges and the 4D attributes. A nonlinear relationshipmay occur in some circumstances (for example, pres-sure change in an overpressured reservoir or gas satu-ration), which would invalidate equation 2. However,even under such conditions, it is believed that the 4Dseismic signatures are still a monotonic function ofpressure and saturation changes, which derive theirtiming from well behavior. Thus, the correlation attrib-ute will remain qualitatively correct. One possible wayto incorporate nonlinearity in the correlation is to usethe Spearman rank correlation (Spearman, 1904, 2010)because this will be sensitive to an ordered relationshipbetween pressure/saturation changes and 4D seismicsignatures.

Closing the 4D loop using well2seis interpretationClosing the loop between 4D seismic and reservoir

engineering data requires integrated workflows tomake sense of the acquired data, of which the key is

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Page 4: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

to update the model in a timely fashion throughout thelife cycle of a field (Tian, 2014). By definition, the well2-seis technique illustrates how the well productionbehavior is related to the spatial distribution of 4D seis-mic signal. The well2seis attribute evaluated at a spe-cific point of the reservoir reflects the degree ofconnectivity of the point of interest to the well location.As a consequence of this, the spatial distribution of thiscorrelation attribute will indicate how the reservoir iscommunicating, compartmentalized, how it is con-nected to the wells, and how the fluid displacementin the reservoir is caused by these various wellbehaviors.

To update the reservoir model using the well2seisattribute, a two-stage workflow is proposed to revisethe static and dynamic reservoir models. In the firststep (so-called direct updating), newly detected/dis-covered key faults, pathways, or active geobodies de-tected by well2seis interpretations are manuallyinserted into the static model depending on their cor-relation with the geologic and geophysical informa-tion. To perform a semiquantitative update, faulttransmissibility multipliers can be adjusted in the dy-namic model according to the discontinuity of thewell2seis attribute across targeted faults. A new term,well2seis gradient (∇W2S), is defined as the absolutedifference of W2S factors across the fault. For exam-ple, the well2seis gradient ∇W2S between cells inter-sected by a fault is defined as

∇W2S ¼ jW2Si −W2Si−1j; (6)

where i and i − 1 are the indices of the adjacent cellsintersecting the fault. Generally, a large well2seis gra-dient indicates small fault transmissibility, and viceversa. To make effective use of this, we first conducta sensitivity study by generating well2seis attributesusing different fault transmissibility multiplier scenar-ios ranging from zero to one, based on the simulationmodel of the field for study (Manzocchi et al., 1999). Inthe test, several (more than 100) fault transmissibilitymultipliers are randomly drawn from a uniform distri-bution to cover all possible outcomes. Each majorfault intersects hundreds of cells in the reservoirmodel, so tens of thousands of well2seis gradients willbe created in total, which is an adequate population ofsamples to represent the possible relationships be-tween ∇W2S and the fault transmissibility multiplier.The seismic vertical resolution (in our case ≈40 m)is always larger than the thickness of reservoir modelcells (≈4 m), which introduces an uncertainty andnonuniqueness into the model update. The generationof multiple model realizations all satisfying theseismic-scale value helps to express this uncertainty.Crossplotting the calculated well2seis gradientsagainst the corresponding fault transmissibility multi-pliers will outline the trend of how these two param-eters are related. Normally, the well2seis gradientincreases with decreasing fault transmissibility multi-

plier. Due to data uncertainty (geological, seismic,and engineering), the linear regression trend line isnot adequate to feature all the relationships. Instead,an envelope of the distribution is constructed from thecrossplots, to make sure that all possibilities are covered.The envelope of this distribution indicates how the well2-seis gradient varieswith the changes of fault transmissibil-ity. Within this envelope, a single well2seis gradient cancorrespond to a range of fault transmissibility multipliers.To update the reservoir simulationmodel, new fault trans-missibility multipliers are selected from the envelope ac-cording to observed well2seis gradients. For instance, tocapture the uncertainties, 100 transmissibility multiplierrealizations are selected for each major fault in the study.In conventional seismic history matching (SHM), a typicalchallenge is to improve the framework of the initial res-ervoir model in a geologically consistent manner. The di-rect updating stage enables us to tackle this problem byadjusting the static and dynamic models to match well2-seis distributions.

With directly updated multiple models from the semi-quantitative process as priors, an AHM is now run tooptimize the reservoir simulation model. History match-ing of multiple, repeated 4D seismic surveys combinedwith production data requires the ability to handle alarge volume of crossdomain data. In addition, if theAHM process is conducted in a traditional way bymatching observations from seismic and productionindependently, it will consume excessive computa-tional resources for history matching and uncertaintyquantification. The well2seis technique condenses the4D signatures from all the seismic surveys and well pro-duction data into one single correlation property, withreduced noise due to the introduction of the well activ-ity. In principle, history matching of the observed well2-seis volume W2Sðx; y; zÞ should improve the matchquality and enhance the computation efficiency be-cause of the compression of the observation data. Asthe well2seis attribute assimilates all the generated4D differences using well production data, the historymatching of W2S should improve the match to eachindividual time-lapse seismic data set as well as the pro-duction observations. To achieve the history match, weuse the objective function (OF) defined by Tarantola(2005) that measures the misfit between observedand modeled well2seis attributes in each grid blockof the simulation model according to

OF ¼ ðW2Sobs −W2SsimðmÞÞTC−1d ðW2Sobs −W2SsimðmÞÞ

þ ðm −mpriÞTC−1m ðm −mpriÞ; (7)

where W2Sobs and W2Ssim are the vectors of observedand simulated well2seis correlations, C−1

d is the inverseof the covariance matrix of uncertainties from W2Sobs,m is a vector that contains the uncertain parametersin the model that should be updated during historymatching, mpri is the vector of uncertain parametersin the prior models, and C−1

m is the inverse of the prior

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Page 5: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

covariance matrix of model parameters. Appendix Asummarizes the equations for calculating uncertaintyin the observed W2S. By using these equations, the cal-culation of the W2Sobs uncertainty in each grid block ofthe simulation model provides the uncertainty covari-ance Cd in the OF. After defining the well2seis OF,the misfit value is to be minimized.

Many methods have been developed to minimize thedifference between observations and predictions fromthe simulation model. Those methods can be dividedinto two categories: gradient-based methods and non-gradient-based methods. Gradient-based methods usetraditional optimization approaches to obtain a localminimum of the OF by calculating local gradientsof the unknown parameters (Zhang and Reynolds,2002). However, in many cases, the calculation of thegradients is time consuming and not straightforward.Non-gradient-based methods do not require any compu-tation of gradients and often treat the function evalu-ation (for example, reservoir simulation) as a “blackbox.” Evolutionary algorithms (Schulze-Riegert et al.,2002), simulated annealing (Sen and Stoffa, 1995),and many other methods fall into this category. Onemain drawback of these methods is that they requirehundreds or thousands of simulations, which demandslarge CPU time. Recently, ensemble-based methods,such as the ensemble Kalman filter (EnKF), have re-ceived attention in the literature and have been success-fully applied to many reservoirs (Aanonsen et al., 2009;Evensen, 2009; Oliver and Chen, 2011). EnKF is a se-quential data assimilation method to estimate a largenumber of model parameters by assimilating differenttypes of data, and it can be readily coupled with reser-voir simulators for automatic history matching. It usesan ensemble of reservoir models to calculate the covari-ance between the model input parameters and themodel responses. The covariance is considered as a gra-dient, which is then used to minimize the OF. In thispaper, we use an ensemble smoother (ES) as an alter-native method (Van Leeuwen and Evensen, 1996;Skjervheim and Evensen, 2011). This differs from EnKFby computing the global update in one step in the space-time domain, rather than using recursive updates intime as in the EnKF. The ESmethod is otherwise similarto EnKF. It can also be iteratively run to further improvethe history matching result (Chen and Oliver, 2013). TheES method is a natural choice for this work because thewell2seis attribute, which is a single property contain-ing information from all seismic surveys and well pro-duction data, is the only constraint to condition to, andthe OF in equation 7 measures the global misfit immedi-ately in the space-time domain. The ES algorithm alsoprovides an ensemble of a posteriori models for sce-nario analysis and uncertainty management.

Application to the North Sea fieldBackground

The methodologies outlined above are applied todata from the North Sea field. The field selected was

discovered in 2004. It is located between two major pro-duction fields A and B (Figure 1). Understanding thecommunications between the study field and its neigh-bors is of great importance for field development. Thereservoir consists of Middle Jurassic sandstones be-longing to the Tarbert Formation (main reserves) andthe Ness Formation of the Brent group. The main pro-ducing reservoir is composed of an insitu Brent Groupstructure (alpha unit) with a sedimentological characterthought to be similar to the neighboring field B. There isa secondary reservoir (beta unit) of the geologic degra-dational complex (DECO), which is believed to be incommunication with the alpha unit. As shown from Fig-ure 2, the Brent Group thins from the in situ areas in thewest (approximately 230 m) to the DECO areas (ap-proximately 25–35 m) in the east. It is unlikely that

Figure 1. (a) Map of the study field with respect to neighbor-ing fields A and B. Blue rectangle shows the area of interest ofthe reservoir model. (b) Geologic interpretation of the studyfield. The red line is a major fault that divides the reservoirinto two main units, alpha and beta. Wells P1 and P2 arethe producers in the study field, whereas well INJ_1 is the in-jector. W1 to W10 are active wells in the neighboring field A.

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the reservoir keeps the same level of homogeneity dur-ing this thinning, which poses challenges for the reser-voir modeling. The study field is relatively small and hasonly two producers and one injector (Figure 1b), withthe first oil produced in the early 2005. The first well P1was produced under primary depletion for 2.5 years be-fore the water injector INJ_1 was put online. The aver-

age reservoir pressure is now almost back to the initiallevel. Production in field A has recently begun, butthere is still a high uncertainty in communication be-tween the two fields. An understanding of the commu-nication mechanism between the two fields is crucialfor the successful development of the two fields.

Figure 3a and 3b shows 3D and 4D seismic sectionsalong line (A-B-C) in the middle of thereservoir model from southwest tonortheast. Top and base reservoirs arethe only horizons interpreted for thefield. With a seismic peak frequency of20 Hz and velocity in the reservoir sec-tion of around 3000 m∕s, expected ver-tical seismic resolution is 37.5 m. Theseismic bin size is 12.5 m whereas theFresnel zone resolves at roughly one-quarter of the wavelength (37.5 m). Asseen from Figure 3a, the base of the res-ervoir is somewhat uncertain due to aweak reflection amplitude. This introdu-ces high uncertainties into the geologicmodel and, as a consequence, the dy-namic model. However, most observeddiscrepancies are away from the mainproducing unit of the field and do not dis-

rupt the general understanding in terms of pressure andsaturation change distributions. Amplitude differencesare clearly seen in the 4D section generated between2010 and 2004 in Figure 3b. Location A shows the mostdominant and laterally extensive 4D signal in the mainproducing part of the study field, which is interpretedas hardening caused by seawater flooding and sub-sequent oil-water contact rise. The 4D anomaly at loca-tion B is related to a gas cap expansion in the southernpart of the field A (at location C), which is mostly a gasprovince. This creates a strong softening 4D signal of theopposite polarity to the water-flooding signal.

This field does not have its own seismic surveys, butit is covered by two independent 4D projects from theneighboring fields, over five repeated seismic surveys(2004, 2005, 2008, 2010, 2011 [shown in Figure 4]). Pri-marily based on the interpretations of the 2004 seismicsurvey (Figure 3a), the reservoir model was first built atthe simulation grid size (lateral size 100 × 100 m andvertical thickness varying from 2 to 4 m). The geologicgrid was created as a refinement of the simulation gridfor property modeling. At the end of this process, anupscaling workflow was carried out to scale the geo-logic grid model back up to the simulation grid model.The field is heavily faulted, and fault seal effects aretherefore critical in the production history. However,the modeling project could not undertake any fault sealanalysis due to limitations with the in-house reservoirmodeling tool. Therefore, the fault transmissibility inthe reservoir model is raised as an immediate challengefor the closing the loop exercise. In the past, the reser-voir simulation model has been first updated by manualperturbations, and then it is history matched to a rela-

Figure 2. Conceptual model of the North Sea field for our study. Cross sectionis from the southern part of the field.

Figure 3. (a) Interpreted seismic section from the 2004 sur-vey along line A-B-C defined in the middle of the reservoirfrom southwest to northeast. The top reservoir is interpretedas the Top Tarbert, whereas the Top Drake is the base reser-voir. (b) The 4D seismic amplitude difference 2010–2004 alongthe same line A-B-C.

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tively high degree using 4D seismic surveys (2004 and2010, Figure 5a) from field A and observed productiondata (Ayzenberg et al., 2013; Alerini et al., 2014; Ayzen-berg and Liu, 2014). Despite this process, the fault seal-ing properties remain uncertain due to the limitedamount of information provided by the observation dataand because each major fault was treated as a single uni-form fault transmissibility multiplier; these are assumedto be the main reasons why the simulation model is stillnot satisfactory. On the other hand, the communicationpatterns between the field of study and its neighbors arestill highly uncertain, which becomes a major problemdue to the recent injection activity in a compartmentof the field A close to the study field. Recently, high-qual-ity seismic for all five of the 4D surveys has been reproc-essed. These seismic data can now be used to improvethe understanding of the communication by leading to amore reliable reservoir model.

Well2seis for enhancing dynamic interpretation ofthe reservoir connectivity

The well2seis method is applied to this field aftercrossequalizing the five seismic vintages to make effec-tive use of all the 4D seismic data (absolute differencecubes of 4D seismic amplitude are generated for well2-seis correlation). Because this reservoir mainly con-tains oil and water phases, and the gas cap is verynarrowly distributed, the correlation equations suitablefor an oil-water system are chosen for this study. The4D seismic signature in the field is mainly dominatedby water, as illustrated in Figure 5a, which shows theseismic difference between 2010 and 2004. The reser-voir development during this period can be seen fromFigure 4, the production is mainly under primarydepletion until water injection started with a very highrate in late 2007. The reservoir pressure increased backto almost the initial value by 2010, and as a conse-quence, the pressure changes duringthe five years of the production periodare difficult to detect with 4D seismic.Originally, only the 4D seismic between2010 and 2004 was used to update thereservoir model because the three otherseismic monitors were not available forthat project. Before applying the well2-seis technique, three points (points a, b,and c in Figure 5a) are selected withinthe reservoir to conduct a feasibility testof the method. Sequences of all the fiveseismic surveys for these points andthe well history sequence of cumulativeoil production from the major productionwell (P1) are created for each time inter-val. Combining the two types of se-quence, the correlation factor W2S iscalculated by the well2seis equation foreach point and displayed on the correla-tion panels in Figure 5b–5d. Because anoil production increase causes an in-

crease in the hardening response on the map of topreservoir, only high-correlation factors are anticipatedif well production alone is responsible for the 4D seismicchanges. Taking point a for example, despite its locationfar away from well P1 and the separation by several ma-jor faults, the calculatedwell2seis attribute is almost 0.60,which means, to some degree, that the production of wellP1 is responsible for the 4D changes at point a. In otherwords, there is a certain degree of connectivity betweenpoint a to well P1. Point b is selected closer to P1, and thistime, the 4D signatures at point b are greater than 0.97correlated with the production well, indicating that themajor fault that separated them did not act as a barrier.Point c, which is even closer to P1, is chosen as an addi-tional test. The W2S value calculated for this point is low,indicating that the two subfaults surrounding point c par-tition this area from the production of well P1.

Once the well2seis attribute is calculated for everypoint in the reservoir as a 3D volume, a new propertyis available that contains the degree of correlation be-tween the 4D changes and well recovery for this field.The correlation property is first generated by linking the4D signature to well P1 using equation 5). A layer viewof this newly generated property is displayed in Fig-ure 6a, in which the distribution of the W2S factorsis observed to be consistent with the location of thefaults. This correlation property mainly explains thewater flooding caused by the major production wellP1. It also indirectly shows the pressure diffusiondue to the volume extraction of this well. From syn-thetic tests on a reservoir simulation model with knownconnectivity properties, a correlation attribute greaterthan 0.45 is found to provide sufficient confidence tovisualize communication to the wells of interest. Com-paring Figure 6a with Figure 5a, it is observed that thecorrelation property not only clearly reflects the water-flooding signal but also reveals extra information re-

Figure 4. 4D seismic coverage on the field. Surveys 2004 and 2010 are acquiredfor the neighboring field A, whereas surveys 2005, 2008, and 2011 are for field B.All seismic surveys were shot during August. Production started from February2005 with one major production well P1. After more than two years of produc-tion, a water injection well INJ_1 was drilled to maintain the reservoir pressure.The other production well P2 started from 2008, but the production rate is rel-atively quite low.

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Page 8: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

garding the reservoir connectivity. In previous work onthis field, each fault was assigned a single constanttransmissibility multiplier along the fault plane duringthe reservoir modeling and updating process. However,as shown in Figure 6a, lateral continuity of the well2seisattributes along the faults is not homogeneous, espe-cially for the faults separating the reservoirs underproduction from those of field A. This indicates that,horizontally, these faults should not be regarded as sin-gle transmissibility multipliers and need to be dealt witha more geologically meaningful way. In the simulationmodel, the faults between the field A compartment andthe study reservoir were adjusted to provide an opentransmission relative to the previous history-matchedmodel. The W2S correlation attribute brings to our at-tention some sealing effects from the faults, identifiableby a distinct discontinuity of the correlation values (Fig-ure 6a). Distinct contrasts in the correlation values are

also identified in the field A region, which are pointedout by black arrows and black dashed lines in Figure 6a.There is a good correlation on one side of the contrastwhereas the correlation is low on the other side of thedashed lines. This suggests the possible existence ofkey barriers that are missed during reservoir interpre-tation and modeling. A second correlation property(Figure 6b) is calculated from equation 1 using waterinjection well INJ_1. From this property, a brighteningeffect is observed in the field A region, which impliesthat pressure changes in this area are significantly cor-related with the injection from INJ_1. Considering noproduction activity in field A region before the latest4D monitor in 2011, it is likely that the water injectionfrom INJ_1 caused strong pressure changes in field A,indicating a high level of communication between thefield of study and field A. This indicates that a largeamount of water injected by INJ_1 moved into the field

Figure 5. (a) Observed 4D amplitude difference between 2010 and 2004. Faults in the reservoir model are displayed using blacklines. The blue shades in the map of the top reservoir represent a reservoir hardening effect, whereas the red shades represent asoftening effect. (b) Profile of the correlation coefficient for point a, showing how the 4D amplitude changes at that point are highlycorrelated with the cumulative well production of P1. (c) Profile of correlation coefficient for point b. (d) Profile of correlationcoefficient for point c. The red line represents 4D seismic signal differences, and the dashed green line represents cumulative fluidvolume differences of P1 during corresponding periods.

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A region due to gravity effects. Even though injectorINJ_1 provided pressure support to the study field,the buildup of local pressure in field A indicates thelow efficiency of this support. Contrasts of correlationvalues are also observed in the field A area in Figure 6b,which gives us more confidence in the existence of newpressure barriers. To check the existence of the twonew proposed fault barriers, we generate vertical crosssections B-B′ and C-C′ (Figure 7a) from the baselineseismic surveys. Clear discontinuities of seismic reflec-tion events and amplitude anomalies are observed atthose proposed locations in cross sections (Figure 7band 7c), justifying the possible existence of the two pro-posed barriers.

In Figure 8a, a 4D seismic section between 2010 and2008 is created from line A-A′ (marked out in Figure 6b)after compensation for time-shift effects. Injection frominjector INJ_1 started in the late 2007 and lasted until2012 (shown in Figure 4), and the 4D difference be-tween 2010 and 2008 fully captures the reservoirchanges caused by the injection well. As is illustratedin Figure 8a and 8b, the fluid contact in the study field

area on the right side of the seismic section moved upbecause of water flooding and production, whereas acertain amount of injected water flowed below and to-ward the neighboring compartment of field A due togravity effects, thus causing a clear local pressure in-crease. The pressure increase in field A caused signifi-cant amplitude changes in the 4D seismic data between2010 and 2008, as can be observed in Figure 8a. In thevertical seismic sections, the amplitude increase anddecrease are due to the (impedance) softening createdby the pressure increase in this region (because waveleteffects combined with geology generate several cycleswithin the reservoir interval that lead to opposing polar-ities). This response is not adequately captured by the4D seismic between 2010 and 2004 because the pres-sure was almost equalized with these time steps. Thevertical cross section from the volumetric well2seisproperty of well INJ_1 is also generated at the same lo-

Figure 6. (a) Lateral view of observed well2seis correlationproperty for the major production well P1. (b) Lateral view ofobserved well2seis correlation property for the injector INJ_1.The dashed lines and black arrows highlight the observed cor-relation contrasts, indicating the possible existence of keyfault barriers at those locations.

Figure 7. (a) Observed well2seis correlation property gener-ated for INJ_1. The yellow lines B-B′ and C-C′ outline the lo-cations for generating vertical cross sections from the seismicsurveys. (b) Vertical cross section B-B′ generated from thebaseline (2004) seismic. (c) As in (b) but cross section C-C′.On the sections, the brown and purple lines represent the res-ervoir top and base, respectively. The black dashed lines markthe location of the proposed fault barriers.

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cation and overlapped with the seismic difference (seeFigure 8c). Comparing Figure 8c with 8a, the correla-tion attribute and 4D difference sections appear consis-tent with each other but the correlation attribute gives amuch clearer image of the reservoir. Clearly, the con-tinuous distribution of high-correlation attributes out-

lines that water injection displaces reservoir fluidstoward the producers, passing through the faults andreaching the field A compartment, thus causing sig-nificant pressure changes. This distribution thereforereflects injected water pathways and the communica-tion status of the reservoir. In a way quite distinct from

Figure 8. (a) Vertical cross section along lineA-A′ for the observed seismic amplitude dif-ference 2010–2008 in Figure 6b. (b) An illus-trative cartoon showing the correspondingreservoir behavior during this period. (c) Ver-tical section of the observedW2S property cal-culated using well INJ_1, overlapping with theseismic difference at the same location A-A′.Yellow and green lines indicate the top andbase of the reservoir, respectively. The blacklines locate the major faults from the field Aside, of which the seal properties are the mainunknowns in the simulation model. Faults 1and 2 are the boundaries between field Aand the field of study. The black arrows pointout the most highly transmissible fault seg-ments. The location of injection well INJ_1is displayed by the blue line, on which dashesindicate the perforated section.

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the 4D seismic section, the correlation property in Fig-ure 8c highlights more details about the vertical com-munication by its continuity across the faults, whichenables understanding of the complexity of the faultconnectivity and how to update the reservoir modelin a more geologically meaningful way.The black arrows in the figure pointout highly conducting vertical segmentsof the main faults, as determined fromanalysis of the well2seis correlationproperty. The remaining portions ofthe fault segments labeled by the blacksolid lines are mainly of low transmis-sibility and perform as barriers in thereservoir. In the compartment abovefield A, the detected pressure increaseindicates that it is a part of the reservoirand that this active geobody should beincluded in the reservoir model.

History matching of the simulationmodel

Based on the interpretations from thewell2seis application, a workflow is de-signed to close the 4D loop for this fieldusing the methodology described above(Figure 9). At the stage of direct/manualupdating, new faults are added to themodel as nonpermeable barriers usingthe well2seis interpretation results. Anew active geobody detected by W2S ly-ing above the field A compartment isalso introduced by enlarging the aquifersize in the model. To quantitatively usethe well2seis correlation properties toupdate the fault transmissibility, a sensi-tivity study is conducted by generating avariety of synthetic correlation proper-ties using the base case simulation modeland applying the proposed scheme. Anexample of the synthetic correlationproperty is shown in Figure 10a, in whichthe synthetic W2S appears consistentlydistributed along the faults becauseeach fault was represented by a singleconstant transmissibility multiplier. TheW2S gradient (Figure 10b) is crossplot-ted against the corresponding faulttransmissibility multiplier (Figure 10c),showing how the W2S attributes relateto fault connectivity. The distributionsof the crossplotted dots form a searchenvelope that will enable us to screenthe fault transmissibility multipliers us-ing the observed well2seis gradient. Toupdate the fault transmissibility in thesimulation model in a geologically con-sistent way, each fault is vertically andlaterally split into several segments ac-

cording to the continuity of the observed W2S propertydistribution along and across the fault. Then, each faultsegment is updated independently. The eight majorfaults on the reservoir are divided in 39 segments inthe simulation model. One hundred realizations of fault

Figure 9. The workflow designed to close the 4D loop on the study field.

Figure 10. (a) An example of the W2S correlation properties generated usingthe base case simulation model. (b) Contacting cells through a fault for W2S gra-dient calculation. (c) W2S gradients versus corresponding fault transmissibilitymultipliers in the simulation models from the sensitivity study. The shadowedarea marks the search envelope for screening the fault transmissibility multi-pliers according to the observed W2S gradient.

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transmissibility multipliers are randomly sampled foreach segment using the distribution range providedby the search envelope. This procedure also variesthe size of the newly introduced geobody. In total,100 updated models are obtained at the end of the directupdating stage.

After direct updating, AHM is launched using the pro-posed OF in equation 7 with the 100 directly updatedsimulation models as an ensemble of prior estimates.Observed W2S values above the preset threshold areregarded as the single observational data in the OFand the misfit value between the observed and pre-dicted data calculated for every reservoir model grid-block in the 3D volume. The errors in the observedW2S attributes are calculated according to the error es-timation equations derived in Appendix A to make anestimation of the covariance Cd in the OF. The averageseismic noise to signal ratio (N/S) is around 20% in thestudy area, which indicates a reasonable degree of reli-ability for quantitative application (Behrens et al.,2002). The uncertainties from the 4D seismic are furthersuppressed in the well2seis correlation property be-cause well behavior does not correlate with randomand coherent seismic noise. In terms of well historicproduction data, the uncertainty is regarded as un-

biased observation error with a magnitude of around5% according to the information provided by reservoirengineers working on this field. By combining the twotypes of errors according to Appendix A, the uncertain-ties from the observed W2S attributes are then calcu-lated to construct the uncertainty covariance Cd,such that the misfit value can be obtained using the pro-posed OF equation. Once the OF is formulated, the min-imization of the OF value is performed by the ESalgorithm with three automatic iterations initially setfor fast quality control. In total, 42 model variablesare screened during the AHM process by the main un-certainties, including fault transmissibility multipliersof the major faults and new faults barriers, and the sizeof the newly introduced geobody, which are assumed tobe the major unknowns in the reservoir model. Appli-cation of the whole workflow takes less than two days.

ResultsFigure 11 illustrates the seismic match quality before

and after applying the workflow. Figure 11a shows ob-served 4D seismic amplitude difference between 2008and 2005. According to the field development historyin Figure 4, there was mainly production activity duringthis period so a pressure depletion response is ex-

pected. Figure 11b shows the simulated4D difference for the same time intervalfrom the simulation model that has beenhistory matched to the individual seis-mic time-lapse data between 2004 and2010. Comparing Figure 11b and 11a,there are two areas in the simulationmodel that are obviously not matchedto the observations: Area I in whichthe hardening effect is found due to sig-nificant pressure depletion because ofthe production from the study field,whereas in the simulation model, no4D response is obtained; and area II inwhich the reservoir model simulatesoil moving into water shown as a soften-ing effect in the synthetic, which is notobserved from the seismic. Figure 11cshows the simulation model after the di-rect updating stage that displays a goodimprovement in the quality of the match.By adding the new active geobody andfault barriers, as well as resetting thefault transmissibility multipliers accord-ing to well2seis analysis, the simulatedresults become much more consistentwith the seismic observations. The ob-served hardening effect in area I isclosely matched, and the problem ofoil displacing water from the base caseat area II is minimized. Figure 11d is thesimulated 4D seismic obtained afterthe AHM, showing slight changes fromthe direct updating, almost similar to

Figure 11. (a) Observed 4D seismic difference between 2008 and 2005. (b) Si-mulated 4D seismic difference between 2008 and 2005 from the simulationmodel, which has been history matched to the 4D signature between 2010and 2004. (c) Simulated 4D seismic difference between 2008 and 2005 fromthe simulation model after direct updating. (d) Simulated 4D seismic differencebetween 2008 and 2005 from the simulation model after the first iteration of theAHM. The dashed black lines mark the areas that are not history matched byusing only 4D surveys of 2010 and 2004.

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those shown in Figure 11c. This obser-vation is mostly because, for this reser-voir, the improvement is caused by therevision of reservoir structures, introduc-tion of new barriers, and the fault trans-missibility multipliers. These parametersin the simulation model have alreadybeen efficiently updated to a quite accept-able degree in the direct updating.

After direct updating, the results of amatch with production data in Figure 12aand 12b show drastic improvement fromthe base case. The simulated productionprofiles from the entire 100 directly up-dated models move from the base casetoward the observations, becoming moreconsistent with the observed historicdata. For the latest period of the produc-tion history (mainly after 2011), most ofthe simulation results are even within theobservation error bars, which means themodel has been matched to an accept-able level. Because the last 4D surveywas acquired in 2011, the updating usingwell2seis interpretations increases thepredictive power of the model. Never-theless, as observed in Figure 12, eventhough the direct updating has achievedsignificant improvements, the simulationresults are still far from the productionobservations in the main historic periodbefore 2011. However, the results arealso widely distributed, which meansthe uncertainty is still high. After the firstiteration of ES in the AHM (the red linesin Figure 12), the 100 models convergequickly toward the observations, improv-ing the match for each realization whilereducing the uncertainties. The historicobservations before 2011 are matchedquite well, whereas the results of predic-tion after 2011 still remain consistentwith the observations.

Figure 13 quantifies how the misfit OF and uncer-tainty of the models (normalized standard deviationof the ensemble) evolve during the workflow. Here,the uncertainties for the base case are normalized toone (denoting the highest uncertainty) before closingthe loop, whereas the uncertainty from the models up-dated at each step of the workflow are normalized byusing the same scalar as the base case. The objective isto minimize the misfit between observation and simula-tion, while reducing the uncertainty in the model tobetween 20% and 10%, which is determined by the un-certainties contained in the observed data. By applyingdirect updating, the misfit value calculated from the OFis reduced by nearly 90% (from 4838 to 517) whereas themodel uncertainty remains more than 60%. After apply-ing the well2seis AHM approach in the second stage, the

Figure 12. Production history-matching improvement after applying the pro-posedworkflow: (a) results of matching to water cut for the well P1 and (b) watercut results for the well P2. The black dots correspond to the observed data; thegray area is the observational error, within which the simulated results are re-garded as history matched; the blue lines are the results from the 100 directlyupdated realizations; and the red lines are the results after the first iterations ofAHM.

Figure 13. Quantification of the evolution of the misfit OFvalue (green line) and the uncertainty (red line) at differentstages of the proposed workflow.

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Page 14: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

uncertainty is narrowed down to 11%, and thus it is re-duced by almost 50%. The models are also further im-proved with the OF value reduced to 168 during the firstiteration, or 3.5% of the initial misfit. The second andthird iterations do not change too much in terms ofthe OF value, but the uncertainty still reduces until fi-nally terminating at a very low value below 5%. How-ever, because the required uncertainty level is set tobe between 10% and 20%, only the direct updatingand first iteration of ES are retained. Overall, the reser-voir model is updated to a satisfactory degree in theseismic and engineering domains. Compared to the pre-vious history-matching work on this field using only asingle 4D difference between 2004 and 2010 (Ayzenberget al., 2013), the proposed workflow is more effective bytaking account of all the multiple 4D seismic surveys atone time.

DiscussionsThe well2seis technique proposed in this paper,

which is a continuation of the work on pressure-con-trolled multiple 4D signatures by Huang and MacBeth(2012), is extended to pressure- and water-saturation-influenced 4D reservoirs, making the technology morewidely applicable. The subsequent well2seis attributeshows the capacity to enhance dynamic reservoir inter-pretations by defining well-centered spatial connectiv-ity. Application of the method in a volumetric 3Dmanner has proved that this technique can effectivelyhelp to detect key reservoir connectivity propertiesin fault compartmentalized reservoirs, such as identify-ing fault barriers or conducting faults at a finer scaleand better resolution, quantifying fault transmissibility,evaluating communications across reservoir compart-ments, and even analyzing active or inactive geobodies.Extension of the technique from 2D maps to 3D vol-umes shows the possibility of working with communi-cation between different formations in stratigraphicreservoirs and assessing connectivity of interreservoirshales, but further studies and field applications are stillneeded.

A series of 4D surveys (at least five) with high repeat-ability, such as with PRM, will help to generate a robustwell2seis correlation attribute. For a successful imple-mentation of well2seis, properly defined threshold val-ues for the correlation attribute are also essential toeliminate spurious correlations. A preliminary under-standing of the reservoir geology including the struc-ture and compartmentalization, and a feasibility studybased on the original reservoir simulation model, willbe important for determining an appropriate thresholdvalue. If there are many wells in the reservoir, the tech-nique may also benefit from abundant well behavior(such as the wells switching on or off) during each timeinterval by generating well2seis attributes for differentwells or groups of wells. However, the contributionsfrom other wells to the correlation attributes shouldbe eliminated to guarantee the localized interpretationsof well-centric reservoir connectivity. As a fundamental

premise, the correct understanding of the communica-tion and connectivity between wells as well as the sim-ilarity of the well behavior will be indispensable forimproving this technique. Understanding the effect ofpressure and saturations underlying the 4D signals isanother important issue for successful application ofthe proposed technique. That is, the chosen 4D seismicsignal should be sensitive to reservoir pressure andwater saturation changes. This requires a linear or ap-proximately linear relationship between the 4D signa-ture and reservoir pressure and saturation changesfor robust interpretation results. When gas exsolvesfrom the reservoir and significantly influences 4D signa-tures, even though Falahat et al. (2013) provide anapproximate linear relationship between pore volumescaled gas saturation changes and 4D attributes, a de-finable relationship between gas saturation changesand well behavior is still required for the success of thistechnique. Otherwise, it could also be an option to di-rectly correlate 4D seismic with gas saturation ob-served at wells. Finally, the time interval of the 4Dsurveys can also have an impact on the applicationof our well2seis technique. For instance, the evolutionof water saturation is relatively slow compared to pres-sure changes in the reservoir. The time spacing of the4D surveys needs to be properly designed to effectivelycapture the changes of water saturation for well2seiscorrelation.

When closing the 4D loop, instead of immediatelyrunning the AHM, the reservoir model is first updateddirectly using the quantitative information interpretedfrom the 4D signatures by the well2seis technique.Only at the end of the process, when the models haveconverged to a certain point, will the AHM be runto optimize the history-matching result. The workflowis capable of updating static and dynamic modelsconsistently and also improves the history-matching ef-ficiency because the direct updating will help to reducethe amount of time-consuming history-matching itera-tions. During the AHM procedure, different from tradi-tional history matching, we only minimize the misfitbetween observed and simulated well2seis attributes.The ES method is selected to perform the optimization.Normally, when performing traditional SHM to history-match multiple 4D seismic surveys as well as produc-tion observations, the ES will require a significantlylarge ensemble size of models, to maintain sufficient de-grees of freedom to accurately match the substantialamount of observational data. This demands a largeamount of CPU power and takes a long time to run. En-semble collapse may also occur due to the large amountobservation data but limited ensemble size. However, thiscorrelation attribute W2S condenses all the 4D differencesignatures and production data; hence, it provides lessbut higher quality observation data for history matching.As a consequence, the history matching of well2seisattribute greatly reduces the computation cost and be-comes more efficient than the traditional procedures.More importantly, the seismic and production history

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Page 15: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

matching results are improved to a high and acceptabledegree. A reliable petroelastic model and seismic model-ing are required to generate accurate synthetic 4D seis-mic attributes for simulated well2seis correlation, whichis necessary for the successful implementation of pro-posed workflow.

The proposed workflow is mainly designed for up-dating fault seal properties and connectivity betweengeobodies and compartments. It still needs to be gener-alized to update other reservoir model variablesthrough proper parameterization. The direct updatingstage reduces the misfit very effectively but uncertaintyand artificial errors may also be introduced during thismanual updating. To solve this problem, a relative largeuncertainty (or parameter search range) will be re-quired for the parameter updates in the followingAHM stage for optimization. When applying the ESfor history matching, a large number of simulationmodel realizations are compulsory. In the study, an en-semble of 100 realizations is the minimum. The largerthe ensemble size is, the more reliable the update modelwill be. This will make the computation quite CPU de-manding especially when the ES runs iteratively. Theseismic resolution for the reservoir also affects the ap-plication of our workflow, especially the vertical reso-lution for updating fault transmissibility. The seismicvertical resolution commonly is regarded as one-quar-ter of the wavelength (≈40 m), whereas the thicknessof reservoir model layers is much less than this(≈4 m). This introduces an uncertainty in the updatedmodels. Multiple model realizations can help to definethe nonuniqueness created by this problem. Insteadof directly correlating to seismic traces, it is recom-mended that colored seismic inversion products canbe used to obtain engineering-consistent interpretationresults in vertical sections (Alvarez, 2014).

ConclusionsThis study further develops a technique to quantita-

tively link well behavior (produced/injected fluids vol-umes or a combination of them) to multiple 4D seismicsurveys in which the 4D signals are controlled by pres-sure or water saturation changes or a combination. Bylinearly crosscorrelating the changes of production/in-jection volumes to multiple 4D signatures in 3D vol-umes, the well2seis method provides high-resolutionimages for robust interpretation of reservoir connectiv-ity and is better than using individual 4D seismic alone.It identifies more detail of key reservoir features inan engineering-consistent manner. Thus, it shows greatpotential to work as an effective tool in updating thereservoir models. A workflow is proposed to use thiswell2seis attribute and its interpretations to close the4D loop by sequential application of direct updatingand AHM. Here, the well2seis attribute is successfullyintroduced as an effective AHM attribute for multiple4D seismic surveys, improving the match quality in seis-mic and engineering domains.

Application of the well2seis method to a compart-mentalized North Sea field reveals the communicationpattern between the producing reservoir and its neigh-boring fields, new pressure barriers and active reservoirgeobodies, and it also evaluates the sealing property ofmajor faults. The proposed workflow efficiently historymatches the model and closes the loop between syn-thetic and observed W2S attributes based on this ben-efit. It improves the match quality by more than 90% andreduces the reservoir model uncertainty by almost 90%.The multiple updated models from the proposed work-flow also enable uncertainty quantification and make itpossible in the future to conduct risk assessment foreffective reservoir planning and management after clos-ing the loop.

AcknowledgmentsWe thank sponsors of the Edinburgh Time-Lapse

Project Phase V (BG, BP, CGG, Chevron, ConocoPhil-lips, ENI, ExxonMobil, Hess, Ikon Science, Landmark,Maersk, Nexen, Norsar, Petoro, Petrobras, RSI, Shell,Statoil, Suncor, Taqa, TGS, and Total) for supportingthis research. We would like to thank Statoil ASA forpermission to show the field data. The authors thankthe group Next Generation Reservoir Managementand Modelling (NGRMM) in Statoil ASA for settingup this project and for the use of their ensemble basedreservoir tool. We also thank Sean Tian for his correc-tions and constructive suggestions on this paper and Ul-rich Theune for help in preparing the figures.

Appendix A

Well2seis attribute error estimationThe well2seis attribute W2S correlates data from 4D

seismic surveys with the well history. The observed 4Dseismic ΔAobs contains signal ΔAsignal and noise cseis

(the nonrepeatability noise is main uncertainty source).Then, ΔAobs can be written as

ΔAobs ¼¼ ΔAsignal þ cseis; (A-1)

where ΔAsignal is the pure 4D seismic signal. To quantifythe 4D seismic noise, the seismic repeatability NRMS ismeasured (as a fraction) according to Kragh and Chris-tie (2002):

NRMS ¼ 2 × rmsðAt1 − At2ÞrmsðAt1Þ þ rmsðAt2Þ

; (A-2)

where At1 and At2 are 4D seismic surveys shot at differ-ent times and rms represents the root mean square. Theseismic N/S can be derived from the NRMS betweentwo surveys (Grion et al., 2000; Behrens et al., 2002):

N∕ S ¼ NRMSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 − NRMS2

p : (A-3)

The 4D seismic noise can then be quantified as

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Page 16: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

cseis ¼ ΔAsignal × N∕ S

¼ ΔAobs

1þ N∕ SN∕ S

¼ ΔAobs × NRMSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 − NRMS2

pþ NRMS

. (A-4)

Similarly, the well observation data ΔVobs can also bewritten as

ΔVobs ¼ ΔV signal þ cprod; (A-5)

where ΔV signal is the true (uncontaminated) productiondata and cprod is the production data uncertainty, whichmay be assumed to be a Gaussian distributed measure-ment error cprod ∼ Nð0; δ2Þ, where δ is the standarddeviation of the measurement errors.

The observed well2seis attribute W2Sobs is calcu-lated as

W2Sobs¼P

Ni¼1ðΔAobs

i −ΔAobsÞðΔVobsi −ΔVobsÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

Ni¼1 ðΔAobs

i −ΔAobsÞ2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

Ni¼1 ðΔVobs

i −ΔVobsÞ2q

¼ covðΔAobs;ΔVobsÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAobs�var½ΔVobs�

p ¼W2Seffð1þcW2SÞ;

(A-6)

where cW2S is the error in the observed well2seis attrib-ute and W2Seff is the effective well2seis attribute de-rived from uncontaminated signals, given by

W2Seff ¼ covðΔAsignal;ΔV signalÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAsignal�var½ΔV signal�

p : (A-7)

Referring to equations A-1 and A-5, equation A-6 is ex-panded as

W2Seffð1þ cW2SÞ

¼ covðΔAsignal þ cseis;ΔV signal þ cprodÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAsignal þ cseis�var½ΔV signal þ cprod�

p ; (A-8)

which, assuming the errors are uncorrelated with eachother and with the signals, gives

W2Seffð1þcW2SÞ

¼ covðΔAsignal;ΔV signalÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðvar½ΔAsignal�þvar½cseis�Þðvar½ΔV signal�þvar½cprod�Þ

p¼ covðΔAsignal;ΔV signalÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

var½ΔAsignal�var½ΔV signal�p

×

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAsignal�var½ΔV signal�

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðvar½ΔAsignal�þvar½cseis�Þðvar½ΔV signal�þvar½cprod�Þ

p¼W2Seff ×

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAsignal�

ðvar½ΔAsignal�þvar½cseis�Þ

s

×

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔV signal�

ðvar½ΔV signal�þvar½cprod�Þ

s; (A-9)

whereffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAsignal�

ðvar½ΔAsignal� þ var½cseis�Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔAobs� − var½cseis�

var½ΔAobs�

s

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 −

var½cseis�var½ΔAobs�

s: (A-10)

Similarly,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½ΔV signal�

ðvar½ΔV signal� þ var½cprod�Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 −

var½cprod�var½ΔVobs�

s.

(A-11)

Incorporating equations A-10 and A-11 into equa-tion A-9, one obtains

jcW2Sj

¼������1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−

var½cseis�var½ΔAobs�−

var½cprod�var½ΔVobs�þ

var½cseis�var½ΔAobs�×

var½cprod�var½ΔVobs�

s ������:(A-12)

As cprod is defined as Gaussian distributed observationerror cprod ∼ Nð0; δ2Þ,

var½cprod� ¼ δ2: (A-13)

The error in observed well2seis attribute W2Sobs is thenobtained as

jcW2Sj

¼������1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−

var½cseis�var½ΔAobs�−

δ2

var½ΔVobs�þvar½cseis�×δ2

var½ΔAobs�var½ΔVobs�

s ������;(A-14)

where var [ΔAobs] and var [ΔVobs] are calculated usingobserved 4D seismic amplitude and production volume

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Page 17: tSpecial section: Monitoring reservoir and overburden ... · Zhen Yin 1, Milana Ayzenberg 2, Colin MacBeth , Tao Feng , and Romain Chassagne1 Abstract We have found that dynamic reservoir

data, and var [cseis] can be calculated using equationsA-2 and A-4. The quantity δ, which is the standarddeviation of production measurement errors, can be es-timated from the production data.

The quantity in equation A-14 is now used in the his-tory-matching procedure.

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Zhen Yin received a B.Eng. (2011) inpetroleum engineering from China Uni-versity of Petroleum, and he is a Ph.D.student at the Edinburgh Time-LapseProject, Heriot-Watt University. Hisindustrial work experience includes in-ternshipswithBP as a reservoir engineer(2010 and 2011) and Statoil as a reservoirgeophysicist (2014). His research inter-

ests include closing the loop using multiple repeated 4D seis-mic monitors. He received the SEG Frans and Alice HammonsAward in 2014.

Milana Ayzenberg received an M.S.(2003) in applied mathematics fromthe Novosibirsk State University anda Ph.D. (2008) in geophysics fromthe Norwegian University of Scienceand Technology. She has been work-ing at Statoil since 2008. Her researchinterests include seismic forwardmodeling, AVO studies, and 4D inver-

sion with applications in reservoir monitoring and fastmodel update.

Colin MacBeth received an M.A. (1980) in mathemati-cal physics from the University of Oxford and a Ph.D.(1983) in geophysics from the University of Edinburgh.He is a professor of reservoir geophysics at the Instituteof Petroleum Engineering (IPE), Heriot-Watt University.He established the reservoir geophysics group at IPE in1999, the main activity of which is the Edinburgh Time-Lapse Project (ETLP), an industry-supported academicconsortium that focuses on effective integration of engi-neering and 4D seismic data for monitoring hydrocarbonreservoirs. He has published more than 200 journal papersand conference publications. He won the Conrad Schlum-berger Award from EAGE for his contributions to geosci-ence and engineering in 2007. He is a member of SEG,EAGE, SPE, AAPG, and PESGB and is a fellow of the In-stitute of Physics and the Royal Scottish Society of Arts.

Tao Feng received a B.S. (1998) andan M.S. (2001) in computational math-ematics from the Shandong Universityand a Ph.D. (2005) in mathematicsfrom the Mid Sweden University. Heis working as a researcher at Statoil.Prior to joining Statoil in 2011, heworked for IFP Energies Nouvellesand UNI CIPR. His research interests

include numerical analysis, inverse problems, and optimi-zation.

Romain Chassagne received an M.S.and a Ph.D. in applied mathematicsfrom the University of Bordeaux,France. He is a research associate atthe Heriot-Watt University. Previ-ously, he worked as a postdoc atSchlumberger Cambridge Researchandasaresearchengineerat theFrenchPetroleum Institute (IFP). His research

interests include reservoir characterization.

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