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1 SPE Aeing the Value of 3D Seimic Data in Reducing Uncertainty in Reervoir Production Forecat Omar J. Varela, SPE, Carlo Torre-Verdín, SPE, and Larry W. Lake, SPE, The Univerity of Texa at Autin Copyright 22, Society of Petroleum Engineer Inc. Thi paper wa prepared for preentation at the SPE Annual Technical Conference and Exhiition held in San Antonio, Texa, 29 Septemer 2 Octoer 22. Thi paper wa elected for preentation y an SPE Program Committee following review of information contained in an atract umitted y the author(). Content of the paper, a preented, have not een reviewed y the Society of Petroleum Engineer and are uject to correction y the author(). The material, a preented, doe not necearily reflect any poition of the Society of Petroleum Engineer, it officer, or memer. Paper preented at SPE meeting are uject to pulication review y Editorial Committee of the Society of Petroleum Engineer. Electronic reproduction, ditriution, or torage of any part of thi paper for commercial purpoe without the written conent of the Society of Petroleum Engineer i prohiited. Permiion to reproduce in print i retricted to an atract of not more than 3 word; illutration may not e copied. The atract mut contain conpicuou acknowledgment of where and y whom the paper wa preented. Write Lirarian, SPE, P.O. Box , Richardon, TX , U.S.A., fax Atract Uing three-dimenional (3D) eimic data ha ecome a common way to identify the ize and hape of putative flow arrier in hydrocaron reervoir. It i le clear to what extent determining the patial ditriution of engineering propertie (e.g., poroity, permeaility, preure, and fluid aturation) can improve prediction (i.e., improve accuracy and reduce uncertainty) of hydrocaron recovery, given the multiple non-linear and often noiy tranformation required to make a prediction. Determining the worth of eimic data in predicting dynamic fluid production i one of the goal of the tudy preented in thi paper. We have approached the prolem of aeing uncertainty in production forecat y contructing a ynthetic reervoir model that exhiit much of the geometrical and petrophyical complexity encountered in clatic hydrocaron reervoir. Thi enchmark model wa contructed uing pacedependent, tatitical relationhip etween petrophyical variale and eimic parameter. We numerically imulated a waterflood in the mo del to reproduce time -varying reervoir condition. Suequently, a rock phyic/fluid utitution model that account for compaction and preure wa ued to calculate elatic parameter. Pre-tack and pot-tack 3D eimic data (i.e., time -domain amplitude variation of elatic repone) were imulated uing local one-dimenional approximation. The eimic data were alo contaminated with noie to replicate actual data acquiition and proceing error. We then attempted to etimate the original di triution of petrophyical propertie and to forecat oil production aed on limited and inaccurate patial knowledge of the reervoir acquired from well and 3D eimic data. We compared the multiple realization of the variou prediction againt prediction with a reference model. Adding eimic data to the tatic decription affected performance variale in different way. For example, the eimic data did not uniformly improve the variaility of the prediction of water reakthrough time; other quantitie, uch a cumulative recovery at a later time, did exhiit an uncertainty reduction a did a gloal meaure of recovery. We evaluate how different degree of patial correlation trength etween eimic and petrophyical parameter may ultimately affect the aociated uncertainty in production forecat. Mot of the prediction exhiited a ia in that there i a ignificant deviation etween the median of the realization and that the value from the reference cae. Thi ia i evidently caued y noie in the variou tranform (ome of which we introduced delierately) coupled with nonlinearity. The key nonlinearitie eem to e in the numerical imulation itelf, pecifically in the tranform from poroity to permeaility, in the relative permeaility relationhip and in conervation equation themelve. Introduction Flow imulation are routinely ued a the main input to the economical evaluation of hydrocaron recovery. Prediction from thee imulation have proven to e enitive to the reervoir decription, which i normally known through geology and petrophyic. Becaue the latter are aed primarily on often parely-paced well, there i uually coniderale uncertainty in the decription and, hence, uncertainty in the prediction. Relatively few reervoir characterization tudie have made ue of quantitative information contained in amplitude variation of 3D eimic data. 1 Three dimenional eimic data ample the entire reervoir and therey offer the poiility of filling the patial gap etween uually pare well location. We are encouraged y thi poiility ecaue in the pat 3D eimic data have een uccefully ued to generate geometrical and tructural map, to ae the patial ditriution and ize of flow unit, and to volumetrically infer ome petrophyical propertie uch a poroity and fluid aturation. 2,3 However, there are limit to the ue of 3D eimic data for quantitative reervoir decription. For intance, (a) the lateral

2 2 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE (horizontal) reolution, eing largely determined y the ditance etween adjacent trace, i often no etter than 2-5 m, () the vertical reolution remain controlled y the frequency content of the underlying eimic wavelet, and i often no etter than 5-15 m, hence normally greater than what i needed to model the patial detail of fluid-flow phenomena, and (c) the tranformation etween what the eimic data meaure and the input to a fluid-flow model are complicated, noiy and non-linear. It i not automatic oviou, therefore, that the incluion of eimic data will improve imulation prediction, even though they are patially exhautive. Determining the enefit and trade-off of the quantitative ue of 3D eimic data in model contruction i the goal of thi paper. We conider different reervoir characterization technique to determine the impact of the tatic reervoir decription (i.e., poroity model) on a dynamic production forecat. Inference and forecat are accomplihed uing everal alternative procedure, namely, (a) a homogeneou reervoir model, () a layered reervoir model, (c) 3D geotatitical technique, and (d) a 3D geotatitical inverion technique that jointly honor 3D eimic data and well log. The contruction procedure implicitly conidered (a) the uncertainty aociated with tatitical relation etween petrophyical and elatic parameter, and () the effect of relative difference in geometrical upport etween the well log and the eimic data. Comparion of reult are performed in model pace (e.g., poroity) and data pace (e.g., volume of oil production and eimic data). The conceptual geological repreentation of the model a well a the recovery proce are the ame for all cae o that the difference otained in dynamic ehavior can e traced ack to the information availale in contructing each of the model. Model Definition Reervoir Model. The ynthetic earth model conit of a reervoir and emedded in a ackground hale. Figure 1 how the geometry and dimenion of the ynthetic reervoir and. The figure alo how the pacing and location of the well and the ditriution of water aturation within the reervoir and after 4 year of production. Approximately 3 million cell were ued to contruct the grid ued to imulate the ynthetic eimic data aociated with the earth model. However, only the reervoir and i dicretized for fluid-flow imulation with aout half a million cell. The ize of the lock ued to imulate eimic data and thoe ued to imulate fluid-flow ehavior are the ame, hence mathematical upcaling wa not neceary. The initial model of poroity wa contructed tochatically (Gauian imulation) uing proaility denity function (PDF ) and emivariogram for each of the two lithologie (and and hale). We aumed the poroity field to e econd-order tationary, normally ditriuted, and having a patial tructure decried y a precried emivariogram. Thi model i hereafter ued a the truth reference cae (refe rred to a cae T). Appendix A preent a detailed ummary of the condition and relation ued to imulate the waterflood. Relationhip etween poroity, permeaility, and water aturation were enforced uing well-documented paradigm. 4 Thee were uequently ued to determine the initial condition of the reervoir. Relative permeaility curve repreentative of a water-wet medium 5 were caled uing power-law function that depend on reidual aturation and endpoint. 6 Figure 2 how the et of capillary preure and normalized relative permeaility curve ued in the fluidflow imulation. Thee petrophyical relation are patially invariant. A five-pot waterflood proce (one injection well and four production well) with an unfavorale moility ratio (endpoint moility ratio of 1.67) wa imulated uing a finitedifference algorithm. Seimic data are not trongly enitive to the denity contrat etween oil and water; hence, a waterflood ecome a tringent tet for the enitivity analyi purued in thi paper. A econd reaon for picking a waterflood recovery proce i o that our reult can provide ome inight into potential waterflood in deepwater reervoir where eimic i a main data ource. The production well were et to a contant ottomhole preure and the injector well y a contant injection preure. Fluid and rock propertie and fluid-flow imulation condition aociated with cae T are decried in Tale 1. Permeaility i not directly availale from eimic information. We ued the tranformation log k= 1φ. 5 to infer permeaility (in md) from poroity (a a fraction). The nonlinear form of thi equation i conitent with empirical oervation that generally how a linear relationhip etween permeaility plotted on a logarithmic cale and poroity. A our reult will how, the nonlinearity of thi relation contriute ignificantly to the accuracy in prediction. Permeaility-poroity relation, however, are notoriouly noiy, a factor that we are neglecting here. The interplay etween the nonlinearity and the noie i known to lead to additional ia in prediction (reference 7, p.212). Addreing thi complication i left to future work. Simulation of Seimic Data. Elatic parameter, uch a compreional velocity, hear velocity, and denity, were calculated uing a rock phyic/fluid utitution model (Appendix B) that include the effect of compaction. Rock phyic/fluid utitution model relate the elatic propertie to fluid and rock propertie (e.g., denity, poroity, and fluid aturation). Model that include compaction provide a realitic depth trend for the elatic parameter; hence making the ynthetic eimic data conitent with actual urial condition. 8 We aumed locally one-dimenional ditriution of acoutic impedance (AI), the product of eimic velocity and ulk denity, to imulate pot-tack eimic data acro the reervoir model. Thi wa accomplihed y a convolution operator 9 implemented with a zero-phae Ricker wavelet centered at 35 Hz. Figure 3 how the Ricker wavelet ued in thi tudy and a cro-ection of pot-tack eimic data along well 1. In addition, pre-tack eimic data were imulated for three angle interval: near (- 15 o ), mid (15-3 o ), and far (3-45 o ), repectively. The eimic

3 SPE ASSESING THE VALUE OF 3D SEISMIC DATA IN REDUCING UNCERTAINTY IN RESERVOIR PRODUCTION FORECASTS 3 wavelet aociated with thee three angle tack are a imple modification of the Ricker wavelet hown in Figure 3. Each angle interval i equivalent to what i normally referred to a an angle peudo-tack in reflection eimology. The three angle peudo-tack were generated with a ditinct ynthetic wavelet for each angle-tack y making ue of the Knott- Zoeppritz equation. 1 Thee equation decrie the amplitude of tranmitted and reflected plane wave a a function of their angle of incidence at a oundary eparating region with unequal elatic propertie. Suequently, random noie (i.e., 1% additive zero-mean, uncorrelated Gauian noie, where the noie percentage i in proportion to the gloal energy of the eimic data et) wa added to the imulated eimic data in an effort to replicate actual noie in eimic meaurement. Numerical Experiment In the model decried aove all the variale are completely known. However, in the numerical experiment, the reervoir propertie are partially and imperfectly known. Figure 4 i a flow diagram that decrie the method adopted for modeling and validating thee reervoir characterization procedure. The amount of data availale for quantitative analyi increae a production proceed. Mot of thee data are dynamic, in the form of production rate and preure. Before production egin, the availale data are motly tatic (i.e., they do not tem from fluid -flow in the reervoir) and it i the value of thi type of data that i the uject of thi tudy. The kind of information we ue i geologic interpretation, noiy eimic data, eimic interpretation (i.e., horizon), well log, and the degree of correlation etween petrophyical and elatic propertie. Well information (e.g., log and core data) i the mot important and direct way to otain inight aout the reervoir propertie. Thi information can e iaed ecaue the well location are not commonly repreentative of the entire population and ecaue of their relatively hort patial upport. Core data, epecially, i uject to iaed ampling. Aide from ia conideration, all of the well data utantially underample the reervoir. It i aid that the knowledge of the reervoir i etter at the end of it life; ut even then the knowledge i retricted to the inference made from tet and production hitory, and to the patial ditriution of the hard data (i.e., well). Normally, major uncertaintie in the geologic model are not fully conidered in the modeling prior and during production ecaue there i a utantial amount of work involved in developing alternative model. The tatic model evaluated here include different degree of information in their contruction. They comprie imple model (e.g., homogeneou and layered), eimic inverion model, and tochatic model (e.g., geotatitical and geotatitical eimic inverion model). Tale 2 ummarize the nomenclature of the etimation model conidered in thi paper. Since we are intereted in evaluating the tatic model and their impact on a production forecat, all variale remain the ame in the waterflood except for poroity and other petrophyical propertie (e.g., permeaility), which are aumed to e poroity-dependent. Thi allow one to perform a direct comparion etween model contruction, influence of eimic data, and production forecat. Simple Model. We ue two imple model, homogeneou and uniformly layered model that are mainly ued when relatively few data are availale, when it i neceary to ue the average undertanding of the field. In the homogeneou cae (H), the poroity i patially contant and equal to the mean value. Cae H contain the mean tatitical information ut can not capture vertical and lateral patial variaility of the petrophyical propertie. The uniformly layered model (L) make ue of the well-log data (i.e., poroity) to calculate average propertie of each of the 51 imulation layer. Cae L contain the vertical patial variaility ut can not capture lateral patial variaility of the petrophyical propertie. Seimic Inverion Model. Seimic inverion i an etimation procedure wherey acoutic impedance (AI) i derived from pot-tack eimic data. Related to the acoutic propertie of the rock, AI i often correlated with reervoir parameter. If there i a relationhip etween AI and petrophyical parameter then a direct tranformation can e ued to generate the reervoir parameter (ee Figure 5). Thi i cae DAI. Here, the AI recovered from the pot-tack eimic inverion i tranformed into poroity uing the relationhip hown in Figure 5 (top panel), which wa calculated uing well-log data. The more correlated the variale are, the more accurate the tranformation of AI into the correponding petrophyical property ecome. Although the Figure 5 how correlation etween AI and poroity, and AI and ulk denity, there i ome catter around the main trend. However, there i not alway a relationhip etween AI and petrophyical parameter. Thi i cae AIW. Here, the AI recovered from the pot-tack eimic inverion i tranformed into poroity uing the relationhip hown in Figure 6 with a mall correlation coefficient (r 2 =.1). Stochatic Model. Stochatic modeling allow the generation of equally proale tatitical realization of the patial ditriution of reervoir propertie. If thee realization are uject to fluid-flow imulation then the dynamic ehavior of the reervoir can alo e interpreted in term of tatitical propertie. Normally, the range of poile olution i an important part of the reervoir evaluation ince in practical cae an analytical olution to the fluid-flow equation i not availale. The tochatic approach i one of the technique that allow one to integrate different kind of information into the tatic decription of the reervoir. In thi ection, the cae tudied include: geotatitical model, and geotatitical eimic inverion of the pot-tack and far-offet volume for poroity and ulk denity. Bia and accuracy are important iue when evaluating reult of tochatic realization ince the value of the inference can e jeopardized y a potential ia in the reult. Bia i a tatitical ampling or teting error caued y ytematically favoring ome outcome over other. Then, it ecome imperative to identify the ource of ia in the

4 4 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE etimation procedure to properly evaluate the reult. In our tudy, the main ource of ia originate from nonlinear equation, noiy relationhip etween variale, the nature of the production cheme, and the correctne of the phyical model, to name ut a few. Geotatitical Model. Geotatitical modeling (cae G) make ue of the information acquired along the five exiting well to uild PDF of reervoir propertie (i.e., poroity). Then, through the ue of emivariogram, it i poile to uild many realization on the deired variale (i.e., poroity). Each realization ha the ame proaility of occurrence and honor the well data that have een impoed in the proce of Gauian tochatic imulation of poroity. The calculation of horizontal emivariogram (x- and y- direction) for each lithology i difficult ecaue there are only a few numer of point availale (i.e., well), which tend to produce pure nugget emivariogram. 11 Figure 7 illutrate the emivariogram ued in thi tudy. We ued zero-nugget pherical emivariogram to contruct the poroity ditriution in the truth reference cae (cae T). Thee emivariogram have two parameter a input: a range, which indicate the extent or ize of the patial autocorrelation, and a variance. The range i different for each of the three coordinate direction in cae T. But ecaue of the difficulty of etimating the range, in the tatitical model we ued horizontal range equal to one-half (ë/ë T =.5) and twice (ë/ë T = 2) thoe ued in the reference cae (ë T ). For the vertical emivariogram, well provide ufficient patial ampling to calculate the correponding parameter. The horizontal range ued in the reference cae were approximately equal to the well pacing. Variance for poroity and denity were et to the value calculated from the ampled well-log data. Geotatitical Inverion Model. Geotatitical inverion provide a framework to quantitatively integrate eimic data, well log, and geological information in one tep. 2 In geotatitical inverion, a prior AI model i uilt and then modified until the gloal mifit etween the meaured eimic data and the imulated eimic data i reduced to a precried value (uually the gloal mifit i le than 5% depending on the amount of noie preent in the eimic data). Becaue AI can often e related to petrophyical parameter, it i poile to directly otain tochatic model of reervoir parameter that jointly honor the eimic and the well-log data. In thi tudy, a geotatitical inverion of the noiy pottack eimic data from cae T wa performed for poroity (cae IP) and ulk denity (cae ID). The PDF of thoe two variale for each lithology are hown in Figure 8. Semivariogram ued in the inverion were the ame a thoe decried earlier (Figure 7). The relationhip ued in the geotatitical inverion etween AI and poroity, and AI and denity for each lithology were calculated from well-log data. Thee are hown in Figure 5. Given that we alo want to make ue of the partial offet of the previouly generated pretack eimic data, a geotatitical inverion wa alo performed of the far offet eimic data for poroity (cae IPEI) and ulk denity (cae IDEI). Far offet of eimic data are important ecaue the AI of the encaing hale i larger than the AI of the reervoir and. 12 The propertie otained from thi inverion (poroity and denity) are uequently ued in the tatic decription of the reervoir. Evaluation of Reult and Dicuion The two main aumption underlying the reervoir contruction method decried aove are the econd-order tationarity of the data and the exiting relationhip etween AI and petrophyical parameter. Another important iue i the degree of repreentativene of the data. 13 It i known that, tatitically peaking, well information i rarely repreentative of the patially variaility and volume under tudy. Often uch a fact i overlooked ut the information i neverthele ued ecaue they are a primary and direct ource of rock and fluid propertie. Conitency in Data Space for Seimic Data. To acertain the conitency of the inferred hydrocaron reervoir model, we performed an aement of the error in predicting the 3D eimic data. Thi wa accomplihed y imulating the eimic data at the onet of production for each of the contruction method decried aove. Suequently, we calculated a correlation coefficient etween the eimic data of each cae and the eimic data aociated with the reference model (cae T). Figure 9 i a map of the correlation coefficient in data pace (i.e., eimic data) for an aritrary tatitical realization of cae G-1. The average correlation coefficient (r 2 ) i.21. Tale 3 ummarize the reult otained for the remaining cae conidered in thi paper. Cae H, L, and G exhiit the mallet correlation coefficient. By contruction, cae that make ue of eimic data in the definition of the reervoir propertie mut exhiit large correlation coefficient. For intance, Cae DAI and AIW exhiit the larget correlation ince the AI i calculated through eimic inverion. Cae IP, ID, IPEI, and IDEI exhiit a large correlation coefficient. Otaining a correlation map like the one hown in Figure 9 help one to validate the predicted reult againt other ource of data. Conitency in Model Space for Poroity. We performed an error aement in model pace (i.e., poroity). We compared the poroity model of the reference cae to the poroity model of all cae. Figure 1 how a map of correlation coefficient etween the actual and predicted poroity for the hydrocaron reervoir model inferred from an aritrary realization of cae G-1. Tale 3 ummarize the reult otained for other cae conidered in thi paper and how that ca e H, L, and G exhiit the mallet correlation coefficient, wherea cae IP, ID, IPEI, and IDEI exhiit a larger correlation coefficient. The average correlation coefficient etween the eimic data are necearily larger than that etween the eimicinferred poroity data. Thi i ecaue the latter make ue of additional petrophyical relationhip that tend to degrade the correlation. The correlation coefficient etween the predicted and true eimic data are primarily meaure of the error introduced in the forward and inverion tep.

5 SPE ASSESING THE VALUE OF 3D SEISMIC DATA IN REDUCING UNCERTAINTY IN RESERVOIR PRODUCTION FORECASTS 5 When determining gloal dynamic ehavior (e.g., cumulative oil production) the agreement in model pace i econdary. For intance, we can get a cloe prediction of oil recovery with a imple model. However, thi agreement ecome important when detailed tudie are neceary uch a in the determination of an infill drilling location. Here, the cae with high correlation in model pace conitently yield the cloet fluid ditriution to that of the reference model. Many of the following reult are hown in the form of Box plot. A Box plot enale one to examine a numer of variale and to extract the more alient characteritic of their ditriution. It alo give one inight to the gloal ehavior of the correponding variale. In a Box plot the y-axi diplay the variation of the data and the x-axi diplay the name of each cae. Each vertical ox encloe 5% of the data with the median value of the variale diplayed a a horizontal line in the ox. Bottom and top oundarie of the ox define the 25 and 75 percentile of the variale population. Line extending from the top and ottom of each ox define the minimum and maximum value that fall within a population range. Any value outide of thi range, called an outlier, i diplayed a an individual point. In a Box plot, the reproduciility of a prediction i given y the ize of the vertical oxe. Bia how itelf a the median value eing ignificantly different from the truth value, or when the vertical ox doe not cover the truth cae. In a ene, then, increaing the preciion of a prediction can contriute the ia if the median value i not rought cloer to the truth value. We note alo that in nearly every practical cae, the truth value i unknown. Semivariogram and Property Relationhip. Increaing the range in the property emivariogram amplifie the variaility of the dynamic ehavior repone for cae that involve the ue of emivariogram (cae G, IP, ID, IPEI, and IDEI). The increaed variaility i conitently oerved in different dynamic variale. A larger range emivariogram produce lightly maller correlation coefficient when comparing the reult in data and model pace (ee Tale 3). If the contruction of the tatic model i aed on AI ut there i no correlation etween AI and petrophyical parameter (ee Figure 6) then the initial tatic decription of the reervoir i poor. Cae AIW wa deigned to how that the lack of correlation etween acoutic and petrophyical propertie caue the eimic data not to contriute poitively in the contruction of a model of reervoir propertie. Neverthele, eimic data could till e ueful for oundary identification. Noiy (cattered) relationhip etween AI and poroity deteriorate the correlation in model pace (ee Tale 3) and lead to dynamic reult that are iaed, hence not repreentative of the reference cae T. Figure 11 decrie the original oil in place and cumulative oil recovery after 7 year of production for cae AIW. Cae AIW i evidently incorrect and therefore excluded from further analyi. Since the tatic model i not accurate, thi cae underpredict the oil in place y 82.6% and oil recovery after 7 year of production y 84.6% compared to cae T. Oil in Place. Etimation of the original oil in place (OOIP) i an important appraial tool in the early tage of the life of the reervoir. In our tudy, OOIP i not critical ince all the model exhiit the ame geometry (i.e., the ame geometrical oundarie). The aumption of a known geometry i aed on the fact that normally availale eimic data can e ued to contruct a geometrical model of reervoir compartment. However, it i eaily een that each contructed model produce a different et of tatic ditriution of propertie (poroity and poroity-dependent variale) and therefore the OOIP i different in each cae. For comparion, the OOIP of each cae wa normalized againt that of cae T. The Box plot of Figure 12 and 13 how that the range of variation of normalized OOIP i mall (within ± 8% of cae T) ecaue it generally atifie the ame gloal tatitic. Variation of OOIP entailed y the realization for a particular cae are alo mall ecaue the realization, while varying locally, exhiit identical average propertie. OOIP, eing itelf a gloal quantity, i more enitive to average than to variaility. More accurate prediction are otained for thoe cae that involve the ue of eimic data. Reult within a cae preent more variaility for the larger range emivariogram. The geotatitical inverion for denity overpredict the OOIP wherea the one for poroity underpredict the OOIP. Thi can e related to the correlation trength etween poroity and AI, and denity and AI (ee Figure 5). Figure 12 and 13 emody a conceptual inight that will e a major concluion of thi work. For none of the geotatitical or eimic inverion cae (G, IP, IPEI, ID and IDEI) do the percentile vertical oxe overlap the prediction yielded y the reference cae. It i difficult to make firm concluion aout thi ecaue of the paucity of realization (1) on which the reult were aed. The ia ha een exacerated y the reduction in uncertainty caued y adding more data, which i mot evident in Figure 12. In neither cae, Figure 12 or 13, i the ia large; however, it will prove to e ignificant in the gloal dynamic repone decried elow. The ource of the ia i the noie and the non-linearity of the variou tranform needed to make the decription. The OOIP for the realization in all the following cae wa et to that of the reference cae (cae T) o that the dynamic reervoir prediction were performed auming a reervoir with the ame initial volumetric. Oil Recovery. Oil recovery repreent a gloal dynamic repone at a pecific time in the life of the reervoir a hown in Figure 14 for an aritrary realization of cae with ë/ë T =.5. It depend mainly on the recovery mechanim, production trategy, and time. Figure 15 and 16 how the reult of evaluating the normalized oil recovery after 21 day of production. For none of the geotatitical or eimic inverion cae do the percentile vertical oxe overlap the prediction yielded y the reference cae. The recovery for cae H, L, and DAI i le than that of cae T y 39%, 36%, and 25%, repectively. Median oil recovery for cae with ë/ë T = 2 (ottom panel) i within ± 19% of cae T. For thoe

6 6 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE cae with ë/ë T =.5 (top panel) the reult are within ± 15% of cae T. Even though the outcome of thi gloal variale remain iaed, the decreae in relative error in oil recovery come a a direct conequence of adding new information in the contruction of the property model. Tale 4 how the difference etween the maximum and minimum value of the normalized oil recovery of the cae hown in Figure 15 and 16. Cae involving eimic data (IP, ID, IPEI, and IDEI) provide etter preciion than the realization otained only through the geotatitical cae (cae G). The latter tatement i clear for cae with ë/ë T =.5. For cae with ë/ë T = 2 the difference are mall a hown in Tale 4. If oil recovery i evaluated at a given pore volume of water injected, there are mall difference and reult are not iaed. However, the water injected i a reult of the elected injection trategy, contant injection preure in our cae, and the initial model decription. Time of Water Breakthrough. Figure 17 how the normalized time of water reakthrough for all cae conidered in our tudy. A wider variaility i oerved than with the variale analyzed efore (e.g., recovery). The range of variation i etween.5 and 2 time the water reakthrough time for cae T. For ome of the cae the percentile vertical oxe overlap the prediction yielded y the reference cae. Reult hown in Figure 17 are le iaed than thoe of Figure 15 and 16 ecaue they do not how an average dynamic ehavior repone a in the cae of oil recovery. Time of water reakthrough repreent a dynamic repone of the patial ditriution of the reervoir propertie, epecially the permeaility ditriution. Value of Information. Figure 18 how the oil recovery at the time of water reakthrough normalized with repect to cae T for ë/ë T =.5. Oil recovery repreent a gloal dynamic ehavior and, a dicued earlier, time of water reakthrough i cloely related to the patial ditriution of propertie. For all cae that involve eimic data the percentile vertical oxe overlap the value from the reference cae. In Figure 18, one can quantitatively ae the enefit of including more information (i.e., eimic data) into the proce of model contruction. Since the meaure of accuracy of a prediction depend on the time at which the prediction i taken, we compared reult with the L-2 norm of the cumulative oil recoverie. The L-2 norm i a gloal meaure of recovery that doe not depend on a pecific time in the life of the waterflood. Figure 19 illutrate the reult of performing uch a calculation. Value were normalized againt the homogeneou cae (T). The horizontal axi identifie the particular cae and can alo e interpreted a a meaure of the information content (cant information content to the left and higher information content to the right). It i clearly een that the cumulative time uncertainty decreae a more information i included in the contruction of the initial model. Linear Relation Experiment. A emphaized earlier, we hypotheize that the main ource of ia in our tudy originate from nonlinear flow equation, noiy relationhip etween elatic and petrophyical variale, the production cheme, and the correctne of the phyical model. We decided to invetigate the importance of ome of thee iae in the reult of oil recovery. To accomplih thi ojective, a pecial cae wa deigned in which all the relationhip ued in the fluid-flow imulator were made linear and precie (relative permeaility, poroity-permeaility) and the fluid exhiited the ame vicoity. Thi cae i not realitic ut provide more inight aout the ource of the ia in the oil recovery. Simulation were redone for the reference cae (T) and cae G-2 (referred a G-2L). Reult were compared with thoe preented in Figure 16 and are hown in Figure 2. The oil recovery of thi experiment i le iaed and more accurate than previou reult. Reult ugget that the ource of the ia in oil recovery i caued y the nonlinearity implicit in the underlying multi-phae fluid-flow equation. Summary and Concluion The work preented in thi paper wa an attempt to ae the value of 3D eimic data in the contruction of a hydrocaron reervoir model. Several trategie were conidered to appraie the influence of the uage of eimic data in the contruction of a reervoir model. We concentrated on the relatively difficult cae of a waterflood production ytem in which water wa injected to diplace oil a a way to enhance production efficiency. Seimic data are relatively inenitive to detecting patial variation in oil and water aturation, epecially in the preence of low-poroity rock formation (poroitie elow 15%). Thu, a waterflood experiment contitute a wort-cenario cae tudy for the uage of eimic data in reervoir characterization tudie (a oppoed to, for intance, the optimal eimic detection prolem of water and ga aturation in thick, high poroity formation). The main appraial tool ued in thi paper to ae the value of eimic data wa the comparion of the time record of fluid production meaurement with repect to that of a enchmark (truth) model. A expected, it wa impoile to iolate the influence of the uage of eimic data in reervoir contruction from technical iue concerning non-uniquene and the definition of ancillary fluid and petrophyical variale unrelated to eimic meaurement. Such ancillary variale included the choice of a poroity-permeaility relationhip, the choice of gloal relative permeaility and capillary preure curve, and the choice of degree of patial moothne of reervoir variale interpolated from well-log meaurement. Depite thi difficulty, we attempted to compare on equal footing a et of model with different degree of patial complexity y tandardizing the role played y oth initial fluid volumetric and the choice of a production cheme on fluid production forecat. Suequently, we integrated the quantitative ue of variou type of eimic data into the contruction of tatic reervoir model with increaing degree of patial complexity. Even with the uage of eimic data, the contruction of reervoir model i non-unique (an

7 SPE ASSESING THE VALUE OF 3D SEISMIC DATA IN REDUCING UNCERTAINTY IN RESERVOIR PRODUCTION FORECASTS 7 uncountale et of model exit that honor the complete et of availale meaurement). Multi-phae fluid-flow imulation aociated with each et of model (1 individual model per et) were performed in order to quantify the predictive power of each et of meaurement and thee time-domain imulation were compared againt thoe of the enchmark model. Finally, an effort wa made to take into account that time variaility of the record of production meaurement a it directly impacted the meaure of appraial. Gloal a well a time dependent meaure of appraial were explored to quantify the added value of eimic data. The following concluion tem from our work: (1) Significant iae in prediction of fluid recovery can e aociated with pure fluid-flow phenomena to which eimic meaurement remain inenitive. Even with the uage of eimic data, ource of prediction ia can e more dominant that an incremental reduction in prediction ia due to the uage of eimic data. Source of prediction ia aociated with fluid phenomena include the nonlinear nature of the underlying multi-phae fluid-flow equation, nonlinear and inaccurate contitutive relationhip (e.g., poroity v. permeaility), noiy meaurement, variation in the patial upport of input meaurement, and the choice of fluid production cheme, among other. (2) Reervoir model are often contructed with geotatitical method that make ue of patial emivariogram. It wa found that a coniderale degree of variaility in tatic and dynamic prediction of reervoir ehavior could e caued y the uage of larger than neceary emivariogram range. Regardle of the uage of eimic data, accurate etimation of emivariogram function and parameter thereof i crucial to performing reliale forecat of fluid production. For intance, the accuracy of predicted oil recovery i adverely affected y an improper choice of emivariogram range. (3) Lack of correlation etween elatic and petrophyical parameter caue the eimic data not to contriute poitively to reduce uncertainty in production forecat. Fluid production forecat aociated with poor input petrophyicalelatic correlation function are rendered iaed and inaccurate. (4) Static and dynamic prediction performed from reervoir model contructed with the ue of eimic data normally exhiit an incremental decreae in their ia with repect to a nominal prediction ia due to pure fluid-flow phenomena. Gloal meaure of prediction ia how a conitent improvement with repect to prediction derived from model that do not make ue of eimic data. Thi concluion i valid a long a a high degree of correlation exit etween petrophyical and elatic parameter, and follow from comparion of production variale uch a recovery efficiency, and time of water reakthrough, for intance. Acknowledgement Thi work wa upported y the US Department of Energy under contract No. DE-FC26-BC1535. We would alo like to expre our gratitude to Jaon Geoytem and Schlumerger for their oftware upport. Larry W. Lake hold the W.A. (Monty) Moncrief Centennial Chair at The Univerity of Texa. Nomenclature AI = Acoutic impedance, ml/l 3 /t c = Fluid compreiility, L 2 /ml/t 2 E = Young modulu, ml/t 2 /L 2 k = Permeaility, L 2 k r = Relative permeaility L = Length, L m = ma, m p = Preure, ml/t 2 /L 2 p BHP = Bottom hole preure, ml/t 2 /L 2 PDF = Proaility denity function S = Saturation, fraction t = Time, t v = Velocity, L/t V = Volume, L 3 Greek Symol = Difference = Derivative operator = Gradient operator, L = Integral operator κ = Bulk modulu, ml/t 2 /L 2 µ = Vicoity, m/lt or hear modulu, ml/t 2 /L 2 ρ = Denity, m/l 3 φ = Poroity, fraction ë = Semivariogram range, L ã = Specific weight, ml/t 2 /L 2 /L σ = Standard deviation í = Poion ratio, dimenionle Sucript = Bulk e = Effective f = Formation or fluid i = Initial or component o = Oil p = Compreional = Unaturated or hear h = Shale = Sand r = Reidual T = Reference cae or Temperature t = Total x, y, z = Coordinate direction w = Water Supercript m, n = Saturation exponent o = Endpoint Reference 1. Pendrel, J.V., and Van Riel, P.: Etimating Poroity From 3D Seimic Inverion and 3D Geotatitic, preented at the 67th

8 8 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE Annual International Meeting of the Society of Exploration Geophyicit. 2. Haa, A., and Durule, O.: Geotatitical Inverion: A Sequential Method fo r Stochatic Reervoir Modeling Contrained y Seimic Data, Firt Break (1994), Vol.12, No.11, Varela, O.J.: Pre-tack Stochatic Seimic Inverion to Improve Reervoir Simulation Forecat, Ph.D. Diertation in progre, The Univerity of Texa at Autin, TX (2X). 4. Tia, D., and Donaldon, E.C.: Petrophyic: Theory and Practice of Meauring Reervoir Rock and Fluid Tranport Propertie, Gulf Pulihing Company, Houton, TX (1996). 5. Hornarpour, M., Koederitz, L.F., and Harvey, A.H.: Empirical Equation for Etimating Two -Phae Relative Permeaility in Conolidated Rock, Journal of Petroleum Technology (1982), Vol. 34, Lake, L.W.: Enhanced Oil Recovery, Prentice Hall, Englewood Cliff, NJ (1989). 7. Jenen, J.L., Lake, L.W., Corett, P.W.M., and Goggin, D.J.: Statitic for Petroleum Engineer and Geocientit, Second Edition, Elevier Science, NY (2). 8. Varela, O. J., Torre -Verdín, C., Sen, M.K., and Roy, I.G.: Synthetic Studie for the Efficient Quantitative Integration of Time-lape Reervoir Production Data, Geological Information, Well Log, and Pre- and Pot-tack 3D Seimic Data, preented at the 21 SEG Development and Production Forum, Tao, NM, June Catagna, J.P., and Backu, M.M.: Offet-Dependent Reflectivity: Theory and Practice of AVO Analyi, Society of Exploration Geophyic, Tula, OK (1993). 1. Aki, K., and Richard, P.G.: Quantitative Seimology: Theory and Method, W.H Freeman and Co., Vol. 1 and 2, NY (198). 11. Pizarro, J.O., and Lake, L.W.: A Simple Method to Etimate Inter-well Autocorrelation, paper preented at the 1997 Fourth International Reervoir Characterization Technical Conference, Houton, TX. 12. Rutherford, S.R., and William, R.H.: Amplitude veru Offet in Ga Sand, Geophyic (1989), Vol. 54, No. 6, Bu, T., and Damleth, E.: Error and Uncertaintie in Reervoir Performance Prediction, paper SPE 364 preented at the 1995 SPE Annual Technical Conference and Exhiition, Dalla, TX, Oct Hamilton, E.L.: V p /V and Poion Ratio in Marine Sediment and Rock, J. Acout. Soc. Am. (1979), Vol. 66, No. 4, Catagna, J.P., Batzle, M.L., and Eatwood, R.L.: Relationhip etween Compreional Wave and Shear Wave Velocitie in Clatic Silicate Rock, Geophyic (1985), Vol. 5, No. 4, Elmore, W.C., and Heald, M.A.: Phyic of Wave, Dover Pulication, Inc., New York, NY (1969). 17. Gamann, F.: Elatic Wave through a Packing of Sphere, Geophyic (1951), 16, Biot, M.A.: The Theory of Propagation of Elatic Wave in Fluid -Saturated Solid, Part I Lower Frequency Range, Part II Higher Frequency Range, J. Acout. Soc. Am. (1956), Vol. 28, Duffy, J., and Mindlin, R.D.: Stre-Strain Relation and Viration of a Granular Medium, J. Appl. Mech. (1957), Vol. 24, White, J.E.: Underground Sound: Application of Seimic Wave, Elevier, New York, NY (1983). 21. Geertman, J., and Smith, D.C.: Some Apect of Elatic Wave Propagation in Fluid-Saturated Porou Solid, Geophyic (1961), Vol. 26, Appendix A. Fluid-Flow Model Modeling fluid-flow in a permeale medium require ma conervation equation, contitutive equation, and fluid and rock property relation. The ma conervation equation for component i i given y ( ρiφs ) i + ( ρivi ) = qvi, (A-1) t where i i the component (water or oil), ρi i the fluid denity, v i the uperficial velocity of phae i, φ i poroity, and q v i i a ource or ink term. For the fluid-flow modeled here, there i mutual immiciility etween oth of the fluid component (water and oil) meaning that phae and component are the ame. The contitutive equation i Darcy law for phae i (oil and water), given y kri vi = k ( pi γ i z), (A-2) µ i where k i the aolute permeaility tenor of the permeale medium and i aumed to e diagonal, k r i the relative permeaility function, µ i vicoity, and γ i the pecific weight of the fluid. A fluid property relationhip i given y the compreiility equation. We aume that fluid ( c i ) and pore ( c f ) compreiilitie, given y and c c i f 1 = ρ i ρ i p 1 φ = φ p T T,, (A-3) repectively, are contant over the preure range of interet. Capillary preure ( p ) and the fluid aturation contraint c are governed y p S = p p, (A-4) c ( w ) o w and S S = 1, (A-5) o + w repectively. Relative permeailitie are neceary to evaluate the fluid-flow performance of multi-phae ytem. We adopted a determinitic power law to govern the dependency of relative permeaility on water aturation. Thi power-law relationhip i contructed in the following manner. Firt define a reduced water aturation a S * w Sw Swi = 1 S S or wi. (A-6) The relative permeaility function are then given y * o * n krw( Sw ) = krwsw, (A-7) and

9 SPE ASSESING THE VALUE OF 3D SEISMIC DATA IN REDUCING UNCERTAINTY IN RESERVOIR PRODUCTION FORECASTS 9 k ro where, * o * ( S ) k ( 1 S ) m w o rw =, (A-8) ro k and w o k ro are the end-point value of the water-oil relative permeailitie, and n and m are the water and oil aturation exponent, repectively. Value of fluid and rock parameter and imulation condition conidered in thi paper are hown in Tale 1. Appendix B. Rock Phyic/Fluid Sutitution Model and Elatic Relation There ha een a great deal of work pulihed concerning the relationhip that link elatic propertie of porou rock to pore fluid propertie, preure, and compoition. Mot of the relationhip are aed on empirical correlation that only apply to a particular ain of the world 14,15 Other are aed on wave theory 16, ut are uject to pecific and often retrictive operating aumption. 17,18 In the preent tudy, we adopted Duffy and Mindlin rock phyic/fluid utitution model 19 to generate the main elatic parameter, namely, the compreional ( v p ) and hear ( v ) velocitie. Thi mo del reproduce a wide variety of velocitie meaured on rock ample. 2 The main reult of the Duffy- Mindlin model are given y and v v 2 p C = 11 2 C11 + C12 2ρ C C κ 3 + φ 1 φ C11 + 2C + κ κ 3κ f ρ , (B-1) =, (B-2) where the ucripted C variale are given y ν 3E p e C 11 = 2 2, (B-3) 2 ν 81 ( ν ) and ν 3E p e 2 2 C 12 =. (B-4) ( 2 ν ) 2 81 ( ν ) Equation B-5 to B-9 elow ummarize the aic definition of the mechanical parameter ued in the Duffy- Mindlin model. Poion ratio,ν, can e written a 3κ ν = 2 2µ ( 3κ + µ ), (B-5) where, κ i the ulk modulu, and µ i the hear (rigidity) modulu. The Young modulu, E, i given y 9κ µ E =, (B-6) 3 κ + µ and p e = p - p, (B-7) overurden pore where p i preure, and the ucript e tand for effective. The ulk denity (ρ ) i a imple average weighted y the volume fraction of each component, i.e., ρ = [( 1 φ ) Vcl ] ρh + [( 1 φ )( 1 Vcl )] ρ (B-8) + φs ρ + φ 1 S ρ If ( w ) w [ ( w )] o p ore i the change in pore preure, then the change in water volume i given y VSw p pore / κw, where w κ i water ulk modulu (invere of water compreiility), and the change in oil volume i given y VS / κ. The total o p pore change in volume i the um of the partial volume change and i equal to V / κ. Conequently, the fluid ulk p pore f modulu ( κ ) i the harmonic average of each of the f elemental component value weighted y their repective volume fraction, i.e., 1 S w So = +. (B-9) κ κ κ f w o Determining elatic parameter of rock from their petrophyical propertie require knowledge of the rock dry ulk modulu ( κ ). Thi i provided y the empirical equation propoed y Geertman and Smith 21 that relate the ulk modulu ( κ ), the rock dry modulu ( κ ), and the rock poroity (φ ), κ κ = 1 ( 1+ 5φ). (B-1) The main aumption made when etimating elatic parameter of rock from their petrophyical propertie i that the motion of intertitial fluid i independent from the motion of the matrix grain (low frequency approximation). Thi aumption caue the hear modulu of the fluid-aturated rock ( µ ) to e the ame a that of the unaturated rock ( µ ), i.e., µ =. (B-11) µ By making ue of the flow diagram decried in Figure 4, and y uing equation (B-1) through (B-11), the elatic parameter ( v p, v, and ρ ) can e calculated for pecific value of the rock petrophyical propertie. Thee parameter contitute the input to the algorithm ued to generate ynthetic eimic data. o

10 1 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE Tale 1. propertie. Fluid Reervoir Simulation Summary of fluid and petrophyical Propertie Value and unit ñ w 1 kg/m 3 ñ o 85 kg/m 3 µ w 1. cp µ o 5. cp c w 3.1x1-6 pi -1 c o 2.x1-5 pi -1 Average S wi.28 Average S or.25 φ( φ, σ ) N(.21,.7) c f 1.7x1-6 pi -1 k o rw.3 k o ro.9 k z/k x.1 k y/k x.7 Depth to top of m and p injection 25 pi p BHP 3 pi Numer of cell 81x81x51 Cell ize ~22x22x6 m Perforation All interval Tale 3. Average correlation coefficient (r 2 ) in model pace (poroity) and data pace (eimic data) etween an aritrary-elected model realization and the reference model. Cae r 2 model pace (poroity) r 2 data pace (eimic data) H L DAI AIW.9.98 G IP IPEI ID IDEI G IP IPEI ID IDEI Tale 2. Summary of nomenclature for the numerical experiment. Cae Key ë/ë T =.5 ë/ë T = 2 Reference (True) model T - - Homogeneou H - - Layered L - - Direct from AI DAI - - Direct from AI (tranform with poor correlation) AIW - - Geotatitic* - G-1 G-2 GSI for poroity (pot-tack)* - IP-1 IP-2 GSI for poroity (far offet)* - IPEI-1 IPEI-2 GSI for denity (pot-tack)* - ID-1 ID-2 GSI for denity (far offet)* - IDEI-1 IDEI-2 GSI = Geotatitical Seimic Inverion *1 realization for each emivariogram Tale 4. Range of variation of normalized oil recovery at 21 day of production. Cae Difference* in Normalized Oil Recovery ë/ë T =.5 ë/ë T = 2 G IP IPEI.48.6 ID IDEI *Difference = (Rmaximum Rminimum) 1524 m 34.8 m 1524 m 34.8 m Figure 1. Three-dimenional view of the ditriution of water aturation in the reervoir and after 4 year of waterflood. Sand dimenion, well pacing, and well location are a indicated on the figure.

11 SPE ASSESING THE VALUE OF 3D SEISMIC DATA IN REDUCING UNCERTAINTY IN RESERVOIR PRODUCTION FORECASTS 11 Normalized relative permeailitie (oil or water) p c k ro Normalized water aturation, fraction Figure 2. Normalized et of relative permeaility and capillary preure curve ued to model the waterflood. Ricker 35 Hz Zero Phae Wavelet.1 Reervoir Sand k rw Synthetic Pot-tack Seimic Data Well 1 t=. t=1.5 Figure 3. Ricker wavelet ued in the imulation of pot-tack 3D eimic data (left panel) and cro-ection of pot-tack eimic data along well 1 (right panel). Pot-tack Well-log Data Initial Fluid & Preure Ditriution Rock Phyic Model Noie Seimic Data Inferred Static Model PDF & Semivariogram Geology & Geomechanic Petrophyical and Fluid Propertie Production Scheme Synthetic Static Model (Cae T) Pre-tack Flow Model Flow Model Seimic Data Production Performance Rock Phyic Model Model & Data Space Comparion Production Performance Figure 4. Integrated flow diagram decriing the method ued in thi tudy for validating tatic decription and dynamic prediction. Capillary preure, pi Acoutic Impedance, (kg/m 3 )(m/) x1-6 Acoutic Impedance, (kg/m 3 )(m/) x hale and Poroity, fraction 8. hale and Bulk Denity, kg/m 3 x1-3 Figure 5. Relationhip etween acoutic impedance and poroity (top panel), and acoutic impedance and ulk denity (ottom panel) contructed from well-log data ampled from the reference cae T. Acoutic Impedance, (kg/m 3 )(m/) x Poroity, fraction Figure 6. Relationhip etween acoutic impedance and poroity for cae AIW. The correlation coefficient (r 2 ) i.1.

12 12 O.J. VARELA, C. TORRES-VERDÍN, AND L.W. LAKE SPE σ 2 1. Semivariance λ/λ Τ =.5 λ/λ Τ =2 Lag ditance/λ 2. Τ Figure 7. Semivariogram within the reervoir and in the x, y, and z direction ued for the tochatic imulation of poroity and denity. The variale ë T i the range of the pherical emivariogram ued in the contruction of the reference model, cae T. 2 Count. Poroity, fraction.4 2 Count x y z x y z and hale 2. Bulk Denity, kg/m 3 x Count 3. Acoutic Impedance, (kg/m 3 )(m/) x Figure 8. Hitogram of poroity (top panel), ulk denity (mid panel), and acoutic impedance (ottom panel) ampled from well-log data within the reervoir and and the emedding hale for cae T. 1.. Figure 1. Map of correlation coefficient (r 2 ) etween vertical column of poroity from the geotatitical cae G-1 and the reference cae T. A coefficient r 2 = 1 (dark hading) at a particular pixel indicate perfect correlation. The average r 2 for all pixel i.19. Tale 3 give average correlation coefficient for additional cae..2 Normalized Parameter X (X = 1 for cae T) OOIP Recovery Figure 11. Plot of the predicted original oil in place and oil recovery after 7 year of production when there i poor correlation etween acoutic impedance and poroity (cae AIW). See Tale 2 for a definition of the cae Figure 9. Map of correlation coefficient (r 2 ) etween vertical column of eimic data from the geotatitical cae G-1 and the reference cae T. A coefficient r 2 = 1 (dark hading) at a particular pixel indicate perfect correlation. The average r 2 for all pixel i.21. Tale 3 give average correlation coefficient for additional cae. Oil in Place (OOIP = 1 for cae T) H L DAI G-1 IP-1 IPEI-1 ID-1 IDEI-1 Figure 12. Box plot of normalized original oil in place for cae with ë/ë T =.5. See Tale 2 for a definition of the cae.