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Ranking of Geostatistical Models and Uncertainty Quantification Using Signal Detection Principle (SDP)

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Ranking of Geostatistical Models and Uncertainty Quantification Using Signal Detection Principle (SDP) Ranking of Geostatistical Models and Uncertainty Quantification Using Signal Detection Principle (SDP) Maureen Ani a,*, Gbenga Oluyemi a, Andrei Petrovski b , Sina Rezaei-Gomari c a School of Engineering, Robert Gordon University, Aberdeen, AB10 7QB, UK b School of Com"#ting, Robert Gordon University, Aberdeen, AB10 7QB, UK c School of Science, Engineering $ Design, Teesside University, 'iddlesbrough, TS1 3B), UK Abstract he selection o" an optimal model "rom a set of multiple realizations "or dynamic reservoir modelling and production "orecasts has been a persistent issue "or reservoir modelers and decision makers. %urrent evidence has shown that many presumably good reservoir models w!ich originally matched the true historic data did not al&ays per"orm well in predicting the future of the reservoir as a result of uncertainties$ 'n this pa#er, a ne& method "or optimal model selection using Signal (etection Princi#le )S(P* a##roach is presented. In princi#le, S(P approach models t!e dissimilarity bet&een various realizations as a cross-"unction of spatial distance, statistical correlation and the inherent noise level in the model+ &hile t!e existing methods estimate the dissimilarity bet&een parameter values o" di""erent realizations as a "unction o" distance )statistical or s#atial distance* or quality "actor. S(P a##roach "ills the model divergence gap by &ay of classi"ying the information-bearing patterns in a model as signals, and identi"ying random patterns &hich bears no in"ormation as noise. hus, it -uanti"ies the mismatch uncertainty and the inherent "udge in every realization as a measure of t!e model.s reliability. he S(P a##roach has been validated &ith !istorical data, and t!e results show that the reliability factor of the best model has a value o" one. hus, i" the strongest reservoir model has a reliability "actor of one, then that model &ill make approximately the closest and best predictions as the true system in every "orecast+ &hereas i" the reliability "actor of the model is less than or greater than one, its predictions &ill al&ays disperse "rom historical data and is unsuitable "or reservoir "orecasts$ T&o examples based on real "ield data are used to demonstrate t!e application o" S(P a#proach. In these case e,amples S(P was used to analyse the di""erence bet&een the reservoir models in a set o" multi#le realizations. he target variable in t!is study &as S O''P )Stock ank Oil 'nitially in Place* . he results s!ow that the models &ith a lower reliability "actor made similar predictions as t!e real reservoir data in almost all the forecasts$ Similarly, t!e models with higher reliability factors made dissimilar and more unreliable predictions in most of the "orecasts$ Key ords! Reservoir Simulation+ Multiple Realizations+ Model Ranking+ /ncertainty 0uanti"ication+ Signal- to-1oise Ratio; Dissimilarity Measure$ * Corresponding Author 2-mail address3 m.n.ani4rgu.ac.uk 1 "#$# %ntroduction 'n recent years, t!e selection of a candidate model "rom a set of model realizations "or the purpose of solving various reservoir modelling problems has attracted a lot of research interests (Shirangi and (urlo"sky, 2016). he areas o" its a##lication in t!e oil and gas industry range "rom history matching )Mtchedlishvili, 8oigt and 9ae"ner, 566:+ Sahni and 9orne, 566:+ Shirangi, 5014; Shirangi and 2merick, 2016), &ell per"ormance );allin, <ournel, and Aziz, 1992), production "orecast )Pratt et al*, 1986*, reservoir property distribution )?anc!i, 5667*, reservoir management )(eutsch and Srinivasan, 1996+ ?ei et al., 2016), uncertainty analysis )@adav, ;ryant and Srinivasan, 5667+ Ra!im, Ai and rivedi, 2015+ Shirangi and (urlo"sky, 2016), &ell placement optimization )Guerra and 1arayanasamy, 5667*, to "ield development planning and decision- making (9egstad and Saetrom, 2014) amongst others$ Aike other type of models, every reservoir model has uncertainties in it. here"ore, a"ter building a reservoir model, multi#le realizations of the model are generated in an e""ort to capture t!e "ull range of the uncertainties associated &it! t!e model. %onventionally, in a reservoir modelling &ork"low+ it is mostly computationally expensive and "utile to carry out "low )dynamic* simulation "or all the realizations, thus a re"erence dynamic model is rather selected "rom a suite o" multiple static models )S!irangi and (urlofsky, 2016). 9owever, the selected model seldom re#resents the optimal model. %onsidering that eac! model !as its own inde#endent probability distribution, it is important to consider the individual "eatures of eac! model to be able to compare one model to another+ given that for any pair o" model realizations, t!ere is a dissimilarity measure that e,ists bet&een t!em. he "ocus of this pa#er is to use a dissimilarity "unction &hich is based on the intrinsic "eatures o" each model to optimize the selection o" the best model "rom a set of multiple realizations+ t!e one that "its as t!e most representative model &it! the least uncertainty "or dynamic modelling. Such "eatures include t!e individual probability distribution o" each model, t!e #attern of inherent in"ormation eac! model is bearing - &hich could either be a signal or a noise. 'n the conte,t o" this #aper, a re"erence model is a model &hic! has eit!er been standardised &ith the !istorical data o" the actual reservoir system, or a model &hich has been calibrated to represent the actual reservoir system as much as possible within reasonable constraints$ "#"# &'isting Model Selection Approac(es Aargely, the selection of representative of models "rom a set of multi#le realizations &orks by basically de"ining a -uanti"iable ranking measure, &!ich can be used to evaluate eac! realization )Sc!eidt and %aers, 2010). he e""iciency of any ranking method however depends on the reliability of the method in selecting realizations t!at closely predict t!e real reservoir system );egg and Celsh, 5014), or at least predict the low, mid and high )P10, PB6 and P=6* reserves quartiles as accurately as possible. Several approac!es have been applied in the selection of models "rom a set o" multiple realizations )(eutsch and Srinivasan, 1996+ Sc!eidt and %aers, 2016+ S!irangi and (urlofsky, 2016; Sahni and 9orne, 566:+ Mtchedlishvili, 8oigt and 9ae"ner, 566:+ Fei, Yarus and Chambers, 2016; Dehdari and Deutsch )2012* and Shari"i et al., 2014*. Model selection by ranking is generally based on the distribution and response of t!e quantity of interest. C!ile each model selection approach di""ers "rom anot!er, the common logic in all is that t!ey all consider a -uanti"iable di""erence function w!ich "orms the basis for di""erentiating bet&een the realizations. 'n the area o" reservoir modelling and optimization, the ranking approaches are broadly classi"ied into t&o maDor types - static and dynamic ranking. Static ranking uses the static geological reservoir properties suc! as 2 porosity, pore volume, stock-tank oil initially in-place )S O''P*, etc$ as a basis "or ranking. On the ot!er hand, dynamic ranking uses the #roperties &hich are linked to t!e dynamic and "luid "lo& behaviour o" the reservoir as a criterion "or ranking. Such dynamic reservoir #roperties include relative #ermeability and connected hydrocarbon volume )%9%8*. 2ven though relative permeability and %9%8 are considered "low properties, they do not actually account "or the "ull "low behaviour of the reservoir as much as "low-physics attributes like tracer )Saad, Maroongroge and Falkomey, 1996), streamline time-of-"light ) O?* and random-&alk )McAennan and Deutsch, 266B)b**$ Pratt et al$ )1986* a#plied Principal %omponent Analysis )P%A* in the ranking of &ell productivity. !is approach is based on the princi#le of orthogonal trans"ormation, &here a set of observations are converted into princi#al components, suc! that the non-correlated principal component has the largest possible variance, and thus accounts "or most o" the variability in the data sample. hey analysed the variability of coalbed methane gas production pro"iles o" di""erent &ells, using the correlation bet&een lineaments and gas #roduction. (ue to the "act that lineaments are not al&ays uni"ormly scaled, they are not reliable static attributes$ here"ore, some of their results were inconsistent and showed that t!e outcomes could be dependent on who mapped t!e lineaments and how t!ey &ere mapped, and thus they recommended that the a#proach should be used &it! caution. ;allin, <ournel, and Aziz, )1992) emerged &ith the use o" a "ast simulator to select models "or "lo& simulation. hey proposed a &ay of reducing considerable computing time and analysing uncertainty by using tracer simulation )"ast simulator* on multiple realizations, and "inally conducting the comprehensive simulation on only the selected realizations. he main idea o" model selection by ranking is to "ind the ideal model &ith the a##ropriate set of input parameters that &ill be able to match the model that !as been calibrated &ith historic data, and thus predicts the #rofile or "uture of the true system. 9owever, the parameter set that can "it any calibrated model is not unique )and this is known as the issue of non-uniqueness*+ this means that di""erent parameter sets from di""erent realizations will be able to match t!e same calibrated model. 'n favour of dynamic ranking measures, (eutsch and Srinivasan )1996* pointed out t!at although no ranking measure had overcome the #roblem of non-uniqueness, they &ere hope"ul t!at streamline and random-&alk simulation could be promising techni-ues "or improved ranking.
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