ExeSum_GRM&UQagiWORKFLOW
- 1. Geostatistical Reservoir Modeling and Uncertainty Quantification A General Integrated Workflows Ángel Alberto Aponte Email: angel.aponte@gmail.com LinkedIn: http://cl.linkedin.com/pub/angel-alberto-aponte/20/289/123/en Phone: 0056 9 57457803 Puerto Montt, X Región de Los Lagos – Chile June 2015 A key step in the overall process of establishing the static model of a hydrocarbon reservoir, is the construction of the so called Quantitative Geological Model (QGM) or Geostatistical Model (GM). The GM is an essential input for (1) volume calculations, (2) fluid flow simulation, and (3) estimation of production forecasts, among other key tasks. The GM is also used to quantify and analyze the uncertainty that inevitably propagates to volume calculations, and the dynamic performance and economics of the reservoir. Uncertainty that underlies all data/measurements used to carried out petrophysical interpretation, seismic interpretation, the definition of the conceptualization of the geological-sedimentological model, and other inputs of the GM; as well as, uncertainty underlying assumptions and approximations of the stochastic modeling process itself. The QGM is therefore a REPOSITORY of all available KNOWLEDGE of the reservoir, as well as the LACK of IT. Following a geostatistical or probabilistic approach, it is considered that variables that described the reservoir are stochastic processes with variability within the volume of interest. Then, from a specific set of inputs, it is possible to obtain MULTIPLE (infinite) equivalent and EQUALLY PROBABLE realizations of the reservoir. Each realization is by construction, consistent with all inputs used, and, as it is ASSUMED in all workflows implemented in commercial software for geostatistical modeling, with ONE and ONLY ONE conceptualization of the geological-sedimentological model. This is a valid assumption only if the conceptualization and parameters of the statistics used in the modeling, have been WELL ESTABLISHED from results of a comprehensive reservoir characterization. The practical use of the above requires to choose a finite sample of realizations of size L "sufficiently large", sample that must be representative of the universe
- 2. of all possible realizations. And upon these circumstances, this set of L realizations constitutes what is called the UNCERTAINTY SPACE of the MODEL (USM). However, there are many situations where it is imperative to generalize the USM, in order to include varied conceptualizations of the geological-sedimentological model and their associated modeling scenarios. Whatever the case, once conformed an USM with a representative number of realizations, it should be continued with the characterization of the dynamic behavior of the reservoir, and estimation of production forecasts. But, which of the realizations contained in the USM will be most suitable for successfully carrying out the dynamic analysis? It will then be imperative also RANK the realizations of the USM, by some valid and easy-to-implement statistical criterion taken as metric or ranking index, and carefully extract from the USM a small number of realizations which are representative of the variability and heterogeneity mapped into the GM. And it is on this REDUCED subset of realizations which will be held ultimately the dynamic characterization of the reservoir. Based on all exposed above, a design of a General Integrated Workflow is proposed, that: (1) EXPLICITLY incorporates in the construction of the QGM, various conceptualization of the geological-sedimentological model and their associated modeling scenarios, in order to generate a comprehensive and more realistic USM that best represents heterogeneities of the reservoir, and (2) EXPLICITLY allows to rank the hundreds or thousands of resulting realizations, by applying and comparing various static/dynamic ranking metrics. And additionally, the proposed workflow should also allows quantifying and analyzing uncertainty, and also provides Uncertainty Management tools with which to estimate a valid number of realizations for each scenario, and evaluates from the full set of realizations of the USM, probability of occurrence, e-type models and other useful summaries that add value and reduce costs; useful results that support for example, the selection of new well locations, optimization of the design of trajectories and monitoring of drilling of horizontal/non-conventional wells, etc. In this work, the uncertainty associated with structural-stratigraphic framework of the GM is not contemplated. This particular topic will be addressed in a future work. The implementation and deployment of the proposed workflow in one commercial software, and its application to real case studies, is ongoing. REFERENCES Pyrcz M. J. and Deutsch C. V.: "Geostatistical Reservoir Modeling". Second Edition 2014. Oxford University Press. IBSN 978-0-19-973144-2. Slatt R. M.: "Stratigraphic Reservoir Characterization for Petroleum Geologists, Geophysics and Engineers". First Edition 2006. Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands. ISBN-13 978-0-444-52818-6.
- 3. Ballin P. R., Journel A. G. and Aziz K.: "Prediction of Uncertainty in Reservoir <performance Forecast". JCPT no.4, 1992. Tang H. and Liu N.: "Static Connectivity and Heterogeneity (SCH) Analysis and Dynamic Uncertainty Estimation". Paper IPTC 12877 Presented at 2008 International Petroleum Technology Conference, Kuala Lumpur Malaysia. December 3-5 2008. http://www.iptcnet.org/2008/pages/technical/documents/IPTC- 12877-MS.pdf Deutsch C. V. and Srinivasan S.: "Improved Reservoir Management Through Ranking Stochastic Reservoir Models". Paper SPE 35441 Presented at the SPE/DOE 10th Symposium on Improved Oil Recovery, Tulsa, OK. April 1996. Li S.; Deutsch C. V. and Si J.: "Ranking Geostatistical Reservoir Models with Modified Connected Hydrocarbon Volumen". 9th International Geostatistics Congress, Oslo Norway June 11-15, 2012. http://geostats2012.nr.no/pdfs/1745403.pdf Scheidt C. and Caers J.: "A Workflow for Spatial Uncertainty Quantification using Distances and Kernels". SCRF-2007. Stanford Center for Reservoir Forecasting, Stanford University. Palo Alto, California – USA. https://pangea.stanford.edu/departments/ere/dropbox/scrf/documents/reports/20/SCRF 2007_Report20/SCRF2007_CScheidt.pdf Scheidt C. and Caers J.: "Uncertainty Quantification using Distances and Kernel Methods –Application to Deepwater Turbidity Reservoir". SCRF-2008. Stanford Center for Reservoir Forecasting, Stanford University. Palo Alto, California – USA. https://pangea.stanford.edu/departments/ere/dropbox/scrf/documents/reports/21/SCRF 2008_Report21/SCRF2008_CelineScheidt_1.pdf Arpat B.: "Sequential Simulation with Patterns". PhD Thesis Dissertation, 2005. Stanford Center for Reservoir Forecasting, Stanford University. https://pangea.stanford.edu/ERE/pdf/pereports/PhD/Arpat05.pdf Suzuki S. and Caers J.: "History Matching with an Uncertain Geological Scenario". SPE Annual Technical Conference and Exhibition, SPE 102154, 2006. https://www.onepetro.org/conference-paper/SPE-102154-MS Schölkopf B., Smola A. and Müller K. R.: "Nonlinear Component Analysis as a Kernel Eigenvalue Problem" Technical Report No. 44. Max-Planck Institut für Biologische Kybernetic, Arbeitsgruppe Bülthoff. Tübingen, Germany, December 1996. http://www.face-rec.org/algorithms/Kernel/kernelPCA_scholkopf.pdf Sarma P.: "Efficient Closed-Loop Optimal Control of Petroleum Reservoirs Under Uncertainty". PhD Thesis Dissertation, 2006. Stanford Center for Reservoir Forecasting, Stanford University * *http://www.researchgate.net/profile/Khalid_Aziz4/publication/35395102_Efficient_closed-loop_optimal_control_of_petroleum_reservoirs_under_uncertainty_/links/5481ed550cf25dbd59e903f5.pdf