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  1. 1. Uncertainty Management Concepts Methods and Applications Ángel Alberto Aponte Email: LinkedIn: Phone: 0056 9 57457803 Puerto Montt X Región de Los Lagos – Chile January 2015 A reservoir can be considered a subsurface volume, with a very complex and heterogeneous internal structure. It could be described through a set of static variables (porosity, net-to-gross, vertical and areal limits,...) and a set of dynamic variables (permeability, fluid saturations, pressure,...). Values for those variables can be obtained from detailed Reservoir Characterization studies: interpretation of laboratory analysis of core samples, interpretation of direct measurements of well logs, pressure tests..., interpretation of indirect measurements of seismic surveys, VSPs,..., analysis of outcrops and analogs, definition of the conceptualization of the geologic and facies models of the reservoir, etc. In general, UNCERTAINTY exists due to lack of knowledge, and it is also inherent to all measure and interpretation processes. Then, it is unavoidable that it propagates to RESERVOIR MODELS that use measurements and interpretations as Inputs, and in the bottom line, that it propagates to volumetric and the ECONOMY of the reservoir. For these reasons, it is mandatory to build reservoir models that: (1) account for all available data and input statistics; (2) represent appropriately conceptualization of the geologic and facies models; (3) allow to access and QUANTIFY uncertainties associated to both, reservoir heterogeneity and these implicit to the modeling approach; and (4) reproduce reservoir dynamic behavior. Regarding the construction of reservoir models, there are deterministic and STOCHASTIC approaches. In the stochastic approach, where GEOSTATISTICS has a central role, variables that describe the reservoir are considered random variables with variations inside reservoir volume. An immediate consequent of this key assumption, is that, from a set of inputs, statistics and conceptualization of the geologic and facies models, it is possible to obtain MULTIPLE (in fact infinites) representations or realizations of the reservoir, all of them consistent with input information. It is clear a priori that not all realizations will be consistent, for example, with production data. However,
  2. 2. just these variations in the realizations, variations that are directly associated to reservoir heterogeneities, input data, interpretations and assumptions regarding the model construction processes itself, would allow to assess and quantify most of the uncertainties underlying the final stochastic model. A practical application of the ideas exposed before, requires a representative sample of size L ("bigger enough") from the universe of all possible geostatistical realizations. This set of realizations will conform what is called the UNCERTAINTY SPACE OF THE MODEL (USM for short); and in principle, this USM will encapsulate most of the stochastic model variability, generated by uncertainties associated with measurements and interpretations, data inputs, and, decisions and assumptions underlying model construction. Thus, each realization will be a Monte-Carlo sample (random and independent) of this USM. The assessment of dynamic reservoir behavior involves running a flow simulator at significant CPU and professional cost. The generation of geostatistical realizations, on the other hand, is relatively quick. Taking this into account, and the fact that one of the main accomplishments of Geostatistics is supply inputs to flow simulation, which realizations are more adequate to perform dynamic characterization of the reservoir? The idea is then, generates a number of realizations (the L realizations of the USM), RANKS them by some fast-to-calculate statistic or ranking metric, and then extracts a limited number of them to process through the full flow simulator. A good ranking metric will identifies and differentiates LOW realizations, MEAN realizations and HIGH realizations. In a broad sense, UNCERTAINTY MANAGEMENT is a generic term which describes integration of Statistics, Geostatistics, Data Analysis and Geosciences concepts, in a collection of techniques and tools, with which accomplish the following objectives: (1) provide QUANTITATIVE criteria to estimate a representative number of realizations to conform the USM; (2) from this set of stochastic realizations, evaluate SUMMARIES and statistics, to both, quantify the uncertainties encapsulated in the USM, and, generate additional products that add value to the project and reduce costs; and finally, (3) provide valid and fast-to-calculate RANKING criteria to rank USM´s realizations, and reduce the number of them to be processed by the flow simulator, in production forecasting, or to be used in other applications. In this Uncertainty Management framework, an eight-steps and READY-TO-USE METHODOLOGY has been proposed. Steps could be applied sequentially or selectively. Although, the proposed methodology was originally implemented in Petrel 2012.2, it could be adapted and also be implemented in previous versions of the same package or another software (Irap-RMS, gOcad,...). The methodology allows to perform a SYSTEMATIC assessment and quantification of the uncertainty underlying the stochastic model. With the first four steps, it is possible to accomplish, and in a reasonable short time (this is very beneficial in VCD and drilling projects, where time is a limiting factor): (1) construction of Opportunity Maps and Cross Sections to support visualization and selection of new well locations (vertical, high angle, non-conventional or
  3. 3. horizontal wells), optimization of design of trajectories of non-conventional or horizontal wells, and real-time well drilling monitoring (geo-navigation); (2) identification of possible coring intervals, and selection and/or optimization of intervals to be perforated; and, (3) support the selection and design of injector- producer well patterns. With the last four steps of the methodology, that must be applied once population of petrophysical properties and preliminary volumetric have been finished, it is possible to complete (through analysis and interpretation of histograms, tornado and sensitivity plots, etc.) a comprehensive description and quantification of uncertainty propagated to volume calculations (Pore Volume, HCPV oil, STOIIP,...), and also, provide ranked realizations, P10, P50 and P90, for dynamic characterization of the reservoir. Application of the proposed methodology was very SUCCESSFUL at every real-case-of-study considered. The proposed methodology did not include any analysis of the uncertainty associated to the structural-stratigraphic framework of the geostatistical model. This particular topic will be addressed in a future work. REFERENCES 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. Pyrcz M. J. and Deutsch C. V.: "Geostatistical Reservoir Modeling". Second Edition 2014. Oxford University Press. ISBN 978-0-19-973144-2. Gringarten E.:"Uncertainty Assessment in 3D Reservoir Modeling". assessment-in-3d-reservoir-modeling/ 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. Santner T. J., Williams B. J. and Notz W. I.: "The Design and Analysis of Computer Experiments". 2010 Edition. Springer-Verlag, New York Inc. ISBN 978-1-4419-2992-1.