1. Uncertainty Management
Concepts Methods and Applications
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
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. 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. 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
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Gringarten E.:"Uncertainty Assessment in 3D Reservoir Modeling".
http://www.pdgm.com/resource-library/articles-and-papers/archive/uncertainty-
assessment-in-3d-reservoir-modeling/
Deutsch C. V. and Srinivasan S.: "Improved reservoir management through
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