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.
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