Page 266 - Intelligent Digital Oil And Gas Fields

216 Intelligent Digital Oil and Gas Fields

the EnKF coupled with the streamline sensitivity-based covariance localiza-
tion (Arroyo et al., 2008). Several techniques and workflows have been
successfully developed in this area, such as methods based on sequential
(or random-walk) McMC, originally developed in the areas of statistical
physics (Neal, 1993).
The McMC method is arguably the most rigorous statistical approach to
sample from the stationary Bayesian distribution; however, when deployed
in direct simulation, it imposes a high computational cost. To improve the
performance of the McMC method, several enhancements were proposed,
based on a two-step proposal of jointly sampling the model and data variables
(Oliver, 1996), by constraining the proxy models using the streamline
sensitivities (Efendiev et al., 2005; Ma et al., 2006; Maucec et al., 2007,
2013a,b) or by coupling with adjoint methods (Schulze-Riegert et al.,
2016). These techniques enhance the sampling efficiency of the McMC
method and make it applicable for the inversion of large-scale reservoir
models without sacrificing scientific rigor.
Recently, Goodwin (2015) proposed an alternative to random-walk
McMC, namely Hamiltonian McMC techniques which progress rapidly
through the sampled space but require derivatives of likelihood that can
be efficiently implemented with proxy models. In parallel, the development
of AHM tools and approaches has also evolved toward “smart” proxy
models in the form of surogate reservoir models (SRM) (Mohaghegh
et al., 2015) and increasingly popular (meta)heuristic methods, such as
PSO (Mohamed et al., 2010a) and differential evolution (Hajizadeh et al.,
2010). Moreover, developments in the area of AHM are also leading toward
joint inversion of the production and time-lapse seismic data, where the
attributes of four-dimensional (4D) seismic inversion (e.g., water saturation)
can provide spatially rich information on the fluid flow dynamics within
subsurface reservoirs (van Essen et al., 2012; Jin et al., 2012). While the
resulting reservoir model updates exhibit a considerable improvement in
matching the saturation distribution in the field, the potential drawback is
the dependence on the inversion data from 4D seismic surveys, which are
difficult and expensive to obtain.
This section continues with a review of modern model calibration and
inversion techniques and then describes the E&P industry’s prevalent model
parameterization, AHM, and finally outlines a few applications of IAM
wokflows. For further reading, Schulze-Riegert and Ghedan (2007),
Oliver and Chen (2011), and Rwenchungura et al. (2011), among others,
provide comprehensive overviews of recent advancements made in the area