Uncertainty quantification of petroleum reservoir models is one of
the present challenges, which is usually approached with a wide range
of geostatistical tools linked with statistical optimisation or/and
inference algorithms. Recent advances in machine learning offer a
novel approach to model spatial distribution of petrophysical properties
in complex reservoirs alternative to geostatistics. The approach
is based of semisupervised learning, which handles both ?labelled?
observed data and ?unlabelled? data, which have no measured value
but describe prior knowledge and other relevant data in forms of
manifolds in the input space where the modelled property is continuous.
Proposed semi-supervised Support Vector Regression (SVR) model has
demonstrated its capability to represent realistic geological features
and describe stochastic variability and non-uniqueness of spatial
properties. On the other hand, it is able to capture and preserve
key spatial dependencies such as connectivity of high permeability
geo-bodies, which is often difficult in contemporary petroleum reservoir
studies. Semi-supervised SVR as a data driven algorithm is designed
to integrate various kind of conditioning information and learn dependences
from it. The semi-supervised SVR model is able to balance signal/noise
levels and control the prior belief in available data. In this work,
stochastic semi-supervised SVR geomodel is integrated into Bayesian
framework to quantify uncertainty of reservoir production with multiple
models fitted to past dynamic observations (production history).
Multiple history matched models are obtained using stochastic sampling
and/or MCMC-based inference algorithms, which evaluate posterior
probability distribution. Uncertainty of the model is described by
posterior probability of the model parameters that represent key
geological properties: spatial correlation size, continuity strength,
smoothness/variability of spatial property distribution. The developed
approach is illustrated with a fluvial reservoir case. The resulting
probabilistic production forecasts are described by uncertainty envelopes.
The paper compares the performance of the models with different combinations
of unknown parameters and discusses sensitivity issues.