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. The paper considers a data driven approach
in modelling uncertainty in spatial predictions. Proposed semi-supervised
Support Vector Regression (SVR) model has demonstrated its capability
to represent realistic features and describe stochastic variability
and non-uniqueness of spatial properties. It is able to capture and
preserve key spatial dependencies such as connectivity, which is
often difficult to achieve with two-point geostatistical models.
Semi-supervised SVR is designed to integrate various kinds of conditioning
data and learn dependences from them. A stochastic semi-supervised
SVR model is integrated into a Bayesian framework to quantify uncertainty
with multiple models fitted to dynamic observations. The developed
approach is illustrated with a reservoir case study. The resulting
probabilistic production forecasts are described by uncertainty envelopes.