Sampling Space of Uncertainty Through Stochastic Modelling of Geological Facies
Authors: Massonnat G.J. 
Published: December 2007

Abstract
The way the space of uncertainty should be sampled from reservoir models is an essential point for discussion that can have a major impact on the assessment, development and economics of hydrocarbon fields. Stochastic modelling of geological and petrophysical reservoir characteristics is a means to obtain the desired data, insofar as the different sources of uncertainty are well assessed and represented in the uncertainty evaluation process.
A classification and hierarchization of the sources of uncertainty is proposed in this paper, and discussed in respect of the type of geological process at the origin of the reservoir.
The impact of the different levels and sources of uncertainty on elements such as volumetrics or final recovery is quantified. It has been demonstrated that decisions as significant as stationarity, organisation of reservoir heterogeneity or confidence in hard data are of prime importance compared to other parameters. Resampling techniques are used to assess on various field cases the uncertainty in relation to the geological representativeness of the wells.
The evolution of this uncertainty with the quantity of hard data (wells) and the quality of knowledge (zonation) has been quantified from synthetic cases (different types of sedimentary bodies) and a real case (Anguille Marine field).
Both a general law to limit uncertainty with the quantity of data, and a possible increase of uncertainty with knowledge development are demonstrated herein.
The assessment phase is a crucial step in the life of a field, since the oil industry is faced today with titanic challenges - deep offshore, increasingly complex and small size reservoirs, fierce international competition - which imposes a triple approach on the industry:–economical risk-taking related to the uncertain aspect of the natural object exploited by the industry,–technological research to reduce these uncertainties and the induced economical risk,–qualification and quantification of these uncertainties so that the risk is known, selected and managed by decision makers.
Many technical branches of knowledge study the natural object during the assessment phase. The uncertain, or even erroneous, results obtained by each individual branch contribute to the overall uncertainty. Among these different sources of uncertainty, geology plays a major role insofar as it is the main thread towards the spatial distribution of characteristics of the reservoir through which fluids will flow during the field production phase.
For this reason, an investigation of the sources of geological uncertainty appears to be a good method of sampling the space of uncertainty. Obviously all the space cannot be uniformly and completely sampled since many other parameters cannot be approached from the point of view of geology: reservoir geometry (seismic uncertainty), flows (fluid mechanics),…
The qualification of the sources of geological uncertainty, their quantification, the evolution of their impact on OOIP values and the final recovery of hydrocarbons are the subject of this paper.
The paper discusses in particular the geological scenarios and the input parameters of stochastic models, and assesses their relative significance in relation to the uncertainty induced by the creation of equiprobable stochastic realizations of the reservoir. The geological representativeness of the wells (and more generally of the hard data) is analysed through bootstrap application on field cases and synthetic models.
The evolution of this uncertainty with the quantity of data and geological knowledge is also studied herein.
P. 273^