A description of an integrated approach to the quantification of uncertainty in the estimation of oil-in-place (OIP) is presented. The approach is unusual in two respects: firstly, the uncertainty is quantified by using traditional stochastic methods combined with an analysis of the representativity of wells, secondly, the oil-in-place is calculated within a sedimentological framework, that is, by genetic sedimentary units. The former step is performed by a method known as the "Bootstrap" technique. The geostatistical modelling is constrained by detailed seismic, well and pressure data.
The statistical and geostatistical methods are presented, along with a discussion of the broader implications for the quantification of uncertainty. The second part of the paper details the application of the technique to an appraisal stage field.
The appraisal phase is a crucial time in the life of a field, particularly as fields are increasingly being exploited on the margins of economic viability. Early estimation of OIP is an important decision making tool for management. If, however, the result is a unique number, it may be at best misleading; quantification of the uncertainty on the estimation of OIP is vital. The increasing power of computers, coupled with increasing competence in their use, has led to a situation in which geostatistical reservoir modelling is developing into a routine aspect of reservoir characterization.
Geostatistical techniques allow for the modelling of spatial variability of geological and petrophysical parameters. Multiple, equiprobable reservoir images can be generated from which the impact of reservoir heterogeneity and variability on OIP uncertainty can be quantified. However, this does not yield a complete analysis of uncertainty, since all of the images are created from a single, fixed heterogeneity model. Although this model is fixed, the parameters therein (facies frequencies, facies geometries …) are generally unknown.
The first part of this paper addresses the problem of uncertainty modelling in a spatial context, where both the impact of local variability and lack of knowledge on model parameters must be evaluated.
The second part presents a case study in which the geological uncertainty, the geostatistical uncertainty and the petrophysical uncertainty (mainly due to thin beds) are quantified. The combined effects of such uncertainty analysis produces a wide range of estimates of oil-in-place (factor of 3). All the results were calculated within the constraints imposed by seismic and well data.
Part 1: Geostatistics and Uncertainty
Traditionally, stochastic simulation is used to produce equally probable realizations of the spatial distribution of reservoir properties in 3D. These realizations are characterized by spatial variations of some property (e.g. lithofacies). Each realization represents a likely image of heterogeneity, around a fixed statistical model whose parameters are assumed known: facies frequencies, indicator variograms, size distributions of objects. These parameters are used as input for subsequent geostatistical algorithms.
The equiprobable realizations may be used to assess the potential variation of dynamic reservoir behaviour due to different spatial arrangements of reservoir properties.