Quantification of Petrophysical Uncertainty and Its Effect on In-Place Volume Estimates: Numerous Challenges and Some Solutions

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe subject of this paper is the quantification of uncertainty in the petrophysical variables porosity, water saturation and net to gross ratio as estimated in wells, and the significance of such uncertainty for in-place volume estimates. If the nature of petrophysical uncertainty is not properly accounted for in this process, directly misleading uncertainty estimates may be derived. This can be the case if one or more of the following issues are disregarded:Firstly, the petrophysical variables are not independent. This can be taken into account by replacing the individual petrophysical variables with the variable Hydrocarbon Pore Fraction, HCPF, in the uncertainty estimation. This variable is the hydrocarbon fraction of the gross rock volume, and uncertainty in this variable can conveniently be combined with uncertainty in gross rock volume to derive the uncertainty in hydrocarbon pore volume (HCPV) Secondly, randomly distributed errors in petrophysical variables are usually insignificant for in-place volume uncertainty, due to averaging of large data volumes. Systematic errors are not removed by averaging, and a key issue is the estimation of such errors, which cannot be done by applying statistical procedures to the data. The effect of such errors on HCPV uncertainty is critically dependent on the degree of correlation between errors in different wells and zones.Thirdly, the errors caused by the combined effect of reservoir properties, differences and limitations in logging tool response functions and the choice of evaluation model and parameters are a major source of uncertainty in any reservoir with some degree of heterogeneity. Therefore, estimating the uncertainty at the log depth increment level by more or less rigorous and comprehensive error propagation or Monte Carlo methods based on log, core measurement, evaluation model and parameter uncertainty only, is insufficient.The systematic nature of the petrophysical uncertainty in wells will cause general HCPV level uncertainty. The uncertainty relating to mapping of properties between wells is an issue by itself. However, in many cases uncertainty related to water saturation mapping functions can be conveniently linked with uncertainty in HCPF in the wells, and quantified by simple spreadsheet methods as part of the petrophysical uncertainty estimation. The methods and algorithms for doing so are also given in this paper.

Judgment in Probabilistic Analysis

“…12,13 For example, the effects of porosity and water saturation in a gas reservoir can be modeled together as hydrocarbon porosity. In this way, the analyst circumvents the need to quantify and quality control the correlation between the parameters.…”

“…Fylling 12 provides a useful examination of these uncertainties as it applies to petrophysical analyses. Murtha 11 describes how distributions, i.e., range and form, can be constructed from three general sources: fundamental principles (primarily on form), expert opinions and historical or analog data.…”

“…For example, different correlations for fluid properties, different models for interpreting log responses, 12 and different velocity mapping techniques may all result in wholly different figures for the uncertain variables. If an analyst considered only one method, he might artificially reduce the actual uncertainty in the result.…”