The 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.
Limiting the subject
In the context of this paper, "petrophysical uncertainty" is limited to the uncertainty in the petrophysical variables porosity (F), water saturation (Sw) and net reservoir definition. Uncertainty in other variables, e.g. permeability, may be very important for reserves estimates, and many aspects of petrophysical uncertainty are relevant for individual well related decisions (e.g. perforate or not). Such aspects will not be discussed here.
The Classical Petrophysical Evaluation.
In this paper it is assumed that a "Classical Petrophysical Evaluation" (hereafter abbreviated CPE) has been performed. CPE is tentatively defined by:The main input to the evaluation are evenly sampled well logs, subject to service company processing, such as environmental corrections and corrections for mud filtrate invasion effects.These well logs are used in an evaluation model where the basic assumption is that the log value at each incremental depth is representative for the corresponding rock properties within one log increment rock thickness.This one increment rock thickness is classified either as net reservoir or as non-net reservoir.Parameter values applied in the model may be based on log data themselves or on other sources, in particular core measurements.
The Classical Petrophysical Evaluation.
In this paper it is assumed that a "Classical Petrophysical Evaluation" (hereafter abbreviated CPE) has been performed. CPE is tentatively defined by:The main input to the evaluation are evenly sampled well logs, subject to service company processing, such as environmental corrections and corrections for mud filtrate invasion effects.These well logs are used in an evaluation model where the basic assumption is that the log value at each incremental depth is representative for the corresponding rock properties within one log increment rock thickness.This one increment rock thickness is classified either as net reservoir or as non-net reservoir.Parameter values applied in the model may be based on log data themselves or on other sources, in particular core measurements.
