Uncertainties in hydrocarbon saturation calculations have to be quantified and managed prior to STOIP/GIP estimations for economics evaluation of reserves. There are numerous statistical tools to do the quantification of variances. This study compares the root-mean-squared (RMS) error in the results of saturation-height-function (SHF) as functions of input variances against Markov Chain Monte Carlo (MCMC) treatment of the same. Deterministic aggregation of errors in SHF (or variances of results -Sw-) via RMS against the simulations of solutions of SHF with randomly selected inputs of a given range (MCMC) are compared to evaluate the error margins in deterministic against probabilistic treatments of the same data and equations.
RMS-driven error estimations are more sensitive than Monte Carlo (MC) simulations of errors when a large error in one of the inputs may produce disproportionate weight on the formulations originating from partial derivatives of the equation. However, Monte Carlo approach has also theoretically questionable treatment of data due to conceptual violation of independency of the individual variables in subject equation because of inter-dependencies of permeability to porosity in our models. However, these potential issues are circumvented by the proper range for the systematic errors (due to measurement and treatments) in RMS and by using Markov Chain method in MC, respectively.
The comparison of variances (error margins) from RMS versus MCMC methods are presented for different forms of SHF (e.g., Leverett-J and modified forms). This study presents the ranges of Sw determined from two different approaches as avenues of selecting the more appropriate methodology for a specific case. The width of the confidence intervals from RMS is proportional to the RMS-driven error margins while Monte Carlo simulation of the Sw by SHF also yielding the boundaries where the outcome of a specific J-function would lie.
Estimations of in-place hydrocarbon volume and reservoir modeling require calculations of uncertainties in petrophysical properties together with other relevant data. Based on outcome of uncertainty computations, field development and required data acquisition need to be managed by putting either tighter constrains on data acquisition and interpretation methods or changing the course of actions and directions of field progress. The impact of uncertainties on net present value or anticipated return on total investments is large enough to demand the quantification of uncertainties at every stage of the field activities and development.