Derivation of Stochastic Equations for Computational Uncertainties in Petro-Physical Properties Using a Simplified Algorithm

Abstract

This paper presents a simple mathematical algorithm or procedure for computing the uncertainties at the various percent of data input, using the stochastic approach of simulating the input variables to compute the output variables. A simple algorithm was used to derive stochastic equations for some selected petrophysical parameters using the relative standard deviations techniques (σ). These equations also known as reference work equations were found to produce reasonably accepted magnitude of uncertainties in the different parameters associated with cores. Equations were derived for the percent uncertainties in the values of the pore volume of the core - V_p, the fluid saturation – S_w, S_or, the porosity of the core – Φ, formation factor - F, bulk density – ρB, the derived porosity - Φ_L and the derived permeability – K_BU, Kro, Krw. The uncertainty equations can also be used to define the maximum level of uncertainty that can be tolerated in any independent variable if the maximum uncertainty to be tolerated in the dependent variable is known

Keywords: Stochastic equations, petrophysical parameters, percent uncertainties, Mathematical algorithm, standard deviations, partial derivatives, degree of accuracy, empirical models.