Boolean Spectral Analysis in Categorical Reservoir Modelling

Summary The work introduces a new method for simulation of facies distribution for two categories based on Fourier analysis of Boolean functions. According this method, two categories of facies distributed along vertical wells are encoded as Boolean functions taking two values. The subsequent simulation process is divided into three consecutive steps. First, Boolean functions of well data are decomposed into a binary version of Fourier series. Then, decomposition coefficients are simulated over 2-dimensional area as stationary random fields. Finally, synthetic data in the interwell space is reconstructed as Fourier sum from simulated coefficients. The new method was implemented in an experimental software and tested on a case of real oil field.