Effectiveness Study of the Spectral Approach to Geostatistical Simulation

The spectral simulation approach is a recently developed geostatistical method of stochastic reservoir property simulation. The method has theoretical advantages over classical methods and the present work studies its practical effectiveness applied to synthetic data and real case of oil reservoirs. The study provides analysis of simulations results and describes strengths and limitations of the spectral method as well as application domain where it is most efficient. The spectral method is based on Fourier analysis of well log data and consists of three major steps: decomposition of the well logs into Fourier series, simulation of Fourier coefficients in the interwell space and reconstruction of synthetic logs at every lateral point as sum of the Fourier series. The method was implemented in a software application and was used by authors for simulation of three-dimensional reservoir properties. The effectiveness of the spectral method was studied based on simulations of continuous variables on a synthetic model. Simulations performed by the spectral method were compared to simulation results obtained on the same data by the more traditional method of sequential Gaussian simulation (SGS) provided by a commercial software. Analysis of the results from quantitative and qualitative points of view showed that the spectral method performed better at reproducing vertical non-stationarities observed in well data. Practical applicability of the spectral method was demonstrated by simulation of porosity on a real oil field model, characterized by increase of porosity along depth with higher values of porosity closer to the bottom of the simulated layer. It was shown that the spectral method handled better this type of heterogeneity and reproduced distribution of porosity along the vertical axis closer to that of well data.