Number of estimators and simulators is used in petroleum engineering applications in order to model the static and dynamic characteristics of hydrocarbon reservoirs. However, the fundamental concepts used in estimators and simulators do vary from each other leading to the necessity of choosing the optimal approach with an extensive care. Geostatistics is perhaps the most widely used technique in simulation which is popularly used in different engineering applications and specifically in reservoir simulation. In this paper, three shortcomings of geostatistics in estimation and simulation are highlighted and alternative methods are proposed. Firstly, Kriging estimator, as is used in geostatistics, guarantees minimum estimation variance if the variogram model is the optimum fit and stationary conditions are met. However, in real situation, these conditions are not always satisfied. Geostatistics is prone to number of deficiencies some of which are discussed in this paper in the context of oil and gas applications and alternative solutions are presented. As such, the incapability of variogram, as being the fundamental tool in geostatistical analysis, in capturing the periodic structure of reservoir formation is shown. Then, it is discussed why the use of signal decomposition tools such as Fourier, fast Fourier and wavelet transform is more advantageous than variogram in this context. Secondly, to overcome the smoothing property associated with geostatistics fractal simulation is recommended as an alternative approach. Finally, it is discussed how intrinsic properties of reservoir can be included in multi-fractal or neural network to improve the estimation and simulation process. This appears to be difficult to apply if geostatistical approaches are used for estimation or simulation purposes.

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