Three methods have been reported by which random fields can be generated to represent permeability fields for use in reservoir simulation. Because these fields would be the basis of the simulations, it is essential that the procedure of their generation, and the qualifications of the methods themselves, should be investigated closely. There seem to have been no attempts reported to identify the general characteristic needed by which to qualify a particular method for this use.
The methods that are considered to generate random fields in this study are: the Fast Fourier Transform Method (FFTM) developed by Gutjahr,1 the Source Point Method (SPM) introduced. by Heller,2 and the Turning Bands Method (TBM) which was originated by Matheron3 and further developed by Montoglou and Wilson.4
A structural analysis, that takes spatial correlations into consideration, has been performed on these three methods. Some serious problems, which had also been observed by McKay,5 have been demonstrated in TBM. Additionally, FFTM, in Which covariance functions are constructed for the generation of the random fields, is shown to be preferable to SPM in depicting the detailed permeability structure.
For most reservoirs, permeability bas been reported to be distributed log-normally. In this work, the Kolmogorov-Smimov normality test was performed on each of the three methods. It was noted that a normality test alone is not a sufficient criterion by which to select a particular method for the generation of a random field. To this must be coupled a structural analysis, so that spatial correlations can be considered.
Geostatistical techniques, kriging, and conditioned simulation are used on the generated fields. These techniques take into account the actual measured data taken from laboratory or field testa. By using these techniques, it becomes possible to discard the conventional assumptions of uniformity that have been used in most reservoir simulations and to accommodate a credible model of the actual non-uniformity (heterogeneiry) of the reservoir.
Adoption or these procedures is expected to lead to more reliable predictions and to make possible the detailed study or the effects of reservoir parameters.
The classic approach to reservoir flow modeling is conceptual and deterministic. The functions representing the classic models are almost always defined by a boundary value problem based on the partial differential equation of flow through porous media. In the classical approach, none of the variables or parameters are defined in terms of probabilities. The need for a probabilistic approach in determining the reservoir parameters will become evident in the following sections.
Non-uniformity arises in sedimentary rock early in the process of sedimentation. The postdepositional spatial variations at larger scale than sedimentation result from diagenesis and tectonic changes. Although these variations are caused by deterministic processes, the natural occurrence of reservoir rock properties can be said to be random, in a sense that is made more precise in the following paragraphs.
Several types of heterogeneity may be found on different scales, and they influence various rock properties. The most important parameter influencing miscible transport is the magnitude and spatial distribution of rock permeability.