Fractals in Reservoir Engineering


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American Journal of Science, Engineering and Technology. Most correlation equations of rock permeability are usually based on the Euclidean geometry concept. Pore geometry and structure of most porous rocks are very complex, therefore non-Euclidean geometry concept, e. This paper presents a new equation for sandstone permeability involving other properties and fractal dimensions of pore space and surface.

It is shown that parameters such as tortuosity, internal surface area, and shape factor can be replaced by fractal dimensions.

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As natural porous media are mostly anisotropic, this study enables us to identify factors that affect the anisotropy. The pore space and surface fractal dimensions for each orthogonal direction for each sample was determined by box counting method. The results of this study demonstrate that calculated directional permeability of the high permeability samples is very close to the measured one after corrections were made for pore sizes of less than one micron.

This finding suggests that micropores of the samples may be a major factor not contributing to fluid flow. For the low and medium permeability samples, however, an additional pore geometrical correction is needed.


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The additional correction factor is considerably different for different directions of fluid flow, indicating that the anisotropy is due to the difference in directional pore structural characteristics. Kozeny, J. Carman, P. Scheidegger, A. Dullien, F.

Fractals in Reservoir Engineering - H. H. Hardy, Richard A. Beier - Google книги

Bear, J. Srisutthiyakorn, N. Haro, C. Krauss, E.


  1. Fractals: Concepts and Applications in Geosciences - CRC Press Book.
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  7. H.H. Hardy (Author of Fractals in Reservoir Engineering);

Civan, F. Mandelbrot, B. Falconer, K.

Katz, A. Pape, H.

Reservoir Engineer, Daniel Ventura Alonso

We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally.

Fractals in Reservoir Engineering

The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Varying the fractal dimension and anisotropy factor of each of these physical properties can tell us how sensitive the reservoir is to uncertainties in its heterogeneity and anisotropy as well as how poroperm cross-plot shapes are controlled.

Initial reservoir simulation results of the tested models with this approach show that heterogeneity in the reservoir's physical parameters has a little effect on high and moderate porosity and permeability reservoirs. The effect is more pronounced in the models representing tight reservoirs. The production from more heterogeneous reservoirs lasts a little longer, but eventually declines faster.


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  • This may be attributed to the fact that water channelling is more significant as heterogeneity increases.

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