Fractal Properties of Braided Fluvial Deposits for Characterization and Simulation of Reservoir Heterogeneity
Authors: Becker Mauro R. , Lake Larry W. , Tyler Noel 
Published: December 2007

Abstract
Integrated geologic and petrophysical analysis of exposure of sandy braided fluvial reservoir allowed the mapping of reservoir flow unit and flow barriers architectures and properties. The geometry of the flow barrier on two different outcrops (squared panels) showed diverse fractal characteristics. The multi storey (amalgamated coarse-grained sandstone) exposure has a fractal dimension of around 1.70, whereas exposure of a single fining-upward storey (conglomerate to fine-grained sandstone) intercalated with tabular mudstone is 1.94. Two-dimensional fractal simulation algorithms were used to transfer the complex reservoir heterogeneity structure to a subsurface analogous production zone. Qualitative and quantitative appraisals indicate that conditioning is essential for obtaining a geologically' acceptable field of heterogeneity by fractal simulations.

INTRODUCTION AND OBJECTIVES
Fractal theory presented a new method for quantitatively describing complex and irregular natural shapes. Fractal structures with characteristic self-similarity, are frequently recognized in geologic objects and data sets over a wide range of scales from reservoir pore systems to faults.
The main objective of this work is to verity the applicability of fractal concepts to the quantitative analysis of the distribution of reservoir properties. The analysis focused on the realm of geometric shapes or objects defined by the variability of rock properties. Therefore, fractal analysis was applied to the geometry and distribution of lithofacies-defined reservoir units.
Two roadcuts in fluvial facies of the Cretaceous A Formation (Potiguar Basin, northeast Brazil) with exposures (300 m long by 7 m high) on both sides of an E-W highway were selected for this study because of the geologic similarity to braided fluvial reservoirs in the same formation. Outcrop 99 km displays an amalgamated coarse-grained multistorey sandstone sheet without a general vertical textural trend. One storey, with a fining-upward textural trend (conglomerate to fine-grained sandstone), intercalated with tabular mudstone layers is recognized at the outcrop 98 km exposures.
Studies on some reservoirs in the Potiguar Basin suggest that oil saturation is controlled by lithofacies characteristics. Only the coarsest porous sandstones were fully oil-invaded. Therefore, the sedimentologic signature is also present in the oil distribution in these reservoirs. So, at the lithofacies scale, the rocks can be distinguished as two reservoir units: oil-bearing coarse sandstones and all other water-saturated lithologies. We obtained a binary mosaic formed by the two reservoir units based on the two-dimensional distribution of these units at the outcrops. These mosaics became the object-image analyzed by box counting fractal and multifractal techniques.
Once the fractal or multifractal character of the reservoir rock property was determined and its dimension measured, stochastic methods transported the spatial distribution of properties to geologically analogous reservoirs where data are limited and property variability unknown. The final purpose of this analysis was to test whether fractal theory can improve the characterization of rocks that store fluids and control fluid-flow in petroleum fields.

FRACTAL AND MULTIFRACTAL ANALYSIS OF OUTCROPS
Fractal and multifractal theories are comprehensively discussed by many authors. A fractal dimension analysis of the interpreted south exposures of the two roadcut outcrops was performed using the basic assumption of two classes of reservoir units with distinct permeability.