Stochastic Simulation of Fracture Density for Permeability Field Estimation
Authors: Olarewaju Joseph , Ghori Saleem , Fuseni Alhasan , Wajid Mohammed 
Published: December 2007

Abstract
One of the most difficult tasks in the characterization of reservoir heterogeneities is the representation of naturally fractured reservoirs. Geocellular models for reservoir simulation often require geological interpretation of the distribution of natural fractures both areally and vertically. The FMI data from horizontal wells provide valuable information about the distribution and orientation of natural fractures. Stochastic approaches can be useful in simulating fracture density derived from the FMI logs that would honor the known data. This paper presents stochastic simulation methods for developing the distribution of fracture density in one of the highly fractured reservoirs in Saudi Arabia. Sequential indicator simulation (SIS) method was used with two different variogram models, namely, the fractal and the spherical correlation models. The resulting fracture density field was useful in generating a 3D fracture permeability field for reservoir simulation by using it as a secondary data set in a permeability co-conditional simulation task reported elsewhere.

Introduction
The purpose of this research was to develop a quantitative measure of the intensity of fracturing in the Hanifa reservoir. The data available for accomplishing this difficult task came from the Formation Micro Scanner borehole imaging log performed on four near-horizontal wells. This high resolution borehole imaging log is an extremely powerful tool that enables geologists, geophysicists, and petroleum engineers to evaluate complex reservoir systems. The high resolution images obtained from this tool allow visualization of the reservoir in the vicinity of the borehole.
This borehole imaging log was run on the four highly deviated wells to accurately characterize the fracture system. The key data used in this work is the interpreted fracture density index traces from all the four wells. Basic statistical and variogram analyses were performed on this data. The sequential indicator conditional simulation approach was chosen for the density field generation due to high deviation of the data from Gaussianity. The resulting 3D field of fracture density index proved useful in developing the fracture permeability description of this reservoir. Some selected areal and cross-sectional slices are presented in the paper.

Geology
The Hanifa reservoir of the Abqaiq field consists of mainly mud-rich carbonates, skeletal wakestone with organic laminations and high amplitude stylolites. The Hanifa reservoir was deposited as a carbonate build-up within the Arabian intrashelf basin. The carbonates are dominated by micropores with porosity higher than 30% and permeability less than 10md. The reservoir and geological studies of this reservoir, showed that the fluid flow system of the Hanifa South Dome reservoir is mainly controlled by the presence of fractures. The fracture system in this reservoir which exists in the form of high angle hairline fractures, possesses relatively high permeability and plays a profound role in fluid deliverability. The fractures, which are all nearly vertical, are usually less than 1mm wide and contain hydrocarbon residue, and calcite cement. Many of these fractures are associated with high amplitude stylolites that also contain hydrocarbon residue.
Stylolites, which are mostly diagenitic rock features present in limestone, dolomite, and sandstone, cause the development of tension fractures. The natural fractures occur in two kinds. The first kind are associated with stylolite; while the second kind are non-stylolitic fractures which are near vertical hairline fractures cemented with calcite or lined with hydrocarbon stain. Stylolite or stylolitic fractures are tectonic in origin due to thrusting. Relaxation in thrusting direction creates unloading fractures, which can subsequently be filled with calcite. This type of concept has been applied to predict fracture intensity by using structural curvature mapping. The approach assumes that the intensity of fracturing depends on the degree of structural curvature.
P. 121^