Characterizing and Modelling of Fractured Reservoirs With Object-Oriented Global Optimization
Authors: Tran N.H. , Chen Z. , Rahman S.S. 
Published: March 2010

Abstract
Modeling of naturally fractured reservoirs is the first step to develop best scenarios for hydraulic fracture treatment, the design of an optimum production method and to evaluate reservoir potential. This paper reviews the state-of-the-art in current methods; hence, presents an integrated modeling methodology, utilizing object-based modeling, stochastic simulation and global optimization. Firstly, as an object-based model, each fracture is presented and treated as a discrete object. A stochastic simulation is carried out to generate an initial fracture network. An objective function is then formulated as the difference in statistics between the initial network and the target. Semi-variogram and other spatial statistical properties (cross variogram, multi-histogram mean and variogram distance) of fracture parameters are included so that the objective function is able to statistically describe representative field data. Subsequently, we use a global optimization algorithm to optimize the objective function. A case study is performed on an actual outcrop fault map to illustrate the proposed methodology's capacity. The results map the outcrop faults very closely.

Introduction
Due to geological reasons, many of the naturally fractured reservoirs (NFR) possess very low permeability, which is inadequate for economic production. Therefore, some permeability enhancement techniques are essential for these reservoirs. However, the underlying principles of such techniques, such as hydraulic fracture stimulation, are complex and progress is hindered due to lack of appropriate geo-statistical fracture description models(1,2). Thus, there are three main reasons for a detailed fracture distribution:To site best locations for production wells;To study the response of natural fractures under stimulation pressure; hence, to develop a best scenario for hydraulic fracture treatment; andTo design an optimum production method and evaluate reservoir potential.
In order to achieve the prescribed objectives, NFR need to be characterized and modeled, which would include descriptions of reservoir boundaries, major faults and medium to small-scale fracture networks(3).

Fracture Modeling Techniques:

State-of-the-Art

Mathematical and Geo-Mechanical Models
Several techniques to simulate NFR have been documented in the literature. Firstly, there are mathematical and geo-mechanical models. Earlier mathematical methods to simulate NFR and fluid flow through them include equivalent continuum(4), discrete network(5) and hybrid models(6). The usual approach relies on simplistic geometrical descriptions of fracture systems (e.g. homogeneous reservoirs, parallel plate fractures, etc.) with primary efforts spent on flow behaviours(7). Many authors use different geo-mechanical approaches for modeling NFR, such as simple curvature analysis, field stress and fracture growth mechanism, and numerical analysis by solving systems of non-linear continuum mechanics equations using finite element methods(8).
However, due to the complex nature of fracture systems, most studies so far have succeeded only in modeling unrealistic homogeneous reservoirs. Moreover, most of these techniques use only a limited source of data, such as seismic or well logs. Hence, in modeling NFR, it is necessary to utilize all data sources in an integrated manner to reach a more comprehensive model(9).

Stochastic Simulation
Stochastic simulation is one of the integrated reservoir modeling approaches. Since explicit fracture information is only