Fractured Reservoir Discrete Feature Network Technologies

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In this task, MIT will extend the hierarchical fracture model to three dimensions and will develop a reliable inference procedure. The model will also be independently validated with Yates field data.

Task 1.2.1: 3D Hierarchical Fracture Model

In this task, MIT will develop a 3D Hierarchical Fracture Model appropriate for fractured reservoirs such as the Yates field. The model will be based on existing work in development of structural models for fractured reservoirs, previous hierarchical fracture models, and Yates field data.

Task 1.2.2: Model Verification

In this task, MIT will demonstrate the applicability of the discrete fracture model developed in Task 1.2.1 by comparison against Yates field data.. The comparison can be performed via statistical tests of simulated exposures against the observed data. In addition to the statistical validation, this task will include geological structural analyses, and will incorporate a subjective probabilistic evaluation process.

Discussion:

A fracture system model will be developed on the basis of the Yates field data but the software and general approach is useful for a wide variety of reservoirs and non petroleum applications. Fracture system models can be grouped into three categories:

• Mechanical Models;
• Geometric Models;
• Combined Geometric-Mechanical Models.

Mechanical modeling is probably the most desirable approach in that it tries to duplicate the actual fracture nucleation and propagation mechanisms which have acted throughout the geologic history. However, only relatively simple fracture patterns can be replicated by mechanical models. In particular, the three dimensional characteristics and the often pervasive clustering can be modeled to a limited extent only. Further development is likely to lift some of these limitations.

Purely geometric models, often called conceptual models, are more common. Such models seek to reproduce features observed about the fracture pattern, rather than to simulate the mechanical processes that formed the fractures. A wide variety of stochastic models exist. Many of them are three-dimensional and capture, at least to a certain extent, the clustering of geometric fracture characteristics. Since they simulate what is observed rather than what caused the fracture pattern, it is not easy to produce complete representations from the limited information from wells or seismic.

Combined geometric-mechanical models consist of geometric modeling procedures which attempt to duplicate typical mechanical processes without explicitly solving the equations thought to govern brittle fracture in rock. Examples are the model by Martel et al. (1991) in which fractal-like objects are created in two dimensions using so called Iterated Function Systems conditioned on geologic information, and the two-dimensional Hierarchical Model developed at MIT (Lee et al. 1990). In the latter, the hierarchy of fracture genesis is modeled by creating fracture sets in sequence and by incorporating dependencies (or independencies if applicable) between different fracture sets in this process. Initially, this model was only applicable to two fracture sets. The Enhanced Hierarchical model (Yu, 1992) lifted these limitations. It also added new features such as linear clustering and the “empty disc” model. The former allows one to model fracture traces which are roughly aligned along a line but not interconnected; the latter makes it possible to represent areas which fracture traces. The Enhanced Hierarchical Model was successfully applied to represent an outcrop map of the Sotra site in Norway.

All current models are limited to two dimensions. Also, so far the hierarchical model has been developed for completely mapped areas and not from the usually much more limited information typical of core, well logs or lineament maps.

The research in this Task will extend the hierarchical fracture model to three dimensions and will develop a reliable inference procedure. The model will also be independently validated with Yates field data.

The main characteristic of the three dimensional version is the modeling of geometric processes which represent mechanical processes. The three major geometric/stochastic processes will be:

1. The plane process,
2. the translation and rotation process, and
3. the termination process.

The proposed plane process represents an extension of what has been developed by Veneziano (1978) and Dershowitz (1979). It will consist of a homogeneous line network with an inhomogeneous marking process. The translation and rotation process will consist of a random shifting of the marked polygons or parts thereof in the vicinity of the original fractures. These two processes are used to create independent fracture sets and dependent fracture sets. The dependencies can be in form of orientation - location - and size/share relations. Finally, the third or termination process will be used to specify the form of the intersection of the independent and dependent fracture sets.

The three basic stochastic geometric processes of the proposed three-dimensional model can be related to the underlying mechanics and geology; the plane process to represent the principal tensile and shear planes defined by the existing stress field; the process of subdividing the planes into fractured and intact regions to model fracture initiation at the points of stress concentration; the translation and rotation process to account for the change of the stress field due to initial fracturing. Various mechanical processes may be represented by the geometric procedures modeled so far, for example:

• the often-encountered zones of closely spaced parallel fractures by clustering of location, orientation and size characteristics;
• the en-echelon or reverse step fractures as produced by Riedel type mechanisms during faulting by a direction dependent rotation and translation;
• the propagation of tensile fractures constrained by existing fractures parallel to the propagation direction, by a termination function.

The inference procedure has two major objectives: first, determination of the model parameters from field data, and second, verification of these parameters through a statistical comparison of the simulated fracture networks to the observed natural fracture patterns. The model parameters which have to be inferred from the available field information are:

• the association of the observed fractures with fracture sets;
• the dependence or independence between different fracture sets;
• the spatial variation of the fracture intensity and the clustering of fractures in space;
• the distribution of fracture orientations within fracture sets;
• the distribution of fracture sizes within fracture sets;
• the connectivity of the fracture system and the termination probabilities.

Various methods proposed by other authors may be suitable for the inference procedures. For example, the procedures used by Lee et al. (1990) and Yu (1992) in the two-dimensional hierarchical model to define fracture trace sets and their interrelation, can be used to determine independent and dependent fracture sets based on data from outcrop maps. The software FracMan developed by Golder Associates, Inc., can assign fractures to sets according to user specified weighted fracture characteristics, based on data from borehole exposures and other field surveys.

Simulations with FracMan have also made it possible to establish empirical relationships between trace length distributions and fracture size distributions (see, for example, Dershowitz and Herda 1992. Most of the standard surveying methods produce data which give limited information about the geometric characteristics of the rock fracture systems. For example, different three-dimensional fracture networks may have the same exposures in well logs and outcrop maps (one- and two-dimensional surveys, respectively), but different, unknown, fracture connectivities in space. It is very important to develop an inference procedure that produces a unique representation of a natural fracture system based on its observed exposures. This is where one of the advantages of the proposed model can be seen. The proposed three-dimensional hierarchical model is a geometric -mechanical model, i.e., a model which uses geometric procedures to model mechanical processes. The geologic history of a region is unique. Therefore, if the relationship between the underlying geologic mechanisms and the fracture geometry are employed in the inference procedure, together with the statistics of the fracture geometry in exposures, it will be possible to produce a unique stochastic representation of an observed fracture system. This is also where another major innovation will be applied. The genesis concepts formulated by geologists familiar with the area will be incorporated through a Bayesian updating procedure. Geologists will be asked to subjectively assess the possible mechanisms and to rank them. This information will be transformed into likelihood functions which in turn will be combined with the original stochastic characteristics of the model to produce updated characteristics.

Once the fracture system is produced, it has to be compared to the real system which is being modeled. The comparison can be performed via statistical tests of simulated exposures against the observed data. For that purpose, the synthetic fracture system is intersected with “planes of outcrops” and “wells” consistent with the field investigation program. Then the statistics of the outcrop and well simulations are compared to the statistics of the observed data. The methods developed by Lee et al. (1990) and Yu (1992) in two-dimensions can be applied for the statistical analysis. In case of significant differences between simulated and observed data, the model parameters have to be modified, and the whole process of fracture system generation repeated. In addition to the statistical validation, we also intend to incorporate a subjective probabilistic evaluation. This is, in essence, an extension of the subjective assessment of possible mechanisms mentioned earlier; however, geologists will now be asked to evaluate the resulting fracture geometry and suggest improvements which will then be incorporated in the updated process.