Implementation of full permeability tensor representation in a dual porosity reservoir simulator

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Li, Bowei

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Transport and flow phenomena in porous media and fractured rock arise in many fields of science and engineering, including petroleum and groundwater engineering. Over the past few decades, there are two classes of models that have been developed for describing flow and transport phenomena in porous media and fractured rock. They are the continuum and discrete models. Continuum models include single porosity and dual porosity models. The latter is popularly applied in simulating flow in naturally fractured systems. Discrete feature models explicitly recognize the fracture system’s geometrical properties, such as orientation and intensity. But shortcomings have been experienced for such discrete models in that large computational efforts are required for a realistic treatment of a heavily fractured system. Such a large fractured system may contain millions of fracture features. The huge demand of computational resources may seriously undermine the application of discrete models for such systems. Moreover, the discrete feature model is more difficult vii to use for multiphase flow and complex recovery mechanisms for oil recovery process. The dual porosity model, a subclass of the continuum model, is a favorable approach to study flow in naturally fractured systems. In the dual porosity approach, it is assumed that the fissured porous media can be represented by two colocated continua called the matrix and the fracture system. High conductivity but low storativity typically characterizes the fracture system, whereas the matrix is usually characterized as low conductivity but high storativity. The matrix generally acts as a source that transfers its mass to the surrounding fractures; then fluid is transported to production wells. There are two main reasons for the acceptance of dual porosity model. The first reason is its ability to handle the length scale inconsistency between matrix and fractures. It is impractical to simulate a fractured system by a single porosity approach if a matrix block is gridded to the fracture’s length scale. But the dual porosity approach may divide the physical problem into two interactive problems. Therefore the dual porosity model captures the length scales of the physical problem, and is much easier to handle computationally. The second advantage of the dual porosity model is its capacity to address complex local phenomena at the matrix boundary surrounded by fractures. Conventional dual porosity models generally use a diagonal permeability tensor to formulate and discretize the flow equations for the fracture system. However, such practice does not always adequately reflect the characteristics of natural fractures characterized by heterogeneity and anisotropy ascribed to the fracture’s varied orientation, apertures, and intensity. Therefore, conventional dual porosity models may overlook the naturally fractured system’s directionality and heterogeneity. This study is designed to develop a novel approach to model fluid flow in natural fractured systems with a dual porosity approach. In the study, a full viii permeability tensor representation of fracture flow is implemented in the UTCHEM dual porosity chemical flood simulator. The full permeability tensor feature in the fracture system adequately captures the system’s characteristics, i.e., directionality and heterogeneity. At the same time, the powerful dual porosity concept is inherited. The capability of modeling the local complex physical phenomena is maintained in the simulator. The implementation has been verified through studying waterflooding in a cylindrical reservoir, and waterflooding in a spherical reservoir. As an application of the implementation, a study on a naturally fractured system was conducted. Simulation results were compared with that generated by the Fracman simulator (Golder Associates, 2000) a discrete feature model. Another application is waterflooding through a fractured system using dual porosity approach. A conclusion can be drawn from all these studies that for a heterogeneous and anisotropic system, full permeability tensor representation of flow is necessary to accurately simulate flow in such system.



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