An Upscaling Procedure for Constructing Generalized Dual-Porosity/Dual-Permeability Models from Discrete Fracture Characterizations

Abstract

Abstract The geological complexity of fractured reservoirs requires the use of simplified models for flow simulation. This is often addressed in practice by using flow modeling procedures based on the dual-porosity/dual-permeability concept. However, in most existing approaches, there is not a systematic and quantitative link between the underlying geological model (in this case a discrete fracture model) and the parameters appearing in the flow model. In this work, a systematic upscaling procedure is presented to construct a generalized dual-porosity/dual-permeability model from detailed discrete fracture characterizations. The technique, referred to as a multiple subregion model, represents an extension of an earlier method that did not account for gravitational effects. The subregions (or subgrid) are constructed for each coarse block using the iso-pressure curves obtained from local pressure solutions of a discrete fracture model over the block. The subregions thus account for the fracture distribution and can represent accurately the matrix-matrix and matrix-fracture transfer. The matrix subregions are connected to matrix in vertically adjacent blocks (as in a dual-permeability model) to capture phase segregation due to gravity. Two-block problems are solved to provide fracture-fracture flow effects. All connections in the coarse scale model are characterized in terms of upscaled transmissibilities, and the resulting coarse model can be used with any connectivity-based reservoir simulator. The method is applied to simulate 2D and 3D fracture models, with viscous, gravitational and capillary pressure effects, and is shown to provide results in close agreement with the underlying discrete fracture model. Speedups of about a factor of 80 are observed for a complex 3D example. 1. Introduction The accurate simulation of fractured reservoirs remains a significant challenge. Although improvements in many technical areas are required to enable reliable predictions, there is a clear need for procedures that provide accurate and efficient flow models from highly resolved geological characterizations. These geological descriptions are often in the form of discrete fracture representations, which are generally too detailed for direct use in reservoir simulation. Dual-porosity modeling is the standard simulation technique for flow prediction of fractured reservoirs. This model was first proposed by Barenblatt and Zheltov [1] and introduced to the petroleum industry by Warren and Root [2]. The key aspect of this approach is to separate the flow through the fractures from the flow inside the matrix. The reservoir model is represented by two overlapping continua---one continuum to represent the fracture network, where the main flow occurs, and another continuum to represent the matrix, which acts as a source for the fracture continuum. The interaction between these two continua is modeled through a transfer function, also called the shape factor. Though very useful, the model is quite simple in that the geological and flow complexity is reduced to a single parameter, the shape factor. This parameter is in general different for each grid block depending on the underlying geology and the type of flow.