Upscaling Fracture Networks for Simulation of Horizontal Wells Using a Dual-Porosity Reservoir Simulator
Authors: Ding Yu , Basquet Remy , Bourbiaux Bernard 
Published: October 2006

Summary
One difficulty in fracture upscaling for field-scale dual-porosity reservoir simulation is the determination of equivalent gridblock fracture permeability, which depends on the type of boundary conditions imposed on the discrete-fracture-network (DFN) simulation. Actually, classical upscaling procedures usually are based on linearly varying pressure boundary conditions, which cannot capture the near-well flow behavior. As a result, the well productivity calculated by a dual-porosity flow simulator can be very different from that calculated on a DFN model.
This paper proposes a near-well fracture-upscaling procedure based on the geological DFN model to improve the accuracy of well productivity in fractured-reservoir simulators. This procedure enables us to represent the actual flow through the fractures and the exchanges between matrix and fractures in the well vicinity. On the basis of the computed near-well flow pattern, equivalent fracture transmissibilities as well as numerical well indices are determined and assigned to the gridblocks of the dual-porosity reservoir simulator. The reliability and necessity of using the near-well upscaling procedure are demonstrated by examples.

Introduction
Advanced characterization methodologies are now able to provide realistic models of geological fracture networks (Cacas et al. 2001). In addition, production logging and transient well tests can be simulated with DFN models to validate the geological fracture-network geometry and calibrate the hydraulic properties of fractures (Sarda et al. 2002). However, because of computational limitations, the complex geological DFN model cannot be used straightforwardly to simulate a multiphase-flow production scenario at field scale (Bourbiaux et al. 2002). For such simulations, a dual-porosity reservoir simulator is typically used. The dual-porosity reservoir model, using large gridblocks to discretize the whole reservoir, is a conceptual representation of the actual geology of the fractured medium. The flow properties of the fracture network are then homogenized on gridblocks through upscaling procedures.
The upscaling of fracture properties is the problem of translating the geological and hydraulic description of fracture networks into reservoir-simulation parameters. The dual-porosity model requires the determination of equivalent fracture permeability and equivalent matrix-block dimensions or shape factors (Bourbiaux et al. 1997; Sarda et al. 1997). This paper discusses methodologies for upscaling the permeability of a fracture network, especially in the vicinity of the well.
Upscaling of fracture permeability has been studied extensively. The commonly used method is numerical, based on flow simulation on a model of the actual fracture network with specific boundary conditions to compute an equivalent gridblock permeability (Sarda et al. 1997). Other methods were also developed; for example, Oda (1985) proposed an analytical equation to calculate the fracture-permeability tensor, and Lough et al. (1997) presented an approach using the boundary-element method, which integrates the contribution of matrix in the equivalent permeability of the fractured medium. When using a numerical approach to determine the equivalent permeability of a fracture network, the upscaled result depends on the type of boundary conditions imposed in the flow simulation. Actually, classical upscaling procedures are usually based on flow simulation in a parallelepipedic model with linear-type pressure boundary conditions, which cannot capture the near-well flow behavior. As a result, the well productivity calculated by a dual-porosity flow simulator can be very different from that calculated on a near-wellbore DFN model.