Effective Fracture Network Permeability: Comparative Study of Calculation Methods
Authors: Cottereau Nicolas , Garcia Michel H. , Gosselin Olivier R. , Vigier Louise 
Published: July 2010

The calculation of effective flow properties of naturally fractured reservoir (NFR) has been the purpose of research works for many years. Based on a static characterization of the fracture system (orientations and densities), equivalent flow properties provide continuum representations of discrete systems from which multiphase flows can be simulated using dual-permeability and dual-porosity models. Common flow properties include anisotropic permeability tensors attached to the fracture system itself, and block sizes or shape-factors, which characterize the capability of the fracture and matrix media, to exchange fluids.

Analytical and numerical calculation methods are now proposed by different commercial software tools, or have been the purpose of in-house developments. All methods rely on some conceptual models that are necessarily simplified representations of actual fracture systems, both complex and very partially known. Whether the underlying conceptual models are relevant certainly depends on the particular features of each fracture system. More important is the capability of models to capture features that are consequential for reservoir production. Only then can one expect to build meaningful NFR models likely to be calibrated to match production history data and to perform reliable reservoir forecasting. The CPU-time or memory requirements of implemented methods may also be a concern, as potentially relevant methods or software are unable to get through the calculations when full-field modelling is required.

It follows that the comparison and validation of equivalent flow-property calculation methods and NFR modelling software is anything but an easy task. As a first contribution to this end, we review and compare several equivalent permeability calculation methods available from two commercial software suites and from our own proprietary tool (GoFraK). We first present the numerical and analytical methods that were tested, including the original ones we developed which were expected to show better calculation and speed performances. We then detail the realistic benchmark case studies used to compare the different methods, from the calculation of equivalent flow properties to the multiphase flow simulation of forecast production. The results are finally presented and discussed. They show that the numerical methods offered by commercial products, based on 3D discrete fracture networks (DFN) to compute equivalent permeability tensors, are generally unable to manage full-field models, and that their simpler analytical methods are to be used with great caution because of important underlying assumptions. These results also validate the approach and methods we developed in GoFraK and demonstrate their robustness and efficiency. Multiphase flow simulations were carried out to evaluate the impact of dual-media models on production forecast. They confirm that permeability tensors are not the only important effective flow properties, block sizes and more generally fracture/matrix transfer functions being also highly consequential. We finally end with preliminary conclusions about the ease of building NFR models and the reliability that can be given to such models.