Estimation of equivalent fracture network permeability using fractal and statistical network properties

Abstract

Mapping fracture networks and estimating their properties such as porosity and permeability to be used as input data in simulation studies are two critical steps in modeling of naturally fractured reservoirs. The data to achieve these two tasks are almost always insufficient and mostly limited to well scale measurements, seismic maps, and outcrop studies. Any quantitative information about fracture networks obtained through these sources would make accurate preparation of static models possible. Hence, it is essential to use limited quantitative data effectively in fracture network studies for accurate estimation of reservoir performance in any subsurface modeling study. This study focuses on one of the critical problems namely practical estimation of effective fracture network permeability (EFNP). First, an investigation on the relationship between statistical and fractal parameters of fracture network geometry and fracture network permeability was presented. Then, twelve statistical and fractal fracture network properties of randomly generated 2D fracture patterns were tested against permeability and correlations were obtained. Approximately half of the properties showed a strong relationship with the EFNP. Correlations obtained through multivariable regression analysis were tested on randomly generated different fracture network types and natural fracture patterns. In this exercise, all fracture network characteristics (density, length, orientation, connectivity, and aperture) were considered. Finally, the capability of artificial neural networks (ANN) was used to capture complex and nonlinear relationships between statistical-fractal parameters and equivalent permeability of 2D fracture networks to further improve empirical EFNP prediction models. To achieve this, a back propagation (BP) neural network with one hidden layer in the middle was used. After training this network, it was used to predict the EFNP. The ANN was observed to be a more powerful approach than the multivariable regression analysis in handling the non-linearity and complexity of the problem.This study showed that certain fractal characteristics of fracture network could be used in fracture network mapping and preparation of permeability data. The correlations obtained and tested could also be useful to calculate equivalent fracture network permeability tensor in 2D practically and efficiently. The proposed method could be potentially extended and further developed to be applicable on 3D models as well.