Pore-Network Models Combined to High Resolution micro-CT to Assess Petrophysical Properties of Homogenous and Heterogenous Rocks
Authors: Youssef Souhail , Bauer Daniela , Han Mei , Bekri Samir , Rosenberg Elisabeth , Fleury Marc , Vizika-kavvadias Olga 
Published: December 2008

Abstract
Reservoir rocks often present complex pore-structures involving multiple porosity systems with various interconnectivity patterns. These pore-systems, from microporosity to vugs/fissures, drastically affect petrophysical properties. This is particularly true for electrical properties (formation factor and resistivity index) for which both the amount and spatial distribution of microporosity plays a crucial role. Pore network models (PNM) are well suited to calculate petrophysical properties of rocks from pore space structure information. The predictability of such models depends on the accuracy with which the complex geometry and topology of the pore network are described. This complex fine structure of the pore network can be captured by high resolution Computed Micro-Tomography (µ-CT). The aim of the present work is to combine a dual pore network approach with the µ-CT information to simulate specific electrical behaviour of a set of selected rocks. The dual PNM combines transport properties of the microporosity (capillary pressure and resistivity index of the microporosity which is considered to be homogeneous) with the deterministic pore network modelling of the macroporosity.
µ-CT is used both to extract some properties of the microporosity and to build the equivalent macropore network. Formation factors, and resistivity indices are simulated and compared to measurements. The experimentally observed specific electrical behaviours of rocks are reproduced and interpreted.

Introduction
Carbonate fields are expected to dominate production through the next years (over 50% of today world reserves) so it becomes a priority for industry to better understand carbonate behaviour. However evaluating reservoir using standard resistivity interpretation [1, 20] generally fails in carbonates which have complex pore structures [9]. The cementation and saturation exponents (m and n) sometimes vary dramatically from the conventionally assumed value of 2 [4, 10, 12]. Understanding how rock properties depend on the pore structure is thus necessary for an optimal recovery strategy. Many research efforts have focussed on the relationship between the porous structure and the electrical properties using theoretical models such as effective medium and percolation theories [21, 26] or numerical models based on 3D reconstructed image and stochastic network [2, 16, 19]. These models work well for rocks with a homogeneous matrix. The development of µ-CT facility gives the opportunity to go further in the complexity of rocks in terms of structure. In recent works, 3D images of the actual structure of bimodal carbonate rocks associated with the random walk technique [13] or finite element modelling [17] have been used to assess the electrical properties. These studies show the direct impact of the spatial distribution of the microporosity on the formation factor and the resistivity index. The objective of the present work is to investigate the effect of pore architecture on electrical properties calculated with a dual-porosity pore network model used in drainage conditions. At first, we carry out 3D µ-CT imaging, Pc, formation factor and resistivity index measurements during drainage on a set of sandstone and carbonate rocks. We additionally explain a methodology to assess microporosity properties from 3D images by three phase segmentation. Then we describe the use of a dual-pore network model taking into account both the actual resolved macropore space and the spatial distribution of the microporous phase. Finally, we present a parametric study to evaluate the impact of the local heterogeneity pattern of the microporous phase.