Extending Predictive Capabilities to Network Models
Authors: Oren P.E. , Bakke S. , Arntzen O.J. 
Published: December 2007

Abstract
We reconstruct 3-D sandstone models which give a realistic description of the complex micro-structure observed in actual sandstones. The essence of our approach is to build sandstone models which are analogs of actual sandstones by stochastically model the results of the main sandstone forming processes - grain sedimentation, compaction, and diagenesis. Topological and geometrical analyses are used to construct pore networks which replicate the microstructure of the reconstructed sandstones. The generated networks are used as input to a two-phase network model. The network model simulates primary drainage and water injection for both water wet and mixed wet systems. Predicted transport properties for different reconstructed sandstones are found to be in good agreement with available experimental data.

Introduction
The micro structure of a porous medium and the physical characteristics of the solid and the fluids which occupy the pore space determine several macroscopic properties of the medium. These properties include transport properties of interest such as permeability, electrical conductivity, relative permeability, and capillary pressure. In principle, it should be possible to determine these properties by appropriately averaging the equations describing the physical processes occurring on the pore-scale. The prediction of average or macroscopic transport properties from the associated pore-scale parameters is a long-standing issue which has been the subject of much investigation. One commonly applied tool in this investigation is the network model.
The premise of the network model is that the pore space can be represented by an equivalent network of interconnected pores in which larger pores (pore bodies) are connected by smaller pores (pore throats). Since the pioneering work of Fatt, network models have been used extensively to study different displacement processes in simple or idealised porous media. Seldom, however, do such models claim to be representative of reservoir rocks.
The extension of network modelling techniques to real porous media is hampered by the difficulty of adequately describing the complex nature of the pore space. Advanced techniques such as microtomographic imaging and serial sectioning provide a detailed description of the pore space at micrometer resolution. In practice, however, information about the microstructure of reservoir rocks is limited to 2-D thin section images and to pore throat entry sizes determined from mercury injection data. These data are insufficient to directly construct a 3-D pore network which replicates the microstructure of the porous medium. As a result, simplifying assumptions about the pore structure must be invoked.
Despite these simplifications. network models have proved to be powerful tools for extrapolating limited measured data and for developing valuable insight into complex multiphase flow phenomena such as capillary pressure and relative permeability hysteresis, the effect of wettability, and three-phase flow. The difficulty in adequately describing the pore network of reservoir rocks has, however, prevented network models from being used as a predictive tool, thus greatly limiting their application in the oil industry.
In the present work, geostatistical information obtained from image analysis of 2-D thin sections are used to generate a reliable reconstruction of the complex rock-pore system in 3-D. The network representation of the pore space is constructed from topological and geometrical analyses of the fully characterised reconstructed sample. The pore network is subsequently used as input to network simulators of single- and two-phase flow. Predicted values for permeability. electrical conductivity, and relative permeabilities for different reconstructed sandstones are compared with experimental data.

Sandstone Reconstruction
A sandstone sample and its petrographical parameters are the end result of all the geological and hydrodynamical processes which have affected the sedimentary basin. We do not attempt to model the detailed dynamics of these processes. P. 369^