Prediction of Relative Permeability and Capillary Pressure from a Pore Model
Authors: Nilsen L. Scandellari , Oren P.E. , Bakke S. , Henriquez A. 
Published: December 2007

Abstract
A pore-scale model consisting of a network of pore bodies inter-connected by pore throats is used to calculate drainage relative permeabilities and capillary pressure for a strongly water wet Berea sandstone core. The architecture and geometry of the pore network which is used in the model is constructed from thin section analysis and numerical modelling of the main sandstone-forming geological processes, i.e., grain sedimentation, compaction, and diagenesis. The effect of different pore network descriptors on relative permeability at low capillary numbers has been simulated. The results show that pore shapes strongly influence wetting phase relative permeability, particularly at low saturations where film flow is important. Simulated relative permeabilities are found to be in good agreement with those predicted from an empirically derived correlation.
Introduction
Macroscopic multiphase flow in porous media is usually described in terms of Darcy's law and measured or empirically derived saturation dependent relationships for phase relative permeabilities and capillary pressure. Accurate and consistent acquisition and interpretation of such data are essential for almost all reservoir engineering calculations and determine to a large extent how reservoir management can optimise oil production and recovery.
Relative permeability measurements, either by steady state or unsteady state methods, are time consuming, expensive, and often difficult to interpret. As a result, too few measurements are usually performed and numerous uncertainties may be associated with the measurements. This prohibits assigning unique relative permeability functions to different architectural units in the reservoir (i.e., channels, crevasse splays, wash-over fans, etc.) and limits the ability of reservoir simulators to accurately predict oil recovery.
Relative permeabilities and capillary pressure are averaged transport properties which represent the physical processes occurring on the pore-scale. On the pore-scale, the displacement of one fluid by another is controlled by interfacial tension, viscous forces, rock-fluid interactions, and the geometry of the pore space. In principle, it should therefore be possible to determine relative permeabilities and capillary pressure by appropriately averaging the equations describing the physical processes occurring on the microscopic or pore-scale. This approach requires a detailed understanding of the displacement mechanisms on the pore-scale and a complete description of the morphology of the pore space. The procedure has successfully been applied to two- and three-phase flow in simple or idealised porous media using pore-scale physics identified in micromodel experiments with the morphology of the pore space represented by a topologically equivalent numerical network.
The difficulty in constructing a realistic three-dimensional (3-D) representation of the complex pore structure of real porous rocks has limited the above approach to idealised porous media. Although advanced techniques such as serial-sectioning and micro-CT are available, information about the pore structure of porous rocks is usually obtained from image analysis of 2-D thin section images of rocks and from mercury injection capillary pressure curves. Thin sections provide aerial information which is relevant to porosity measurements whilst mercury injection data provide information about the volume of pores which may be invaded through pore throats within specified size ranges. These data are insufficient to provide a complete 3-D description of the architecture and geometry of the pore space and do not allow construction of 3-D pore networks which accurately represent the complex pore space of a given porous rock.
In the present work, stochastic modelling of the main sandstone-forming geological processes (i.e., sedimentation, compaction, and diagenesis) are combined with 3-D image analysis techniques to generate a realistic and fully characterised 3-D representation of the pore network for a Berea sandstone.
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