We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. Starting with a network representation of Berea sandstone the pore-size distribution is adjusted to match mercury injection capillary pressure for different rock types, keeping the rank order of pore sizes and the network topology fixed. Then predictions of single and multiphase properties are made with no further adjustment of the model. We successfully predict relative permeability and oil recovery for water- oil- and mixed-wet datasets. For waterflooding we introduce a method for assigning contact angles to match measured wettability indices. The aim of this work is not simply to match experiments, but to use easily acquired data to predict difficult to measure properties. Furthermore, the variation of these properties in the field, due to wettability trends and different pore structures can now be predicted reliably.
In network modeling the void space of a rock is represented at the microscopic scale by a lattice of pores connected by throats. By applying rules that govern the transport and arrangement of fluids in pores and throats, macroscopic properties, for instance capillary pressure or relative permeability, can then be estimated across the network, which typically consists of several thousand pores and throats representing a rock sample of a few millimeters cubed.
Until recently most networks were based on a regular lattice. The coordination number can vary depending on the chosen lattice (e.g. 5 for a honeycombed lattice or 6 for a regular cubic lattice). As has been noted by many authors1,2 the coordination number will influence the network model behavior significantly, both in terms of breakthrough and relative permeability. In order to match the coordination number of a given rock sample, which typically is between 3 and 83, it is possible to remove throats at random from a regular lattice4,5, hence reducing the connectivity. The pore and throat size distributions will also affect the estimated macroscopic properties. By adjusting the size distributions to match capillary pressure data, relatively good predictions of absolute and relative permeabilities have been reported for unsaturated soils6,7.
All these models are, however, still based on a regular topology which does not reflect the random nature of real porous rock. The use of networks derived from a real porous medium was pioneered by Bryant et al. They extracted their networks from a random close packing of equally-sized spheres where all sphere coordinates had been measured8–10. Predictions of relative permeability, electrical conductivity and capillary pressure were compared successfully with experimental results from sand packs, bead packs and a simple sandstone. Øren and coworkers at Statoil have extended this approach to a wider range of sedimentary rocks11,12. For more complex sandstones it is usually necessary to create first a 3D voxel based representation of the pore space that should capture the statistics of the real rock. This can be generated directly using X-ray microtomography13,14, where the rock is imaged at resolutions of around a few microns, or by using some numerical reconstruction technique15,16. From this voxel representation an equivalent network (in terms of volume, throat radii, clay content etc) can then be extracted16,17. Using these realistic networks water-wet experimental data have been successfully predicted for Bentheimer12 and Berea sandstones18.
Most hydrocarbon bearing reservoirs exhibit mixed-wet characteristics, where parts of the rock are oil-wet with the remainder being water-wet. Following primary drainage it is assumed that the part of the rock in direct contact with hydrocarbon will alter its wettability19. From Amott tests and nuclear magnetic resonance (NMR) it is possible to get a bulk indication of the wettability20. How the mixed wettability is distributed on the pore scale is, however, much more difficult to evaluate. Kovscek and coworkers proposed a model where the smaller pores become oil-wet while the larger ones remain water-wet19. Using cryo- and environmental scanning electron microscopy it is possible to visualize directly the distribution of fluids at the pore scale21–23. These studies suggested that the distribution of clay, in particular kaolinite, plays a very important role in determining what parts of the rock becomes oil-wet. Only very limited mixed-wet experimental data have been predicted using pore-scale network modeling, though some promising results have been shown12.