Pore scale rock typing and upscaling
Rock-typing is an important part for micro pore scale flow simulation and macro scale reservoir simulation. It is the linkage between pore geometries and fluid flow properties. Recent research advances on pore scale flow simulation enable rock properties to be calculated based on the digital images. But the calculation results doesn’t reflect the properties of whole rock sample. Therefore a suitable upscaling method is needed. In this study we first illustrate three different rock types: depositional rock type, petrographic rock type and hydraulic rock type. Depositional rock type is defined within the context of the large-scale geologic framework and represent those original rock properties present at deposition. Petrographic rock type is also described in the context of the geological framework established from the depositional rock types, but is based on a pore-scale microscopic imaging. Hydraulic rock types is also quantified on the pore scale but represent the physical rock flow and storage properties as controlled by the pore structure. Then we introduce a work flow process that accurately solves the problem of rock typing and upscaling. The reservoir rock is a thin-bedded sandstone from an aeolian environment. For petrographic rock typing, we suppose thin-bedded rock sample as a layer system and define a measurement window moving along the z -axis of the core with Δ z =1 voxel, perpendicular to the bedding direction. Minkowski functions namely total volume, surface area, integral of mean curvature, and integral of Gaussian curvature, are calculated based on the measure windows and kmeans clustering is applied to detect layer interface. Furthermore, the integration of spatial interpolation and kmeans clustering is proved to detect the dipping interface successfully. The classification results match well with corresponding properties and stratigraphic pitch-out can be found, which reflects the aeolian process, e.g., the activity of the winds to enable sediment transport. For hydraulic rock typing, the size, geometry, and distribution of pore throats, as determined by capillary pressure measurements, control the magnitude of porosity and permeability for a given rock. Therefore dynamic geometrical properties during the physical rock flow should be considered and we use percolation test data which includes critical diameter and Minkowski functions. All of these data are calculated based on the pore throats, which the fluid flows on it. The key to successful and efficient characterization is to exploit natural scales. Values and variability of each property are function of scale due to heterogeneities. Therefore, representative elementary volumes should be selected suitably to stabilize the data measurements. We first choose different sizes of subsample and measure corresponding percolation test data, permeability and effective conductivity. After selecting suitable representative elementary volumes, bottom blocks of subsamples are used for unsupervised Gaussian mixture model clustering and top blocks of subsamples are used for supervised Gaussian mixture model clustering based on the calculated centroid which means the mean value and covariance matrix of the percolation test data for each rock type in bottom blocks. The results demonstrate that different rock types are well separated with each other and match well with the corresponding geometrical properties and petrophysical properties. Three formulas which are based on layer system, undulating surfaces and hydraulic rock typing results, are developed to do upscaling. Local permeabilities and effective conductivities are computed to predict whole rock sample’s permeabilities and effective conductivities. The results indicate that upscaling formula based on the hydraulic rock typing results is most accurate.