This is a laboratory and field technique of scaling-up rock mechanical and petrophysical properties, such as compressive strength and bulk compressibility, from grain-scale to log-resolution scale. The main scaling tools are the point-load wedge penetrometers. The objective is to extrapolate the physical and mechanical properties from core samples to larger volumes of gridded numerical geotechnical models. The scaling method starts at grain-scale using a conventional point-load indenter that creates a conical depression onto the rock surface. A single conical indentation has a scale of investigation of a few grain diameters, but contiguous point-indentations, or linear wedge indentations expand the investigated volume geometrically. As shown by previous investigators, the shape, width, and depth of the dent is a function of rock strength, modulus, petrophysical properties, indenter geometry and applied normal force. Point- and line-indentations were calibrated with plug-measured uniaxial compressive strength, P-wave velocity, and modulus. Laboratory and field examples are presented. Grain-scale strengths show wide variances relative to whole-core strengths. However, the penetrometer indices of compressive strengths are shown to compare favorably with conventional measurements on plugs, core ultrasonic velocity, scratch-tester, and with those predicted by the well?s sonic and density logs. These indenting tools have the advantages of portability, reliability, and speed, especially in field strength indexing and upscaling.


In digital subsurface models, it is preferable to use input data representative of the dimensional volume of the model?s cells or grids. However, most laboratory geomechanical and petrophysical measurements are performed on small specimens (~50cc-100cc), whereas gridded cells of geo-models are in wellbore-scale and larger (~bed-thickness, 1m3-1000m3). It is therefore necessary to upscale; i.e., the extrapolation of physicalmechanical properties from small-scale to larger volumes. Upscaling is complicated by rock heterogeneity, anisotropy, mineralogy, fabric, and datascarcity. In gridded models of the near-borehole region, fine grids could be in the cm-range, in the same dimensions as most rock strength tests on cylindrical "plug" samples. Away from the borehole, the grid dimensions gradually increase to meter-scales, necessitating upscaled values of strength and modulus. In reservoir-scale geomechanics, cells are much larger, with fine-gridding in 10m-scales within the reservoir, and 100m-scales in the overburden and its lateral boundaries; requiring larger degrees of upscaling.

1.1. Scaling methods

Upscaling is a well-studied process in reservoir engineering and geological "geocellular" modeling. Petroleum reservoir flow-simulators use geostatistical and analytical techniques to upscale the petrophysical properties from a geocellular model to a reservoir flowmodel (see for examples, Durlovsky [1], Lohne and Durlovsky, [2], Salazar [3], Shafer and Ezekwe [4]). The petrophysical properties upscaled are porosity, permeability, oil and water relative permeabilities, gas-, water- and oil saturations, fluid and capillary pressure, A stratigraphic or depositional geocellular model guides the coarsening of the reservoir flow-model. Sources of fine-scale data are core samples and their laboratory tests, thin-sections, and borehole image logs. For the intermediate scale, common sources are processed welllogs of Gamma-ray, density-neutron, resistivity, and sonic. Downhole well-testing also provides bed- and wellbore-scale flow data. Then maps of 3D seismic attributes guide the upscaling from bed

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