A review of up-scaling and cross-scaling issues in core and log data interpretation and prediction

This paper is part of the special publication Core-log integration (eds P.K. Harvey and M.A. Lovell). In a heterogeneous geological formation, each rock petrophysical property (e.g., permeability, porosity, and electrical conductivity) reflects the heterogeneity and varies in a manner related to the underlying changes in fabric (grainsize, mineralogy, lamination, wettability, etc.). However, measurements, both laboratory and downhole, are made at certain volume scales dictated by the size of the core plug used or the wireline log resolution. The comparison of core and log data needs to account for both the scale and physics of the particular measurements and how these relate to the underlying scale of the geological heterogeneity of the formation. In this review, these two fundamental issues are addressed as follows: (a) measurement scale and how it relates to the 'true' or 'required' petrophysical properties of the formation is defined as 'up-scaling'; (b) measurement physics and how we relate the physics of one measurement (e.g. permeability) to that of another (e.g. density, electrical, or acoustic properties) is termed 'cross-scaling'. We illustrate how these two issues arise in the comparison and prediction of permeability using several published studies. We also outline an approach to petrophysical measurement reconciliation termed 'genetic petrophysics'. This combines all three elements - measurement scale, measurement physics, and geology - to provide an integrated and robust model. We illustrate this approach for permeability to provide fit-for-purpose models of anisotropy in the near-well region of a reservoir.