On the Relationship between Resistivity and Permeability Anisotropy

Abstract

Abstract Measurement of resistivity anisotropy is critical to reserve estimation and permeability anisotropy determination is key to efficient hydrocarbon exploitation. It is now possible to measure resistivity anisotropy with new wireline, multi-component induction hardware. However, it is difficult to directly measure or determine permeability anisotropy. Thus, it would be beneficial to be able to relate resistivity and permeability anisotropy and predict kv:kh from Rh:Rv (where kv and kh are the vertical and horizontal permeabilities, and Rv and Rh are the vertical and horizontal components of formation resistivity). We know that both resistivity and permeability anisotropy are scale dependent. In our study, we define three scales for formation anisotropy properties: The Micro-scale relates directly to the properties of individual components (e.g., sand and shale). The Macro-scale is an intermediate scale defined by the vertical resolution of the measurement tools. Most logging tools are not capable of resolving the individual lamina in laminated sand-shale sequences. In this case, the "macroscopic anisotropy" can be described by the well-known rules for conductors connected in parallel and/or in series. At the Reservoir-scale, anisotropy is governed by interconnected channels formed by gaps in the relatively impermeable shale layers. We have developed a numerical simulator that allows us to model at all scales the anisotropy for resistivity and permeability for arbitrary three-dimensional, periodic structures. The simulation results have been verified with known analytical solutions. With this model we have explored reservoir-scale anisotropy as a function of the lateral extent of the shales and sands. By varying the thickness of the sands and shales, we investigated the effect of net-to-gross on the electrical and permeability anisotropy. From our studies we conclude that the relationship between resistivity and permeability anisotropy is not trivial. On the smaller scales it is controlled by the spatial distribution of the pore-space properties and on the larger reservoir scales by the spatial distribution of the sand bodies and gaps in the shale barriers. We show both numerically and theoretically for 2D structures that resistivity and permeability anisotropy are identical for cells with inverse property contrasts. This implies that fluid and current flow anisotropy are equal. However, this does not hold for every 3D geometry and in general there is no correlation between permeability and resistivity anisotropy on the macroscopic or reservoir scale for laminated sand-shale systems.