On the Relationship between Resistivity and Permeability Anisotropy

摘要

Measurement of resistivity anisotropy is critical to reservernestimation and permeability anisotropy determination is key tornefficient hydrocarbon exploitation. It is now possible tornmeasure resistivity anisotropy with new wireline, multicomponentrninduction hardware. However, it is difficult torndirectly measure or determine permeability anisotropy. Thus,rnit would be beneficial to be able to relate resistivity andrnpermeability anisotropy and predict kv:kh from Rh:Rv (where kvrnand kh are the vertical and horizontal permeabilities, and Rvrnand Rh are the vertical and horizontal components ofrnformation resistivity).rnWe know that both resistivity and permeability anisotropyrnare scale dependent. In our study, we define three scales forrnformation anisotropy properties: The Micro-scale relatesrndirectly to the properties of individual components (e.g., sandrnand shale). The Macro-scale is an intermediate scale definedrnby the vertical resolution of the measurement tools. Mostrnlogging tools are not capable of resolving the individualrnlamina in laminated sand-shale sequences. In this case, thern“macroscopic anisotropy” can be described by the well-knownrnrules for conductors connected in parallel and/or in series. Atrnthe Reservoir-scale, anisotropy is governed by interconnectedrnchannels formed by gaps in the relatively impermeablernshale layers.rnWe have developed a numerical simulator that allows us tornmodel at all scales the anisotropy for resistivity andrnpermeability for arbitrary three-dimensional, periodicrnstructures. The simulation results have been verified withrnknown analytical solutions. With this model we have exploredrnreservoir-scale anisotropy as a function of the lateral extent ofrnthe shales and sands. By varying the thickness of the sandsrnand shales, we investigated the effect of net-to-gross on thernelectrical and permeability anisotropy.rnFrom our studies we conclude that the relationshiprnbetween resistivity and permeability anisotropy is not trivial.rnOn the smaller scales it is controlled by the spatial distributionrnof the pore-space properties and on the larger reservoir scalesrnby the spatial distribution of the sand bodies and gaps in thernshale barriers.rnWe show both numerically and theoretically for 2Drnstructures that resistivity and permeability anisotropy arernidentical for cells with inverse property contrasts. This impliesrnthat fluid and current flow anisotropy are equal. However, thisrndoes not hold for every 3D geometry and in general there is norncorrelation between permeability and resistivity anisotropy onrnthe macroscopic or reservoir scale for laminatedrnsand-shale systems.