caa a22 4500 469064870 CHVBK 20180323132905.0 cr unu---uuuuu 170328e19921101xx s 000 0 eng 10.1007/BF00894656 doi (NATIONALLICENCE)springer-10.1007/BF00894656 Modeling permeability in imperfectly layered porous media. I. Derivation of block-scale permeability tensor for thin grid-blocks [Elektronische Daten] [W. Zijl, J. Stam] Practical expressions are given for the nine components of the block-scale permeability tensor of a thin block. These expressions are derived from the local-scale continuity equation and Darcy's law in an anisotropic layered porous medium. The flow problem is separated in a bottom-flux problem and a top-flux problem, both of which can be solved in essentially the same way. The bottom-flux problem has been worked out in detail, and has been separated in two parts: a vertical potential difference and a horizontal potential difference part. Each is solved with a different approach specially designed for it. Depth-averaged expressions are obtained first, after which block-scale expressions are obtained by assuming a constant depth-averaged flux. In the zeroth order, this results in the well-known Dupuit approximation in geohydrology, and the vertical equilibrium (VE) approximation in petroleum reservoir engineering. The novelty of the theory presented here stems from the application of a perturbation technique to obtain first-order corrections to these well-known results. The local-scale laws are applied in the coordinate system coinciding with the principal axes of the local-scale permeability tensor. Only in this coordinate system the local-scale permeability tensor has zero off-diagonal components. However, since the porous medium is imperfectly layered, the first-order corrections show that the off-diagonal components of the block-scale permeability tensor are not zero. Furthermore, the block-scale permeability tensor is generally nonsymmetric, which implies that a coordinate system in which the off-diagonal terms disappear does not exist. International Association for Mathematical Geology, 1992 block-scale permeability tensor nationallicence block-scale Darcy's law nationallicence imperfectly-layered porous media nationallicence thin grid-blocks nationallicence Zijl W. TNO Institute of Applied Geoscience, P.O. Box 6012, 2600 JA, Delft, The Netherlands aut Stam J. TNO Institute of Applied Geoscience, P.O. Box 6012, 2600 JA, Delft, The Netherlands aut Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/8(1992-11-01), 865-883 0882-8121 24:8<865 1992 24 11004 https://doi.org/10.1007/BF00894656 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00894656 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zijl W. TNO Institute of Applied Geoscience, P.O. Box 6012, 2600 JA, Delft, The Netherlands aut NATIONALLICENCE 700 1- Stam J. TNO Institute of Applied Geoscience, P.O. Box 6012, 2600 JA, Delft, The Netherlands aut NATIONALLICENCE 773 0- Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/8(1992-11-01), 865-883 0882-8121 24:8<865 1992 24 11004 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer