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Ground Water 42 4 — Rock Mech Rock Eng 40 1 :3— Chinese J Rock Mech Eng 15 4 — Rock and Soil Mech 17 4 :1—7. The values of elements k 11 , k 12 and k 22 of are presented in the figure. The ideas discussed are now considered in the context of a realistic application. Our problem is to find a coordinate system that lets us accurately model fluid flow in a channel sand with the two permeability regions in Fig. We can highlight important features of the relationship between grid orientation and the assumption of diagonalized permeability by assuming the permeability in each region is anisotropic with a maximum permeability k max and a permeability k T that is transverse to the direction of k max.
Consider two cases. In Case A, permeability is homogeneous and anisotropic, and in Case B, permeability is heterogeneous and anisotropic. The two cases are illustrated in Figs. Coordinate system is more closely aligned with the spatial orientation of Region I than coordinate system , while coordinate system is more closely aligned with the spatial orientation of Region II than coordinate system. The grid orientation cases allow us to consider the effect of different coordinate systems on the permeability tensor in each region.
We also assume the simulator allows different grid orientations in different regions of the model; otherwise, grid orientation cases 2 and 3 are not feasible. Our analysis does not include multidimensional numerical dispersion, [5] which can also affect the accuracy of flow calculations. Results of the analysis are summarized in Table 1. An "ok" in the "Permeability Tensor" column in Table 1 indicates that the diagonal permeability tensor is aligned with the grid.
An "X" indicates that the magnitudes of the diagonal terms in the permeability tensor must be corrected with Eq. An "ok" in the "Formulation" column in Table 1 indicates that the formulation of the fluid flow equations is correct. An "X" indicates that the formulation of the fluid flow equations is incorrect because the formulation does not include off-diagonal terms in the permeability tensor. Based on the results in Table 1 , we observe that the grid orientation in Case A. Ramey, H.
Carslaw, H. Conduction of heat in solids 2nd ed. Earlougher, R. SPE Bookstore or Worldcat. Hahn, D. Heat Conduction. Kreyszig, E. Advanced Engineering Mathematics. Online Resource or Worldcat. Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro. Mathematics of fluid flow. Numerical methods analysis of fluid flow. Vector analysis of fluid flow. If the symmetricity is forced, diagonal components of relative permeability tensors will not necessarily match with the eigenvalues of the tensor, regardless of the type of the methodology.
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In: SPE symposium on improved oil recovery. Saidi AM Simulation of naturally fractured reservoirs. Sedaghat MH The relative permeability of layered fractured rocks Doctoral dissertation. The University of Melbourne. Sedaghat MH, Azizmohammadi S Representative-elementary-volume analysis of two-phase flow in layered rocks.
Comput Geosci. Sedaghat M, Azizmohammadi S, Matthai S a How fracture capillary pressure affects ensemble relative permeability of naturally fractured reservoirs. Energy Procedia — J Pet Sci Eng — Sedaghat M, Matthai S, Azizmohammadi S Tensorial fracture-matrix ensemble relative permeabilities in naturally fractured reservoirs: evidence from discrete fracture and matrix simulations.
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McGraw-Hill, London. Download references. You can also search for this author in PubMed Google Scholar. Correspondence to Mohammad Sedaghat. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Reprints and Permissions. Sedaghat, M. Does the symmetry of absolute permeability influence relative permeability tensors in naturally fractured rocks?. J Petrol Explor Prod Technol 10, — Download citation. Received : 19 June Accepted : 17 August
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