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Effective Permeability of Isotropic Overlapping Sandbodies in 2D Using Percolation Theory

Fatemi, Amin | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39832 (06)
  4. University: Sharif University of Technology
  5. Department: Chemical and Petroleum Engineering
  6. Advisor(s): Masihi, Mohsen
  7. Abstract:
  8. Permeability is an essential parameter used for reservoir evaluation, simulation and management to optimize oil recovery. The conventional approach to estimate reservoir connectivity, conductivity, sweep efficiency and other critical information for decision-making is to build detailed geological models, which are then upscaled to a coarser grid where flow simulations are run. However, this takes many hours to be carried out even for a single realization practically. In practice, a very small number of realizations are considered and consequently the true uncertainty in the results is very poorly estimated. In this study, a statistical model of isotropic overlying sandbodies is used to quantitatively evaluate the conductivity of sandbodies network. Percolation theory here is a tool to generate universal curves which could be used as rules of thumb for fast estimation of the network conductivity. To generate these curves, we model a large number of realizations for the continuum sandbodies model. This model is considered to be an impermeable square within which permeable objects, indicating sandbodies, are randomly distributed. Then a standard algorithm is used to generate the percolating cluster/s at various system sizes with which the critical exponents are found. On these generated percolating cluster/s the Darcy equation along with continuity equation are used and consequently the effective permeability of the system is found. This is then repeated for other system sizes and the results are used to obtain a single universal curve for effective permeability. This universal curve along with other universal curves enable us to predict the conductivity, mean connectivity and its associated uncertainty for any system size very quickly, without performing any explicit realizations.

  9. Keywords:
  10. Conductivity ; Percolation Theory ; Permeability ; Connectivity ; Universal Curve ; Overlapping Sandbodies

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