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Dependency of Percolation Sub-networks (Backbone, Dangling-end) Variation on Rock Properties and Well Spacing

Karami, Karim | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52266 (06)
  4. University: Sharif University of Technology
  5. Department: Chemical and Petroleum Engineering
  6. Advisor(s): Masihi, Mohsen
  7. Abstract:
  8. Water flooding is one of the improved oil recovery methods that has been used for past decades. The water flooding efficiency is calculated in two different scale; macroscopic scale and microscopic scale. The efficiency in macroscopic scale is called volume sweep efficiency (Ev) and in microscopic scale, displacement sweep efficiency (Ed). A special type of hydrocarbon reservoirs are composed of several permeable units in an impermeable shaley background in a way that hydrocarbon can just flow through the permeable units. The predominant feature of such reservoirs is continuity of permeable units that affecting the flow behavior. This simplification enables us to model such reservoirs by using percolation theory. Percolation theory is a mathematical framework that is used for investigation of connectivity and conductivity in geometrically complicated systems. In the water flooding of such reservoirs, willy-nilly, some part of them is kept unswept, even in the spanning cluster. Thus, all the injected water just sweep a particular part of reservoir which is called backbone.In this thesis, with percolation theory concepts and a flow based criterion and by defining a threshold for fluid flow rate from each grid, the volume sweep efficiency (backbone) of various systems with anisotropy coefficient equal to 1, 2 & 4 was calculated. It’s necessary to say that the MATLAB was used for implementing the algorithms.After some investigation, we obtain the following results. First, the flow rate threshold must be dependent to model size, in order that we determine the backbone and dangling-end parts of diferrent models with a same and equal manner. Second, the threshold was determined 100/(2×the area perpendicular to flow direction) due to two criteria: 1) the flow rate quantity passed from backbone after dividing the spanning cluster. 2) The flow rate quantity passed from sensitive grids. Finally, In finite-size scaling of connectivity, backbone and dangling end, the connectivity exponent, the correlation length exponent, the backbone exponent and the dangling end exponent were considered 0.1405, 4/3, 0.3 and -0.27, respectively. In addition, the percolation theory quantities was scaled with respect to model isotropy or anisotropy
  9. Keywords:
  10. Percolation Theory ; Heteroscedasticity ; Connectivity ; Water Flooding ; Scaling ; Dangling-End ; Backbone

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