Low Frequency Electromagnetic Investigation of Fractures and Reservoirs using Proppants

Open Access
Author:
Hassan, Muhammed Kabiru
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 27, 2014
Committee Members:
  • Raj Mittra, Dissertation Advisor
  • James Kenneth Breakall, Committee Chair
  • Lynn A Carpenter, Committee Member
  • Michael T Lanagan, Special Member
Keywords:
  • electromagnetics
  • finite element method
  • fractures
  • reservoirs
  • shale
  • dipole moment
Abstract:
An electromagnetic method is developed to analyze materials at different frequencies by modeling the materials as equivalent dipoles. This method enabled us to understand the scattering behavior of materials. The formulation of this new approach, which is based on the Dipole Moment Method, is useful for solving electromagnetic scattering problems at low frequencies and in finding the scattered fields of the scattering object at any given distance from the object. By replacing scatterers with their equivalent dipole moment weight, the method can be used to analyze a wide variety of materials, including magneto-dielectric materials. This approach is first investigated using simple geometries. Following this simple and useful method, the method was extended to the study of multiple scattering objects. The dipole weights for these objects can be obtained using either the near field or the far field approach. More complex and realistic bodies and three-dimensional problems can be solved by using this new electromagnetic method. Once the materials have been modeled, the developed technique is then compared with effective medium theories, to decide which one can use to choose a mixing rule. For the case of complex reservoirs and large fractures, one can easily use the effective medium theory formulations, and the results do not show much difference, which serves as a validation to the dipole moment method. A low-frequency Finite Element Method was implemented to handle forward modeling of fractures with magnetic permeability contrasts that can be created by injecting fluids with magnetic proppants. The Finite Element Method is found to handle complex geometries and overcomes the limitations of the Finite Difference Time Domain Method at low frequencies, as is needed to investigate deep fractures. The depth of the fractures was correlated with the scattered fields. Given the measured value of the fields scattered by a given fracture, we can estimate the depth of the fracture. The research enhanced our understanding of fracture propagation and sensing with magnetic proppants using electromagnetic waves, which is very important in enhancing resource recovery and evaluating reserves.