Systems and Methods for Determining Dielectric Constant or Resistivity from Electromagnetic Propagation Measurement Using Contraction Mapping
First Claim
1. A method comprising:
- placing a downhole tool in a wellbore in a geological formation;
using the downhole tool to obtain an electromagnetic attenuation measurement and an electromagnetic phase shift measurement; and
with a processor, solving for dielectric constant or electrical resistivity, or both, via contraction mapping to iteratively solve for wavenumber using a function of wavenumber having attenuation and phase shift as a complex constant.
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Abstract
Identifying the dielectric constant and/or the electrical resistivity of part of a geological formation may reveal useful characteristics of the geological formation. This disclosure provides methods, systems, and machine-readable media to determine dielectric constant or electrical resistivity, or both, using contraction mapping. Specifically, contraction mapping may be used with a function of wavenumber k to iteratively solve for values of dielectric constant and electrical resistivity until convergence is achieved. This may allow for convergence to a solution without computing partial derivatives and/or with fewer iterations than previous techniques.
4 Citations
20 Claims
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1. A method comprising:
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placing a downhole tool in a wellbore in a geological formation; using the downhole tool to obtain an electromagnetic attenuation measurement and an electromagnetic phase shift measurement; and with a processor, solving for dielectric constant or electrical resistivity, or both, via contraction mapping to iteratively solve for wavenumber using a function of wavenumber having attenuation and phase shift as a complex constant. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A system comprising:
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a transmitter configured to emit an electromagnetic signal of a first frequency into a geological formation; a near receiver configured to receive the electromagnetic signal; a far receiver configured to receive the electromagnetic signal, wherein the far receiver is spaced farther from the transmitter than the near receiver; and a processor configured to use contraction mapping to iteratively solve for a dielectric constant and an electrical resistivity of the geological formation using a function of wavenumber having an attenuation of the electromagnetic signal between the near receiver and the far receiver and based on a phase shift of the electromagnetic signal between the near receiver and the far receiver as a complex constant. - View Dependent Claims (12, 13, 14, 15, 16)
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17. One or more non-transitory machine-readable media comprising instructions to:
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receive an attenuation measurement and a phase-shift measurement of a geological formation obtained by an electromagnetic downhole tool at a depth of the geological formation in a wellbore; and without computing any partial derivatives, use contraction mapping to iteratively solve for a dielectric constant and a resistivity of the geological formation at the depth based on the attenuation measurement and the phase-shift measurement until the solution for dielectric constant converges and the solution for resistivity converges. - View Dependent Claims (18, 19, 20)
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Specification