Subsurface formation parameters from tri-axial measurements
AssigneeSchlumberger Technology Corporation
InventorDzevat Omeragic
Life of this patent
Estimating the term…
Abstract
Systems and methods are provided for determining various subsurface formation parameters from electromagnetic measurements. Formulas are disclosed for field components in a coordinate system tied to the logging tool. Closed form expressions for a magnetic field distribution in a homogeneous anisotropic medium are derived from Moran-Gianzero formulas. A complete coupling of a tri-axial system of transmitters and receivers is derived in the tool coordinate system, allowing direct inversion of the measurements for horizontal and vertical conductivity and dip and strike (dip-azimuth) angles. Closed form expressions for these four quantities in the low frequency limit are also derived.
Claims21
A method for determining a parameter of a subsurface formation from electromagnetic measurements acquired with a logging tool disposed within said formation, said tool adapted with a tri-axial system of transmitter and receiver antennas, comprising:
- a) determining couplings associated with said measurements;
- and
- b) calculating the following expression derived from said couplings to determine the horizontal conductivity (σh) of said formation:
- (T′zz−Lh)(T′xx−Th)=(T′xz)2,
- where
- T′zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna;
- T′xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna;
- T′xz is the coupling between an x-axis receiver antenna arid a z-axis transmitter antenna;
- Lh, Th are elementary functions corresponding to said couplings of said antennas:
- T h = ⅇ ik h r 4 π r 3 ( - 1 + ik h r + k h 2 r 2 ) , L h = ⅇ ik h r 2 π r 3 ( 1 - ik h r ) ;
- r is the separation distance between the antennas;
- and kh2=iωμσh.
A method for determining a parameter of a subsurface formation from electromagnetic measurements acquired with a logging tool disposed within said formation, said tool adapted with a tri-axial system of transmitter and receiver antennas, comprising:
- a) determining couplings associated with said measurements;
- and
- b) calculating the following expression derived from said couplings to determine the horizontal conductivity σh of said formation:
- σ h = 8 π r Im { T xx ′ } Im { T zz ′ } - Im { T xz ′ } 2 ωμ 2 Im { T xx ′ } - Im { T zz ′ } ,
- where
- T′xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna;
- T′zz the coupling between a z-axis receiver antenna and a z-axis transmitter antenna;
- T′xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna;
- ω represents an angular frequency;
- r is a separation distance between said antennas;
- and
- μ is a magnetic permeability constant.
A system for determining a parameter of a subsurface formation from electromagnetic measurements, comprising:
- a tool adapted for disposal within said formation, said tool equipped with a tri-axial system of transmitter and receiver antennas for acquiring said measurements;
- and
- computation means for
- (i) determining couplings associated with said measurements;
- and
- (ii) calculating the following expression derived from said couplings to determine the horizontal conductivity (σh) of said formation:
- (T′zz−Lh)(T′xx−Th)=(T′xz)2,
- where
- T′zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna;
- T′xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna;
- T′xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna;
- Lh, Th are elementary functions corresponding to the couplings of said antennas:
- T h = ⅇ ik h r 4 π r 3 ( - 1 + ik h r + k h 2 r 2 ) , L h = ⅇ ik h r 2 π r 3 ( 1 - ik h r ) ;
- r is the separation distance between the antennas and kh2=iωμσh.
A system for determining a parameter of a subsurface formation from electromagnetic measurements, comprising:
- a tool adapted for disposal within said formation, said tool equipped with a tri-axial system of transmitter and receiver antennas for acquiring said measurements;
- and
- computation means for
- a) determining couplings associated with said measurements;
- and
- b) calculating the following expression derived from said couplings to determine the horizontal conductivity σh of said formation:
- σ h = 8 π r Im { T xx ′ } Im { T zz ′ } - Im { T xz ′ } 2 ωμ 2 Im { T xx ′ } - Im { T zz ′ } ,
- where
- T′xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna;
- T′zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna;
- T′xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna;
- ω represents an angular frequency;
- r is a separation distance between said antennas;
- and
- μ is a magnetic permeability constant.
Dependencies are inferred from the claim text.