US 8,135,542 B2 · Simultaneous inversion of induction data for dielectric permittivity and electric conductivity

Abstract

A method of inverting induction logging data for evaluating the properties of underground formations surrounding a borehole, the data including induction voltage measurements obtained from a tool placed close to the formations of interest, the method includes: (a) defining a relationship relating the induction voltage to wave number, dielectric permittivity and conductivity; defining a cubic polynomial expansion of the relationship; and solving the cubic polynomial relationship using the voltage measurements to obtain values for conductivity that includes skin-effect correction, and apparent dielectric permittivity; and (b) using the obtained values for conductivity and apparent dielectric permittivity to derive a simulated value of induction voltage; determining the difference between the simulated value of the induction voltage and the measured induction voltage; and iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimize its difference with respect to the measured value.

Claims12

Dependent claims

A method of inverting induction logging data for evaluating the properties of underground formations surrounding a borehole, the data comprising induction voltage measurements obtained from a tool placed close to the formations of interest, the method comprising:

(a) operating a tool in a borehole to obtain induction voltage data;
(b) defining a relationship relating the induction voltage to wave number, dielectric permittivity and conductivity;
defining a cubic polynomial expansion of the relationship;
and
solving the cubic polynomial relationship using the voltage measurements to obtain values for conductivity that includes skin-effect correction, and apparent dielectric permittivity;
and
(c) using the obtained values for conductivity and apparent dielectric permittivity to derive a simulated value of induction voltage;
determining the difference between the simulated value of the induction voltage and the measured induction voltage;
and
iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimise its difference with respect to the measured value.

7 more elements

(a) operating a tool in a borehole to obtain induction voltage data;
(b) defining a relationship relating the induction voltage to wave number, dielectric permittivity and conductivity;
defining a cubic polynomial expansion of the relationship;
and
solving the cubic polynomial relationship using the voltage measurements to obtain values for conductivity that includes skin-effect correction, and apparent dielectric permittivity;
and
(c) using the obtained values for conductivity and apparent dielectric permittivity to derive a simulated value of induction voltage;
determining the difference between the simulated value of the induction voltage and the measured induction voltage;
and
iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimise its difference with respect to the measured value;
wherein the step of iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimise its difference with respect to the measured value comprises minimising the squared difference between measured induction voltage Umeas voltage and their simulated reproduction Usimul according to the relationship, wherein k is wave number:
L
=
1
2
⁢
(
U
meas
-
U
simul
)
2
⇒
ⅆ
ⅆ
k
⁢
L
=
(
U
meas
-
U
simul
)
⁢
ⅆ
U
simul
ⅆ
k
=
0.

43 more elements

(a) defining a relationship relating the induction voltage to wave number, dielectric permittivity and conductivity;
defining a cubic polynomial expansion of the relationship;
and
solving the cubic polynomial relationship using the voltage measurements to obtain values for conductivity that includes skin-effect correction, and apparent dielectric permittivity;
and
(b) using the obtained values for conductivity and apparent dielectric permittivity to derive a simulated value of induction voltage;
determining the difference between the simulated value of the induction voltage and the measured induction voltage;
and
iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimise its difference with respect to the measured value.
wherein the induction logging data is obtained from a three-coil tool comprising a transmitter coil with magnetic dipole moment MT, a main receiver coil with magnetic dipole moment M1 at distance r1 from the transmitter coil, and a bucking coil with a magnetic moment M2 at distance r2 from the transmitter coil, the dipole moments being aligned parallel to the axis of the tool, the cubic polynomial expansion comprising:
U
l
=
-
ⅈωμ
⁢
⁢
M
T
2
⁢
π
⁢
(
(
M
1
2
⁢
r
1
-
M
2
2
⁢
r
2
)
⁢
k
2
+
ⅈ
⁡
(
M
1
3
-
M
2
3
)
⁢
k
3
)
wherein U1 is the induction voltage and k is wave number.

56 more elements

Dependencies are inferred from the claim text.

Simultaneous inversion of induction data for dielectric permittivity and electric conductivity

Life of this patent

Simultaneous inversion of induction data for dielectric permittivity and electric conductivity

Life of this patent

Abstract

Claims12