US 8,942,925 B2Granted

Determination of complex dielectric constants from electromagnetic propagation measurements

AssigneeSchlumberger Technology Corporation

InventorMartin Luling

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Abstract

A method of determining the dielectric constant of a formation, comprising acquiring phase-related and amplitude-related measurements for electromagnetic signals propagating though the formation from a transmitter to a receiver; deriving a complex-valued quantity comprising terms relating to the phase shift and attenuation of the signals; defining a one-component complex-valued relationship relating the phase shift, attenuation and complex dielectric constant; and using the derived complex-valued quantity in the defined relationship to obtain a calculated value of the complex dielectric constant. An apparatus for determining the dielectric constant of a formation, comprises a transmitter for transmitting electromagnetic signals into the formation; a receiver for receiving the electromagnetic signals that have propagated from the transmitter through the formation; and means for determining the dielectric constant of the formation in accordance with a method according to the first aspect of the invention.

Claims11

Dependent claims

A method of determining the dielectric constant of a formation, comprising:

conveying a resistivity sonde within a well that extends into the formation, wherein the resistivity sonde comprises an electromagnetic transmitter and receiver;
acquiring with the resistivity sonde phase-related and amplitude-related measurements for electromagnetic signals propagating though the formation from the transmitter to the receiver, wherein the phase-related measurement is phase and/or phase shift, and the amplitude-related measurement is amplitude and/or attenuation;
transmitting the acquired phase-related and amplitude-related measurements to a surface unit via a wireline cable extending between the surface unit and the resistivity sonde in the well;
and
operating the surface unit to execute instructions for:
deriving a complex value comprising terms relating to the phase or the phase shift and the amplitude or the attenuation of the signals;
defining a one-component complex-valued relationship relating the phase-amplitude pair or the phase-shift-attenuation pair and the complex dielectric constant;
and
using the derived complex value in the defined relationship to obtain a calculated value of the complex dielectric constant
wherein the relationship has the iterative form
ɛ
r
*
(
n
)
=
ɛ
r
*
(
n
-
1
)
+
(
∂
(
PS
+
ⅈ
⁢
⁢
AT
)
∂
ɛ
r
*
)
-
1
⁢
(
(
PS
meas
-
PS
simul
(
n
-
1
)
)
+
ⅈ
⁡
(
AT
meas
-
AT
simul
(
n
-
1
)
)
)
where ∈r* is the complex dielectric constant, the superscripts n−1 and n relate to the n−1th and nth iterations respectively, and the subscripts meas and simul indicate measured and simulated values respectively.

71 more elements

Dependencies are inferred from the claim text.