# Method for Finding the Signal Strength in EM Telemetry

Publication Date: 2017-Mar-29

## Publishing Venue

The IP.com Prior Art Database

## Abstract

The EM telemetry is applied for transmission of signals from BHA to surface while drilling. The current source is attached to the isolating gap sub near the BHA. The current propagates along the conducing drill string towards the surface and induces some measurable voltage drop between two electrodes on the surface. The EM telemetry operates stably when the signal on the surface reaches a certain level (say 1mV peak-to-peak) to be distinguished from the noise. Therefore, simulation is needed to evaluate the expected signal in each particular case. Straightforward simulation using well-known methods like finite element or finite difference methods faces certain difficulties caused by the large range of sizes (the length-to-diameter ratio of the drill string has order ) and resistivities (the ratio of resistivities of the formation and the tube has order ). We propose to decompose the computations into the following steps:

1. Given the current applied to the gap sub, find the current along the drill string at some distance (several diameters of the drill string), i.e., estimate the local current leakage. This step depends crucially on the construction of the gap sub and is not discussed in the invention. 2. Given the current at some distance from the gap sub, find the current distribution along the drill string up to the surface within the layered earth model. The distribution (besides the initial current) depends on the layer resistivity, the frequency, and other parameters. 3. Given the current distribution along the drill string near the surface (approx. 300m), find the voltage drop on the surface between the electrodes.

The computations of Steps 2 and 3 are problematic for the reason mentioned above. Therefore, approximate methods like the transmission line approach [1, 2] are widely applied. In this disclosure we propose a modification of this method which is derived immediately from the integral equations and takes the frequency effects into account. Namely,

• From the Maxwell equations in the 2D case we derive the system of integro-differential equations in the tangential components of the field ( and ) on the boundary between the tube and formation • Since the resistivity contrast is high, the change rate of both field and current along the tube is small. Using this observation we replace the original system of integro-differential equations with the approximate system of ordinary differential equations. Its coefficients are integrals of known functions depending on the parameters (resistivities, frequency, etc.). • The latter system being a second-order system is solved explicitly in terms of elementary functions. • Using the above method and also the method of images, we find the current distribution in each layer up to the surface • From the Maxwell equations in the 2D case we derive the integral equations which connect the current leaking from the drill string into formation near the surface and the component of the field on the surface, whence we immediately obtain the formula for the voltage drop.

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1

**Method for Finding the Signal
Strength in EM Telemetry**

2

**The Essence of the Invention
**

The EM telemetry is applied for transmission of signals from BHA to surface while drilling. The current source is attached to the isolating gap sub near the BHA. The current propagates along the conducing drill string towards the surface and induces some measurable voltage drop between two electrodes on the surface.

The EM telemetry operates stably when the signal on the surface reaches a certain level (say 1mV peak-to-peak) to be distinguished from the noise. Therefore, simulation is needed to evaluate the expected signal in each particular case.

Straightforward simulation using well-known methods like finite element or finite difference methods faces certain difficulties caused by the large range of sizes (the length-to-diameter ratio

of the drill string has order 510 ) and resistivities (the ratio of resistivities of the formation and the

tube has order 86 1010 ). We propose to decompose the computations into the following steps:

1. Given the current applied to the gap sub, find the current along the drill string at some distance (several diameters of the drill string), i.e., estimate the local current leakage. This step depends crucially on the construction of the gap sub and is not discussed in the invention.

2. Given the current at some distance from the gap sub, find the current distribution along the drill string up to the surface within the layered earth model. The distribution (besides the initial current) depends on the layer resistivity, the frequency, and other parameters.

3. Given the current distribution along the drill string near the surface (approx. 300m), find the voltage drop on the surface between the electrodes.

The computations of Steps 2 and 3 are problematic for the reason mentioned above. Therefore,
approximate methods like the *transmission line approach *[1, 2] are widely applied. In this
disclosure we propose a modification of this method which is derived immediately from the
integral equations and takes the frequency effects into account. Namely,

From the Maxwell equations in the 2D case we derive the system of integro-differential

equations in the tangential components of the field ( *zE *and *H *) on the boundary between

the tube and formation Since the resistivity contrast is high, the change rate of both field and current along the tube

is small. Using this observation we replace the original system of integro-differential equations with the approximate system of ordinary differential equations. Its coefficients are integrals of known functions depending on the parameters (resistivities, frequency, etc.).

The latter system being a second-order system is solved explicitly in terms of elementary functions.

Using the above method and also the method of images, we find the current distribution in each layer up to the surface

From the Maxwell equations in the 2D case we derive the integral equations which connect the cur...