Journal of Sensors

Volume 2018, Article ID 4645878, 12 pages

https://doi.org/10.1155/2018/4645878

## Design and Optimization of Annular Flow Electromagnetic Measurement System for Drilling Engineering

^{1}School of Manufacturing Science and Engineering, Sichuan University, Chengdu 610065, China^{2}College of Mechanical and Electronic Engineering, Southwest Petroleum University, Chengdu 610500, China^{3}Department of Engineering, Durham University, Durham DH1 3LE, UK^{4}Southwest Branch, Engineering Design Co., CNPC, Chengdu 610413, China

Correspondence should be addressed to Liang Ge; moc.361@daorgc

Received 28 June 2017; Accepted 18 October 2017; Published 25 February 2018

Academic Editor: Bruno Andò

Copyright © 2018 Liang Ge et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Using the downhole annular flow measurement system to get real-time information of downhole annular flow is the core and foundation of downhole microflux control drilling technology. The research work of electromagnetic flowmeter in recent years creates a challenge to the design of downhole annular flow measurement. This paper proposes a design and optimization of annular flow electromagnetic measurement system for drilling engineering based on the finite element method. Firstly, the annular flow measuring and optimization principle are described. Secondly, a simulation model of an annular flow electromagnetic measurement system with two pairs of coil is built based on the fundamental equation of electromagnetic flowmeter by COMSOL. Thirdly, simulations of the structure of excitation system of the measurement system are carried out, and simulations of the size of the electrode’s radius are also carried out based on the optimized structure, and then all the simulation results are analyzed to evaluate the optimization effect based on the evaluation indexes. The simulation results show that optimized shapes of the excitation system and electrode size can yield a better performance in the annular flow measurement.

#### 1. Introduction

In recent decades, oil and gas exploration is being carried out in some extremely harsh and challenging environmental conditions [1]. Drilling safety issues become increasingly prominent when exploring complex and deep formations. Downhole microflux control drilling technology can effectively solve drilling accident such as kick and lose in narrow density window drilling scenarios, so using the measurement system to get the real-time information of downhole annular flow is the core and foundation of downhole microflux control drilling technology.

A huge array of flow technology options is on offer which provides options in selecting the correct annular flow measurement for the application of drilling engineering. A broad range of factors regarding the special environment of downhole drilling, such as downhole space, velocity profile, temperature, and fluid properties, should be considered. Electromagnetic measurement has the advantages of simple structure, no moving parts, and no obstruction of fluid flow throttle parts. Also, the flow path does not cause any additional pressure loss, and it does not cause wear or blockage, in particular when measuring slurry with solid particles, sewage and other liquid-solid two-phase bodies, or a variety of viscous slurry, and so on. In addition, because the structure has no moving parts, so any corrosion will be attached to the insulation lining. After selecting corrosion-resistant electrode material with a very good corrosion resistance, it can be used for a variety of corrosive media measurements. In 2017, Liang et al. propose a new method for an annular flow measurement system based on the electromagnetic induction principle [2]. However, this paper does not describe how to design and optimize the downhole annular flow electromagnetic measurement system. Based on the above reasons, this study mainly focuses on the design and optimization of downhole annular flow electromagnetic measurement system for drilling engineering.

For the traditional electromagnetic flowmeter used in a round pipe, the signal voltage is dependent on the average flow velocity, the magnetic flux density, and the pipe diameter. The signal voltage is expected to be linearly related to the average flow velocity if the magnetic field is a uniform magnetic field. In this ideal case, the flow rate can be considered to be immune to the velocity profile of the pipe flow, especially when the flow has been fully developed. However, it is difficult for the annular flow electromagnetic measurement system to yield a uniform magnetic field for an annular flow path, and also, the velocity profile of the annular flow also cannot be considered axisymmetrically distributed under this special drilling environment. These effects affect the accuracy of the annular flow electromagnetic measurement system. According to Bevie’s vector weight function theory [3], if the result of the magnetic flux density cross-product density of virtual current is constant, the annular flow electromagnetic measurement system can be considered to be immune to the velocity profile of the annular flow. When the electrode and the structure of the flow path are fixed, the density of the virtual current is fixed. So the shape of the excitation system can be derived based on this constant condition. Similarly, when the shape of excitation system and the structure of flow path are fixed, the density of virtual current only depends on the electrodes. In this case, the size of the electrode was selected to be optimized to reduce the distortion caused by the velocity profile.

In the past few decades, great efforts about the structure of excitation systems and electrodes have been made to reduce the effects of the velocity profile. Horner B improved the measurement accuracy of flow measurement by increasing the number of electrodes [4, 5]. Michalski et al. investigated the design of the coils of an electromagnetic flowmeter in 1998 [6]. Wang et al. analyzed the relationship between velocity profile and distribution of induced potential for an electromagnetic flow meter in 2007 [7]. An optimum excitation coil for an open channel electromagnetic flowmeter was reported by Michalski et al. in 2001 [8]. Vieira et al. developed an enhanced ellipsoid method for electromagnetic device optimization and design in 2010 [9]. At the same time, some simulation methods were designed with the development of finite element software for multifields. Lim and Choong analyzed the relative errors in evaluating the electromagnetic flowmeter signal using the weight function method and the finite volume method [10]. Michalski et al. applied 3D approach to designing the excitation coil of an electromagnetic flowmeter in 2012 [11]. Yin et al. investigated the theoretical and numerical approaches to the sensitivity calculation of a novel contactless inductive flow tomography [12]. Although great efforts about the structure of the excitation system and electrodes have been made to reduce the effects of velocity profile, most of the design and optimization was focused on the round pipe. The main objective of this paper is to design and optimize the downhole annular flow electromagnetic measurement system with two pairs of electrodes using the method of numerical finite element analysis.

#### 2. Background Theory of the Annular Four-Electrode Electromagnetic Flowmeter

Following Faraday’s law, the flow of a conductive liquid through a magnetic field will cause a voltage signal to be sensed by electrodes located on the flow pipe walls. Faraday’s formula can be expressed as where is the signal voltage in a conductor, is the average flow velocity, is the magnetic flux density, and is the pipe diameter.

Equation (1) indicates that the signal voltage is dependent on the average flow velocity, the magnetic flux density, and the pipe diameter.

The signal voltage is expected to be linearly related to the average flow velocity if the magnetic field is a uniform magnetic field. So (1) can be rewritten as

Here, represents a constant.

However, the annular flow electromagnetic measurement system is difficult to yield a uniform magnetic field for an annular flow path, and the velocity profile of the annular flow also cannot be considered axisymmetrically distributed under this special drilling environment. This affects the accuracy of the annular flow electromagnetic measurement system. So the design and optimization of the downhole annular flow electromagnetic measurement system with two pairs of electrodes cannot be investigated based on the traditional Faraday theory.

According to Bevir’s theory [3], the theoretical expression of the induced potential in annular flow electromagnetic measurement system can be given as a volume integral of the weight function vector and the annular flow velocity as follows: where is given by .

Here, is the induced potential, is the weight function vector, is the velocity of the annular flow, is the magnetic flux vector, is the virtual current vector, and is the integration of annular volume. The velocity of the annular flow weight function vector is dependent on the magnetic flux density vector and virtual current vector .

According to Bevie’s vector weight function theory, if the result of the magnetic flux density cross-product density of virtual current is constant, the annular flow electromagnetic measurement system can be considered to be immune to the velocity profile of the annular flow. When the electrode and the structure of the flow path are fixed, the density of virtual current is fixed. Thus, the shape of excitation system can be derived based on this constant condition. Similarly, when the shape of the excitation system and the structure of the flow path are fixed, the density of the virtual current only depends on the electrodes. In this case, the radius of the electrode was selected to be optimized to reduce the distortion caused by the velocity profile.

Figure 1 shows a schematic diagram of the downhole annular four-electrode electromagnetic flowmeter and the flow path. A1, A2, B1, and B2 represent four electrodes placed on the outer wall at intervals of 2*γ* inside the annular flow path ( while in simulation), *a* and *b* are the distance of the inner and outer surfaces to the center, and and represent the inner and outer surfaces of the annular flow path.