Introduction

Against the backdrop of the global oilfield development gradually entering the mature stage, the number of water injection wells is showing a continuous upward trend. Water injection wells occupy an indispensable and crucial position in the process of oilfield development. They can effectively maintain the pressure of the oilfield, thereby creating favorable conditions for improving the oil recovery rate. Under such circumstances, realizing real-time intelligent control of water injection wells has become one of the major challenges in the current industry1,2,3.

At present, the cable control method is mainly adopted for separate-layer water injection. During the construction process, a cable is bound outside the oil pipe and is interconnected with the water distributor to measure parameters such as flow, pressure, and temperature and effectively control the water volume. Although the wired cable downhole water injection control system can complete the adjustment task of water injection work, the wired system equipment is complex and difficult to operate. In addition, the cable will inevitably wear in the downhole environment, which leads to high maintenance costs1,2. Therefore, developing an efficient downhole wireless real-time control system has become the key to solving the water injection problem.

Currently, wireless transmission technology can be mainly divided into three types: mud pressure wave, acoustic wave, and electromagnetic wave3,4. Among them, the mud pressure wave has been widely used in the measurement work of deep wells and ultra-deep wells. However, due to the fact that the bandwidth and transmission rate of the pressure wave signal are strictly limited by the flow characteristics of the mud, the efficiency of its two-way communication is low. In addition, this technology is complex to operate and has high requirements for the density and flow rate of the mud. These factors work together to greatly restrict its real-time performance and reliability. Although the acoustic wave transmission technology has a certain propagation distance and transmission capacity, in the complex downhole environment, the acoustic wave is extremely vulnerable to the interference of background noise and other sound sources, seriously reducing the reliability of data transmission3,4,5. The electromagnetic wave transmission technology has attracted wide attention due to its high efficiency, convenience, and economy3,4,6,7,8. Its basic principle is to achieve the purpose of remote communication by transmitting and receiving electromagnetic signals. Compared with the first two wireless transmission methods, the electromagnetic wave transmission technology has the remarkable advantages of simple operation, low cost, and strong adaptability9,10,11,12. Since high-frequency electromagnetic waves attenuate severely in the formation, extremely low-frequency (ELF) electromagnetic waves are commonly used for downhole electromagnetic transmission.

In addition, in the field of extremely low-frequency electromagnetic transmission, Chun Shao10 and others used the finite element method to model open-hole wells, and deeply explored the influence of various underground factors on the strength of the received signal. However, they only studied the attenuation characteristics of electromagnetic waves in open-hole wells, and their research did not involve cased wells. Sihan Li11 and others focused on solving the problem of the transmission distance in open-hole wells, and carried out in-depth research on electromagnetic wave relay technology and relay methods, and proposed a new method of electromagnetic wave relay using a spiral loop antenna. Yan Wu14 proposed an innovative method, that is, by connecting two connectors to the metal casing, the transmitter and the casing form a loop, so that the electromagnetic waves can penetrate the casing to achieve long-distance telemetry. However, this method has certain limitations. Connecting the transmitter to the casing requires relatively mature technological conditions, and its reliability still needs further verification and improvement. Nie16 found through research that when guided by a metal string, the attenuation of the near field of extremely low-frequency electromagnetic waves is much smaller than the attenuation of the space wave without the guidance of a metal string in the same lossy medium.

Currently, people only focus on solving the transmission problem of the excitation source outside the casing, and the transmission of electromagnetic signals in cased wells faces huge challenges. Specifically, the transmission is difficult, the transmission distance is severely limited, and the problem of a serious mismatch between the transmitter impedance and the load impedance is also extremely prominent. We urgently hope to find an effective method to make the difficulty of electromagnetic signal transmission and the transmission depth in cased wells comparable to those in open-hole wells, so as to improve the performance of electromagnetic transmission technology in cased wells. However, at present, in the complex downhole environment, our understanding of the transmission mechanism of electromagnetic waves in cased wells is still vague, which has become a key factor restricting technological breakthroughs.

In this study, we first described the form and principle of the intelligent water injection system and wireless electromagnetic transmission. Based on the theory of electromagnetic fields, we established a two-dimensional axisymmetric finite element model. Through this model, we can deeply and systematically explore the influence of various factors on the electromagnetic signal transmission in cased wells. Aiming at the problem of the contact between the oil pipe and the casing in cased wells, we innovatively proposed the concept of contact resistance. To solve the key problems such as impedance mismatch and difficult electromagnetic wave transmission in cased wells, we innovatively proposed a method of wrapping insulating materials outside the oil pipe, providing new ideas and methods for improving the electromagnetic signal transmission situation in cased wells.

The finite element theory of the electromagnetic field and the principle of wireless electromagnetic transmission in water injection wells

The principle of wireless electromagnetic transmission in water injection wells

The basic structure of a water injection well consists of an oil pipe and a casing. To achieve communication between the downhole and the surface, an extremely low-frequency telemetry technology that combines a transmitter with the oil pipe is proposed. Based on this, an intelligent water injection system and a wireless electromagnetic transmission system for water injection wells are proposed. By combining the electromagnetic wave communication system with the water distributor, the downhole data can be uploaded to the surface, thus realizing wireless communication13,15,17,18,19.

Fig. 1
figure 1

Principle of the Wireless Electromagnetic wave Transmission Intelligent Water Injection System.

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The wireless electromagnetic transmission system of the water injection well mainly consists of two major parts: the downhole signal transmitting part and the ground signal receiving part, and its working principle diagram can be referred as Fig. 1.

In the downhole signal transmission section, the oil pipe is separated into two segments by the transmitter, which respectively serve as the two poles for signal transmission. By taking advantage of the unique structure of the oil pipe, an asymmetric dipole antenna is formed. Its main function is to guide the extremely low-frequency (ELF) electromagnetic wave to transmit to the ground. Compared with the single-antenna form, using the oil pipe as a radiating antenna can greatly improve the radiation efficiency. This type of antenna can excite the quasi-TEM mode of the ELF wave and guide and propagate this signal. There are two excitation methods. One is excitation through a voltage gap, and the other is excitation by means of a magnetic current loop. These two excitation methods can generate the same TEM field outside the equivalent source region, and both can effectively excite the quasi-TEM mode, thus realizing the efficient coupling, transmission, and reception of the ELF signal. In this paper, the antenna form of the voltage gap is selected, and the principle diagram is shown in Fig. 2.

During the signal transmission process, the sensor first collects relevant information, and then the downhole instrument converts these parameters into electrical signals and applies them to the oil pipe. After the electromagnetic signal is generated, it will be transmitted to the ground through the transmission channel composed of the oil pipe, mud, casing, and formation, and the ground wire antenna or the helical loop in the well is used for reception. Finally, the signal transmission between the downhole and the ground is realized17,18,20.

Fig. 2
figure 2

Theoretical Model of Wireless Electromagnetic Transmission with Voltage Gap.

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Among them, due to the relationship between electric field and magnetic field, at the field point15,21:

$$-j\omega {\varepsilon ^*}\vec {E}=r( - \frac{{\partial {{\vec {H}}_\varphi }}}{{\partial z}})+z(\frac{{\partial r{{\vec {H}}_\varphi }}}{{r\partial r}})$$
(1)

Where:

$${\vec {E}_z}=\frac{1}{{\omega {\varepsilon ^*}}}(\frac{{\partial r{{\vec {H}}_\varphi }}}{{r\partial r}})$$
(2)

The potential difference received on the ground is actually the component of the radial integration of the ground electric field between two receiving points, specifically:

$${V_r}= - \int_{{{r_A}}}^{{{r_B}}} {{{\vec {E}}_r}} dr$$
(3)

Vr is the surface received voltage, \({\vec {E}_r}\) is the r-component of the surface electric field.

The input voltage of the transmitting antenna can be obtained by integrating the axial component of the electric field on the surface of the insulated section:

$${V_{in}}=\int_{l} {{{\vec {E}}_z}} dz$$
(4)

l is the length of the insulation gap, and Ez is the axial component of the electric field in the insulation gap.

Vin is the excitation voltage, and Iin is the excitation current.

The input impedance of the transmitting antenna has nothing to do with the current excitation and voltage excitation, and the transmitting power can be expressed as:

$${P_{in}}=\frac{1}{2}{V_{in}}{I_{in}}$$
(5)

Similarly, according to the Biot-Savart law, by only measuring the value of the magnetic field around the oil pipe, the magnitude of the current on the oil pipe and its attenuation condition can be obtained. Combined with the magnitude of the received voltage on the ground, the transmission characteristics of the electromagnetic signal can be analyzed.

The finite element theory of the electromagnetic field

In this study, we use the finite element method (FEM) to simulate the electromagnetic field distribution in complex formations. The finite element method solves the problem by discretizing the complex continuous electromagnetic field problem into small and simple elements. Due to its flexibility in dealing with complex geometries and boundary conditions, it has become an effective tool for numerical simulation of electromagnetic problems18,21.

When studying the downhole electromagnetic transmission problem, the electromagnetic field is a time-harmonic field, and the instantaneous field vectors are differentiated with respect to time. Maxwell’s equations can be written in the following form:

$$\nabla \times \vec {E}= - j\omega \mu \vec {H}$$
(6)
$$\nabla \times \vec {H}={\vec {j}_0}+j\omega \vec {D}m$$
(7)

Where \(\vec {E}\) is the electric field intensity; \(\vec {B}\) is the magnetic flux density; \(\vec {H}\) is the magnetic field strength; \(\vec {D}\) is the electric displacement field; \({\vec {j}_0}\) denotes the conduction current density; ω is the angular frequency; µ is the magnetic permeability.

Under extremely low frequency conditions, using the quasi-static approximation and substituting (6) into (7), the Helmholtz equation can be obtained, which is the governing equation of the finite element method:

$$\nabla \times \left( {\frac{1}{{{\mu _r}}}\nabla \times \vec {E}} \right) - {k_{\text{0}}}^{2}{\varepsilon _r} \cdot \vec {E}= - j\omega {\mu _0}\vec {J}$$
(8)

Where k0 is the wave function in free space, and \(\vec {J}\) is the external current density. It is clear that for analyzing low-frequency electromagnetic field problems, obtaining the current density in the loop and the transmission potential is sufficient.

Physical model construction

The wireless transmission channel of electromagnetic waves in a cased well mainly consists of mud, formation, oil pipe, casing, etc. In the actual drilling process, the size of the insulated antenna is small and the formation conditions are complex. To study the characteristics of wireless electromagnetic transmission more conveniently, the geometric construction of the entire simulation model is carried out. The following preset conditions are set for constructing the geometric model: (1) The same type of formation and mud are both homogeneous media; (2) The sizes of the oil pipe and insulated antenna are the same, and the influence of couplings is not considered; (3) The wellbore trajectory is a vertical well and the central axis of the wellbore coincides with the central axis of the oil pipe. Based on the above conditions, the wireless electromagnetic transmission model of the cased well is simplified as shown in Fig. 2, and the corresponding 2D axisymmetric model is shown in Fig. 3(a). Figure 3(b) is the corresponding meshing diagram.

Fig. 3
figure 3

(a) 2D axisymmetric model. (b) Meshing diagram.

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The model is 1500 m wide and 3000 m high, with the formation height set at 2000 m and the air layer height at 1000 m, and a perfectly matched layer is set at the corresponding position. The drilling depth is 1500 m, and the oil pipe length is initially set at 1500 m, with an inner diameter of 46 mm, an outer diameter of 76 mm, and a thickness of 15 mm. The diameter of the insulated antenna is the same as that of the oil pipe and its length is 0.4 m. The casing length is 150 m, with an inner diameter of 124 mm and an outer diameter of 154 mm. The excitation source is at a depth of 1000 m underground, and the distance between the ground electrode and the wellhead is 100 m.

Meshing

For structures with relatively large contrasts such as oil pipes, casings, and mud, it is necessary to constrain the size and number of their boundary meshes. For the formation and air, free triangular meshes are adopted. For the boundary of the solution ___domain, a perfectly matched layer needs to be set up, and the corresponding meshes should be refined.

Analysis of results and influencing factors

The attenuation of electromagnetic signals is affected by multiple factors, including the excitation frequency, the resistivity of mud and formation, the conductivity of casing and so on. In this study, we conduct numerical research using the parameters of equipment commonly used in the petroleum industry. In order to evaluate the influence of various parameters more accurately, the control variable method is adopted in this paper. That is to say, when discussing a certain parameter, other parameters remain unchanged.

The influence of frequency

Based on the characteristics of electromagnetic wave propagation, the frequency range of the electromagnetic waves studied is set between 5 Hz and 100 Hz. The electrical conductivity of the oil pipe and casing is 107 S/m. The resistivity of the mud is 1 Ω·m, with a relative dielectric constant of 80. The resistivity of the formation is set at 10 Ω·m. The excitation source is located 1000 m underground, with a power of 1 W. In an open-hole well environment, the relationship between the transmitting frequency and the value of the magnetic field around the oil pipe is shown in Fig. 4(a), and the relationship between the change in frequency and the intensity of the received signal on the ground is shown in Fig. 4(b). In a cased well, the relationship between the transmitting frequency and the value of the magnetic field around the oil pipe is shown in Fig. 5(a), and the relationship between the change in frequency and the intensity of the received voltage on the ground is shown in Fig. 5(b).

Fig. 4
figure 4

(a) Relationship between transmission frequency and magnetic field value around oil pipe in open hole well. (b) Relationship between frequency in open hole well and ground received voltage and load impedance.

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Fig. 5
figure 5

(a) Relationship between transmission frequency and magnetic field value around oil pipe in cased well. (b) Relationship between frequency in cased well and ground received voltage and load impedance.

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By comparing Figs. 4 and 5, it can be seen that in the open-hole well environment, whether it is the attenuation of the magnetic field around the oil pipe or the situation of the ground-received voltage, there are significant advantages compared to the cased well. However, it can also be observed that the magnetic field around the oil pipe experiences strong attenuation when approaching the ground. Therefore, when using in-well signal reception, the signal should be received at least 10 m away from the wellhead. As shown in Fig. 4(a), when the frequency is 5 Hz and the transmission distance is 900 m, the magnetic field attenuation is only 26.6 dB, and the attenuation per 100 m is approximately 2.96 dB. When the casing exists, as can be seen from Fig. 5(a), in the initial stage, the magnetic field around the oil pipe shows a sharp and significant decrease in intensity. After the initial intense attenuation, the attenuation rate of the magnetic field gradually slows down. Although the intensity is still decreasing, the decrease value is significantly reduced. For example, when the transmission distance is 200 m and the excitation frequency is 5 Hz, the magnetic field attenuation is about 58.5 dB. However, when the transmission distance is in the range of 200 –900 m, the magnetic field value only attenuates by 16 dB. It can be seen from this that the excitation frequency has a relatively large impact on the near-field region of the antenna.

In Fig. 4(b) and Fig. 5(b), the left vertical axis represents the ground-received voltage, and the right vertical axis represents the external load impedance. It has been found that the ground-receiving effect in the open-hole well is better than that in the cased well environment. Besides, the load impedance of the transmitter in the cased well is much smaller than that in the open-hole well environment, which is the main reason why the wireless electromagnetic transmission system is difficult to be used in the cased well environment. Figure 5(b) shows that when the frequency increases from 5 Hz to 100 Hz, the ground-received voltage decreases by 50.1 dB. Obviously, in order to ensure the transmission distance, a lower excitation frequency should be selected as much as possible. In the follow-up research, the excitation frequency will be set at 5 Hz.

The impact of formation resistivity

When the downhole excitation emits signals outward, the formation is the main transmission medium for the electromagnetic waves radiating outward. During the transmission process of electromagnetic signals, a strong leakage current will occur in the formation. The formation conditions are extremely complex and involve numerous factors. The formation conductivity is a key indicator for measuring the conductive ability of the formation and has a huge impact on the transmission effect of electromagnetic signals. The range of the formation resistivity is set to be from 1 Ω·m to 10,000 Ω·m.

Fig. 6
figure 6

(a) Relationship between formation resistivity and magnetic field value around oil pipe at different transmission distances. (b) Relationship between formation resistivity and ground received voltage and load impedance.

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As shown in Fig. 6 (a), when the transmission distance is 200 m, the magnetic field value is scarcely affected by the formation resistivity. However, it can also be found that as the formation resistivity increases, the range of the near-field region of the dipole antenna gradually expands, and the attenuation of the magnetic field value within the overall range increases. The reason is that the high resistivity of the formation causes most of the magnetic field inside the casing to be dissipated in the casing. Looking at the far-field region, it can be observed that when the formation resistivity is in the range of 1 Ω·m to 10 Ω·m, as the formation resistivity rises, the magnetic field attenuation gradually decreases and then tends to stabilize. Moreover, it can be seen that when the formation resistivity is 10 Ω·m, the effect of receiving with the helical loop inside the casing is the best. Figure 6(b) shows the relationship between the formation resistivity and the ground-received voltage and impedance. It can be seen that the increase in the formation resistivity has almost no impact on the load impedance, but the ground-received voltage gradually increases. When the formation resistivity increases to 10 Ω·m, the ground-received voltage tends to stabilize.

The impact of mud conductivity

Due to the differences in geological environments in different regions, the properties of mud in water injection wells also vary greatly. Therefore, mud conductivity is set within the range of 0.1 S/m to 100 S/m, with a relative dielectric constant of 80. Other parameters remain unchanged. Figure 7(a) shows the magnitude of the received magnetic field under different mud environments. Figure 7(b) shows the relationship between the change in the conductivity of the mud and the ground-received voltage.

As can be seen from Fig. 7(a), in the cased well, the conductivity of the mud has a relatively large impact on the magnetic field value around the oil pipe. In the mud with low conductivity, the attenuation of the magnetic field is relatively small. And as can be seen from Fig. 7(b), the factor that has a greater impact on the external load impedance of the transmitter is the conductivity of the mud. When the conductivity of the mud increases from 0.1 S/m to 100 S/m, the impedance decreases by 40 times and the ground-received voltage decreases by 10.9 dB. All in all, the mud with low conductivity is more conducive to the generation and transmission of electromagnetic waves.

Fig. 7
figure 7

(a) Relationship between mud conductivity and magnetic field value around oil pipe at different transmission distances. (b) Relationship between mud conductivity and ground received voltage and load impedance.

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The impact of casing properties

In order to deeply explore the influence mechanism of metal casings on electromagnetic wave transmission, it is necessary to analyze three important characteristics of the casings. Firstly, the electrical conductivity of the casing is one of the key factors affecting electromagnetic wave transmission. The model adopted in this study is consistent with the model mentioned previously. Since casings are usually made of steel, the value range of the casing’s electrical conductivity is set to be from 10⁶ S/m to 2 × 10⁷ S/m. When studying the influence of the casing’s magnetic permeability on signal transmission, we set the electrical conductivity of the casing to be 10⁷ S/m and determine the range of its relative magnetic permeability to be from 1 to 5,000. In addition, the inner diameter of the casing is also a factor that cannot be ignored. Under different drilling conditions, the selected casing sizes will vary. Common inner diameters of casings include 139.7 mm, 177.8 mm, 219.1 mm and so on. In order to study the influence of the casing’s inner diameter on signal transmission, we set the size range to be from 124 mm to 273 mm.

Fig. 8
figure 8

(a) Relationship between casing conductivity and magnetic field value around oil pipe at different transmission distances. (b) Relationship between casing conductivity and ground received voltage and load impedance.

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Fig. 9
figure 9

(a) Relationship between casing permeability and magnetic field value around oil pipe at different transmission distances. (b) Relationship between casing permeability and ground received voltage and load impedance.

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Fig. 10
figure 10

(a) Relationship between casing size and magnetic field value around oil pipe at different transmission distances. (b) Relationship between casing size and ground received voltage and load impedance.

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As can be seen from Fig. 8(a), as the electrical conductivity of the casing increases, the range of the antenna’s near-field region will increase accordingly, the overall attenuation degree will also increase correspondingly, and the magnetic field value at the corresponding position will become smaller. From Fig. 8(b), it can be known that when the electrical conductivity of the casing increases, the ground-received voltage shows a linear decreasing trend, and the external impedance also decreases significantly. It can be seen that the casing with high electrical conductivity will lead to a substantial increase in electromagnetic losses, which is not conducive to the transmission of electromagnetic waves. Therefore, under the condition of meeting the requirements of practical engineering applications, the casing with low electrical conductivity is more conducive to the transmission of electromagnetic waves.

Figure 9(a) shows the influence of the casing’s magnetic permeability on the magnetic field. It can be clearly seen that the increase in the casing’s magnetic permeability will intensify the attenuation of the magnetic field. According to Fig. 9(b), it can be found that as the relative magnetic permeability continues to increase, the ground-received voltage will experience significant attenuation. For example, when the relative magnetic permeability increases from 1 to 2,000, the magnitude of the ground-received voltage attenuates by 23 dB. However, when the relative magnetic permeability is greater than 2,000, its attenuation effect on the electromagnetic signal will tend to stabilize.

Figure 10(a) presents the strength of the magnetic field around the oil pipe under different casing sizes. When the transmission distance is within 400 m, the larger-sized casing corresponds to a smaller magnetic field attenuation, and the magnetic field strength at the same position is also stronger; while when the transmission distance is greater than 400 m, the situation is different, and the thinner casing instead shows a better transmission effect. Figure 10(b) shows the influence of the casing size on the impedance and the ground-received voltage. It has been found through research that the load impedance will increase as the casing size increases, and the attenuation of the voltage shows a trend of first increasing and then decreasing.

Based on the above analysis results, it can be concluded that the casing with low electrical conductivity, low magnetic permeability, and medium size is more conducive to the transmission of electromagnetic waves.

Influence of contact resistance

In practical engineering application scenarios, the oil pipe and casing usually have a considerable length. Affected by a variety of complex factors, the oil pipe is not always in an ideal state of being completely parallel and upright. Due to the existence of various external forces and internal stresses, the oil pipe may be inclined or bent. There is a high probability that it will come into contact with the metal casing, as shown in Fig. 11(a). And the concept of contact resistance is proposed for the first time. In a metal cased well, contact resistance refers to the local resistance formed due to the physical contact between the oil pipe and the casing. This resistance is jointly determined by the material properties of the contact interface, the contact area, and the mechanical stress. It can be equivalent to a distributed resistance network, and the resistance value generally ranges from 10⁻³ Ω·m to 10⁻⁵ Ω·m. The contact between the oil pipe and the casing is equivalent to two squares with a thickness equal to the distance between the oil pipe and the casing. At the same time, the material conductivity is set to 10⁵ S/m, and the relative magnetic permeability is set to 100. The distance range between the contact position and the excitation source is 0.1 –100 m, and a two - dimensional axisymmetric model is established, as shown in Fig. 11(b). Figure 12(a) shows the relationship between the distance from the contact position to the excitation source and the ground - received voltage, and Fig. 12(b) shows the relationship between the distance from the contact position to the excitation source and the change of load impedance.

Fig. 11
figure 11

(a) Theoretical model of contact resistance. (b) 2D axisymmetric model.

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It has been found through research that the contact position between the oil pipe and the casing has a relatively large impact on both the impedance and the reception of ground signals. Specifically, when the contact position is close to the excitation source, the external load impedance will decrease significantly. Meanwhile, the ground-received voltage will also experience a relatively large degree of attenuation. The reason for this phenomenon is that due to the contact between the oil pipe and the casing, the current will flow from the oil pipe to the casing through the contact point, and most of the energy is consumed at this ___location, which greatly reduces the radiation efficiency of the asymmetric dipole antenna.

Fig. 12
figure 12

(a) The relationship between the distance from the contact position to the excitation source and the received voltage on the ground. (b) The relationship between the distance from the contact position to the excitation source and the change of the load impedance.

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An optimization design based on insulation sleeve

It can be seen from the above analysis that the change in the conductivity of the mud has a significant impact on the impedance of the external load, which increases the difficulty of impedance matching for the transmitter. Due to the special properties of the casing, the electromagnetic field will suffer relatively large losses when passing through the casing, resulting in the weakening of the signals received on the ground. If the oil pipe contacts the casing at a position close to the excitation source, the excitation current will form a loop through the transmitter, the oil pipe, the comes into contact with contact position and the casing, and most of the energy will be dissipated during this process.

Therefore, the key to solving the problem of wireless electromagnetic transmission in cased wells lies in increasing the external load impedance of the transmitter in cased wells so as to improve its applicability under different geological conditions. In addition, the contact between the oil pipe and the casing near the transmitter should be avoided. Based on these requirements, we propose a method of wrapping an “insulation sleeve” outside the oil pipe near the transmitter, as shown in Fig. 13. The resistivity of the insulating material is set to 104 S/m, and the length of the insulation sleeve is set to be between 0.4 m and 200 m.

Fig. 13
figure 13

(a) Optimization Design Model Based on insulation sleeve. (b) 2D axisymmetric Model.

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Fig. 14
figure 14

(a) Relationship between insulation length and received voltage at different mud conductivitis. (b) Relationship between insulation length and load impedance at different mud conductivitis.

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The research reveals that as the length of the insulating section increases, the intensity of the ground - received voltage shows an upward trend, as depicted in Fig. 14(a). Simultaneously, the load impedance also increases significantly, with the specific manifestations shown in Fig. 14(b). When the length increases to 150 m, the magnitude of the received voltage tends to stabilize. At this time, when the conductivity of the mud is 0.1 S/m, the intensity of the received voltage is increased by 1.8 dB and the load impedance is raised to three times the original value; when the conductivity of the mud is 5 S/m, the intensity of the received voltage is increased by nearly 8 dB and the load impedance is raised to six times the original value. All in all, the method of wrapping an “insulation sleeve” outside the oil pipe near the transmitter can significantly improve the transmission efficiency of electromagnetic waves.

The intervention of the insulation sleeve effectively blocks the current circulation path that may be formed between the oil pipe and the casing near the transmitter, greatly reducing the unnecessary loss of energy. This enables the energy that was originally wasted during the electromagnetic transmission process in conventional cased wells to be guided into the effective emission and propagation of electromagnetic waves, thereby directly improving the intensity and quality of the ground-received voltages. In addition, in the mud environment with high conductivity, electromagnetic transmission technology often faces difficulties such as serious mismatch of external impedance and severe signal attenuation. After adopting this insulation sleeve method, not only can stable signal transmission be ensured, but also a significant increase in the intensity of the received voltage can be achieved. Meanwhile, it also provides a new basis for the design and improvement of relevant electromagnetic transmission equipment, prompting R & D personnel to re-examine the structure and performance optimization direction of the transmitter so as to better match the insulation sleeve method and thus build a more efficient and reliable overall solution for the wireless electromagnetic transmission system in cased wells.

Field experimental

Experimental instrument

Based on the relevant theories mentioned above, a wireless electromagnetic transmission system for cased wells was designed. The wireless electromagnetic transmission system consists of a downhole transmitting system and a surface receiving system. Figure 15 shows the diagram of the experimental instrument.

The signal modulation method of the downhole transmitter is Frequency - Shift Keying (FSK), and the carrier frequency is 5 Hz. The surface chassis continuously receives the electromagnetic wave signals transmitted from the downhole. The distance between the surface electrodes and the wellhead is 100 m.

Fig. 15
figure 15

Experimental Instrument.

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Downhole experiment

A one-way electromagnetic wave transmission experiment was carried out in a water injection well of an oilfield. The water injection well in this oilfield is a cased well, and the wellbore wall shows slight corrosion, as depicted in Fig. 16(a). The depth of the casing is approximately 1500 m, and its inner diameter is 150 millimeters. The water surface in the casing is located at a depth of about 250 to 300 m. Through on-site water sample collection and measurement using a resistivity meter, the resistivity was determined to be 1.268 Ω·m.

Fig. 16
figure 16

Cased well and situation of the on-site experiment.

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The downhole transmitter was properly connected, and it was ensured that the connection was firm and the sealing was excellent to prevent any loosening or water ingress failures downhole. The bottom of the downhole transmitter was connected to 6 oil pipes, each with a length of 9.6 m, and the upper end could be connected to a maximum of 122 oil pipes. Figure 16(b) shows the situation of the on-site experiment.

After lowering the instrument to a depth of 200 m, we started to conduct continuous surface monitoring of the electromagnetic wave signals transmitted from the downhole. We continued to lower the downhole instrument, pausing every 50 m. After waiting for the receiving antenna to stabilize, we recorded the waveform of the received signal and relevant parameters. After each adjustment, multiple signal collections were carried out, with a time interval of 20 s between each collection. Figure 17 shows the relevant waveforms received by the experimental well. When the downhole instrument was lowered to a depth of 1100 m, we continuously collected and recorded the received signal data to observe the stability of the signals.

Fig. 17
figure 17

The received waveform.

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Comparison between simulation results and experimental results

Based on the above experiment, the received signals were processed, and a graph showing the relationship between the surface received voltage and the transmission depth was drawn and compared with the simulation results. Figure 18 is a comparison diagram between the on-site verification results and the calculated results.

The results show that there is a good consistency between the simulation and the experimental data, verifying the accuracy of the theoretical model. This lays a foundation, enabling us to use theoretical research to optimize and design the electromagnetic wave transmission system of water injection wells.

In this experiment, the signal-to-noise ratio is good, and the decoding basically meets the requirements of the telemetry of water injection wells, proving that the two-way transmission mode between the surface and the downhole is feasible.

Fig. 18
figure 18

Comparison chart of simulation results and field experiment.

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Conclusions

This paper constructs a 2D axisymmetric finite element model for wireless electromagnetic transmission in water injection wells based on the electromagnetic field theory. It focuses on comparing the attenuation status of extremely low frequency electromagnetic waves in cased wells and open-hole wells as well as the changes in external load impedance. The research finds that in the cased well environment, the load impedance decreases significantly, which undoubtedly increases the difficulty of excitation. After that, the influences of factors such as formation, mud, and casing on wireless electromagnetic transmission are deeply explored. The research shows that the mud with low conductivity can effectively improve the characteristics of load impedance and then significantly enhance the transmission efficiency. The casing with low electrical conductivity, low magnetic permeability, and moderate size has been proved to be more conducive to the transmission of electromagnetic waves in cased wells.

The concept of contact resistance is proposed for the first time and verified by simulation experiments. In order to improve the efficiency of wireless electromagnetic transmission, a method of wrapping an “insulation sleeve” outside the oil pipe near the transmitter is proposed. This method effectively blocks the current circulation path that may be formed between the oil pipe and the casing near the transmitter, solves the problem of severe signal attenuation in the high-conductivity mud environment, greatly reduces the unnecessary loss of energy, and significantly improves the intensity of ground signal reception. The finite element model constructed in this study is strictly verified by the data collected from on-site experiments. The results show that the theoretical calculations are highly consistent with the actual measurement data, fully demonstrating the accuracy and reliability of the model.

In conclusion, this study conducts an in-depth analysis of the electromagnetic wave transmission mechanism in cased wells and successfully verifies the feasibility of remote telemetry in cased wells. The research achievements obtained are of great significance in the field of downhole electromagnetic transmission and are expected to open up broad prospects for the innovation and development of intelligent water injection systems, reservoir monitoring, and other related downhole electromagnetic application technologies, providing a powerful technical guarantee for the efficient production and refined management in the petroleum engineering field. Meanwhile, this study also provides a useful reference for the follow-up in-depth research on the application of electromagnetic transmission technology in complex downhole environments. In the future, expansion research can be carried out for more actual working conditions and factors to continuously improve and optimize the relevant technical systems.