Measuring Method of Solid-Liquid Two-Phase Flow in Slurry Pipeline for Deep-Sea Mining

Abstract

In order to reduce the influence of fluid noise on the measurement of solid-liquid two-phase flow in slurry pipeline for deep-sea mining, the technique of virtual inductance is introduced to traditional capacitively coupled contactless conductivity detection (C⁴D), a measuring method for solid-liquid two-phase flow based on differential C⁴D is proposed, and the structure of differential C⁴D based on three electrodes is designed. The measuring device was verified in conductive fluid channels at different salinity. The results demonstrated that the amplitude of output voltage of the measuring device decreased obviously with the increase of the salinity of the fluid, and linearly associated with the size and volume concentration of the polymetallic nodules. Virtual inductance could reduce the requirement of C⁴D sensor for the excitation power. The measuring device had less noise of output signal and high accuracy. When the KCl solution containing salinity is at the average salinity of seawater 3.5% and the particle size of polymetallic nodules is from 0 to 25 mm, the output voltage increased from 0 to 87 mv. The maximum relative error in two-phase flow velocity measurement is 5.2%, which showed that the measuring method for two-phase flow in the slurry pipeline based on the differential C⁴D is effective.

Introduction

The ocean is not only rich in oil and gas resources but also has abundant metal mineral resources, such as nickel, copper, cobalt, manganese, and gold. The reserves of some mineral resources in the ocean are tens to several thousand times corresponding to reserves of land. These metal mineral resources in the form of polymetallic nodules and polymetallic sulfides are located at thousands of meters below the seabed (Xiao et al. 2014). Deep-sea mining capacity depends on the development of mining equipment which can adapt to extremely harsh operating environment of deep-sea. Among the three major existing deep-sea mining systems, the pipe-lifting system is the most application potential, as shown in Fig. 1. This system mainly consisted of a collector, soft pipe, middle bin, riser pipe, lifting motor pump, and mining vessel (Liu et al. 2014).

Fig. 1

Pipe-lifting system of deep-sea mining. (1)Mining vessel. (2) lifting motor pump. (3) Riser pipe. (4) Middle bin. (5) Soft pipe. (6) Collector

The structure of the collector is shown in Fig. 2. In order to improve the cutting efficiency and reduce the mining pollution, the collector adopted the integrated working method of combining and cutting mineral nodules (Liu et al. 2016).

Fig. 2

Collector for deep-sea mining. (1) Left roller. (2) Right roller. (3) Collecting cover. (4) Pump. (5) Rocker arm. (6) Ore trolley. (7) Soft pipe

The structure of the lifting motor pump is shown in Fig. 3. It is a kind of a slurry pump; in addition, it must meet the performance of anti-high pressure, non-blocking, high lift, wear and corrosion resistance, and good reliability.

Fig. 3

Structure of lifting motor pump. (1) Flange of suction. (2) Motor, (3) Annular channel. (4) Nut and bolt. (5) multistage pump. (6) Pump barrel. (7) Flange of spit out

Fluid transported in deep-sea slurry pipeline is a solid-liquid two-phase flow. Its parameters’ accurate measurement is directly related to the stability and economic operation of deep-sea mining system.

The measurement of multiphase flow parameters was a difficult problem, which was urgently to be solved in industrial. At present, due to the physical properties of multiphase fluid and the mechanisms of flow process complex, there was not a single measuring method that can fully adapt to various multiphase flows. With the development of science and technology, some new technologies were applied to measure multiphase flow, such as fiber technology, ultrasonic technology, particle image technology, laser technology, and process tomography technology (Pu et al. 2006; Du et al. 2015; Zhang et al. 2014). Industrial multiphase flow parameter measurement requires non-invasion, high-reliability, high-precision, real-time measurement; many scholars had done a lot of creative work in these areas. Li et al. (2014) proposed an improved EEMD filtering method for multiphase flow signal. Experiments revealed that this method could improve the accuracy of multiphase flow measurement. Wang et al. (2014) proposed a measurement method of oil and gas multiphase flow that combined with the relevant flow measurement method and electromagnetic flow measurement method. Zheng et al. (2008a) achieved gas-liquid two-phase flow measurement by applying conductivity sensor combined with turbine flowmeter. Yang et al. (2017) developed a droplet-capable conductivity probe for the measurement of liquid-dispersed two-phase flow. Xiuzhong and Hideo (2014) proposed a newly developed complete four-sensor probe signal processing algorithm for local instantaneous 3-dimensional bubble velocity vector. Khasani et al. (2017) studied on the transient behaviors of two-phase flow in a geothermal production well for a short period of continuous measurement. Wang et al. (2016) proposed a method for measuring gas-liquid two-phase flow based on near-infrared spectroscopy. He et al. (2016) designed an on-line measuring device to measure the gas-liquid flow rate in wet gas by using a V-shaped conical throttle device. Fang et al. (2018) proposed two-phase fluid phase content measurements based on near-infrared absorption and decay techniques.

In recent years, capacitively coupled contactless conductivity detection (C⁴D) technology has been more and more concerned by the fluid parameter measurement field, as it can avoid effectively electrode corrosion and polarization issues in traditional conductance detection. Ji et al. (2014) developed a C⁴D sensor for millimeter pipeline fluid measurement in the industrial field. Zheng et al. (2008b) proposed a C⁴D measurement method based on parallel resonance and applied this method successfully to the measurement of microparticles in fluid. Huang et al. (2009, 2012) proposed a C⁴D measurement method based on the impedance cancellation principle and designed a C⁴D sensor with a single shield.

Achievements mentioned previously were mainly for the measurement of gas-liquid two-phase flow in small pipelines. These achievements and methods had more or less a certain reference to the measurement of solid-liquid two-phase flow parameters. But fluid transported in pipeline-lifting system of deep-sea mining is a solid-liquid two-phase flow consisting of polymetallic nodule particles and sea water, its mechanism and state are significantly different from the gas-liquid two-phase flow, so it is necessary to further study the measurement method of solid-liquid two-phase flow in pipeline-lifting system of deep-sea mining. In this study, the objective was to meet the requirements of the parameter measurement of two-phase flow in pipeline-lifting system of deep-sea mining. Therefore, a differential C⁴D method was used to measure solid-liquid two-phase flow parameters in the proposed mineral pipeline transportation. The conclusion has some reference significance to improve the accuracy of measurement for multiphase flow transporting in pipeline.

Materials and Methods

Composition and Working Principle of C⁴D for Fluid in a Pipeline

Construction and equivalent of C⁴D sensor are shown in Fig. 4. It consists of five main components: insulation pipe, AC excitation signal source, driving electrode, detecting electrode, and signal processing section. Electrodes of driving and detecting were two ring metal electrodes, which were closed to the outer wall of the insulation pipe. So the metal electrodes, insulated pipe, and conductive fluid formed an AC signal path. When the excitation signal with a certain frequency was applied to the excitation electrode, the response signal associated with the conductivity of the fluid could be detected at the detecting electrode.

Fig. 4

Construction and equivalent of C⁴D sensor. a Construction of C⁴D sensor. b Equivalent of C4D sensor

In the equivalent of C⁴D sensor, R_S is the equivalent resistance of measured fluid. C₁ and C₂ are the capacitors formed by two metal electrodes coupling with conductive liquid. C₀ is the stray capacitor formed by two metal electrodes with coupling through air. It is detrimental to the conductance measurement and could be eliminated by adding a ground shield between the two metal electrodes (Pumera 2007) as shown in Fig. 4. The total impedance of C⁴D is expressed as follows:

$$ Z=R+{jX}_C=\frac{R_S{C}_S^2{\omega}^2-j\left[\omega \left({C}_S+{C}_0\right)+{R}_S^2{C}_0{C}_S^2{\omega}^3\right]}{\left({R}_S{C}_0{C}_S{\omega}^2\right)+{\left[\omega \left({C}_S+{C}_0\right)\right]}^2} $$

(1)

where R and X_C are the real and imaginary parts of the capacitively coupled contactless reactance, respectively; ω = 2πf, f is the frequency of the excitation signal; C_S is the series value of the coupling capacitors C₁ and C₂. In conductance measurement circuit, the equivalent resistance of fluid R_S is a useful signal, but coupling capacitors C₁ and C₂ are unfavorable background signals. Due to the large size of the pipeline for transporting solid-liquid two-phase flow, therefore, the equivalent resistance of fluid R_S was small and the capacitances of coupling capacitor C₁ and C₂ were large, resulting in a low signal-to-noise ratio of the measurement device and low measurement sensitivity (Laugere et al. 2002).

A New Structure of Serial-Resonant C⁴D Sensor Introducing Virtual Inductor

In order to improve the sensitivity of conductivity measurement, we can use series resonant to eliminate the effects of coupling capacitors and use the metal electrode shield to eliminate the effects of stray capacitors. In serial-resonant C⁴D sensor, the resonant frequency is determined by the coupling capacitors and inductor. When the condition of fluid in the pipeline is determined, therefore, the coupling capacitance is constant. If the actual inductance is used in the sensor, the range of resonant frequencies is limited. Since the virtual inductance has the advantages of adjustable inductance and low resistance, if we use it instead of the actual inductance in the serial-resonant C⁴D sensor, it can easily adjust the range of resonant frequency and reduce the requirements of sensor to excitation signal source. In this paper, we proposed an improved virtual inductor on the basis of traditional virtual inductor with grounded structure, it can overcome the defect of one end of the grounded virtual inductor that must be grounded. So this virtual inductor can be integrated into a separate module, which can be directly applied to the C⁴D sensor. The circuit of the improved virtual inductor is shown in Fig. 5.

Fig. 5

Circuit of virtual inductance

The analysis of the circuit in Fig. 5 shows that:

$$ \frac{\left({u}_1-{u}_m\right)}{R_4}=\frac{\left({u}_m-{u}_2\right)}{R_5}=\frac{V_{\mathrm{out}2}-{u}_1}{R_6} $$

(2)

$$ \frac{\left({u}_1-{V}_{\mathrm{out}1}\right)}{\frac{R_2}{1+ j\omega {cR}_2}}=\frac{V_{\mathrm{out}2}-{u}_1}{R_3} $$

(3)

where u₁ and u₂ are the input voltage signal and the output voltage signal of the virtual inductive circuit respectively, V_out1 and V_out2 are the output signals of the operational amplifiers A₁ and A₂, and u_m represents the voltage value between the resistors R₄ and R₅.

By combining Eqs. (2) and (3), the input current i₁ of the entire circuit is expressed as follows:

$$ {i}_1=\frac{u_1-{V}_{\mathrm{out}1}}{R_1}=\frac{\left({V}_{\mathrm{OUT}2}-{u}_1\right){R}_2}{R_1{R}_3\left(1+ j\omega {cR}_2\right)}=\frac{\left({u}_1-{u}_m\right){R}_2{R}_6}{R_1{R}_3{R}_4\left(1+ j\omega {cR}_2\right)} $$

(4)

Similarly, it can be seen that the output current i₂ of the entire circuit is:

$$ {i}_2=\frac{\left({u}_m-{u}_2\right){R}_7{R}_9}{R_5{R}_8{R}_{10}\left(1+ j\omega {cR}_9\right)} $$

(5)

In order to make the virtual inductance be applied to the C⁴D sensor as a separate module, it needs to satisfy i₁ = i₂, which is:

$$ \frac{\left({u}_1-{u}_m\right){R}_2{R}_6}{R_1{R}_3{R}_4\left(1+ j\omega {cR}_2\right)}=\kern0.5em \frac{\left({u}_m-{u}_2\right){R}_7{R}_9}{R_5{R}_8{R}_{10}\left(1+ j\omega {cR}_9\right)}\kern1em $$

(6)

It is known from the Eq. (2):

$$ \frac{\left({u}_1-{u}_m\right)}{R_4}=\frac{\left({u}_m-{u}_2\right)}{R_5} $$

(7)

By substituting Eq. (7) into Eq. (6), Eq. (6) can be reduced as follows:

$$ \frac{R_2{R}_6}{R_1{R}_3\left(1+ j\omega {cR}_2\right)}=\frac{R_7{R}_9}{R_8{R}_{10}\left(1+ j\omega {cR}_9\right)} $$

(8)

In order to conveniently calculate the above equation, the resistance in the circuit can be selected according to the following rules:

$$ \frac{R_2}{R_9}=\frac{R_7}{R_6} $$

(9)

$$ \frac{R_1}{R_{10}}=\frac{R_8}{R_3} $$

(10)

By calculating Eq. (4)~Eq. (10), the impedance of the virtual inductance Z_v is as follows:

$$ {\displaystyle \begin{array}{l}{Z}_v=\frac{V_i-{V}_O}{I_{in}}=\frac{u_1-{u}_2}{i_1}\\ {}=\frac{R_1{R}_3\left({R}_4+{R}_5\right)}{R_2{R}_6}+ j\omega c\frac{R_1{R}_3\left({R}_4+{R}_5\right)}{R_6}\\ {}={R}_v+ j\omega {L}_v\end{array}} $$

(11)

Eq. (11) indicates that the circuit of the virtual inductor can be equivalent to the resistance R_v and the inductor L_v in series. R_v and L_v are calculated as follows:

$$ {R}_v=\frac{R_1{R}_3\left({R}_4+{R}_5\right)}{R_2{R}_6} $$

(12)

$$ {L}_v=c\frac{R_1{R}_3\left({R}_4+{R}_5\right)}{R_6} $$

(13)

Eq. (13) indicates that in the circuit of the virtual inductor shown in Fig. 5, even if the other circuit parameters remain unchanged, the value of inductance can be changed by adjusting the slide resistance R₅.

The serial-resonant C⁴D sensor introducing virtual inductor proposed in this paper is shown in Fig. 6; its equivalent circuit is shown in Fig. 7, where C₁ and C₂ are the capacitors formed by two metal electrodes coupling with conductive liquid. R_S is the resistance of the conductive fluid and R_V and L_V are the equivalent resistance and inductance of the virtual inductor circuit, respectively. So the total impedance of the serial-resonant C⁴D sensor z can be expressed as follows:

$$ Z={R}_v+{R}_S+j2\pi {fL}_v-\frac{j\left({C}_1+{C}_2\right)}{2\pi {fC}_1{C}_2} $$

(14)

Fig. 6

Serial-resonant C⁴D sensor based on virtual inductance

Fig. 7

Equivalent of serial-resonant C⁴D sensor based on virtual inductance

where f is the frequency of the excitation signal. When the circuit is resonant, the capacitive reactance generated by the coupling capacitors C₁ and C₂ is offset against the inductive reactance generated by the inductor. At this time, the total impedance of the sensor is Z₀ = R_V + R_S. The resonance frequency of the circuit f₀ is calculated as follows:

$$ {f}_0=\frac{1}{2\pi}\sqrt{\frac{C_1+{C}_2}{L_v{C}_1{C}_2}} $$

(15)

Measurement of Two-Phase Flow in Slurry Pipeline Based on Differential C⁴D

The structure of the measuring device for two-phase flow in a slurry pipeline based on differential C⁴D sensor is shown in Fig. 8. It consists of two serial-resonant C⁴D sensors, while it has only three electrodes. The center electrode was shared by the two C⁴D sensors, as driving electrode, which was applied the excitation signal with a certain frequency at the time of operation. The upper and lower of the measuring device are detecting electrodes. The differential signal between the two detecting electrodes was amplified and then filtered out the high-frequency noise components, so the output signal of the measuring device represents the voltage difference between the two C⁴D sensor output signals. The equivalent of the differential C⁴D circuit is shown in Fig. 9. The differential signal between the two C⁴D sensors Δu = U_out1 − U_out2 was amplified by the measuring device, but the common mode signal such as noise in fluid motion was offset. So this construction could reduce the influence of the fluid noise on the measurement.

Fig. 8

Structure of measuring device for two-phase flow in slurry pipeline based on C⁴D differential sensor

Fig. 9

Equivalent of measuring device for two-phase flow in slurry pipeline based on C⁴D differential sensor

The fluid transported in slurry pipeline for deep-sea mining is a solid-liquid two-phase flow that is composed of polymetallic nodules and seawater. Because the conductivity of seawater is high, usually (3~5) s/m, so in the conductance detection process; the total impedance between electrodes is small. In the equivalent circuit, the capacitance depended primarily on the stray capacitor C₀ between the pairs of metal electrodes. When the metal electrodes were fixed, the stray capacitor C₀ between electrodes was constant and could even use a shield to eliminate the influence of stray capacitor C₀. Therefore, when mineral particles move in the pipeline, the conductivity of the fluid mainly depended on the fluid change in the cross section of the pipeline. The equivalent of solid-liquid two-phase flow based on C⁴D is shown in Fig. 10. Assume that polymetallic nodule particles were equivalent to spherical particles of diameter H₂, and the internal pipeline surrounded by electrodes was divided into three sections of length H₁, H₂, and H₃. The first section H₁ and the last section H₃ contain only homogeneous fluids such as seawater, while the middle section H₂ contains a mixture of seawater and polymetallic nodules. The corresponding electrode coupling capacitor was also divided into three parts such as C₁₁, C₁₂, and C₁₃. So the total impedance of the equivalent circuit Z is expressed as follows:

$$ {\displaystyle \begin{array}{l}Z={R}_v+{R}_S+{R}_{S3}+{R}_0+ j\omega {L}_v\\ {}+\frac{1}{j\omega {C}_2}+\frac{X}{Y}\end{array}} $$

(16)

$$ {\displaystyle \begin{array}{l}X=j-\left[\left({C}_{S1}+{R}_{S2}\right){C}_{11}+{C}_{12}{R}_{S2}\right]\\ {}-{jC}_{11}{C}_{12}{R}_{S1}{R}_{S2}{\omega}^2\end{array}} $$

(17)

$$ {\displaystyle \begin{array}{l}Y={C}_{11}{C}_{12}{C}_{13}{R}_{S1}{R}_{S2}{\omega}^3-\omega \left({C}_{11}+{C}_{12}+{C}_{13}\right)\\ {}-j{\omega}^2\left[\left({C}_{12}+{C}_{13}\right){C}_{11}{R}_{S1}+\left({C}_{11}+{C}_{12}\right){C}_{13}{R}_{S2}\right]\end{array}} $$

(18)

Fig. 10

Equivalent of solid-liquid two-phase flow based on C⁴D

Among them, the resistance and capacitance are as follows:

$$ {R}_{S1}=\rho \frac{4{H}_1}{\pi {D}^2} $$

(19)

$$ {R}_{S2}=\rho \frac{4{H}_2}{\pi \left({D}^2-{H}_2^2\right)} $$

(20)

$$ {R}_{S3}=\rho \frac{4{H}_3}{\pi {D}^2} $$

(21)

$$ {C}_{11}=\frac{H_1}{H}{C}_2 $$

(22)

$$ {C}_{12}=\frac{H_2}{H}{C}_2 $$

(23)

$$ {C}_{13}=\frac{H_3}{H}{C}_2 $$

(24)

where D is the diameter of the measured pipe, ρ is the resistivity of seawater, and ω = 2πf, f represents the frequency of the excitation signal.

Measurement Experiment

The experimental device of the measurement for two-phase flow in a slurry pipeline based on the differential C⁴D is shown in Fig. 11. It consisted mainly of the conveying pipeline, mining ship simulation platform, control cabinet, differential C⁴D sensor, and data acquisition system. The geometric parameter of the measuring device based on the differential C⁴D is shown in Table 1. In the test process, the excitation signal with a peak value of 8 V and a frequency of 120 kHz was first applied on the center electrode of the differential C⁴D sensor, and then, its virtual inductance was adjusted until the circuit resonates. At the same time, the output signal of the differential C⁴D was collected by the data acquisition card to the computer for data processing, then, the parameters of the two-phase flow in the slurry pipeline could be obtained by computer processing. The control cabinet could adjust the pump speed through a frequency changer and change the velocity of the two-phase flow in the slurry pipeline.

Fig. 11

Experimental device of measurement for two-phase flow in slurry pipeline based on C⁴D

Table 1 Geometrical parameters of the measuring device

Conductive fluid used in the experiment is KCl solution with salinity ranging from 0 to 4%. The nodules are artificial manganese nodules with the nodule density of 2000 kg/m³, as shown in Fig. 12. The manganese nodules of different particle sizes were mixed with different salinity fluids in the middle bin, then the mixture was pumped into the slurry pipeline, as shown in Fig. 13.

Fig. 12

Simulated manganese nodules of different particle sizes. a 5 mm. b 10 mm. c 20 mm

Fig. 13

Mixture of nodules and conductive fluids. a The maximum particle size of a single nodule = 10 mm, fluid salinity 3.5%. b The maximum particle size of a single nodule = 20 mm, fluid salinity 1.5%

Results and Discussion

The output voltage signal of the measuring device when nodules passed through electrodes is shown in Fig. 14. There were no spikes in the output signal, indicating that the use of the differential structure in C⁴D can effectively restrain the influence of fluid noise. The two positive and negative peaks of the output voltage signal represent the time when the polymetallic nodules reach the geometric center of the two electrodes, respectively. According to the distance L between the geometric center of two electrodes and the time difference ΔT between the positive and negative peaks of the output voltage, the particle’s velocity V of two-phase flow in the pipeline can be calculated as follows:

$$ V=\frac{L}{\Delta T} $$

(25)

Fig. 14

Output voltage signal of the device when particles pass through electrodes

As shown in Fig. 14, the two points A and B are the geometric center of the upper and lower electrodes of the measuring device, respectively. The distance between them is 210 mm. When the measuring device outputted a negative peak, that is the time the nodules passed through point A, which was 218 ms. When the measuring device outputted a positive peak, that is the time the nodules passed through point B, which was 276 ms. So, it could be calculated that the particle velocity of two-phase flow in pipeline is 3.62 m/s. This result is in good agreement with the speed of 3.8 m/s calculated by the trajectory of solid particles collected by a high-speed camera, as shown in Fig. 15.

Fig. 15

Trajectory of solid particles collected by the high-speed camera

In fact, nodules in the slurry transported by deep-sea pipelines consist of a variety of particles. On the whole, the volume fraction of the nodules is relatively low, generally less than 8% (Tang et al. 2015). Therefore, when multiple nodules passed through the electrode of the measuring device at the same time, the multiple nodules can be equivalent to a larger size nodule according to the actual flow of the fluid in the cross section of the pipelines.

The output voltage of the measuring device was related to the salinity of two-phase flow and the particle size of polymetallic nodules. In fluids with different salinity, the output voltage signal of the measuring device when nodules with different sizes passed through the electrode is shown in Fig. 16. The results indicated that the amplitude of the output voltage signal of the measuring device increases with the increase of the size of the polymetallic nodules in the pipeline. When the salinity of the KCl solution, as a conductive fluid in the pipeline, is at an average salinity of seawater 3.5%, the diameter of polymetallic nodules increased from 0 to 25 mm, and the amplitude of the output voltage signal increased from 0 to 87 mv. In addition, the amplitude of the output voltage signal decreased along with the increased salinity of two-phase flow. When the diameter of the polymetallic nodules is 20 mm, the salinity of two-phase flow increased from 1.5 to 3.8%, and the amplitude of the output voltage signal decreased from 150 to 47 mv.

Fig. 16

Relationship between output voltage and particle size at different salinity of fluid

In addition, the output voltage of the measuring device was related to the slurry density. Since the slurry transported by deep-sea pipelines is a mixture of nodules and seawater, the relationship between the mixture density and the volume concentration of the manganese nodules is shown in Fig. 17. When the volume concentration of the manganese nodules increased from 0 to 10%, the density of the mixture increased from 1037 to 1133 kg/m³.

Fig. 17

Relationship between the mixture density and the volume concentration of manganese nodules

In a slurry with a constant salinity of 3.5%, but with different densities, when the manganese nodules with a maximum particle size of 20 mm passed through the electrodes, the output voltage amplitude of the measuring device increased as shown in Fig. 18. When slurry density increased from 1037 to 1133 kg/m³, the output voltage amplitude of the measuring device increased from 61 to 69 mv, indicating that slurry density had a certain degree of influence on electrical conductivity.

Fig. 18

Relationship between output voltage and slurry density

Through the repeated measurement experiment of two-phase flow in a slurry pipeline, the results showed that the measuring method proposed in this paper had a high accuracy. The experimental results of a typical velocity measuring for two-phase flow are shown in Fig. 19. The results demonstrated that the relative error of the two-phase flow velocity was 5.2% and most of the relative error was less than 5% when the KCl solution was 3.5% and the particle size of the polymetallic nodules was 20 mm. Therefore, the measuring method for two-phase flow in a slurry pipeline proposed in this paper is effective.

Fig. 19

Typical group of velocity measurement results of two-phase flow

Conclusion

Through analysis, the C⁴D with three-electrode differential structure can effectively reduce the influence of fluid noise on the measurement parameters. The serial-resonant C⁴D sensor incorporating a virtual inductance has the advantages of adjustable inductance and small internal resistance, thereby reducing the requirements of C⁴D sensor to excitation signal source. The output voltage signal of differential C⁴D is related to the salinity of two-phase flow and the particle size and volume concentration of polymetallic nodule. When the conductive fluid in the pipeline is at the average salinity of seawater 3.5%, the amplitude of the output voltage signal of the differential C⁴D sensor increases along with the increased particle size of polymetallic nodules in pipeline. When the particle size is constant, the amplitude of the output voltage signal decreases along with the increased salinity of two-phase flow. In the differential C⁴D-based measurement process, according to the distance between two electrodes and the time difference between the positive and negative peaks of the output voltage, the particle’s velocity of two-phase flow in the pipeline can be calculated. The measurement accuracy of the differential C⁴D is high, and the maximum relative error of flow velocity measurement in the experiment is 5.2%. The proposed measurement method of two-phase flow in slurry pipeline based on differential C⁴D is effective.