Introduction

The beneficial reuse of industrial waste oil is important to alleviate energy shortage and improve environmental protection. The first key link of reuse is the demulsification of the waste oil emulsion [1,2,3]. In general, demulsification of water-in-oil emulsion is difficult to achieve by a single process efficiently. Demulsification technologies usually couple and integrate two and more processes or units to complete the separation process; thus, they are difficult to adapt to the conventional process [4,5,6]. For the W/O industrial waste oil of high water content and complex components, the dewatering-type hydrocyclone can be used as the body and the high-voltage electrode is embedded to generate and couple high-voltage electric and swirling centrifugal fields for realizing the efficient separation and treatment of the waste oil emulsion [7].

At present, there are several studies that the demulsification of water-in-oil emulsion is achieved by coupling the electric and centrifugal fields [8]. Bailes et al. [9] used a combination of high-voltage DC electric and centrifugal fields to complete the demulsification of crude oil. The results confirmed that the demulsification efficiency of the combination of electric and centrifugal fields is better than that of the combination of electric and gravity fields. Similarly, Eow et al. [10, 11] performed a centrifugal electrocoalescer-separator, studied the separation efficiency by experimental methods, and found that the maximum separation efficiency was about 93%. Yang et al. [12] mainly studied the problem of droplet deformation and optimal demulsification frequency under the combination of centrifugal and pulsed electric fields. Wang and Sun et al. [13, 14] explored the influence of swirling field structure on the separation of water-in-oil emulsion under the combination of centrifugal and pulsed electric fields. Li et al. [15] conducted an experiment of water separation from W/O emulsion by a new equipment which coupled electric and centrifugal fields, investigated the influence of electric field frequency and voltage on the water separation efficiency and achieved the optimal operation parameters. In the double-field coupling demulsification technology, two important processes are integrated: the electric field demulsification and the swirling centrifugal separation [16,17,18,19].

In electric field demulsification, one of the key factors affecting the efficiency of demulsification is the electric field strength [15, 20,21,22]. In the double-field coupling demulsification process, the electric field increases the concentration of small droplets in the water-in-oil emulsion, and the appropriate electric field strength can achieve a reasonable size of droplet of water-in-oil emulsion effectively. As a result, the centrifugal force in the swirling field is high and the efficiency of oil–water separation is improved [22]. The inlet velocity of the fluid in the swirling flow field is also important for oil–water separation [23]. In addition, the emulsion properties also influence the separation process, such as the density difference, water volume fraction, interfacial tension, and the oil viscosity [24,25,26]. The oil viscosity can be affected by changing the oil temperature [27].

In this study, the influence of oil viscosity on the centrifugal separation of water-in-oil emulsion droplets is considered. Thus, a heat-strengthening double-field demulsification process is proposed to enhance the separation effect of double-field coupling unit. And the effect of heat-strengthening on the improvement in the demulsification efficiency of double-field coupling unit is investigated by numerical simulation and experimental methods.

Mechanisms and process

Mechanisms of separation

When electric field is applied in emulsion, the coalescence of dispersion droplets in oil occurs, resulting in the size of droplets increasing constantly [28]. Under the action of electric field, the coalescence between droplets occurs in three stages: droplets approaching each other, film thinning and film rupture [29]. For two spherical droplets with the radius of r1 and r2, the electric field force of radial (Fr) and angular (Fθ) directions can be expressed as [15]:

$$F_{\text{r}} = \frac{{ - 12\pi \varepsilon_{0} \varepsilon_{\text{r}} r_{1}^{2} r_{2}^{2} E_{0}^{2} }}{{\left( {d + r_{1} + r_{2} } \right)^{4} }}\left( {3\cos^{2} \theta - 1} \right)$$
(1)
$$F_{\theta } = \frac{{ - 12\pi \varepsilon_{0} \varepsilon_{\text{r}} r_{1}^{2} r_{2}^{2} E_{0}^{2} }}{{\left( {d + r_{1} + r_{2} } \right)^{4} }}\sin 2\theta$$
(2)

where E0 is the applied electric field strength, and d and θ are the initial separation between two dipoles and the angle between the line joining the centers of droplets with applied direction of applied electric field, respectively.

For the droplets with the same radius (r1 = r2) and θ is zero, the electric field force can be written as [15]:

$$F_{\text{e}} = \frac{{ - 24\pi \varepsilon_{0} \varepsilon_{\text{r}} r_{1}^{2} r_{2}^{2} E_{0}^{2} }}{{\left( {d + r_{1} + r_{2} } \right)^{4} }}$$
(3)

In this case, the force Fe is proportional to E 20 . And increasing the electric field strength can effectively improve the coalescence of water droplets in oil to enlarge the size of droplets.

For the emulsion with large size of droplets, the centrifugation method can be used for separating water from oil effectively. The separation of oil and water by centrifugal is based on the density difference [30]. Due to the centrifugal forces, the water droplets with higher density than the oil move to the region far from the axis of rotating [31]. And the larger density difference is, the dispersion phase separated from the oil is more easily. For example, in liquid–liquid hydrocyclone, the density difference is proportional to the separation efficiency of hydrocyclone, and the larger the density difference, the greater the centrifugal field strength [32]. In addition, the centrifugal sedimentation velocity is also proportional to the density difference. The relation between the he centrifugal sedimentation velocity and density difference can be described [19]:

$$v_{\text{s}} = a\frac{{d_{j}^{2} \Delta \rho }}{{18\mu_{\text{m}} }}$$
(4)

where the vs is the centrifugal sedimentation velocity of the droplets, Δρ is the density difference, a and μm are the acceleration of the droplets and dynamic viscosity of the emulsion, respectively.

Therefore, by coupling electric and centrifugal fields, the size of the droplets enlarges and separates from the oil quickly and effectively in a short time, improving the separation efficiency of oil and water. For instance, Eow et al. [11] developed a centrifugal electrocoalescer separator that uses combined electrical and centrifugal effects, studied the effect of applied pulsing frequency on the separation efficiency, and found that the separation efficiency can up to 93% when the applied potential, pulsing frequency and inlet drop diameter are 4 kV, 100 Hz, and 1.15 mm. Their work demonstrated that separating the water droplets from the oil by coupling electric and centrifugal fields is feasibility.

Heat-strengthening separation process

As shown in Fig. 1, the water-in-oil emulsion is pumped into the heating tank. The heating tank has a heating control system that can increase the oil temperature to a set value in a relatively short period. Heating can effectively reduce the viscosity of the oil. Through the screw pump, the water-in-oil emulsion quickly enters the double-field coupling demulsification unit at a set flow rate, and the heat-strengthening separation treatment of water-in-oil emulsion is realized. By the coupling unit, water in the oil can be separated from the emulsion and flows into the underflow tank, and the oil with little water flows into the overflow tank.

Fig. 1
figure 1

Heat-strengthening double-field demulsification process

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Numerical models and calculations

Numerical model

The high-voltage electrode electric field is embedded in a swirl chamber segment and uses a dewatering-type double cone hydrocyclone as the main structure. The application of a high-voltage electric field completes the coalescence of small emulsion droplets in a short time. The sedimentation and separation of coalesced droplets can be realized in a short time in the swirling centrifugal field. The demulsification efficiency of the water-in-oil emulsion can be improved as a whole. The efficient and rapid dewatering of the waste oil can be realized [33]. The geometric model of the coupling unit of the swirling centrifugal and high-voltage electric fields is established and shown in Fig. 2. A high-voltage electric field is formed between the cylindrical outer surface of the overflow orifice section and the corresponding cylinder surface of the swirl chamber section.

Fig. 2
figure 2

Geometry model of double-field coupling unit, including I: the swirl chamber section, II: large cone section, III: small section, and IV: the straight pipe section (D = 26 mm, Di = 12 mm, Do = 18 mm, Lo = 45 mm, α = 20°, β = 3°, Du = 10 mm, and Lu = 400 mm)

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In this work, the liquid–liquid two-phase flow in a double-field coupled unit was simulated transiently by Mixture model. The oil–water mixture fluid satisfies the following governing equations of continuity and Navier–Stokes (N–S) equations.

$$\frac{{\partial \rho_{\text{m}} }}{\partial t} + \nabla \cdot \left( {\rho_{\text{m}} v_{\text{m}} } \right) = 0,$$
(5)

where \(\rho_{\text{m}} = \sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} }\) and \(v_{\text{m}} = \sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} } v_{k} /\rho_{\text{m}}\).

$$\frac{\partial }{\partial t}\left( {\rho_{\text{m}} v_{\text{m}} } \right) + \nabla \cdot \left( {\rho_{\text{m}} v_{\text{m}}^{2} } \right) = - \nabla p + \nabla \cdot \tau + \rho_{\text{m}} g + F_{e} + \nabla \cdot \left( {\sum\limits_{k = 1}^{n} {\alpha_{k} \rho_{k} v_{\text{dr,k}}^{2} } } \right),$$
(6)

where \(\tau = \mu_{\text{m}} \left[ {\nabla v_{\text{m}} + \left( {\nabla v_{\text{m}} } \right)^{T} } \right]\), \(\mu_{\text{m}} = \sum\limits_{k = 1}^{n} {\alpha_{k} \mu_{k} }\), and \(v_{\text{dr,k}} = v_{\text{k}} - v_{\text{m}}\).

Considering the anisotropy of flow in the coupling unit, the rotating turbulent flow is described by the Reynolds Stress Model (RSM) turbulence model.

In addition, the action of the electric field is considered. Under the action of electric field, the electric field force of droplets can be expressed by Maxwell stress tensor in the physical model of double-field coupling unit [34].

$$T_{ij} = \varepsilon_{0} \varepsilon_{\text{r}} \left( {E_{i} E_{j} - \frac{1}{2}\delta_{ij} E_{{^{0} }}^{2} } \right)$$
(7)

where Tij is the element of Maxwell stress tensor and δij is the Kronecker delta.

The volume force of the electric field is added as an external volume force to the N–S equation. The physical model of the double-field coupling unit uses the Descartes coordinate system. Thus, the electric field force can be expressed as the volume force component, fx, fy, fz, of three electric fields.

$$\varvec{F}_{\text{e}} = \left( {f_{x,} f_{y,} f_{z} } \right) = \nabla \cdot \varvec{T}$$
(8)

Under the action of electric field, the size of the droplets changes. In accordance with the Atten droplet pairing model [35], when N droplets with radius R are aggregated into 0.5N droplets with radius 21/3R, the coalescence time can be calculated by the following Stokes formula:

$$t_{1} = \frac{8}{15}\frac{{\mu_{o} }}{{\varepsilon_{\text{r}} \varepsilon_{0} E_{0}^{2} }}\left[ {\left( {\frac{\pi }{6\varphi }} \right)^{5/3} - 1} \right].$$
(9)

where μo and φ are the viscosity of oil phase and water volume fraction in oil, respectively.

Therefore, when the residence time t of the droplet in the electric field zone is calculated and the coalescence time is obtained by Eq. (9), the size of the droplets is \(\left( {2^{n} } \right)^{1/3} R\) where n is the ratio of t to t1 is determined and rounded off.

Flow field and boundary conditions

This study uses 20# oil (the viscosity grade is 20) as continuous phase, water as dispersed phase, and 200 μm as droplet diameter. The oil is heated at 60 °C, 65 °C, 70 °C, and 75 °C, and the underflow split ratio, which is defined as the ratio of the underflow rate to the total inlet flow rate, is set to 10%. Table 1 shows the related parameters of the flow field.

Table 1 Parameters of flow field
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The entrance boundary is used as the velocity entrance, and the entrance section normal velocity is 10 m/s. The two other direction speeds are 0, the water content in the emulsion is 10%, the inlet turbulence intensity is 5%, and the entrance diameter is 12 mm. The export boundary is outflow that is a free export. The wall surface is under a no-slip boundary condition, and the standard wall function is used to process the near wall area. The unidirectional DC electric field voltage amplitude is 11 kV. The overflow pipe extends into the wall surface of the segment as the high-voltage input terminal of the electric field, and the inner wall surface of the swirl chamber acts as the ground of the electric field.

In this study, the Fluent (ANSYS 15.0) is used for the numerical simulation. A user-defined function method is used to establish the potential equation of the physical model of the multi-field coupling unit. The electric field strength is solved by the Maxwell stress tensor method based on the aforementioned equation. The electric field force can be calculated and the volume force is added to the N–S equation as the source term [36, 37]. The finite volume method is used to control the equation and the time step is 0.05 s.

Experimental methods

The experimental setup used to conduct the demulsification experiment of W/O emulsion is shown in Fig. 3. The setup mainly includes a high-voltage source, single-screw pump, two-field coupling unit, overflow tank, underflow tank, and heating tank. The output voltage, frequency, and duty ratio of the high-voltage source (HD15-1.0), supported by Tianjin Huida co., can be adjusted, and the values are within 0–20 kV, 0.1–5000 Hz, and 30–60%. The single-screw pump (G35-1), supported by Shanghai An Huai Pump co., Ltd., can provide the steady flow, avoiding the further emulsification and shearing actions of the emulsion samples. And the geometry structure and the corresponding parameters of two-field coupling unit are shown in Fig. 2. The volume of the overflow tank is 70 L and the volume of the underflow tank is 23 L. In addition, the heating tank can be used to heat 100 L emulsion. In addition, some valves are also applied in the setup. By adjusting the inlet and delivery valves, the underflow split ratio can be controlled. The oil samples used to measure the water content can be collected at the sampling valves and the separation efficiency of the setup can be obtained.

Fig. 3
figure 3

The experimental setup for conducting the demulsification experiment of W/O emulsion

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In the experiment, the oil selected the continuous phase and the water, dispersed in the oil, was selected as the dispersed phase. A kinematic viscosity tester (BF-03) was used to measure the kinematic viscosity of the oil and water samples at the room temperature. At the same time, a density tester (BF-18A) was used to measure the density. The corresponding physical parameters are shown in Table 1. The W/O emulsion was prepared by mixing the oil and water samples using a power basic stirrer (MGD699). The volume fraction of water was 10%. To keep the stability of the emulsion, 5 g/L of Span-80 was added as a surfactant. The split ratio of under orifice was specified as 0.1. The unidirectional DC electric field voltage amplitude was specified to 11 kV. Additionally, a trace moisture tester (SYD-2122C) was used to measure the water content of oil samples. The experiment was repeated at different temperatures (60 °C, 65 °C, 70 °C, and 75 °C). The experimental results were calculated from an average of three experiments for each specific temperature: 60 °C, 65 °C, 70 °C, and 75 °C.

Results and discussion

Effect of heating temperature on flow field

The fluid movement characteristics of the inner coupling unit at 60 °C, 65 °C, 70 °C, and 75 °C are studied in the underflow straight pipe section (z = 100 mm), small cone section (z = 620 mm), large cone section (z = 750 mm), and swirling chamber section (z = 790 mm) on the x = 0 cross section. Separation efficiency is an important indicator for evaluating a separation device, such as a liquid/liquid hydrocyclone. The separation efficiency is the ratio of the flow rate of overflow to the flow rate of inlet and is defined as follows [38]:

$$E_{\text{S}} = \frac{{\alpha_{\text{o}} Q_{\text{o}} }}{{\alpha_{\text{in}} Q_{\text{in}} }} = 1 - \frac{{\alpha_{\text{u}} Q_{\text{u}} }}{{\alpha_{\text{in}} Q_{\text{in}} }}$$
(10)

In the double-field coupling unit, discretely distributed water droplets move toward the side wall under the action of centrifugal force to separate the oil–water two-phase flow. The separation efficiency of the device is directly related to the tangential velocity of the water droplets, which dominates the three velocity components. Figure 4 shows the distribution of tangential velocity curves on four cross sections. The figure shows that, when the temperature changes, the tangential speeds change considerably. In particular, in the z = 100 mm section, the tangential velocity increases when the temperature increases from 60 to 75 °C. Therefore, as the temperature of the water-in-oil emulsion rises, the distribution of the internal speed of the coupling unit changes, which can improve the separation efficiency of the emulsion. The reason is that the centrifugal force, which promotes the separation of the oil–water two-phase flow, is exerted on the droplets of the dispersed phase in the water-in-oil emulsion and increases with the increase of tangential velocity, thereby improving the separation efficiency. The tangential velocity on the section of the cone changes remarkably with no obvious increasing or decreasing trend. In particular, when the temperature is 60 °C or 70 °C, the tangential velocity in the small cone shows no obvious M-type symmetry. This velocity is much larger than that at the two other temperatures in the R < 0 area, and the opposite result is found in the R > 0 area. This phenomenon indicates that the flow in the cone is unstable and the tangential velocity is greatly affected by the temperature. In the z = 790 mm section, the tangential velocity increases slightly from 60 to 75 °C except in the peak area. In the peak area, the maximum speed at 70 °C is higher than the maximum speed at the other temperatures. The variation in tangential velocity occurs in the inner and outer vortex area except in the vicinity of the wall surface. The reason is that the no-slip boundary condition was applied.

Fig. 4
figure 4

The radial distribution of tangential velocity profiles for different emulsion temperatures at four different sections: a z = 100 mm; b z = 620 mm; c z = 750 mm; d z = 790 mm. Green line + symbol: 60 °C, magenta line + symbol: 65 °c, blue line + symbol: 70 °c, red line + symbol: 75 °c

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Effect of heating-strengthening temperature on separation

Figure 5a shows the contour of oil volume fraction on x = 0 and 0 < z < 925 mm at different temperatures. The figure shows that, as the temperature increases, the fluid area with oil volume fraction higher than 0.95 is concentrated in the swirl chamber and the large cone section. In particular, when the temperature rises from 60 to 65 °C, or from 65 to 70 °C, the range of high oil concentration changes obviously, and the oil volume fraction of the bottom is reduced by 0.05. When the temperature rises further to 75 °C, the oil volume fraction distribution does not change considerably. Therefore, the effect of oil–water separation is obvious when the temperature is raised from 60 to 70 °C, or from 65 to 70 °C, the separation efficiency of the coupling unit is obviously improved. However, the increase in temperature will not continuously improve the water separated from emulsion oil. Thus, the effect of the separation efficiency is also weakened. Figure 5b shows the distribution of oil concentration in x = 0 and 730 mm < z < 840 mm section. The figure shows that, when the temperature rises, the area of oil volume fraction higher than 95% increases. When the temperature rises from 60 to 70 °C, or from 65 to 70 °C, the change in high oil concentration range is most obvious. This finding indicates that the increase in temperature is beneficial to the gathering of oil to the area near the overflow orifice. As a result, the water content of the oil discharged through the overflow is low and the dewatering efficiency of the overflow is improved. However, the distribution of the oil concentration will not change considerably when the temperature rises further to 75 °C and the separation efficiency will not be greatly improved owing to the limit of the structural parameters of the overflow orifice. When the temperature is 60 °C or 65 °C, the oil concentration equivalents are thinning with the oil concentration less than 95%, and the concentration equivalents become homogeneous and dense when the temperature rises to 70 °C or 75 °C. Therefore, the increase in temperature will promote the oil–water separation process, and the effect of liquid flow on the distribution of oil concentration in the junction area between the swirl chamber and the large cone section is small.

Fig. 5
figure 5

The contour of oil volume fraction for four different emulsion temperatures (A: 60 °C, B: 65 °C, C: 70 °C, and D: 75 °C): a at x = 0, 0 < z < 925 mm of double-field coupling unit; b at x = 0 and 730 mm < z < 840 mm

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Figure 6 shows the distribution of the oil volume near the underflow and overflow orifices under different temperature conditions. Figure 6a shows that, as the temperature rises, the oil concentration gradually decreases. It indicates that, as the temperature increases, the separation of the oil–water two-phase flow within the coupling device is promoted. As a result, the water flow rate of the liquid flow discharged through the underflow orifice is increased, and the oil–water separation is improved. When the temperature rises from 65 to 70 °C, the degree of separation promotion is high. Figure 6b shows that, when the temperature rises, the volume fraction of oil gradually increases and the range of high oil volume is wide. Therefore, the increase in temperature expands the area of high oil concentration in the area near the overflow orifice, that is, the increase in temperature effectively improves the separation efficiency. When the temperature increases from 70 to 75 °C, the oil volume fraction in the − 15 mm < R < 15 mm range unremarkably changes. This finding shows that, when the temperature is 70 °C, the separation of oil–water in the junction area between the swirl chamber and the cone section is already sufficient. The continuous increase in temperature will inconsiderably increase the separation efficiency. Overall, the increase in temperature can improve the oil–water separation efficiency of the coupling unit.

Fig. 6
figure 6

Radial distribution of oil volume fraction for four different emulsion temperatures at two sections: a z = 100 mm; b z = 790 mm. Green line + symbol: 60 °c, magenta line + symbol: 65 °c, blue line + symbol: 70 °c, red line + symbol: 75 °C

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The separation efficiency calculated from experimental results was obtained using the Eq. (5). Similarly, for numerical simulation, the separation efficiency was obtained by selecting the area-weighted average values of variables at the surfaces of overflow orifice and inlet and using the Eq. (5). Figure 7 shows the separation efficiency curves predicted by numerical method compared to the experimental results at different temperatures. The simulated results of separation efficiency are in good agreement with the experimental results. The separation efficiency gradually increases with the increase in temperature. The reason is that the increase in temperature reduces the viscosity of the continuous phase and it influences the drainage of the thin film between the water droplets to reduce the drainage time and the water droplets coalesces easily in relatively low viscosity oil [39, 40]. Furthermore, as the temperature increases, the interfacial tension is also reduced to promote coalescence [41]. When the emulsion temperature is 75 °C, the separation efficiency is best. In particular, when the temperature is raised from 60 to 65 °C, and from 65 to 70 °C, the separation efficiency increases by approximately 4.1% and 6.7%, respectively. Gong et al. [42] studied the effects of inlet velocity and voltage amplitude on the separation efficiency of the double-field coupling device and found that the device has a greatly separation performance at 11 kV and 8 m/s. Therefore, changing the heating temperatures can be the other valuable method for improving the separation performance of coupling device.

Fig. 7
figure 7

The double-field coupling unit separation efficiency versus four different emulsion temperatures. The emulsion temperature of 75 °C has higher efficiency

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Conclusions

In this study, the effects of different heating temperatures (60 °C, 65 °C, 70 °C, and 75 °C) in the heat-strengthening process on the separation efficiency of two fields were investigated by numerical simulation and experimental methods. A user-defined function method was used to couple the flow field control equations with the electric field control equations to achieve the coupling simulation of the double-field coupling device. The liquid–liquid two-phase flow in a double-field coupled device was simulated transiently using a Mixture model and an RSM turbulence model. The results show that the separation efficiency predicted by numerical simulation is in good agreement with the experimental results. And the increase in heating temperature can effectively enhance the separation effect of two fields and improve the efficiency of the oil–water separation of industrial waste oil.