Numerical simulation of a gas-flotation oil–water hydrocyclone separator

2.1. Physical model

Hydrocyclone separators can be designed in various structural forms. In this study, the liquid-liquid hydrocyclone employed is based on the conventional Thew-type double-cone configuration [2], optimized to include two tangential inlets and two conical sections. The upper outlet serves as the overflow, while the lower outlet functions as the underflow. A schematic representation of the hydrocyclone geometry is presented in Fig. 1, and the corresponding geometric parameters are listed in Table 1 [10].

Fig. 1Schematic of the hydrocyclone geometry

2.2. Mathematical model

This section introduces the fluid dynamics theory underlying the present study, which provides the theoretical basis for the numerical simulations. Considering the wide distribution of oil droplet diameters inside the hydrocyclone, as well as the strong interphase coupling and slip effects, direct application of the Eulerian model would result in high computational cost and complexity. Therefore, in this work, the Mixture model, which offers higher computational efficiency and is well suited for simulating oil-water separation processes, was selected [11].

The governing continuity and momentum equations are expressed as follows [12]:

where ${\rho }_m$ represents the density of the mixture, $\overrightarrow{v_m}$ indicates its mass-averaged velocity, $P$ denotes the pressure, $g$, $F$ are the gravitational and other external body forces, and $\tau$ is the viscous stress tensor.

To capture turbulence effects, the Realizable $k$-$\epsilon$ closure was applied. Its transport equations can be expressed as follows [12]:

where $C_1=\mathrm{m}\mathrm{a}\mathrm{x}\left[0.43,\frac{\eta }{\eta +5}\right]$, $\eta =S\frac{k}{\epsilon }$, $G_k$ represents the production of turbulence kinetic energy due to velocity gradients, $G_b$ denotes the contribution of buoyancy, $Y_M$ is the correction term for compressible fluctuation expansion in the dissipation rate, while $C_2$ and $C_{1\epsilon }$ are model constants. ${\sigma }_k$ and ${\sigma }_{\epsilon }$ denote the turbulent Prandtl numbers corresponding to the kinetic energy of turbulence and its dissipation rate, respectively.

2.3. Grid and boundary conditions

Within the CFD simulations, the boundary setup at inlet 1 and inlet 2 were defined as velocity inlets, where an oil–water mixture was injected at an inlet velocity of 8 m/s. In this work, both the overflow and underflow exits were defined as pressure outlets. The numerical calculation proceeded for 12,000 steps with a time increment of 0.005. Table 2 provides the fluid-phase parameters applied in the model.

A polyhedral mesh with minimum cell mass of 0.3 was applied to the oil-water hydrocyclone. To accurately simulate air injection through the special microporous section, a porous medium region of 3 mm thickness was introduced in the large cone section, through which air was injected.

To verify grid independence, five different grid sizes (260,000, 640,000, 930,000, 1,440,000, and 2,160,000 elements) were simulated. The results show that with a grid size of 260,000 elements, the separation efficiency is relatively low, as shown in Fig. 2. As the grid size increases, the separation efficiency gradually improves and stabilizes. When the grid size reaches approximately 1.44 million elements, the simulation results no longer exhibit significant variations with further grid refinement. Therefore, a grid size of 1.44 million elements was selected as the base grid for the study.

3.1. Influence of air injection on separation efficiency

The hydrocyclone is used for oil-water separation, where the ratio of the overflow outlet to the inlet flow rate is referred to as the split ratio (m³/s). For the present work, a split ratio of 20 % was specified. The oil-water separation efficiency is defined as [11]:

where the oil concentration at the overflow is denoted as $C_u$, and $C_i$ corresponds to the inlet concentration.

Fig. 2Grid independence study

Fig. 3 illustrates the oil volume fraction distribution at the $X$ = 0 cross-section of the hydrocyclone. Most of the oil phase after injection is discharged through the overflow outlet, and the oil-water separation efficiency reaches 83.56 %. When 40 μm air bubbles are introduced, the oil droplet volume fraction within the gas-assisted hydrocyclone increases significantly relative to operation without air injection. Microbubbles transport the oil core, and the oil phase volume fraction approaches unity near the overflow port. The majority of the oil phase is discharged via the overflow outlet, leading to an improved separation efficiency of 95.96 % in the hydrocyclone.

In order to better clarify the phase distribution inside the air-assisted hydrocyclone, axial and tangential cross-sections of the large cone section of the hydrocyclone were selected for analysis. The locations of the cross-sections are $X$ = 0 mm and $Z$= 45 mm, respectively.

Fig. 3(a) shows the oil phase volume fraction distribution at the $X$-section inside the hydrocyclone. The results indicate that oil droplets predominantly gather in the vicinity of the overflow outlet, and the oil core is substituted by a gas core once air is introduced. Due to the carrying effect of microbubbles, the fine oil droplets originally distributed near the wall and difficult to separate can rapidly migrate to the reverse flow core region and flow out through the overflow port. Fig. 3(b) illustrates the oil-phase radial velocity distribution at the $Z$-section for cases with and without air injection. It can be observed that under air injection conditions, In the primary operating region of the separator (large cone section), the radial movement speed of oil droplets toward the center is markedly increased, promoting faster droplet coalescence and thereby enhancing oil–water separation efficiency.

3.2. Influence of bubble size on separation efficiency

In order to examine how bubble size influences the separation performance of the oil-water hydrocyclone, five different air bubble diameters were selected for comparison. The results are shown in Table 3. A reduction in bubble diameter leads to a progressive improvement in the hydrocyclone separation efficiency.

When the air injection rate is kept constant, the size of microbubbles markedly affects the radial drift of oil droplets. Analysis shows that the centrifugal force acting on small microbubbles is much smaller than that on large bubbles, allowing them to approach the wall more effectively.

Fig. 3Oil phase at the section with and without air injection

a) Oil volume fraction

b) Radial velocity distribution of oil phase

As shown in Fig. 4, when small bubbles are injected, the oil phase exhibits greater radial velocity at the $Z$-section, which confirms that smaller microbubbles have a stronger ability to migrate oil droplets. This enables fine oil droplets, originally distributed near the wall and difficult to separate, to rapidly migrate to the reverse flow core region and eventually be discharged from the overflow port, thereby significantly improving the separation efficiency of the hydrocyclone. Under the condition of 5 μm microbubbles, the separation efficiency of the hydrocyclone reaches 97.73 %.

Fig. 4Radial velocity distribution of oil phase under different bubble sizes