Fluid Domain Characteristics and Separation Performance of an Eccentric Pipe Separator Handling a Crude Oil-Water Mixture

Abstract

This study presents an eccentric pipe separator (EPS) designed according to the shallow pool principle and Stokes’ law as a compact alternative to conventional gravitational tank separators for offshore platforms. To investigate the internal oil-water flow characteristics and separation performance of the EPS, both field experiments with crude oil on an offshore platform and computational fluid dynamics (CFD) simulations were conducted, guided by dimensional analysis. Crude oil volume fractions were measured using a Coriolis mass flow meter and the fluorescence method. The CFD analysis employed an Eulerian multiphase model coupled with the renormalization group (RNG) k-ε turbulence model, validated against experimental data. Under the operating conditions examined, the separated water contained less than 50 mg/L of oil, while the separated crude oil achieved a purity of 98%, corresponding to a separation efficiency of 97%. The split ratios between the oil and upper outlets were found to strongly influence the phase distribution, velocity field, and pressure distribution within the EPS. Higher split ratios caused crude oil to accumulate in the upper core region and annulus. Maximum separation efficiency occurred when the combined split ratio of the upper and oil outlets matched the inlet oil volume fraction. Excessively high split ratios led to excessive water entrainment in the separated oil, whereas excessively low ratios resulted in excessive oil entrainment in the separated water. Crude oil density and inlet velocity exhibited an inverse relationship with separation efficiency; as these parameters increased, reduced droplet settling diminished optimal efficiency. In contrast, crude oil viscosity showed a positive correlation with the pressure drop between the inlet and oil outlet. Overall, the EPS demonstrates a viable, space-efficient alternative for oil-water separation in offshore oil production.

1. Introduction

Oil-water separation is a critical preprocessing step for produced fluids during crude oil extraction [1]. After removing associated gas from the produced fluids, the oil and water phases must be separated. The recovered oil is stored in an oil tank for further purification, while the remaining water-rich phase undergoes additional treatment to reduce residual oil content to emission standards (e.g., oil-in-water, OIW < 25 mg/L) [2]. Traditionally, offshore oil-water separation is performed in gravitational separation tanks [3]. These tanks require substantial space because oil droplets need time to coalesce and form a separate layer. As the water cut in the produced fluids increases, higher extraction flow rates are needed to maintain oil production, placing significant demands on separation systems. In some mature offshore fields, the oil-water separation capacity must be increased seven- to eightfold—from ~2000 m³/d to ~14,000 m³/d—to sustain production rates [4]. However, due to space and load-bearing constraints on offshore platforms, installing additional gravity separators is impractical. This has created urgent demand for compact, lightweight oil-water separators. In this context, pipe separators offer a promising alternative: in a confined pipe space, the migration distance for oil droplets is much shorter than in a separation tank, enabling more compact installations.

A hydrocyclone is a choice under such conditions; with the replacement of gravity acceleration by centrifugal acceleration, the oil phase can be gathered and collected more efficiently. Compared with tangentially induced hydrocyclones, axially induced hydrocyclones perform better with a simpler structure, smaller pressure drop, and less space demand [5,6]. The swirl flow inside an axial hydrocyclone is induced by blades, and the oil phase is collected by a tube [7]. The fluid domain properties and discrete phase behavior have been carefully investigated and are able to deal with an oil-water mixture whose oil volume fraction is up to 40% [6,8,9]. Beyond cyclone separation, T-junction separators have been studied and applied for multiphase separation for decades, with numerous researchers examining phase behavior, separation performance, and parameter optimization [5,6,7,8,9,10,11,12,13,14,15]. T-junctions are widely recognized for gas-liquid separation, and field trials on offshore platforms have demonstrated their effectiveness for oil-water-gas mixtures, offering reduced space requirements, lower pressure drops, and high separation efficiency [16]. However, because the density difference between oil and water is far smaller than that between gas and liquid, oil-water separation performance differs substantially from gas-liquid separation. Most T-junction designs consist of a horizontal main pipe with a branch outlet. Yang et al. tested kerosene-water mixtures in a horizontal main pipe with a vertically upward side-arm T-junction [11]. They found the configuration worked well as a partial phase separator, particularly when the branch split ratio was close to the inlet oil volume fraction. Pandey et al. [17] reported similar findings, and Wang et al. [18] confirmed the trend using white-oil-water mixtures. Wang further observed that separation efficiency increased with the oil-branch split ratio up to a point, after which it declined. Wei et al. [19] showed that increasing the number of T-junctions from one to six raised separation efficiency from below 40% to over 70% and maintained high efficiency over a wider split-ratio range. Nonetheless, the oil content in the separated water from T-junctions remains too high to replace the conventional gravity separator [20]. Therefore, significant innovation is needed for T-junction technology to serve as a full replacement for gravitational separation.

In practice, inlet mixtures are not always fully segregated and may be dispersed. T-junction configurations must therefore be adapted to handle such flow regimes. In a separation chamber, Stokes’ law and the shallow-pool principle can be expressed as Equations (1) and (2) [21,22,23]:

$$v_{stokes}={\displaystyle \frac{\left({\rho }_w-{\rho }_o\right)g{d}_o^2}{18{\mu }_w}}$$

(1)

$$L_s/H_s=v_{hor}/v_{stokes}$$

(2)

where v_stokes is the sedimentation velocity, ρ_w is the density of water, ρ_o is the density of oil, d_o is the oil droplet diameter, μ_w is the viscosity of water, L_s is the horizontal length of the separation chamber, H_s is the height of the separation chamber, and v_hor is the horizontal velocity. According to Equation (2), for fixed L and v, if H diminishes, v_stokes becomes smaller, which further corresponds with a smaller droplet diameter, d_o. Hence, the separation chamber is able to deal with finer droplets. Based on this principle, internal structures such as corrugated plates, inclined plates, and parallel plates have been incorporated into gravity separation tanks [24]. These components not only divide the separation volume into smaller compartments—shortening droplet settling distances—but also promote droplet coalescence, enhancing phase concentration and separation efficiency.

The mechanisms (Stokes law shallow pool theory) described above can be extended to T-junction configurations to improve oil-water separation efficiency. However, most existing studies on liquid-liquid T-junction flow domains are based on kerosene or other oils under laboratory conditions, rather than crude oil in on-site operations, and without modifications to T-junction design [13,18,19,25]. To address this gap, the present work proposes an eccentric pipe separator (EPS) configuration derived from the conventional T-junction. Field tests were conducted on an offshore platform using crude oil-water mixtures, combined with computational fluid dynamics (CFD) simulations employing the Eulerian multiphase model coupled with the RNG k-ε turbulence model, to investigate fluid domain characteristics and separation performance.

2. EPS Configuration and Dimension Analysis

2.1. EPS Configuration

Figure 1a illustrates oil droplet behavior in a traditional T-junction. In this configuration, oil droplets travel within the continuous water phase. If a droplet is sufficiently small, only minimal settling displacement occurs as it passes the branch entrance, causing the droplet to enter the branch along with the continuous water phase. According to the shallow pool principle, inserting a slotted pipe into the horizontal main pipe forms a core-annulus flow space. Even when droplets originating in the core region pass through the slot into the annulus region while still within the continuous phase, their required settling distance to avoid branch entry is reduced. Following this principle, the EPS (Figure 2) incorporates a double-layer horizontal core-annulus structure. As is shown in Figure 2a, the core and annulus axes are deliberately offset by several millimeters (eccentricity e) to enhance oil-water phase exchange between the regions. Slots with fixed interval distance (m_top and m_down) are mounted to connect the core and annulus to promote oil-phase gathering and oil-water exchange. Additionally, a partial annular chamber is mounted above the upper-layer pipe to collect and separate additional oil phase. The partial annular and main annulus chambers are interconnected by multiple holes (with interval m_top) to promote phase exchange. Similarly to conventional T-junctions, the two-layer pipes are connected by vertical branches. The EPS inlet is located on the top-layer core pipe. The device includes three outlets: the up-outlet for oil collected in the partial annulus chamber, the oil outlet for oil from the main pipe, and the water outlet for separated water. During operation, the oil-water mixture enters the top-layer core region, where larger droplets rise, while smaller droplets migrate to the annulus zone. In the annulus zone, larger droplets float upward into the partial annulus chamber for oil enrichment, while smaller droplets pass into the lower-layer annulus. Within the lower layer, oil-water stratification continues. Water-rich liquid enters the lower-layer core through slots at the inner pipe bottom, while oil-rich liquid re-enters the top-layer annulus via downstream branches. This continuous circulation promotes effective oil-water separation and collection.

2.2. Dimensional Analysis

Several key geometry parameters of EPS are the core diameter D₁, annulus outer diameter D₂, branch diameter D₃, upper outlet diameter D₄, EPS length L, EPS height H, and eccentricity e. The parameters applied in the EPS of this study are listed as follows:

• Inner pipe diameter, D₁[L] = 50 mm;
• Outer pipe diameter, D₂[L] = 80 mm;
• Branch diameter, D₃[L] = 50 mm;
• Upper outer diameter, D₄[L] = 15 mm;
• Length, L[L] = 5 m;
• Height, H[L] = 0.62 m;
• Eccentricity, e[L] = 10 mm;
• Volume of fluid domain, V[L³].

In addition, 22 and 9 slots are mounted on the top and bottom layers, respectively.

• The flow variables are as follows:
• Inlet mixture velocity, U_m[L.T⁻¹];
• Water density, ρ_w[L.M⁻³];
• Water apparent viscosity, μ_w[M.L⁻¹T⁻¹];
• Oil density, ρ_o[L.M⁻³];
• Oil apparent viscosity, μ_o[M.L⁻¹T⁻¹];
• Entrance oil volume fraction, α_o[-];
• Oil droplet diameter, d_o[L];
• Oil outlet split ratio, β[-];
• Up-outlet split ratio, γ[-];
• Oil droplet residence time, t_rd[T⁻¹];
• Outlet oil volume fraction, φ_j (where j = 1, 2, 3 with correspondence of up-outlet, oil outlet, and water outlet) [-];
• Pressure, p[M.L.T⁻²];
• Coordinate system, x[L], y[L], z[L];
• Separation efficiency η, defined as Equation (3), η[-].

$$\eta ={\displaystyle \frac{\beta {\phi }_2+\gamma {\phi }_1}{\alpha }}-{\displaystyle \frac{\beta \left(1-{\phi }_2\right)+\gamma \left(1-{\phi }_1\right)}{1-{\alpha }_o}}$$

(3)

Here, φ₁ denotes the oil volume fraction at the up-outlet, and φ₂ denotes the oil volume fraction at the oil outlet. In the flow field, pressure and separation efficiency can be characterized as follows:

$$\left[p,\eta ,{\phi }_{i,i=1-3}\right]=f\left(x,y,z,D_{i,i=1-4},L,H,e,g,U_m,{\rho }_w,{\mu }_w,{\rho }_o,{\mu }_o,{\alpha }_o,\beta ,\gamma \right)$$

(4)

With fixed ratios among geometric parameters and D₁ as a characteristic geometric parameter, Equation (4) can be reduced to

$$\left[p,\eta ,{\phi }_{i,i=1-3}\right]=f\left(x,y,z,D_1,U_m,{\rho }_w,{\mu }_w,{\rho }_o,{\mu }_o,{\alpha }_o,\beta ,\gamma \right)$$

(5)

For ESP outlets, the coordinate system location is fixed, and Equation (5) can be expressed as

$$\left[p,\eta ,{\phi }_{i,i=1-3}\right]=f\left(D_1,U_m,{\rho }_w,{\mu }_w,{\rho }_o,{\mu }_o,{\alpha }_o,\beta ,\gamma \right)$$

(6)

Taking U_m, D₁, and ρ_w as basic parameters yields

$$\left[{\displaystyle \frac{p}{1/2{\rho }_w{U}_m^2}},{\displaystyle \frac{\beta {\phi }_2+\gamma {\phi }_1}{\alpha }}-{\displaystyle \frac{\beta \left(1-{\phi }_2\right)+\gamma \left(1-{\phi }_1\right)}{1-\alpha }},{\phi }_{i,i=1-3}\right]=f\left({\displaystyle \frac{{\mu }_w}{{\rho }_w{U}_m{D}_1}},{\displaystyle \frac{{\rho }_o}{{\rho }_w}},{\displaystyle \frac{{\mu }_o}{{\mu }_w}},{\alpha }_o,\beta ,\gamma \right)$$

(7)

$$\left[p^{*},\eta ,{\phi }_{i,i=1-3}\right]=f\left(Re,{\lambda }_{\rho },{\lambda }_{\mu },{\alpha }_o,\beta ,\gamma \right)$$

(8)

From Equation (8), EPS separation performance and pressure drop are governed by the Reynolds number, density ratio λ_o, viscosity ratio λ_μ, inlet oil volume fraction, and outlet split ratios β and γ. To further evaluate these effects, experimental tests and CFD simulations were conducted using these parameters.

3. Experimental Methods

3.1. Testing Flow Loop

A field experiment was performed on an offshore platform with mixed fluids supplied from an upstream gas-liquid separator. As shown in Figure 3, the oil-water mixture entered the EPS via a turbine flowmeter and sampling port 1. After separation, fluids from the upper outlet and oil outlet entered a test separator, while water outlet fluids were directed to a flotation separator. Each outlet line was equipped with a flowmeter and sampling port. The EPS was fabricated from stainless steel, with ball valves on each line for flow rate control and pressure gauges for pressure measurements.

3.2. Working Fluids

Water and crude oil were used as working fluids. Under test conditions, water density and viscosity were 1000 kg/m³ and 1 mPa·s, respectively, while crude oil density and viscosity were 827 kg/m³ and 24 mPa·s.

3.3. Measurement Method and Systematic Errors

Mixture velocity and density were measured using a Coriolis mass flowmeter (sensor model R200S418NCACEZZZZ, Emerson Electric, St. Louis, MO, USA) with an average relative error of 0.82%. The oil volume fraction in the water outlet was measured offline using an InfraCal 2 Oil-in-Water Analyzer (Spectro Scientific, Chelmsford, MA, USA), with a systematic error of ±0.2%. The entrance oil droplet size distribution was measured by a Malvern droplet size analyzer using (RTsizer, Malvern Instruments, Worcestershire, UK), with a less than 15% error. All measurements were repeated three times to minimize random error.

3.4. Operating Conditions

Due to production schedule constraints, the inlet mixture velocity varied around 4.0 m³/h, and the inlet oil volume fraction ranged from 30% to 40%. To further investigate the EPS fluid domain and separation performance, CFD simulations were performed under varying β, γ, and inlet velocity conditions, using the validated experimental data as a reference.

4. Numerical Methods

4.1. CFD Model

For the complex oil-water flows within the EPS, a multiphase model was required to solve the Navier-Stokes equations for both phases. Based on previous studies. Considering the relatively dense oil-water mixture flow and intricate flow structure, the Eulerian multiphase model was selected over the mixture model or Lagrangian model [6,26]. For a given phase i, continuity and momentum equations are expressed in Equations (9) and (10) [27,28]:

$${\displaystyle \frac{\partial }{\partial t}}\left({\alpha }_i{\rho }_i\right)+\nabla \cdot \left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i\right)=0$$

(9)

$${\displaystyle \frac{\partial }{\partial t}}\left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i\right)+\nabla \cdot \left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i{\overrightarrow{u}}_i\right)=-{\alpha }_i\nabla p+\nabla \cdot \overline{\overline{{\tau }_i}}+{\alpha }_i{\rho }_i\overrightarrow{g}+{\displaystyle \sum _{i=1}^n{K}_{ji}}\left({\overrightarrow{u}}_j-{\overrightarrow{u}}_i\right)+{\alpha }_i{\rho }_i\left({\overrightarrow{F}}_i+{\overrightarrow{F}}_{lift,i}+{\overrightarrow{F}}_{vm,i}\right)$$

(10)

where i is the ith phase; α is the volume fraction; ρ is the density; u_i is the velocity; K_ij represents the phase exchange coefficient, which characterizes the drag force; ${\overrightarrow{F}}_i$ is the body force; ${\overrightarrow{F}}_{lift,i}$ is the lift force; and ${\overrightarrow{F}}_{vm,i}$ is the virtual mass force.

The renormalization group (RNG) k-ε turbulence model was selected as the turbulence closure, given its suitability for the present application [16]. The governing equations for the RNG k-ε model are expressed as follows [5,29]:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho k{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_k{\mu }_{eff}{\displaystyle \frac{\partial k}{\partial x_j}}\right)+G_k+G_b-\rho \epsilon$$

(11)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho \epsilon u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_{\epsilon }{\mu }_{eff}{\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right)+G_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}\left(G_k+G_{3\epsilon }{G}_b\right)-G_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}-R_{\epsilon }$$

(12)

Here, k denotes the turbulent kinetic energy, and ε represents the turbulent dissipation rate. Gₖ is the production of turbulent kinetic energy due to mean velocity gradients, while G_b accounts for buoyancy-induced turbulence generation.

4.2. Geometry Model and Mesh Scheme

Figure 2 shows the fluid domain geometry of the EPS model used in this study. Due to the geometric complexity—particularly the presence of multiple slots and holes—an unstructured mesh strategy was adopted, with local refinement in regions surrounding the slots and holes. To assess mesh resolution adequacy for CFD simulations, three mesh densities were evaluated under identical operating conditions (U_m = 0.68 m/s, α_o = 0.4, β = 0.4, γ = 0): a coarse mesh (1.6 million cells), a medium mesh (3.3 million cells), and a fine mesh (5.3 million cells). Figure 4 presents the relative pressure and oil-phase velocity profiles along the axis of the upper-layer core pipe. The curves exhibit distinct oscillations in both relative pressure drop and oil-phase velocity, attributable to the inner-pipe slots. These slots connect the core and annulus regions through small openings, causing localized acceleration of the fluid mixture as it passes through, which in turn induces velocity and pressure fluctuations. Notably, the profiles for the medium and fine meshes were nearly identical, whereas substantial discrepancies were observed between the coarse and medium meshes. This indicates that the medium mesh offers sufficient accuracy for CFD analysis; therefore, it was selected for subsequent simulations.

4.3. Solution Settings and Boundary Conditions

Based on these findings, the Eulerian multiphase model coupled with the RNG k-ε turbulence model was employed to solve the oil-water Navier-Stokes equations in the EPS domain. Ansys Fluent was applied to perform the CFD code. Water was defined as the primary phase and oil as the secondary phase.

For the numerical schemes, the phase-coupled SIMPLE algorithm was used for pressure-velocity coupling, and the PRESTO scheme was applied for pressure discretization. The second-order upwind scheme was employed for momentum discretization [16], while the quadratic upstream interpolation for convective kinetics (QUICK) scheme was used for volume-fraction discretization [27,30]. The residual convergence criterion for all equations was set to 10⁻⁵ to ensure numerical accuracy [31].

Regarding boundary conditions, the inlet was defined as a velocity inlet, with both velocity and inlet oil volume fraction specified. Characteristic secondary phase droplet size was obtained from the entrance droplet size distribution measured by a Malvern droplet size analyzer (Figure 5), with consideration of possible droplet size coalescence. The outlets were set as outflow boundaries with varying split ratios, while all other surfaces were treated as stationary walls.

For operational settings, 25 CFD cases were defined based on prior dimensional analysis (

Table 1. Operating parameters in CFD.

Case No.	Inlet Velocity, m/s	Oil Density, kg/m3	Oil Viscosity, mPa·s	αo	β	γ
1	0.68	827	24	0.40	0.25	0
2	0.68	827	24	0.70	0.89	0
3	0.68	827	24	0.40	0.30	0
4	0.68	827	24	0.40	0.35	0
5	0.68	827	24	0.40	0.40	0
6	0.68	827	24	0.40	0.45	0
7	0.68	827	24	0.40	0.30	0
8	0.68	827	24	0.40	0.55	0
9	0.68	827	24	0.25	0.15	0
10	0.68	827	24	0.25	0.20	0
11	0.68	827	24	0.25	0.25	0
12	0.68	827	24	0.25	0.30	0
13	0.68	827	5	0.40	0.40	0
14	0.68	827	50	0.40	0.40	0
15	0.68	827	100	0.40	0.40	0
16	0.68	800	24	0.40	0.40	0
17	0.68	850	24	0.40	0.40	0
18	0.68	900	24	0.40	0.40	0
19	0.50	827	24	0.40	0.40	0
20	0.85	827	24	0.40	0.40	0
21	1.00	827	24	0.40	0.40	0
22	0.68	827	24	0.40	0.35	0.02
23	0.68	827	24	0.40	0.35	0.035
24	0.68	827	24	0.40	0.35	0.05
25	0.68	827	24	0.40	0.35	0.08

), considering variations in inlet velocity, crude oil density, inlet oil volume fraction, crude oil viscosity, and split ratios β and γ.

5. Results and Discussion

5.1. CFD Validation

As the EPS is constructed from stainless steel, direct observation of internal multiphase flow is impractical on an offshore platform. Therefore, CFD validation was performed by comparing simulated and measured oil volume fractions. As shown in Figure 6a, for all cases, the deviation between simulated and experimental oil volume fractions at the water outlet was less than 7%, with all values below 50 mg/L. A consistent trend was that measured values were slightly higher than simulated values, likely due to the complex composition of the inlet fluids. Nonetheless, the correspondence between simulation and experiment was strong. Similarly, Figure 6b compares oil volume fractions at the oil outlet between CFD and experiments, showing close agreement with minimal discrepancies. Overall, these results confirm that the CFD approach is sufficiently reliable for investigating the internal flow characteristics of the EPS and evaluating its oil-water separation performance.

5.2. Fluid Domain Properties

Figure 7 presents the fluid trajectories within the EPS for Case 4 and Case 24, with local fluid vectors recorded near junctions. The flow paths conform to expected patterns. Upon entering the EPS, part of the fluid gradually moves into the annular space of the upper layer, while the remainder exits through the oil outlet. Within the upper-layer annulus, some fluid flows upward into the partial annulus chamber, whereas the majority flows downward into the annulus chamber of the bottom layer. In the bottom-layer annulus chamber, most of the fluid continues downward, entering the core pipe via slots at the base of the inner pipe and exiting through the water outlet. A smaller fraction flows upward into the upper layer via branch passages. This backflow is visible in the local vectors near branch joints, where some re-enter the core region of the upper layer, and others enter its annular region. When γ = 0, the top outlet is closed, creating a stagnant “dead zone” in the partial annulus chamber (Figure 6a). Once the top outlet is opened, significant flow develops within the chamber.

Under these flow conditions, the phase, pressure, and velocity fields inside the EPS exhibit distinctive characteristics. As shown in Figure 8, the incoming oil-water mixture becomes stratified upon entering the separator, consistent with the findings of Dahmani et al. (2025) on oil-in-water dispersed flow stratification in horizontal pipes [32]. As the mixture descends toward the exit, the branch passages become filled with mixed phases when β < 0.35. This observation, confirmed by the local velocity vectors near branch joints in Figure 6, supports the occurrence of phase exchange within the branches. Under these operating conditions, the annular and partial annulus chambers are predominantly occupied by the crude oil phase, while the core region of the bottom layer contains very little crude oil. Figure 9 provides crude oil-phase distributions along the EPS boundaries. Compared with Figure 8, the boundaries of the annulus, partial annulus, and branches act as a transition zone, restricting crude oil penetration. In contrast, the core regions of both the upper and bottom layers are directly connected to the outlets and carry fluid that has already undergone phase separation.

Figure 10 shows the relative pressure distribution within the EPS, defined as the local pressure relative to the inlet pressure. In the upper layer, the core region pressure is significantly higher than that of the annular region, while the partial annulus region exhibits the lowest pressure. These zones form a “three-step” pressure gradient, created by the small cross-sectional slots and holes connecting them, which induce considerable pressure drops. In the bottom-layer core region, with the left boundary closed, fluids from the annulus and upper layer gradually enter through the slots, accelerating as they progress and causing further pressure reduction.

Figure 11 presents the water-phase velocity distribution inside the EPS. A large velocity zone is observed in the entrance pipe section. At the junction of the upper-layer annulus and branches, striped high-velocity regions appear, resembling parabolic trajectories, due to gravitational effects. Another pronounced high-velocity zone occurs at the bottom-layer slots. Here, high-water-content fluid enters from the annulus, and the velocity rises sharply because the slot cross-section is much smaller than that of the pipe. This elevated velocity gradually diminishes, particularly near the upward dead zone. The influence of the oil outlet split ratio on these patterns is examined in the next subsection.

5.3. Influence of the Oil Outlet Split Ratio β

The oil outlet split ratio (β) strongly affects the flow field and separation performance when the upper outlet is closed. Using Figure 8 and Figure 9, the crude oil phase distribution can be assessed. For αₒ = 0.40 and β = 0.25, crude oil dominates the transition zone (annulus, partial annulus, and branch passages). Crude oil accumulation becomes more pronounced downstream, and significant oil flux enters the bottom-layer core region—the intended outlet for separated water. This occurs because, in the upstream section, the oil-water mixture is not yet fully separated; thus, oil-rich fluid enters the upper-layer annulus and continues to stratify. Since β ≪ αₒ, the EPS cannot discharge all incoming crude oil, leading to progressive accumulation near the outlet. Eventually, the transition zone becomes saturated with crude oil, which then spills into the bottom-layer core region. When β = 0.35, this carryover effect is much less evident, and crude oil is absent from the bottom-layer core region, despite still dominating the transition zone. The reduced accumulation is due to the increased discharge capacity. At β = 0.40, crude oil presence in the transition zone decreases further, being concentrated mainly in the upper-layer annulus and partial annulus, while nearly all oil-phase outflow occurs through the oil outlet. For β = 0.50, exceeding αₒ, crude oil is confined to the upper-layer core region, and a substantial amount of water is discharged through the oil outlet.

Figure 10 shows the relative pressure distribution inside the EPS. As β increases, the relative pressure in the upper layer decreases. When β = 0.25, the low-pressure zone is located near the water outlet; when β = 0.50, it shifts toward the oil outlet, with intermediate cases representing transitional states. This behavior is reasonable: since the total energy of the system is relatively constant, an increase in velocity results in a greater portion of the energy being converted to kinetic form, leading to a pressure drop. Figure 12 presents the axial pressure profiles (dimensionless Euler number, Eu) for the two core regions in both the upper and lower layers. As discussed above, the slot between the core and the annulus induces localized pressure fluctuations, particularly upstream in the upper layer and downstream in the lower layer, where momentum exchange is relatively strong. In the downstream section of the upper layer, where the phases are fully developed, less fluid passes through the slots, resulting in a relatively stable pressure profile. Similarly, in the upstream section of the lower layer, near the dead zone where momentum exchange through the slots is minimal, the pressure profile remains gentle. A clear trend is observed with increasing β. In the upper layer, the pressure profile becomes less steep, which can be attributed to the increased flow rate toward the oil outlet. According to Bernoulli’s equation, higher velocity corresponds to lower local pressure. In contrast, the pressure curve for the lower layer shifts upward with increasing β. As β increases, the flow rate toward the water outlet decreases, leading to a corresponding increase in pressure. An abrupt change occurs when β = 0.4, which can also be explained using Bernoulli’s equation (Equation (3)). The pressure along the core axis of the lower layer exceeds that at the entrance. According to Equation (13), where subscript 1 denotes the entrance and subscript 2 denotes a local point along the core axis of the lower layer, Equation (14) is obtained:

$${\displaystyle \frac{v_1^2}{2g}}+{\displaystyle \frac{p_1}{\rho g}}+h_1={\displaystyle \frac{v_2^2}{2g}}+{\displaystyle \frac{p_2}{\rho g}}+h_2+\varphi$$

(13)

$${\displaystyle \frac{v_1^2-v_2^2}{2g}}+\Delta h={\displaystyle \frac{p_2-p_1}{\rho g}}+\varphi$$

(14)

Here, p denotes pressure, v is velocity, ρ is the density, and ϕ is the hydraulic loss along the profile, which depends on velocity and oil content. As β increases, v₂ decreases, and the oil content along the axis is reduced. Consequently, the hydraulic loss ϕ decreases significantly because both the mixture viscosity and the square of the velocity are reduced. This explains why, in Figure 12b, the curve shifts upward when β corresponds to α_o, the condition at which oil content undergoes a sudden, drastic reduction.

Figure 11 presents the water-phase velocity distribution for various β values. As β increases, the water-phase velocity near the water outlet decreases, indicating a negative correlation between velocity and β in this region. Following this trend, the high-velocity zone near the slots in the lower layer becomes less pronounced as the overall velocity decreases. Conversely, as more water exits through the oil outlet, the local water-phase velocity in that region increases. Figure 13 shows the oil-phase velocity profile along the core axis of the upper layer. The curve exhibits jagged fluctuations caused by fluid acceleration through the slots. At the EPS entrance, the oil-water mixture is partially stratified, and the oil-phase velocity increases until reaching the first slot, where flow splitting occurs. Thereafter, the velocity gradually decreases until the final slot along the flow path. With increasing β, the oil-phase velocity curve shifts upward. At β = 0.55, when fluid from the last branches enters the inner core of the upper layer, a small-amplitude fluctuation appears—representing a distinct trend compared to the other cases.

From analysis of velocity and pressure profiles above, slots have an influence on the local pressure and velocity distribution, which may further exert influence on the fouling characteristics. Under such conditions, backwashing can be applied for the cleaning of the contaminants. However, as crude oil components and fluid properties vary from field to field, this operation and design should be further discussed on a case-by-case basis.

Figure 14 presents the oil volume fraction at the outlets along with the separation efficiency curve. Photographs of sampled fluids for Case 1 are also included. As shown in Figure 14a, the oil volume fraction decreases at both the oil and water outlets as the split ratio β increases, consistent with the previously discussed crude oil-phase distribution within the EPS. When β is less than the inlet oil volume fraction α_o, the flow rate at the oil outlet is insufficient to discharge all the crude oil. Consequently, crude oil accumulates in the transitional section and penetrates the core region of the pipe’s bottom layer, contaminating the discharged water at the water outlet. In this regime, the oil volume fraction at the oil outlet approaches 100%, and the water outlet also exhibits a high oil concentration. When β equals α_o, the crude oil flow discharged from the oil outlet matches the inlet oil flow rate. Under this condition, the oil volume fraction at the water outlet is approximately 28 mg/L, indicating a relatively balanced separation. If β continues to increase beyond α_o, most of the crude oil remains concentrated in the upper-layer core region. The residual dispersed oil is carried toward the oil outlet along with a significant volume of water. While the oil volume fraction still decreases, an increasing amount of water appears in the oil outlet discharge. The larger the β, the more pronounced this effect becomes, ultimately reducing separation performance. To quantify this, the separation efficiency η is defined as the percentage of crude oil collected at the oil outlet relative to the crude oil entering the EPS, minus the percentage of water discharged from the oil outlet relative to the water entering the EPS. As shown in Figure 14a, η initially increases with β, indicating improved crude oil recovery through the oil outlet. However, once β exceeds α_o, η progressively decreases, signifying that the maximum crude oil recovery has been reached and that an increasing proportion of water is contaminating the oil outlet stream. Therefore, the optimal split ratio for maximum separation efficiency occurs when β = α_o. This can be summarized as the double-linear model below:

$$\mathrm{For}\beta <{\alpha }_o,\eta =k_1\cdot \beta$$

(15)

$$\mathrm{For}\beta >{\alpha }_o,\eta =-k_2\cdot \beta +{\eta }_{\max }\left(\beta -{\alpha }_o\right)$$

(16)

In this study, the EPS achieves a maximum separation efficiency of 97% under this condition—substantially higher than that reported for T-junctions by Pandey et al. [18]. Figure 14b further presents the separation efficiency for a T-junction with α_o = 0.3. Obviously, the curve amplitude is far smaller than that of EPS, and the optional split ratio is larger than α_o compared with that of EPS. This can be attributed to a simple T-junction configuration, which has a smaller circulation time inside.

5.4. Influence of Up-Outlet Split Ratio γ

In addition to the oil outlet, the EPS upper outlet is also utilized for oil collection. Figure 15 illustrates the crude oil distribution for α_o = 0.40, β = 0.35, and U_m = 0.68 m/s under varying upper outlet split ratios γ. Increasing γ enhances crude oil discharge and mitigates oil accumulation in the transition zone. At γ = 0, the annulus, partial annulus, and branch regions are almost entirely filled with crude oil. When γ increases to 0.02, crude oil in the bottom-layer annulus is nearly eliminated. At γ = 0.035, high-oil-content regions are confined to the annulus and partial annulus. When γ reaches 0.05, only the downstream sections of the upper-layer annulus and partial annulus retain high oil content. At this point, the combined flow rates from the upper and oil outlets account for 40% of the inlet flow rate—matching the inlet oil content—which is a reasonable operational balance. These observations confirm that when β is less than α_o, crude oil tends to accumulate in the transition zone. Because the upper outlet is located at the high point of this zone, discharging fluid from it effectively relieves crude oil buildup by directly removing oil rather than relying on counter-pressure-driven migration into the upper-layer core region.

Figure 16 shows the oil volume fraction at the outlets and the corresponding separation efficiency. As γ increases from 0 to 0.08, the oil volume fraction at the oil outlet remains close to 100%, while the oil volume fraction at the water outlet decreases from 3% to less than 10 mg/L. The separation efficiency initially increases, reaching a maximum at γ = 0.05, and then decreases. These trends closely resemble those observed for the oil outlet split ratio β. When γ + β < α_o, not all crude oil is discharged through the oil outlet and upper outlet. Under this condition, an increase in γ results in a greater proportion of crude oil being discharged through the upper outlet, with less oil remaining in and entering the core region of the bottom layer. Consequently, the oil volume fraction at the water outlet decreases progressively. Simultaneously, because a greater percentage of oil is discharged via the oil and/or upper outlet, the separation efficiency η increases. However, when γ increases such that γ + β > α_o, although the oil volume fraction at the water outlet continues to decline due to reduced oil accumulation in the bottom-layer core region, the proportion of water discharged through the upper outlet rises. According to the definition of η, this increase in water discharge causes the separation efficiency to decrease. Overall, the upper outlet enables fine-tuning of EPS separation performance, with the optimal operating condition achieved when γ + β ≈ α_o.

5.5. Influence of the Entrance Condition on the Separation Performance

The inlet conditions are primarily determined by the inlet velocity (U_m) and the inlet oil volume fraction αₒ. Figure 17 illustrates the variations in oil volume fractions and separation efficiency as U_m increases from 0.5 m/s to 1.0 m/s. As U_m increases, the oil volume fraction at the water outlet rises, while both the oil volume fraction at the oil outlet and the separation efficiency decline. According to the shallow pool principle [Equation (2)], an increase in Uₘ increases the local horizontal velocity v_hor. Since the EPS geometric configuration parameters remain fixed, maintaining the same separation performance would require a corresponding increase in v_stokes. However, from Equation (1), v_stokes remains constant when droplet fragmentation during continuous-phase acceleration is neglected [33,34]. As a result, a higher U_m reduces the migration of oil-phase droplets to the upper-layer core region, leaving more crude oil in the downstream region of the bottom-layer core. This leads to a reduction in separation efficiency.

For hydrocylones, the influence of the entrance condition is distinct. As the entrance velocity increases, the separation is enhanced first as the centrifugal forces become stronger until a plateau corresponding to the entrance flow rate Q_min. As the entrance flow velocity continues to increase, the separation efficiency almost stays constant until the entrance flow rate reaches Q_max, after which the separation efficiency drops dramatically. In the plateau region, a balance between decreasing residence time and increasing centrifugal force is found, whereas in the region above Q_max, droplet breakup and a lack of a sufficient pressure gradient make the separation perform poorly [35].

As shown in Figure 14, for inlet oil volume fractions of 0.25 and 0.40, the oil/water outlet volume fraction curves are similar and nearly parallel, as are the separation efficiency curves. This indicates that the variation trends are governed by the relative difference between α_o and β rather than the absolute value of β. When β is 0.05 less than α_o, the outlet oil volume fractions are similar, and the reverse is also true. The separation efficiency curves show a clear amplitude: when β = α_o (γ = 0), the maximum separation efficiency is achieved. Under the present operating conditions, this maximum efficiency is approximately 97%. Combined with the discussion in Subsection C, it can be concluded that, for a given α_o, the maximum separation efficiency occurs when β + γ = α_o, representing the optimal split ratio for the given inlet conditions.

5.6. Influences of Crude Oil Properties

Dimensional analysis further indicates that oil properties, such as density and viscosity, influence the EPS fluid domain and separation performance. Figure 18 shows the outlet oil volume fractions and separation efficiency as crude oil density increases from 800 kg/m³ to 900 kg/m³. As density increases, the oil volume fraction at the water outlet rises from <10 mg/L to 290 mg/L, while the oil volume fraction at the oil outlet decreases from 98.2% to 97.2%. This behavior can be explained using Stokes’ law and the shallow pool principle. From Equation (1), a smaller density difference between crude oil and water reduces v_stokes. From Equation (2), with inlet velocity and geometry unchanged, this reduction in v_stokes decreases the upward migration of the oil phase to the upper-layer core region and increases oil retention in the bottom-layer core. These effects are reflected in the curves of Figure 18a. Consequently, when β = α_o and γ = 0, the reduced proportion of oil discharged through the oil outlet lowers the separation efficiency η.

Figure 19 presents the pressure drop and pressure variation curves along the upper layer. As crude oil viscosity increases from 0.005 Pa·s to 0.1 Pa·s, the pressure drop between the inlet and the oil outlet rises from approximately 160 Pa to 460 Pa. As discussed earlier, higher viscosity promotes crude oil accumulation in the upper-layer core region, particularly downstream near the oil outlet. Given the positive correlation between viscosity and pressure drop, this trend is expected. The pressure profiles along the upper-layer core axis also exhibit substantial differences. Higher viscosity results in a greater amplitude of pressure fluctuations, which is likewise attributable to the positive relationship between crude oil viscosity and pressure variation.

5.7. Feasibility of EPS Scalability

On the basis of the discussion above, in terms of scalability to industrial scale, the basic principle of the Reynolds number, density ratio λ_o, viscosity ratio λ_μ, inlet oil volume fraction, and outlet split ratios β and γ in Equation (8) should be inconsistent with a test EPS. Furthermore, total residence time should be expressed as Equation (17):

$$t_{rd}=\psi \left(Q,L,D_1,H,g,{\rho }_w,{\rho }_o,{\mu }_w,d_o,{\alpha }_o\right)$$

(17)

$$t_{rd}\sqrt{{\displaystyle \frac{g}{D_1}}}=\psi \left({\displaystyle \frac{Q}{D_1^3}}\sqrt{{\displaystyle \frac{D_1}{g}}},k_l,k_h,{\lambda }_{\rho },{\displaystyle \frac{{\mu }_w}{{\rho }_w{D}_1\sqrt{g{D}_1}}},{\lambda }_{drop},{\alpha }_o\right)$$

(18)

$$t_{rd}^{*}=\psi \left(Q^{*},k_l,k_h,{\lambda }_{\rho },\mu *,{\lambda }_{drop},{\alpha }_o\right)$$

(19)

in which Q is the mixture entrance flow rate. If we choose D₁, g, and ρ_w as basic variablse, Equation (18) can be obtained, in which k_l and k_h are the geometry ratios of the separator length and height-to-entrance diameter. t*_rd is non-dimensional residence time; Q* is non-dimensional residence time. It can be seen that, as D₁ is subject to a scale factor k, t_rd* is multiplied by a factor k^−0.5, whereas Q* is multiplied by a factor k^−2.5. This means a more abrupt change in Q* rather than t_rd*. According to the discussion in Section 5.4, a smaller Q* brings about a better separation performance, meaning a larger residence time. In order to ensure enough total residence time, as the entrance flow rate increases, the diameter should increase equivalently, on the basis of small-scale EPS. The same goes for EPS length L and height H. However, as space is limited, the EPS geometric parameter should be scaled up on the basis of space limitations. Furthermore, according to discussion in Section 5.5, the entrance velocity should not be much larger than 1.0 m/s to ensure relatively ideal separation performance from the perspective of hydrodynamic properties. Under such conditions, the EPS can deal with oil-water mixtures of various entrance α_o (no larger than 0.5) with ideal split ratios under the separation efficiency defined in this work. Scaling up is feasible for EPSs to deal with larger Q. In consideration of space limitations, the entrance diameter D₁ can be enlarged to ensure that the entrance velocity is not so large.

6. Conclusions

This work proposes the EPS as a compact alternative to the conventional gravitational separator tank for offshore platforms, leveraging Stokes’ law and the shallow pool principle. Based on dimensional analysis, field experiments with crude oil were conducted on an offshore platform to measure outlet oil volume fraction, using a Coriolis mass flow meter and fluorescence detection. The experimental results were used to validate CFD simulations employing a Eulerian multiphase model coupled with the RNG k-ε turbulence model. The fluid domain characteristics and the effects of key parameters—including inlet conditions, split ratio, and crude oil properties—on EPS separation performance were then investigated. The main findings are as follows:

(1)

High separation performance achievable: With appropriate split ratio settings, the oil volume fraction at the water outlet can be reduced to below 50 mg/L, while the oil volume fraction at the oil outlet can reach 98% simultaneously.

(2)

Split ratio as a critical control parameter: The split ratios of the oil and upper outlets strongly influence the phase distribution, velocity field, and pressure distribution within the EPS. Higher split ratios lead to increased crude oil concentration in the upper-layer core and annulus regions. The presence of slots induces localized pressure and velocity fluctuations along the flow path. For a given inlet oil volume fraction (αₒ), optimal separation efficiency occurs when the sum of the oil outlet split ratio (β) and the upper outlet split ratio (γ) equals αₒ. When β + γ < αₒ, the separated water contains excessive oil; when β + γ > αₒ, the separated oil contains excessive water.

(3)

Influence of inlet velocity and crude oil density: Higher inlet velocity and crude oil density hinder oil droplet settling, reducing separation efficiency. Conversely, lower inlet velocity and density enhance droplet settling, improving separation. Crude oil viscosity shows a positive correlation with the pressure drop between the inlet and oil outlet.

(4)

Recommendations for future work: future work could shed light on aspects such as (1) breakup and coalescence behavior inside the EPS fluid domain, especially near slots; (2) influence of short-term fluctuations and startup/shutdown conditions; and (3) how emulsion stability and crude components influence EPS separation.