High Viscous Oil–Water Two–Phase Flow: Experiments & Numerical Simulations

An experimental study on viscous oil-water two-phase flow conducted in a 5.5 m long and 25.4 mm internal diameter (ID) pipeline is presented. Mineral oil with viscosity ranging from 3.5 Pa.s – 5.0 Pa.s and water were used as test fluid for this study. Experiments were conducted for superficial velocities of oil and water ranging from 0.06 to 0.55 m/s and 0.01 m/s to 1.0 m/s respectively. Axial pressure measurements were made from which the pressure gradients were calculated. Flow pattern determination was aided by high definition video recordings. Numerical simulation of experimental flow conditions is performed using a commercially available Computational Fluid Dynamics code. Results show that at high oil superficial velocities, Core Annular Flow (CAF) is the dominant flow pattern while Oil Plug in Water Flow (OPF) and Dispersed Oil in Water (DOW) flow patterns are dominant high water superficial velocities. Pressure Gradient results showed a general trend of reduction to a minimum as water superficial velocity increases before subsequently increasing on further increasing the superficial water velocity. The CFD results performed well in predicting the flow configurations observed in the experiments.


Background
Water usually accompanies crude oil during production especially during enhanced recovery when water is deliberately injected into older or marginal wells to aid production. In some cases, water is added for lubrication as this reduces pumping requirements for crude transport in cases where heavy or highly viscous oils are involved. Based on the above premise, the study of oil-water flow is therefore essential for production systems design and crude oil pipeline transport networks. Concurrent flow of oil and water results in a wide variety of flow patterns depending on the conditions during transportation.
The continuous depletion of light (conventional) oil reserves due to long term production has in recent years, increased the attractiveness of unconventional fossil fuels (e.g. shale gas, shale oil and especially heavy oil). Heavy oil, defined as a petroleum liquid with API gravity of <22° and viscosity >100 cP, has generated so much interest due to its huge reserves. The literature is awash with studies of light oils, but scarce in the case of heavy oils. However due to significant differences in rheological characteristics between light and heavy oils, research into the production and transportation of heavy oils has thus become important. As stated earlier, water is used to assist the flow of highly viscous oils and hence the study of the flow patterns, pressure gradients, and other characteristics is imperative for heavy oil-water liquid-liquid flows.

Previous works
Bannwart et al. [1]  Poesio et al. [3] studied two phase oil-water flow in a horizontal plastic pipeline with internal diameter of 50 mm. Oil and water viscosities used in the studies were 0.9 Pa.s (20°C) and 0.001 Pa.s respectively. Superficial oil and gas velocities ranged from 0.13 -Corresponding author email: y.baba9550@gmail.com 0.52 m/s and 0.04 -0.85 m/s respectively. For the low superficial velocities, flow patterns observed were the oil in water dispersion; and mixture of oil in water dispersion with bubbly flow. For the medium oil superficial velocities; three flow patterns were identified: a combination of oil in water dispersion and bubbly flow, a combination of Core Annular Flow (CAF) and oil in water dispersion; and the CAF. At high oil superficial velocities, a combination of CAF and oil in water dispersion; CAF; and the fully eccentric CAF flow patterns were observed. The authors presented the pressure gradient measurement in terms of Reduction Factor, R defined as the ratio of the pressure drop of the two-fluid flow and the pressure drop calculated using the Hagen Poiseuille law for the single-phase laminar flow of oil having the same flow rate as the oil phase in the two-phase case. They stated that R gave maximum values when CAF was observed and this was attributed to the sharp decrease in oil fouling of the pipe walls.
Sridhar et al. [4] conducted an experimental study and model assessment on high viscosity oil/water flows using the same facility as Vuong et al. [2]. Test fluid used was ND 50 with viscosity of 0.223 Pa.s and water with viscosity of 0.001 Pa.s. Superficial velocities for oil and water were 0.1 -1 m/s and 0.1 -0.5 m/s respectively. Test was conducted at temperature range of 60 -100 F. Flow patterns observed included; Stratified Wavy Flow, Stratified Wavy with Dispersed Oil Droplets at Interface & Oil Film Stratified Wavy with Dispersed Oil Droplets at Interface (SOW&DO/W) and Core Annular Flow with Oil Film Core Annular Flow (CA). This flow regime was observed at increased water flow rates. Oil film was not observed at the pipe walls and the core was asymmetric. For the range of experimental data and inclination angle, there was no significant change in the flow patterns observed. The study also concluded that pressure gradient is a function of oil viscosity and flow pattern in oil-water two phase flows.
Corresponding author email: y.baba9550@gmail.com Wang et al. [5] studied the flow characteristics of heavy crude oil-water two-phase flow in a 0.0254 m pipe ID with length of 50 m. Oil viscosity used was 0.6 Pa.s. In their study, five flow patterns were observed, water-in-oil emulsion dispersed flow (EW/O), intermittent flow of (EW/O) and partial segregated water layers, EW/O with water stratified flow, EW/O and water semi-annular flow and EW/O and water annular flow. Oil in water emulsion was present for all the flow conditions investigated. For water cut below 50% and low mixture velocities, a flow pattern in which water was dispersed in oil (DW/O) was observed. The oil's high viscosity was observed to retard the film drainage between dispersed drops thereby reducing coalescence. An increase in the mixture velocity at low water cut saw a transitions from DW/O to DW/O with partial segregated water flow. Pressure gradient in the low water cut flow patterns generally increased with in-creasing water fraction but decreased when the water in flow segregated and formed a layer. At high water fractions (>50%), oil water emulsion was not formed Rodriguez and Baldani [6] conducted experiments on two phase liquid-liquid flows using a 15.5-m long borosilicate glass pipe with 0.026 m ID. Oil and water viscosities used were 0.28 Pa.s and 0.001 Pa.s respectively. The mixture velocities ranged from 0.13 -0.15 m/s and water cut from 40 -83%. Pressure gradient and holdup data were collected and analyzed in the study with emphasis on the stratified flow pattern. Commercial CFD code, ANSYS CFX was used to simulate a simplified liquid-liquid pipe flow with no interfacial dispersion. Numerical simulation in the study captured the interfacial waves observed in experimental video recordings and images. Generally, the qualitative and holdup predictions of the CFD code were good however; the pressure gradient predictions were inaccurate.
Corresponding author email: y.baba9550@gmail.com From the aforementioned review, it is seen that oil-water flow studies using high viscosity oils were mostly carried out for oil viscosities not exceeding 1.0 Pa.s, the present work will experimentally investigate oil-water two-phase flow for oil viscosities ranging from 0.75 -5.0 Pa.s. Additionally, only Rodriguez and Baldani [6] carried out numerical simulations of experimental results to assess the performance of commercial code, in this work, numerical simulation of flow patterns of some of the flow conditions will be presented in other to evaluate the performance of a commercially available code.

Test Facility Description
A test facility consisting of a 5.5-m long and 0.0254-m (1 inch) internal diameter pipe fabricated from Perspex material is used in this study. The test facility's observation and measuring instruments are placed at a distance of at least 100 pipe diameters from the water and oil injection points into the main test section. This is done to facilitate complete flow development. The temperature controller for oil and water is a refrigerated bath circulator manufactured by Thermo Fisher Scientific ® . Copper coils submerged in the oil and water tank are connected to the circulator; by running cold or hot glycol in the coils for a certain period of time, the temperature of oil and water in the tank can be controlled based on heat transfer.
The circulator temperature ranges from -5 to +50 0C. To ensure equitable temperature of the oil, a recirculation flow for about 15 minutes is carried out. Two GE Druck pressure transducers, PMP 1400, with pressure range 0-4 barg and accuracy 0.04 % over the full scale is used to obtain the static pressure in the test section. The transducers are placed 2.17 m apart. A differential pressure transducer, Honeywell STD120, with minimum pressure drop measurement of 100 Pa and accuracy of ± 0.05 % is used to measure the differential pressure. J-type thermal couples with accuracy of ± 0.1 0C placed at different locations were used in measuring the test fluid temperature. Data acquired from the Corresponding author email: y.baba9550@gmail.com flowmeters, differential pressure transducers, pressure transducers and temperature sensors are saved to a Desktop Computer using a Labview® version 8.6.1 based system.
The system consists of a National Instruments (NI) USB-6210 connector board interfaces that output signals from the instrumentation using BNC coaxial cables and the desktop computer. Three Sony camcorders, DSCH9 with 16 megapixels, high definition and 60 GB HDD are used for video recordings during the test to aid visual observations. The test facility schematic is shown in Fig. 1 below.

Test Materials
CYL 680, a mineral oil manufactured by TOTAL and water were used as the test fluids in this study. Physical properties of the test fluids are shown in Table 1.

Test Matrix
In this work the oil and water superficial velocities varied from 0.06 -0.6 and 0.03 -1.0 m/s respectively. Viscosity of the mineral oil used as the high viscosity liquid phase ranged from 3.40 -5.10 Pa.s.

Description of CFD Model
Numerical modeling of high viscous oil-water flow was performed using the commercial CFD code ANSYS Fluent Version 14.5 [7]. In multiphase flow systems simulations, two main techniques are generally employed: The Eulerian-Eulerian and the Eulerian-Lagrangian. In the later, the technique involves coupling the Eulerian model with a particle model while in Kaushik et al., [9]). The VOF method treats all phases as continuous, but does not allow the phases to be inter-penetrating.

Governing Equations
In the VOF model, a single set of momentum equations is shared by the two fluids. The key assumptions made in this model are: the flow is unsteady, immiscible liquid pair, isothermal, no mass transfer and no phase change.
The governing equations are: where , , , and are the density, velocity, time, mass source and the fluid type respectively. The mass source for this set up is considered to be zero based on initial assumption of no mass transfer.

 Momentum Equation:
( ) where , , , , , and are the density, velocity, pressure in the flow field, viscosity, acceleration due to gravity and the body force respectively. The body force Corresponding author email: y.baba9550@gmail.com

Phase Tacking
Interfacial tracking of the primary (water) and secondary (oil) phases is accomplished by finding the solution of the conservation equation for secondary phase. If the volume fraction of the secondary phase is denoted by , then the conservation equation is given by: The phase volume fraction has a value of 1 when a computational cell (control volume) is entirely filled with the secondary phase, a value of 0 when the cell is void of the secondary phase and a value between 0 and 1 if an interface is present in the computation al cell. It is noted that the phase volume fraction does not uniquely identify the interface. The volume fraction of the primary phase is computed from the relationship:

Fluid Property estimation
Properties of the fluid in each computational cell are determined from the volume fraction of the different phases in the cell's domain. For a two-phase oil-water flow as in the case of this study, the physical properties of the fluid in a computational cell can be defined as:

Wall Adhesion and Surface Tension
The Continuum Surface Force (CSF) proposed by Brackbill et al [10] is used to model the surface tension whose effect on the flow is included in the VOF model. A resultant source term is included in the momentum equation as a result of adding the surface tension to the VOF model computation. If the surface curvature is measured by two radii, 1 and 2 , orthogonally Corresponding author email: y.baba9550@gmail.com and the coefficient of the surface tension is given by , the pressures on either sides of the surface is given by 1 and 2 , then the pressure drop across the surface is deduced based on the Young-Laplace equation as: If is the volume fraction of the ℎ phase of the multiphase flow, the CSF model of the surface curvature is computed from the local gradients of the surface normal to the interface.
If depicts the surface normal, then it can be expressed as (Fluent Theory Guide for Version 14.5 [7]): The curvature can be defined in terms of the divergence of the unit normal, ̂ thus: The surface tension can be expressed in terms of the pressure drop across the surface. The surface force can be expressed as a volume force using the divergence theorem where the volume force is the source term, in the momentum equation. For two-phase oil-water, the source term can be expressed as: Wall adhesion effect at the interfaces between the fluids and the rigid boundaries (pipe walls) is accounted for within the CSF model proposed by Brackbill et al. [10]

Turbulence Model
In numerical simulations of multiphase flow, turbulence models must be considered if one or Menter [12] developed the SST k-ω model based on the k-ω model developed by Wilcox [13] and the free-stream independence of the k-ε model. By modifying the constant values and the turbulent viscosity to account for the transport of the turbulent shear stress; designing the blending function to be one in the near-wall and zero away from the surface thus activating the k-ω and k-ε models respectively; and introducing a cross-diffusion derivative term to the k-ω model, the SST k-ω model relatively more accurate and reliable for a wide class of applications Alagbe [11]. The model is given by: and denotes the cross-diffusion term, calculated as described below. ̃ and denotes the generation of turbulence kinetic energy due to mean velocity gradients and the generation of respectively. and represent the effective diffusivity of k and ω, respectively. and represent the dissipation of k and ω due to turbulence. and are user-defined source terms. The effective diffusivities for k-ω are the same as in standard k-ω model.

Model Geometry Design and Meshing
A three-dimensional geometry depicting the experimental test rig was created and shown in  Fig. 3 shows partial meshed geometry. A dependence study was carried out using sensitivity analysis to determine the minimum mesh density that ensures that the simulation results are independent of the mesh size. After the careful study, the mesh used for the present simulations consisted of 1 197 440 hexahedral cells.

Boundary Conditions
The outlet pressure is applied at the outlet.
where is the Reynolds number for the fully developed flow.

Discretization Setup
In this study, following the hydrodynamics of the two-phase flow, all simulation runs are  Table 2 shows representative images obtained from high speed video recordings for each of the flow patterns.
Characteristic feature of the flow patterns observed in the study are described below with pictures obtained from video recordings shown in Table 2  Core Annular Flow (CAF) pattern observed in this study was characterized by continuous oil phase flowing through the center of the pipe with water flowing at the walls and enveloping the oil phase. Higher water flow rates resulted in higher annulus a thinner oil core. The oil core was observed to be wavy, with its waviness increasing as the superficial water velocity increases.
Oil Plugs in Water Flow (OPW) was observed in the study, it is described as a flow pattern in which intermittent oil plugs flowed concurrently in continuous water phase. Oil was observed to foul the pipe walls in the form of streaks with the fouling reducing as water superficial velocity increased.
Dispersed Oil in Water Flow (DOW) was observed at the highest superficial velocities studied. The increase in superficial velocities of water relative to OPW was observed to result in fragments of oil plugs into tiny dispersed oil in a continuous water phase. Table 2 shows the flow patterns obtained in the experimental campaign of this study.
Flow patterns identified in the study were constructed on the x-y Cartesian plane. The x and y axes are assigned to water and oil superficial velocities respectively. Flow pattern obtained for each flow condition (superficial velocity of water and oil) investigated is shown in Fig. 4 and Fig. 5 below. It is important to note that nominal viscosity of 3.50 and 4.95 Pa.s were used in this study; however the maps shown are presented using the oil viscosity range recorded during the experimental test campaign for a particular oil nominal viscosity.
Corresponding author email: y.baba9550@gmail.com From the maps shown in Fig. 4, it is observed that at the lowest oil superficial velocity in this study (0.06 m/s) and water superficial velocity of 0.035 m/s, flow pattern observed is WPO. An increase in water superficial velocity to 0.05 m/s resulted in a transition to the RIV. Beyond this to a water superficial velocity of 0.7 m/s, flow pattern observed is SWF.
Additional increase in water superficial velocity saw a transition to the OPW and DOW.
Similar flow behaviour is observed in Fig. 5, however, at different superficial velocities.
CAF flow was not observed at the low oil superficial velocity, this is attributed to the relatively smaller in situ oil holdup which results in the inability of the oil in the flow line to form and maintain a core. At increased oil superficial velocities, this was not the case as the oil in situ holdup were sufficient hence enabling a core formation and thus CAF.
Additionally, it is observed that at higher oil superficial velocities within this experimental test matrix, CAF flow was the dominant flow pattern.
In comparison to flow patterns reported in other high viscosity oil-water studies conducted by Sridhar et al. [4] and Vuong et al. [2], it is noted that the RIV flow patterns was not observed in their studies. Additionally, Vuong et al. [2] studies over predicted the DOW flow region. For flow conditions where CAF was observed in the present study, the Vuong et al.

Pressure Gradient
Pressure gradient obtained in the study were plotted as functions of water cut for different oil superficial velocities and are as shown in Fig. 6 and 7 below. It is observed that the pressure gradient is a strong function of the water cut & flow patterns.
Generally, for water cut below 20% (most of which correspond to water superficial velocities less than 0.15 m/s), flow patterns observed were oil dominant, this results in increased shear on the pipe walls and thus, the relatively high pressure gradient observed for these flow conditions. As the water cut (and thus the water superficial velocity) is further increased, pressure gradient reduces as water helps to lubricate and thus reduce shear on the pipe wall.
The most significant reduction in pressure gradient is observed mostly around the CAF flow pattern region, this is attributed to water being constantly in contact with the pipe walls and thus reducing the pipe wall shear. Beyond the minimum pressure gradient, oil at the core fragments and moves in flow as either oil plugs or dispersed oil in continuous water flow (OPW and DOW respectively), this results in a gradually increasing pressure gradient due mainly to the fact that some of the dispersed oil and oil plugs are now in contact with the pipe walls and the increased flow mixture velocity results in a more turbulent flow thereby contributing to this increase.

Comparison of Current Pressure Gradient with Previous Studies
Shi et al [16] did an extensive study of water-lubricated flow using the same experimental rig but with a different lube oil (also see Al- At developed water-lubricated flow conditions, increasing concentricity is established at larger oil superficial velocities, resulting in less oil contact with the pipe walls. Furthermore, a higher water velocity can flush oil fouling films on the pipe wall more effectively. As two groups of data were conducted in the same pipeline, it is suspected that the difference shown is due to different wettability of the pipe wall by the two different oils, and these results in different degrees of oil fouling. The wettability between the Perspex pipe and oils were not measured quantitatively in the present study. Nevertheless, we noticed that the oil fouling on the pipe wall was generally more severe for experiments with CYL 1000 oil. A quantitative study on the influence of wettability on the pressure gradient of waterlubricated flow is recommended for future studies.
Pressure gradient models by Bannwart et al. [1], Arney et al. [14], Joseph et al. [15] and Corresponding author email: y.baba9550@gmail.com Yusuf et al. [16] are evaluated against measured pressure gradient data obtained in this studies experiment. A plot of predicted pressure gradient as a function of the measured pressure gradient is shown in Fig. 8. The plot shows large disparity between the measured and the predicted pressure gradient. This discrepancy may be attributable to the large differences in viscosity between the present study and the studies in which models/correlations were based on as a result of the differences in flow patterns. Another key reason for the discrepancies is as a result of the pipeline fouling. In this study, it was observed that oil fouled the inside walls of the pipelines, for flow patterns were water was not the continuous phase, this effect was very prominent. This will ensure that the friction factor of the pipe walls will increase and hence the pressure gradient, a factor not accounted for in the pressure gradient prediction correlations evaluated, for oil-water flow in pipelines as earlier explained. This work therefore establishes a need for future experimental and theoretical work to be carried out on two-phase high viscosity oil-water flow to ensure deeper understanding of the flow hydrodynamics for a very wide viscosity range and to ensure further development of predictive models are based on this experimental dataset. This will form a framework on future research work in this field.

Comparison of CFD Simulation and Experiments
In this section, CFD simulation results for selected flow patterns are presented. Flow patterns simulated include the stratified wavy flow (SWF), the Core Annular Flow (CAF) and Oil Plugs in Water Flow (OPW). Results obtained for pressure gradient from each of the simulated flow condition is also presented. predicted. Fig. 9 (a) shows the SWF with discontinuous thin water film at the top. From video recordings as shown in flow pattern map of Fig. 4 With an increase water superficial velocity from 0.05 m/s to 0.1 m/s, Fig. 9 (b) shows a thicker top water film and wavier interface compared to Fig. 6(a); CAF is formed and predicted. In Fig. 9 (c), at water superficial velocity of about 0.20 m/s (input water volume fraction of 0.67), fluctuations of the oil core as a whole is observed; heavy oil fouling on the internal pipe wall is seen due to oil core intermittently making contact with the pipe walls.

Flow Pattern Predictions from CFD Simulation
CFD prediction is consistent with the experimental observations. The oil core is much wavier (especially at the top interface) compared to Fig. 9 (b). Additionally, a bit of oil fouling is captured. On further increasing the water superficial velocity, the oil core fragments into oil plugs as shown in Fig. 9 (d). Oil film can be seen from experimental videos, while for this condition no oil film is captured. This may be as a result of the mesh density. In general, CFD simulation gives a good prediction of the flow patterns observed in experiments.
Corresponding author email: y.baba9550@gmail.com Similar conclusions were also made for CFD simulation comparison with experiments reported by [6] for oil viscosity of 0.28 Pa.s. This implies that the VOF model is reasonably sufficient for the prediction of flow patterns in oil-water two phase flows for oil viscosity up to 5.0 Pa.s.

Pressure Gradient Prediction from CFD Simulation
Pressure gradient results predicted from CFD simulation is shown in Table 3 below. Results show that CFD numerical simulation overestimates pressure gradient for the CAF flow pattern and underestimates pressure gradients in the SWF and OPW flow patterns. In general, unlike the flow pattern configurations, pressure gradient prediction from CFD numerical simulation gave not as much similarity when compared to the experimental measurements. Hence, more advanced numerical approaches will need to be implemented in future studies. These include the use of finer meshes near the wall for all flow rates, and for CAF flow patterns, this should be extended to cover regions of expected liquid film flow.

Conclusions
High viscous oil-water two phase flow has been experimentally investigated. New indicates that for heavy oil fields with low water cut, producing such fields using the CAF technology may be promising while the emulsion techniques may be promising for fields with high water cut.
Pressure Gradient results showed a general trend of reduction to a minimum as water superficial velocity increases before subsequently increasing on further increasing the superficial water velocity. Pressure gradient predictive models found in literature were compared with present experimental dataset, huge discrepancies in were observed and a need to develop new models or modify existing ones is established. CFD numerical simulation performed moderately well in predicting the flow configurations observed in this study. However, results for the pressure gradient predictions were not as good.