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. 2024 Mar 1;9(10):11181–11193. doi: 10.1021/acsomega.3c05290

Two-Phase Crude Oil–Water Flow Through Different Pipes: An Experimental Investigation Coupled with Computational Fluid Dynamics Approach

Shirsendu Banerjee †,*, Anirban Banik ‡, Vinay Kumar Rajak §, Tarun Kanti Bandyopadhyay ∥, Jayato Nayak ⊥, Michał Jasinski #, Ramesh Kumar , Byong-Hun Jeon ¶,*, Masoom Raza Siddiqui ∇, Moonis Ali Khan ∇, Sankha Chakrabortty †, Suraj K Tripathy †,*
PMCID: PMC10938452  PMID: 38497000

Abstract

graphic file with name ao3c05290_0015.jpg

The present study deals with two-phase non-Newtonian pseudoplastic crude oil and water flow inside horizontal pipes simulated by ANSYS. The study helps predict velocity and velocity profiles, as well as pressure drop during two-phase crude-oil–water flow, without complex calculations. Computational fluid dynamics (CFD) analysis will be very important in reducing the experimental cost and the effort of data acquisition. Three independent horizontal stainless steel pipes (SS-304) with inner diameters of 1 in., 1.5 in., and 2 in. were used to circulate crude oil with 5, 10, and 15% v/v water for simulation purposes. The entire length of the pipes, along with their surfaces, were insulated to reduce heat loss. A grid size of 221,365 was selected as the optimal grid. Two-phase flow phenomena, pressure drop calculations, shear stress on the walls, along with the rate of shear strain, and phase analysis were studied. Moreover, velocity changes from the wall to the center, causing a velocity gradient and shear strain rate, but at the center, no velocity variation (velocity gradient) was observed between the layers of the fluid. The precision of the simulation was investigated using three error parameters, such as mean square error, Nash-Sutcliffe efficiency, and RMSE-standard deviation of observation ratio. From the simulation, it was found that CFD analysis holds good agreement with experimental results. The uncertainty analysis demonstrated that our CFD model is helpful in predicting the rheological parameters very accurately. The study aids in identifying and predicting fluid flow phenomena inside horizontal straight pipes in a very effective way.

1. Introduction

Transporting crude oil from remote sources to refineries poses significant challenges, primarily when dealing with heavy crude oil. This transportation relies on pipelines with powerful pumps, but it encounters issues such as pressure loss and friction-induced deceleration or acceleration.1 To mitigate these challenges, a common approach involves mixing the heavy crude oil with water, which reduces viscosity and aids in transportation. However, this introduces complexity through multiphase oil–water flow, where various parameters like the velocity of the mixture, transport pipe diameter, temperature, volume fraction, and pressure significantly impact the flow behavior. Furthermore, the substantial viscosity difference between crude oil and water complicates this process, necessitating careful engineering considerations for efficient and safe transportation of crude oil over long distances from its remote sources to processing facilities.2

Computational modeling and analysis of two-phase crude oil–water systems may enhance our present knowledge related to the transport mechanisms of oil–water mixtures in pipelines. The mainstream experimental and research work on two-phase oil–water flow focuses on flow pattern identifications such as intermittent, stratified, dispersed, core-annular, and the amalgamation of all the above.3,4 However, computational modeling and analysis, like 3D computational fluid dynamics (CFD), have grown over the years as very important simulation tools due to their flexibility and cost-effectiveness for in-house studies.5 The application of the CFD-based solver ANSYS for single and two-phase crude oil flow through pipes has been utilized by Kumar et al.,6 Parvini et al.,7 and Walvekar et al.8 Pouraria et al.9 applied CFD-based models for determining the flow patterns of oil–water. They utilize a general k-epsilon turbulence model in conjunction with the Eulerian–Eulerian method. The numerical results acquired were juxtaposed with experimental data found in the literature, focusing on either the in situ Sauter mean diameter or water volume fraction. The comparison between the numerical findings and the previously published experimental data revealed a satisfactory level of agreement. Similarly, Bannwart10 developed a suitable model for investigating aspects of oil–water core annular flow. In that study, mass and momentum-balanced phenomenological models were exploited to investigate volume fractions and changes in pressure. The predicted outcomes were weighted against vertical and horizontal oil–water core annular flows. The study demonstrated that predicted values followed the actual ones with high accuracy. Bandyopadhyay and Das11 investigated non-Newtonian fluid flow and proposed empirical correlations for different piping components. They conducted experiments to estimate the frictional pressure drop across various piping components for non-Newtonian pseudoplastic flow under laminar conditions. They proposed an empirical correlation model for pronouncing frictional pressure drop in physical and dynamic variable forms. Castro-Gualdrón et al.12 incorporated CFD techniques for simulating the homogenization of crude oil on a small scale. The effect of the mesh size and time step size was studied since, in this type of simulation, computational effort became a major parameter that had to be reduced to a minimum. Experimental data taken from two different points in the tank at regular time intervals was available to compare the results of the simulations, concluding in good agreement. Desamala et al.13 conducted a detailed CFD study of two-phase oil–water flow characteristics inside horizontal pipes. The simulation successfully predicted slug, stratified wavy, stratified mixed, and annular flow, with the exception of the dispersion of oil in water and the dispersion of water in oil. Simulation results were validated with horizontal literature data, and good conformity was observed. Abed and Auda14 conducted an experimental and simulation study of oil–water flow inside the horizontal pipe to investigate heat transfer effects on the same. Yuan et al.15 suggested a novel real-gas model for characterizing and predicting gas leakage in pipelines where gas is flowed at high pressures. They derived thermodynamic formulas based on the basic governing equations and concluded that the newly derived model worked better than the previous models in the same fields of study. Wang et al.3 simulated flow behaviors of heavy oils in pipelines and predicted mesoscopic flow with the drag force model and KTGF models. From their experimental and modeling results, the filtered model was adopted for the flow as it provided better accuracy. Zhang et al. developed a VOF-DEM model for studying the particle dynamic behaviors in fractured-vuggy reservoirs. They predicted that the injection velocity, particle volume fraction, and diameter may alter the accumulation of particle plugging agents and affect channel flow control.16 Saleh et al.17 investigated the flow of heavy crude oil through pipelines using CFD. They used Ansys Fluent software for the study of the rheological flow behavior of Iraqi oil and found that the developed model was on par with the experimental results. Meriem-Benziane et al.18 used CFD to study oil–water flow in a pipeline and their boundary layer separation investigation. Their analytical analysis was in good agreement with the numerical investigations. Songyi et al.19 suggested a novel model for predicting the dependence of the shape of the interface between oil and water on their stratified flow. To solve the momentum equations, they used contact angle theory and the minimum energy method. Ballesteros et al.20 used CFD to study the liquid holdup characteristics in a two-phase low liquid-loaded flow. Their investigation implied that smooth flow was possible using pipe inclination in the downward direction, while a lesser liquid holdup was seen for the same. Alade21 introduced two new models, namely Cross-Logistic and Logistic, along with CFD, to study the complex flow behavior of crude oil and bitumen-solvent mixtures for using them to flow through porous media. Shadloo et al.22 used an artificial neural network to estimate the pressure drop for the 2-phase flow of crude oil through long horizontal pipes using the experimental data for the same. Their findings suggested that their model predicted the pressure drop with much more accuracy than other empirical models employed for the same. Zheng et al.23 used response surface methodology and sensitivity analysis to predict and optimize the viscosity of nano-oil containing ZnO2 nanoparticles.

The mentioned studies cover a broad spectrum of investigations on fluid flow and transport phenomena, offering valuable insights into various aspects of crude oil flow. Among them, the CFD model can offer detailed insights into crude oil behavior within pipelines, aiding researchers in understanding the impact of factors like viscosity, temperature, pressure, and flow rate on flow patterns, turbulence, and mixing. However, studies on the velocity profile, pressure drop, phase analysis, and flow pattern of crude oils through pipelines have not reached widespread research. In this regard, the current research investigates the phenomenon of non-Newtonian pseudoplastic crude oil–water mixture flow through horizontal pipes. The study includes the presence of water as a secondary phase in crude oil, which gives rise to complex phenomena like emulsion formation, which may affect the crude oil quality. The ANSYS Fluent CFD solver has been used to solve the flow structure, static pressure, pressure drop, friction factor, shear strain, and wall shear stress. These simulated results can be used for the optimum selection of design parameters for the horizontal pipelines used for transporting non-Newtonian crude oil–water flow. Information regarding the pumping cost of the crude oil–water flow through the pipeline can be gathered from the pressure drop analysis. The finding can contribute to the efficient identification and prediction of heavy crude flow phenomena within horizontal straight pipes.

2. Experimental Description

The experimental setup comprises an oil bath of 30 L volume containing a temperature regulator and mechanical impeller, a stainless steel double pipe heater, a gear pump (DFD), valves for the regulation of crude oil flow, and thermocouples for temperature reading. The test segment comprises three horizontal independent stainless steel pipes (SS-304) of 0.0508 m or 2 in. (relative roughness (ε/d) = 0.000295), 0.0381 m or 1.5 in. (relative roughness (ε/d) = 0.000393), 0.0254 m or 1 in. diameter (relative roughness (ε/d) = 0.00059), and 2.5 m length (Figure 1). The relative roughness was measured by dividing the roughness ε of the pipe by the diameter. The value of epsilon ε was provided by the manufacturer, while the internal diameter was calculated using calipers. The entire pipeline and exposed surfaces are totally insulated for minimizing the loss of heat. The crude oil as already mentioned, is collected from the western oilfield of India. Circulation of the crude oil through pipes has been done by a gear pump (Moyno_ 500 Pumps, 600 series). The flow rate of crude oil through different pipelines is measured by a digital flow meter (Everest EMAG series). Pressure drop was measured by a pressure transducer (manufactured by Rosemount Co. series 3051s) that measures the pressure loss linked to the inlet and outlet at a distance of 2.5 m. Fluid was kept in circulation mode in anticipation of the loop reaching its stabilized state for different flow rates and temperatures. Temperature was maintained by a shell and tube heat exchanger. A thermocouple (J-type, ThermoSensors) was placed in the middle of the flow line to measure temperature. All the experiments have been run at four different temperatures of 25–40 °C. The relay section comprised flow meters, pressure transducers, and temperature sensors, all relaying to a control panel through which the set values were adjusted. Water was added to the crude oil in the crude oil bath in different proportions and mixed thoroughly using a stirrer. A de-emulsifier was added to the mixture to prevent emulsion formation. The heated water from the water bath was circulated inside the jackets to make sure all the waxes or crude oils stuck in the inner walls of the pipelines were removed after the completion of each experiment.

Figure 1.

Figure 1

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Schematic of the experimental setup for pipeline studies.

33. Computational Fluid Dynamics

CFD is an approach that uses algorithms to obtain extremely accurate outcomes by considering various phenomena, such as fluid dynamics and mass transfer.24,25 In this study, a fully developed length is assumed for model development to reduce costs. Optimal computer memory has been utilized for grid generation, which reduces convergence time during the simulation process. Initial investigations indicated laminar flow since the Reynolds number was found to be less than 2300. Non-Newtonian pseudoplastic crude oil–water flow through a horizontal pipe is a highly multifaceted study and is usually governed by the continuity and momentum equations in laminar flow. The continuity and momentum equations can be defined as eqs 1 and 2, respectively

33. 1
33. 2

In eq 1, αi = fraction for the ith phase; ρi = density of the ith phase; ▽ = nabla, defined as

33.

and ui = velocity of the ith phase, ms–1; mij = mass flow rate, kg s–1.

In eq 2, g = acceleration due to gravity, ms–2; Inline graphic = stress–strain tensor of the ith phase; Rij = interaction force between the phases, N; Fi = external body force, N; Flift = lift force, N; Fvm = virtual mass force, N. The interphase exchange force can be defined by eq 3

33. 3

where Kij = fluid–fluid exchange coefficient. The flow being laminar, the power law model was selected as the viscous model, and the mixture model was selected for the multiphase model for CFD simulation.

The rheology of crude oil–water flow is found to be reliant on the apparent viscosity of the fluid flowing through the horizontal pipe. From the study, it has also been found that apparent viscosity depends on velocity and shear rate. The apparent viscosity of the crude oil–water mixture reduces with the increase in flow velocity and shear strain rate. The fluid inside the horizontal pipe follows the non-Newtonian pseudoplastic power law model. The apparent viscosity of a non-Newtonian fluid is given as eq 4

33. 4

where μapp is apparent viscosity, which is expressed in (Pa s). The boundary conditions were that the inlet and outlet of the pipes were considered to be velocity inlet and pressure outlet, respectively. Figure 2 shows the general steps involved in CFD simulation.

Figure 2.

Figure 2

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General steps involved in CFD analysis.

3.1. Assumption

To simulate the flow inside the pipe, the following assumptions and concepts were taken into consideration for the current study:

  • •The temperature of the crude oil–water mixture through the horizontal pipes was maintained at 25 to 40 °C.

  • •Crude oil–water is assumed to be incompressible and an isothermal non-Newtonian pseudoplastic fluid (The composition of crude oil makes it non-Newtonian as it includes suspended particles, saturates, aromatics, resins, asphaltenes, etc. Moreover, the shear stress-shear rate plot confirmed the crude oil as a pseudoplastic fluid).

  • •The model that has been developed is limited to a flow model (not a density model or a segregation model, etc.).

  • •The model is assumed to follow a two-phase laminar, non-Newtonian pseudoplastic power law model.

We assume no-slip conditions at the walls (to showcase the minimum velocity adjacent to the wall as a result of the high adhesive force between the pipeline wall and the fluid molecule as opposed to the center of the pipe).

3.2. Computational Approach, Convergence Criteria, and Grid Independency Test

Gambit 2.4.6 was utilized to generate a 3D tetrahedral grid geometry due to its excellent modeling flexibility and its ability to easily perform mesh skewness tests with minimal deviation. The boundary conditions and the continuum are specified within the geometry. The skewness of the tetrahedral grid was thoroughly examined, and it was found to be below 0.9. To get the simulated results, the geometries are exported to the CFD pressure-based solver (Fluent 6.3). To streamline the CFD procedures, a first-order upwind scheme is employed for the solution, and a simple pressure–velocity coupling is selected with relaxation.

Criteria of convergence were selected to be 10–5 for all the equations except the transport equation (whose convergence criteria is 10–3). The domain of computation (Lf = 0.05id) was selected for the laminar, fully developed flow through the various diameters of straight horizontal pipes. The test for grid independence is a function of the grid geometry of the pipelines. The concluding outcome of grid independence indicated 3–5% errors in pressure drop and velocity. A grid size of 221,365 was used for optimized grid results from the grid independence test (Figure 3). The results of CFD were on par with the data obtained from experiments.

Figure 3.

Figure 3

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Tetrahedral mesh of the horizontal straight pipe.

3.3. Procedures for CFD

The general procedural steps to simulate the two-phase crude oil–water flow through different pipes are outlined below:

  • A

    Meshing of geometry using Gambit 6.3

    • a

      Preparing a computational domain for the defined flow region.

    • b

      Meshing of the geometry done by implementing boundary layer hexahedral and tetrahedral meshes.

    • c

      Implementing a size function to allow smooth transitions in mesh size.

    • d

      Defining boundaries and types of continuum.

    • e

      Examined meshes to ensure that the skewness value is below 0.5 and 0.9 for hexahedral and tetrahedral meshes, respectively.

  • B

    Importing the mesh file to Fluent 6.3 and investigating the mesh

  • C

    Defining an unsteady, implicit, and pressure-based solver.

  • D

    Implementing a two-phase laminar non-Newtonian power law model.

  • E

    Activating the crude oil and water properties with laminar flow conditions.

  • F

    Enabling the operating conditions by activating gravity and defining the operating density.

  • G

    Methodology for solution control

    • a

      Under relaxation factors of 0.5 and 0.3 for pressure and momentum, respectively, and default values were considered for other parameters.

    • b

      Implementing a first-order upwind scheme for obtaining the solutions.

    • c

      Activating simple pressure–velocity coupling.

  • H

    Solution initialization: activating the residual plotting during the calculation, and enabling the default convergence criteria of 10–5 for all residuals except for the transport equation, which was selected to be 10–3.

4. Results and Discussions

4.1. Effect of Diameter on Pressure Drop

An important parameter that affects pressure drop is the pipe diameter and the relative roughness of the pipe (ε/d). Higher relative roughness leads to an increase in the skin friction factor. It is obvious that local turbulence near the surface of the pipeline changes with pipe relative roughness, and that would affect the thickness of the viscous sublayer. Therefore, when the thickness of the viscous sublayer becomes equal to or greater than the pipe roughness, the pipes are considered hydrodynamically smooth. The experimental results on the effect of pipe diameter on the drop in pressure for the flow of crude oil through different pipelines are shown in Figure 4A–C. The results indicate that pressure drop decreases with increasing pipe diameter when other parameters are fixed. The reduction in pressure drop was from about 125–42.5 kPa at a flow rate of 40 LPM under the same temperature conditions. This is attributed to the fact that huge eddy currents exist in the pipes with larger diameters, absorbing more energy from the main flow. In smaller pipelines, several small eddy currents are formed, whereas for larger-diameter pipes, the number of large eddies will be greater.

Figure 4.

Figure 4

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Comparative plot between pressure drop (kPa) and flow rate (L/min) for different pipe diameters (A) 1 in., (B) 1.5 in., and (C) 2 in.

4.2. Effect of Velocity

The velocity profiles of crude oil flow through pipelines were calculated using the results obtained from pressure drop analysis during experimental investigations. Figure 5A,B illustrates the contour of static pressure (Pa), which increases with the increase in velocity of the crude oil–water through a horizontal pipe having a constant diameter (2 in.) operating at a constant temperature (25 °C). Pressure drop analysis showed that the change in pressure across the pipe increased with the inlet velocity of the fluid. The static pressure inside the pipe gradually decreases along the length of the pipe.

Figure 5.

Figure 5

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Contour of static pressure (Pa) for crude oil–water flow through a 2 in. horizontal pipe at 25 °C and velocity: (A) 0.11 m/s and (B) 0.62 m/s.

Figure 6A,B illustrates the velocity of the crude oil–water flow inside the horizontal straight pipe at 25 °C at every 0.5 m distance from the inlet. In the study, all the parameters like pipe diameter (2 in.), temperature, and concentration are kept constant, and the only parameter that has been varied is velocity. The study has been conducted for 2 dissimilar velocities (low = 0.11 m/s and high = 0.62 m/s). The study shows that the velocity of the fluid flow is at its maximum at the center and gradually decreases toward the wall. Adhesive force near the wall is maximum as compared to cohesive force.26 This makes the velocity near the wall’s minimum.

Figure 6.

Figure 6

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Contour of velocity (m/s) for crude oil–water flow at every interval of 0.5 m from the inlet through a 2 in. pipe at 25 °C and velocity: (A) 0.11 m/s (B) 0.62 m/s.

Figures 7 and 8 illustrate the contour of the wall shear stress and rate of shear strain for the crude oil–water mixture through the horizontal pipe at 25 °C at every 0.42 m interval from the inlet. It indicates that shear stress and strain rate are maximum near the wall and gradually decrease toward the center of the pipe. The velocity of the fluid at the wall is less because of friction between the pipe wall and the fluid, and hence drag is generated near the wall. The velocity of the adjacent layer fluid is changed up to the center from the wall, causing velocity distribution (shear strain = velocity gradient = Inline graphic). Therefore, velocity changes from the wall to the center, causing velocity gradient/shear strain rate. However, at the center, no velocity variation (velocity gradient) between the layers of the fluid is seen. This means velocity at the center is the maximum and unique. According to the Newtons law of viscosity, wall shear stress (τ) = Inline graphic, where n = flow behavior index, and μapp is apparent viscosity. Hence, the shear stress of the fluid layer near the wall will be high and less at the center.

Figure 7.

Figure 7

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Contour of wall shear stress (Pa) for crude oil–water flow through a 2 in. horizontal pipe at every 0.42 m interval from the inlet at 25 °C and velocity: (A) 0.11 m/s and (B) 0.62 m/s.

Figure 8.

Figure 8

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Contour of shear strain rate (s–1) for crude oil–water flow inside the 2 in. horizontal straight pipe at every 0.42 m interval from the inlet at 25 °C and velocity (A) 0.11 m/s and (B) 0.62 m/s.

4.3. Effect of Temperature

The effect of temperature on the non-Newtonian pseudoplastic crude oil–water fluid flow inside the 2 in. horizontal straight pipe was investigated. Figure 9 illustrates the contour plot of the static pressure of the crude oil–water flow inside the pipe. From the analysis, it is clear that the static pressure inside the horizontal straight pipe decreases with an increase in temperature. It was also observed that the static pressure reaches its maximum at 25 °C (0.1 kPa) and its minimum at 40 °C (0.06 kPa).

Figure 9.

Figure 9

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Contour of static pressure (Pa) of non-Newtonian pseudoplastic crude oil–water flow inside the horizontal straight pipe of diameter 2 in., velocity of 0.11 m/s, and temperatures (A) 25, (B) 30, (C) 35, and (D) 40 °C.

4.4. Effect of Pipe Diameter

Figure 10A–C depicts the contours of static pressure (Pa) for crude oil–water pseudoplastic non-Newtonian fluid flow inside various pipe diameters (1 in., 1.5 in., and 2 in.) operating at 25 °C, along with a constant velocity of 0.11 cm/s. The static pressure inside the pipe gradually decreases along the length of the pipe. The study also revealed that static pressure and pressure drop inside the horizontal straight pipe decrease with an increase in pipe diameter. The static pressure in the 1 in. horizontal straight pipe is found to be the maximum, and in the 2 in. horizontal straight pipe, it is the minimum.

Figure 10.

Figure 10

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Contour of static pressure (Pa) of non-Newtonian pseudoplastic crude oil–water flow at 25 °C and velocity of 0.11 m/s and the diameter of the horizontal straight pipe (A) 1 in., (B) 1.5 in., and (C) 2 in.

Figure 11A–C indicates the contour of the velocity (m/s) inside the horizontal straight pipes of various diameters. From the contour, it has been found that pipe size affects the flow pattern inside the pipe. The velocity of the crude oil–water fluid flow decreases with an increase in pipe diameter, because at unvarying flow rates, velocity becomes inversely related to the cross-sectional area.

Figure 11.

Figure 11

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Contour of velocity (m/s) of non-Newtonian pseudoplastic crude oil–water flow at every 0.5 m intervals from the inlet at 25 °C and velocity of 0.11 m/s and diameter of the horizontal straight pipe (A) 1 in. (B) 1.5 in. (C) 2 in.

4.5. Phase Analysis

Figure 12 shows the phase analysis of crude oil–water flow through a 2 in. horizontal straight pipe at 25 °C at four equal intervals from the inlet. In this study, velocity, diameter, and temperature are kept constant, while the concentration of water is varied. The crude oil mostly accumulates in the midsection of the pipe due to the density difference, as seen in the figure. Since the density of the crude oil is lighter than that of the water, the crude oil remains in the midsection of the horizontal straight pipe. The bulk velocity of the fluid mixture strips the denser component (water) compared to the lighter component (crude oil) from the mixture toward the wall side as an exchange of momentum transfer. This results in the water being more concentrated toward the wall side and the crude oil at the center.

Figure 12.

Figure 12

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Contour of the crude oil–water fluid flow through a 2 in. straight horizontal pipe at every 0.625 m interval from the inlet at 25 °C and a velocity of 0.11 m/s.

4.6. Comparison of Experimental and CFD Results

The results obtained from CFD were compared with experimental results in each pipeline and depicted in Table 1 and Figure 13A–C.

Table 1. Comparison between Experimental and Simulated Data.

    pressure drop (kPa)
  
condition velocity (cm/s) experimental CFD deviation (%)
pure crude +5% water, pipe dia: 2″, temp: 25 °C 11.75 3.25 3.37 3.56
  18.98 5.251 5.5 4.54
  35.26 9.751 9.93 1.81
  44.72 12.37 12.7 2.37
  54.01 14.94 15.1 1.13
  62.02 17.15 17.4 1.21
pure crude +5% water, pipe dia: 1″, temp: 25 °C 25.52 28.22 28.3 0.42
  32.92 36.4 36.6 0.44
  63.71 70.46 70.7 0.37
  89.77 99.29 99.4 0.15
  119 131.6 132 0.11
  131.7 145.6 146 0.13
pure crude +5% water, pipe dia: 0.5″, temp: 25 °C 17.63 8.664 8.77 1.25
  22.39 11.01 11.2 1.61
  43.89 21.57 21.7 0.69
  54.86 26.97 27.1 0.52
  70.79 34.8 35 0.49
  84.4 41.49 41.7 0.43
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Figure 13.

Figure 13

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Comparison of pressure drop and velocity between experimental and CFD data: (A) 1 in., (B) 1.5 in., and (C) 2 in.

As seen in the figures, pressure drop increased with velocity in both the experimental and CFD work in each pipeline. Similarly, if we look at Table 1, there is a small difference between the experimental and simulated results (Figure 14). Maximum deviations were observed in the 2 in. diameter pipeline, while minimum deviations were observed in the 1 in. diameter pipeline. The deviation between experimental and simulated data is very small (i.e., <5%), which means that the simulated results and the flow equations used for simulation studies can properly predict the flow behavior of crude oil with minimal error. The results of velocity profile and flow patterns were also compared with various data reported in literature, as shown in Table 2. It is noteworthy that our CFD predictions exhibit a close match with the trends reported in the literature, affirming the predictive capability of our simulation methodology. This consistency lends credibility to our numerical approach and supports the validity of our findings.

Figure 14.

Figure 14

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Comparison of experimental and CFD pressure drop.

Table 2. Prior Experimental Investigations Concerning the Flow of Oils in Horizontal Pipes with Oil–Water Mixtures.

author pipe material flow orientation density (kg/m3) viscosity (mPa s) ID (m) measured parameters reference
Mukherjee et al. metal vertical and horizontal 850 3.5 0.0381 pressure gradient and holdup (27)
Abduvayt et al. St-steel vertical and horizontal 800 1.88 ± 0.19 0.1064 flow pattern, holdup, and pressure drop (28)
Soleimani St-steel   801 1.6 0.0243 flow pattern, and pressure drop (29)
Kumara et al. steel –5° ∼ + 5° 790 1.64 0.056 flow pattern, local water fraction, and pressure drop (30)
Alkaya et al. acrylic   849 12.9 0.0501 flow pattern, holdup, and pressure drop (31)
Rodriguez and Oliemans steel horizontal 830 7.5 0.0828 flow pattern, holdup, and pressure drop (32)
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4.7. Uncertainty Analysis

The precision of the developed CFD model was evaluated by implementing four error parameters, such as Nash-Sutcliffe efficiency (NSE), the RMSE-standard deviation ratio of observation (RMSE-standard deviation of the observation ratio (RSR)), and mean square error (MSE). The following error parameters can be estimated using eqs 5–7.33,34

4.7. 5
4.7. 6
4.7. 7

In eqs 5–7, the experimental values and CFD predicted values are denoted by yi,act, and yi,prd, respectively. The mean of the experimental values is represented by yi,mean. The recommended best values of NSE, RSR, and MSE are 1, 0, and 0, respectively.35 The calculated values are considered acceptable if they are found close to the best values. Table 3 shows the uncertainty analysis. The estimated values of all three error parameters are close to the best, demonstrating the model’s acceptability and accuracy. Moreover, the total error values for three pipe diameters (1 in., 1.5 in., and 2 in.) models show a similar trend, and the values demonstrate very less deviation from each other. Thus demonstrating the stability and accuracy of the developed CFD model.

Table 3. Uncertainty Analysis.

models NSE RSR MSE total error value
1 in. diameter pipe 0.99 0.014 0.028 1.03
1.5 in. diameter pipe 0.99 0.0061 0.073 1.07
2 in. diameter pipe 0.99 0.045 0.051 1.08
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5. Conclusions

This extensive investigation delved into the complex dynamics of non-Newtonian pseudoplastic mixtures of crude oil and water as they traverse horizontal pipes. The study provided valuable insights into critical factors such as pipe diameter, velocity, and temperature, elucidating their profound impact on flow patterns and pressure drop. Utilizing CFD, specifically the ANSYS Fluent solver, proved essential for simulating and analyzing these intricate fluid behaviors. The research revealed key findings: larger pipes exhibited reduced pressure drop due to the formation of more substantial eddies, velocity profiles displayed a peak at the pipe center diminishing toward the wall, influenced by adhesive forces, and temperature fluctuations affected static pressure, with higher temperatures resulting in lower static pressure. Phase analysis uncovered water’s affinity for the wall and crude oil’s concentration in the center. Comparison with experimental data confirmed the CFD model’s accuracy, with deviations below 5%, and uncertainty analysis affirmed the model’s reliability. Additionally, the predicted flow pattern from CFD aligned well with the existing literature.

Future studies in this domain could focus on exploring the impact of varying parameters such as pipe roughness, fluid rheology, and composition on the observed phenomena. Investigating the behavior of multiphase flow under different operational conditions, such as varying pressures and temperatures, could provide a more comprehensive understanding. Furthermore, studies assessing the scalability of the findings to real-world pipeline systems and the development of improved modeling approaches for even more accurate predictions would contribute to the continued advancement of knowledge in crude oil–water transport dynamics.

Acknowledgments

The authors express their gratitude to the School of Biotechnology and Chemical Technology, KIITUniversity, and the Chancellor, Vice-Chancellor, and Management of Mahindra University, Hyderabad, India, for the required infrastructure and visionary leadership. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. RS-2023-00219983). Moonis Ali Khan acknowledges the financial support through Researchers Supporting Project number: RSP2024R345, King Saud University, Riyadh. Saudi Arabia. One of the authors (R. Kumar) acknowledges the financial support through the National Research Foundation (NRF) of the Republic of Korea under the Creative and Challenging Research Program (2021R1I1A1A01060846).

Glossary

Nomenclature

αi

fraction for the ith phase

ρi

density of the ith phase

▽

Inline graphic

ui

velocity of the ith phase, ms–1

mij

mass flow rate, kg s–1

g

Acceleration due to gravity, ms–2

Inline graphic

stress–strain tensor of the ith phase

Rij

interaction force between the phases, N

Fi

external body force, N

Flift

lift force, N

Fvm

virtual mass force, N

Kij

fluid–fluid exchange coefficient

μappp

apparent viscosity, Pa s

Inline graphic

shear strain OR velocity gradient

n

flow behavior Index

yi,act

experimental values

yi,prd

CFD predicted values

Glossary

Glossary

CFD

computational fluid dynamics

RMSE

root mean square error

RSR

RMSE-observations standard deviation ratio

VOCs

volatile organic compounds

KTGF

kinetic theory of granular flow

VOF-DEM

volume of fluid-discrete element method

NSE

Nash-Sutcliffe efficiency

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c05290.

  • Pressure drop, flow rate, and viscosity values of crude oil flow through different pipes (XLSX)

The authors declare no competing financial interest.

Supplementary Material

ao3c05290_si_001.xlsx (89.8KB, xlsx)

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ao3c05290_si_001.xlsx (89.8KB, xlsx)

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