Numerical simulation of twophase flow regime in horizontal pipeline and its validation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 09615539
Publication date: 4 June 2018
Abstract
Purpose
The purpose of this paper is to investigate oilgas slug formation in horizontal straight pipe and its associated pressure gradient, slug liquid holdup and slug frequency.
Design/methodology/approach
The abrupt change in gas/liquid velocities, which causes transition of flow patterns, was analyzed using incompressible volume of fluid method to capture the dynamic gasliquid interface. The validity of present model and its methodology was validated using Baker’s flow regime chart for 3.15 inches diameter horizontal pipe and with existing experimental data to ensure its correctness.
Findings
The present paper proposes simplified correlations for liquid holdup and slug frequency by comparison with numerous existing models. The paper also identified correlations that can be used in operational oil and gas industry and several outlier models that may not be applicable.
Research limitations/implications
The correlation may be limited to the range of material properties used in this paper.
Practical implications
Numerically derived liquid holdup and holdup frequency agreed reasonably with the experimentally derived correlations.
Social implications
The models could be used to design pipeline and piping systems for oil and gas production.
Originality/value
The paper simulated all the seven flow regimes with superior results compared to existing methodology. New correlations derived numerically are compared to published experimental correlations to understand the difference between models.
Keywords
Citation
Ban, S., Pao, W. and Nasif, M. (2018), "Numerical simulation of twophase flow regime in horizontal pipeline and its validation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 6, pp. 12791314. https://doi.org/10.1108/HFF0520170195
Download as .RISPublisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited
Nomenclature
 A

= Pipe crosssectional area (m^{2});
 D

= Pipe diameter (m);
 F

= External body forces (kg/(m^{2} s^{2}));
 f_{S}

= Liquid slug frequency (1/s);
 g

= Gravitational acceleration (m/s^{2});
 G_{G}

= Mass flux of gas phase (kg/(m^{2} s));
 G_{L}

= Mass flux of liquid phase (kg/(m^{2} s));
 l

= Pipe length (m);
 p

= Pressure (Pa);
 t

= Time (s);
 T

= Temperature (°C);
 U

= Fluid velocity (m/s);
 U_{d}

= Drift velocity (m/s);
 U_{M}

= Mixture velocity (m/s);
 U_{SG}

= Superficial gas velocity (m/s);
 U_{SL}

= Superficial liquid velocity (m/s);
 N_{f}

= Dimensionless inverse viscosity number ();
 Re

= Reynolds number; and
 Fr

= Mixture Froude number.
Greek symbols
 θ

= Pipe angle with the horizontal;
 α_{k}

= Volume fraction of phase k;
 α_{G}

= Gas volume fraction;
 α_{L}

= Liquid volume fraction;
 ρ_{k}

= Density of phase k (kg/m^{3});
 µ_{k}

= Viscosity of phase k (Pa s);
 λ

= Dimensionless parameter;
 µ

= Viscosity (Pa s);
 µ_{L}

= Viscosity of liquid (Pa s);
 µ_{W}

= Viscosity of water (Pa s);
 ρ

= Fluid density (kg/m^{3});
 ρ_{a}

= Density of air (kg/m^{3});
 ρ_{G}

= Density of gas (kg/m^{3});
 ρ_{L}

= Density of liquid (kg/m^{3});
 ρ_{W}

= Density of water (kg/m^{3});
 σ

= Gasliquid surface tension (N/m);
 σ_{W}

= Water surface tension (N/m); and
 ψ

= Dimensionless parameter.
Subscripts
 a

= Air phase;
 G

= Gas phase;
 k

= Phase No.;
 L

= Liquid phase;
 M

= Gasliquid mixture;
 W

= Water phase;
 SG

= Superficial gas; and
 SL

= Superficial liquid.
1. Introduction
Due to the wide occurrence of slug flow in oil and gas industry, a vast amount of work has been dedicated to the understanding and prediction of the slug transition in horizontal and near horizontal pipes. Slug flow is known to cause mechanical fatigue to the pipelines. Consequently, accurate numerical prediction of pressure drop along the pipe, slug body length, slug holdup and slug frequency were necessary for downstream infrastructure and separation process design before actual work being carryout.
Fan et al. (1993) conducted the experimental works to investigate the initiation of airwater slugs flow in horizontal 0.095m inner diameter (ID) pipe at atmospheric pressure. The test experiments observed the form of slugs in a stratified flow and the gas superficial velocities were less than 3 m/s. They concluded that initiation of slug position was strongly affected by the superficial gas velocity as well as liquid holdup. Similarly, Ujang et al. (2006) studied the evolution and slug initiation of airwater twophase experiments in horizontal pipe of 0.078m ID and 37m length. The experimental study investigated the effects of gas and liquid superficial velocities and the atmospheric pressure 4 bar (a) and 9 bar (a) were carried out for the slug initiation and growth. To study initiation and the evolution of hydrodynamic slugs, the structural measurements of interfacial developments were created at 14 axial locations along the pipe. They found that at the first 3 m from the inlet of the test section, a large number of slugs were initiated. This investigation also found that the effect of pressure on the slug initiation frequency was very small. In the meantime, the increase in pressure delays the slug initiation.
Taitel and Barnea (1990) proposed a consistent approach for calculating pressure drop in steadystate slug flow in a 0.5m and 0.05m diameter pipeline. The pressure drop was calculated by using an overall momentum balance over the slug unit. This method considered only gravitational and frictional pressure drop terms in the horizontal slug flow. They studied and compared the pressure drop by using variable film thickness model with simplified submodels of slug flow. The results showed that the suggested method for the pressure drop calculation using a global control volume was closer to the exact solution. Likewise, Petalas and Aziz (2000) suggested a mechanistic model for predicting the flow regimes in the pipes. It was found that their available mechanistic models for the calculations of flow patterns could improve the capability of predicting the pressure gradient along the pipe and liquid holdup in pipe. These new empirical correlations were applied to all the fluid properties and pipe geometries. The liquid/wall and liquid/gas interfacial friction in the stratified regime, liquid volume fraction and interfacial friction in intermittent flow and the distribution coefficient were taken into account during the development of these correlation models. Later, the mechanistic model and the submodel of Taitel and Barnea (1990) was reformulated by Orell (2005) to improve the Reynolds number for calculating the friction factor and slug pressure drop in the horizontal pipes. The proposed model was developed to test extensively against 12 pressure drop and eight liquid holdup data for both airwater and airoil horizontal slug flow over wide ranges of operating conditions and pipe diameters.
Issa and Kempf (2003) demonstrated the transient slug flow of two fluid model to capture the slug flow initiation process in horizontal and near horizontal pipes and categorized them into empirical slug specification, slug tracking and slug capturing models. In the simulations, the liquid volume fraction can increase until it eventually becomes unity, leading to the onset of a slug. Slugs develop, grow, merge and collapse solely based on the solution of the transport equations for mass and momentum for each phase. The results of their computation for the transition from stratified to slug flow were compared with the experimental data and concluded that the transitional numerical model conformed to the widely accepted boundaries drawn by Taitel and Dukler (1976). In addition, when slugs develop to form a fully intermittent slug flow, the slug characteristics such as slug length and frequency were predicted quite well.
Similar to Ujang et al. (2006), each used a different liquid phase. The influence of the operation pressure on hydrodynamic slug length in near horizontal pipe flow for gas and liquid were observed by Kadri et al. (2010). The operations were conducted with pipe length of 103 m and internal diameter of 0.069 m. Air or sulfur hexafluoride (SF_{6}) gas and oil (ExxsolD80) were used for the fluids in the experimental work. Air was used when operating at atmospheric conditions, whereas SF_{6} was used in higher pressure experiments. SF_{6} is a dense gas with density approximately 5.5 times of air. Therefore, it simulated high pressure conditions (natural gas up to 65 bar). This study identified three types of slugs based on the difference of liquid levels between the slug front and slug tail. It was found that only short slugs existed at high pressure.
Loh et al. (2016) conducted experimental flow loop to study the pressure and gas density effects on air and water horizontal transition from stratified to slug flow. The different pressures in the range 010 Barg were tested using internal diameter pipe of 4in (108.2mm ID) and length of 40m long loop. The stratifiedslug boundary moves up in the flow regime map with increasing in the pressure. Furthermore, they found that the sudden changes of average liquid holdup were linked to the flow transition when the pressure changed.
The flow visualization experiments of characterization of airwater slug flow subregimes in 8m long transparent pipe of 25 ± 0.15 mm ID were implemented by Thaker and Banerjee (2015). Five different slug flow subregimes such as slug formation zone, less aerated slug zone, highly aerated slug zone, slug and wavy zone and slug and plug zone were identified based on the visual observations. These studies observed the minimum and maximum slug frequencies in slug formation zone and highly aerated slug zone, respectively. They developed an empirical correlation to predict the nondimensional slug frequency as a function of superficial Reynolds number of gas (Re_{SG}) and liquid (Re_{SL}) and length to diameter ratio (L/D). The relationship of nondimensional slug frequency was represented as a product of Strouhal number and Froude number. Recently, Thaker and Banerjee (2017) studied the horizontal transition of plug to slug flow and associated fluid dynamics using the same experimental measurements and test fluid. The inlet flow conditions of 13 different data points were reported carefully based on the intermittent flow subregime map of Thaker and Banerjee (2015) to analyze the interfacial structure of plug flow subpattern and its transition to slug. This developed map was represented in terms of superficial Reynolds number of gas (Re_{SG}) and liquid (Re_{SL}) for horizontal pipe. They found that Re_{SG} had significant influence on liquid slug velocity, however it had only marginal effect on liquid film velocity. Re_{SG} plays an important role for onset of bubble entrainment process inside the liquid slug leading to transition from plug to slug flow.
In the oil and gas industries, the transportation of the gasoil twophase flow always involves slug flow which not only damages the flowlines but also causes difficulty in phase separation process. As a result, the main objective of this work is to explore oilgas slug flow in horizontal straight pipes. The developed numerical correlations for pressure gradient, slug liquid holdup and slug frequency were compared with the existing models in the literature. The quantitative validation was performed using the experimental data from Mohmmed (2016). Morphology of the slug flow regime, slug translational velocity, slug body length and slug frequency from experiments were compared with present model to ensure the correctness of the methodology. The horizontal airwater twophase flow regimes were reproduced and compared with the experimental data from the Baker chart (Baker, 1954). Furthermore, the produced numerical results and flow regime were crossvalidated by superimposing the numerical solution onto Taitel and Dukler (1976) flow regime map for quality assurance.
1.1 Numerical simulation of twophase slug flows
In the oil and gas production and transportation industry, gasliquid twophase flow in pipes is one of the most common occurrences. Accurate predictions of the liquid holdup, pressure drop and flow behavior are imperative for maintenance and uninterrupted operation of the facilities. At the same time, it is almost impossible to design consistently accurate production facilities that take into account the complete life cycle of a reservoir. As reservoir depleted and matured, its multiphase flow behavior changed. Compounding to the complexity of the issue are parameters such as pipe diameter, inclination angle, gas and liquid flow rates and fluid properties (densities, viscosities and surface tension). In the industry, multiphase flows have been examined mainly analytically and experimentally due to their complexity. Most of the existing experimental results and the empirical correlation for complex flow are limited due to experimental constrains such as cost and construction space. Computational fluid dynamics (CFD) offers an easier and flexible method to design and use largescale computational models to predict this complex twophase flow with huge saving in terms of laborious and expensive experimental research (Lun et al., 1996).
Among the CFD model, the volume of fluid (VOF) method enables accurate tracking and capturing of twophase interface. In VOF, the motion of the interface is not tracked directly by itself, but rather the volume of each phase in each cell is evolved in time and the interface of both phases at the new time is reconstructed from the values of the volumes at new time. For this reason, the VOF models are sometimes referred to as volume tracking methods (Rider and Kothe, 1998).
Several methods have been proposed for generating slug flow and its formation. Similar method of interface tracking was implemented in the commercial CFX5.7 which used to model airwater twophase slug flow regime in horizontal pipes by Frank (2005). The slug formation, propagation and liquid holdup in a horizontal circular pipe was investigated. Moreover, Ghorai and Nigam (2006) used FLUENT 6.0 to model airwater twophase flow in a horizontal pipe. The VOF models were found more suitable for simulating interface between two or more fluids in this work. This approach was used to study the liquid volume fraction, gas velocity and interfacial roughness. The comparison of their numerical model between the predicted interfacial roughness and the data in the literature was validated. Lu et al. (2007) performed experimental and numerical investigations on the characteristics of an oilgas flow in a largescale horizontal pipe with an ID of 125 mm by means of VOF technique. They concluded that, for a flow transition from stratified flow to slug flow, a critical liquid superficial velocity of 0.113 m/s is required. Also, the gas superficial velocity decreased with the increasing liquid superficial velocity. In addition, the appearance of a slug flow was found to be independent of the gas superficial velocity. The results were shown to match well between their computations and the measured data in the experiments. De Schepper et al. (2008) claimed that the existing commercial CFD codes by using VOF formulation were able to predict the gasliquid flow regimes in horizontal pipes. They compared their numerical results with Baker chart and claimed that all horizontal flow regimes from the chart could be predicted and simulated. Similarly, Rahimi et al. (2013) used commercial CFD model with the VOF method to predict the gasliquid twophase flow regimes in a pipeline. They tried to improve all flow regimes from Baker chart by using CFD method. More recently, VOF method has been used by Deendarlianto et al. (2016) to study airwater twophase plug flow in the horizontal pipe with 0.026m ID and 9.5m length. They found that the gas superficial velocity was significantly affected to the liquid plug holdup, and it was fluctuated strongly with the time variation by increasing the superficial velocity of gas. From their experimental results, it was found that the gas slug length was higher than liquid slug length for all conditions. The gas, liquid and total slug lengths were increased with the increase in gas superficial velocities, but they were decreased with the increase of liquid superficial velocities. However, Horgue et al. (2012) pointed out that some numerical simulation problems related to the VOF method were associated with poor model parametrization because of the discretization scheme and were unsuitable and the time steps too large. For that reason, they suggested that the simulation of slug flows using VOF model needs a suitable parameterization to improve accuracy and computational speed. In this work, the VOF of multiphase flow technique was applied to model the slug flow patterns and determine the slug flow characteristics to obtain the accurate results with less computational time.
1.2 Slug holdup correlations for validation
In twophase gasliquid flow, the slug flow always happens due to an increasing gas superficial velocity. The liquid slugs and gas pockets propagate alternatively in the pipe. The liquid volume fraction in the slug body of gasliquid twophase flow is recognized as the slug liquid holdup. The slug liquid holdup is an important parameter for modeling of slug flow transition. Most of the pressure gradient in the slug flow along the pipe occurs in the slug body. The liquid film acceleration also causes significant pressure gradient in the mixing zone at the slug front. As a result, the overall pressure gradient depends greatly on the slug liquid holdup and slug length (Brito et al., 2013; Kora et al., 2011; Lu et al., 2007; Lu, 2015; Pao et al., 2015, 2016; Sam et al., 2017; Wang et al., 2013).
The widely used correlation for gas fraction prediction as a function of mixture velocity was proposed by Gregory et al. (1978). Their correlation was based on air and lightoil twophase mixtures in pipes with internal diameter of 0.0258 and 0.0512 m. They mentioned that the correlation should be limited to cases for the superficial mixture velocity which was less than 10 m/s to decrease the feasibility of entering the transitional zone between the annular and slug flows, where the correlation model would not be appropriate. Kokal and Stanislav (1989) conducted the experimental study on a series of oilair twophase flow in horizontal and inclined pipes with the three different internal diameters (0.0258, 0.0512 and 0.0763 m) and 25m long. The correlation of liquid holdup in the slug body model was considered an interfacial shear term which was added for the gas film. Therefore, the correlation had an added term of (1−ρ_{G}/ρ_{L})^{0.5} in the gasphase drift velocity (U_{d}) relation of their correlation model. This additional term in the gasphase drift velocity (U_{d}) relation would not impact the results significantly, as the density ratio (ρ_{G}/ρ_{L}) was very small for most gas and liquid combinations. The experimental studies on a unified correlation model for airkerosene twophase slug flow in the pipe with internal diameter of 0.051 m and length of 15 m were developed by Felizola and Shoham (1995). The entire range of inclination angles of the pipe from horizontal (0^{°}) to upward (90^{°}) vertical flow was considered for these studies. However, the correlation methods were based entirely on empirical data. As a result, extrapolation beyond the range of experimental conditions needs to be treated with reserve. Furthermore, the correlation of liquid holdup in the slug body was based on their own experimental data only, and it required 15 coefficients for different inclination angles. For the horizontal flow, the correlation did not give the right trend. Later, Gomez et al. (2000) used the data from various different authors. The dimensionless correlation of liquid holdup in the slug body was developed with the pipe diameters from 0.051 to 0.203 m, pressures from 150 to 2000 kPa and the inclination angles of the pipe from horizontal to upward vertical flow. The data were relied on inclination angle of the pipe, Reynolds number and void fraction of the slug.
Alternatively, phenomenological models (Brito et al., 2013; Felizola and Shoham, 1995; Gomez et al., 2000; Gregory et al., 1978; Gregory and Scott, 1969; Kokal and Stanislav, 1989; Kora et al., 2011; Lu, 2015; Mattar and Gregory, 1974; Neal and Bankoff, 1965; Nicklin et al., 1962; Wang et al., 2013) measured the slug liquid holdup and proposed a simple correlation as a function of mixture velocity. These models generally rely on the estimation through experimental correlations as shown in Table I for horizontal pipe flows. However, AlSafran et al. (2004) noticed that the accuracy of the models correlations was not good unless the application scenario was closer to the experimental condition where the correlation came from.
Table I summarized all the eight published mean liquid holdup correlations available in the open literature. The majority of the correlation is reported with internal diameters of 0.753 inches, which is too limited as far as operational usage is concerned. The only exception is Gomez et al. (2000) who collected data from different sources and reported the holdup correlation for 28 inches pipe.
1.3 Slug frequency correlations for validation
A critical issue in modeling the slug flow behavior is the slug frequency prediction and the relevance of slug lengths. Accurate prediction of the slug frequency is important for design of transportation pipelines and gasliquid receiving facilities. The frequency of slug flow is required as an input in mechanistic models to predict slug lengths and slug characteristics such as pressure gradient and liquid holdup accurately (Gokcal et al., 2009).
Gregory and Scott (1969) proposed one of the first slug frequency correlations based on their experimental data using 0.75inch ID horizontal pipe with carbon dioxide and water. The authors concluded that the slug frequency was dependent on pipe diameter. This conclusion was based on a comparison of their data collected from the experiment of airwater system with data from literature reviews. Later, Greskovich and Shrier (1972) reformulated the Gregory and Scott slug frequency correlation using the Froude number and noslip liquid holdup. The slug frequency correlation was tested by using a kerosenenitrogen system in the pipe diameter of 1.25”, 1.5” and 6”. By using the data collected from a 6inch ID line, they suggested that the diameter effects are overpredicted by Gregory and Scott (1969) model. To overcome this, they recommended that their graphical correlation should be used instead, for cases involving large diameters. Zabaras (1999) compared numerous correlations and mechanistic models for the slug frequency prediction in horizontal and inclined pipes against open data. The data set included both his experimental results and published slug frequency results. He found that the performance of existing methods was not sufficiently accurate for inclined slug flow. He modified the correlation of Gregory and Scott (1969) model, taking into account the effect of inclination angle.
Gokcal et al. (2009) conducted the experimental works of horizontal gasliquid twophase flow in a pipe with oil viscosities between 0.181 and 0.589 Pa.s. The experimental results showed that viscosity was a major parameter that affected the slug frequency significantly. The slug frequency was increased with increasing liquid viscosity. Based on dimensionless analysis, the slug frequency closure model for high viscosity of oil in the horizontal pipes was developed. Although this correlation model was a better alternative than the rest of the above correlations for high viscosity of oils, the comparison against published data indicated that this model was not valid for kerosene or water fluids that had very low viscosity.
Perez et al. (2010) recently reported the existence of wisplike structures in a vertical airwater flow revealed by wire mesh sensor studies with a 67mm diameter pipe at atmospheric pressure. They studied a mixture of air and water with gas superficial velocities in the range 0.055.7 m/s and the liquid superficial velocities of 0.2, 0.25 and 0.7 m/s. The frequencies of the periodicity of the flow obtained from power spectral density analysis were seen to decrease with increasing gas superficial velocity. In contrast, the frequencies for the occurrence of wisps were seen to increase as the gas velocity was increased.
Slug flow is one of the most observed flow pattern in the industry that characterize the gasliquid twophase flow in multiphase transportation pipelines. The most distinctive characteristic of the slug flow or slug tracking models is the need for the slug properties such as velocities, slug liquid holdups, lengths and frequencies to be considered at the inlet or along the pipelines. The reviews of previous models and correlations (AlSafran, 2009; Gokcal et al., 2009; Gregory and Scott, 1969; Greskovich and Shrier, 1972; Perez et al., 2010; Zabaras, 1999) were proposed for slug frequency prediction based on experimental data of gasliquid twophase flow in horizontal and inclined pipes as summarized in Table II. Overall, slug frequency decreases with increasing gas superficial velocity but vice versa with increasing liquid superficial velocity.
2. Numerical modeling
2.1 Multiphase flow modeling
Depending on the operating conditions, different flow regimes from one to another are displayed in multiphase flow processing. In modeling multiphase flow, there are three main steps that need to be addressed. Defining the number of phases and the flow regime in which they are flowing is the first step in the procedure of model selection. Second, the governing equations formulation plays an important role in the development of multiphase flow model. All the flow problems and any flow behavior for the motion of all phases in numerical simulation are developed by formulating local, instantaneous conservation of mass, momentum and energy equations in the control volume. Finally, these governing equations are solved for the multiphase flow model (Ranade, 2002).
FLUENT 16.1 is based on the finite volume method to discretize the governing equations (Versteeg and Malalasekera, 1995). The present work used the Eulerian approaches with VOF model where liquid and gas were treated as two distinct phases. The VOF model is a method used to track and capture the gasliquid immiscible interface finding the solution for the single set of momentum equations and tracking the volume fraction of gas and liquid phase throughout the domain (Ranade, 2002). The kε model was used to treat turbulence phenomena in the fluids.
If α_{k} is the volume fraction of the kth phase in a computational cell, when α_{k} equals 0 means that the cell is empty of the kth fluid, α_{k} equal to 1, the cell is full of the kth fluid and the cell consists of the mixture of the kth fluid and one or more types of fluids when α_{k} is between 0 and 1. Therefore, based on these appropriate properties of α_{k}, variables are assigned to each computational cell.
The flow processes around each dispersed phase particles are resolved using the VOF method. In this approach, a surfacetracking technique was applied to a fixed Eulerian mesh. A single set of mass conservation equation, equation (1), and momentum equation, equation (2), are solved continuously and shared by the fluids and volume fraction of both phases in each computational cell. The volume fraction of the phase in interface tracking between the phases is accomplished by solving an additional continuity equation as expressed in equation (3). The expression of continuity equation, equation (3), is to introduce for the volume fraction of the primary phase which is gas, α_{G}. Therefore, the volume fraction of the secondary phase is liquid, α_{L} that is computed as 1− α_{G} (Ansys Fluent, 2016; Ranade, 2002):
The body force, F, in equation (2) accounts for the surface tension, σ and the contact angle. This body force is computed in FLUENT as the continuum surface force model (CSF), F_{CSF} (Brackbill et al., 1992). The model used the value of contact angle to adjust the interface normal in each cells near the wall rather than imposing the effect of contact angle as the boundary condition of the wall.
The CFD code with VOF multiphase flow model, the sum of gas and liquid volume fractions in each control volume is equal to one. When the mixture is fully saturated:
Generally, in the VOF model, the mixture properties of density (ρ) and viscosity (µ) are defined in the usual way (Ghorai and Nigam, 2006):
2.2 Mesh quality and mesh dependency study
The horizontal pipe considered for present analysis had an internal diameter of 0.08 m and a length of 8 m. This pipe geometry was divided into a hexahedral mesh, which was generated with the help of a mesh generating tool known as ICEM/CFDHexa. In this work, the 3D geometry was meshed using different numbers of elements from 65 to 1,536 thousands hexahedral cells. To present the apparent 3D computational domain with hexahedral cells, Figure 1 illustrated four different types of the volume tessellation in the computational domain with different level of grid refinement.
Poor mesh quality may lead to inaccurate solution and/or slow convergence. To avoid the effect of poor mesh quality, the mesh quality check was generally taken prior to performing the numerical simulation. Mesh expansion factor measures the magnitude of the rate of change of the adjacent element areas or volumes. The most important mesh matrices for FLUENT, such as maximum aspect ratio and minimum orthogonal quality check, are involved in quantifying the quality. The mesh aspect ratio is determined by dividing the smallest element edge length by the largest; usually it should be less than 40. Orthogonal quality is computed for cells using the vector from the cell centroid to each of its faces, the corresponding face area vector and the vector from the cell centroid to the centroids of each of the adjacent cells. The worst cells will have an orthogonal quality closer to 0, with the best cells closer to 1. The minimum orthogonal quality for all types of cells should be more than 0.01. The primary mesh quality check was executed with ICEMCFD meshing then the report mesh quality was doublechecked and displayed in the console in FLUENT simulation.
All the seven 3D computational domains with different number of elements have been checked for the quality before the simulation. The lowest mesh quality and the mesh used for the main study are presented in Table III, and it is found that the lowest mesh quality still meets the requirement of acceptable mesh quality. Hence, good quality mesh for the numerical simulation has been met for all the seven 3D computational domains. The geometry with number of elements of 629.3 thousands hexahedral cells was found to be the lowest mesh quality. Table III shows the detail ICEM/CFDHexa and FLUENT criteria used in this work to determine the acceptable mesh quality for the simulation solver (Ansys Fluent, 2016; Ansys ICEMCFD, 2016).
However, the mesh quality check was effectively completed, the optimum numbers of elements for the mesh dependency study is a crucial step that one needs to compromise and carry out. Therefore, model validation was started with mesh dependency check analysis. This analysis was conducted to study the mesh dependent convergence behavior. To study the convergence behavior, several runs of simulation had been performed by varying total number of hexahedral cells. The pressure gradient distribution in the horizontal pipe was the criteria selected to check on the convergence behavior. To ensure the solution independency from grid size, the geometry was meshed using different numbers of elements cell between 65 and 1,536 thousands hexahedral cells as shown in Figure 1. The pressure gradient values obtained corresponding to each number of elements are tabulated in Table IV. Moreover, the calculations were carried out under the same setup and physical parameters such as the velocity desired flow regime, turbulence model and time step. The results are illustrated in Figure 2 for the cases of airwater twophase slug flow regime. At the inlet was gas and liquid superficial velocities and at the outlet was pressure outlet. Air and water superficial velocities of slug flow were U_{SG} = 3.26 m/s and U_{SL} = 0.4 m/s, respectively. The simulations were performed under the atmospheric pressure (101.3 kPa) with temperature 24°C.
Figure 2 shows the model’s convergence behavior of different numbers of elements cell based on the pressure gradient obtained along the whole length, 8 m, of the horizontal pipe. The pressure gradient increases gradually until it plateaus to a constant value at around 500 thousands hexahedral cells. Figure 2 shows that the solution with coarser meshes is unstable and varied with the changes of numbers of elements cell. This error on the coarser mesh is due to insufficient element fineness to capture the solution. The pressure gradient curve converges as the mesh was refined, showing that the numerical solution is converging toward the “true” solution. The simulation time for the model with the finest mesh, Figure 1(d), took about three weeks to complete. A balance approach of computing time and accuracy of solution has to be compromised. It was decided that the 3D model with 522.5 thousands hexahedral cells are the lowest limit of the required mesh resolution to achieve a reasonable converged results. From here onwards, unless otherwise stated, the mesh configuration shown in Figure 1(c) is the mesh used for the simulation in this study.
2.3 Initial and boundary conditions
The boundary conditions are critical components of FLUENT simulations, and it is important to note that the initial and boundary conditions of the present study are specified appropriately. Based on the previous investigations, there are two techniques which were used in the boundary conditions for the simulation of flow regimes and especially slug flow. The first technique was as used by Frank (2005), where perturbations of the free surface were imposed at the inlet producing initially set sinusoidal agitation of free surface in time. In this work, the technique was modified where the perturbations were as a result of the volume fraction of liquid phases entering the pipe as a function of time as shown in equation (7). This idea was to improve the CFD codes in the present study to provide better observation of airwater flow patterns and make it independent of pipe diameter and pipe length. The key points of the present simulations are the constant gas and liquid superficial velocities that were input at the inlet of the pipe according to Baker chart, and a transient liquid level at the inlet cross section was set as the following function:
The second technique, the initial condition was set in such a way that the gasliquid volume fraction has a 5050 share in volume with only liquid occupying the bottom of the pipeline and gas phase filling the top of the liquid surface. This implicitly implied that the starting condition is the stratified gas and liquid twophase flow with zero velocity (Frank, 2005; Ghorai and Nigam, 2006; Lu et al., 2007; Lu, 2015; Mo et al., 2014). The initial and boundary conditions of gas and liquid in horizontal pipe are demonstrated schematically in Figure 3.
The noslip boundary condition was applied at the pipe walls and atmospheric pressure is set at the outlet boundary condition. The influence of the gravitational force on the flow has been taken into account. All of the inlet values of the velocities desired flow regimes for all cases of numerical simulation were taken from the Baker chart (Baker, 1954).
2.4 Solution method
The PRESTO (pressure staggering options) scheme was applied for pressure interpolation. A combination of the PISO (pressure implicit with splitting of operators) algorithm for pressure–velocity coupling and the secondorder upwind calculation scheme for the determination of volume fraction and momentum were used to perform the calculations (Versteeg and Malalasekera, 1995).
Gas was chosen as primary phase and liquid was secondary phase. The surface tension was set a constant value, for airwater of σ_{W} = 0.072 N/m and oil and gas of σ = 0.018653 N/m. Gasliquid twophase flow was the dynamic flow behavior; therefore, all cases of numerical simulation for unsteady state calculation were carried out with a time step of 0.001 s. All the calculations were run, and the Courant number (Co) was fixed at 0.25 for the volume fraction equations. The residual value of the calculated variables for the mass, velocity components and volume fraction of twophase was contributed to the convergence criterion. When the scaled residuals of the different variables were lowered by four orders of magnitude, the numerical calculations were considered converged in this works.
3. Results and discussions
3.1 Airwater twophase flow simulation
3.1.1 Airwater twophase flow conditions.
The horizontal pipe with internal diameter of 0.08 m (3.15 inches) and 8 m length was used to validate the airwater twophase flow model. The general geometry of horizontal pipe flow for the case studies modeled is shown in Figure 4.
Based on the regime map of flow characteristic in the literature review, the Baker Chart (Baker, 1954) was used to generate the flow regimes in this work. The selected data points for different regimes in this validation are shown in Figure 5. The Baker flow pattern map and the boundaries of the various flow pattern regions is the function of the mass flux of gas (air), G_{G} and the ratio of mass flux of liquid and gas, G_{L}/G_{G} is illustrated in Figure 5. The dimensionless parameters λ and ψ are included to make the chart useful for any gasliquid combination different from the standard combination. The parameters λ and ψ equal unity when the standard combinations are air and water at atmospheric pressure and at room temperature 25°C. By using the accurate calculation of λ and ψ, the geometry of twophase flows with any gas (G_{G}) and liquid (G_{L}) at different temperatures and pressures conditions can be predicted using the same chart. Although solid lines are used to represent the transition flow regimes from one region to another in Figure 5, however, these lines represents broad transition zones in reality.
To use the map, first the mass flux of the liquid and gas (air, vapor) must be determined. Then Baker’s parameters λ and ψ are calculated. The gasphase parameter is λ and the liquidphase parameter is ψ. The values of the xaxis and yaxis are then determined to identify the particular flow regime. These dimensionless parameters of mass flux of gas and liquid phase are given by (Baker, 1954):
In this study, the commercial FLUENT 16.1 was used to simulate twophase flow model to reproduce the seven flow regimes for airwater twophase flow in a horizontal pipe as a mean to validate the correctness of the CFD procedures. The established methodology will be applied in Section 3.3 to evaluate the effect of fluid properties for oilgas twophase slug flow predicted by Baker chart, using the suitable values for factors of λ and ψ [equations (8) and (9)].
The threedimensional simulations of the twophase flow regimes for air and water are presented in this work. All seven cases, representing seven flow regimes in the Baker Chart, of airwater twophase flow under atmospheric pressure and at room temperature were implemented. The superficial velocities of water and air, determined from the Baker chart, were used as inlet conditions for the calculation. The selected operating conditions are listed in Table V. The inlet temperature was set at a constant value of 25°C. The fluid pressure at the pipe outlet was set to 101,325 Pa (atmospheric pressure). The physical properties of air and water used for the simulation are tabulated in Table VI.
3.1.2 Volume fraction contour of flow regimes.
All seven flow regimes that appeared in the Baker chart (Baker, 1954) were simulated and the discussion of them now follows. The mixture density contour for seven different horizontal flow regimes is illustrated in Figure 6. The air and water twophase mixture density in the horizontal pipe is proportional to its phase composition. The red color denotes water phase and the blue color represents air phase. Figure 6(a) depicts the resultant stratified flow regime according to data selected from Baker chart (Figure 5 and Table V). The air and water are separated by a smooth interface at low gasliquid velocity of U_{SG} = 1.22 m/s and U_{SL} = 0.003 m/s, respectively. A normal condition of gravitational effect is that the heavy liquid flows at the bottom, while the gas flows over the liquid in the pipe. Figure 6(b) shows the density contour of wavy flow regime based on the data selected from Baker chart in Figure 5 at U_{SG} = 20.41 m/s and U_{SL} = 0.0063 m/s. The flow started from stratified flow and the higher gas velocity causes the gasliquid interface to travel in a wavy fashion along the pipe in the flow direction. Figure 6(c) presents the simulation results of plug flow regime obtained from Baker chart in Figure 5 at U_{SG} = 0.16 m/s and U_{SL} = 1 m/s. Intermittent flow is usually called plug flow regime which has medium flow rates of water and low air flow rates. The liquid plugs are separated by elongated gas bubbles and the large bubbles travelling along the top of the pipe whereby large waves are presented on the stratified layer. From the contour, small bubbles and elongated bubbles flow and rise at the upper part of the horizontal pipe because of the upward force of buoyancy. Plug flow is also sometimes referred to as elongated bubble flow. The numerical simulation results of slug flow pattern according to the Baker chart as shown in Figure 5 and with U_{SG} = 3.26 and U_{SL} = 0.4 m/s is illustrated in Figure 6(d). When gas velocities increase to 3.26 m/s, aeration takes place at the liquid slugs and contains small gas bubbles. The gas bubbles grow and it becomes elongated bubbles. The liquid slugs separating such elongated bubbles can also be described as large amplitude waves. These waves touch the top wall of the pipe and form a liquid slug which passes rapidly along the pipe. The CFD prediction results of annular flow regime given by Baker chart in Figure 5 at gas and liquid superficial velocities U_{SG} = 16.33 and U_{SL} = 0.2 m/s, respectively can be seen in Figure 6(e). The gas velocity increased further through the central core, the liquid forms a continuous annular film around the perimeter of the pipe, and the liquid film is thicker at the bottom than the top due to gravity. Figure 6(f) indicates the bubble flow regime as reported by the data selected from Baker chart in Figure 5 and U_{SG} = 32.65 m/s and U_{SL} = 40.1 m/s. In this case, the flow is called dispersed bubble flow, the small gas bubbles move along the pipe or at the top of the pipe in continuous flow of the liquid phase (gas phase discontinuous) and both bubbles and liquid are approximately the same velocity. Figure 6(g) illustrates the spray/dispersed flow consistent with the Baker chart as shown in Figure 5 at U_{SG} = 85.71 m/s and U_{SL} = 1.16 m/s. As mentioned by Baker (1954), the spray flow is the type of flow in the group of dispersed flow. It can be clearly seen from axial direction of the contour, small droplets of water are entrained along the pipe as spray by the air phase. The small water droplets are dispersed in continuous air phase. The contour clearly showed that small liquid film and some liquid droplets flow at the bottom of the pipe due to gravity effect.
3.1.3 Model comparison of flow regimes.
The comparisons between present models of mixture density in horizontal layout for airwater flow with the model of De Schepper et al. (2008) are shown in Figure 7. However, it can be seen that the model prediction of De Schepper et al. (2008) on the righthand side in Figure 7(d) shows poor slug flow regime. It is important to note that based on the finding of De Schepper et al. (2008), the liquid slugs do not touch the upper part of the pipe as expected from the observation of their study. Furthermore, the authors themselves explained that it was very difficult to simulate a good slug flow regime due to the transition zones of Baker chart, and the region of slug flow pattern for airwater flow is very small compared to the other flow pattern regions. This is one possible explanation to a poor simulation result of slug flow regime. Conversely, remember that the slug flow should be presented as intermittent nature or plug flow according to Baker flow pattern map. The slug behavior is found to be unsteady, and hence the liquid slug jumps to plug the pipe section and travels along the pipe with gas bubbles and elongated gas bubbles on the top of the pipe which makes a series of slug (slug body length) as shown in Figure 7(d) on the lefthand side.
For annular flow in Figure 7(e), De Schepper et al. (2008) contour showed almost no liquid film at the bottom of the pipe. The present model clearly showed the presence of a thin liquid film at the bottom of the pipe, which is the characteristic of annular. Due to the gravity effect and the different density of both phases, in addition to higher flux momentum in the liquid, a thin liquid film should appear at the perimeter of the pipe. Furthermore, the liquid film should be thicker at the bottom and thinner at the top of the pipe.
The comparisons of contours of mixture density between present CFD model and the model of Rahimi et al. (2013) for airwater twophase flow regimes in horizontal pipe are represented in Figure 8. In Figure 8(c), both models are plug flow, but Rahimi et al. (2013) results do not look like plug flow at all. Based on Baker’s (1954) explanation, plug flow is the flow in which gas bubbles and elongated gas bubbles move along the upper part of the pipe. The slug flow model of Rahimi et al. (2013) in Figure 8(d) shows a very poor slug regime. No liquid is seen touching the upper part of the pipe his result for slug flow as expected from the observation of Baker (1954).
Figure 8(e) compares the bubble flow of both models. Again, Rahimi et al.’s (2013) results do not show the pattern of bubble flow. According to Baker (1954), bubble flow is the flow in which gas bubbles mix with the liquid moving along a horizontal pipe at approximately the same velocity as the liquid. This flow is similar to Froth flow where the whole pipe is filled with gas bubbles mix with water.
3.1.4 Comparison with Taitel and Dukler map.
The simulation data for different flow regimes were obtained and superimposed on Taitel and Dukler (1976) map as shown in Figure 9 for the sake of comparison purpose. Cluster of data points for each regime is taken at different time steps at the outlet of the pipe of the test section, as is typically done in a physical experiment. The superficial velocities that are plotted in Figure 9 are averaged superficial velocities at the outlet face. A reasonably good agreement of the present numerical results with the Taitel and Dukler (1976) map was observed. Some data points of plug flow are “spilled over” in slug region and some data points of slug flow are “captured numerically” in the plug flow region of the Taitel and Dukler (1976) map. This means that the gasliquid twophase flow in a horizontal pipe could be either plug flow or slug flow depending upon the flow time. It is also observed that some data points of “supposedly” annular flow are in the slug flow region. The elongated bubbleslug or plug flow can become either slug or annular flow by increasing the superficial gas velocity.
It can be concluded that the numerical validation for horizontal airwater two phase flow gave a reasonably good qualitative prediction with the expected flow patterns of the experimental data reported by Baker chart and then cross referenced and validated with Taitel and Dukler (1976) flow regime map. Therefore, all different flow patterns can be generated by using the threedimensional CFD FLUENT 16.1 models.
3.1.5 Airwater twophase slug flow transitions.
Figure 10 shows the contours of water volume fraction and the different time frames of the simulation for airwater slug transitions. The red color represents liquid and blue color is representing gas. The flow is from left to right. Time evolution of slug flow in the horizontal can be clearly seen. The liquid slugs touch the upper part of the pipe respected to Baker (1954) chart.
From Figure 10, it can be observed that initially the pipe was filled with stratified air and water with 5050 equal volume percentile and zero velocity. The water phase was steady, and it took some simulation time until the generation of the first wave was crested, growing to a slug which blocks the crosssection of the pipe (at time 0.1 s) and then progressing further along the pipe. The long slug was observed from 0.2 to 2.5 s. These disturbances were captured by the model and as the simulation proceeds further in time, they grew into slugs which completely block the cross section of the pipe.
3.2 Model validation against experimental data
3.2.1 Experimental details.
In the previous validation, the slug flow was validated qualitatively. The second validation was based on the comparison of the present solution with experimental work of Mohmmed (2016), where photographs of water volume fraction of slug flow, numerical data for slug translational velocity, lengths and frequencies were available. The present study used the experimental work of Mohmmed (2016) for the validation of the present model. The boundary conditions of the CFD simulations in terms of representing the experimental configuration of the twophase flow in the horizontal pipe were chosen based on the experimental setup. A pipe model exactly the same as the experimental test section with 0.074 m (3 inches) ID and 8m long was built. Air and water were used for twophase flow. The gas and liquid physical properties from the experiment is shown in Table VII, and air and water superficial velocities were in the ranges U_{SG} = 13.5 m/s and U_{SL} = 0.71 m/s, respectively. The entire experimental tests were performed under the atmospheric pressure (101.3 kPa) in the room temperature of 24°C.
The measurement points were specified along the test pipe for the appropriate calculations of slug flow regime. As shown in Figure 11, the distance of each point from the reference section 54D was taken to be 7D, 10D, 12D and 14D to make sure that the distance between the two sections were not affecting the obtained results and also to calculate the slug velocity along this test section.
3.2.2 Comparison between computational fluid dynamics and experiment.
The steps of slug development in a horizontal pipe between the present model and experimental photographs are shown in Figure 12. The red color represents the water and the blue color represents the air. The slug development started from the slug initiation which was initially equal to 50 per cent water volume fraction in the test section as shown in Figure 12(a). As can be seen by the red ellipse in Figure 12(b) and 12(c), the slug was initiated after the occurrence of the hydraulic jump which the liquid holdup was increased about to H_{Ls} = 0.75, and then this slug of liquid holdup was developed into the downstream as the form of liquid slug. When the liquid superficial velocity increased to 0.93 m/s, the momentum of the liquid was increased which could be a reason to delay the hydraulic jump occurrence. Consequently, the slug flow regime developed further in the pipeline. There are reasonable agreement between experimental photographs and present contours of liquid phase, indicating that the VOF model has been used correctly to capture the gas and liquid interface. The slug initiation is consistent with the results reported by Wang et al. (2007).
The comparison of slug flow morphology along the horizontal pipe with the time sequences between the present model and the experiment were illustrated in Figure 13. The slug movement along the pipe at U_{SG} = 2.44 m/s and U_{SL} = 0.86 m/s. There are reasonable agreement between experimental photographs and present contours of liquid phase, indicating that the VOF model has been used correctly to capture the gas and liquid interface.
The slug flow appeared in Figure 13 could be interpreted as elongated slug flow. Based on the experimental procedure, the photograph of Slug 1 in Figure 13 has the length of 1.24 m and used the camera resolution of 960 × 480 pixels that physically covered 1 m from the pipe length. In Figure 13, each 1 cm of scale represented 0.034 m of reality; therefore, the first photograph of Figure 13 showed a segment of about 0.95 m length from total length of Slug 1.
3.2.3 Slug translational velocity.
Slug flow regime is unsteady; therefore, its translational slug velocity varied along the pipe, and this makes it difficult to be measured accurately. Based on the experimental works, to determine the average velocities magnitude for each case of different superficial air and water velocities, translational velocities at four positions, 61D, 64D, 66D and 68D (Figure 11), were taken and averaged. These averaged translational slug velocities were reported for three superficial liquid velocities at U_{SL} = 0.7, 0.86 and 1 m/s corresponding to four superficial gas velocities U_{SG} = 1, 2.1, 2.44, 2.79 and 3.14 m/s.
As illustrated in Figure 14, a good agreement can be achieved for the comparison of translational slug velocity between present model and experimental data for the various gas and liquid superficial velocities. The translational slug velocity for a constant superficial liquid velocity increased with increasing gas superficial velocity. Also, as liquid superficial velocity increases, the translational slug velocity is increased.
3.2.4 Slug body length.
By multiplying the slug velocity, U_{s}, and the time difference between the slug nose, t_{n}, and the slug tail, t_{t}, when the slug passing along the monitoring station 54D and 81D (Figure 11), the mean slug length, L_{s}, could be determined as:
Figures 15 and 16 illustrate the comparison between present model and experimental data of mean liquid slug length for difference gas and liquid superficial velocities. The slug body length as shown in Figures 15 and 16 were measured at the station 54D and 81D, respectively. It can be observed that when the gas superficial velocity increases at constant liquid superficial velocity, the slug length also increased. However, the mean slug length decreased when the liquid superficial velocity increased. The present model compares favorably to the experimental study, and a good agreement can be obtained. Moreover, the interesting results were found for slug length by increasing the gas superficial velocity at different liquid superficial velocities. It has been noticed that the slug length results of CFD and experimental studies were observed to increase with decreasing liquid superficial velocities. This phenomenon could be explained that the slug length increases as more liquid is scooped up at the slug front than is shed from its tail. Behind the slug, the liquid level drops. These results are expected. In a slug unit, mass is conserved from the input gas and liquid flow rates. The ratio of gas to liquid in the slug unit will be increased with increasing gas superficial velocity at constant liquid superficial velocity. Typically, higher ratio of gas to liquid leads to larger mixing zone for same slug unit length. As a result, increasing gas superficial velocity, the unit length will be increased. At higher gas and liquid velocities, the gas volume fraction in the slug will be much greater due to higher turbulence leads. To some extent, the mixing zone will be decreased; however, the length of film region will be remained relatively constant. In this case, the length of slug unit will be decreased.
Figure 16 shows that the mean slug length at section 81D is about 6 m. The comparison of slug length between two sections at x = 54D and x = 81D shows that the liquid slug length in section 81D is larger than liquid slug length in section 54D. This is because the slug length at section 54D is not fully developed. Based on the explanation of Rogero (2009), this is due to the rate of liquid pickup at the slug nose is larger than the rate of liquid shedding at the slug tail. Consequently, the slug body length is increased as the slug travelled along the downstream pipeline.
3.2.5 Slug frequency.
Based on the experimental procedure, the frequency of the slug (f_{S}) was monitored at the section x = 54D and x = 81D from the pipe inlet (Figure 11). The reason for selecting these two positions, according to Mohmmed (2016), is that it is desirable to measure the slug frequency near the inlet and outlet of the test section, and there were numerous cases in his study at which the slugs were initiated after Section 54D from the inlet, so it was not possible to determine the liquid slug frequency for such cases unless they were measured at another section.
Figures 17 and 18 show the comparison of slug frequency between the present model and experimental data (Mohmmed, 2016) at Section 54D and 81D, respectively. It can be concluded that the slug frequency increased with increasing liquid superficial velocity. Conversely, the slug frequency decreased when gas superficial velocity is increased for the constant liquid superficial velocity. The present model matched the experimental data with reasonable agreement.
3.3 Oilgas twophase flow simulation
3.3.1 Oilgas twophase slug flow condition.
The horizontal pipe with internal diameter of 0.08 m (3.15 inches) and 8m length as shown in Figure 19 was used to simulate the oilgas twophase flow model.
The Baker chart was used to generate the slug flow regime in this section. The selected data points for the slug flow regime area were shown in Figure 20.
The 3D simulations of slug transition performed for twophase oilgas flow in horizontal pipe is reported. It is important to note that there is no reported twophase oilgas flow regime map similar to Baker chart or Tiatel and Dukler map for these investigations. Therefore, to carry out the investigation, parameters λ and ψ [equations (8) and equations (9)] were calculated using the Baker chart. The superficial velocities of slug flow regime for the oilgas phases were set as initial and inlet velocity for each phase. Oil and gas superficial velocities selected are in the ranges U_{SL} = 0.050.3 m/s and U_{SG} = 0.21.5 m/s, respectively. The range of operating conditions covered in this investigation is summarized in Table VIII. The physical properties of oilgas are shown in Table IX.
The simulation was performed with the outlet boundary condition prescribed at atmospheric pressure of 101,325 Pa. The constant temperature of 25°C is assumed. The components and the corresponding physical properties as shown in Table IX are given to the authors from PETRONAS Exploration and Production Company.
3.3.2 Slug flow transitions.
The results of the CFD modeling for oilgas twophase slug transition in horizontal pipe are discussed. Figure 21 shows the contours of oil volume fraction and oilgas twophase slug evolution in horizontal pipe. The red color represents the oil and the blue color represents the gas. Flow is from left to right. Figure 21 should be compared morphologically with Figure 10. The formation of slug body in Figure 21 is seen to be more “orderly” and less chaotic in comparison to Figure 10 for air and water. This can be attributed to the increased oil viscosity effect. Initially, the flow is stratified and the interface is flat and smooth. After 0.5 s, the first wave is developed and blocks the pipe cross section, indicating the start of a slug flow. The slug body propagates along the horizontal pipe and grows in size (from 1.0 to 3.5 s). It was intended point out that this large slug is generated using the perturbation condition at the interface.
3.3.3 Pressure gradient.
In the industry, the pressure gradient can be used as an indicator to reflect the flow characteristics and can be obtained easily. Lu et al. (2007) observed the characteristics of the flow patterns from stratified to slug flow by using the pressure gradient to compare with the experimental data. They showed that the variation of pressure gradient is mainly dependent on the flow patterns. The time series pressure gradient measurements of slug flow are quite complicated because of its intermittent nature and the slug behavior. Despite that, it is possible and relatively easy to compare the mean pressure gradient along the test section. In this study, the pressure gradient was calculated by the time averaged pressure drop over the entire length of the test section. Because of nonavailability of experimental time series pressure gradient data and the difficulty in extracting time series data points from open literature, the time series comparison of the present numerical results with experimental data can only be presented as shown in Figure 22.
To check the accuracy of the present model, Figure 22 shows the comparison of mean pressure gradient versus superficial gas velocity among the present model and the theoretical models by Petalas and Aziz (2000) and Orell (2005) for the constant superficial liquid velocity of 0.05 m/s. As can be seen that the pressure gradient increases with increasing superficial gas velocity.
Figure 23 shows the average pressure gradient in a slug unit against superficial gas velocity at difference liquid velocity. As expected, the pressure gradient increases with increasing superficial gas velocity for a given superficial liquid velocity. Also, the pressure gradient continuously increases with increasing superficial liquid velocity.
3.3.4 Slug liquid holdup.
The liquid volume fraction in the slug unit is recognized as the slug liquid holdup. The slug liquid holdup is a mixture of liquid and gas phases, and it can carry different amount of entrained gas. Slug liquid holdup is an important parameter for the processing slug flow in pipeline.
Figure 24 presents the comparison between the present numerical results of liquid holdup at constant U_{SL} = 0.3 m/s. As can be seen, the present model and correlations follow the trend of decreasing slug liquid holdup as the superficial gas velocity increases. The results are in good agreement between the present model and the correlations, but substantial deviation is observed with the correlation by Gomez et al. (2000), Gregory et al. (1978) and Gregory and Scott (1969).
The correlation of Gomez et al. (2000) proposed a general dimensionless correlation to predict slug liquid holdup for inclination angle from horizontal to vertical upward based on six sets of data points. The results are unsatisfactory probably because the model is highly dependent on the parameter slug Reynolds number. This shows that at very low liquid velocity relative to the gas velocity, similar to the present study, this correlation may overestimate the liquid holdup.
The correlation by Gregory et al. (1978) overpredict the liquid holdup, whereas the correlation by Gregory and Scott (1969) underpredict it. The real reason for these deviations is not known but could be attributed to various reasons:
In Gregory et al. (1978), experiments, the pipe diameter is limited to 1” and 2”, while in Gregory and Scott (1969), the pipe diameter is 0.75” and 1.38”. In the current model, the pipe diameter is 3.15”, much larger than their experiments.
The overprediction by Gregory et al. (1978) model could be attributed to the fact that they used mixture velocity, U_{M}, as the only correlating parameter, even though all other components of parameters fit within the range of the present case.
The underprediction of liquid holdup by Gregory and Scott (1969) could be attributed to the range of superficial velocities they had chosen even though it is within the slug flow regime.
The mean liquid holdup from the present study is compared with eight reported experimental correlations in Table X. The percentile error is calculated based on the correlation model from the present study. It should be mentioned here that the present correlation is obtained by fitting the curve using the Excel polynomial trend line function. The least square residual from fitting the present numerical data yield R^{2} = 0.9996, showing that the polynomial is a good fit.
Figure 25 shows the liquid holdup versus superficial gas velocity at various superficial liquid velocity. The liquid holdup increases with an increase in superficial liquid velocity. Also, the liquid holdup continuously decreases with an increase in superficial gas velocity for a given various liquid superficial velocities. However, the slug behavior can be explained at low gas superficial velocity. The flow regime can be defined as bubbly flow. The short gas bubbles separated by short oil plug with high values of holdup, and the increase in gas velocity leads the typical of slug flow to longer gas bubbles and the liquid holdup in the slug body gets lower.
Figure 26 illustrates an increase in superficial liquid velocity for a given superficial gas velocity leads to an increase in the liquid holdup value. Also, the liquid holdup decreases with an increase in superficial gas velocity.
3.3.5 Slug frequency.
Slug holdup and slug frequency are important parameters for predicting the gasliquid two phase flow in pipe. The frequency of slug flow in the pipeline is described as the number of slugs traversed at a specific point along a horizontal and inclined pipes over a certain period.
Figure 27 shows the comparison of the present model with the correlations in Table XI at U_{SL} = 0.2 m/s. The numerical results are compared to seven experimental correlations available in literature and the comparison showed a reasonable agreement with correlations by Greskovich and Shrier (1972), Gregory and Scott (1969) and Perez et al. (2010). A substantial difference, almost 100 per cent deviation, is found with the correlation by Gokcal et al. (2009) correlation, which is valid only for high viscosity oil. Table XI shows the correlation developed from the present model and its comparison to five other correlations. The percentile error was calculated based on the correlation model from the present study. It should be mentioned here that the present correlation is obtained by fitting the curve using the Excel polynomial trend line function. The least square residual from fitting the present numerical data yields R^{2} = 1, showing that the polynomial is a good fit. It is noticed that the best results one can obtain for slug frequency is about 20 per cent deviation.
Figure 28 illustrates the slug frequency plotted against superficial gas velocity for different oil superficial velocities. It can be seen that the slug frequency increases with the increase in superficial oil velocity. However, the slug frequency at first increases and then slightly decreases with the increase in gas superficial velocity. This happened because of the high liquid level in the pipe when superficial liquid velocity increase, which makes the frequency of the slug sensitive to the change in gas superficial velocity. After certain value, the gas phase suppresses liquid holdup. So, the results of slug frequency were decreased.
4. Conclusions
The transition of flow regime into another is a very common phenomenon in pipeline networks, which is potentially hazardous for the structural integrity of the pipeline. The understanding of flow regime and its underlying physics is therefore, of prime importance to oil/gas operator. All the objectives of this study have been successfully achieved. The present CFD with VOF model was able to accurately predict all flow regimes presented in Baker (1954) chart, Taitel and Dukler (1976) and experimental study (Mohmmed, 2016).
Quantitative validation using experimental data from Mohmmed (2016) gives more confident to the correctness of the established methodology.
Comparison of density contour with De Schepper et al. (2008) and Rahimi et al. (2013) is generally favorable. However, De Schepper et al. (2008) density contour failed to show a formation of proper slug regime. Their annular flow contour showed almost no liquid film at the bottom of the pipe. On the other hand, Rahimi et al. (2013) density contour for plug, slug and bubble flow showed completely different flow pattern with great deviation from the conventional flow regime definition given by Baker (1954).
Once the modeling methodology was established, attention was turned to investigate of oilgas slug flow behavior in horizontal pipe. Pressure gradient, slug liquid holdup and slug frequency were numerically simulated and compared to existing correlations in the literature to gauge and quantify the deviation of numerical results from experimental correlations. The present numerical models were found to produce favorable and agreeable comparison with majority of experimental correlations. At the same time, few exceptional experimental correlations were also identified, which were not applicable to the range and limits of the present investigation.
Oilgas slug flow behavior in horizontal pipe with 3.15inch ID and 8m length was generated respected to Baker chart. The evolution of slug for oil and gas two phase flow was observed as early as 0.5 sections with increasing slug length as time increased to 3.5 s.
Pressure gradient from the present model compares favorably with simplified Orell (2005) model and the Petalas and Aziz (2000) model.
Liquid holdup correlation from the present model compares favorably with four experimental correlations, and moderately favorable with Felizola and Shoham (1995) and Gregory and Scott (1969) with error 28 and 20 per cent, respectively. The experimental correlations from Gomez et al. (2000) and Gregory et al. (1978) produced an error in exceed of 60 per cent when compared with the present numerical model.
The slug frequency correlation from the present model compares favorably with the correlations from Perez et al. (2010), Greskovich and Shrier (1972) and Gregory and Scott (1969) with an error below 20 per cent. The model from Zabaras (1999) produced an error of 33per cent, while Gokcal et al. (2009) produced an error of 90 per cent.
Predictive models were proposed for pressure gradient, liquid holdup and slug frequency. Pressure gradient increased with increasing gas superficial velocity for each constant liquid superficial velocity. The slug liquid holdup decreased with increasing gas superficial velocity however increased with increasing liquid superficial velocity. Furthermore, slug frequency was observed to decrease with increasing gas superficial velocity for each constant liquid superficial velocity.
Figures
Figure 7.
Comparisons between present models of mixture density in horizontal pipe layout (kg/m^{3}) for airwater flow with the model of De Schepper et al. (2008)
Figure 8.
Comparisons between present models of mixture density in horizontal pipe layout (kg/m^{3}) for airwater flow with the model of Rahimi et al. (2013)
Figure 9.
Comparison of the CFD simulation data with Taitel and Dukler (1976) map for airwater twophase flow in horizontal pipe
Figure 14.
The comparison of translational slug velocity between present model and experimental data (Mohmmed, 2016) for different gas and liquid superficial velocities
Figure 15.
The comparison of mean liquid slug length between present model and experimental data (Mohmmed, 2016) measured at the section 54D
Figure 16.
The comparison of mean liquid slug length between present model and experimental data (Mohmmed, 2016) measured at the section 81D
Figure 17.
Comparison of liquid slug frequency between present model and experimental data (Mohmmed, 2016) at section 54D
Figure 18.
Comparison of mean liquid slug frequency between present model and experimental data (Mohmmed, 2016) at the section 81D
Figure 22.
Pressure gradient comparison between the simplified Orell (2005) model, the Petalas and Aziz (2000) model and CFD model for U_{SL}= 0.05 m/s
Figure 24.
Comparison between CFD simulation result of liquid holdup at U_{SL} = 0.3 m/s and the theoretical models of Gomez et al. (2000), Felizola and Shoham (1995), Kokal and Stanislav (1989), Gregory et al. (1978), Mattar and Gregory (1974), Gregory and Scott (1969), Neal and Bankoff (1965) and Nicklin et al. (1962)
Figure 27.
Comparison between CFD simulation result of frequency at U_{SL} = 0.2 m/s and the theoretical models of Perez et al. (2010), Gokcal et al. (2009), Zabaras (1999), Greskovich and Shrier (1972) and Gregory and Scott (1969)
Slug liquid holdup correlations, H_{Ls}
Author  D (m)  L (m)  θ (^{o})  U_{SL} (m/s)  U_{SG} (m/s)  Fluids  p (kPa)  H_{Ls} () 

Gomez et al. (2000)^{a}  0.0510.203  15418  090  0.1, 0.2, 0.5, 1, 1.02  1, 1.05, 1.07, 1.98, 2, 2.22, 3.02  Air^{c}water^{d}, Air^{c}kerosene^{e}, Air^{c}light oil^{f}  1502000 

Felizola and Shoham (1995)  0.051  15  090  0.05, 0.1, 0.5, 1.0, 1.5  0.5, 1.0, 2, 3  Air^{c}kerosene^{e}  250 
(θ = 0^{°}, horizontal flow) 
Kokal and Stanislav (1989)^{b}  0.0258, 0.0512, 0.0763  25  0, ±1, ±5, ±9  0.033  0.415.3  Air^{c}light oil^{f}  230350 

Gregory et al. (1978)  0.02580.0512  15, 17  0  0.032.32  0.0915.37  Air^{c}light oil^{f}  255, 3.45 

Mattar and Gregory (1974)  0.0254  27.43  0, 3, 6, 10  0.091.52  0.37.62  Air^{c}light oil^{f}  0345 

Gregory and Scott (1969)  0.01905, 0.0351  –  0  0.4421.3  1.057.7  Carbon dioxide^{g}water^{d}  101.325 

Neal and Bankoff (1965)  0.0254  1.524  090  0.430.9  0.53  Mercurynitrogen  101.325 

Nicklin et al. (1962)  0.057  1.83  90  0.120.27  0.0030.12  Air^{c}water^{d}  101.325 

where Re = (ρ_{L} U_{M} D)/µ_{L} and 0 ≤ θ ≤ π/2;
Density of air ρ_{G} = 1.225 kg/m^{3};
Density of water ρ_{L} = 998.2 kg/m^{3} and Viscosity of water µ_{L} = 0.001003 Pa s;
Density of kerosene ρ_{L} = 800 kg/m^{3} and Viscosity of kerosene µ_{L} = 0.0016 Pa s;
Density of light oil ρ_{L} = 858 kg/m^{3} and Viscosity of light oil µ_{L} = 0.007 Pa s;
Density of carbon dioxide ρ_{G} = 1.98 kg/m^{3}
Correlations for the slug frequency, f_{s}
Author  D (m)  L (m)  θ (^{o})  U_{SL} (m/s)  U_{SG} (m/s)  Fluids  p (kPa)  f_{s} (sec^{−1}) 

Perez et al. (2010)  0.067  6  090  0.12.5  0.540  Air^{c}water^{d}  600 

Gokcal et al. (2009)^{a}  0.0508  18.9  090  0.050.8  0.12  Air^{c}high oile  758.42 

AlSafran (2009)  0.0508  420  0  0.061.25  0.644.3  Air^{c}mineral oil^{f}  – 

Zabaras (1999)  0.0254, 0.1016  –  011  –  –  Air^{c}water^{d}  – 

Greskovich and Shrier (1972)^{b}  0.0381, 0.1524  –  0  –  –  Air^{c}water^{d}  – 

Gregory and Scott (1969)  0.01905, 0.0351  –  0  0.4421.3  1.057.7  Carbon dioxide^{g}water^{d}  101.325 

where
Density of air ρ_{G} = 1.225 kg/m^{3};
Density of water ρ_{L} = 998.2 kg/m^{3} and Viscosity of water µ_{L} = 0.001003 Pa s;
Density of high oil ρ_{L} = 889 kg/m^{3} and Viscosity of high oil µ_{L} = 0.1810.589 Pa s;
Density of paraffinic mineral oil ρ_{L} = 890.6 kg/m^{3} and Viscosity of paraffinic mineral oil µ_{L} = 0.0102 Pa s;
Density of carbon dioxide ρ_{G} = 1.98 kg/m^{3}
ICEMCFD and FLUENT criteria to determine acceptable mesh quality
CFD tool  Key factor  Requirement  Lowest mesh quality  Optimum mesh for the study 

ICEMCFD  Minimum determinant  >0.2  0.71  0.74 
Minimum angle  Preferably >18^{o}  46.71  47.88  
FLUENT  Maximum aspect ratio  <40  11.58  11.6 
Minimum orthogonal quality  >0.01 (best cells closer to 1)  0.75  0.8 
Source: Fluent (2016); ICEM (2016)
The different number of elements with convergent criteria of pressure gradient
No. of elements  Pressure gradient, dp/dx (kPa/m) 

65,000  0.2243 
1,02,300  0.2452 
2,12,800  0.6758 
3,03,690  0.8059 
5,22,500  0.8505 
6,29,300  0.8521 
15,36,000  0.8543 
Selected operating conditions for the waterair simulations
Flow regime  G_{G}/λ (kg/(m^{2} s))  G_{G} (kg/(m^{2} s))  U_{SG} (m/s)  G_{L}λψ/G_{G}  G_{L} (kg/(m^{2} s))  U_{SL} (m/s) 

Stratified  1.5  1.5  1.22  2  3  0.003 
Wavy  25  25  20.41  0.25  6.25  0.0063 
Plug  0.2  0.2  0.16  5000  1000  1 
Slug  4  4  3.26  100  400  0.4 
Annular  20  20  16.33  10  200  0.2 
Bubble  40  40  32.65  1000  40,000  40.1 
Spray  105  105  85.71  11  1,155  1.16 
Physical properties of waterair
Operating phase  ρ (kg/m^{3})  µ (Pa s)  σ (N/m) 

Water  998.2  0.001003  0.0719404 
Air  1.225  1.7894e05 
Physical properties of air and water in the experiment (Mohmmed, 2016)
Operating phase  ρ (kg/m^{3})  µ (Pa s)  σ (N/m) 

Water  998.6  0.08899  0.074 
Air  1.185  0.001831  – 
Range of operating conditions for the oil and gas slug simulations
Flow regime  G_{G}/λ (kg/(m^{2} s))  G_{G} (kg/(m^{2} s))  U_{SG} (m/s)  G_{L}λψ/G_{G}  G_{L} (kg/(m^{2} s))  U_{SL} (m/s) 

Slug flow  1.027.62  3.4225.65  0.21.5  39.31768.48  40.52243.09  0.050.3 
Physical properties of oil and gas
Operating phase  ρ (kg/m^{3})  µ (Pa s)  σ (N/m) 

Oil  810.3  0.004652  0.018653 
Vapor  17.1  0.0000115 
Comparison of slug liquid holdup correlations, H_{LS} and the percentile deviation
Author  H_{LS} ()  Error (%) 

Present study 


Gomez et al. (2000)^{a} 

65.64 
Felizola and Shoham (1995) 

28 
Kokal and Stanislav (1989)^{b} 

9.95 
Gregory et al. (1978) 

62.2 
Mattar and Gregory (1974) 

9.52 
Gregory and Scott (1969) 

19.93 
Neal and Bankoff (1965) 

1.64 
Nicklin et al. (1962) 

6.93 
where Re = (ρ_{L} U_{M} D)/µ_{L} and 0 ≤ θ ≤ π/2;
Comparison of correlations for the slug frequency f_{S}, and percentile deviation
Reference  f_{S} (Hz)  Error (%) 

Present study 


Perez et al. (2010) 

19.86 
Gokcal et al. (2009)^{a} 

90.49 
Zabaras (1999) 

33 
Greskovich and Shrier (1972)^{b} 

19.65 
Gregory and Scott (1969) 

19.86 
where
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Acknowledgements
The authors appreciate the financial and administrative support from the Universiti Teknologi PETRONAS (UTP) through the Graduate Assistantship Program to Cambodian national (first author), Ministry of Education Malaysia through the FRGS 0153ABL03 and PETRONAS Foundation through YUTP Fundamental Research Grant 0153AAE03. The authors would also like to acknowledge the UTP Gas Separation Research Centre for the office space, software licenses and highend computing facilities to perform the simulation.