Study on hydrodynamic slug flow mitigation with wavy pipe using a 3D–1D coupling approach

Computers & Fluids 99 (2014) 104–115

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Computers & Fluids j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d

Study on hydrodynamic slug flow mitigation with wavy pipe using a 3D–1D coupling approach Lanchang Xing a,b,⇑, Hoi Yeung b, Yanfeng Geng a, Yi Cao b, Joseph Shen c a

College of Information and Control Engineering, China University of Petroleum, Qingdao 266580, China Process Systems Engineering Group, School of Engineering, Cranfield University, Bedfordshire MK43 0AL, United Kingdom c Chevron Energy Technology Company, Houston, TX 77002, United States b

a r t i c l e

i n f o

Article history: Received 16 December 2012 Received in revised form 30 August 2013 Accepted 22 April 2014 Available online 2 May 2014 Keywords: Hydrodynamic slug flow 3D–1D coupling CFD STAR–OLGA coupling Slug mitigation Wavy pipe

a b s t r a c t Objective: A wavy pipe, constructed by connecting standard piping bends in series in one plane, was proposed to mitigate hydrodynamic slug flows in horizontal pipelines. Methods: A newly developed 3D–1D co-simulation method, i.e. STAR–OLGA coupling, was applied to model the wavy-pipe systems experiencing hydrodynamic slug flows. The flow characteristics of slug flow in the wavy-pipe systems were investigated, through which the effectiveness of the wavy pipe on slug mitigation and how the geometrical parameters of the wavy pipe affecting its performance were examined. Results: It has been found that the upstream liquid slug degenerates into a ‘liquid dense zone’ of a greater length downstream of the wavy pipe due to the gas penetration into the slug body. A reduction of the effective density of the ‘liquid dense zone’ from that of the upstream slug body is resultant showing the effectiveness of the wavy pipe on mitigating the adverse impacts of slug flow. The amount of gas penetration increases then decreases with the increasing wavy-pipe amplitude indicating that excessively higher amplitude is even less effective on introducing the gas phase into the slug body. Differently a wavy pipe with the same amplitude but a greater length, i.e. more bends, is more effective. Conclusions: It is concluded that the wavy pipe works by reducing the effective density of the liquid slug through introducing the gas phase into the slug body in the push-out process in each bend of the wavy pipe and the geometrical parameters need to be designed properly in specific applications. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Gas/liquid slug flow is frequently encountered during the transportation of oil and gas in pipelines. There is usually a significant length of multiphase flowline upstream of the processing facilities in the offshore production systems and it often happens that significant gas surges and liquid slugs are generated in the flowline. The liquid slugs generated in oil and gas multiphase flowlines can be classified into three different types based on their initiation mechanisms [1,2]:  Terrain-induced slugs: caused by periodic accumulation and purging of liquid in elevation changes along the flowline, particularly at low flowrates.

⇑ Corresponding author at: College of Information and Control Engineering, China University of Petroleum, Qingdao 266580, China. Tel.: +86 18561597851. E-mail addresses: [email protected], [email protected] (L. Xing). http://dx.doi.org/10.1016/j.compfluid.2014.04.023 0045-7930/Ó 2014 Elsevier Ltd. All rights reserved.

 Hydrodynamic slugs: formed due to wave instabilities at the gas/ liquid interface and grow or shrink depending on the flowline topography.  Operation-induced slugs: formed in the system during the operation transfer between steady state and transient state such as start-up or pigging operations. The terrain-induced slugs mainly include hilly-terrain-induced slugs and riser-induced slugs. The corresponding flow regimes are ‘hilly-terrain-induced slugging’ and ‘riser-induced slugging’, respectively. The ‘riser-induced slugging’ is often called ‘severe slugging’, while the flow regime corresponding to the hydrodynamic slugs is called ‘hydrodynamic slug flow’. All the three types of slugs may be encountered in a multiphase flowline during the life span of a production well. At the early and late stages of production terrain-induced slugs may form due to the low gas and liquid flowrates, while hydrodynamic slugs may appear at the middle stage and operation-induced slugs may be induced by the startup and regular pigging operations throughout the life span.

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Slug mitigation has become one of the most challenging topics of flow assurance in oil and gas production systems [3–6]. For severe slugging in pipeline/riser systems the fast moving liquid slugs of great lengths and violent gas surges may cause serious problems to the production system, such as flooding of downstream processing facilities, severe pipe corrosion and structural instability of the pipeline, production loss and poor reservoir management [7,8]. Vázquez and Fairuzov [9] conducted a theoretical and experimental study to investigate the effects of the riser on the dynamics of the hydrodynamic slugs longer than the riser. A transient mechanistic model was developed and then used to simulate the hydrodynamic slug flow in an offshore production system with a large-diameter pipeline of 36 in. It was found that the long slugs can accelerate in the riser to a velocity of five times greater than the average slug velocity in the pipeline. Therefore, hydrodynamic slugs in pipeline/riser systems can be as problematic as those in severe slugging due to their great lengths and high velocities. The major methods for mitigating severe slugging in the literature can be grouped into two categories: Active and passive slug mitigation, based on whether the ‘external interference’ is needed or not in the operation [10]. An external interference is essential to the implementation of the active methods [11–15]. The passive methods usually take the form of design changes to the facility itself such as sizing of slug catcher, gas lifting by rerouting the gas in the pipeline to the riser [7] and flow regime modification by a flow conditioner in the pipeline [16,17]. The function of the passive methods can be achieved without any external interference. A new flow conditioner, a wavy pipe layout, was proposed to modify the stratified flow in the pipeline so as to mitigate severe slugging in pipeline/riser systems. The performance and working principle of the wavy pipe on severe slugging mitigation such as reducing the severe slugging region and severity of the resultant problems to the production systems have been investigated experimentally and numerically [8,10,18]. In the work reported in this paper the newly developed wavy pipe layout previously used for severe slugging mitigation was applied to hydrodynamic slug flow in horizontal pipelines. The effectiveness of the wavy pipe on mitigating hydrodynamic slug flow and the effects of the wavy-pipe geometrical parameters were investigated through numerical modelling and experiment. It is still a challenge to predict the slug flow characteristics accurately for a wide range of pipeline configurations and flow conditions

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with models. OLGA is one of the multiphase flow simulation codes widely used in the oil and gas industry [19]. Essentially OLGA is a transient one-dimensional (1D) modified two-fluid model [20,21]. The slug tracking model in OLGA is capable of predicting the characteristic parameters of slug flow such as slug length, liquid holdup in the slug body and void fraction in the elongated bubble region. However, OLGA models cannot provide details of the phase distribution in the pipeline. CFD (Computational Fluid Dynamics) plays an important role in exploring the underlying physics and flow characteristics of the multiple phases in multiphase flow because the flow field in the two-dimensional (2D) and three-dimensional (3D) spaces can be exhibited [22–24]. However, CFD models are computationally expensive to obtain the time dependent solutions for slug flows in long pipelines. It is an interesting idea to make the most of the advantages of the 1D and 3D models for achieving a tradeoff between the computation speed and details of the model solutions. Recently, a 3D–1D modelling method, CFD–OLGA coupling, has been developed and validated with a case study on slug flow induced forces on pipe bends [25,26]. In this work the wavypipe system experiencing hydrodynamic slug flows were modelled with the CFD–OLGA coupling method. In the coupling model the wavy pipe was modelled with a 3D CFD code, STAR-CCM+ [25], while the upstream and downstream pipelines were modelled with a 1D code OLGA [19]. The flow characteristics in the wavy pipe, upstream and downstream were presented by the 3D model, through which the effects of the wavy-pipe geometrical parameters were examined. This study lays a foundation for understanding the underlying physics of hydrodynamic slug flows in wavy pipes and for designing wavy pipes to mitigate the adverse impacts of hydrodynamic slug flows.

2. Experimental setup 2.1. Geometry of wavy pipe A wavy pipe is a pipe section constructed by connecting a series of standard piping bends in one plane. The elementary unit in a wavy pipe is one piping bend, which can be described with three geometrical parameters, i.e. the internal diameter of the tube (d), the bend radius (R) and the bend angle (a) as shown in Fig. 1(a). Different geometries can be created by joining several bends together in different manners. Four 90° bends connecting together

(c) Wavy pipe with 5 bends Fig. 1. Piping bend, doughnut geometry and wavy pipe.

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without any twist forms a doughnut geometry (Fig. 1(b)), having a circle central line with a radius of R. A wave-shaped pipe (Fig. 1(c)), or wavy pipe, can be made by twisting each connection between two bends by 180°. As illustrated in Fig. 1(c) the wavy pipe can be described by three geometrical parameters: amplitude (A), which is the maximum distance between the bend centreline and the centreline of wavy pipe; pitch (P), which is the distance between the adjacent two peaks or dips; length (L), which is the distance between the central points of the two ends of wavy pipe. Two-inch wavy pipes were constructed for experiment purpose. To visualise the flow development in the wavy pipe the 2in. wavy pipes were made of clear PVC components. The 2in. ‘bend’ was constructed by connecting one 90° elbow and two straight pipe sections at the two ends of the elbow as shown in Fig. 2(a). The geometrical parameters of such a ‘bend’ were: d = 0.052 m, R = 0.096 m, a = 90°. Fig. 2(b) shows the schematic of a 2in. wavy pipe with 7 bends. The geometrical parameters of the wavy pipe were: A = 0.057 m, P = 0.281 m, L = 1.061 m. Two elbows of 45° were placed at the two ends of the wavy pipe to ensure that the wavy pipe could match the upstream and downstream pipelines. 2.2. Two-phase flow test rig Experiments were conducted on the 2in. air/water two-phase flow test rig (as shown in Fig. 3) at the PSE (Process Systems Engineering) Laboratory at Cranfield University. A Worthington Simpson centrifugal pump with a maximum capacity of 40 m3/h and a

(a) 2in. bend

maximum discharge pressure of 5 barg was employed. The water was pumped into the flowline from a water tank with a capacity of 4.4 m3. The water flow to the flowline was controlled by the two valves located in the flowline and bypass line, respectively. The bypass line could direct a portion of the water from the pump outlet back to the tank. The other portion of the water passed the liquid metering station then mixed with the air flow at the mixing point. The air was supplied by a Screw Engineering compressor with a maximum supply capacity of 400 m3/h and a maximum discharge pressure of 10 barg. The compressed air accumulated in a tank receiver of 2.5 m3 to reduce the pressure fluctuation from the compressor. Then the air from the receiver flowed to the gas metering station through a needle valve. At the mixing point the air was fed into the water flow perpendicularly on the top of the pipeline. The air/water two-phase mixture flowed through the test section located 15 m (about 300d, d = 0.052 m, the pipe diameter) downstream of the mixing point. Then the two-phase flow was returned to the water tank, which was open to the atmosphere. The water flow was metered by an electromagnetic flow meter with a range of 0–4.5 m3/h. The air flow was metered by two turbine flow meters for the low and high flowrates, with measuring ranges of 1–8 m3/h and 6–60 m3/h, respectively. At the gas metering station the temperature and pressure were measured by pressure transducers and thermocouples, respectively. The test section consisted of a 2in. wavy pipe with 7 bends and a view section downstream as shown in Fig. 4. Four conductivity cells (A, B, C and D) provided a continuous measurement of the liquid holdup.

(b) 2in. wavy pipe with 7 bends

Fig. 2. Schematics of 2in. bend and 2in. wavy pipe with 7 bends.

Fig. 3. Schematic of the two-phase flow test rig.

Fig. 4. Schematic of the test section. A, B, C and D: Upstream and downstream conductivity cells.

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Each set of the conductivity cells employed in the experiment included one pair of ring electrodes flush-mounted to the pipe wall. The ring electrodes, with a width of 3.7 mm each, were made of stainless steel and spaced 17 mm apart to form one cell. 3. Development of the coupling model The STAR–OLGA coupling method was implemented in STARCCM+ v5.04 [25] and OLGA v5.3 [19]. To model the wavy-pipe system experiencing hydrodynamic slug flows, the wavy pipe was simulated in STAR-CCM+ and the pipelines upstream and downstream of the wavy pipe were simulated in OLGA. Compared with a pure OLGA model the coupling model is able to provide increased details of a specific part by replacing that part with a 3D element from a STAR-CCM+ model (called STAR model for brevity below). Compared with a pure 3D STAR model the computation time can be significantly reduced by applying the high-speed 1D code OLGA to the long sections of pipelines. Thus the coupling provides a good compromise between the speed of the 1D code and the amount of details obtained from the 3D code simulations.

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pipes with different amplitudes and lengths, respectively, were created as shown in Figs. 6 and 7. Wavy I has the same amplitude with the tested wavy pipe in the experiment. Wavy II and III are variants of Wavy I. Wavy II and III were obtained by extending each end of the bend in Wavy I by a straight pipe section with a length of 1d and 2d, respectively (d = 0.052 m, the pipe diameter). The amplitudes of Wavy I, Wavy II and Wavy III are 0.057 m, 0.095 m and 0.132 m, with the ratios of amplitude to diameter (A/d) of 1.1, 1.8 and 2.5, respectively. Three wavy pipes with 7, 5 and 3 bends were created for Wavy I. The lengths of the three wavy pipes are 1.061 m, 0.857 and 0.575, with the ratios of length to diameter (L/d) of 20.4, 16.5 and 11.1, respectively. It needs to be mentioned that there were two pipe sections with lengths of 2 m upstream and downstream of the wavy pipe in the STAR model, respectively. Both of the pipe sections were used for monitoring the flow characteristics upstream and downstream of the wavy pipe. The upstream and downstream OLGA pipes were 20 m long. Longer pipes than the experiment were used to allow for the establishment of a steady hydrodynamic slug flow and increase the numerical stability of the model. 3.2. Boundary conditions

3.1. Model geometry A schematic of the coupling model for the wavy-pipe system is shown in Fig. 5. The outlet of the upstream OLGA pipe (called OUTLET-1) is coupled with the inlet of the STAR pipe and the outlet of the STAR pipe is coupled with the inlet of the downstream OLGA pipe (called SOUR-2). The fluids enter the computation domain at the inlet of the upstream OLGA pipe (called SOUR-1), flow down the upstream OLGA pipe model, into the STAR pipe model and finally into the downstream OLGA pipe model. Two groups of wavy

The inlet boundary conditions of the STAR–OLGA coupling model shown in Fig. 5 were specified at the inlet of the upstream OLGA pipe (SOUR-1) and the outlet boundary conditions were specified at the outlet of the downstream OLGA pipe (OUTLET-2). Both of the upstream and downstream OLGA pipe models have the same boundary types, i.e. mass flow inlet and pressure outlet. At the coupling points, i.e. OUTLET-1/Inlet and Outlet/SOUR-2, the boundary conditions of the STAR pipe model were set to be provided by the upstream and downstream OLGA pipe models, respec-

Fig. 5. Schematic of the STAR–OLGA coupling model.

(a) Wavy I (A/d = 1.1)

(b) Wavy II (A/d = 1.8)

(c) Wavy III (A/d = 2.5) Fig. 6. Schematics of the wavy pipes with different amplitudes (Wavy I, Wavy II and Wavy III with 7 bends).

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(a) 7 bends (L/d = 20.4)

(b) 5 bends (L/d = 16.5)

(c) 3 bends (L/d = 11.1) Fig. 7. Schematics of the wavy pipes with different number of bends (Wavy I).

tively. The specific physical parameters exchanged between the STAR and OLGA models at the coupling points are determined by the boundary types. The upstream and downstream OLGA models have a mass flow inlet and pressure outlet while the STAR model has a velocity inlet and a pressure outlet. The parameters received by the STAR model from the OLGA models include [25,26]: (a) mass flux, velocity and density of each phase from the upstream OLGA model; (b) mass flux of each phase (if there is reverse flow from OLGA to STAR), pressure and temperature from the downstream OLGA model. At the coupling point I in Fig. 5 the 1D data from the outlet boundary of the upstream OLGA model have to be converted into 3D data for the inlet boundary of the STAR model and the 3D data from the inlet of the STAR model need to be converted into 1D data for the outlet boundary of the upstream OLGA model. Similar conversions are required to be conducted at the coupling point II. The conversion of the 1D data from the upstream OLGA model to 3D data for the STAR model inlet boundary is achieved by assuming that the phases are distributed as stratified layers. The position and occupied area of each phase on the cross section of the STAR model inlet are determined according to their densities and volume fractions. The pressure and temperature from the downstream OLGA model are applied uniformly on the cross section of the STAR model outlet. The 3D data from the STAR model inlet and outlet are averaged and then sent to the upstream and downstream OLGA models as the outlet and inlet boundary conditions, respectively. It needs to be stressed that the assumption of the phase distribution as stratified layers on the cross section at the inlet of the STAR pipe model is reasonably realistic for the slug body and slug tail, while the slug front has not been represented well due to the high-degree turbulence and more evenly distributed gas bubbles. However, the adverse impacts of this assumption can be alleviated by extending the pipe section between the inlets of the STAR pipe and wavy pipe. In this pipe section the two-phase flow can develop further and the phases can re-distribute themselves before reaching the wavy pipe. Air and water were used as the test fluids and the mass flowrate of each phase was controlled to be constant upstream of the mix-

ing point during the experiment as introduced in Section 2.2. Therefore, in the coupling model air and water were assigned as the gas and liquid phase and constant mass flowrates were specified for each phase at the inlet of the upstream OLGA pipe (SOUR1) as the inlet boundary condition. The compressibility of the gas phase was taken into account by specifying the air to be a compressible ideal gas and the liquid phase had the same physical properties with those of water. As introduced in Section 2.2 the gas/liquid two-phase flow was returned to a water tank open to the atmosphere. Thus a standard atmospheric pressure was specified at the outlet of the downstream OLGA pipe (OUTLET-2) as the outlet boundary condition of the coupling model. The temperature change along the pipe sections in the coupling model was not considered. The same temperature, 20 °C, was specified at the inlet and outlet of the coupling model (SOUR-1 and OUTLET-2). 3.3. Physical models In the standard model of OLGA physically sharp liquid holdup fronts at slug fronts are smeared out numerically, especially in horizontal or near-horizontal transient flows (which is the case in this study). Hydrodynamic slugs are treated only in an average manner without giving any information on the characteristics of liquid slugs [19]. To obtain the characteristic parameters of hydrodynamic slug flow, in this work, the slug tracking model was employed in the OLGA pipe model in the STAR–OLGA coupling. The slug tracking model incorporated into OLGA is able to track and maintain the physically sharp fronts in hydrodynamic slug flows. With the slug tracking model incorporated, OLGA applies a hybrid Lagrangian–Eulerian scheme where a Lagrangian front tracking scheme is superimposed on a standard Eulerian model [19]. The movement, growth and disappearance of liquid slugs are realised by tracking individual slug. Each liquid slug is described with Lagrangian coordinates giving the position of the tail and the front as a function of time. K-Epsilon turbulence model was employed in the STAR model of the STAR–OLGA coupling model. A K-Epsilon model is a twoequation model in which transport equations are solved for the turbulent kinetic energy and its dissipation rate. The k–e models

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have become the most widely used model for industrial applications due to their robustness, economy and reasonable accuracy [25]. Among the variable K-Epsilon models available in STARCCM+ the Realizable K-Epsilon model [27] combined with the two-layer approach [28] was selected in the STAR model. It is claimed that the Realizable K-Epsilon model is substantially better than the standard K-Epsilon model for many applications and can generally be relied upon to give solutions that are at least as accurate [25]. In the two-layer approach the computation is divided into two layers. The turbulent viscosity and turbulent dissipation rate are represented as functions of the wall distance in the layer adjacent to the wall. The turbulent dissipation rates specified in the near-wall layer are blended smoothly with the values computed from solving the transport equation far from the wall. The equation for the turbulent kinetic energy is solved in the entire flow. The two-layer approach in STAR-CCM+ works with either low-Reynolds number type meshes or wall-function type meshes. Thus the two-layer approach adds more flexibility of an all y+ wall treatment to the Realizable K-Epsilon model. Volume of Fluid (VOF) model [29] is a simple multi-phase model that is well suited to simulating flows of several immiscible fluids on numerical grids capable of resolving the interface between the mixture’s phases. The VOF modelling is a surfacetracking technique applied to a fixed Eulerian mesh. The volume fraction of each fluid in each computational cell is tracked throughout the computational domain. The fluid properties and flow variables are assigned to each cell based on the volume fraction. The VOF approach has been successfully used for modelling the hydrodynamic slug flows and predicting the flow characteristics [22,23], thus it was also selected in this study to track the volume fraction of each phase of gas/liquid two-phase flow in the STAR model. The second-order discretization scheme was used to obtain sharp interfaces between the two phases. 3.4. Model solution The STAR model usually uses a smaller time step than the OLGA models. The data are exchanged at each time step of the OLGA model. Then the STAR model interpolates the data from OLGA for the intermediate steps. At the start of the calculation, the STAR solver runs for one time step to generate the boundary values for the OLGA solver. Then OLGA runs for two time steps with Dt apart to generate the data at t0 and t1. After that OLGA is allowed to choose its own time step within the upper and lower limits specified by the user. Then STAR will step from t0 to t1 interpolating the data from OLGA in between for boundary conditions. A fixed time-step scheme was used for the implicit unsteady solver in the STAR model; while the minimum and maximum time steps in the OLGA models were set properly with the time step in the STAR model as a reference. For the cases discussed below the time step in the STAR model was 0.001 s and the minimum/maximum time steps in the OLGA model were 0.001 s and 0.003 s respectively. A series of ‘plane sections’ were created along the STAR pipe model. The plane sections took the form of cross sections at the specified positions of interest. The area-averaged pressure and liquid holdup on the specific cross sections were monitored. The phase distribution on the cross sections, pipe wall and longitudinal section of the STAR pipe were also recorded in terms of gas volume fraction contour plots. The coupling models were solved by two computers in the same network. The calculation of the STAR model was conducted on the computational ‘‘Grid’’. The ‘‘Grid’’ compute nodes were HP DL160G5 servers running Linux. Each node had two dual-core processors. The STAR model was run in parallel on one compute node with 4 cores. The OLGA model was solved on a Windows desktop with a single-core processor. The IP (Internet Protocol) address of

Table 1 Meshes of the OLGA models.

Mesh Mesh Mesh Mesh Mesh

I II III IV V

Cell count

Cell size (m)

20 40 80 160 320

1.0 0.5 0.25 0.125 0.0625

the Windows desktop running OLGA was specified in the STAR model so that the Windows machine could be recognised by the Grid node running STAR-CCM+. All the data exchanged between the OLGA and STAR models were transmitted through the internet. 3.5. Mesh selection The meshes of the STAR and OLGA pipe models were selected based on the examination of the mesh dependency of the solutions following the procedures below: (1) The upstream OLGA pipe was divided into different numbers of sections, then a proper mesh for the upstream OLGA pipe model was selected (The mesh of the downstream OLGA pipe model is the same.); (2) A straight STAR pipe was discretised with different levels of meshes and the upstream/downstream OLGA pipes with the selected mesh were coupled with the straight STAR pipe with different levels of meshes, then an appropriate level of mesh for the STAR model was determined; (3) The wavy pipes were meshed with the same level of mesh with that of the straight STAR pipe. The mesh details of the OLGA and straight STAR pipe models are listed in Tables 1 and 2, respectively. The OLGA models and STAR–OLGA coupling models have been solved with a typical hydrodynamic slug flow case. The inlet mass flowrates for water and air are WL = 0.6360 kg/s and WG = 0.0051 kg/s, corresponding to superficial velocities of USL = 0.30 m/s and USG = 2.0 m/s (101,325 Pa and 20 °C), respectively. The characteristics of hydrodynamic slug flow such as slug frequency, gas entrainment in slug body and liquid film thickness can be obtained from the liquid holdup time traces. Therefore, the liquid holdup is of concern when examining the model solutions. As the outlet of the upstream OLGA pipe is coupled with the downstream STAR pipe, the liquid holdup at the last section of the upstream OLGA pipe is more important. Fig. 8(a) compares the liquid holdup at the last section of the OLGA pipe of different levels of meshes. It can be observed that there are significant differences among the liquid holdup time traces due to different levels of meshes. The model of Mesh I with 20 sections provides the worst predictions of the maximum/minimum liquid holdup compared with the others. The maximum and minimum have been under predicted and over predicted, respectively. Moreover, the distribution of gas/liquid two phases derived from the liquid holdup shows the distortion of the predicted slug and liquid film shapes. With the increase of the section count until 80 (Mesh III) the maximum liquid holdup increases and the minimum decreases. A further increase of the section counts to 160 and 320 for Mesh IV and Mesh V has not resulted in significant variations in the maximum/minimum liquid holdup, but only the shape

Table 2 Meshes of the STAR models.

Level 1 Level 2 Level 3

Total cell count

Cell count on the cross section

Average cell size on the cross section (10 6 m2)

78,000 128,000 190,000

156 256 380

13.6 8.30 5.59

L. Xing et al. / Computers & Fluids 99 (2014) 104–115

Liquid holdup H

L

Liquid holdup H

L

Liquid holdup H

L

Liquid holdup H

L

Liquid holdup H

L

110

1 20 sections 0.5 0 20 1

25

30

35 40 sections

0.5 0 20 1

25

30

35 80 sections

0.5 0 20 1

25

30

35 160 sections

0.5 0 20 1

25

30

35 320 sections

0.5 0 20

25

30

35

Flow time t, s

(a) Liquid holdup time traces Time step, s

-3

4

x 10

20 sections 3 2 1 20

25

30

35

Time step, s

-3

4

x 10

40 sections

3 2 1 20

25

30

35

Time step, s

-3

4

x 10

80 sections

3 2 1 20

25

30

35

Time step, s

-3

4

x 10

160 sections

3 2 1 20

25

30

35

Time step, s

-3

4

x 10

320 sections

3 2 1 20

25

30

35

Flow time t, s

(b) Time step series Fig. 8. Liquid holdup time traces and time step series obtained from the OLGA models with different levels of meshes (USL = 0.30 m/s, USG = 2.0 m/s).

of slugs. Based on the above discussion it is concluded that the upstream OLGA pipe model should have at least 80 sections. Fig. 8(b) shows the time step series adopted by the OLGA model

with Mesh I to Mesh V during the calculation. A time step control scheme based on the mass transport criterion of Courant–Friedrich–Levy (CFL) has been used in the OLGA model (SPT Group,

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with 256 cells on the cross section and the average cell size of 0.01 m in the axial direction of the pipe.

4. Results and discussion 4.1. Slug mitigation with wavy pipe The hydrodynamic slug flow was generated in the upstream OLGA pipe model and fed into the wavy pipe, then flowed into the downstream OLGA pipe. The liquid holdups upstream and downstream of the wavy pipe were monitored in the STAR model during the calculation. The phase distribution on the pipe wall and longitudinal section of the STAR pipe model were recorded in terms of gas volume fraction contour plots. Fig. 10 compares the liquid holdup upstream and downstream of the wavy pipe (Wavy I with 7 bends) between the model predictions and experimental data. The inlet mass flowrates for water and air are WL = 0.9964 kg/s and WG = 0.0052 kg/s, corresponding to superficial velocities of USL = 0.47 m/s and USG = 2.05 m/s (101,325 Pa and 20 °C), respectively. It can be seen in Fig. 10(a) that the slug frequency predicted by the coupling model agrees with the experimental data reasonably well. The average slug frequencies obtained from the experimental data and model prediction are 0.7921 Hz and 0.7984 Hz respectively. For most of the slug units the maximum liquid holdup in slug body and the minimum in liquid film are under predicted by the model. The predicted minimum liquid holdup in the elongated bubble region is about 0.03 while in the experimental data it is about 0.17. The lower liquid holdup in the liquid film indicates that a certain amount of liquid has gone into the slug body. Consequently, the predicted liquid slugs are longer than those in the experiment. The longer liquid slugs can be evidenced by the longer duration time of slug body

1.4

Experiment Simulation

L

1.2

Liquid holdup H

2006). Based on the CFL criterion the time step is adjusted to ensure that no mass is transported across a whole section of the OLGA pipe within one time step. This means that a smaller time step is required for a finer mesh. The upper and lower limits of the time step are specified by the user, for example 0.003 s and 0.001 s in the sample case, respectively. It can be seen in Fig. 8(b) that the time steps for Mesh I of 20 sections to Mesh III of 80 sections are limited by the user-specified upper limit, 0.003 s. For Mesh IV of 160 sections and Mesh V of 320 sections the time step varies with the passage of the liquid slugs and films between the user-specified lower and upper limits. Compared with Mesh IV even smaller time steps are required by Mesh V. A ‘smoother’ time step series is more favourable to improve the numerical stability of the coupling model. Furthermore, the time step of the STAR model is usually smaller than that of the OLGA model. Therefore, larger time steps of the OLGA model are preferable to reduce the total computation time of the coupling model. Mesh IV and Mesh V are not recommended for the above reasons. To summarise, the OLGA model with Mesh III of 80 sections provides reasonable predictions of the liquid holdup (Fig. 8(a)) and can reduce the computation time of the coupling model compared with Mesh IV and Mesh V. Therefore, Mesh III of 80 sections was selected for the upstream and downstream OLGA pipe models. The OLGA model with Mesh III of 80 sections was then coupled with the straight STAR pipe model of different levels of meshes as listed in Table 2. The straight pipe is 6 m long and has the same diameter with the wavy pipe (d = 0.052 m). Fig. 9 compares the time traces of liquid holdup in the STAR pipe predicted by the coupling model of different meshes. Four slug units including slug bodies and elongated bubble regions have been shown in the figure. It can be observed that the major differences among the three predictions take place in the elongated bubble regions. The liquid holdup in slug body agrees with each other reasonably well except that the maximum liquid holdup of the last slug from the coarse mesh (Level 1) is much lower than that from the other two meshes. It needs to be noted that the liquid holdup in the elongated bubble regions with the medium mesh (Level 2) and fine mesh (Level 3) agree with each other reasonably well but the liquid holdup with the coarse mesh behaves differently. To summarise, the coarse mesh is abandoned because the prediction of the liquid holdup in both slug body and liquid film deviates from that from the medium and fine meshes. Compared with the medium mesh the cell count of the fine mesh has increased by about 50%, but there is only slight improvement on the prediction of liquid holdup in elongated bubble regions. Therefore, the medium mesh (Level 2) was selected for the straight STAR pipe model. In the coupling models discussed below the upstream and downstream OLGA pipe models were divided into 80 sections with 0.25 m for each section and the STAR pipe (wavy pipe) was meshed

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Fig. 10. Comparison of the liquid holdup upstream and downstream of the wavy pipe between the model predictions and experimental data (USL = 0.47 m/s, USG = 2.05 m/s).

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indicated by the liquid holdup time traces in Fig. 10(a). Similarly the maximum and minimum liquid holdup downstream of the wavy pipe are also under predicted by the coupling model as shown in Fig. 10(b). It can be observed through the comparison between Fig. 10(a) and (b) that the maximum liquid holdup in slug body downstream of the wavy pipe is lower than that upstream in both experiment and model predictions. The reduction of the maximum liquid holdup in slug body reflects the increase of the gas penetration into slug body. However, the gas penetration into slug body tends to be over predicted by the model compared with the experimental data. To summarise, the coupling model is capable of predicting the phenomenon that an increase of the gas penetration into slug body is induced by a wavy pipe although the effects tend to be over predicted. The phase distribution in the wavy pipe, upstream and downstream pipe sections has been presented to examine how the two phases interact with each other and with the wavy pipe. It is still a challenge to measure the phase distribution on cross sections through experimental means; however, this can be achieved by monitoring the phase fraction in the 3D STAR model. The contour plots of the gas volume fraction when a liquid slug appears upstream of the wavy pipe, in the wavy pipe and downstream of the wavy pipe are shown in Figs. 11–13, respectively. In each figure there are two contour plots showing the gas volume fraction on the pipe wall and on the longitudinal section of the pipe, respectively. The slug flow is generated in the upstream OLGA pipe and then fed into the STAR pipe. A liquid slug body followed by a elongated bubble region in the pipe section upstream of the wavy pipe is shown in Fig. 11. The gas phase in the slug body is mainly located at the top and significant gas entrainment in the slug front can be observed. After the slug body moves into the wavy pipe the liquid phase tends to slow down and accumulate in the first upward limb. Consequently the flow path of the gas in the following elongated bubble region is blocked at the trough of the first bend. However, the blockage cannot maintain because the gas keeps moving in and accumulates there. Then the liquid in the first upward limb is pushed into the next bend. This push-out process provides an opportunity for the gas phase to penetrate into the liquid and the penetration effect can be enhanced by the following bends as shown in Fig. 12. Eventually a highly aerated ‘slug’ comes out of the wavy pipe. The highly aerated ‘slug’ can be identified as a ‘liquid dense zone’ downstream of the wavy pipe as shown in Fig. 13. The ‘liquid dense zone’ here refers to a fluid region downstream of the wavy pipe, where the liquid holdup is higher than

that in the elongated bubble region of the corresponding slug unit (including a liquid slug body and an elongated bubble region) upstream. The ‘liquid dense zone’ can be divided into two subzones: Zone I and Zone II. As can be observed in Fig. 13 Zone I is occupied by a gas/liquid mixture while Zone II is characterised by a gas core and a swirling flow of liquid and gas/liquid mixture. To examine the flow characteristics at Zone II the gas volume fraction contour plot on a cross section is shown (1.0 m downstream) in Fig. 14. It can be seen in Fig. 14 that: (a) A liquid film attaches to the pipe wall; (b) A gas core forms in a region close to the pipe centre; (c) A two-phase flow mixture of swirling behaviour is located between the gas core and liquid film. It is postulated that the swirling flow of liquid and gas/liquid mixture occurs as a result of the interaction between the gas/liquid two phases and the bends of the wavy pipe. In the swirling flow the liquid phase tends to move towards the pipe wall due to its higher density and decelerates due to the friction of the wall. Consequently a thin liquid film forms and a ‘liquid dense zone’ longer than the corresponding slug body is produced. The effectiveness of the wavy pipe on mitigating hydrodynamic slug flow has been shown in both the experimental and simulation data. It has been found that the upstream liquid slug degenerates into a ‘liquid dense zone’ of a greater length downstream of the wavy pipe. Due to the gas penetration into the slug body in the push-out process the effective density of the ‘liquid dense zone’ becomes lower than that of the corresponding slug body upstream of the wavy pipe. As a result, the adverse impacts of the slug body on the downstream receiving facilities can be mitigated. It can be concluded that the wavy pipe works by reducing the effective density of the liquid slug through introducing the gas phase into the slug body in the push-out process in each bend of the wavy pipe. It is postulated that the performance of the wavy pipe for mitigating hydrodynamic slug flows is affected by the geometrical parameters of the wavy pipe such as amplitude and length. Therefore, the effects of the amplitude and length of the wavy pipe are examined in Section 4.2 and 4.3, respectively, through the STAR– OLGA coupling model. 4.2. Effects of the wavy-pipe amplitude Three wavy pipes with different amplitudes, i.e. Wavy I, Wavy II and Wavy III with 7 bends have been introduced in Fig. 6 in Section 3.1. The three wavy pipes with amplitudes of 1.1d, 1.8d and 2.5d were tested by applying the STAR–OLGA coupling models to

Fig. 11. Contour plots of the gas volume fraction upstream of the wavy pipe (USL = 0.47 m/s, USG = 2.05 m/s; flow direction: from left to right).

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Fig. 12. Contour plots of the gas volume fraction in the wavy pipe (USL = 0.47 m/s, USG = 2.05 m/s; flow direction: from left to right).

Fig. 13. Contour plots of the gas volume fraction downstream of the wavy pipe (USL = 0.47 m/s, USG = 2.05 m/s; flow direction: from left to right).

examine the effects of the wavy-pipe amplitude. The inlet mass flowrates for water and air are WL = 2.0139 kg/s and WG = 0.0055 kg/s, corresponding to superficial velocities of USL = 0.95 m/s and USG = 2.14 m/s (101,325 Pa and 20 °C), respectively. The same flow conditions have been achieved upstream of the three wavy pipes. Therefore, the effects of the wavy-pipe amplitude can be identified by analysing the differences in the flow characteristics downstream. It has been found in Section 4.1 that the gas in the elongated bubble region can penetrate into the slug body in each push-out process during the travelling in the wavy pipe. As a result, the liquid slug upstream of the wavy pipe degenerates into a ‘liquid dense zone’ downstream of it. The liquid holdup and phase distribution in the ‘liquid dense zones’ have been compared among the three wavy-pipe systems. The maximum liquid holdup and the length of the ‘liquid dense zone’ are indicators of the amount of gas penetration into the slug body. Either a lower maximum liquid holdup or a greater length indicates more gas penetration into the slug body. More gas penetration results in an even lower effective density of the liquid slug, by which the adverse impacts of the slug flow can be mitigated further. The liquid holdup time traces downstream of the wavy pipe from the STAR pipe models are compared in Fig. 15 for the three wavy-pipe systems. The comparison among the ‘liquid dense

zones’ downstream of Wavy I, Wavy II and Wavy III are illustrated in Electronic Annex for brevity. The three ‘liquid dense zones’ are those with the maximum liquid holdup appearing between t = 13 s and t = 14 s in Fig. 15. Those ‘liquid dense zones’ correspond to the same slug upstream of the wavy pipes. Therefore, the effects of the wavy-pipe amplitude can be examined by comparing the characteristics of the ‘liquid dense zones’. The variations of the averaged maximum liquid holdup and length of the ‘liquid dense zone’ against the ratio of wavy-pipe amplitude to diameter are plotted in Fig. 16. It can be seen from Fig. 15 that, for most ‘liquid dense zones’, the highest maximum liquid holdup appears with Wavy III and the lowest can be obtained with Wavy II. The maximum liquid holdup decreases and then increases with the increase of the wavy-pipe amplitude from 1.1d to 1.8d until 2.5d, i.e. from Wavy I to Wavy III, as shown in Fig. 16. The longest ‘liquid dense zone’ appears downstream of Wavy II, followed by those of Wavy I and Wavy III. The length of the ‘liquid dense zone’ increases and then decreases with the increasing wavy-pipe amplitude from 1.1d to 1.8d until 2.5d, i.e. from Wavy I to Wavy III. To summarise the above it is worth noting that there is a non-monotonous relationship between the amount of gas penetration and wavy-pipe amplitude. A wavy pipe with excessively higher amplitude is even less

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effective on introducing the gas phase into the slug body. It is postulated that the liquid phase tends to accumulate in the longer upward limbs rather than mixing with the gas phase. The longer upward limbs allow for the liquid phase to accumulate therein leading to the formation of new liquid slugs. Therefore, the amplitude of the wavy pipe needs to be selected properly to obtain a better performance of slug mitigation for specific applications. 4.3. Effects of the wavy-pipe length

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The wavy pipes with different lengths, i.e. 7 bends, 5 bends and 3 bends have been introduced in Fig. 7 in Section 3.1. The three wavy pipes with lengths of 20.4d, 16.5d and 11.1d were tested to examine the effects of the wavy-pipe length by applying the coupling models. The inlet mass flowrates for water and air are WL = 2.0139 kg/s and WG = 0.0055 kg/s, corresponding to superficial velocities of USL = 0.95 m/s and USG = 2.14 m/s (101,325 Pa and 20 °C), respectively. The same flow conditions are achieved upstream of the three wavy pipes, thus the effects of the wavy-pipe length are identified by comparing the flow characteristics at the ‘liquid dense zones’ downstream. Fig. 17 illustrates the comparison among the liquid holdup time traces downstream of the wavy pipes from the STAR pipe models for Wavy I with 7, 5 and 3 bends. The ‘liquid dense zones’ downstream of Wavy I with different lengths are compared in Electronic Annex for brevity. The three ‘liquid dense zones’ are those with the maximum liquid holdup appearing between t = 10.2 s and t = 11 s in Fig. 17, which correspond to the same slug upstream of the wavy pipes. The variations of the averaged maximum liquid holdup and length of the ‘liquid dense zone’ against the ratio of wavy-pipe length to diameter are plotted in Fig. 18. As shown in Fig. 17, for most ‘liquid dense zones’, the highest maximum liquid holdup appears with the 3-bend wavy pipe and the lowest can be obtained with the 7-bend wavy pipe. The maximum liquid holdup decreases with the increasing length of wavy pipe from 11.1d to 16.5d until 20.4d, i.e. from 3 bends to 7 bends. It can be observed from Fig. 18 that the longest ‘liquid dense zone’ is obtained with the 7-bend wavy pipe, followed by the 5-bend wavy pipe and the shortest appears downstream of the 3-bend wavy pipe. The length of the ‘liquid dense zone’ increases with the increasing wavy-pipe length from 11.1d to 16.5d until 20.4d, i.e. from 3 bends to 7 bends. It can be summarised based on the above that there is a monotonous relationship between the amount of gas penetration and wavy-pipe length. A wavy pipe with the same amplitude but a greater length, i.e. more bends, is more effective on introducing the gas phase into the slug body, as such more favourable to reduce the effective density of the liquid slug. As analysed in Section 4.1 the push-out process in each bend of

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tion (ZR2013EEQ033) and the Fundamental Research Funds for the Central Universities (13CX02099A). The authors would like to express sincere thanks to the support and permission to publish this work from Chevron Energy Technology Company. The financial support from the Overseas Research Students Awards Scheme (ORSAS) and Cranfield University is also acknowledged. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.compfluid.2014. 04.023. References

Ratio of length to diameter L/d Fig. 18. Variations of the averaged maximum liquid holdup and length of the ‘liquid dense zone’ against the ratio of wavy-pipe length to diameter (Wavy I with 7, 5 and 3 bends; USL = 0.95 m/s, USG = 2.14 m/s).

the wavy pipe provides an opportunity for the gas to penetrate into the liquid. Thus the more bends of the wavy pipe provide more push-out processes for the gas/liquid two phases to interact with each other. Consequently more gas is able to penetrate into the liquid slug, resulting in more reduction in the effective density of slug body during the journey in the wavy pipe. However, it needs to be noted that the addition of the bends may be restricted by the requirement for space and mechanical stability in real applications. 5. Conclusions A wavy pipe was proposed to mitigate hydrodynamic slug flows in horizontal pipelines. A newly developed 3D–1D co-simulation method, i.e. STAR–OLGA coupling, was applied to model the wavy-pipe systems experiencing hydrodynamic slug flows. In the coupling model the wavy pipe was modelled with a 3D CFD code STAR-CCM+, while the upstream and downstream pipelines were modelled with a 1D code OLGA. The flow characteristics of slug flow in the wavy-pipe systems were investigated, through which the effectiveness of the wavy pipe on slug mitigation and the effects of the wavy-pipe geometrical parameters on its performance were examined. The following conclusions have been drawn: (1) The wavy pipe is effective on mitigating the adverse impacts of the hydrodynamic slug flow on the downstream receiving facilities. The upstream liquid slug degenerates into a ‘liquid dense zone’ of a greater length downstream of the wavy pipe due to the gas penetration into the slug body. The wavy pipe works by reducing the effective density of the liquid slug through introducing the gas phase into the slug body in the push-out process in each bend of the wavy pipe. (2) The effectiveness of the wavy pipe on slug mitigation is affected by the geometrical parameters. The amount of gas penetration increases then decreases with the increasing wavy-pipe amplitude indicating that excessively higher amplitude is even less effective on introducing the gas phase into the slug body. Differently a wavy pipe with the same amplitude but a greater length, i.e. more bends, is more effective. The wavy-pipe geometrical parameters need to be designed properly in specific applications.

Acknowledgements This work is supported by National Natural Science Foundation of China (51306212), Shandong Provincial Natural Science Founda-

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