Experimental and computational investigations on severe slugging in a catenary riser

Severe slugging can occur in a pipeline-riser system at relatively low liquid and gas flow rates during gas-oil transportation, possibly causing unexpected damage to the production facilities. Experiments with air and water are conducted in a horizontal and downward inclined pipeline followed by a catenary riser in order to investigate the mechanism and characteristics of severe slugging. A theoretical model is introduced to compare with the experiments. The results show that the formation mechanism of severe slugging in a catenary riser is different from that in a vertical riser due to the riser geometry and five flow patterns are obtained and analyzed. A gas-liquid mixture slug stage is observed at the beginning of one cycle of severe slugging, which is seldom noticed in previous studies. Based on both experiments and computations, the time period and variation of pressure amplitude of severe slugging are found closely related to the superficial gas velocity, implying that the gas velocity significantly influences the flow patterns in our experiments. Moreover, good agreements between the experimental data and the numerical results are shown in the stability curve and flow regime map, which can be a possible reference for design in an offshore oil-production system.


Introduction
During the exploitation of offshore oil and gas, the pipeline-riser system, including a downward inclined pipeline and a vertical riser or a catenary riser, is necessary for transporting oil (with some water) and associated gas from subsea wellheads up to offshore platform systems (Borges Sertã, 2004). It has been proved that such pipeline system can investigate various kinds of dynamics while transporting gas and oil (Blevins and Coughran, 2009;Li et al., 2010;Cifuentes and Kim, 2015;Fan et al., 2015;Bai et al., 2015Bai et al., , 2017. Besides, gas-liquid two-phase flow during the transportation can unavoidably lead to a phenomenon named severe slugging. Severe slugging arises when the gas-liquid flow streams from a pipeline into a riser at low rates of gas and liquid. The liquid slug that equals or exceeds the riser's length blocks the passage of the gas flow at the bottom of the riser (Schmidt et al., 1985;Fabre et al., 1990). As a result, the gas is compressed in the pipeline and the gas pressure keeps increasing with continuous gas income. Once the gas pressure is enough to counter the liquid slug, the gas begins to inject into the riser and the separator with liquid, resulting in a violent expulsion.
During the process of petroleum production, the production equipments can be damaged by such a severe slug flow, which can cause sudden fluctuations of pressure and flow mass in the pipeline-riser system, reducing the production capability (Sarica et al., 2000). It is worse that the blowout of gas and liquid may lead to overflow or interruption of the terminal gas-liquid separator. Therefore, this harmful flow pattern is highly undesirable in ocean engineering. And it is of great significance to study the mechanism and characteristics of severe slugging.
For decades, severe slugging in a pipeline-riser system has been studied experimentally. The experiments mainly focus on the formation mechanism and flow characteristics, as well as the elimination methods of severe slugging. In an early study, an experiment was conducted in a pipeline with different inclined angles (Schmidt, 1977). The different stages of severe slugging and flow regimes were identified by analyzing the pressure fluctuations at the bottom of the riser. And several flow pattern maps of air-kerosene twophase flow in a pipeline-riser system were made based on his experimental data. Such severe slugging could be eliminated when an effective method named choking was tested and introduced in a later study (Schmidt et al., 1980). For the first time, the liquid slugs were proved to range in lengths that could exceed the height of riser, which laid a solid foundation for the further researches of severe slugging (Brill et al., 1981). Recently, severe slugging has been researched experimentally in horizontal pipeline-riser systems and S-shaped pipeline-riser systems (Fabre et al., 1990;Montgomery, 2002;Yeung et al., 2003;Li et al., 2013). The flow cycles were divided into different stages. And various flow patterns were also observed in their experiments. But compared with the typical severe slugging in a vertical riser, it showed some different behaviors in Sshaped pipeline-riser systems. For instance, the gas intrusion in the downcomer of the riser into the upper limb was the reason for the fluid blowout in an S-shaped riser. And the amplitude of pressure fluctuations in the horizontal pipeline-riser system was found to be relatively small (Fabre et al., 1990). For the pipeline-catenary-riser system, the influence of pressure on the multiphase flow behavior, in particular, the initiation and characteristics of severe slugging was investigated experimentally (Wordsworth et al., 1998;Malekzadeh et al., 2012b). In their experiments, a variety of flow patterns such as severe slugging, oscillation flow and other flow patterns were identified. Meanwhile, different elimination methods of severe slugging have been investigated and a combination of gas-lifting and choking was considered as the best elimination method to stabilize the flow (Jansen et al., 1996). Based on these experiments, five types of flow patterns are determined, including severe slugging of Type 1 (SS1), severe slugging of Type 2 (SS2), and severe slugging of Type 3 (SS3), unstable oscillations (USO) and stable flow (STB) (Malekzadeh et al., 2012b).
Numerical method is another effective way to investigate severe slugging, especially when experimental attempts can hardly be achieved. A model was first used to calculate time variations of pipeline pressure, position of the accumulation region, flow rates into the riser and mean holdup (Schmidt et al., 1985). Compared with the experiments, the numerical results show good agreement in most cases, except for the blowout stage. Thereafter, several models were proposed, such as the simplified transient model and the transient drift flux model (Sarica and Shoham, 1991;Balino et al., 2010;Nemoto and Baliño, 2012;Malekzadeh et al., 2012a;Balino, 2014). These models considering continuity equations for liquid and gas phases are capable of simulating discontinuities of severe slugging and predicting the loc-ation of the liquid accumulation in the pipeline and the liquid slug in the riser. The numerical results for slugging cycle, stability and flow regime maps show a good agreement with the experimental results. Besides, OLGA, a commercial transient two-fluid multiphase simulator, has also been widely used to simulate the severe slugging (Mokhatab and Towler, 2007;Malekzadeh et al., 2012b).
It is noticed that most of the previously reported researches have focused on severe slugging in a downward inclined pipe followed by a vertical riser. Recently, severe slugging in such a system, a downwardly inclined pipe followed by a catenary riser, has been more frequently investigated. However, the characteristics of the severe slugging process in a catenary riser system are not fully analyzed, e.g. a stage when the gas-liquid mixture slug form is discussed in our work while it is mostly ignored in previous studies. Hence, we present this paper on the experimental study of the severe slugging caused by the two-phase flow of air and water in a horizontal and downward inclined pipeline followed by a catenary riser. The experimental campaign is explained in Section 2. To compare with the experimental results and reproduce the characteristics of severe slugging, a theoretical model proposed by Balino et al. (2010) is introduced to simulate the performance of severe slugging in Section 3. The numerical and experimental results, including stability curve and flow pattern map, are analyzed and discussed in Sections 4 and 5. The overall conclusions are given in Section 6.

Experimental campaigns
The experiment was conducted in a pipeline-riser system consisting of a horizontal pipeline, a inclined pipeline and a catenary riser (Fig. 1). All the pipelines and risers are PMMA tubes with an inner diameter of 0.026 m and an external diameter of 0.030 m (Figs. 2 and 3). They are transparent in order to observe the flow behavior inside visually. The water control system includes water collector, water pump, water storage vessel and water flowmeters while the air control system is made of air compressor, air storage vessel, air controllers and flowmeters. As is seen in Fig. 1,   Fig. 1. Schematic of the experimental facilities.
IJ represents a horizontal pipeline with a length while JP represents an inclined pipeline with a length 16.692 m and an angle . PK is a catenary riser with the vertical height and the horizontal length . And the inclination angle at the top of the riser is . ψ In Fig. 4, the experimental riser can be characterized by the catenary riser geometry. The inclination angle at the bottom is assumed as . A function expressing the coordinates of the points belonging to the riser can be used to determine the local position along the riser and the local inclination angle.
The local height z of a point belonging to the catenary riser can be given as: where the constants k and c are obtained from the solution of the following transcendental equation according to the experiment: The local position s is given as: The local inclination angle θ can be written as: Air and water were used as experimental fluids and mixed at position I, which is 4.455 m away from the entrance of water, H ( Fig. 1). At the top of the catenary riser, a separation vessel was set to separate the air-water mixture. The water was returned to a water collector while the air was vented.

L/ min
During the experiment, the air and water were first stored respectively by the gas buffer vessel and the water storage vessel (Figs. 1 and 2). Then they flew out and were both controlled by PID controller and electric control valve, which could automatically provide an almost constant mass flow rate. The air flow rates were measured by a flowmeter from ALICAT with a maximum measurement capacity of (with an accuracy of 1%). The water was measured by the TI600-9 thermal mass flowmeter with a maximum measurement capacity of (with an accuracy of 1%). Pressure transducers with a maximum measurement capacity of 50 kPa (with an accuracy of 1%) were located at the inlet of the riser, P. High-definition digital cameras were used to record the flow characteristics in the system. The superficial velocities of water and air ranged from v sl = 0.036and , respectively. During the experiment, the gas and liquid flow rates were controlled. The gas flow rate was first set to be constant. The experiment was conducted by increasing the liquid flow rate gradually under the constant gas flow rate. Then the gas flow rate was changed. Correspondingly, the liquid flow rate was changed under different values of gas flow rates.
The measurement devices are calibrated carefully prior to the experiments. Both visual observations and pressure fluctuation measurement at the bottom of the riser are applied to identify the flow patterns of severe slugging in our study, since the pressure variation at the riser bottom can reflect the dynamic characteristics of severe slugging in the riser. The maximum relative uncertainties of variables are all smaller than 5% during the whole experiments.

Theoretical model
To investigate the severe slugging numerically, a theoretical model proposed by Balino et al. (2010) is introduced here. In this model, continuity equations for the phases and   DUAN Jin-long et al. China Ocean Eng., 2017, Vol. 31, No. 6, P. 653-664 a simplified momentum equation for the mixture are considered under the standard condition. A drift-flux model is used as a closure law. The type of severe slugging can be determined by the model.

Void fraction in the pipeline
In the pipeline, the flow is assumed stratified. The void fraction in the pipeline can be determined and derived from the following equation (Taitel and Dukler, 1976).
where S g , S i and S 1 represent respectively the gas, interfacial and liquid wetted perimeters. , and represent respectively the wall-gas, interface and wall-liquid shear stresses. These parameters can be calculated by referring to the method of Taitel and Dukler (1976). and are the gas and liquid densities respectively. A is the flow passage area ( , where D is the internal diameter). Variations of the void fraction α p in the pipeline are neglected.

Models for phases in the pipeline and catenary riser
In this work, one-dimensional isothermal flow in both pipeline and riser is considered. The liquid is assumed incompressible, while the gas is ideal and incompressible. Mass transfer between the liquid and gas is neglected. The flow pattern in the pipeline is assumed stratified. For simplicity, severe slugging is controlled mainly by gravity in both pipeline and riser.

Pipeline model
The pipeline-riser system investigated here consists of a downwardly inclined pipeline and a catenary riser with twophase flow of water and air, as shown in Fig. 5.
The continuity equations for the liquid and gas here are given as (Balino et al., 2010): where t, g and ρ 1 are the time, the gravity acceleration and the liquid density; P 0 , P b and P g represent respectively the atmospheric pressure, the pressure at the bottom of the riser and the gas pressure in the pipeline; L is the pipeline length; L p is the liquid slug length in the pipeline; and represent respectively the superficial gas and liquid velocities at the inlet of the pipeline; represents the superficial liquid velocity at the bottom of the riser; is the pipeline inclination angle; L e represents an equivalent pipeline length; α p can be obtained by Eq. (5). Moreover, the superficial gas velocity at the bottom of the riser, v rsg , is related to L p . When L p = 0, v rsl = v sl and v rsg = v r -v rsl (v r is the total superficial velocity at the riser base), i.e., the liquid flowing into the pipeline contributes to the liquid slug in the riser completely. While L p > 0, v rsl = v r and v rsg = 0, i.e., there is no gas entering the riser at the moment.

Catenary riser model
For the gas and liquid in the riser, using the continuity equation and the mixture momentum equation yields where and represent respectively the superficial gas and liquid velocities at the liquid top in the riser when the liquid slug has not reached the riser top yet. If the liquid flows out the riser, and represent the superficial gas and liquid velocities at the riser top. α r is the void fraction; P is the pressure; s and θ are the position and the inclination angle along the riser (Fig. 5); ρ m is the mixture density, namely ; τ w represents the wall shear stress and can be obtained by the method of Nicklin (1962).

Initial values
It is important to assure the initial values before the calculation begins. The transient state when the riser is full of liquid and the gas-liquid interface is located at the bottom of the riser is assumed as the initial state. Hence, P ñ z where is the pressure corresponding to the specific position, represents the vertical height between the specific position and the riser top. Variables with superscript ~ are used as initial values. Meanwhile, setting the time derivatives in the dynamic equations to zero yields

Discretization
The dynamic equations are discretized by the implicit finite difference method. A moving grid is adopted for the flow in the riser. Firstly, the flow is divided with N nodes. And node i ( ) moves with the gas in the riser. When the node N -1 catches up with and merges with Node N, a new node is generated at the bottom of the riser, namely Node 1, in order to keep the node number as constant. Node N always moves with the liquid top if the liquid slug has not reached the riser top. But it will be fixed at the riser top if the liquid slug length exceeds the riser length. Hence, the time step Δt can be obtained by where and represent the positions of the N and N-1 Nodes; is the superficial liquid velocity at Node N; and is the superficial gas velocity at Node N-1. It can be deduced from Eq. (14) that Δt is constantly changed with the progress of the calculation. The convergence of the calculation is checked through the error between the pressure at Node N and the standard atmospheric pressure.

Experimental analyses
Severe slugging is a kind of terrain dominated phenomenon which occurs at the case where the gas passage in the pipeline has been blocked by the liquid slug at the riser base until the upstream gas pressure overcomes the hydrostatic pressure caused by the liquid level in the riser. According to such a formation mechanism of the severe slugging, flow patterns in the pipeline are one of the important factors on whether severe slugging can happen in the pipeline-riser system. Therefore, flow patterns in the pipeline are first observed and analyzed.

Flow patterns in pipeline
Two types of flow patterns in the pipeline are observed within the experimental range of air and water flow rates, which are stratified and intermittent flows respectively. Stratified flow is a continuous flow phenomenon that the gas and liquid phases are stratified due to the gravity effect for which the gas phase is always located above the liquid phase. Intermittent flow is such a flow phenomenon that the pipeline is discontinuously blocked due to the alternate occurrence of liquid and gas slugs. Fig. 6 presents two-phase v sl = 0.1 m/s gas-liquid flow pattern maps observed for the test loop studied at different air and water superficial velocities. Stratified flow appears at low superficial liquid velocities within the entire range of the superficial gas velocities. The transition from the stratified flow to intermittent flow occurs at a nearly constant value for superficial liquid velocity.
It is also shown that severe slugging does not occur under intermittent flow in the pipeline, because the riser base can be penetrated alternately by liquid and gas slugs and no complete gas blockage can be formed. For stratified flow in the pipeline, based on visual observations and analysis of pressure drop in the riser, five types of flow patterns in the riser have been identified by changing the gas and liquid flow rates, including severe slugging of Type 1 (SS1), severe slugging of Type 2 (SS2), severe slugging of Type 3 (SS3), unstable oscillations (USO) and stable flow (STB). The formation mechanism and characteristics for severe slugging are investigated in the following sections.

Severe slugging
Similar to the severe slugging in the vertical riser, severe slugging consists commonly of four stages: slug formation; slug production; gas-liquid blowout, and liquid fallback (Schmidt et al., 1985;Taitel, 1986). And three types of severe slugging emerge in the catenary riser, which are severe slugging of Type 1 (SS1), Type 2 (SS2) and Type 3 (SS3). But difference on characteristics of severe slugging can be discovered between the two kinds of risers.

Severe slugging of Type 1
Severe slugging is a transient cyclic phenomenon. For SS1, each cycle consists of four basic stages, including slug formation, slug production, gas-liquid blowout and liquid fallback according to previous studies. The gas-liquid distribution during one cycle of SS1 in the pipeline-catenary riser system is illustrated in Fig. 7 and the pressure difference between the top and bottom of the riser is given in Fig. 8. As mentioned in Section 4.1, a stratified flow pattern in the pipeline is of necessity to the emergence of severe slug- Fig. 6. Flow patterns in the horizontal and downward inclined pipeline. Fig. 7. Evolution of SS1 in a catenary riser. DUAN Jin-long et al. China Ocean Eng., 2017, Vol. 31, No. 6, P. 653-664 ging. After the stratified fluid enters into the declination pipe from the horizontal pipe, liquid accumulation occurs at the bottom of the catenary riser due to the gravity effect and will creates a slug if sufficient liquid accumulates. As a result, the gas is blocked in the pipeline. However, the gas cannot be absolutely sealed during the formation of liquid slug so that a small amount of gas intermittently enters into the liquid slug in the riser, leading to the formation of a gas-liquid mixture slug, as shown in Fig. 7a.
With continuous entrance of stratified fluids into the bottom of the catenary riser, the length of the mixture slug increases continually in the catenary riser and gas appears in the form of intermittent bubble in the mixture slug. The variation of the interface position between the gas and the slug in the pipeline is relatively small and the mixture slug mainly grows in the catenary riser. With the growth of the mixture slug, the blockage to the gas is strengthened, which makes it more difficult for the gas to enter the slug. Meanwhile, the bubbles in the mixture slug vent at the top of the slug due to the gravity. As a result, the void fraction in the mixture slug starts to decline gradually then. After the head of the mixture slug arrives at a critical position of the catenary riser, gas is completely blocked in the pipeline, leading to a pure liquid slug in the riser. The inclination angle of the catenary at this critical position is defined as . The whole process is called gas-liquid mixture slug formation. During this process, the pressure difference between the top and bottom of the riser majorly shows an increase trend with time and remarkable fluctuations can be observed in the curve, which are caused by the formation and escape of bubbles in the mixture slug, as shown in Fig. 8 corresponding to and . The value of during this process increases approximately from to . Then the height of the pure liquid slug in the catenary riser increases and the pressure at the riser base increases simultaneously as a consequence. The gas-liquid interface in the pipeline is pushed away from the riser bottom and the accumulated gas in the pipeline is compressed, resulting in that the gas-liquid interface begins to move along the pipeline, namely the pure liquid slug develops its length at 3.9 × 10 4 Pa both ends. This stage is called pure liquid slug formation here, as shown in Fig. 7b. During this process, continuously increases due to the growth of pure liquid slug, as shown in Fig. 8. However, for a catenary riser increases more slowly due to its geometry, especially at the beginning of the slug formation, compared with that in a vertical riser (Malekzadeh et al., 2012b). When the pure liquid slug arrives at the riser top, reaches its maximum, approximately equal to . Actually, the total duration of gas-liquid mixture slug formation and pure liquid slug formation is considered a slug formation stage in previous studies while the pressure fluctuation at the beginning of the slug is not specifically discussed and its reason remains unclear. In this work, the fluctuation is discovered to be closely associated to the entrance and escape of the gas in the slug. The gas-liquid mixture slug formation and pure liquid slug formation can be easily distinguished through the gas-liquid distribution and the curve of pressure difference. Therefore, it is reasonable to separate the slug formation stage to two more detailed individual processes, the gas-liquid mixture slug formation and the pure liquid slug formation. It should be also noted that for a pipeline-vertical-riser system, once liquid accumulates at the riser base and forms a liquid slug, the gas is completely blocked in the pipeline. As a result, the slug is pure liquid without any bubbles initially for SS1, i.e. no gasliquid mixture slug formation can be observed in a vertical riser. For SS1, after the first two stages, the liquid level can reach the outlet of the riser and the length of the pure liquid slug in the catenary riser no longer increases. The pressure of the compressed gas in the pipeline continues to increase due to the sequential entrance of stratified fluids into the horizontal pipe. When the upstream gas pressure exceeds the hydrostatic pressure head in the catenary riser, the slug tail in the pipeline is pushed toward the riser bottom and the liquid in the catenary riser starts to flow out at its top, as shown in Fig. 7c. This is the liquid production stage and remains almost constant at its maximal value 10 4 Pa. When the pressure of the compressed gas in the pipeline is high enough to overcome the hydrostatic pressure head in the catenary riser, the gas penetrates into the catenary riser, and the gas-liquid blowout stage begins, as shown in Fig.  7d. As a result of gas penetration into the catenary riser, the remaining pure liquid slug is rapidly flushed out of the riser, resulting in that the hydrostatic pressure in the catenary riser begins to decrease. Once the gas reaches the outlet of the catenary riser, gas and liquid flow out alternately at the outlet of the catenary riser. As shown in Fig. 8, a low decreasing rate of the pressure difference , approximately from to , appears at the beginning of the blowout stage, which is caused by the relatively slow gas elevation along the slow-slope part of the catenary riser. With the increase of the inclination angle along the catenary riser, the gas elevation is accelerated, resulting in the dramatic decrease of . It can be seen in Fig. 8 that decreases from about to rapidly. Besides, fluctuations of with small amplitudes are observed due to the intermittent gas penetration during the process. When the gas pressure becomes insufficient to push up the liquid slug, the remaining liquid in the catenary riser starts to fall down due to the gravity and accumulates at the riser base, forming a new liquid slug and then repeating the cycle, as shown in Fig. 7e. This is known as the liquid fallback stage. In this stage, fluctuates with significant amplitudes around its minimum value due to the liquid oscillation, as shown in Fig. 8.
Define the inclination angle of new liquid slug head at the position of the catenary riser as .
is defined as the critical angle where the gas is totally blocked, as seen in Fig. 7. If , the new liquid slug still needs to experience the process of the gas-liquid mixture slug formation in the new cycle of SS1. If , the new slug has already become a pure liquid slug at the beginning of the cycle of SS1 and skips the gas-liquid mixture slug formation.
Generally, SS1 in a catenary riser is a regular and cyclic phenomenon, including the gas-liquid mixture stage, pure liquid slug formation, slug production, gas-liquid blowout and liquid fallback. Compared with the severe slugging in a vertical riser, a particular the gas-liquid mixture slug stage occurs before the pure slug formation in a catenary riser, which is the most evident distinction.

Severe slugging of Type 2 and Type 3
Under different superficial gas and liquid velocity conditions, the pattern of severe slugging can be changed to Type 2 (SS2) or Type 3 (SS3). For SS2, the slug production stage is absent. The gas-liquid distribution during one cycle of SS2 in the pipeline-catenary-riser system is illustrated in Fig. 9 and the pressure difference is given in Fig. 10.
As shown in Figs. 9 and 10 (corresponding to v sg = and ), a cycle of SS2 also contains several distinguishable stages, but the most significant Pa distinction between SS1 and SS2 is the absence of slug production stage. Such phenomenon is caused by the fact that in SS2, gas penetrates into the riser and blowout before the liquid level of the slug reaches the riser top, which means that the gas-liquid blowout stage occurs right after the pure liquid slug formation and the slug production stage is skipped. Note that in SS2, can hardly reach the maximum value or just be equal to it transiently. The maximal value for in Fig. 8 is only . Besides, in the other stages such as the gas-liquid mixture slug formation, pure liquid slug formation, gas-liquid blowout and liquid fallback, the characteristics of SS2 and SS1 are similar. Therefore, the existence of the slug production stage can be a sign for distinguishing SS2 from SS1. Besides SS1 and SS2, SS3 is another type of severe slugging, also observed in the experiments. As SS3 is still a cyclic phenomenon, the evolution of one cycle of SS3 and the pressure difference during one cycle of SS3 in the pipeline-catenary-riser system are given in Figs. 11 and 12 (corresponding to and ). The main distinction between SS3 and the other two severe slugging types is that the gas cannot be completely blocked during the whole process due to the relatively high superficial gas velocity, resulting in the intermittent entrance of gas into the riser during the whole cycle (Fig. 11). Note that SS3 in Malekzadeh et al. (2012b) is divided into transient slugs, aerated slug growth, fast aerated liquid production and gas   Fig. 11. Evolution of SS3 in a catenary riser. DUAN Jin-long et al. China Ocean Eng., 2017, Vol. 31, No. 6, P. 653-664 blowdown. However, the formation mechanism for SS3 is uniform, i.e. the liquid cannot completely block the gas during the whole process. It should be also noted that when the angle , there still exists relatively small amount of gas slug in the catenary riser during SS3 (Fig. 11b). Hence, the liquid slug stage of SS3 can be also defined as a gas-liquid mixture slug. In Fig. 11, the variation of pressure difference follows an unsmooth curve and violent pressure fluctuation can be observed, which is caused by the active behavior of gas. The minimal and maximal values of in Fig. 11 are approximately and 10 4 Pa. Moreover, the periods and the amplitudes of variation in SS3 are smaller than those in SS1 and SS2.
SS2 and SS3 are commonly considered the transition between SS1 and flow patterns without severe slugging. Compared with SS1, the absence of slug production is the main characteristics of SS2. For SS3, the total gas blockage cannot be observed during its evolution. These three types of severe slugging emerge at different superficial gas and liquid velocities and the conditions will be discussed in Section 5 with numerical results.

Unstable oscillations and stable flow
Typical severe slugging will disappear if the gas or liquid flow rates reach a high level and the flow pattern in the riser will be unstable oscillations or stable flow. At relatively high superficial gas velocities, unstable oscillations (USO) arise. Under such circumstances, the liquid slug oscillates first at the riser base due to the high-speed gas (Fig.  13a). Then the liquid slug is pushed upwards from the riser base by the gas (Fig. 13b). If the liquid slug is not long enough to form a strong blockage which can resist the gas penetration, the high speed gas will penetrate through the short slug, causing the collapse and fallback of the liquid (Fig. 13c). Otherwise, the liquid slug will be elevated to the top of the riser by the gas (Fig. 13d). For USO, the amplitude of is remarkably smaller than that of severe slugging due to the unstable gas penetration (Malekzadeh et al., 2012b).
When the liquid flow rates are relatively high, the flow pattern, defined as stable flow (STB), is observed. During stable flow, the gas and liquid flow out of the riser altern- (Fig. 14). Note that stable flow is mainly caused by intermittent flow in the horizontal pipeline during our experiments. For STB, a small fluctuation amplitude of is commonly observed and compared with USO, the mean value of is slightly higher while the amplitude is smaller (Malekzadeh et al., 2012b).

Comparisons and discussion
In this section, the numerical results are presented and comparisons are made between experiments and computational simulations.

Comparison between numerical and experimental results
The characteristics of different flow patterns are analyzed based on from both computations and experiments. Table 1 shows the typical cases for all five flow patterns. The period T of , the amplitude of and types of severe slugging are presented. Superficial gas and liquid velocities in the pipeline and are calculated according to the inflow rates. The pressure P b at the bottom of the riser is measured directly in the experiments. is obtained by subtracting the standard atmospheric pressure P 0 . It should be noted that the errors are acceptable according to Balino et al. (2010), which means that the results of the experiments and simulations are comparable. Fig. 15 depicts     Table 1 that of severe slugging flow patterns (SS1, SS2 and SS3) is obviously larger than that of USO and STB in most cases while in some particular cases of SS1, is very small because the slug is still long after the fallback, causing a large minimum value of . Among the severe slugging flow patterns, SS1 and SS2 share the close maximum of and the maximum of for SS3 is smaller. Between the other two flow patterns, of USO is larger than that of STB. Actually, the pressure fluctuation of STB is sometimes too slight to be detected. Severe slugging flow patterns also have larger period T compared with USO and STB. Generally, it follows that the period T of SS1 and SS2 are close and larger than that of SS3. The performance of USO shows a very short period while sometimes the periodic behavior can hardly be observed in STB. The periods are almost 100 s longer than that for small v sg in Fig. 16. When the value of v sg increases to 0.2 m/s, small periods less than 100 s are observed. With higher superficial gas velocity, it takes less time for the pressure of the compressed gas to reach its maximum, resulting in an earlier gas-liquid blowout. Besides, the duration of gas-liquid blowout is reduced because the blowout becomes more viol-  DUAN Jin-long et al. China Ocean Eng., 2017, Vol. 31, No. 6, P. 653-664 661 ent under higher superficial gas velocity condition. The period T is thus shortened.
Likewise, the variations of for severe slugging with different v sg and v sl are illustrated in Fig. 17, where increases firstly and then decreases with the increase of superficial gas velocity. Actually, represents the difference between the maximum and minimum value of , where reaches the maximum just before the blowout and the minimum after the blowout. When v sg is relatively small, the maximum of almost remains unchanged as the gas penetration is weak, but the minimum value of decreases with higher v sg because the blowout is more violent and less liquid falls back to form a shorter slug, resulting in the rising of . When v sg grows large enough, the maximum of decreases with higher v sg with the growth of gas penetration and the variation of the minimum value of is relatively small. Therefore, declines with the growth of v sg . In our experiments, reaches its maximum at approximately . When , the values of almost keep stable with the increase of ( Fig. 17).
P amp The amplitudes and the periods T calculated with the model show a good agreement with the experimental results. However, errors in some cases are large (Table 1), which may be caused by the factor that the control of the flow rates is not precise in the experiments. Another plausible reason is that the accuracy of the theoretical model cannot be guaranteed and needs to be improved.

Comparison with other experiments
Several experiments that are close to this presented work are listed in Table 2 and the parameters and results are also demonstrated with different classifications of severe slugging patterns. These classifications together with those considered in this work share certain similarities despite the different experimental conditions but also have some diversities.
The situations of SS1 and SS2 are respectively similar in different studies. For SS1, the values at the riser base ( ) firstly increase gradually then stabilize at a maximum, and finally decrease dramatically during gas-liquid blowout. For SS2, the slug production is absent, the maximum value of can just reach or smaller than that in SS1. No matter the riser is vertical or catenary, one cycle of severe slugging mainly includes four stages: slug formation, slug production, gas blowout and liquid fallback, except for the gas-liquid mixture slug considered in this paper. One minor difference can be found that the value of in a vertical riser grows linearly during slug formation while the increase of is relatively sluggish in a catenary riser, resulting from the different geometry of riser. This phenomenon can be apparently observed in the analyses of Wordsworth et al. (1998) and our experiments.
The situations of SS3 in different studies are more complicated. In most of the studies listed in Table 2, SS3 is classified according to its continuous gas penetration during one whole severe slugging cycle. However, the SS3 is classified   according to the fallback liquid length in Luo et al. (2011). During one cycle of SS3 in Luo et al. (2011), the whole riser is filled with liquid at the end of blowout, no liquid cutoff occurs at the pipe outlet and flow pattern with continuous gas penetration into the riser was not observed. This classification of SS3 is similar to the cyclic flow without fall back in the experiments of Jansen et al. (1996). The appearance of such a SS3 pattern exists under low superficial gas velocity and high superficial liquid velocity while the SS3 in other literatures and this paper exists under high superficial gas velocity and low superficial liquid velocity.  Fig. 18 shows the flow regime map made according to experimental data and numerical results, indicating the flow pattern and stability of flow under different superficial gas and liquid velocities. Besides, the curve given by Bøe (1981) criterion, which can distinguish the stable flow from unstable oscillations, is also depicted in the map. Note that the markers represent the data points from the experiments while the lines represent the boundaries between different flow patterns according to the computation. It can be observed that SS1 occurs at relatively low superficial gas and liquid velocities. The severe slugging occurs while and according to our experiment. With the increase of superficial gas velocity, the flow patterns transform from SS1 to SS2, SS3 or USO. The transition trends are consistent with those in Malekzadeh et al. (2012b). The stable region appears mainly at high superficial liquid velocity, . As SS2 and SS3 are regarded as transitional flow patterns, the regions corresponding to these two types are relatively small. Therefore, it can be stated here that severe slugging occurs totally in the stable region defined by Bøe (1981) criterion. Furthermore, the boundaries of SS1-SS2 and SS2-SS3 estimated by the numerical work shows a good agreement with the experimental data despite some discrepancies. The boundary between severe slugging and other flow patterns (USO and STB), i.e. the stability curve, shows a reasonable agreement with the experimental data. Severe slugging oc-curs totally in the unstable region. Another note is that the region near the Bøe curve is occupied by unstable flows. The possible reason is that some points may be classified incorrectly in the experiment.
Since flow patterns play an important role in the prediction of the emergence of severe slugging, such a flow regime map can be used as a reference for design in an offshore oil-production system.

Conclusions
Experiments are conducted to investigate characteristics of severe slugging in a pipeline followed by a catenary riser. Correspondingly, a theoretical model considering transient characteristics proposed by Balino et al. (2010) is introduced and compared with the experiments.
In the experiments, five flow patterns in the catenary riser are obtained. Among these five patterns, three of them are severe slugging types, including SS1, SS2 and SS3. The features of the three severe slugging types, such as the time period and the amplitude of the riser pressure drop are quantitatively analyzed. For SS1 and SS2, a gas-liquid mixture slug stage is observed at the beginning of one cycle, which is seldom reported in the previous works. In the gasliquid mixture slug stage, obvious pressure drop fluctuations resulted from intermittent gas penetration are detected, indicating that the stage can be distinguished from the whole slug formation stage. The theoretical model is used to reproduce the characteristics of some typical experimental cases. By comparison with the experimental data, the numerical results show a good agreement in many respects. Based on both experiments and computations, it is found that at certain superficial liquid velocity and in spite of the severe slugging type, the period T decreases with the increase of superficial gas velocity while the pressure drop amplitude increases initially and then decreases with the increase of .
Based on numerical results, the boundary curves of SS1-SS2 and SS2-SS3 as well as the stability curve which determines the division of severe slugging and other two flow patterns (USO and STB) are obtained. A flow regime map is built on the experimental data with the numerical curves. Reasonable agreements can be found on the map between the experiments and computations with some discrepancies. Since no severe slugging can be observed at high superficial gas velocities, it can be concluded that severe slugging can be eliminated by increasing the superficial gas velocities. But this conclusion needs to be experimentally investigated in the future.