Study on mud discharge after emergency disconnection of deepwater drilling risers

Journal of Petroleum Science and Engineering 190 (2020) 107105

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Study on mud discharge after emergency disconnection of deepwater drilling risers Xianglei Wang , Xiuquan Liu *, Shenyan Zhang , Guoming Chen , Yuanjiang Chang Centre for Offshore Engineering and Safety Technology, China University of Petroleum, Qingdao, 266580, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Riser Emergency disconnection Mud discharge CFD

Mud is often discharged into seawater after emergency disconnection of risers in offshore oil and gas drilling engineering. The discharged mud needs to be simulated accurately since it can produce a huge load on risers. Several mud discharge models have been proposed, such as Young’s slug model, SFM model, WFC model and one-dimensional finite volume model. However, the mud is taken as a one-dimensional rigid body in existing mud discharge models. As a consequence, the radial velocity of mud, the mixing interface between mud and seawater, and mud discharge in complicated riser flow channels cannot be simulated. In this paper, a more accurate and applicable three-dimensional (3D) computational fluid dynamics (CFD) model is established to simulate the mud discharge process. The proposed method is demonstrated by its application to a case. It turns out that the actual mud discharge process can be simulated based on the 3D CFD model. Characteristics of the mud discharge including the radial velocity, axial velocity and the interface between two fluids are calculated based on the 3D CFD model, which improves the understanding of the mud discharge. Besides, the applicability of each mud discharge model is determined through model comparison. The influence of key factors including drill pipes with pipe joints, riser inner diameter, mud density and mud dynamic viscosity on the mud discharge is also analyzed based on the 3D CFD model.

1. Introduction Drilling risers are key equipment for connecting drilling platform with subsea wellhead in offshore oil and natural gas exploration (Liu et al., 2013, 2016). Emergency disconnection of risers from LMRP is occasionally required in harsh environments or loss of dynamic posi­ tioning control (Chang et al., 2018; Nie et al., 2019). Drilling mud is often discharged into seawater directly after the emergency disconnec­ tion of risers, or else risers may be broken due to the heavy weight of mud (Miller and Young, 1985; Ma et al., 2013). The discharged mud produces a huge load on risers, which affects the recoil response and structural safety of risers (Wang and Wang, 2018). Therefore, the mud discharge process after the riser emergency disconnection needs to be simulated accurately to provide a hydrodynamic load for riser recoil analysis. Some scholars carried out research on the simulation of mud discharge after riser emergency disconnection. Young et al. (1992) firstly simulated the falling mud column through an auxiliary program, without considering seawater refilling from the riser refill valve. The

mud discharge model in the program was called the Young’s slug model. Miller et al. (1998) used a time-domain computer program called “STARR” to simulate axial riser disconnection transients, which focused on changes in pressure during mud discharge. Puccio and Nuttall (1998) pointed out that the mud fluid column was often ideated as a single accelerating cylinder in practical engineering applications. Shear force at the riser wall caused by discharged mud was considerably large in heavier mud weights and played an important role in inhibiting the riser recoil. Lang et al. (2009) described the simulation of mud column through Euler equation in one-dimensional space combined with the finite volume model. Grytøyr et al. (2011) calculated the velocity of discharged mud based on a differential equation that utilized dynamic equilibrium between the weight of the mud column inside the riser, the friction forces between the mud column and the riser, and the hydro­ static pressure at the lower end of the riser. Li et al. (2012) introduced Herschel-Bulkley rheological model to simulate mud flow and used 2HRECOIL to simulate the drilling fluid column. The discharged mud after emergency disconnection was regarded as the developing flow and unstable flow. Grønevik (2013) took into account refilled seawater and

* Corresponding author. E-mail address: [email protected] (X. Liu). https://doi.org/10.1016/j.petrol.2020.107105 Received 17 October 2019; Received in revised form 1 February 2020; Accepted 18 February 2020 Available online 20 February 2020 0920-4105/© 2020 Elsevier B.V. All rights reserved.

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derived slug fluid model (SFM) in detail based on Newton’s second law, which is the commonly adopted mud discharge method at present. Li et al. (2016) analyzed mud discharge after emergency disconnection by whole fluid column (WFC) model and one-dimensional finite volume model respectively. Both of the two models are solved in one-dimensional space. The proposed mud discharge models have been applied in the riser recoil analysis. Meng et al. (2018) summarized and compared SFM model and WFC model, and analyzed the influence of the discharge fluid on riser recoil response based on the two models. Wang and Gao (2019) conducted riser recoil analysis based on mechanical model of mass-spring-damping and WFC model. In the aforementioned investigations, Young’s slug model, SFM model, WFC model and one-dimensional finite volume model have been proposed to simulate the mud discharge process. Young’s slug model, SFM model and WFC model are all established based on Newton’s sec­ ond law, in which the discharged mud is simplified into an integral rigid body. One-dimensional finite volume model is presented based on finite volume method and computational fluid dynamics (CFD), in which the discharged mud is divided into several one-dimensional finite volume segments. Compared with models based on Newton’s second law, onedimensional finite volume model can simulate the mud discharge pro­ cess more accurately since it can calculate the movement of each mud segment in detail. However, the radial velocity of the discharged fluid and the mixing interface between mud and seawater cannot be simu­ lated based on existing models. Moreover, these models cannot analyze the mud discharge in complicated riser flow channels, such as the riser channel with drill pipes and pipe joints. Therefore, a more accurate 3D CFD model needs to be established to simulate the mud discharge process. Problems that involve the simulation of mud discharge after emer­ gency disconnection of risers based on 3D CFD are addressed in this study. The remainder of this paper is organized as follows. Section 2 illustrates the physical model and existing models of mud discharge. Section 3 presents a 3D CFD model of mud discharge. Section 4 conducts the mud discharge analysis based on different models and compared with each other. The influence of key parameters on the mud discharge is also analyzed in this section. Section 5 provides conclusions.

Fig. 1. Emergency disconnection and mud discharge.

slug model. The Young’s slug model is established based on Newton’s second law, which can be written as: mm a ¼ ðp0

pw ÞAin þ Gm

fm

(1)

fend

where mm is the mass of the discharged mud, a is the acceleration of the discharged mud, p0 - pw represents the pressure difference between the bottom and the top of the discharged mud, p0 - pw ¼ -ρwgL, ρw is the density of refilled seawater, Ain is the cross-sectional area of the annulus inside the riser, Gm is the gravity of the discharged mud, Gm ¼ ρmgAinLm, Lm is the length of the discharged mud in the riser system, ρm is the density of mud, fm is the force between the discharged mud and riser wall, fend is the frontal force that resist mud entering seawater.

2. Basic models 2.1. Physical model

(2) SFM model

Fig. 1 shows the physical model of the emergency disconnect and mud discharge of a riser system. The riser system may disconnect in the bottom due to harsh environments or loss of dynamic positioning con­ trol. As soon as the riser system is disconnected in the bottom, mud in the riser system discharges into seawater. The discharged mud leads in a low pressure in the riser system. Then a refill valve at the top of the riser system opens automatically owing to the low pressure. Seawater flows into the riser system through the refill valve and discharges with the internal mud together. The discharged fluid experiences stages from laminar flow to transition flow and then turbulence flow. The stages of laminar flow and transition flow are very short. The discharged fluid is mostly in the full turbulence stage.

Fig. 2(b) shows SFM model. The discharged mud and refilled seawater are regarded as two rigid bodies in SFM model. The discharge acceleration and velocity of refilled seawater and mud are assumed to be the same. The SFM model is also established based on Newton’s second law, which can be given as: ðmw þ mm Þat ¼ ðpa

pb ÞAin þ ðρm

ρw ÞgAin Lm

fw

fm

fend

(2)

where at is the acceleration of the total fluid column (mud and refilled seawater), pa - pb ¼ (ρm - ρw)gLm represents the difference in hydrostatic pressure experienced by the mud column, (ρm - ρw)gAinLm represents the effective gravity of the mud column, fw is the force between the refilled seawater and riser wall.

2.2. Existing analysis models

(3) WFC model

Existing analysis models for mud discharge are Young’s slug model, SFM model, WFC model and one-dimensional finite volume model, as shown in Fig. 2. Each mud discharge model will be introduced in the following.

Fig. 2(c) shows the WFC model. The discharged mud and refilled seawater are regarded as an integral rigid body in WFC model. The WFC model established based on Newton’s second law can be written as: ðmw þ mm Þat ¼ ðp0

(1) Young’s slug model

pb ÞAin þ Gw þ Gm

fw

fm

fend

(3)

where p0 - pb ¼ -ρwgL represents the difference in hydrostatic pressure suffered by the whole liquid column, Gw ¼ ρwgAinLw is the weight of refilled seawater.

Fig. 2(a) shows Young’s slug model. The discharged mud is regarded as a rigid body and the refilled seawater is not considered in Young’s 2

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Fig. 2. Existing mud discharge models. (a) Young’s slug model; (b) SFM model; (c) WFC model; (d) One-dimensional finite volume model.

(4) One-dimensional finite volume model

3. 3D CFD model

Above mentioned models including Young’s slug model, SFM model and WFC model are all established based on Newton’s second law, in which the discharged mud is simplified as a rigid body. Fig. 2(d) shows another more accurate model which is called one-dimensional finite volume model. The discharged mud and refilled seawater are divided into finite sections along the riser system. The flowing state of the dis­ charged fluid is analyzed by one-dimensional N-S equations, which can be expressed as:

3.1. CFD theory

∂v ∂p ∂v þ þ ρv ¼ ρg Ff ∂t ∂z ∂z ∂ ∂ ðρvAin Þ þ ðρAin Þ ¼ 0 ∂t ∂t

where u is the velocity field, F is volume force, p is pressure. The discharged mud is in a laminar flow in the initial stage. The laminar flow can be solved by Eq. (5) directly. However, the mud discharge enters a turbulent region quickly. The turbulence character­ istics needs to be described by statistical characteristics due to the complexity of the turbulence flow. Reynolds average method is often selected for the solving of turbulence flow. The Reynolds average N-S equation (RANS) is given as (Kharoua et al., 2017):

ρ

In 3D CFD theory, the fluid N-S equations can be written as (Naha­ vandi and Farzaneh-Gord, 2014; Pereira et al., 2016):

ρ

� ∂u þ ρðu⋅rÞu ¼ r⋅ ∂t

pI þ μ ru þ ðruÞT

��

þF

ρg

(5)

ρr⋅u ¼ 0

(4)

where Ff is the interaction force between fluid and riser wall in per unit volume, which is related to the empirical friction coefficient f, ρ is fluid density of each volume, v is velocity of each volume at time t, z is the axial position. The discharged velocity of the mud is calculated one section by one section based on one-dimensional finite volume model. Characteristics of mud discharge can be simulated more accurately based on the onedimensional finite volume than that based on Newton’s second law. However, the radial velocity of mud, the mixing interface between mud and seawater, and mud discharge in complicated channels cannot be simulated based on existing models. A more accurate and applicable 3D CFD model needs to be presented based on the existing one-dimensional finite volume model.

ρ

� ∂U 0 0 þ ρU⋅rU þ r⋅ðρu � u Þ ¼ rP þ r⋅μ rU þ ðrUÞT þ F ∂t ρr⋅U ¼ 0

ρg (6)

where U is the average velocity field, � is the outer vector product. Some auxiliary equations need to be introduced to solve the Rey­ nolds average equation shown in Eq. (6). Various turbulence models have been proposed to perform turbulence flow analysis, such as the standard k-ε model, RNG k-ε model and Realizable k-ε model (Launder and Spalding, 1972; Yakhot and Orszag, 1986). Among them, the stan­ dard k-ε model is the most popular model in solving the turbulence problem for its suitability at high Reynolds numbers and unsteady 3

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conditions (Zheng et al., 2015; Bagheri et al., 2016; Burlutskii, 2018; Adaze et al., 2019; Wang et al., 2019). Therefore, the standard k-ε model is adopted in the simulation of the mud discharge. Two additional equations of turbulent kinetic energy k and turbulent dissipation rate ε are introduced in the standard k-ε turbulence model (Launder and Spalding, 1972). The transport equation for k is (Zheng et al., 2015): �� � � ∂k μ ρ þ ρu ⋅ rk ¼ r ⋅ μ þ T rk þ Pk ρε (7) ∂t σk where Pk is: � � Pk ¼ μT ru: ru þ ðruÞT

2 ðr⋅uÞ2 3

�

2 ρkr⋅u 3

The transport equation for ε is: � � �� ∂ε μ ε ρ þ ρu ⋅ r ε ¼ r ⋅ μ þ T r ε þ C ε 1 Pk ∂t σε k

roughness elements, the turbulence parameters κν and B have the values 0.41 and 5.2 respectively, and Cs ¼ 0.26, ks corresponds to the equiva­ lent sand roughness height proposed by Nikuradse. Velocity boundary conditions and shear stress conditions are:

n⋅σ

(8)

Cε2 ρ

ε2

k2

where Cμ is a model constant, Cμ ¼ 0.09. The eddy viscosity model of Reynolds stress tensor under the stan­ dard k-ε turbulence model can be written as: 2 2μT Sij þ ρkδij 3

ρui uj ¼

ρ ¼ ρ1 þ ðρ2 μ ¼ μ1 þ ðμ2

(11)

A 3D CFD model is established based on the CFD theory in COMSOL Multiphysics, as shown in Fig. 3. COMSOL Multiphysics is a professional multiphysics simulation software that integrates CFD module. The software is famous for its good modular modeling and secondary development environment, and stable solution capabilities. Fig. 3(a) presents the established 3D CFD model. Fig. 3(b) illustrates the inlet and the mesh of the 3D model. The boundary layer of the discharged mud near the riser wall is set according to the wall function shown in Section 3.2. Fig. 3(c) shows the outlet of the 3D CFD model. The outlet is set much larger than the diameter of risers to eliminate the influence of boundary on the discharged mud. Fig. 3(d) is a two-dimensional sche­ matic diagram of the 3D CFD model. The left diagram shows the dis­ charged mud at the initial discharge state while the right diagram shows the mixing interface between two fluids after a time of discharge. The mixing interface of the two fluids is calculated according to Level set theory.

For walls with a certain roughness, Cebeci (2013) proposed a wall lift δþ w in viscosity unit: � þ � ks hþ δþ ; 11:06; (12) w ¼ max 2 2 where hþ is the height of the boundary mesh cell in viscosity units. The friction velocity of riser wall uτ is: juj � ln δþ w þB

8 0 > > > > � � > þ > k 2:25 <1 þ Cs k þ sin 0:4258 ln kþ ln s s s ΔB ¼ κv 87:75 > > > > > � 1 > : ln 1 þ Cs kþ s κv where kþ s is the roughness in viscosity units: pffiffi k ρC1=4 μ kþ ¼ ks s

μ

(13)

ΔB

(19)

3.4. CFD model

3.2. Wall function

κv

ρ1 Þϕ μ1 Þϕ

where ρ1 and ρ2 are the density of mud fluid and refilled seawater respectively, μ1 and μ2 are the dynamic viscosity of mud fluid and refilled seawater, respectively, the region in the condition of ϕ < 0.5 corresponds to mud fluid, the region in the condition of ϕ > 0.5 corre­ sponds to refilled seawater fluid.

where δij is the Kronecker delta, Sij is strain rate tensor. The standard k-ε turbulence model has been proved to be a good model in a full turbulence region. However, this model is not applicable to boundary layer region with low Reynolds number (Adaze et al., 2019). Therefore, the viscous stress of fluid on riser wall needs to be processed by a wall function.

uτ ¼ 1

(17)

where ε determines the thickness of the interface, ε ¼ hc/2, and hc is the characteristic mesh size in the area through which the interface passes. γ determines the number of reinitializations. Density and viscosity are defined as:

(10)

ε

ρuτ

Seawater enters the riser system through refill valves during the mud discharge process. There is an interface between the two fluids. Level set theory is a good choice to track the interface between two fluids (Li et al., 2016), which can be written as (Olsson and Kreiss, 2005): � � ∂ϕ rϕ (18) þ u ⋅ rϕ ¼ γr⋅ εrϕ ϕð1 ϕÞ jrϕj ∂t

where Cε1 ¼ 1.44, Cε2 ¼ 1.92, σk ¼ 1.0, σ ε ¼ 1.3. The turbulence viscosity model of the k-ε turbulence model is written as (Wilcox, 2006):

μT ¼ ρCμ

u � 1 log δþ w þB κv � σ ¼ μ ru þ ðruÞT

ðn⋅σ ⋅nÞn ¼

3.3. Level set theory

(9)

k

(16)

u⋅n ¼ 0

kþ s � 2:25 �� 0:811 2:25 � kþ s � 90

4. Results and discussions 4.1. 3D CFD analysis

kþ s � 90 (14)

The proposed 3D CFD method is applied to an engineering case. The mud fluid is considered as the Newtonian fluid to compare with existing models. Parameters in the present study are the same as that in the numerical experiment of Grønevik (2013). The total length of the riser system is 500 m, and the inner diameter of risers is 0.489 m. The density and kinematic viscosity of mud are 1600 kg/m3 and 1 � 10 4 m2/s, respectively. The density and kinematic viscosity of refilled seawater are 1025 kg/m3 and 1.15 � 10 6 m2/s, respectively. A 3D CFD model is

(15)

where the roughness height ks is the peak-peak value of the surface variation, Cs is a parameter related to the shape and distribution of the 4

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Fig. 3. 3D CFD model. (a) Overall model diagram; (b) Inlet and mesh; (c) Outlet; (d) Two-dimensional schematic diagram.

established and analyzed based on the basic data. The shape change of mud flowing profile and mixing interface between two fluids are shown in Figs. 4 and 5, respectively. Fig. 4 shows the flowing profiles of the discharged fluid at different time. A is a flowing profile at the initial moment, B and C are flowing profiles of the discharged fluid at a laminar phase, and D is a flowing profile in a turbulent phase. Once the riser system is disconnected in the bottom, mud starts to discharge and show stratification due to the viscous forces. The flowing profile changes from A to B and C due to the viscosity of drilling mud. Then the mud goes further into a full turbulent state as the discharged velocity increases and the flowing profile changes from C to D. Fig. 5 shows the density variation at the mixing

interface between two fluids, in which blue parts present seawater while red parts indicate drilling mud. It can be seen that there is a certain degree of mixing between the two fluids at the interface due to the particle motion between two fluids. Color gradients in Fig. 5 also shows that the flowing profile at this time is approximately a parabolic shape, which is in good agreement with results shown in Fig. 4. It turns out that the radial velocity of the discharged fluid and the mixing interface between mud and seawater can be simulated based on the 3D CFD model, as shown in Figs. 4 and 5. The detailed discharge velocities at different positions along the axial and radial directions are further monitored to study characteristics of mud discharge, as shown in Figs. 6 and 7. Fig. 6 shows that axial discharge velocities at different 5

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Journal of Petroleum Science and Engineering 190 (2020) 107105

Fig. 4. Flowing profiles of the discharged fluid.

positions is not the same. However, the axial velocity does not change much at different positions for the continuous of fluid flow. Fig. 7 shows discharge velocities at different positions along the radial direction are different from each other. The discharge velocity in the center of risers is largest. The closer to the center a position is, the larger velocity the position will have. The change gradient of velocities is not large in most region while the change gradient is large near the riser wall, which is consistent with the flowing profile D, as shown in Fig. 4.

Fig. 5. The mixing interface between two fluids.

fraction in risers is approximately in a linear change rule during the discharge process, which is also consistent with the conclusion of Grytøyr et al. (2011). However, the calculated results based on different models are different from each other in quantitative terms. Results based on 3D CFD model are similar to those based on WFC model, while results based on Young’s slug model and SFM model are different from results based on other models. Each model will be discussed in the following respectively.

4.2. Model comparison In order to identify the difference between models and determine the applicability of each model, the mud discharge is simulated based on Young’s slug model, SFM model, WFC model and 3D CFD model respectively and compared with each other. The velocity, mud volume fraction of the discharged fluid and viscous force on risers are calculated based on different models, as shown in Figs. 8–10. Figs. 8 and 10 show that both the discharge velocity and the force on risers increase rapidly at first and then decrease gradually, which is the same with previous studies (Young et al., 1992; Grønevik, 2013; Li et al., 2016; Meng et al., 2018). Fig. 9 shows the change of mud volume

(1) Young’s slug model The velocity of fluid in risers increases and then reduces quickly based on Young’s slug model while the velocity of fluid based on other 6

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Journal of Petroleum Science and Engineering 190 (2020) 107105

Fig. 6. Discharge velocities at different positions along the axial direction.

Fig. 9. Mud volume fraction based on different models.

Fig. 7. Discharge velocities at different positions along the radial direction.

Fig. 10. Force on risers based on different models.

(2) SFM model The results based on SFM model and WFC model are in agreement with the calculation results of Meng et al. (2018). However, calculated results based on SFM model and WFC model are obviously different from each other, as shown in Figs. 8–10. Unfortunately, Meng et al. (2018) do not explain the reason for the difference. The difference between SFM model and WFC model is derived in the present study, as shown in Fig. 11. Fig. 11 shows the difference of between SFM model and WFC model is “the difference in hydrostatic pressure of mud”. SFM model believes that “the effective gravity of mud” and “the difference in hydrostatic pressure of mud” have different effects, as shown in Eq. (2). Actually, the hydrostatic pressure difference caused by the change in the height of the liquid column is essentially the performance of effective gravity. The item of “the difference in hydrostatic pressure of mud” should not be added in SFM model. Therefore, the modified SFM (mSFM) model can be written as Eq. (20). The modified SFM (mSFM) model are consistent with results based on the WFC model and 3D CFD model, as shown in Figs. 8–10.

Fig. 8. Velocities based on different models.

models reduces slowly, as shown in Fig. 9. The main reason is that Young’s slug model does not consider refilled seawater during the discharge process, as shown in Eq. (1). The dynamic balance of the discharged fluid is likely to be reached without refilled seawater. Therefore, the Young’s slug model is appropriate for mud discharge simulation of risers without refill valve.

ðmw þ mm Þat ¼ ðρm

ρw ÞgAin Lm

fw

fm

fend

(20)

(3) 3D CFD model and WFC model Results based on the 3D CFD model and WFC model are basically the 7

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Fig. 11. The difference between SFM model and WFC model.

same. However, the force calculated based on 3D CFD model is smaller than that based on WFC model by 9.74%, as shown in Fig. 10. The main reason for the deviation is that the force calculation method adopted in two models is different. According to Newton’s internal friction law of fluid, the friction force between fluid and riser wall is essentially caused by viscosity of fluid and velocity gradient. The friction force of the 3D CFD model is calculated with the gradient of the radial velocity based on Newton’s internal friction law. However, the WFC model can only calculate the average axial velocity, which leads to that the friction force can only be solved by the empirical friction coefficient. Li et al. (2016) have proved that an improper selection of friction coefficient at different stages can cause a large variation of friction force. Therefore, the friction force calculated by the 3D CFD model is recommended. In summary, Young’s slug model is appropriate for mud discharge simulation of risers without refill valve. SFM model needs to be modified before being used for mud discharge calculation. WFC model is accurate in the mud discharge simulation. 3D CFD model is more accurate and can simulate the radial velocity, axial velocity and the interface between two fluids during the mud discharge.

Fig. 12. Discharged velocities in risers with different diameters of drill pipe joints.

4.3. Analysis of influencing factors In fact, there may be drill pipes with pipe joints in riser flow chan­ nels. The 3D CFD model can also be applied for the simulation of the mud discharge in complicated riser flow channels with drill pipes and pipe joints. The influence of drill pipes with pipe joints on the mud discharge is analyzed based on the 3D CFD model. Besides, the influence of some fluid and structural parameters, such as mud density, dynamic viscosity and inner diameter of risers on the mud discharge is also dis­ cussed in this part. (1) Drill pipes with pipe joints Several 3D CFD models in complicated riser flow channels consid­ ering drill pipes with different pipe joints are established. The diameter of drill pipes is 0.127 m. The diameter of different pipe joints is 0.172 m, 0.191 m, and 0.216 m, respectively. The number of pipe joints is 52, and the length of each pipe joint is 0.6 m. Discharged velocities and axial force in complicated riser flow channels are analyzed based on the established 3D CFD models, as shown in Figs. 12 and 13. The drill pipes

Fig. 13. Forces on pipes with different diameters of drill pipe joints.

8

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and pipe joints can bring additional resistance force for the mud discharge, which leads to the decrease of the mud discharge velocity in risers, as shown in Fig. 12. Although the mud discharge velocity de­ creases, the axial forces on pipes increase, as shown in Fig. 13. The main reason is that the area of the friction force on the pipe wall increases when drill pipes and pipe joints are considered. Besides, the impact force of the discharged fluid on the stepped surface of pipe joints increases with the diameter of pipe joints. (2) Inner diameter of risers The mud discharge with different riser inner diameters is calculated based on the 3D CFD model, as shown in Figs. 14 and 15. Fig. 14 shows that the discharge velocity increases with riser inner diameter. The main reason is that the viscous effect on the discharged mud in the center of risers decreases as the riser inner diameter increases. The fluid can discharge more fluently with large riser inner diameter. Fig. 15 shows that the force on risers increases with riser inner diameter. As the riser inner diameter increases, the action area of viscous force on risers in­ creases. The corresponding viscous force on risers increases with riser inner diameter.

Fig. 15. Forces on risers with different inner diameters.

(3) Mud density The fluid discharge velocity and force on the riser wall under different mud densities of 1200 kg/m3, 1400 kg/m3, 1600 kg/m3, 1800 kg/m3 and 2000 kg/m3 are calculated respectively, as shown in Figs. 16 and 17. The results show that the discharge velocity and force on risers increase obviously with mud density. As the mud density increases, the viscous force on risers increases due to a large viscous resistance of mud, as shown in Fig. 17. Besides, the gravity of the discharge fluid also in­ creases with mud density. The increase of the mud gravity is dominant compared with the increase of viscous resistance. Therefore, the discharge velocity increases with the mud density, as shown in Fig. 16. (4) Mud dynamic viscosity The fluid discharge velocity and force on risers under different mud dynamic viscosity of 0.02 Pa s, 0.04 Pa s, 0.08 Pa s, 0.10 Pa s and 0.12 Pa s are calculated respectively. Figs. 18 and 19 show that the discharge velocity decreases and force on the riser wall increases with mud dy­ namic viscosity. The main reason is that viscous force on the riser wall increases as the mud dynamic viscosity increases. The discharge mud velocity is then reduced due to a large viscous force.

Fig. 16. Discharged velocities in risers with different mud density.

Fig. 17. Forces on risers with different mud density.

5. Conclusions The discharged mud needs to be simulated accurately since it can produce a huge load on risers. Existing models including Young’s slug model, SFM model, WFC model, and one-dimensional finite volume model cannot simulate the radial velocity of mud, the mixing interface

Fig. 14. Discharged velocities in risers with different inner diameters. 9

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that fluid properties, especially mud density, have great influence on the discharge velocity and the force on the riser wall. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Xianglei Wang: Methodology, Software, Investigation, Writing original draft. Xiuquan Liu: Conceptualization, Supervision. Shenyan Zhang: Writing - review & editing. Guoming Chen: Project adminis­ tration. Yuanjiang Chang: Resources. Acknowledgements

Fig. 18. Discharged velocities in risers with different mud dynamic viscosity.

This work was supported by National Natural Science Foundation of China (Grant No: 51809279), Major National Science and Technology Program (Grant No. 2016ZX05028-001-05), National Program on Key Basic Research Project (Grant No. 2015CB251203), Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT14R58), Fundamental Research Funds for the Central Univer­ sities (Grant No. 17CX02025A), and Research Initiation Funds of China University of Petroleum (Grant No. Y1703008). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.petrol.2020.107105. References Adaze, E., Badr, H.M., Al-Sarkhi, A., 2019. CFD modeling of two-phase annular flow toward the onset of liquid film reversal in a vertical pipe. J. Petrol. Sci. Eng. 175, 755–774. Bagheri, M., Alamdari, A., Davoudi, M., 2016. Quantitative risk assessment of sour gas transmission pipelines using CFD. J. Nat. Gas Sci. Eng. 31, 108–118. Burlutskii, E., 2018. CFD study of oil-in-water two-phase flow in horizontal and vertical pipes. J. Petrol. Sci. Eng. 162, 524–531. Cebeci, 2013. Analysis of turbulent flows. Chem. Heterocycl. Compd. 13 (10), 1083–1086. Chang, Y., Chen, G., Wu, X., Ye, J., Chen, B., Xu, L., 2018. Failure probability analysis for emergency disconnection of deepwater drilling riser using Bayesian network. J. Loss Prev. Process. Ind. 51, 42–53. Grønevik, Arid, 2013. Simulation of Drilling Riser Disconnection - Recoil Analysis. Master thesis of Norwegian University of Science and Technology. Grytøyr, G., Sharma, P., Vishnubotla, S., 2011. Marine Drilling Riser Disconnect and Recoil Analysis. American Association of Drilling Engineers, AADE-11-NTCE, p. 80. Kharoua, N., Alshehhi, M., Khezzar, L., Filali, A., 2017. CFD prediction of black powder particles’ deposition in vertical and horizontal gas pipelines. J. Petrol. Sci. Eng. 149, 822–833. Lang, D.W., Real, J., Lane, M., 2009. Recent developments in drilling riser disconnect and recoil analysis for deepwater applications. In: ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. Launder, B.E., Spalding, D.B., 1972. Lectures in Mathematical Models of Turbulence (London, England). Li, C.W., Fan, H.H., Wang, Z.M., Ji, R.Y., Ren, W.Y., Xu, F., 2016. Two methods for simulating mud discharge after emergency disconnection of a drilling riser. J. Nat. Gas Sci. Eng. 28, 142–152. Li, S., Campbell, M., Howells, H., Powell, S., 2012. Effect of mud shedding on riser antirecoil control at emergency disconnect. In: ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. Liu, X., Chen, G., Chang, Y., Liu, K., Zhang, L., Xu, L., 2013. Analyses and countermeasures of deepwater drilling riser grounding accidents under typhoon conditions. Petrol. Explor. Dev. 40 (6), 791–795. Liu, X., Chen, G., Chang, Y., Ji, J., Fu, J., Song, Q., 2016. Drift-off warning limits for deepwater drilling platform/riser coupling system. Petrol. Explor. Dev. 43 (4), 701–707. Ma, P., Pyke, J., Vankadari, A., Whooley, A., 2013. Ensuring safe riser emergency disconnect in harsh environments: experience and design requirements. In: The 23 International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers, Anchorage, Alaska, p. 7.

Fig. 19. Forces on risers with different mud dynamic viscosity.

between mud and seawater and the mud discharge in complicated riser flow channels. A more accurate and applicable 3D CFD model for mud discharge is proposed. The standard k-ε turbulence model is used to calculate the full turbulent region. The wall function method is used to simulate the near-wall region. The Level set theory is adopted to track the mixing interface between mud and refilled seawater. The mud discharge process is simulated based on the established 3D CFD model. Flowing profiles of the discharged fluid and the mixing interface between two fluids are successfully captured through the 3D CFD model. Besides, characteristics of the mud discharge including the radial velocity and axial velocity are studied. It turns out that the radial velocity and axial velocity of the discharged fluid are not uniform. The radial velocity gradient near the riser wall is large and small in other regions. The axial velocity gradient is small. The 3D CFD model is compared with other models based on New­ ton’s second law. The reasons for differences among each model are also analyzed in detail. In summary, Young’s slug model is appropriate for mud discharge simulation of risers without refill valve. SFM model needs to be modified before being used for mud discharge calculation. WFC model is accurate in the mud discharge simulation. 3D CFD model is more accurate and applicable. Extensional functions such as the simulation of flow field and mud discharge in complicated riser flow channels can also be realized through the proposed 3D CFD model. Several main factors including drill pipes with pipe joints, riser inner diameter, mud density and mud dynamic viscosity affecting the mud discharge are investigated based on 3D CFD method. The results show 10

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Journal of Petroleum Science and Engineering 190 (2020) 107105 Puccio, W.F., Nuttall, R.V., 1998. Riser recoil during unscheduled lower marine riser package disconnects. In: IADC/SPE Drilling Conference. Society of Petroleum Engineers, Dallas, Texas, p. 20. Wang, K., Shi, T., He, Y., Li, M., Qian, X., 2019. Case analysis and CFD numerical study on gas explosion and damage processing caused by aging urban subsurface pipeline failures. Eng. Fail. Anal. 97, 201–219. Wang, Y., Gao, D., 2019. Recoil analysis of deepwater drilling riser after emergency disconnection. Ocean Eng. 189, 106406. Wang, T., Wang, K., 2018. Analysis of resilient response of emergently disentangled drilling risers. China Offshore Oil Gas 30 (2), 120–125. Wilcox, D.C., 2006. Turbulence Modeling for CFD. DCW Industries. Yakhot, V., Orszag, S.A., 1986. Renormalization group analysis of turbulence. I. basic theory. J. Sci. Comput. 1, 3–51. Young, R.D., Hock, C.J., Karlsen, Geir, Miller, J.E., 1992. Analysis and design of antirecoil system for emergency disconnect of a deepwater riser: case study. In: Offshore Technology Conference, p. 10. Houston, Texas. Zheng, C., Liu, Y., Wang, H., Zhu, H., Liu, Z., Ji, R., Shen, Y., 2015. Structural optimization of downhole fracturing tool using turbulent flow CFD simulation. J. Petrol. Sci. Eng. 133, 218–225.

Meng, S., Che, C., Zhang, W., 2018. Discharging flow effect on the recoil response of a deep-water drilling riser after an emergency disconnection. Ocean Eng. 151, 199–205. Miller, J.E., Stahl, M.J., Matice, C.J., 1998. Riser collapse pressures resulting from release of deepwater mud columns. In: Offshore Technology Conference, p. 9. Houston, Texas. Miller, J.E., Young, R.D., 1985. Influence of mud column dynamics on top tension of suspended deepwater drilling risers. In: Offshore Technology Conference. Offshore Technology Conference, Houston, Texas, p. 6. Nahavandi, N.N., Farzaneh-Gord, M., 2014. Numerical simulation of filling process of natural gas onboard vehicle cylinder. J. Braz. Soc. Mech. Sci. Eng. 36 (4), 837–846. Nie, Z.Y., Chang, Y.J., Liu, X.Q., Chen, G.M., 2019. A DBN-GO approach for success probability prediction of drilling riser emergency disconnection in deepwater. Ocean Eng. 180, 49–59. Olsson, E., Kreiss, G., 2005. A conservative level set method for two phase flow. J. Comput. Phys. 210, 225–246. Pereira, T.W.C., Marques, F.B., Pereira, F.D.A.R., Ribeiro, D.D.C., Rocha, S.M.S., 2016. The influence of the fabric filter layout of in a flow mass filtrate. J. Clean. Prod. 111, 117–124.

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