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Study on the static behavior of installing a deep-water drilling riser on a production platform
Journal of Petroleum Science and Engineering xxx (xxxx) xxx
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Study on the static behavior of installing a deep-water drilling riser on a production platform Deqiang Tian a, *, Honghai Fan a, Bernt J. Leira b, Svein Sævik b a b
College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China Department of Marine Technology, Norwegian University of Science and Technology, Trondheim 7052, Norway
A R T I C L E I N F O
A B S T R A C T
Keywords: Riser installation Tension leg platform Riser interference Finite-difference-method Weather window
Riser interference caused by wake effects between adjacent risers severely threatens the safety during riser installation process on a Dry-Tree Tension Leg Platform (TLP) system. Due to the ignorance of interference effect, the static deflection of the drilling riser during installation is highly over-estimated in previous work. To obtain a static behavior of a drilling riser during installation, this paper built a dual-riser model where two risers are arranged in tandem and considered as Bernoulli beam subjected to steady ocean current. The modified Huse model is applied to study the interference between object risers. Then, the structural equation is solved by FiniteDifference-Method (FDM). Case studies show that an upstream production riser can largely reduce the deflection of a downstream hung-off drilling riser, hence increasing the probability of the collision of two risers. The in fluence of water depth, riser wall thickness, Blowout Preventer (BOP) weight, etc. are also studied. Finally, the current condition based weather windows with respect to wind and tidal current velocity are obtained corre sponding to different operation conditions. Results show that installing a drilling riser with lower BOP weight in shallow water is most feasible for multi-riser TLP systems. Moreover, drilling riser installation operability can be improved by increasing the top tension of the production riser.
1. Introduction Riser installation is of great significance to a successful deep-water drilling operation and an economic efficiency of the whole project as oil and gas industry moves to deep water. In recent years, there has been a trend to bring production online with a few pre-drilled wells and then drill and complete the rest of the field using a production platform (Koska et al., 2013). This can help the developers start to recover the up-front capital costs more quickly and eliminating the need for a separate drilling vessel. This reduces the overall cost to develop the field. However, due to economical and practical considerations, marine risers on offshore platforms are commonly arranged in clusters with relatively close spacing (i.e, with a typical center to center spacing be tween adjacent wellbays of 5~6 m). Riser collision is therefore more likely to occur for such compact arrangements. Wake interference plays an important role in increasing the probability of collision of two risers, which takes place when a downstream riser is located in the wake field of an upstream riser. The wake interference will change the flow around the downstream riser, i.e. reducing the local flow velocity, and, conse quently reduce the associated drag force. This effect in turn can reduce
the clearance between adjacent risers and will accordingly imply a po tential for collision between them. This issue will be further complicated when installing a drilling riser near top tensioned production risers on a platform. As show in Fig. 1, before drilling a well in the ocean, the conductor needs to be installed primarily. Then, the BOP/LMRP are installed, by using the drilling riser, through the water column in order to connect the subsea well head above the mudline. During the instal lation process, the drilling riser is in the hung-off mode and the length of the drilling riser is variable at different stages. Fan et al. (2017) reported that a suspended riser without any restriction at its lower end is more flexible and more unstable in complex sea states than a connected riser. How to safely and quickly installing a drilling riser near a top tensioned production riser has become a key challenge for deep water Dry Tree TLP systems. Restricted wellbay and seabed spacing, high current con ditions, and requirements for no contact with adjacent production riser are all contributors to the challenges faced during the design phase. In the last four decades, significant advances have been made on the mechanical property of connected marine riser. Burke (1974) performed a static analysis for a marine riser by using a beam model and deduced the general riser control differential equation based on elastic mechanic method. Azpiazu and Nguyen (1984) analyzed the vertical dynamics of
* Corresponding author. College of Petroleum Engineering, China University of Petroleum-Beijing, No.18 Fuxue Road, Beijing 102249, China. E-mail address: [email protected] (D. Tian). https://doi.org/10.1016/j.petrol.2019.106652 Received 7 June 2019; Received in revised form 27 October 2019; Accepted 4 November 2019 Available online 9 November 2019 0920-4105/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Deqiang Tian, Journal of Petroleum Science and Engineering, https://doi.org/10.1016/j.petrol.2019.106652
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Nomenclature E I Te ðzÞ wa fðzÞ Kuf Klf Lpr; Ldr M θ CDu ; CDd du ; dd b
Ttop Ttc Wb
Young’s modulus, Pa rotational inertia of the riser cross section, m4 effective axial force in riser, N apparent weight per unit length of riser, N/m hydraulic force per unit length of riser, N/m rotation stiffness of Upper Flex Joint (UFJ), N⋅ m=rad rotation stiffness of Lower Flex Joint (LFJ), N⋅ m=rad total length of production and drilling riser, m bending moment in the riser, N⋅m slope of riser drag coefficient of upstream and downstream riser, respectively diameter of upstream and downstream riser, m half width of the wake, m
ρw
uw ut h Δz Cm
ρs ρf
WD Δdu ; Δdd Δs
top tension force acting on the production riser, N top tension coefficient total mass of BOPS and LMRP attached to drilling riser, t density of sea water, kg/m3 wind current velocity, m/s tidal current velocity, m/s total water depth, m length of riser segment, m mass coefficient riser density, kg/m3 production fluid density, kg/m3 water depth, m wall thickness of upstream and downstream riser, m Riser spacing, m
investigation emphasizing on nonlinear free vibrations of marine risers to determine the nonlinear natural frequencies and their corresponding mode shapes. Montoya-Hern� andez et al. (2014) presented a numerical algorithm to evaluate the vibrations of vertical rigid production risers under internal multiphase flow behavior. Other researchers also did some work about the mechanical behavior of marine risers during installation or in hung-off mode. Patel and Jesudasen (1987) presented a theoretical and experimental investiga tion of the lateral dynamics of free hanging marine risers. The in-plane behavior was investigated through a finite element analysis of the riser pipe and its hydrodynamic loading. Ambrose et al. (2001) studied the possibilities of using the soft hung-off option and compares the perfor mance characteristics of the drilling riser in the soft hung-off and hard hung-off configurations, particularly for ultra-deep water applications down to 10,000 ft. Itoh et al. (2006) presented an experimental and numerical investigation of behavior characteristics of hung-off riser that considered oscillation of floating structure. Dai et al. (2009) investigated the mechanical behavior of drilling riser under hung-off working con ditions by using FEM software ABAQUS. Williams (2010) discussed optimization of drilling riser operability envelopes for harsh environ ments, in which the soft/hard riser hung-off configurations for storm events were assessed. Wu et al. (2014) presented a dynamical model to simulate the dynamic response of hard hung-off drilling riser consid ering the wave and current effects, the platform motion and the large deformation of drilling riser. Wang et al. (2014a, 2014b, 2015a, 2015b) presented some common formulations for deep water riser static and dynamic analysis during its installation on a drill ship. Fan et al. (2017) established a time-domain dynamic FEM method by the Wilson-θ algo rithm for a hung-off riser and compared the dynamic envelops of the hung-off riser in different situations. Hu et al. (2018) developed a novel analysis model with varying riser length to analyze the dynamic be haviors of a marine riser during the installation of a subsea production tree. Though these significant researches have been done, more work is still required within this area. For instance, most of the studies mentioned above are about riser mechanical behavior after subsea wellhead and floating platform have been connected. The research of riser mechanical behavior during installation is insufficient. Although several other researchers did a few investigations on the riser mechan ical characteristics in hung-off mode, they didn’t consider the interfer ence effects generated by the adjacent production risers. The importance of interference effects to deep-water drilling riser has been discussed above. Ignoring this effect will make the static deflection of the drilling riser being highly over-estimated during the installation process. In addition, little literature on collision assessment of riser installation was found. Accordingly, the present study established a dual-riser model
Fig. 1. Sketch of dual-riser model.
marine riser to determine the amplitude of dynamic forces and displacement caused by heave action. Patel et al. (1984) developed a two-dimensional finite element computational method for determining marine riser displacement and stresses due to self-weight, buoyancy, internal and external pressures, surface vessel motions and environ mental forces arising from currents and waves. Moe and Larsen (1997) presented an asymptotic solution of the differential equation describing the motions of marine risers in more than 1000 m water depth. Atadan et al. (1997) made some analytical and numerical analysis of the dy namics of a marine riser connected to a floating platform. The effects of the structural and hydrodynamic parameters on motion amplitude are evaluated and analytically studied based on an approach developed by Butenin. Furnes (2000) developed a mathematical formulation for solving the beam equation by considering arbitrary currents that vary continuously with depth and time. Kaewunruen et al. (2005) made an 2
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with consideration of interference effects to fill this gap. In the model, the production riser and the installation drilling riser are arranged in tandem for the purpose of the example study. The modified Huse wake model is used to investigate the interference caused by the production riser. Finally, to predict whether a drilling riser can be installed safely on a platform, the weather window (safe installation window) is deter mined by using a novel calculating procedure.
2.2. Interference model The ocean current profile must be determined before calculating hydrostatic forces on the riser body. The current velocity will be changed due to the presence of the upstream riser. Huse (1992) introduced the concept of a ‘virtual source’, which is illustrated in Fig. 2, in order to estimate the local flow velocity in the wake field. The mean flow velocity at any position in the two-dimensional wake field, e.g. Pðx0 ; y0 Þ, can be expressed as: 8 > uðx0 ; y0 Þ ¼ U0 uðx0 ; y0 Þ > > > sffiffiffiffiffiffiffiffiffiffiffiffiffi > > � > �y �2 � > CDu ⋅du > 0 < ⋅exp 0:693 uðx0 ; y0 Þ ¼ U0 xs b (4) > > pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > bðx0 Þ ¼ 0:25⋅ CDu ⋅du ⋅xs > > > > :x ¼ x þ x s 0 v
2. Analytic model 2.1. Dual-riser model A typical configuration for a production riser and a drilling riser is shown in Fig. 1. The steady ocean current is assumed to flow from the production riser to the drilling riser. Since the drilling riser is often surrounded by production risers in reality, so it is reasonable to set the production riser upstream in the static analysis process. The production riser is tensioned by a tensioner system at the top and is connected by a Lower Flex Joint (LFJ) at the bottom on the subsea well head. The top of the drilling riser is supported at the drilling floor and with a mass block (BOP/LMRP) connected to the bottom end. Both the production riser and the drilling riser are assumed to be homogeneous, isotropic and linear elastic with constant diameters. The connection point between the riser top and the platform is selected as the origin of the local coordinate system. The production riser and the hung-off drilling riser share the same governing differential equation (Sparks, 2007; Chen et al., 2017) which can be represented as: EI ⋅
d4 x dz4
Te ðzÞ ⋅
d2 x dx þ wa ⋅ ¼ f ðzÞ dz2 dz
where uðx0 ; y0 Þ is the wake velocity deficit at position Pðx0 ; y0 Þ, U0 is the inflow velocity, CDu and du are the drag coefficient and diameter, respectively, of the upstream riser located in free stream. b is the half width of the wake which is defined as: when y ¼ b, u � 0:5U0 . The parameter Xv represents the distance from the virtual source to the up stream riser center. It is written as: (5)
xv ¼ 4du =CDu
Apparently, the wake velocity distribution of the upstream riser now can be computed by using this model. However, the problem is that the properties of the wake field vary over the area occupied by the down stream riser. In order to solve this problem, the root-mean-square (RMS) value, i.e. Urms ðxd Þ, averaged over the cross-section area of the down stream riser is used for calculating the hydrostatic force. The RMS ve locity can be expressed as:
(1)
where EI is the bending stiffness of the riser along the z axis, N⋅ m2 . x is the local riser deflection in the positive direction (which is the same as the current direction); the positive direction of z is vertical (directed towards the Mean Sea Level (MSL)). The boundary conditions of the production riser and the drilling riser are different corresponding to the different top and end connectivity conditions. Because the production riser is top tensioned by a tensioner and bottom hinged by a spherical joint, so the deformation equal to zero at the top and bottom of the production riser. The bending moment could be expressed by using elastic mechanical equations. Therefore, the boundary conditions of the top tensioned production riser can be written as: 8 xjz¼0 ¼ 0; xjz¼Lpr ¼ 0; > > > > � � > 2 > > < Mj ¼ EI⋅d x�� ¼ K ⋅dx�� uf z¼0 dz2 �z¼0 dz�z¼0 (2) > > � � > 2 > > d x� dx� > > ¼ Klf ⋅ �� : Mjz¼Lpr ¼ EI⋅ 2 �� dz z¼Lpr dz z¼Lpr
8 < 1 Z Urms ðxd Þ ¼ :πR2d
Rd
Z
Rd
912 =
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi R2d ðx xd Þ
2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi u ðx; yÞdxdy R2d ðx xd Þ
;
(6)
where Rd is the radius of the downstream riser, xd represents the dis tance between the downstream center and origin pf coordinate. 2.3. Forces on the riser 2.3.1. Effective axial force Similar to pipe string mechanics problems (Chen et al., 2015), effective axial force on the riser body should be determined firstly. Since the production riser is top tensioned and pinned at the bottom with the LFJ, the effective axial force is represented by: � Tep ðzÞ ¼ Ttop wa ⋅z (7) Ttop ¼ Ttc⋅wa ⋅Lpr where Tep ðzÞ is the effective axial force of the production riser at a depth coordinate equal to z m; Ttop is the top tension force acting on the
Since the bottom end of the hung-off drilling riser is free, so both the bending moment and slope equal to zero at the bottom end; Due to the top end of the drilling is supported at the drilling floor, so the defor mation and slope equal to zero at the top end. Hence, the boundary conditions of the hung-off drilling riser are given by: � 8 dx�� > xjz¼0 ¼ 0; θj ¼ ¼ 0; > z¼0 > > dz�z¼0 > > > > � < d 2 x� (3) Mjz¼Ldr ¼ EI⋅ 2 �� ¼ 0; > dz z¼Ldr > > > � > > � > > : θjz¼Ldr ¼ dx� ¼0 dz�z¼Ldr where M is the bending moment in the riser, and θ is the slope of the riser.
Fig. 2. Sketch of two-dimensional wake flow downstream of a riser. 3
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production riser; Ttc is the top tension coefficient. The BOP and LMRP are connected at the end of the hung-off drilling riser. The total mass of the BOP and the LMRP is defined as Mb , while the effective axial force on the drilling riser section can be expressed as: Ted ðzÞ ¼ wa ⋅ ðLpr
(8)
zÞ þ Wb ⋅g
2.3.2. Lateral force Morison’s Equation is used to calculate the lateral hydraulic force per unit riser length, which is represented as: 1 f ðzÞ ¼ ρw ⋅ d ⋅ CD ⋅uðzÞ2 2
(9)
where ρw is the density of sea water, kg/m3; d is the outside diameter of the riser; CD is the drag coefficient; uðzÞ is the inflow velocity at a depth coordinate of z m. It is evident from the foregoing that uðzÞ should be replaced with Urms ðxd ; 0; zÞ when calculating the hydrostatic force acting on the downstream drilling riser. The sea current profile at a certain depth coordinate, e.g. z m, can be computed by Eq. (10) if there is no measured data of the marine envi ronment (Fang and Duan, 2014): uðzÞ ¼ ut ⋅
� h
�1 z 7 h
þ uw
� h
z
� (10)
h
where uw is the wind current velocity, m/s; ut is the tidal current ve locity, m/s and h is the water depth, m. Fig. 3. Schematic of dual-riser model discretization.
3. Numerical model 3.1. Solving governing equations
8 x3 ¼ 0; xn 2� ¼ 0 > > > > < 2EI Kuf ⋅Δz�⋅x2 4EI⋅x3 þ 2EI þ Kuf ⋅Δz� ⋅x4 ¼ 0 > > > > 2EI þ Klf ⋅Δz�⋅xn 3 4EI⋅xn 2 þ : 2EI Klf ⋅Δz ⋅xn 1 ¼ 0
In order to compute the lateral deformation of the riser, the Finite Difference Method (Xu et al, 2018) is used to solve Eq. (1). The models of the production riser and the drilling riser are discretized, respectively, as shown in Fig. 3. Taking the production riser as an example, the following finite dif ference schemes are used to discretize Eq. (1): 8 dx xiþ1 xi 1 > ¼ > > 2Δz > dz > > > > > d2 x xiþ1 2xi þ xi > > ¼ > > < dz2 ðΔzÞ2 > d3 x xiþ2 > > ¼ > > > dz3 > > > > > > d4 x xiþ2 > : ¼ dz4
There are n equations in total with n variables when combining Eq. (12) and Eq. (13), which can be transformed into the following matrix equation: ½A� ⋅ ½x� ¼ ½B�
1
xi
½xi � ¼ ½x1 ; x2 ; x3 ; ⋯; xn 2 ; xn 1 ; xn �T is the matrix of the production riser
(11)
2
lateral deformation; ½B� ¼ ½0; 0; fð3Þ; fð4Þ; ⋯; fðn 2Þ; 0; 0�T is the force matrix. The static deflection of the upstream production riser can be easily obtained by solving the linear system Eq. (14). The hung-off drilling riser have the same form of discretized governing equation as Eq. (12). The discretized boundary conditions are represented as: 8 ex3 ¼ 0 > > < ex2 þ e x4 ¼ 0 (15) exm 3 2e xm 2 þ e xm 1 ¼ 0 > > : exm 3 þ exm 1 ¼ 0
2ðΔzÞ3 4xiþ1 þ 6xi
(14)
where ½A� is the coefficient matrix with respect to αi , βi , γ i , ϕi , ηi ;
1
2xiþ1 þ 2xi
(13)
4xi
1
þ xi
2
ðΔzÞ4
The discretized production riser governing equation can be deduced by taking Eq. (11) into Eq. (1), which gives: 8 αi xi 2 þ β xi 1 þ γ xi þ ϕ xiþ1 þ η xiþ2 i i i i > > > > > ¼ f ðiÞ ð3 � i � n 2Þ > > > > > EI > > > αi ¼ ηi ¼ > 4 > ðΔzÞ > > > > < 4EI Tep ðzÞ wa βi ¼ > ðΔzÞ4 ðΔzÞ2 2Δz > > > > > > 6EI 2Tep ðzÞ > > γi ¼ þ > > 4 > ðΔzÞ ðΔzÞ2 > > > > > > Tep ðzÞ wa > : ϕ ¼ 4EI þ i ðΔzÞ4 ðΔzÞ2 2Δz
The matrix equation for the drilling riser is then expressed as: e ⋅ ½e e ½A� x� ¼ ½B�
(12)
(16)
e is the coefficient matrix with respect to e ei , e where ½A� αi , eβi , eγi , ϕ ηi ; T x2 ; e x3 ; ⋯; e xm 2 ; e xm 1 ; e xm � is the matrix of the production riser ½e x� ¼ ½e x1 ; e e ¼ ½0; 0; efð3Þ; efð4Þ; ⋯efðn 2Þ; 0; 0�T is the force lateral deformation; ½B� matrix.
The discretized boundary conditions for the production riser can also be obtained by substituting Eq. (11) into Eq. (2), which gives:
3.2. Iterative solution Based on Eq. (9), the lateral hydraulic force on the downstream 4
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drilling riser highly depends on the RMS wake velocity Urms ðxd ; 0; zÞ, which, however, is a function of the clearance between the two risers. Thus, the drag force profile will vary along the drilling riser due to the curved production riser and the corresponding altered wake profile. Since the dual-riser model has been discretized in the previous sec tion, the downstream wake profile can be established by calculating the relative distance between each pair of riser segments, from the curved upstream riser to the deformed downstream riser which is obtained by using the upstream current profile. To determine the equilibrium posi tion of the dual-riser system, an iteration procedure is introduced: (1) Calculate the configuration of the upstream production riser and the downstream drilling riser by using the origin current profile; (2) Determine the vertical wake profile Urms ðxd ; 0; zÞi based on the deformation of the dual-riser system; (3) Perform the static analysis by updating the downstream wake profile, and then, calculate the average distance between each pair of riser segments, i.e. xi ; (4) Calculate Urms ðxd ; 0; zÞiþ1 based on the new xi ; (5) Repeat steps 2–4 until the algorithm convergences. The flow field around the production riser is assumed to be steady, which implies that it will not be influenced by the deflection of the drilling riser. In addition, the drag coefficients for both risers are taken to be constant in time. The entire solution procedure is summarized in Fig. 4. 4. Case study
Fig. 4. Flowchart of the calculation procedure.
4.1. Benchmark The entire static analysis is performed by using a self-developed MATLAB program which is based on the Finite Difference Method. The program is verified by comparing it with the global riser analysis software Riflex (2017). Fig. 5 provides the static lateral deformation of a top tensioned production riser with a length of 327 m. The outside diameter is 0.324 m and the wall thickness is 0.0165 m; the top tension coefficient is 1.5; the wind current velocity and tidal current velocity are both 0.5 m/s. The comparison shows that the result calculated by the self-developed MATLAB program agrees well with the Riflex result. 4.2. Case study parameters For the purpose of investigating this problem, an actual deep-water drilling and production platform is taken as an example. A drilling riser is to be installed near a top tensioned production riser. The riser spacing is 5 m. Key properties of the dual-riser system are given in Table 1. 4.3. Results and discussions
Fig. 5. Verification of the program code.
Based on the previous discussion, the lateral deformation of the drilling riser will be influenced by the upstream production riser due to the wake effect. Fig. 6 gives the detailed riser deformation for a relative mild weather condition where the wind current velocity and tidal cur rent velocity are both 0.4 m/s. Five installation stages: 20%, 40%, 60%, 80% and 100% of the water depth are considered, respectively. The top tension coefficient of the production riser is 1.5; the total mass of the connected BOP is 150t; the wall thickness of the production riser and drilling riser are 0.65 inch and 0.625 inch, respectively; the origin riser spacing Δs is 5 m. In Fig. 6, the dashed lines represent the results without considering the wake effect from the upstream production riser. It is obvious that the upstream production riser has a great impact on the downstream drilling riser during installation. The lateral deflection of the drilling riser will decrease significantly in the downstream region of a production riser.
Table 1 Properties of the dual-riser system. Parameters
Values
Parameters
WD(m)
500
Cm
2.0
7850
ρw (m)
1025
ρs (kg.m3)
ρf (kg.m3)
1200
E(Gpa)
210
du (m)
Wb (T)
100–300
Ttc
1.2–1.85
0.324
Δdu (m)
0.0123–0.0254
dd (m)
0.5334
Δdd (m)
0.0123–0.0254
Kuf (N.m/rad)
12880
CDu ; CDd
Klf (N.m/rad)
5
Values
1.2 27116
uw (m/s)
0.2–0.6
Ldr(m)
100–500
ut (m/s)
0.3–0.75
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Fig. 6. Riser configurations at different installation stages.
Fig. 8. Dual-riser configuration for various production riser sizes.
Furthermore, the decrease of the amplitude of the riser deflection still tends to be increasing for increasing installation depth. Therefore, there is a potential for collision between the production riser and the drilling riser during the installation process, especially when the weather con dition is not sufficiently mild, as shown in Fig. 7. All of the parameters giving the results in Fig. 7 are the same as for Fig. 6 except the weather condition, for which the tidal current velocity and wind current velocity are replaced with 0.42 m/s and 0.6 m/s, respectively. It is clear that the drilling riser can potentially collide with the production riser at the 40%–50% installation stage which can be defined as the relevant colli sion area. Installation of a drilling riser in this specific condition is not to be recommended. Clearly, the feasibility of performing the installation will depend largely on the weather condition. Still, some other factors, such as the riser size (wall thickness), the weight of the BOP and the top tension, will also have an influence on the configuration of drilling riser during installation. In order to provide a best possible guidance in relation to the riser installation, the above mentioned factors are all discussed in more detail in the following sections.
results in Fig. 6 except the production riser wall thickness. From Fig. 8, the deformation of the production riser will decrease for increasing riser wall thickness. This will reduce the wake effect for the drilling riser and consequently increase the drilling riser deformation. Fig. 9 provides the variation of the riser deformation for different values of the drilling riser wall thickness. In the figure, all the parame ters are kept constant except the drilling riser wall thickness. As shown in Fig. 9, the deformation of the drilling riser will gradually decrease for increasing drilling riser wall thickness. This is because the increasing riser wall thickness will increase the bending stiffness EI and the apparent weight wa of the riser body. These two effects will in turn reduce the drilling riser deformation. In order to reduce the tension level of the drilling riser and extend the clearance between dual-riser system to avoid collision, a relatively large production riser wall thickness and small drilling riser wall thickness is a good combination in relation to the installation process.
4.3.1. Riser wall thickness The production and drilling riser wall thickness will affect the configuration of the dual-riser system in two ways. Fig. 8 shows the riser deformation under different wall thicknesses of the production riser. In this case, all parameters are kept constant for the
4.3.2. Mass of BOP In this case, all the parameters are kept constant for the results shown in Fig. 6 except the BOP weight which is varied from 100 T to 300 T. Fig. 10 shows riser deformations under different BOP weights. As shown in Fig. 10, the drilling riser deformation decreases for increasing BOP weight. This is because the effective axil force of the riser body is increased due to the increasing BOP weight. It is clear that the drilling riser deformation is comparatively sensitive to the variation of the BOP
Fig. 7. Riser collision during installation process in bad weather condition.
Fig. 9. Dual-riser configuration for various drilling riser sizes. 6
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Fig. 10. Dual-riser configuration for various BOP weights.
Fig. 12. Dual-riser configuration for various tidal current velocities.
weight. Therefore, connecting a lighter BOP is also a good option during the installation process.
4.3.4. Tidal current velocity and wind current velocity Weather conditions are key factors that need to be considered prior to installing the drilling riser. Based on the foregoing discussion, the collision area near the largest deformation point of the production riser should be focused on. In this case, a particular position is considered, i.e. when BOP is lowered to half of the water depth. This is selected as the reference point for the calculations.
Fig. 12 gives the variation of riser deformation for different tidal current velocities ranging from 0.2 m/s to 0.6 m/s, whereas all other parameters are kept constant. It can be seen clearly that the tidal current velocity has a significant influence on both the production riser and the drilling riser. However, it should be noticed that the deformation magnitude of production riser is much larger than for the drilling riser. This might eventually result in riser collision once the tidal current ve locity exceeds the critical value, e.g. 0.6 m/s in this case. Fig. 13 shows the variation of riser configuration for different wind current velocities ranging from 0.3 m/s to 0.75 m/s. Similarly, all the other parameters are kept constant. It is can been seen that the riser deformation is more sensitive to the tidal current velocity than the wind current velocity. Furthermore, there is also a critical value for the wind current velocity, e.g. 0.75 m/s in this case, when the tidal current ve locity is kept constant. Typically, the installation process should be performed for mild weather conditions with tidal current velocity and wind current velocity as low as possible. Large wind and tidal current velocity can result in large bending deformations and higher stresses for the riser body; sec ond, it will significantly reduce the clearance between the drilling riser and the production riser, and consequently make them prone to collide with each other. However, perfect weather condition is usually difficult to achieve, which will have a negative impact on the TLP project economy. Hence, the weather windows for installation corresponding to different operation conditions are important to establish.
Fig. 11. Dual-riser configuration for various top tension coefficients.
Fig. 13. Dual-riser configuration for various wind current velocites.
4.3.3. Production riser top tension It is clear that the deformation of the drilling riser partly depends on the production riser lateral deflection. However, the top tension can significantly reduce the deformation of production riser. The results presented in Fig. 11 are based on varying the top tension coefficient of the production riser in the range 1.2–1.85, whereas other parameters are kept constant. As shown in Fig. 11, the deformation of the production riser decreases significantly by increasing the top tension coefficient. This is because a large top tension will increase the effective axial ten sion of the production riser. Subsequently, the decreasing production riser deformation will reduce the wake effect for the drilling riser and accordingly reduce the drilling riser deformation. So, it is feasible to increase the top tension coefficient within permission when suffering from riser interference effect during drilling riser installation.
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4.3.5. Weather windows As can be seen from section 4.3.4, for a given tidal current velocity, there is a critical value for the wind current velocity with respect to mechanical collision, and vice versa. Therefore, the weather window can be obtained by taking the values of wind current velocity and tidal current velocity as the x axis and y axis, respectively. The difference is that the calculation point is not fixed at half the water depth anymore, but runs from MSL to the mudline. The model can then be applied to evaluate whether collision happens or not for a specific weather condition. Fig. 14 gives the current condition based weather windows for different water depths, BOP weights, and top tension coefficients. Fig. 14-(a) illustrates that the drilling riser connected with lighter BOP will have a wider installation weather window. However, the difference is not obvious for smaller water depths, e.g. 500 m in this case. Fig. 14(b) shows the result for 1000 m water depth. It can be seen clearly that the BOP weight has a significant influence on the allowable current conditions. This implies that reducing the BOP weight can extend the installation weather window. Nevertheless, it should be noted that the weather window at 1000 m water depth is obviously narrower than that at 500 m water depth. Fig. 14-(c) and Fig. 14-(d) show the variations of current condition based weather window for different top tension co efficients at 500 m and 1000 m water depth respectively. Higher top tension coefficients give a wider weather window during installation.
Furthermore, the weather window is obviously quite sensitive to the top tension coefficient whenever in shallow or deep water depth. It thus can be concluded that installing a drilling riser in more shallow water with smaller BOP weight and higher top tension coeffi cient can maximize the drilling riser installation operability. 5. Conclusions Considering wake interference from the upstream production riser is of great importance for a safe installation of a drilling riser on a dry tree TLP. To study the static performance of installing a drilling riser near a production riser, a dual-riser model is developed based on small-angle beam deflection theory and numerically solved by Finite Difference Method. Some conclusions can be summarized as follows: (1) The upstream production riser has a great impact on the down stream installation drilling riser. The calculation results without concerning wake effect from production riser are apparently on the larger side. Furthermore, this error will grow for the increasing installation water depth. (2) The drilling riser tends to clashing with the curved production riser in the collision area which is located near the largest deformation point of production riser.
Fig. 14. Weather windows for installation in different operation conditions. 8
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(3) Drilling riser bending deformation increases for increasing water depth, for increasing production riser wall thickness, for increasing production riser top tension coefficient, for increasing tidal current velocity and wind current velocity, but decreases for the increasing drilling riser wall thickness and connected BOP weight. (4) Installing a drilling riser at shallower water with lighter BOP and higher top tension coefficient can maximize the weather window for the installation operation.
Fang, H., Duan, M., 2014. Offshore Operation Facilities: Equipment and Procedures. Gulf Professional Publishing, pp. 19–22. https://doi.org/10.1016/B978-0-12-3969774.00001-9. Furnes, G.K., 2000. On marine riser responses in time-and depth-dependent flows. J. Fluids Struct. 14 (2), 257–273. https://doi.org/10.1006/jfls.1999.0266. Huse, E., 1992. Current Force on Individual Elements of Riser Arrays, International Offshore and Polar Engineering Conference, pp. 256–262. Sam Francisco, USA. Hu, Y., Cao, J., Yao, B., et al., 2018. Dynamic behaviors of a marine riser with variable length during the installation of a subsea production tree. J. Mar. Sci. Technol. 23 (2), 378–388. https://doi.org/10.1007/s00773-017-0473-7. Itoh, K., Tamura, K., Maeda, K., et al., 2006. Behavior characteristics of hang off riser that considers oscillation of floating structure. In: The 25th International Conference on Offshore Mechanics and Arctic Engineering, pp. 235–240. https://doi.org/ 10.1115/OMAE2006-92222. Kaewunruen, S., Chiravatchradej, J., Chucheepsakul, S., 2005. Nonlinear free vibrations of marine risers/pipes transporting fluid. Ocean Eng. 32, 417–440. https://doi.org/ 10.1016/j.oceaneng.2004.07.007. Koska, R., Kaculi, J., Campbell, M., Mills, D., 2013. Minimizing interference between top tension risers for tension Leg platforms. In: ASME 2013 32nd International Conference on Ocean. https://doi.org/10.1115/1.4024270. Moe, G., Larsen, B., 1997. Dynamics of deep water marine risers-asymptotic solutions. In: The Seventh International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers. Montoya-Hern� andez, D.J., V� azquez-Hern� andez, A.O., Cuamatzi, R., et al., 2014. Natural frequency analysis of a marine riser considering multiphase internal flow behavior. Ocean Eng. 92, 103–113. https://doi.org/10.1016/j.oceaneng.2014.09.039. Patel, M., Sarohia, S., Ng, K., 1984. Finite-element analysis of the marine riser. Eng. Struct. 6, 175–184. https://doi.org/10.1016/0141-0296(84)90045-2. Patel, M.H., Jesudasen, A.S., 1987. Theory and model tests for the dynamic response of free hanging risers. J. Sound Vib. 112 (1), 149–166. https://doi.org/10.1016/S0022460X(87)80099-8. SINTEF, O., 2017. RIFLEX 4.10. 1 User Guide. SINTEF Ocean: Trondheim, Norway. Sparks, C.P., 2007. Fundamentals of Marine Riser Mechanics: Basic Principles and Simplified Analyses. PennWell Books. Wang, Y., Gao, D., Fang, J., 2014. Axial dynamic analysis of marine riser in installation. J. Nat. Gas Sci. Eng. 21, 112–117. https://doi.org/10.1016/j.jngse.2014.07.031. Wang, Y., Gao, D., Fang, J., 2014. Static analysis of deep-water marine riser subjected to both axial and lateral forces in its installation. J. Nat. Gas Sci. Eng. 19, 84–90. https://doi.org/10.1016/j.jngse.2014.04.019. Wang, Y., Gao, D., Fang, J., 2015. Mechanical behavior analysis for the determination of riser installation window in offshore drilling. J. Nat. Gas Sci. Eng. 24, 317–323. https://doi.org/10.1016/j.jngse.2015.03.044. Wang, Y., Gao, D., Fang, J., 2015. Study on lateral vibration analysis of marine riser in installation-via variational approach. J. Nat. Gas Sci. Eng. 22, 523–529. https://doi. org/10.1016/j.jngse.2014.12.012. Williams, D., 2010. Optimization of Drilling Riser Operability Envelopes for Harsh Environments. https://doi.org/10.4043/20775-MS. OTC-20775-MS. Wu, W., Wang, J., Tian, Z., et al., 2014. Dynamical Analysis on Drilling Riser Evacuated in Hard Hang-Off Mode. ISOPE-I, p. 14e189. Xu, S., Feng, Q., Wang, S., Javadpour, F., Li, Y., 2018. Optimization of multistage fractured horizontal well in tight oil based on embedded discrete fracture model. Comput. Chem. Eng. 117, 291–308.
Acknowledgments The authors gratefully acknowledge financial support from “the National Natural Science Foundation of China” with fund number 51874326 and 51574261. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.petrol.2019.106652. References Ambrose, B.D., Grealish, F., Whooley, K., 2001. Soft Hangoff Method for Drilling Risers in Ultra Deepwater. https://doi.org/10.4043/13186-MS. OTC-13186-MS. Atadan, A., Calisal, S., Modi, V., Guo, Y., 1997. Analytical and numerical analysis of the dynamics of a marine riser connected to a floating platform. Ocean Eng. 24, 111–131. https://doi.org/10.1016/0029-8018(96)87670-0. Azpiazu, W., Nguyen, V., 1984. Vertical dynamics of marine risers, offshore technology conference. In: Offshore Technology Conference. https://doi.org/10.4043/4738-MS. Burke, B.G., 1974. An analysis of marine risers for deep water. J. Pet. Technol. 26, 455–465. https://doi.org/10.2118/4443-PA. Chen, P., Gao, D., Wang, Z., Huang, W., 2017. Study on aggressively working casing string in extended-reach well. J. Pet. Sci. Eng. 157, 604–616. https://doi.org/ 10.1016/j.petrol.2017.07.059. Chen, P., Gao, D., Wang, Z., Huang, W., 2015. Study on multi-segment friction factors inversion in extended-reach well based on an enhanced PSO model. J. Nat. Gas Sci. Eng. 27, 1780–1787. Dai, W., Gao, F., Bai, Y., 2009. FEM analysis of deepwater drilling risers under the operability and hang-off working conditions. J. Mar. Sci. Appl. 8, 156–162. https:// doi.org/10.1007/s11804-009-8114-0. Fan, H., Li, C., Wang, Z., Xu, L., Wang, Y., Feng, X., 2017. Dynamic analysis of a hang-off drilling riser considering internal solitary wave and vessel motion. J. Nat. Gas Sci. Eng. 37, 512–522. https://doi.org/10.1016/j.jngse.2016.12.003.
9
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Study on the static behavior of installing a deep-water drilling riser on a production platform Deqiang Tian a, *, Honghai Fan a, Bernt J. Leira b, Svein Sævik b a b
College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China Department of Marine Technology, Norwegian University of Science and Technology, Trondheim 7052, Norway
A R T I C L E I N F O
A B S T R A C T
Keywords: Riser installation Tension leg platform Riser interference Finite-difference-method Weather window
Riser interference caused by wake effects between adjacent risers severely threatens the safety during riser installation process on a Dry-Tree Tension Leg Platform (TLP) system. Due to the ignorance of interference effect, the static deflection of the drilling riser during installation is highly over-estimated in previous work. To obtain a static behavior of a drilling riser during installation, this paper built a dual-riser model where two risers are arranged in tandem and considered as Bernoulli beam subjected to steady ocean current. The modified Huse model is applied to study the interference between object risers. Then, the structural equation is solved by FiniteDifference-Method (FDM). Case studies show that an upstream production riser can largely reduce the deflection of a downstream hung-off drilling riser, hence increasing the probability of the collision of two risers. The in fluence of water depth, riser wall thickness, Blowout Preventer (BOP) weight, etc. are also studied. Finally, the current condition based weather windows with respect to wind and tidal current velocity are obtained corre sponding to different operation conditions. Results show that installing a drilling riser with lower BOP weight in shallow water is most feasible for multi-riser TLP systems. Moreover, drilling riser installation operability can be improved by increasing the top tension of the production riser.
1. Introduction Riser installation is of great significance to a successful deep-water drilling operation and an economic efficiency of the whole project as oil and gas industry moves to deep water. In recent years, there has been a trend to bring production online with a few pre-drilled wells and then drill and complete the rest of the field using a production platform (Koska et al., 2013). This can help the developers start to recover the up-front capital costs more quickly and eliminating the need for a separate drilling vessel. This reduces the overall cost to develop the field. However, due to economical and practical considerations, marine risers on offshore platforms are commonly arranged in clusters with relatively close spacing (i.e, with a typical center to center spacing be tween adjacent wellbays of 5~6 m). Riser collision is therefore more likely to occur for such compact arrangements. Wake interference plays an important role in increasing the probability of collision of two risers, which takes place when a downstream riser is located in the wake field of an upstream riser. The wake interference will change the flow around the downstream riser, i.e. reducing the local flow velocity, and, conse quently reduce the associated drag force. This effect in turn can reduce
the clearance between adjacent risers and will accordingly imply a po tential for collision between them. This issue will be further complicated when installing a drilling riser near top tensioned production risers on a platform. As show in Fig. 1, before drilling a well in the ocean, the conductor needs to be installed primarily. Then, the BOP/LMRP are installed, by using the drilling riser, through the water column in order to connect the subsea well head above the mudline. During the instal lation process, the drilling riser is in the hung-off mode and the length of the drilling riser is variable at different stages. Fan et al. (2017) reported that a suspended riser without any restriction at its lower end is more flexible and more unstable in complex sea states than a connected riser. How to safely and quickly installing a drilling riser near a top tensioned production riser has become a key challenge for deep water Dry Tree TLP systems. Restricted wellbay and seabed spacing, high current con ditions, and requirements for no contact with adjacent production riser are all contributors to the challenges faced during the design phase. In the last four decades, significant advances have been made on the mechanical property of connected marine riser. Burke (1974) performed a static analysis for a marine riser by using a beam model and deduced the general riser control differential equation based on elastic mechanic method. Azpiazu and Nguyen (1984) analyzed the vertical dynamics of
* Corresponding author. College of Petroleum Engineering, China University of Petroleum-Beijing, No.18 Fuxue Road, Beijing 102249, China. E-mail address: [email protected] (D. Tian). https://doi.org/10.1016/j.petrol.2019.106652 Received 7 June 2019; Received in revised form 27 October 2019; Accepted 4 November 2019 Available online 9 November 2019 0920-4105/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Deqiang Tian, Journal of Petroleum Science and Engineering, https://doi.org/10.1016/j.petrol.2019.106652
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Nomenclature E I Te ðzÞ wa fðzÞ Kuf Klf Lpr; Ldr M θ CDu ; CDd du ; dd b
Ttop Ttc Wb
Young’s modulus, Pa rotational inertia of the riser cross section, m4 effective axial force in riser, N apparent weight per unit length of riser, N/m hydraulic force per unit length of riser, N/m rotation stiffness of Upper Flex Joint (UFJ), N⋅ m=rad rotation stiffness of Lower Flex Joint (LFJ), N⋅ m=rad total length of production and drilling riser, m bending moment in the riser, N⋅m slope of riser drag coefficient of upstream and downstream riser, respectively diameter of upstream and downstream riser, m half width of the wake, m
ρw
uw ut h Δz Cm
ρs ρf
WD Δdu ; Δdd Δs
top tension force acting on the production riser, N top tension coefficient total mass of BOPS and LMRP attached to drilling riser, t density of sea water, kg/m3 wind current velocity, m/s tidal current velocity, m/s total water depth, m length of riser segment, m mass coefficient riser density, kg/m3 production fluid density, kg/m3 water depth, m wall thickness of upstream and downstream riser, m Riser spacing, m
investigation emphasizing on nonlinear free vibrations of marine risers to determine the nonlinear natural frequencies and their corresponding mode shapes. Montoya-Hern� andez et al. (2014) presented a numerical algorithm to evaluate the vibrations of vertical rigid production risers under internal multiphase flow behavior. Other researchers also did some work about the mechanical behavior of marine risers during installation or in hung-off mode. Patel and Jesudasen (1987) presented a theoretical and experimental investiga tion of the lateral dynamics of free hanging marine risers. The in-plane behavior was investigated through a finite element analysis of the riser pipe and its hydrodynamic loading. Ambrose et al. (2001) studied the possibilities of using the soft hung-off option and compares the perfor mance characteristics of the drilling riser in the soft hung-off and hard hung-off configurations, particularly for ultra-deep water applications down to 10,000 ft. Itoh et al. (2006) presented an experimental and numerical investigation of behavior characteristics of hung-off riser that considered oscillation of floating structure. Dai et al. (2009) investigated the mechanical behavior of drilling riser under hung-off working con ditions by using FEM software ABAQUS. Williams (2010) discussed optimization of drilling riser operability envelopes for harsh environ ments, in which the soft/hard riser hung-off configurations for storm events were assessed. Wu et al. (2014) presented a dynamical model to simulate the dynamic response of hard hung-off drilling riser consid ering the wave and current effects, the platform motion and the large deformation of drilling riser. Wang et al. (2014a, 2014b, 2015a, 2015b) presented some common formulations for deep water riser static and dynamic analysis during its installation on a drill ship. Fan et al. (2017) established a time-domain dynamic FEM method by the Wilson-θ algo rithm for a hung-off riser and compared the dynamic envelops of the hung-off riser in different situations. Hu et al. (2018) developed a novel analysis model with varying riser length to analyze the dynamic be haviors of a marine riser during the installation of a subsea production tree. Though these significant researches have been done, more work is still required within this area. For instance, most of the studies mentioned above are about riser mechanical behavior after subsea wellhead and floating platform have been connected. The research of riser mechanical behavior during installation is insufficient. Although several other researchers did a few investigations on the riser mechan ical characteristics in hung-off mode, they didn’t consider the interfer ence effects generated by the adjacent production risers. The importance of interference effects to deep-water drilling riser has been discussed above. Ignoring this effect will make the static deflection of the drilling riser being highly over-estimated during the installation process. In addition, little literature on collision assessment of riser installation was found. Accordingly, the present study established a dual-riser model
Fig. 1. Sketch of dual-riser model.
marine riser to determine the amplitude of dynamic forces and displacement caused by heave action. Patel et al. (1984) developed a two-dimensional finite element computational method for determining marine riser displacement and stresses due to self-weight, buoyancy, internal and external pressures, surface vessel motions and environ mental forces arising from currents and waves. Moe and Larsen (1997) presented an asymptotic solution of the differential equation describing the motions of marine risers in more than 1000 m water depth. Atadan et al. (1997) made some analytical and numerical analysis of the dy namics of a marine riser connected to a floating platform. The effects of the structural and hydrodynamic parameters on motion amplitude are evaluated and analytically studied based on an approach developed by Butenin. Furnes (2000) developed a mathematical formulation for solving the beam equation by considering arbitrary currents that vary continuously with depth and time. Kaewunruen et al. (2005) made an 2
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with consideration of interference effects to fill this gap. In the model, the production riser and the installation drilling riser are arranged in tandem for the purpose of the example study. The modified Huse wake model is used to investigate the interference caused by the production riser. Finally, to predict whether a drilling riser can be installed safely on a platform, the weather window (safe installation window) is deter mined by using a novel calculating procedure.
2.2. Interference model The ocean current profile must be determined before calculating hydrostatic forces on the riser body. The current velocity will be changed due to the presence of the upstream riser. Huse (1992) introduced the concept of a ‘virtual source’, which is illustrated in Fig. 2, in order to estimate the local flow velocity in the wake field. The mean flow velocity at any position in the two-dimensional wake field, e.g. Pðx0 ; y0 Þ, can be expressed as: 8 > uðx0 ; y0 Þ ¼ U0 uðx0 ; y0 Þ > > > sffiffiffiffiffiffiffiffiffiffiffiffiffi > > � > �y �2 � > CDu ⋅du > 0 < ⋅exp 0:693 uðx0 ; y0 Þ ¼ U0 xs b (4) > > pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > bðx0 Þ ¼ 0:25⋅ CDu ⋅du ⋅xs > > > > :x ¼ x þ x s 0 v
2. Analytic model 2.1. Dual-riser model A typical configuration for a production riser and a drilling riser is shown in Fig. 1. The steady ocean current is assumed to flow from the production riser to the drilling riser. Since the drilling riser is often surrounded by production risers in reality, so it is reasonable to set the production riser upstream in the static analysis process. The production riser is tensioned by a tensioner system at the top and is connected by a Lower Flex Joint (LFJ) at the bottom on the subsea well head. The top of the drilling riser is supported at the drilling floor and with a mass block (BOP/LMRP) connected to the bottom end. Both the production riser and the drilling riser are assumed to be homogeneous, isotropic and linear elastic with constant diameters. The connection point between the riser top and the platform is selected as the origin of the local coordinate system. The production riser and the hung-off drilling riser share the same governing differential equation (Sparks, 2007; Chen et al., 2017) which can be represented as: EI ⋅
d4 x dz4
Te ðzÞ ⋅
d2 x dx þ wa ⋅ ¼ f ðzÞ dz2 dz
where uðx0 ; y0 Þ is the wake velocity deficit at position Pðx0 ; y0 Þ, U0 is the inflow velocity, CDu and du are the drag coefficient and diameter, respectively, of the upstream riser located in free stream. b is the half width of the wake which is defined as: when y ¼ b, u � 0:5U0 . The parameter Xv represents the distance from the virtual source to the up stream riser center. It is written as: (5)
xv ¼ 4du =CDu
Apparently, the wake velocity distribution of the upstream riser now can be computed by using this model. However, the problem is that the properties of the wake field vary over the area occupied by the down stream riser. In order to solve this problem, the root-mean-square (RMS) value, i.e. Urms ðxd Þ, averaged over the cross-section area of the down stream riser is used for calculating the hydrostatic force. The RMS ve locity can be expressed as:
(1)
where EI is the bending stiffness of the riser along the z axis, N⋅ m2 . x is the local riser deflection in the positive direction (which is the same as the current direction); the positive direction of z is vertical (directed towards the Mean Sea Level (MSL)). The boundary conditions of the production riser and the drilling riser are different corresponding to the different top and end connectivity conditions. Because the production riser is top tensioned by a tensioner and bottom hinged by a spherical joint, so the deformation equal to zero at the top and bottom of the production riser. The bending moment could be expressed by using elastic mechanical equations. Therefore, the boundary conditions of the top tensioned production riser can be written as: 8 xjz¼0 ¼ 0; xjz¼Lpr ¼ 0; > > > > � � > 2 > > < Mj ¼ EI⋅d x�� ¼ K ⋅dx�� uf z¼0 dz2 �z¼0 dz�z¼0 (2) > > � � > 2 > > d x� dx� > > ¼ Klf ⋅ �� : Mjz¼Lpr ¼ EI⋅ 2 �� dz z¼Lpr dz z¼Lpr
8 < 1 Z Urms ðxd Þ ¼ :πR2d
Rd
Z
Rd
912 =
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi R2d ðx xd Þ
2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi u ðx; yÞdxdy R2d ðx xd Þ
;
(6)
where Rd is the radius of the downstream riser, xd represents the dis tance between the downstream center and origin pf coordinate. 2.3. Forces on the riser 2.3.1. Effective axial force Similar to pipe string mechanics problems (Chen et al., 2015), effective axial force on the riser body should be determined firstly. Since the production riser is top tensioned and pinned at the bottom with the LFJ, the effective axial force is represented by: � Tep ðzÞ ¼ Ttop wa ⋅z (7) Ttop ¼ Ttc⋅wa ⋅Lpr where Tep ðzÞ is the effective axial force of the production riser at a depth coordinate equal to z m; Ttop is the top tension force acting on the
Since the bottom end of the hung-off drilling riser is free, so both the bending moment and slope equal to zero at the bottom end; Due to the top end of the drilling is supported at the drilling floor, so the defor mation and slope equal to zero at the top end. Hence, the boundary conditions of the hung-off drilling riser are given by: � 8 dx�� > xjz¼0 ¼ 0; θj ¼ ¼ 0; > z¼0 > > dz�z¼0 > > > > � < d 2 x� (3) Mjz¼Ldr ¼ EI⋅ 2 �� ¼ 0; > dz z¼Ldr > > > � > > � > > : θjz¼Ldr ¼ dx� ¼0 dz�z¼Ldr where M is the bending moment in the riser, and θ is the slope of the riser.
Fig. 2. Sketch of two-dimensional wake flow downstream of a riser. 3
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production riser; Ttc is the top tension coefficient. The BOP and LMRP are connected at the end of the hung-off drilling riser. The total mass of the BOP and the LMRP is defined as Mb , while the effective axial force on the drilling riser section can be expressed as: Ted ðzÞ ¼ wa ⋅ ðLpr
(8)
zÞ þ Wb ⋅g
2.3.2. Lateral force Morison’s Equation is used to calculate the lateral hydraulic force per unit riser length, which is represented as: 1 f ðzÞ ¼ ρw ⋅ d ⋅ CD ⋅uðzÞ2 2
(9)
where ρw is the density of sea water, kg/m3; d is the outside diameter of the riser; CD is the drag coefficient; uðzÞ is the inflow velocity at a depth coordinate of z m. It is evident from the foregoing that uðzÞ should be replaced with Urms ðxd ; 0; zÞ when calculating the hydrostatic force acting on the downstream drilling riser. The sea current profile at a certain depth coordinate, e.g. z m, can be computed by Eq. (10) if there is no measured data of the marine envi ronment (Fang and Duan, 2014): uðzÞ ¼ ut ⋅
� h
�1 z 7 h
þ uw
� h
z
� (10)
h
where uw is the wind current velocity, m/s; ut is the tidal current ve locity, m/s and h is the water depth, m. Fig. 3. Schematic of dual-riser model discretization.
3. Numerical model 3.1. Solving governing equations
8 x3 ¼ 0; xn 2� ¼ 0 > > > > < 2EI Kuf ⋅Δz�⋅x2 4EI⋅x3 þ 2EI þ Kuf ⋅Δz� ⋅x4 ¼ 0 > > > > 2EI þ Klf ⋅Δz�⋅xn 3 4EI⋅xn 2 þ : 2EI Klf ⋅Δz ⋅xn 1 ¼ 0
In order to compute the lateral deformation of the riser, the Finite Difference Method (Xu et al, 2018) is used to solve Eq. (1). The models of the production riser and the drilling riser are discretized, respectively, as shown in Fig. 3. Taking the production riser as an example, the following finite dif ference schemes are used to discretize Eq. (1): 8 dx xiþ1 xi 1 > ¼ > > 2Δz > dz > > > > > d2 x xiþ1 2xi þ xi > > ¼ > > < dz2 ðΔzÞ2 > d3 x xiþ2 > > ¼ > > > dz3 > > > > > > d4 x xiþ2 > : ¼ dz4
There are n equations in total with n variables when combining Eq. (12) and Eq. (13), which can be transformed into the following matrix equation: ½A� ⋅ ½x� ¼ ½B�
1
xi
½xi � ¼ ½x1 ; x2 ; x3 ; ⋯; xn 2 ; xn 1 ; xn �T is the matrix of the production riser
(11)
2
lateral deformation; ½B� ¼ ½0; 0; fð3Þ; fð4Þ; ⋯; fðn 2Þ; 0; 0�T is the force matrix. The static deflection of the upstream production riser can be easily obtained by solving the linear system Eq. (14). The hung-off drilling riser have the same form of discretized governing equation as Eq. (12). The discretized boundary conditions are represented as: 8 ex3 ¼ 0 > > < ex2 þ e x4 ¼ 0 (15) exm 3 2e xm 2 þ e xm 1 ¼ 0 > > : exm 3 þ exm 1 ¼ 0
2ðΔzÞ3 4xiþ1 þ 6xi
(14)
where ½A� is the coefficient matrix with respect to αi , βi , γ i , ϕi , ηi ;
1
2xiþ1 þ 2xi
(13)
4xi
1
þ xi
2
ðΔzÞ4
The discretized production riser governing equation can be deduced by taking Eq. (11) into Eq. (1), which gives: 8 αi xi 2 þ β xi 1 þ γ xi þ ϕ xiþ1 þ η xiþ2 i i i i > > > > > ¼ f ðiÞ ð3 � i � n 2Þ > > > > > EI > > > αi ¼ ηi ¼ > 4 > ðΔzÞ > > > > < 4EI Tep ðzÞ wa βi ¼ > ðΔzÞ4 ðΔzÞ2 2Δz > > > > > > 6EI 2Tep ðzÞ > > γi ¼ þ > > 4 > ðΔzÞ ðΔzÞ2 > > > > > > Tep ðzÞ wa > : ϕ ¼ 4EI þ i ðΔzÞ4 ðΔzÞ2 2Δz
The matrix equation for the drilling riser is then expressed as: e ⋅ ½e e ½A� x� ¼ ½B�
(12)
(16)
e is the coefficient matrix with respect to e ei , e where ½A� αi , eβi , eγi , ϕ ηi ; T x2 ; e x3 ; ⋯; e xm 2 ; e xm 1 ; e xm � is the matrix of the production riser ½e x� ¼ ½e x1 ; e e ¼ ½0; 0; efð3Þ; efð4Þ; ⋯efðn 2Þ; 0; 0�T is the force lateral deformation; ½B� matrix.
The discretized boundary conditions for the production riser can also be obtained by substituting Eq. (11) into Eq. (2), which gives:
3.2. Iterative solution Based on Eq. (9), the lateral hydraulic force on the downstream 4
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drilling riser highly depends on the RMS wake velocity Urms ðxd ; 0; zÞ, which, however, is a function of the clearance between the two risers. Thus, the drag force profile will vary along the drilling riser due to the curved production riser and the corresponding altered wake profile. Since the dual-riser model has been discretized in the previous sec tion, the downstream wake profile can be established by calculating the relative distance between each pair of riser segments, from the curved upstream riser to the deformed downstream riser which is obtained by using the upstream current profile. To determine the equilibrium posi tion of the dual-riser system, an iteration procedure is introduced: (1) Calculate the configuration of the upstream production riser and the downstream drilling riser by using the origin current profile; (2) Determine the vertical wake profile Urms ðxd ; 0; zÞi based on the deformation of the dual-riser system; (3) Perform the static analysis by updating the downstream wake profile, and then, calculate the average distance between each pair of riser segments, i.e. xi ; (4) Calculate Urms ðxd ; 0; zÞiþ1 based on the new xi ; (5) Repeat steps 2–4 until the algorithm convergences. The flow field around the production riser is assumed to be steady, which implies that it will not be influenced by the deflection of the drilling riser. In addition, the drag coefficients for both risers are taken to be constant in time. The entire solution procedure is summarized in Fig. 4. 4. Case study
Fig. 4. Flowchart of the calculation procedure.
4.1. Benchmark The entire static analysis is performed by using a self-developed MATLAB program which is based on the Finite Difference Method. The program is verified by comparing it with the global riser analysis software Riflex (2017). Fig. 5 provides the static lateral deformation of a top tensioned production riser with a length of 327 m. The outside diameter is 0.324 m and the wall thickness is 0.0165 m; the top tension coefficient is 1.5; the wind current velocity and tidal current velocity are both 0.5 m/s. The comparison shows that the result calculated by the self-developed MATLAB program agrees well with the Riflex result. 4.2. Case study parameters For the purpose of investigating this problem, an actual deep-water drilling and production platform is taken as an example. A drilling riser is to be installed near a top tensioned production riser. The riser spacing is 5 m. Key properties of the dual-riser system are given in Table 1. 4.3. Results and discussions
Fig. 5. Verification of the program code.
Based on the previous discussion, the lateral deformation of the drilling riser will be influenced by the upstream production riser due to the wake effect. Fig. 6 gives the detailed riser deformation for a relative mild weather condition where the wind current velocity and tidal cur rent velocity are both 0.4 m/s. Five installation stages: 20%, 40%, 60%, 80% and 100% of the water depth are considered, respectively. The top tension coefficient of the production riser is 1.5; the total mass of the connected BOP is 150t; the wall thickness of the production riser and drilling riser are 0.65 inch and 0.625 inch, respectively; the origin riser spacing Δs is 5 m. In Fig. 6, the dashed lines represent the results without considering the wake effect from the upstream production riser. It is obvious that the upstream production riser has a great impact on the downstream drilling riser during installation. The lateral deflection of the drilling riser will decrease significantly in the downstream region of a production riser.
Table 1 Properties of the dual-riser system. Parameters
Values
Parameters
WD(m)
500
Cm
2.0
7850
ρw (m)
1025
ρs (kg.m3)
ρf (kg.m3)
1200
E(Gpa)
210
du (m)
Wb (T)
100–300
Ttc
1.2–1.85
0.324
Δdu (m)
0.0123–0.0254
dd (m)
0.5334
Δdd (m)
0.0123–0.0254
Kuf (N.m/rad)
12880
CDu ; CDd
Klf (N.m/rad)
5
Values
1.2 27116
uw (m/s)
0.2–0.6
Ldr(m)
100–500
ut (m/s)
0.3–0.75
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Fig. 6. Riser configurations at different installation stages.
Fig. 8. Dual-riser configuration for various production riser sizes.
Furthermore, the decrease of the amplitude of the riser deflection still tends to be increasing for increasing installation depth. Therefore, there is a potential for collision between the production riser and the drilling riser during the installation process, especially when the weather con dition is not sufficiently mild, as shown in Fig. 7. All of the parameters giving the results in Fig. 7 are the same as for Fig. 6 except the weather condition, for which the tidal current velocity and wind current velocity are replaced with 0.42 m/s and 0.6 m/s, respectively. It is clear that the drilling riser can potentially collide with the production riser at the 40%–50% installation stage which can be defined as the relevant colli sion area. Installation of a drilling riser in this specific condition is not to be recommended. Clearly, the feasibility of performing the installation will depend largely on the weather condition. Still, some other factors, such as the riser size (wall thickness), the weight of the BOP and the top tension, will also have an influence on the configuration of drilling riser during installation. In order to provide a best possible guidance in relation to the riser installation, the above mentioned factors are all discussed in more detail in the following sections.
results in Fig. 6 except the production riser wall thickness. From Fig. 8, the deformation of the production riser will decrease for increasing riser wall thickness. This will reduce the wake effect for the drilling riser and consequently increase the drilling riser deformation. Fig. 9 provides the variation of the riser deformation for different values of the drilling riser wall thickness. In the figure, all the parame ters are kept constant except the drilling riser wall thickness. As shown in Fig. 9, the deformation of the drilling riser will gradually decrease for increasing drilling riser wall thickness. This is because the increasing riser wall thickness will increase the bending stiffness EI and the apparent weight wa of the riser body. These two effects will in turn reduce the drilling riser deformation. In order to reduce the tension level of the drilling riser and extend the clearance between dual-riser system to avoid collision, a relatively large production riser wall thickness and small drilling riser wall thickness is a good combination in relation to the installation process.
4.3.1. Riser wall thickness The production and drilling riser wall thickness will affect the configuration of the dual-riser system in two ways. Fig. 8 shows the riser deformation under different wall thicknesses of the production riser. In this case, all parameters are kept constant for the
4.3.2. Mass of BOP In this case, all the parameters are kept constant for the results shown in Fig. 6 except the BOP weight which is varied from 100 T to 300 T. Fig. 10 shows riser deformations under different BOP weights. As shown in Fig. 10, the drilling riser deformation decreases for increasing BOP weight. This is because the effective axil force of the riser body is increased due to the increasing BOP weight. It is clear that the drilling riser deformation is comparatively sensitive to the variation of the BOP
Fig. 7. Riser collision during installation process in bad weather condition.
Fig. 9. Dual-riser configuration for various drilling riser sizes. 6
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Fig. 10. Dual-riser configuration for various BOP weights.
Fig. 12. Dual-riser configuration for various tidal current velocities.
weight. Therefore, connecting a lighter BOP is also a good option during the installation process.
4.3.4. Tidal current velocity and wind current velocity Weather conditions are key factors that need to be considered prior to installing the drilling riser. Based on the foregoing discussion, the collision area near the largest deformation point of the production riser should be focused on. In this case, a particular position is considered, i.e. when BOP is lowered to half of the water depth. This is selected as the reference point for the calculations.
Fig. 12 gives the variation of riser deformation for different tidal current velocities ranging from 0.2 m/s to 0.6 m/s, whereas all other parameters are kept constant. It can be seen clearly that the tidal current velocity has a significant influence on both the production riser and the drilling riser. However, it should be noticed that the deformation magnitude of production riser is much larger than for the drilling riser. This might eventually result in riser collision once the tidal current ve locity exceeds the critical value, e.g. 0.6 m/s in this case. Fig. 13 shows the variation of riser configuration for different wind current velocities ranging from 0.3 m/s to 0.75 m/s. Similarly, all the other parameters are kept constant. It is can been seen that the riser deformation is more sensitive to the tidal current velocity than the wind current velocity. Furthermore, there is also a critical value for the wind current velocity, e.g. 0.75 m/s in this case, when the tidal current ve locity is kept constant. Typically, the installation process should be performed for mild weather conditions with tidal current velocity and wind current velocity as low as possible. Large wind and tidal current velocity can result in large bending deformations and higher stresses for the riser body; sec ond, it will significantly reduce the clearance between the drilling riser and the production riser, and consequently make them prone to collide with each other. However, perfect weather condition is usually difficult to achieve, which will have a negative impact on the TLP project economy. Hence, the weather windows for installation corresponding to different operation conditions are important to establish.
Fig. 11. Dual-riser configuration for various top tension coefficients.
Fig. 13. Dual-riser configuration for various wind current velocites.
4.3.3. Production riser top tension It is clear that the deformation of the drilling riser partly depends on the production riser lateral deflection. However, the top tension can significantly reduce the deformation of production riser. The results presented in Fig. 11 are based on varying the top tension coefficient of the production riser in the range 1.2–1.85, whereas other parameters are kept constant. As shown in Fig. 11, the deformation of the production riser decreases significantly by increasing the top tension coefficient. This is because a large top tension will increase the effective axial ten sion of the production riser. Subsequently, the decreasing production riser deformation will reduce the wake effect for the drilling riser and accordingly reduce the drilling riser deformation. So, it is feasible to increase the top tension coefficient within permission when suffering from riser interference effect during drilling riser installation.
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4.3.5. Weather windows As can be seen from section 4.3.4, for a given tidal current velocity, there is a critical value for the wind current velocity with respect to mechanical collision, and vice versa. Therefore, the weather window can be obtained by taking the values of wind current velocity and tidal current velocity as the x axis and y axis, respectively. The difference is that the calculation point is not fixed at half the water depth anymore, but runs from MSL to the mudline. The model can then be applied to evaluate whether collision happens or not for a specific weather condition. Fig. 14 gives the current condition based weather windows for different water depths, BOP weights, and top tension coefficients. Fig. 14-(a) illustrates that the drilling riser connected with lighter BOP will have a wider installation weather window. However, the difference is not obvious for smaller water depths, e.g. 500 m in this case. Fig. 14(b) shows the result for 1000 m water depth. It can be seen clearly that the BOP weight has a significant influence on the allowable current conditions. This implies that reducing the BOP weight can extend the installation weather window. Nevertheless, it should be noted that the weather window at 1000 m water depth is obviously narrower than that at 500 m water depth. Fig. 14-(c) and Fig. 14-(d) show the variations of current condition based weather window for different top tension co efficients at 500 m and 1000 m water depth respectively. Higher top tension coefficients give a wider weather window during installation.
Furthermore, the weather window is obviously quite sensitive to the top tension coefficient whenever in shallow or deep water depth. It thus can be concluded that installing a drilling riser in more shallow water with smaller BOP weight and higher top tension coeffi cient can maximize the drilling riser installation operability. 5. Conclusions Considering wake interference from the upstream production riser is of great importance for a safe installation of a drilling riser on a dry tree TLP. To study the static performance of installing a drilling riser near a production riser, a dual-riser model is developed based on small-angle beam deflection theory and numerically solved by Finite Difference Method. Some conclusions can be summarized as follows: (1) The upstream production riser has a great impact on the down stream installation drilling riser. The calculation results without concerning wake effect from production riser are apparently on the larger side. Furthermore, this error will grow for the increasing installation water depth. (2) The drilling riser tends to clashing with the curved production riser in the collision area which is located near the largest deformation point of production riser.
Fig. 14. Weather windows for installation in different operation conditions. 8
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(3) Drilling riser bending deformation increases for increasing water depth, for increasing production riser wall thickness, for increasing production riser top tension coefficient, for increasing tidal current velocity and wind current velocity, but decreases for the increasing drilling riser wall thickness and connected BOP weight. (4) Installing a drilling riser at shallower water with lighter BOP and higher top tension coefficient can maximize the weather window for the installation operation.
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