Coupling Effects of A Deep-Water Drilling Riser and the Platform and the Discharging Fluid Column in An Emergency Disconnect Scenario

As drilling operations move into remote locations and extreme water depths, recoil analysis requires more careful considerations and the incidence of emergency disconnect is increased inevitably. To accurately capture the recoil dynamics of a deep-water riser in an emergency disconnect scenario, researchers typically focus on modelling the influential subsystems (e.g., the tensioner, the mud discharge and seawater refilling process) which can be solved in the preprocessing, and then the determined parameters are transmitted into an existing global riser analysis software. Distinctively, the current study devotes efforts into the coupling effects resulting from that the suspended riser reacts the platform heave motion via the tensioner system in the course of recoil and the discharging fluid column follows the oscillation of the riser in the mud discharge process. Four simulation models are established based on lumped mass method employing different formulas for the top boundary condition of the riser and the discharging flow acceleration. It demonstrates that the coupling effects discussed above can significantly affect the recoil behavior during the transition phase from initial disconnect to the final hang-off state. It is recommended to develop a fully-coupled integrated model for recoil analysis and anti-recoil control system design before extreme deep-water applications.


Introduction
A drilling riser is required to perform emergency disconnect (ED) of the LMRP (Lower Marine Riser Package) and BOP (Blow-Out Preventer) in case of drift off, driveoff, storms and internal solitary waves (Chang et al., 2018). At the moment of ED, the stored energy resulting from the initial stretch of the riser is released and the drilling mud should be discharged to avoid undesired axial loading from resonance in the mud column (Miller and Young, 1985). ED is a much more critical event than a planned disconnect as there is no time for reducing the tension and circulating out the drilling mud. An anti-recoil system should be equipped to control the recoil response during the transition phase from initial disconnect to the final hang-off state. There are formal standards available to industry for the selection, design, operation and maintenance of drilling risers. However, these documents do not include guidelines with respect to riser dynamics during this transition phase (Dupal et al., 2018). Nowadays, drilling operations have been driv-en into extreme deep-waters which are characterized by long distance from the mainland, great water depth, severe and capricious weather, which imposes great challenges to a drilling riser system (Brekke, 2001;Capeto et al., 2017). It is emphasized that harsher environment inevitably leads to a much higher incidence of ED. Moreover, the suspended riser under evacuation starts exhibiting new dynamic features owing to the altered physical properties (e.g., increased flexibility, higher top tension, more stored energy and larger quantities of drilling mud). It is noted that the cause of Deepwater Horizon accident in 2010 involves the failure of ED system (Grønevik, 2013;Cai et al., 2013). In 2016, the disconnect operation of the deep-water drillship offshore Nova Scotia led to the failure of tensioner support and loss of the riser/LMRP to the seabed (Dupal et al., 2018). Motivated by the fact that an understanding of what can go wrong is the best way to avoid failures, researchers are continuously devoting efforts to recoil analysis to figure out the weak links.
The recoil behavior of a deep-water drilling riser during an ED is a complex and sensitive phenomenon. To fully understand the transient nature, the most critical concern is to identify the influential factors that should be accounted for and how the related key variables are properly modelled. There is a consensus that the parameters, such as water depth, tension setting, and mud discharge induced drag force, can significantly affect the recoil dynamics (Miller and Young, 1985;Stahl et al., 2004;Lang et al., 2009;Grønevik, 2013;Ma et al., 2013). However, recoil analysis in case of ED still suffers from a lack of information and the factors which are not normally considered in former study requires evaluations before extreme deep-water applications, recalling that a very small negative LMRP-BOP clearance can lead to the failure of recoil control (Ma et al., 2013). For example, Lang et al. (2009) have found that the response of individual tensioners may differ considerably, as one of the tensioner may experience significant amount of slack while the total tension is positive at all time. In recoil analysis of an ED, researchers typically devote efforts on the modelling of the subsystems (e.g., the tensioner system, mud discharge and seawater refilling process), and various outstanding packages have been developed which can be incorporated into the existing global riser analysis software (e.g., Flexcom, Orcafex, Rifex). For the top boundary condition of the suspended riser, it usually assumes that the riser is fixed to the MODU (Mobile Drilling Unit) and the motion of the MODU is transmitted directly to the riser (Grytøyr et al., 2011;Grønevik, 2013). The coupling effect which occurs when the recoiling riser reacts the MODU excitation via the tensioner system is generally not considered. Moreover, although several in-house codes have been developed to account for the mud discharge effect (Grytøyr et al., 2011;Li et al., 2016), the coupling effect resulting from the fact that the discharging fluid column follows the oscillation of the recoiling riser is ignored. However, Meng et al. (2018) have highlighted the significance of the added inertial acceleration produced by this coupling effect. Moreover, API RP 16Q recommends the use of factors in the calculation of steel weight and buoyancy uplifts to account for uncertainties in component weights. Ma et al. (2013) have demonstrated the strong influence of this added inertial force on the recoil performance. This study is thereby motivated to investigate the two coupling effects of the suspended riser system after an ED. One is that the riser reacts the platform heave motion via the tensioner system in the course of recoil. The other is that the discharging fluid column follows the oscillation of the riser in the mud discharge and seawater refilling process.

Mathematical model
2.1 Drilling riser model with adopted coordinates Fig. 1 illustrates a typical drilling riser system under ρ r (r, t) ∂()/∂t emergency evacuation. The riser is connected to a top floating platform via a direct acting tensioner system (DAT) and the slip joint. The pipe has a length of L with density , modulus of elasticity E and mass per unit length m p . The external and internal diameters of the pipe are D e and D i respectively which are relatively small compared with L. The external and internal cross-sectional areas of the riser are A e and A i , and thus the cross-area of the pipe is A=A e -A i . The current study is one dimensional (1-D) parametric analysis (i.e. only in the axial direction), which aims to figure out the coupling effect of a recoiling drilling riser and the platform and the discharging fluid column during an ED. Then it assumes that the platform positioned directly over the wellhead. Eulerian coordinate x is adopted with the origin O 1 set at MSL (Mean Sea Level), where t is time and x is in the direction of gravity. Lagrangian coordinate X and a curvilinear coordinate along the riser's centerline are also employed with the origin set at the top end of the riser O 2 . Thus, the elastic deformation of the riser is d=r-X. x * denotes the clearance of the LMRP and the BOP in the opposite direction of gravity. In the following sections, an overdot stands for .

Platform heave motion
The platform heave motion can be described as a function of its amplitude and phase. For simplicity, this study assumes the platform heaves harmonically as: φ where a and T w are the heave amplitude and period, and is the phase angle of the wave at the time of disconnect.

Tensioner system
There are mainly two types of tensioners (i.e. DAT and wire line tensioner system), and both systems utilizes hydraulic pulling cylinders. The main function of the tensioner system is to maintain the top tension of the riser, and an anti-recoil valve is usually installed and programmed for the sake of ED. Typical global riser analysis tensioner models are available in ISO (2009). Pestana et al. (2016) proposed a new model by adding dampers, mass and rigid beam elements. According to Grønevik (2013), the telescopic joint can be modelled by giving a beam element close to zero axial stiffness, and then it is free to elongate and retract. This study proposes a new model based on the developed model in Pestana et al. (2016) as shown in Fig. 2, in which Node 1 is fixed to the floating platform, tensioner 2 is modelled as a spring-damper element, and Node 3 is connected to the riser top end. Since this study focuses on the coupling effects of the platform and the riser and the inner fluid column, the declination of individual tensioner cylinders which has been examined in Lang et al. (2009) is not accounted for. Moreover, in order to accurately capture the coupling effects on the recoil performance, the anti-recoil valve is not involved in the model. According to Okret (2016) and Kuiper et al. (2008), the tensioner's stiffness k 1 can be chosen to compensate the submerged weight of the riser system assuming the platform heaves at a critical amplitude as: where w LMRP is the submerged weight of the LMRP. The submerged weight of the riser per unit length w s can be formulated as: where M m is the mass of the drilling mud column per unit length. The critical heave amplitude of the platform a c is typically set as 10 m in practice, and a c =10 m can be utilized for simulation study (Kuiper et al., 2008).
The tensioner system is required to provide a certain amount of "overpull" at the LMRP connector during normal drilling operations to avoid buckling and to meet other structural criteria. Two calculation algorithms of the riser top tension have been proposed by American Petroleum Institute and Institute of French Petroleum. Typical values are in the range of 266.9 kN to 533.8 kN, with some variation according to local company procedures, or special require-ments from the recoil analysis (Grytøyr et al., 2011). However, based on the simulations in which three over-pull values are considered (444.8 kN, 889.6 kN and 1334.5 kN), Ma et al. (2013) have found that since successful ED only occurs in a narrow range of top tension for each riser stackup, industry codes are recommended to adopt water-depth dependent factors for the calculation of top tension requirements. According to Kuiper et al. (2008), it is common for a TLP (Tension Leg Platform) in practice to use a pre-tension T m that is 1.3 times higher than the submerged weight of the riser system expressed as: in which the tension is riser-length dependent. Eq. (4) is quite feasible for parametric analysis (e.g., the coupling effect) and scaled experiments design employing riser models with different lengths. The current simulation aims to provide a workbench for scaled experiments, and thus Eq.
(4) is adopted here. As the heave motion of the platform imparts a time-varying component, the true wall tension T 0 exerted on the top end of the drilling riser can be calculated by 2.4 Mud discharge model As the drilling mud is being discharged, seawater needs to refill the riser in order to avoid collapse of the riser. Various fill-up valves are equipped along the riser to avoid the negative water hammer effect and refill seawater fast enough. Several models have been developed to model the mud discharge and seawater refilling process. In the notable finite volume model, the mud column is generally represented by a large number of finite volumes (Lang et al., 2009;Ma et al., 2013). However, the fluid model formulas are not provided in the relevant publications, although they have given a detailed literal description. Grytøyr et al. (2011) found that a constant velocity gave the best possible fit to the expected velocity variation and proposed slug force mode based on the dynamical equilibrium of the mud column. Li et al. (2016) developed the whole fluid column mode by applying Newton's Second Law to the whole drilling mud and refilled seawater column.
This study adopts the slug force mode, and the forces exerted on the inner fluid column and the riser structure are depicted in Fig. 3. After a force analysis of the mud column in Fig. 3a, the slug force model can be derived in a rigorous way expressed as: (6) where m m and m w are the masses of the drilling mud column and refilled seawater column per unit length; a f is the acceleration of the total column (drilling mud and refilled seawater). L w and L m are the lengths of seawater and drilling mud columns. f w is the frictional force between the seawater column and the riser structure. f m is the frictional force between the drilling mud column and the riser structure. f w and f m can be calculated employing the Haaland formula (Grytøyr et al., 2011). p am and p bm are the pressure at the top and bottom ends of the mud column. The hydrostatic pressure difference of the mud column can be calculated by . The pressure drop due to the friction forces can be computed based on Darcy-Weisbach formula (Grytøyr et al., 2011). The effective gravity force of the mud column is . The frontal force f end is created when the falling column hits seawater at riser bottom, and is obtained based on Bernoulli's equation where U is the discharging flow velocity. A detailed force analysis can be found in Grønevik (2013) and Meng et al. (2018).

Analysis methodology
The first stage is static analysis by use of finite element method. This is to find the riser tension distribution and the stretch along riser at the time of disconnect. This step is not discussed in detail for brevity.
The second step is recoil analysis. To cope with the solid fluid column, the riser is formulated by a two-element mass-damper-spring model by use of the lumped mass method as shown in Fig. 4. It is stated that the displacements of the riser in global Eulerian coordinate x is the resultants of the platform's heave motion x 0 , the deformation of the tensioner and the elastic deformation of the riser. The displacement vector x and the elastic deformation of the riser in Lagrangian coordinate d are defined at first as: Then the governing equation of the riser is obtained as which can be solved by Newmark-β method. The global mass matrix M, damping matrix C, stiffness matrix K, the external force vector F and the solution vector u can be expressed as: k 2 = EA/L where the axial stiffness of the riser is , c 1 and c 2 are the damping coefficients of the tensioner and the riser, F 1 and F 2 are the resultant external forces exerted on the lumped masses. The definition of vector u and the calculation of vector F depend on the adopted simulation models as will be explained later. There are typically two methods to account for an end-mass effect: (1) The end-mass is included in the motion equation via a Dirac delta function.
(2) The end-mass is accounted for in the boundary condition. Although Païdoussis (2014) has demonstrated that the first method is right for a cantilevered pipe discharging fluid, the modelling of the LMRP requires more careful considerations since the density of the inner fluid varies with time and space along the pipe. As the current simulation is the first-step study on the coupling effect prior to scaled experiments, the LMRP mass is neglected for simplicity. Then the lumped masses of the riser system m 1 and m 2 are It means that the entire fluid column weight is assumed to be evenly distributed along the riser. The corresponding gravitational forces G 1 and G 2 are Apart from simplicity, one more advantage of this model is that it is quite convenient to account for discharging flow effect. The total frictional force is applied on the lumped mass m 1 and the frontal force is always acting on the lumped mass m 2 . The mass loss effect can be represented by the time-varying mass of the internal fluid column in Eq. (8). The total damping force caused by the surrounding seawater f D is imposed on the lumped mass m 1 , which can be calculated by with the dimensionless tangential drag coefficient C t =0.015 (Gobat and Grosenbaugh, 2006).  Based on the calculations of the internal fluid column acceleration a f in Eq. (6) and the external load matrix F in Eq. (7), four simulation models can be obtained as follows: Model A: This model neglects the coupling effect between the riser and the platform and the discharging fluid column. Same as former studies (Lang et al., 2009;Grytøyr et al., 2011;Grønevik, 2013), a stand-alone code is developed based on Eq. (6) to account for discharging flow effect, and then the computed variables are assembled to the riser model at each time-step. Then a f is calculated by Same as former studies (Lang et al., 2009;Ma et al., 2013;Grønevik, 2013), the upper ends of the tensioner and the riser are assumed to be fixed to the platform. Then the expression of F is obtained as: In this model, the solution u is the elastic deformation of the riser (i.e. u=d). Once the model is solved, the displacement of the riser in Eulerian coordinate x is obtained by simply superposing the platform heave motion as ] . Model B: This model only accounts for the coupling effect between the recoiling riser and the discharging fluid column. Referring to Meng et al. (2018), a f is formulated as: In this model, F is given in Eq. (12). The solution u is the elastic deformation of the riser (i.e. u=d), and thus ] . Model C: This model only accounts for the coupling effect between the recoiling riser and the platform. The formula of a f is given in Eq. (11). The platform heave excitation is accounted for by the relative movement of the platform and the upper node of the riser. The expression of F is formulated as: In this model, the solution u is the displacement of the riser in Eulerian coordinate (i.e. u=x).
Model D: This model accounts for the combined coupling effect between the recoiling riser and the platform and the discharging fluid column. In this case, the formula of F is given in Eq. (14). The solution u is the displacement of the riser in Eulerian coordinate (i.e. u=x). The acceleration of the internal fluid column a f is expressed as (i.e. ).

Riser recoil simulations
The deep-water drilling riser in Grønevik (2013) is em-ϵ φ ployed here, and the riser system parameters are listed in Table 1. The structural damping forces of the tensioner and the riser are neglected with c 1 =c 2 =0. is the internal roughness parameter of the riser. The gravitational acceleration is g=9.8 m/s 2 . Simulations are performed at a=1 m, =0 rad, and T w increases from 5 s to 20 s with a step increase of 1 s.
It is stated that the present simulation is a direct extension of the study in Meng et al. (2018), which has analyzed the discharging flow effect on recoil dynamics of the riser based on Model A. The developed code has been verified by comparisons with previous studies in Meng et al. (2018), and it has been updated in the present study for Model B, model C and model D.
At first, simulations are conducted adopting Model A. The time trace of the discharging flow velocity U is illustrated in Fig. 5. The time history of U is the same at different T w as the coupling effect between the platform and the internal fluid column is not considered. Mud discharging process is stopped when the riser is fully refilled by seawater. The internal fluid column is accelerated to the maximum velocity, and then slowed down when the frictional force is sufficiently large. These observations show good coherence in comparison with the simulations in Grønevik (2013), which has been discussed in Meng et al. (2018). The minimum LMRP-BOP clearance x min * with the increase of T w is depicted in Fig. 6 where the negative value means LMRP clashes with the BOP. The recoil dynamics of the riser based on simulations of Model A are summarized as follows: The riser under emergency evacuation is always experiencing an oscillation with two dominant frequencies, which can be ascribed to the simple superposition of the riser response u and the platform heave motion x 0 . The beat phenomena become quite obvious when T w =7 s and 8 s. The minimum LMRP-BOP clearance x min * always occurs at the first trough of the periodic vibration of the LMRP. x min * decreases when T w =5-6 s, and increases when T w =6-9 s and then decreases when T w =9-20 s gradually. As examples, the time traces of the LMRP-BOP clearance x * at T w =6 s, 8 s and 12 s are illustrated in Fig. 7 respectively.
Secondly, simulations are performed adopting Model B which only accounts for the coupling effect of the riser and the inner fluid column. The time trace of the discharging flow velocity U is plotted in Fig. 5, and it is obvious that U has a fluctuating component ascribed to the coupling effect of the riser and the internal fluid column, which has been discussed in Meng et al. (2018). The time trace of U is the  (1) The minimum LMRP-BOP clearances x min * at different T w are depicted in Fig. 6. The varying trend of x min * with the increase of T w in Model B is similar to the results in Model A. Moreover, x min * in Model B always occurs at the first trough of the vibration; (2) At a fixed T w , the predicted x min * in Model B is larger than that in Model A, and the vibration amplitudes of the LMRP is reduced by this coupling effect in Model B. As examples, the time traces of the LMRP-BOP clearance x * at T w =6 s, 8 s and 12 s are illustrated in Fig. 7. Moreover, quite distinct from the simulations in Model A, the vibration of the LMRP in Model B is characterized by one dominant frequency and no beat phenomenon has been captured. To figure out the intrinsic mechanism, the time traces of the clearance x 0 without considering the platform excitation, and the time trace of the platform at a=1 m, T w =5 s, =0 rad are plotted in Fig. 8. It is found that the vibration amplitudes of the LMRP in Case 1 (Model A without considering the platform excitation) and the platform heave amplitude are comparable. However, the vibration amplitude of the LMRP in Case 2 (Model B without considering the platform excitation) is quite small and it can be neglected when superposed to the platform heave motion in Model B. It is emphasized that the disparities of the simulations in Model A and Model B can only be contributed to the effect of the added inertia force on the acceleration of the inner fluid column a f in Eq. (13). Although the fluctuation component of U induced by this coupling effect seems to be insignificant as shown in Fig. 5, the coupling effect can affect the discharging flow effect (including the resulting frictional forces, internal pressure gradient, the fluid mass distribution and variation) dramatically. Hence, it can be concluded that the assumption in Model A that the acceleration of the inner fluid column a f in Eulerian coordinate equals the derivative of the relative velocity of the internal flow (i.e. neglecting the coupling effect of the recoiling riser and the inner fluid column) can lead to incorrect predictions of the recoil performance.
Then, simulations are carried out adopting Model C which only account for the coupling effect of the riser and    the top platform. The time history of the discharging flow velocity U is plotted in Fig. 5, which coincides with the result in Model A since the coupling effect between the riser and the internal fluid column is not considered. To investigate the coupling effect of the riser and the platform, the predicted recoil dynamics of the riser in Model C is analyzed by comparing with the results in Model A as follows: (1) The LMRP is always undergoing a periodic vibration with two dominant frequencies ascribed to the coupling of the recoiling riser and the heaving platform.
(2) The minimum LMRP-BOP clearance x min * are depicted in Fig. 9, and the varying trend with the increase of T w differs greatly with the results in Model A. Same as the results in Model A, the negative x min * occurs at the first trough of the vibration at T w =5 s and 6 s. However, the negative value of x min * increases when T w =5-6 s. At T w =7 s and 8 s, the beat phenomena are quite distinguished and x min * occurs at the trough of the first "beat" shape, which can also explain the jump drop feature when T w =6-7 s in Fig. 9. As an example, the time trace of x 0 at T w =8 s is illustrated in Fig. 10a. From T w =9 s, the beat phenomenon becomes less remarkable, and the occurrence of x min * shifts to an earlier trough in the vibration. The time trace of x 0 at T w =9 s is illustrated in Fig. 10b. x min * occurs at the first trough of the vibration when T w ≥12 s and that is why there is an increment when T w =11-12 s in Fig. 9. The value of x min * decreases when T w =12 -20 s gradually. The time trace of x 0 at T w =15 s is illustrated in Fig. 10c. When comparing Model A with Model C, it is concluded that the simple superposition of the riser response u and the platform heave motion x 0 cannot accurately represent the coupling of the recoiling riser and the platform.
Finally, simulations are conducted adopting Model D which accounts for the combined coupling effect of the riser and the platform and the internal fluid column. The dynamics of the internal fluid column varies at different T w owing to the effect of the platform excitation. However, the time trace of U gets more coincident with that in Model C when T w is large enough, which means that the platform excitation at flow frequency has a slight effect on the discharging flow dynamics. As examples, the time traces of U at T w =8 s and 15 s are plotted in Fig. 5. The predicted minimum LM-RP-BOP clearance x min * are depicted in Fig. 9, and the varying trend with the increase of T w is similar to the results in Model C, which can be ascribed to the coupling of riser and the platform. Compared with the results in Model C, x min * is increased and the vibration amplitudes of the riser are reduced which can be contributed to the coupling effect of the riser and the internal fluid column, as has been explained when comparing the simulations in Models A and B. The comparison of the simulations in Models C and D are made as follows: (1) Same as the results in Model C, the negative x min * occurs at the first trough of the vibration at T w =5 s and 6 s. The value of x min * is negative and increases when T w =5-6 s. At T w =7 s and 8 s, the beat phenomena are distinguished and x min * occurs at the trough of the first " beat " shape which can explain the jump drop feature when T w =6-7 s. The time trace of x 0 at T w =8 s is illustrated in Fig. 11a. (2) Different from the simulations in Model C, once the riser departs from the beat vibration at T w =9 s, x min * occurs in the first trough of vibration which can explain that the value of x min * decreases when T w =9-20 s continuously. The time trace of x 0 at T w =9 s is illustrated in Fig. 11b. One more significant finding is that when T w ≥ 14 s, the predicted recoil dynamics get more consistent with the results in Model C and the riser starts undergoing onefrequency dominant vibration. It means that the coupling effect of the riser with the platform becomes dominant when T w is sufficiently high in the combined coupling effect of  MENG Shuai et al. China Ocean Eng., 2020, Vol. 34, No. 1, P. 21-29 27 the riser and the platform and the internal fluid column. It can also explain why the time trace of U at T w =15 s becomes similar to the result in Model C in Fig. 5.

Conclusions and future study
As the recoil behavior of a deep-water drilling riser system after an emergency disconnect is a transient dynamic response, it is quite difficult to conduct experiments owing to the transient fluid-structure interaction nature. Thus, outstanding simulation models have been developed which can be incorporated into the existing global riser analysis software packages for recoil analysis. Moreover, simulations are essential to figure out the key influential factors, which is quite beneficial for scaled experiment design to capture the transient dynamics. This study aims to investigate the coupling effect of the floating platform and the suspended riser and the discharging flow during an ED scenario which has been neglected in previous studies. Based on the present study employing the derived four models, conclusions have been drawn as follows: (1) When accounting for the coupling effect of the riser and the discharging fluid column, the discharging flow velocity has an obvious fluctuating component in the mud discharge process, the minimum LMRP-BOP clearance is increased obviously and the vibration amplitude of the riser can be reduced remarkably. Therefore, the assumption in preceding studies that the acceleration of the inner fluid column in Eulerian coordinate equals the derivative of the relative velocity of the internal flow may not be acceptable in recoil analysis.
(2) When accounting for the coupling effect of the riser and the platform, the varying trend of minimum LMRP-BOP clearance with the increase of platform heave period is altered significantly. One essential finding is that the distinguished beat phenomena have been captured, where the minimum LMRP-BOP clearance occurs at the trough of the first beat shape and the minimum LMRP-BOP clearance is reduced dramatically. Therefore, the simple superposition of the riser response and the platform heave motion in previous studies cannot capture the coupling effect of the recoiling riser and the floating platform.
(3) When accounting for the combined coupling effect of the recoiling riser and the floating platform and the internal fluid column, the varying trend of minimum LMRP-BOP clearance with the increase of platform heave period is similar to that when only considering the coupling effect of the riser and the platform. However, the predicted dynamics of the suspended riser at a fixed heave frequency depends on the dominance of the coupling effects with the platform and the discharging fluid column. For example, when the platform heave period is adequately large, the discharging flow effect is dominant, and then the recoil dynamics get consistent with the prediction when only considering the coupling effect of the recoiling riser and the internal fluid column.
As former recoil analysis in an ED scenario typically performed based on global riser analysis software packages, it is recommended to develop a fully-coupled integrated program for recoil simulations based on the present study. This study is beneficial for optimizing the riser stack-up and anti-recoil control system design before extreme deep-water applications, as computer simulation has been demonstrated to be a reliable method of developing robust solutions for riser recoil control (Stahl and Hock, 2000). It is stated that this study has deficiencies as follows: (1) This study is limited to 1-D analysis. There is usually an offset of the platform during drilling operations owing to the waves and currents. 3-D analysis is required to more accurately capture the coupling effects of the riser system; (2) Eq. (4) which is commonly employed in a TLP is adopted here for the drilling riser system; (3) the effect of LMRP mass is neglected; (4) the effect of heave phase angle at the time of disconnect is not examined. A scaled model experiment based on the present simulation model is going to be conducted in the circulation channel at Shanghai Jiao Tong University. The experimental observations together with the revised simulations will be presented in the next paper. For example, the mass of the wet weight of the riser is much smaller compared with that of the LMRP. In order to analyze the effect of LMRP mass, the riser system can be modelled as a suspended cable attached with a bottom end-mass.