Loads Calculation and Strength Calculation of Landing String during Deepwater Drilling

Abstract

As an important drilling tool, the landing string will be directly exposed to seawater during surface riserless drilling operations, and it will undergo complex deformation under the action of environmental loads such as ocean currents and waves and the displacement, heave and vibration of the drilling platform. At the same time, with the increase in water depth, the floating weight of drill pipe and casing also increases significantly, and the landing string will bear great tensile loads, which can easily cause accidents. Therefore, in this paper, based on ANSYS software, the finite element analysis models of three stages of the landing string lowering operation were established, and finite element simulations under different combinations of working conditions were carried out. Through theoretical analysis and numerical simulation, the ultimate load and stress distribution of the string under different operating sea conditions were obtained, and the external force requirements for restraining the lateral displacement of the string were proposed according to the existing standards of the industry. Thereby, the recommended safe operating time, safe operating conditions window and the required restraint reaction force of the support mechanism are given for landing string lowering operation throughout the year.

1. Introduction

During casing operation of drilling without riser section in the deep-water surface, the landing string is in contact with the sea water, and bending deformation occurs under the action of wind force, sea current force and wave force [1,2,3]. The upper part of the string is connected to the drilling platform, and the deformation of the string cannot be reduced by changing the top tension [4,5]. Therefore, the deformation of the string will generate large bending stress, which threatens the safety of the string [6,7,8]. It is of great significance for the simulation and calculation of the stress and deformation characteristics of the string to identify the operation stages and dangerous points of casing of the landing string, and to clarify the calculation method of the marine environmental load [9,10,11]. The schematic diagram of the calculation requirements for the landing string is shown in Figure 1.

There have been many works in the field of force analysis and load analysis of landing strings. In 2001, Adams [12] proposed a method for designing the string strength, but no specific mechanical analysis was conducted for deepwater drilling landing strings. In 2005, Everage et al. [13] concluded that it is not enough to consider only static load and established a mathematical model to predict the axial dynamic load of the landing string resulting from the response of the drilling platform to the action of the current. In 2009, Bradford et al. [14] conducted kaware crush tests on the tubular column with five different designs of wellhead feeder operating equipment, including elastic load tests near the yield limit and overload tests beyond the yield limit, to determine the stresses on the tubular column at the wellhead during deepwater drilling when a heavy tubular string is lowered. In 2010, Zhang Hui et al. [15] established a static model of the string during deepwater catheter injection installation, gave calculation methods, derived the deformation and stress distribution law of the tubular column, and proposed a corresponding optimization plan for the drilling sting structure. In 2012, Gao Deli et al. [16] elaborated the longitudinal and transverse bending deformation mechanical model and longitudinal vibration model of the landing string, analyzed the factors affecting the deformation of the string and its variation law, and proposed the strength design and calibration method of the landing string. In 2014, Jellison et al. [17] proposed a series of engineering measures to improve the load-bearing capacity of the landing string from the perspective of production design in view of the current engineering situation where the existing landing string needs to bear huge tensile loads. In 2016, Plessis et al. [18] proposed a structure capable of bearing a more than 2,500,000-lbf deepwater drilling landing string and presented a series of related support technologies to guide drilling engineers in the design of deepwater solutions [19]. However, few of the aforementioned studies have suggested the constraints on the lateral displacements to which the tubular column is subjected and the effects on the stresses to which the string is subjected by incorporating a support device during the lowering process.

Therefore, this paper combines the existing studies and divides the lowering process into three stages: single casing lowering, drill pipe lowering with casing, and drill pipe lowering with casing into the wellhead. The finite element analysis models of the three lowering stages were established, respectively, and finite element simulations were carried out under different combinations of working conditions. The lateral displacement and stress of the landing string and the restraint reaction force of the BOP trolley–tubular column contact surface are obtained from the known data under multi-year monthly average and extreme conditions. In turn, the recommended safe operating time, safe operating condition window and BOP trolley design restraint reaction force results throughout the year are given. At the same time, the following assumptions are made to facilitate the solution of the finite element model: (1) the landing string is an isometric slender rod, ignoring the effects of joints and section changes; (2) the material of the pipe column is linear elastic, homogeneous and isotropic; (3) the top of the string is connected to the platform, and the bottom is regarded as the free end, ignoring the influence of the platform movement on the string.

2. Stage Analysis

During casing operation of drilling without riser section in the deep-water surface, the lower part of the landing string is connected with the running tool and casing [20]. The operating water depth is limited to 1600 m, and the casing running process can be divided into three stages: casing entering water, drill pipe carrying casing into water, and drill pipe carrying casing entering the wellhead, shown in Figure 2.

The finite element models of the three stages are shown in Figure 3. These three models impose full constraints on the upper boundary conditions of the string; for the models built in the first two stages, no constraints are applied to the bottom of the string, and the model of the third stage imposes constraints UX and UY on the bottom of the string. Since the landing string has an excessive slenderness ratio, we treat it as a rod model for analysis when modeling with ANSYS. We then used the PIPE 59 unit for simulation, which is a uniaxial unit that can withstand tensile, compressive and bending effects and can simulate ocean waves and currents. The unit supports linear and nonlinear materials, as well as large displacements and deformations, and also supports special dynamic analysis. It can perform linear and nonlinear static and structural linear and nonlinear dynamic analysis of the structure under the action of loads in the marine environment. The unit is used for simulation to obtain the magnitude of lateral displacement and column stress under different working conditions of the landing string. Since the model is a rod model, the size of the divided mesh does not affect the output results too much.

2.1. Casing Entering Water Stage

String combination: 400 m 9-5/8in casing; the upper end of the string is connected to the drilling ship and suspended on the chuck, which is regarded as a fixed constraint. The string will vibrate laterally under the load of wind, wave and current, and great stress may occur at the top of the landing string and near the water surface, resulting in yield failure of the string [21].

2.2. Drill Pipe Carrying Casing into Water Stage

String combination: 1228.8 m 5-7/8in drill pipe and 400 m 9-5/8in casing; the upper end of the string is connected to the drilling ship, and the lower end is constrained by the subsea wellhead, which can be regarded as fixed constraints. The water surface acts as the current load boundary, where the string stress will have its maximum value [22].

2.3. Drill Pipe Carrying Casing into Wellhead Stage

String combination: 1628.8 m 5-7/8in drill pipe and 400 m 9-5/8in casing; at this time the casing has completely entered the wellbore position. The upper end of the string is connected to the drilling ship, and the lower end is constrained by the subsea wellhead, bearing the additional dead weight of 400 m casing, and the string is in the state of maximum ultimate tensile load in the axial direction. The water surface acts as the current load boundary, where the string stress will have its maximum value [23].

3. Load Analysis

3.1. Dangerous Point Analysis of the String

During the drill pipe carrying casing into water stage and the drill pipe carrying casing into wellhead stage, the landing string needs to bear the floating weight of all the drill pipe, casing and other ancillary equipment below it, and the contact point between the upper end of the string and the chuck is in a high tensile load state, which is necessary to judge whether the ultimate tensile load of the dangerous point is within the allowable tensile load range of the string [24,25].

In these three stages, the position of the string near the water surface is affected by the coupling effect of wind, wave and current, and the string will have obvious lateral displacement coupled with lateral load and axial tensile load and is in a state of high stress. Under the influence of large ocean currents, the stress state in this area will be even worse, and it is the weakest point of the landing string [26,27]. It is necessary to study and judge the environmental conditions required for the safe operation of the string. The above-mentioned string danger points are shown in Figure 4.

3.2. Marine Environmental Load Analysis

Lateral forces on the string are generated by waves and currents. If dynamic effects are ignored, the combined force of waves and currents can be calculated by the following formula [28,29]:

$$F(x)=\frac{1}{2}{C}_{\mathrm{D}}\rho D\left(v_{\mathrm{w}}+v_{\mathrm{c}}\right)\left|v_{\mathrm{w}}+v_{\mathrm{c}}\right|+\frac{1}{4}{C}_{\mathrm{m}}\rho \pi D^2{a}_{\mathrm{w}}$$

(1)

where F is the wave load per unit length of the string, N; C_D is the drag force coefficient, taken as 1.2 (0–150 m)/0.7 (>150 m); $\rho$ is the density of sea water, kg/m³; D is the outer diameter of the string, m; v_w is the current velocity at a certain depth below the sea surface, m/s².

4. Basic Parameters

Detailed string data and accurate multi-year statistical data of wind, wave and current in the operating area are the basis for completing the mechanical calculation of string stability.

4.1. String Parameters

Based on GB/T 19830-2011 Petroleum and Natural Gas Industries-Steel Pipes for Use as Casing or Tubing for Wells [30] and GB/T 24956-2010 Recommended Practice for Petroleum and Natural Gas Industries-Drill Stem Design and Operating Limits [31], the data of mechanical simulation calculation of the stability of the landing string are shown in

Table 1. Landing string data involved in mechanical simulation calculation of string stability.

Parameter	$\mathbf{\Phi }$244.48 mm Casing (9-5/8in)	$\mathbf{\Phi }$149.2 mm Drill Pipe (5-7/8in)
Outer Diameter, mm	244.48	149.2
Inside Diameter, mm	220.5	118.7
Wall Thickness, mm	11.99	15.25
Cross-sectional Area, mm2	8757	6417
Single Length, m	12–13	14.09
Weight Per Meter, N/m	685.51	697.27
Tensile Strength, kN	8450	5974
Torsional Strength, kN·m	/	186
Anti-extrusion Strength, MPa	56	192
Internal Compressive Strength, MPa	63.2	181
Yield Strength, MPa	758.42	930.83
Connector Specifications	BC	5-1/2 FH (7.625 × 3.375)
Joint Tensile Strength, kN	8192	7558
Joint Torsional Strength, kN·m	/	104
Steel Grade	P110	S-135
Elastic Modulus, GPa	210	210
Poisson Ratio	0.3	0.3

.

4.2. Wind and Current Internal Wave Parameters

The following data come from the “Overview of Meteorological and Hydrodynamic Background in the LS17-2 Deepwater Drilling Operation Area”, which summarizes the multi-year monthly average environmental loads in the operating area, the extreme value distribution of environmental loads during the multi-year monsoon recurrence period and the typhoon multi-year recurrence period [32], and the distribution of extreme values of environmental loads and characteristic data of oceanic internal waves.

The annual and monthly average environmental load statistics of sea wind, waves and currents in the operation area are shown in

Table 2. Statistics on the average monthly environmental load in the vicinity of the operation area for many years.

Month	Water Depth, m	Surface	200	400	800	Bottom	Wind Speed, m/s	Wind Direction, °	Significant Wave Height, m	Cycle, s	Wave Attack Angle, Deg
1	Flow Velocity, m/s	0.254	0.156	0.076	0.035	0.008	7.4	54.9	1.7	5.4	58.3
	Flow Direction, °	217.2	228.2	217.1	191.5	325.3
2	Flow Velocity, m/s	0.091	0.068	0.035	0.03	0.006	5.4	71.8	1.6	5.3	67
	Flow Direction, °	201	220.3	186.5	139.1	88.1
3	Flow Velocity, m/s	0.081	0.017	0.034	0.042	0.007	4.3	106.1	1.4	5	85.3
	Flow Direction, °	73.5	120.1	142.3	138.4	81.2
4	Flow Velocity, m/s	0.201	0.057	0.029	0.036	0.005	4.4	135.1	1.3	4.7	99.4
	Flow Direction, °	60.4	73.9	149.8	154.3	316.9
5	Flow Velocity, m/s	0.221	0.069	0.027	0.025	0.01	3.9	156.6	1.1	4.5	115.7
	Flow Direction, °	50	66	146.4	176.8	339.1
6	Flow Velocity, m/s	0.189	0.02	0.045	0.021	0.014	4.6	175.7	1	4.2	149
	Flow Direction, °	35.9	120.1	196.2	197.5	328.8
7	Flow Velocity, m/s	0.2	0.019	0.054	0.036	0.009	4.6	180.1	1	4.1	160
	Flow Direction, °	32.3	184.5	200.2	197.1	332.2
8	Flow Velocity, m/s	0.055	0.059	0.067	0.038	0.016	2.9	192.2	1	4.4	155.9
	Flow Direction, °	26.3	211.2	207.4	198.4	330.6
9	Flow Velocity, m/s	0.017	0.054	0.044	0.025	0.01	14	125.5	1.1	4.5	120.3
	Flow Direction, °	63.8	210.6	197.6	172.7	337.8
10	Flow Velocity, m/s	0.16	0.154	0.056	0.018	0.012	5.3	58.9	1.6	5.2	68.7
	Flow Direction, °	222.6	235.5	225.2	173.6	350.8
11	Flow Velocity, m/s	0.282	0.187	0.079	0.024	0.01	8.5	47.2	2	5.7	60
	Flow Direction, °	218.8	233.6	225.3	178	15.7
12	Flow Velocity, m/s	0.345	0.225	0.097	0.025	0.013	9.4	45.4	2.2	5.9	59.4
	Flow Direction, °	221.1	233.4	231	204.5	351.6

. The statistical data of the extreme value distribution of environmental load return period under monsoon sea conditions are shown in

Table 3. Statistical data of extreme value distribution of environmental load return period under monsoon sea conditions near the operation area.

Return Period, Year	Wind Speed, m/s	Significant Wave Height, m	Spectral Peak Period, s	Surface Velocity, m/s	Bottom Flow Rate, m/s
200	22.1	7.0	7.2	1.89	0.27
100	21.4	6.6	7.1	1.75	0.25
50	20.7	6.2	7.0	1.61	0.24
40	20.5	6.1	6.9	1.56	0.23
25	19.9	5.8	6.8	1.47	0.22
20	19.7	5.7	6.8	1.42	0.22
10	18.9	5.2	6.6	1.28	0.20

. The statistical data of extreme value distribution of environmental load return period under typhoon sea conditions are shown in

Table 4. Statistical data of extreme value distribution of environmental load return period under typhoon sea conditions near the operating area.

Return Period, Year	Wind Speed, m/s	Significant Wave Height, m	Spectral Peak Period, s	Surface Velocity, m/s	Bottom Flow Rate, m/s
200	45.6	20.1	16.4	2.27	0.33
100	40.8	16.8	15.4	2.17	0.32
50	36.5	13.9	14.5	2.06	0.30
40	35.2	13.1	14.2	2.03	0.29
25	32.6	11.4	13.6	1.96	0.28
20	31.4	10.7	13.3	1.92	0.28
10	28.0	8.6	12.4	1.82	0.26

.

Based on Table 3, Table 4 and the given extreme operating sea conditions, we set the BOP trolley to limit the lateral displacement of the pipe string and limit the constraint reaction force calculation to refer to the extreme conditions of wind, waves and currents, as shown in

Table 5. The BOP trolley limits the lateral displacement limit of the pipe string and the limit constraint reaction force calculation refers to the extreme conditions of wind, waves and currents.

Return Period, Year	Surface Velocity, m/s		Wind Speed, m/s	Wave Height, m	Cycle, s
1	Min	0.35	9.4	2.2	5.9
	Max	0.70
5	Min	0.56	20.0	5.4	9.2
	Max	1.40
10	Min	0.61	28.0	8.6	12.4
	Max	1.49
25	Min	0.67	32.6	11.4	13.6
	Max	1.59
40	Statistics	2.03	35.2	13.1	14.2
50	Statistics	2.06	36.5	13.9	14.5
100	Statistics	2.17	40.8	16.8	15.4
200	Statistics	2.27	45.6	20.1	16.4

.

According to the Internal Wave Remote Sensing and Hydrological Observations in the “General Survey of Meteorological and Hydrodynamic Background in the LS17-2 Deepwater Drilling Area”, it can be seen that the depth of the water layer where the isolated internal waves are located is about 40–80 m, and the maximum wave-induced strong current is 1.6 m/s. The amplitudes of most of the isolated internal waves are distributed between 20 and 29 m, the oceanic internal waves with an amplitude of more than 80 m have appeared once, and the duration of most isolated internal waves is distributed between 11 and 20 min, as shown in

Table 6. Mechanical simulation calculation of landing string and strength check load data of isolated internal wave condition.

Water Layer Depth, m	Amplitude 1, m	Amplitude 2, m	Amplitude 3, m	Amplitude 4, m	Amplitude 5, m	Max Wave Speed, m/s
60/1600	20	40	60	80	100	1.6

.

4.3. Hydrodynamic Parameters

According to “Riser Analysis Design Premises CNOOC (10001089936-PDC-000)”, the hydrodynamic parameters used in the mechanical analysis of the landing string stability are shown in

Table 7. Hydrodynamic parameters for landing string analysis.

Name	Sign	Value
Drag Coefficient	$C_D$	1.2 (0–150 m below sea level)
		0.7 (150 m below sea level to the seabed)
Lateral Drag Coefficient	$C_T$	0.02
Coefficient Of Inertia	$C_M$	2.0

.

5. Calculation and Check

The ultimate tensile load and stress–strain of the string are the two important reference indicators for strength checking [33,34]. Therefore, the mechanical simulation calculation of the pipe column is divided into three operation stages. The strength check models of the string are established and the respective mechanical simulation calculations are carried out. The ultimate tensile load, lateral displacement and Von MISES stress calculation results are used to recommend the safe operating time of landing string, the working condition window and the design restraint reaction force that should be available for the BOP trolley centralizing mechanism to limit the lateral displacement of the string.

5.1. Calculation Method of Static Tensile Load of String

Based on “GB/T 24956-2010 Recommended Practices for Drill String Design and Operating Limits in the Oil and Gas Industry” [31], the ultimate tensile load calculation model is used to analyze the safety of the landing string tensile strength calculation and check [35,36]. Under the dangerous condition of lowering, the floating load of the landing string and casing string is calculated according to the following formula:

$$P=[(L_{\mathrm{dp}}\times W_{\mathrm{dp}})+(L_{\mathrm{c}}\times W_{\mathrm{c}})]\times K_{\mathrm{b}}$$

(2)

where $P$ is the floating weight of the landing string below the drill pipe in this section, N; $L_{\mathrm{dp}}$ is the drill pipe length, m; $W_{\mathrm{dp}}$ is the mass of drill pipe per meter in air, kg/m; $L_{\mathrm{c}}$ is the casing length, m; $W_{\mathrm{c}}$ is the mass of casing per meter in air, kg/m; $K_{\mathrm{b}}$ is the buoyancy coefficient, taken as 0.869.

The theoretical tensile strength specified by the API standard is not the specific point at which the material begins to deform permanently but the stress at which a certain deformation has already begun [37,38]. If the drill pipe is loaded to the limits, a slight permanent elongation may occur and it will be difficult to keep the drill pipe straight. In order to avoid this situation, the maximum allowable design tensile load of the string is taken as 90% of its theoretical tensile strength during the design check:

$$P_{\mathrm{a}}=P_{\mathrm{t}}\times 0.9$$

(3)

where $P_{\mathrm{a}}$ is the maximum allowable design tensile load, N; $P_{\mathrm{t}}$ is the theoretical tensile strength obtained from the table, N; $0.9$ is the relevant scaling factor for the yield strength.

The difference between the ultimate tensile load $P$ and the maximum allowable tensile load $P_{\mathrm{a}}$ is calculated as the tensile allowance (MOP):

$$MOP=P_{\mathrm{a}}-P$$

(4)

The ratio of the maximum allowable tensile load $P_{\mathrm{a}}$ to the calculated ultimate tensile load $P$ is called the safety factor (SF):

$$SF=\frac{P_{\mathrm{a}}}{P}$$

(5)

5.2. Design of Checking the Static Tensile Load of the String

Comparing the working conditions of the three stages, the static tensile load of the string in the latter two stages is the largest [39]. (Maximum allowable design tesile load = Theoretical tensile strength* × Safety factor; theoretical tensile strength is only related to the material properties.)

Using the safety factor method (SF = 1.3) and the tension margin method (MOP = 500 kN), respectively, the tensile load for 5-7/8in landing string carrying 9-5/8in casing is calculated. The tensile load curves of the 5-7/8in landing string in the two operating stages of the drill pipe carrying the casing and the drill pipe carrying the casing into the wellhead are given in Figure 5 and Figure 6, respectively.

Table 8. Checking the maximum safe tensile load of the pipe string.

String Combination	Ultimate Tensile Load, kN	Tension Allowance Method, kN	Safety Factor Method, kN	Allowable Tensile Load, kN
1200 m 5-7/8in drill pipe and 400 m 9-5/8in casing	965.40	1465.40	1905.02	5376.6
1600 m 5-7/8in drill pipe and 400 m 9-5/8in casing	1207.77	1707.77	2220.10	5376.6

shows the maximum safe tensile load of the drill pipe carrying the casing into the water stage and the drill pipe carrying the casing into the wellhead stage under the three string strength design methods based on the ultimate tensile load, the tensile allowance method and the safety factor method, respectively. The maximum tensile loads of the incoming string calculated by the safety factor method are 1905.02 kN and 2220.10 kN, respectively, and the corresponding safety margins are 3471.58 kN and 3156.5 kN, respectively, which meet the requirements of the maximum allowable design tensile load of the landing string.

5.3. Strength Check of Casing Entering Water Stage

Based on the data in Table 2, there are two types of displacement boundary conditions: no trolley constraint and trolley constraint imposed. A total of 24 sets of simulations were carried out to solve the lateral displacement of the string, the Von MISES stress and the restraint reaction force of the pipe string–trolley interface during the casing entering water stage throughout the year.

5.3.1. Calculation of Lateral Displacement

Figure 7 shows the calculation results of the maximum lateral displacement of the string without trolley restraint during the casing entering water stage of the year. Figure 8 shows the calculation results of the maximum lateral displacement of the string restrained by the trolley during the casing entering water stage of the year. Figure 9 combines the calculation results of Figure 7 and Figure 8, and the maximum lateral displacement of the string under the condition of whether or not the trolley is constrained during the casing entering water stage in the whole year is given. Figure 10 and Figure 11 show the schematic diagram of the collision and interference between the lateral displacement of the string and the inner diameter of trolleys 1 and 2, respectively, during the casing entering water stage throughout the year.

The simulation results of the casing entering stage under the action of average wind and wave flow in different months throughout the year show that the maximum lateral displacement of the string is located at the lower edge of the casing. The lateral displacement of the operational string in March was the smallest (5.58 m without casing restraint and 4.04 m with casing restraint), and the lateral displacement of the operational string in December was the largest (216.37 m without casing restraint and 187.26 m with casing restraint). Adding the DOF constraints of the trolley will significantly reduce the lateral displacement of the string. From the perspective of limiting the risk of collision between the string and the inner diameter of the trolley, there is no risk of collision with the inner diameter of trolley 1 during the casing entering water stage throughout the whole year, but there is a risk of collision with the inner diameter of trolley 2 in September, November and January of the following year. Therefore, it is recommended that the safe operation time of the casing entry stage is from February to August and October throughout the whole year.

5.3.2. Calculation of Von MISES Stress

Figure 12 shows the calculation result of the maximum value of Von MISES stress of the string without trolley restraint during the casing entering water stage in the whole year. Figure 13 shows the calculation result of the maximum value of Von MISES stress of the string restrained by the trolley during the casing entering water stage in the whole year. Figure 14 combines the calculation results of Figure 12 and Figure 13 to give the maximum value of the Von MISES stress of the string under the condition of whether the trolley is constrained during the casing entering water stage in the whole year.

The simulation results of the casing entering stage under the action of average wind and wave flow in different months throughout the year show that the maximum Von MISES stress of the string is located at the offshore position of the string. In March, the Von MISES stress of operational string is the smallest (26.1 MPa without casing restraint and 23.7 MPa with casing restraint). In December, the Von MISES stress of the operational string is the largest (646 MPa without casing restraint and 598 MPa with casing restraint), which exceeds the allowable yield strength of the string. Adding the DOF constraints of the trolley will significantly reduce the Von MISES stress of the string. In consideration of the safety of casing lowering, the recommended operating months are from January to October, and casing lowering operations are not recommended in November and December.

5.3.3. Calculation of BOP Trolley Limiting the Lateral Displacement of the String and Restraining the Reaction Force

Figure 15 shows the restraint reaction force that the BOP trolley should have to limit the lateral displacement of the string during the casing entering water stage throughout the year.

Table 9. Results of restraint reaction force of righting mechanism under extreme working conditions.

Results of Restraint Reaction Force of Righting Mechanism under Extreme Working Conditions (String Combination: 400 m 9-5/8in Casing, Safety Factor: 1.2)
Return Period, year	1		5		10		25		40	50	100	200
Surface Velocity m/s	Min	Max	Min	Max	Min	Max	Min	Max	Statistic	Statistic	Statistic	Statistic
	0.35	0.7	0.56	1.4	0.61	1.49	0.67	1.59	2.03	2.06	2.17	2.27
Wind Speed, m/s	9.4		20		28		32.6		35.2	36.5	40.8	45.6
Wave Height, m	2.2		5.4		8.6		11.4		13.1	13.9	16.8	20.1
Cycle, s	5.9		9.2		12.4		13.6		14.2	14.5	15.4	16.4
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fx, kN	4.451	17.407	11.32	69.363	13.383	78.532	16.09	89.39	145.54	149.87	166.27	181.93
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fy, kN	0	0	0	0	0	0	0	0	0	0	0	0
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fz, kN	93.942	93.942	93.942	93.942	93.942	93.942	93.942	93.942	93.942	93.942	93.942	93.942
Full Drill Stem Stage Simulation to Solve Bending Moment, kN·m	922.68	3689.6	2361.8	14,757	2802.3	16,716	3380.5	19,035	31,027	31,951	35,454	38,797
Combined with Safety Factor Simulation to Solve the Support Force kN	5.3412	20.8884	13.584	83.2356	16.0596	94.2384	19.308	107.268	174.648	179.844	199.524	218.316
Combined with Safety Factor Simulation to Solve Bending Moment, kN·m	1107.216	4427.52	2834.16	17,708.4	3362.76	20059.2	4056.6	22,842	37,232.4	38,341.2	42,544.8	46,556.4

shows the calculation results of the restraint reaction force and bending moment of the centralizing mechanism under extreme working conditions (string combination: 400 m 9-5/8in casing, safety factor 1.2).

The restraint reaction force that should be available for the BOP trolley to limit the lateral displacement of the string in different months of the year shows that the minimum restraint reaction force (76.46 N) is required for the string in February and the maximum restraint reaction force (1838.56 N) is required for the string in December.

In order to ensure the safe operation of the BOP trolley restraint mechanism under extreme operating conditions, the results of the restraint reaction force of the restraint mechanism under extreme operating conditions for each return period of extreme environmental conditions show that the calculated restraint reaction force of the restraint mechanism is 20.8884 kN (2.08884 tons) for the 1-year return period, 83.2356 kN (8.22356 tons) for the 5-year return period, 94.2384 kN (9.42384 tons) for the 10-year return period, 107.268 kN (10.7268 tons) for the 25-year return period and 218.316 kN (21.8316 tons) for the 200-year return period (21.8316 tons).

In summary, the recommended safe operation time for the casing entering water stage throughout the year is from February to August, the safe operation surface flow velocity is required to be less than 0.18 m/s and the design restraint reaction force of the BOP trolley to limit the lateral displacement of the string is greater than 218.316 kN (21.8316 tons).

5.4. Strength Check of Drill Pipe Carrying Casing into Water Stage

5.4.1. Calculation of Lateral Displacement

As in the previous method, we obtain the following Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.

The simulation results of the drill pipe carrying casing into the water stage by the average wind and wave flow in different months throughout the year show that the maximum lateral displacement of the string is located at the 1/2 position of the string. The smallest lateral displacement of the string is operated in February (52.9767 m without casing restraint and 50.2786 m with casing restraint), and the largest lateral displacement is operated in December (356.712 m without casing restraint and 331.144 m with casing restraint). Adding the DOF constraints of the trolley will significantly reduce the lateral displacement of the string. From the perspective of limiting the risk of collision between the string and the inner diameter of the trolley, there is no risk of collision with the inner diameter of trolley 1 during the drill pipe carrying casing into water stage throughout the whole year, but there is a risk of collision with the inner diameter of trolley 2 from April to July, September, November and January of the following year. Therefore, the recommended safe operating time of the drill pipe carrying casing into the water stage throughout the year are February, March, August and October.

5.4.2. Calculation of Von MISES Stress

As in the previous method, we obtain the following Figure 21, Figure 22 and Figure 23.

The simulation results of the drill pipe carrying casing into the water stage under the action of average wind and wave flow in different months throughout the year show that the maximum Von MISES stress of the string is located at the offshore position of the string. In February, the Von MISES stress of operational string is the smallest (377 MPa without casing restraint and 370 MPa with casing restraint). In December, the Von MISES stress of the operational string is the largest (1790 MPa without casing restraint and 1710 MPa with casing restraint). The allowable yield strength of the string is exceeded from November to January of the following year and from April to July. Adding the DOF constraints of the trolley will significantly reduce the Von MISES stress of the string. In consideration of the safety of casing lowering, the recommended operating months are February, March, August and September, while casing lowering operations are not recommended from October to January of the following year and from April to July.

5.4.3. Calculation of BOP Trolley Limiting the Lateral Displacement of the String and Restraining the Reaction Force

As in the previous method, we obtain the following Figure 24.

The restraint reaction force that should be available for the BOP trolley to limit the lateral displacement of the string in different months of the year shows that the minimum restraint reaction force (158.98 N) is required for the string in February and the maximum restraint reaction force (1763.32 N) is required for the string in December.

In order to meet the safety operation of the BOP trolley restraint mechanism without damage under extreme operating conditions, the longest suspension of the string is taken as the critical and dangerous condition, that is, the drill pipe carrying the casing is about to enter the wellhead stage, as shown in Figure 25.

Then we obtain

Table 10. Comparison of mechanical simulation calculation results of drill pipe carrying casing into wellhead and about to enter wellhead.

Month	Mechanical Simulation Calculation Results of Drill Pipe Carrying Casing into Wellhead			Mechanical Simulation Calculation Results of Drill Pipe Carrying Casing about to Enter Wellhead
	X-Displacement-Max, m	Y-Displacement-Max, m	Sum-Displacement-Max, m	Von MISES-Max, MPa	X-Displacement-Max, m	Y-Displacement-Max, m	Sum-Displacement-Max, m	Von MISES-Max, MPa
1	211.772	102.065	235.083	1140	289.868	160.5	331.336	2030
2	48.7292	21.0568	52.9767	377	79.244	55.6839	96.8519	534
3	33.2295	65.2673	73.2228	399	70.8989	136.942	154.206	689
4	61.3072	133.118	146.174	793	115.613	152.259	146.174	1230
5	612647	125.558	139.386	810	95.6712	133.69	164.396	1220
6	45.891	80.3666	92.1734	691	67.3231	70.2032	97.2671	826
7	68.9892	97.9518	118.946	691	115.323	80.3086	140.531	963
8	31.1511	4.08785	31.1937	271	50.7588	58.2531	77.265	324
9	12.8537	143923	12.8761	229	23.6349	20.1292	31.045	227
10	80.1755	30.0721	85.6296	548	102.09	50.9934	114.117	818
11	230.171	73.0539	241.39	1210	297.791	64.6474	304.728	2060
12	294.904	200.69	356.712	1790	370.201	276.955	462.334	3160

and

Table 11. Results of restraint reaction force of righting mechanism under extreme working conditions.

Results of Restraint Reaction Force of Righting Mechanism under Extreme Working Conditions (String Combination:1200 m 5-7/8in Drill Pipe + 400 m 9-5/8in Casing, Safety Factor: 1.2)
Return Period, year	1		5		10		25		40	50	100	200
Surface Velocity m/s	Min	Max	Min	Max	Min	Max	Min	Max	Statistic	Statistic	Statistic	Statistic
	0.35	0.7	0.56	1.4	0.61	1.49	0.67	1.59	2.03	2.06	2.17	2.27
Wind Speed, m/s	9.4		20		28		32.6		35.2	36.5	40.8	45.6
Wave Height, m	2.2		5.4		8.6		11.4		13.1	13.9	16.8	20.1
Cycle, s	5.9		9.2		12.4		13.6		14.2	14.5	15.4	16.4
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fx, kN	10.686	42.317	27.134	168.84	32.169	191.23	38.779	217.73	354.83	365.39	405.43	443.65
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fy, kN	0	0	0	0	0	0	0	0	0	0	0	0
Full Drill Stem Stage Simulation to Solve Constrained Reaction Forces Fz, kN	290.47	290.47	290.47	290.47	290.47	290.47	290.47	290.47	290.47	290.47	290.47	290.47
Full Drill Stem Stage Simulation to Solve Bending Moment, kN·m	8598.9	34,394	22,012	137,570	261,180	155,830	315,090	177,450	289,250	297,860	330,520	361,680
Combined with Safety Factor Simulation to Solve the Support Force kN	12.8232	50.7804	32.5608	202.608	38.6028	229.476	46.5348	261.276	425.796	438.468	486.516	532.38
Combined with Safety Factor Simulation to Solve Bending Moment, kN·m	10318.68	41272.8	26414.4	165,084	313,416	186,996	378,108	212,940	347,100	357,432	396,624	434,016

.

Analyzing tthe stage when the drill pipe carrying the casing is about to enter the wellhead, the restraint reaction force of the support mechanism is calculated for extreme operating conditions at each recurrence period. The results of the analysis show that the calculated restraint force of the restraint mechanism is 50.7804 kN (5.07804 tons) for the 1-year recurrence of extreme environmental conditions; 202.608 kN (20.2608 tons) for the 5-year recurrence period; 229.476 kN (22.9476 tons) for the 10-year recurrence period. For the 25-year recurrence period, the calculated restraint force is 261.276 kN (26.1276 tons), and for the 200-year recurrence period, the calculated restraint force is 532.38 kN (53.238 tons).

In summary, the recommended safe operation time for the drill pipe carrying casing into the wellhead stage throughout the year is February, March and August, the safe operation surface flow velocity is required to be less than 0.18 m/s, and the design restraint reaction force of the BOP trolley to limit the lateral displacement of the string is greater than 261.276 kN (26.1276 tons).

5.5. Strength Check of Drill Pipe Carrying Casing into Wellhead Stage

5.5.1. Calculation of Lateral Displacement

As in the previous method, we obtain the following Figure 26, Figure 27, Figure 28, Figure 29 and Figure 30.

The simulation results of the drill pipe carrying casing into wellhead stage by the average wind and wave flow in different months throughout the year show that the maximum lateral displacement of the string is located at the 1/2 position of the string. The smallest lateral displacement of the string is operated in February (68.112 m without casing restraint and 64.683 m with casing restraint), and the largest lateral displacement is operated in December (455.82 m without casing restraint and 423.436 m with casing restraint). Adding the DOF constraints of the trolley will significantly reduce the lateral displacement of the string. From the perspective of limiting the risk of collision between the string and the inner diameter of the trolley, there is no risk of collision with the inner diameter of trolley 1 during the drill pipe carrying casing into wellhead stage throughout the whole year, but there is a risk of collision with the inner diameter of trolley 2 from April to July, September, November and January of the following year. Therefore, the recommended safe operating time of the drill pipe carrying casing into the wellhead stage throughout the year are February, March, August and October.

5.5.2. Calculation of Von MISES Stress

As in the previous method, we obtain the following Figure 31, Figure 32 and Figure 33.

The simulation results of the drill pipe carrying casing into wellhead stage under the action of average wind and wave flow in different months throughout the year show that the maximum Von MISES stress of the string is located at the offshore position of the string. In February, the Von MISES stress of operational string is the smallest (573 MPa without casing restraint and 545 MPa with casing restraint). In December, the Von MISES stress of the operational string is the largest (1970 MPa without casing restraint and 1890 MPa with casing restraint). The allowable yield strength of the string is exceeded from October to January of the following year and from April to July. Adding the DOF constraints of the trolley will significantly reduce the Von MISES stress of the string. In consideration of the safety of casing lowering, the recommended operating months are February, March, August and September, while casing lowering operations are not recommended from October to January of the following year and from April to July.

In summary, the recommended safe operation time for the drill pipe carrying casing into the wellhead stage throughout the year is February, March and August, and the safe operation surface flow velocity is required to be less than 0.18 m/s.

5.5.3. Calculation of BOP Trolley Limiting the Lateral Displacement of the String and Restraining the Reaction Force

Figure 34 shows the restraint reaction force that the BOP trolley should have to limit the lateral displacement of the string in the stage when the drill pipe carries the casing into the wellhead in the whole year. It is not difficult to find that the minimum reaction force (159.02 N) is required for the operation string in February and that the maximum reaction force is required for the operation string in December (1764.42 N).

6. Discussion

The landing string is a key component of deepwater oil and gas extraction systems. Due to the complex marine environment, the oil and gas string and related equipment will be subject to the combined effect of waves, currents, platform drift and other loads in the process of lowering and lateral deflection; if the deflection is too large, it will cause the failure of not being docked with the subsea equipment and other serious consequences. In order to prevent the lateral displacement of the string, there is some research, such as on the use of guide devices to lower the subsea equipment, which can control the lateral offset of the landing string and realize the accurate docking of the deep-water landing string and the subsea wellhead equipment. However, the solution of adding the supporting device proposed in this paper can limit the lateral displacement of the string more effectively, which greatly reduces the risk of the drill pipe colliding with the platform. At the same time, this paper compares and analyzes the results of ultimate tensile load and Von MISES stress produced by the lateral displacement limitation of the pipe column with and without the BOP trolley under different working conditions and operation stages throughout the year, and gives the safe operation time of the landing string, the working condition window and the design restraint reaction force that should be available for the BOP trolley holding mechanism to limit the lateral displacement of the string. The conclusions of this paper are of high reference value for engineering practice. However, the analysis of this paper is carried out under the condition of maximum environmental load, and the influence of dynamic changes of environmental load on the tensile load and lateral displacement of the string is not considered. Thus, new related research can be carried out. At the same time, the lowering of the pipeline column cannot be a uniform process, so the influence of the change in acceleration of the landing string on the lateral displacement of the column during the lowering process needs to be explored in depth.

7. Conclusions

In this paper, the parameters of the landing string, the statistical data of the average monthly wind and wave current in the operation area for many years, and the statistical data of the return period of extreme environmental conditions were used as inputs for simulation calculations. Then, we divided the running process of the landing string into three operation stages: the casing entering stage, the drill pipe carrying the casing into the water stage, and the drill pipe carrying the casing into the wellhead stage. Moreover, we established finite element analysis models of the string in ANSYS software and carried out finite element simulation calculations under different combined working conditions. In addition, we obtained the lateral displacement, stress and BOP trolley-pipe string contact surface constraint reaction force under the monthly average and extreme working conditions. Taking the yield strength of the string and the displacement limit in the trolley as the check standard, the recommended safe working time, safe working condition window and recommended BOP trolley design constraint reaction force results are given for the whole year of the landing string lowering operation. The results are as follows:

(1) The ultimate tensile load of the deep-water landing string is less than the allowable tensile strength, which meets the tensile design requirements:

The maximum axial stress of the landing string is distributed along the axial direction of the string and reaches the maximum at the top. The maximum horizontal stress and the maximum MISES stress both appear at the sea entry surface. The allowable tensile strength of the string is 5376.6 kN, the maximum tensile loads of the string calculated by the safety factor method are 1905.02 kN and 2220.10 kN, respectively, and the corresponding safety margins are 3471.58 kN and 3156.5 kN, respectively, all of which meet the requirements of the maximum allowable design tensile load of the landing string.

(2) Recommended working time and safe working conditions for deep-water landing strings:

It is judged that the 1628.8 m 5-7/8in drill pipe and 400 m 9-5/8in drill pipe carries the casing into the wellbore as a dangerous condition. The position of the string near the water surface is in a state of great stress due to the action of wind and wave current, and when the drill pipe carrying the casing is about to enter the wellhead, it is the operation stage with the greatest stress in the whole process of the landing string operation. According to statistical data, the recommended working time is February, March and August, and the recommended safe working surface velocity is <0.18 m/s. See Figure 35 for the safe working surface velocity–wave height working window.

(3) BOP trolley restraint reaction force:

It is judged that the string combination of 1200 m 5-7/8in drill pipe and 400 m 9-5/8in casing is run down as a dangerous condition. Taking the extreme operating conditions of the 25-year return period (surface velocity of 1.59 m/s) and the safety factor of 1.2, it is recommended that the design restraint reaction force of the BOP trolley is >261.276 kN (26.1276 tons).

Although this paper ignores the influence of the dynamic changes of the environmental load and the changes in the lowering speed on the analysis process of the lowering condition of the landing string, the paper still has some engineering reference value. Meanwhile, the influence of these two parts can be studied in depth in future research.