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Steel catenary riser s , (SCR) usually installed between seabed wellhead and floating platform are subjected to vortex shedding. These impose direct forces, hence cyclic stresses, and fatigue damage on the SCR. Riser failure has both economic and environmental consequences; hence the design life is usually greater than the field life, which is significantly reduced by vortex induced vibration (VIV). In this study, SCR and metOcean data from a field in Offshore Nigeria were substituted into linearized hydrodynamic models for simulations. The results showed that the hang off and touchdown regions were most susceptible to fatigue failure. Further analysis using Miner-Palm green models revealed that the fatigue life reduced from a design value of 20-years to 17.04-years, shortened by 2.96-years due to VIV. Furthermore, a maximum wave load of 5.154 kN was observed. The wave loads results corroborated with those obtained from finite element Orca Flex software, yielding a correlation coefficient of 0.975.

The floating platform represents a new technology with promising future for the upstream oil and gas industries. Risers are used to interface the wellhead on the seabed to these floating surface production facilities. A steel catenary riser (SCR) is a rigid steel pipe of parabolic shape with considerable bending stiffness which is controlled mainly by weight, buoyancy and hydrodynamics forces due to currents and waves [

It is therefore obvious that their failure is undesirable and associated with serious economic and environmental impacts. Curbing this requires the performance of detailed analyses of the riser using actual environmental load data. Environmental loads are the main source of dynamic excitation of offshore structures [

Vessel motions and hydrodynamic loading results in two critical fatigue regions of the SCR, namely:

1) At the vessel hang-off point (Tension Leg Deck) and

2) At the touch down zone (TDZ) (region of riser-soil interaction).

In the TDZ, cyclic motions of the SCR lead to complex interactions between the seabed and the riser. The severity of these interactions depends on the nature of the soil at the seabed for the geographical location involved. A SCR profile at the TDZ is shown in

According to Langer and Langer [

profile that minimizes the shear forces in the SCR at the TDZ and consequently reduces the fatigue damage in the vicinity of the TDZ. The primary design criteria of SCRs are the usual internal and external pressure requirements and a requirement that the predicted minimum fatigue life of the riser must exceed the field life by a specified design factor. Fatigue damage is caused by cyclic bending of the riser, induced by the combination of platform motions and direct wave and current loadings on the riser [

The procedure adopted to estimate the wave forces on the modeled FPSO and SCR include:

v Physical modeling of FPSO and SCR;

v Select an appropriate wave theory (linearized waves, Morrisons equation or others, if necessary);

v Select the appropriate C_{M} and C_{D} based on Reynolds number and strouhal number, other factors;

v Perform bending moment analysis;

v Perform fatigue analyses;

v Perform statistical analysis

Physical model is a larger or smaller physical copy of an object. It allows visualization for examining the model of information about the things the model represents. A physical OrcaFlex model of a single riser and floating production storage and offloading (FPSO) undergoing the Ochi-Hubble wave pattern typical to GoG is shown in

It is known that fluid motion past the SCR gives rise to Vortex shedding, which causes a lift force on the member at right angles to the fluid flow direction at a frequency corresponding to the eddy-shedding frequency. For steady flow past a cylinder (of diameter D) due to a current velocity (U_{max}) the main measure of the vortex shedding frequency (f) of the forces is the strouhal number (S) in Equation (1) which in turn depends on the Reynolds number (Re) expressed as Equation (2).

S = D f U max (1)

R e = U max D ϑ (2)

where υ―knematic viscosity of the fluid.

By the concept of linear wave theory, the linearized hydrodynamic (Morrison) equation for calculating the total wave force (F) is given by Equation (3).

F = 2 π ρ r H 2 L T 2 [ A 1 C m sin θ + A 2 C d | cos θ | cos θ ] (3)

where A_{1} and A_{2}―constants, C_{d}―drag coefficient, C_{m}―inertia coefficient, L―wavelength for intermediate water depth, H―significant wave height, ρ―water density, r―riser radius, θ―theta in radians, T―period.

The total force (F) in Equation (4) has two components, namely: 1) the drag component (F_{d}) expressed as Equation (5) and 2) Inertia component (F_{m}) expressed as Equation (6). The effect of marine growth was not considered in this study hence a drag coefficient value of C_{d} = 0.7 and inertia coefficient value of C_{m} = 1.5 was utilized in the models.

F = F d + F m (4)

F d = 2 π ρ r H 2 L T 2 [ A 2 C d | cos θ | cos θ ] (5)

F m = 2 π ρ r H 2 L T 2 [ A 1 C m sin θ ] (6)

The Morrison equation can also be expressed in terms of flow velocity (U), flow acceleration ( U ′ ), riser cross-sectional area (A) and volume (V) as in Equation (7).

F = ρ C m V U ′ + 1 2 ρ C d A U | U | (7)

where the drag force F_{D} and inertia force F_{m} are given by Equation (8) and Equation (9), respectively.

F d = 1 2 ρ C d A U | U | (8)

F m = ρ C m V U ′ (9)

The resulting overall bending moment (M) of the structure is given by Equation (10).

M = 2 π ρ r H 2 L 2 T 2 [ A 3 C m sin θ + A 4 C d | cos θ | cos θ ] (10)

where A_{3} and A_{4}―constants.

Similar to the total force, the resulting overall bending moment given in Equation (10) has two components, namely: 1) the drag component (M_{d}) in Equation (11) and 2) the inertia component of moment (M_{m}) in Equation (12).

M d = 2 π ρ r H 2 L 2 T 2 A 4 C d | cos θ | cos θ (11)

M m = 2 π ρ r H 2 L 2 T 2 [ A 3 C m sin θ ] (12)

The wave equation constants A_{1} and A_{2} can be expressed as Equation (13) and Equation (14), respectively.

A 1 = π r 2 H (13)

A 2 = 1 16 sinh 2 k d [ 2 k d + sinh ( 2 k d ) ] (14)

where k―wave-number.

The overall bending moment equation constants A_{3} and A_{4} can be expressed by Equation (15) and Equation (16), respectively.

A 3 = π r 4 H sinh ( k d ) [ 1 + ( k d ) sinh ( k d ) − cosh ( k d ) ] (15)

A 4 = π r 64 sinh 2 ( k d ) [ 2 k 2 d 2 + 2 ( k d ) sinh ( 2 k d ) + 1 − cosh ( 2 k d ) ] (16)

The basic fatigue capacity (N―number of cycles to failure) is expressed in terms of the shear stress (S) as Equation (17).

N = a S − m (17)

where a and m―empirical constants.

By taking the log of both sides, Equation (17) is reduced to Equation (18).

log N = log a − m log S (18)

The Miner-Palmgreen rule for the estimation of accumulated fatigue damage (D_{f}) from number of stress cycles (N) with variable range and stress due to shear force (S_{i}) is given by Equation (19).

D f = ∑ i n ( S i ) N ( S i ) (19)

where n―number of values.

According to Miner-Palmgreen rule, as used by Ebunuoha [

v D_{f} > 1 implies that the damage is significant;

v D_{f} < 1 implies that there is no damage;

v D_{f} = 1 implies that there is imminent or impending damage.

Bivariate data that measure two different variables are important and frequently encountered in statistical analysis. Correlation analysis provides techniques for analyzing the relation between two variables [

r = N ∑ X Y − ( ∑ X ) ( ∑ Y ) [ N ∑ X 2 − ( ∑ X ) 2 ] [ N ∑ Y 2 − ( ∑ Y ) 2 ] (20)

where X―Representative of linear force values, Y―Representative of nonlinear force values, N―number of values.

The plot of drag force against water depth obtained is shown in

trend in the figure shows that the drag force decreases with increasing water depth. This is due to the current velocity which drastically reduces as water depth increases. At about 879 m it suddenly increased due to increased flow velocity in this depth. The continuous decrease is also associated with lower contribution of the wave drag force arising from the existence of waves at the air-water interface and near-surface region as the disturbance caused by this phenomenon decreases with water depth.

The trend of the total wave force with respect to water depth is shown in

The plot of bending moment versus water depth is shown in

The combined plot of wave loads (shear force) against theta in radians is shown in

The performance modeling of deep water steel catenary riser has been carried out. It was shown that the SCR structure operates in environments where it is adversely affected by varying conditions of currents and waves. These flow conditions subjects the riser to direct forces which results to cyclic stresses and with time culminates to fatigue damage. These led to the application of proven linearized hydrodynamic model to evaluate the deep water marine riser performance. MetOcean data were taken from a field in Offshore Nigeria. Simulations were carried out using OrcaFlex software. It revealed that hydrodynamic loadings results in two critical fatigue regions, namely: the vessel hang-off point and the

TDZ-the area of soil-riser interaction. Also, a detailed fatigue analysis revealed that the remaining SCR life is 17.04-years, that is, 2.96-years less than the 20-years design life. Furthermore, the statistical analysis carried out on total wave forces proved that both approach are highly correlated.

Ebunuoha, C. and Ossia, C.V. (2017) Steel Catenary Riser Fatigue Life Prediction Using Linearized Hydrodynamic Models. World Journal of Engineering and Technology, 5, 564-573. https://doi.org/10.4236/wjet.2017.54048