Research On The Influence Of Jack-up's Random Vibration On Drilling System Under The Working Conditions

As the main equipment in exploration and development of offshore oil,jack-up plays the leading role in the continental shelf waters.Jack-up is designed to adapt the deeper water as the increasing oil and gas demand,which decreases the platform's lateral rigidity.Under the random environment loads,the jack-up platform generates noteworthy random dynamic response.Therefore,it's important to study the computing method of the platform's random response and the influence of the platform's vibration exerting on the drilling system at both design and applied stage.Supported by the project foundation of China Ministry of Industry and Information Technology “Jack-up platform brand project(II)”,this paper investigated the influence of jack-up's random vibration on drilling system under the working conditions.Transverse natural vibration characteristics of both jack-up platform and riser were studied firstly.Considering the platform's weight and the additional water's mass,this paper deduced the formula to compute the platform's transverse natural vibration period based on energy approach.The research results show that the equal probability between platform's natural vibration period and random wave's motion period is big.Based on the Euler beam theory,this paper respectively studied the riser's lateral natural vibration characteristics under both surface blowout preventers(BOP)and subsea BOP working conditions;and the frequency equation with compressive axial load and the length of the riser above the seabed as independent variable was derived in this paper.According to the frequency equation,the compiling method of the riser's resonate rotate speed table was proposed.The results show that: there is a nonlinear relationship between the frequencies of the riser and the length of the riser above the seabed,and the frequencies decrease with the increasing length;under the general working conditions of jack-up,the relationship between the frequencies of the riser and axial compressive load is almost linear,and the frequencies decrease with the increasing axial compressive load;the resonant frequency range of the riser with drill string depends on the length of the riser,and the resonant frequency range is extended by the increasing length.Secondly,the random dynamic response calculation method of the Euler beam with axial load and time-dependent boundary conditions was investigated.The mathematic model of the influence research of the platform's random vibration exerting on the riser was elaborated.An analytical procedure for investigating the response spectrum of uniform Bernoulli-Euler beam with axial compressive load subjected to random support excitations is implemented based on the Mindlin-Goodman method and the mode superposition method in frequency domain.An experiment of Euler beam's dynamic response test was designed,an experimental system was established,and the Euler beam's response test experiment was finished.The experimental results show that the Mindlin-Goodman method is effective to solve the Euler beam's lateral vibration response.The random displacement response of the simply supported beam subjected to white noise excitation and Pierson-Moskowitz spectrum excitation were investigated respectively,the effect of axial compressive load was investigated,and a method to determine the axial load was proposed.The research results show that the response spectrum is mainly consist of the beam's additional displacement response spectrum when the excitation is white noise,the axial load has a greater influence on the beam's response,and the amplitude of the power spectral density function decreased as the axial compressive load increased.The quasi-static displacement response spectrum is the chief component when the excitation is Pierson-Moskowitz spectrum,the influence of axial load can be ignored,and the frequency band of the vibration response spectrum increased with the increasing axial compressive load.The method proposed in this paper can also be applied to solve Euler beam's lateral random support response with other time-dependent boundary conditions.Thirdly,the influence of jack-up's random vibration on drilling system under the working conditions was studied by the proposed method.The mathematical model of the platform's lateral vibration was established,and the computing method of the platform's random wave force was derived based on the random wave theory.By the Mindlin-Goodman method,Borgman linearization technique,and the spectral method,an analytical method was presented to estimate the jack-up riser's random wave load in frequency domain.By the quantitative research,an approximate formula was proposed to compute the random wave force spectrum of the small-scale structures according to the infinite water depth dispersion relationip.The power spectral density function of the platform's random displacement response is derived by the spectral method.The results show that the power spectral density function of the platform has two peak frequencies which are wave force spectrum's dominant frequency and the platform's natural frequency;and the frequency band of the platform is mainly between these two peak frequencies.The influence of the platform's vibration on the riser under both surface BOP and subsea BOP working conditions were studied respectively.The results show that the response of jack-up riser is a narrow band random vibration;under the same load,the riser with surface BOP has the bigger stress response amplitude.The dynamical response calculation method of the pinned-clamped Euler beam and the simply supported Euler beam with axial tensile load were presented in the frequency domain.A quantitative research was executed to determine the distribution characteristics of the riser,and an analytical method was proposed to estimate the jack-up riser's fatigue life.According to the grade-B fatigue characteristic curve,the fatigue life estimation was carried out by the riser's fixed end.The obtained results can be used to assess whether a special sea area and its sea state are available for the jack-up,adjust the riser's installment order,and improve the whole riser system's working life.Finally,based on the finite element method and spectral method,the derrick's dynamic response was investigated by taking the platform's random displacement power spectral density function as the derrick's support excitation.Taking a tower type derrick as the blueprint,a multi-freedom model of derrick was established by the finite element method;and the spectrum of the multi-freedom system was derived by the mode superposition method and the spectral method.The results show that the vibration in X and Y direction are derrick's main vibration.The vibration in X direction main consists of the third,sixth,and twelfth order modes.The vibration in Y direction main consists of the seventh,fourteenth,and eighteenth order modes.The platform's random vibration has little impact on the derrick;however,the research method in this paper can provide some technical support in the derrick's optimization design.