Riser and well casing analysis during drift-off: a coupled solution in the time domain

One of the most serious incidents that can occur in offshore drilling and exploration is damage to the well structure and subsea components which can result in uncontrolled hydrocarbon release to the environment and present a safety hazard to rig personnel. Over decades, there have been substantial developments to the mathematical models and algorithms used to analyze the stresses on the related structure and to define the operational and integrity windows in which operations can proceed safely and where the mechanical integrity of the well is preserved. The purpose of this work is to present a time-domain solution to the system of equations that model the dynamic behavior of the riser and casing strings, when connected for well drilling/completion during the event of drift-off of the rig. The model combines a solution using finite differences for the riser dynamics and a recursive method to analyze the behavior of the casing in the soil. It allows for the coupling between the equations related to the riser and casing and for the coupling with the equations that describe the dynamics of the rig when station keeping capabilities are lost. The use of the forward–backward finite-differences coupled with the recursive method does not require linearization of the forces acting on the structure making it an ideal methodology for riser analysis while improving convergence. The findings of this study can help improve understanding of the impact of the watch circle limits to riser/well integrity, whether these limits are set based on a quasi-static drive-off/drift-off or fully dynamic. The gain in accuracy in using the fully coupled equations of drift-off dynamics, where there is interaction between the rig and the top of the riser during drive-off/drift-off, is evaluated, and the effects of varying the riser top tension and the compressive loads on the casing string are also analyzed. In particular, it is shown that the results of the fully coupled system of equations representing the dynamics of the riser and casing during drift-off/drive-off are less conservative than the quasi-static approach. Another important finding is that the gain in accuracy in coupling the top of the riser and the rig during drift-off/drive-off is not substantial, which indicates that solving separately the rig dynamics equations and the riser-casing equations is an approach that provides reasonable results with less computational effort. The model can also be used to evaluate wellhead and casing fatigue during the life of the intervention. Finally, the model limitations are discussed.

Construction Solutions of Ordinary and Partial Differential Equations using the Analytical and Numerical Methods

In this paper we studied the solution of partial differential equations using numerical methods. The paper includes study of the solving partial differential equations of the type of parabolic, elliptic and hyperbolic, and the method of the net was used for the numerical nods, which represents a case of finite differences. We have two types of solution which are the internal solution and boundary solution. The internal solution is based on the internal nodes of the net. The boundary solution depends on the boundary nodes of the net, in addition to finding the analytical solution of the equations to compare the results. We also discussed solving the problem of Laplace, Poisson, for the importance of these equations in the applied side; Mat lab was used to find the values of tables for the values of border differences. We have derived a new formula for the solution of partial differential equations containing three independent variables.

The Succession of Heat and Mass Driven Natural Convection Regimes Along a Vertical Impermeable Wall

This paper presents the analysis of the natural convection process that takes place near a vertical plane wall embedded in a constant temperature and linearly mass stratified fluid (the Prandtl number and the Smith number are smaller than 1.0, while the Lewis number is greater than 1.0). The wall has a constant temperature, while the flux of a certain constituent is constant at this boundary. The scale analysis and the finite differences method are used as techniques of work. The scale analysis proves the existence, at equilibrium, of heat and/or mass driven convection regimes along the wall. The finite differences method is used solve the governing equations and to verify the scale analysis results using two particular parameters sets.

The comparison of a discrete-continuous approach and a method of finite differences in solving the problem of unsteady-state heat and moisture transfer in the building envelope

This article is devoted to the development of methods for calculating heat and humidity regime in the building envelope. The equation of steady-state thermal conductivity with boundary conditions of the third kind and the formula for calculating heat losses of a building based on the heat transfer equation have been considered. The equation of unsteady-state thermal conductivity as well as its solution using the discrete-continual approach has also been studied. The solution of the unsteady-state heat conductivity problem with invariable over time boundary conditions using the discrete-continuous approach was proposed by A.B. Zolotov and P.A. Akimov. The subsequent modernization of the solution was conducted by V.N. Sidorov and S.M. Matskevich. The unsteady-state equation of moisture transfer based on Fick’s second law using the theory of moisture potential is derived. The solution of the unsteady-state moisture transfer equation using the finite difference method according to an explicit difference scheme as well as the solution of the unsteady-state moisture transfer equation using the discrete-continuous approach is demonstrated. To prove the effectiveness of using the discrete-continuous approach in the area of the unsteady-state humidity conditions we compared the calculation results of the distribution of moisture in a single-layer enclosing structure made of aerated concrete using two methods of moisture potential theory. It was found that the difference in the results of calculation by the discrete-continual formula and by the method of finite differences does not exceed 3.2%.

Evaluation of the Accident Rate of a Plant Equipped with an Aging Single Protective Channel by the Method of Supplementary Variables

This work calculates the reliability of protective systems of industrial facilities, such as nuclear, to analyze the case of equipment subject to aging, important in the extension of the qualified life of the facilities. By means of the method of supplementary variables, a system of partial and ordinary integral-differential equations was developed for the probabilities of a protective system of an aging channel. The system of equations was solved by finite differences. The method was validated by comparison with channel results with exponential failure times. The method of supplementary variables exhibits reasonable results for values of reliability attributes typical of industrial facilities.

An enhancement of instruments for solution of general transmission line equations with method of lines, impedance-/admittance and field transformation in combination with finite differences

The Method of Lines (MoL) in combination with impedance-/admittance and field transformation (IAFT) is used to analyze electromagnetic waves. The used cases are wave-guiding structures in microwave technology and optics. The core of the theory is the solution of generalized transmission line equations (GTL). In the case of complex structures, a combination with finite differences (FD) can be used. The quality of this solution essentially depends on the effectiveness of the used interpolation of the differences. The individual steps of the FD are permanently linked to the steps of the fully vectorial impedance-/admittance and/or field transformation, so standard libraries cannot be used. Two approaches based on the linear and quadratic interpolation were built into the impedance-/admittance and field transformation in the past. However, the degree of improvement due to one or another kind of interpolation depends on the concrete behavior of the solution sought. In the case of complex structures, choosing the appropriate type of interpolation should be an effective aid. In this paper, an extension of the family of built-in methods is proposed - with the possibility of being able to build any known numerical method from the class of one-step or multi-step methods into the GTL solution. These can be higher-order methods, including fast explicit methods, or particularly stable implicit methods. The transmission matrices for the impedance-/admittance and field transformation serve as the building site. To illustrate the procedure, some different methods are integrated into the GTL solution. The accuracy of the solutions is tested on selected complex structures and compared with each other and with existing solutions. It is shown that the optimal choice of method and the quality of the solution can depend on concrete structures. Keywords: Method of lines, generalized transmission line equations, impedance/admittance transformation, waveguide structures, finite differences, finite differences with second order accuracy.

The resolution of a mathematically bad-defined problem in the approximation of a cellular automation by the example of the description of human states

A mathematical model describing the mutual influence of bad-defined various human characteristics is constructed. This model is described by a system of differential equations that reflect the “rate” of change in a characteristic as a function of the frequency of interaction with other characteristics. The transition from differential equations to equations in finite differences and the introduction of the von Neumann neighborhood on the resulting square space of the frequency of interaction of various human characteristics allows us to introduce a cellular automaton. The sequential execution of iterations in the cellular automaton allows to track how each of the entered characteristics depends on the behavior of other characteristics.