Abstract. A mathematical model of the glaciation dynamics of the multilayer cylinder is suggested. The model reflects the specific feature of glaciation in salt water. The choice of effective model parameters and thermal characteristics of the increasing ice is considered. The calculations of problem using front-tracking finite difference method and using analytical solution found in quasi-stationary approximation are presented.
The paper introduces a method for calculating the depressurization coordinate of an extended ultra-high pressure gas pipeline from the data measurements of pressure and flow rate at the outlet. The method is based on a mathematical model of a non-isothermal steady single-phase gas mixture flow through a pipeline of constant section on the quasi-linearization method. It allows to calculate the depressurization coordinate for extended underground and offshore ultra-high pressure gas pipelines with high accuracy, while considering varying leakage size and location. Examples of solving problems of practical interest are given. The influence of the flow rate and pressure settings error on the coordinate of depressurization calculating error has been demonstrated.
Different approaches to the modeling of thermodynamic processes in a gas flow at hyper-pressure are discussed and their equivalence is proved for any form of equation of state. The article presents arguments in favor of the approach in which temperature and density are chosen as independent thermodynamic variables and equation of sate is written in one of its analytical forms, for example, in the form of Redlich-Kwong equation of state. Explicit analytical expressions are obtained for the dependences of internal energy and specific heat at constant volume on gas temperature and density. It is proved that simplifications of the model of thermodynamic processes, which are based on the assumption of incompressibility of gas flow, are inadmissible, even in case of negligibly small inertial forces.
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