Slug Frequency Prediction Model for Fluid Flow in Flowline Bends

The prediction of slug frequency for two-phase slug flow during multiphase transportation of oil reservoir productions is crucial in the design of slug controllers for petroleum processing installations. Mechanistic based slug prediction models have not had much successful application due to the difficulty in modelling the non-linear interface motion during slug development. The mechanism of slugging in offshore flowline-riser is complicated and requires rigorous experimental sampling and testing. This process can be time-consuming and costly. In this study, a new correlation is developed for the prediction of severe slugging frequency. The new model is developed based on the results of scaled experimental design. Dimensional analysis approach using the Buckingham pi-theorem is used in developing the two-phase correlation. The model development involves non-dimensional empirical correlations in terms of relevant dimensionless groups, which are obtained based on the design of the experiment. A broad range of experimental data from 10 varied choke opening size was used. The new correlation predicts 92.3% of the measurements within ±8% absolute error and the mean absolute deviation of the correlation is about 6.13%. The newly developed correlation can be applied for flow rates between 0.1 kg/s and 0.6 kg/s and choke openings between 10-98%.

Modeling of Thermal Conductivity in a Medium with Phase Transition with a Moving Boundary of Phase Change

This work is devoted to the theoretical study of the effect of the phase interface motion on thermal conductivity in a liquid-solid nonlinear medium with a phase transition. The problem under consideration deals with the Stefan problems. Its most significant feature is the jump in the phase properties at separation of their moving boundaries. The objective was achieved by solving the following tasks: the construction of the process mathematical model based on its cell representation and with the use of the Markov chain theory mathematical apparatus, performing numerical experiments with the developed model, demonstrating its operability and the possibility to achieve the set goal. The most significant scientific results were as follows. First was an algorithm for the construction of a cell mathematical model of nonlinear thermal conductivity in a phase transitions medium with a moving phase interface for domains of a canonical shape (plane wall, cylinder, ball). Second, the results of the numerical experiments, showing that the jump of properties affected greatly the kinetics of the process. The significance of the results obtained consisted in the development of a simple but informative mathematical model of the media heat treatment kinetics with phase transformations, available for a direct use in the engineering practice. The proposed algorithm for constructing the model can be effectively used in prediction the open water pipes freezing in cold regions, in modeling the heat treatment of metals, in choosing the freezing modes of food products for a long-term storage, and other thermo-physical processes.

The hodograph equation for slow and fast anisotropic interface propagation

Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

Analytical Modeling of Outward Solidification With Convective Boundary in Cylindrical Coordinates

Solidification consists of three stages at macroscale: subcooling, freezing and cooling. Classical two-phase Stefan problems describe freezing (or melting) phenomenon initially not at the fusion temperature. Since these problems only define subcooling and freezing stages, an extension to characterize the cooling stage is required to complete solidification. However, the moving boundary in solid-liquid interface is highly nonlinear, and thus exact solution is restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, like a small Stefan number. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder. By assuming a small Stefan number, three temporal regimes and four spatial layers are considered in the asymptotic analysis. The results are compared with numerical method. Further, effects of Biot numbers are also investigated regarding interface motion and temperature profile.