Abstract
Many numerical studies have been conducted regarding laminar miscible displacement flow in narrow, vertical, eccentric annuli. For the next decade it is likely that primary cementing flows on the scale of the well will continue to be simulated predominantly with 2D gap-averaged (2DGA) models. However, 3D simulations are less common due to the computational cost. The comparison between 2D and 3D models needs further attention, to understand the main discrepancies and thus help to understand primary cementing flows better. In this paper, comparisons of 3D against 2DGA model results show a range of interesting different phenomena, e.g. static layers, dispersive spikes, and instabilities. The predictions of the 2DGA model are the same as the 3D results to a degree. In particular, they are consistent with each other regarding the evolving process, interface shape, etc. However, the main difference with the 2DGA concentration arises from dispersion on the scale of the annular gap. From the recent research of Renteria and Frigaard (J. Fluid Mech., vol. 905, 2020) [1], a variety of dispersive effects are the main discrepancy between experiments and 2DGA results as well. We give representative examples of these flows in surface casing geometries and suggest methods for improvement of the 2DGA model.
Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm
