Application of Semi-Segregated Finite Element Method to Two-Phase Problems with a Surface Tension Effect

Aimed at deflection fracturing by oriented perforation, a two-dimensional, non-steady and two-phase Finite Element Method (FEM) is established. Taking a battery of wells in the inverted nine-spot rhombus pattern as object of study, it is reported that law of different crack initiation angle (CIA) affecting deflection fracturing. In the respect of daily oil production and cumulative oil production, the dual fracture with different CIA is more than straight fracture. So it is feasible to use deflection fracturing of oriented perforation to increase the production of the special low permeability oilfield. In contrast to dual fractures with different fracturing initiation angles, we can see that the wider CIA, the higher cumulative oil production. So we can draw such a conclusion that when deflection fracturing is implemented, angle should be increased if the working condition is permitted so as to increase the production of oil well.

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Chapter V A Finite Element Method For Incompressible Two-Phase Flow

Mathematical Models and Finite Elements for Reservoir Simulation - Single Phase, Multiphase and Multicomponent Flows through Porous Media - Studies in Mathematics and Its Applications ◽

10.1016/s0168-2024(08)70083-3 ◽

1986 ◽

pp. 311-364

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Two Phase Flow ◽

Phase Flow ◽

Two Phase ◽

Element Method

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Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-07-2019-0599 ◽

2019 ◽

Vol 30 (3) ◽

pp. 1407-1426 ◽

Cited By ~ 12

Author(s):

Xuejuan Li ◽

Ji-Huan He

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Method ◽

Two Phase Flow ◽

Polymer Melt ◽

Phase Flow ◽

Filling Process ◽

Two Phase ◽

Content Type ◽

Element Method

Purpose The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface. Design/methodology/approach The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time. Findings The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems. Originality/value For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

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