scholarly journals Well-posedness of the two-phase flow problem in incompressible MHD

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Changyan Li ◽  
Hui Li
Keyword(s):  
Two Phase Flow ◽  
Flow Problem ◽  
Well Posedness ◽  
Phase Flow ◽  
Two Phase ◽  
Incompressible Mhd

scholarly journals Numerical modeling of local effects on the petroleum reservoir using fixed streamtubes for typical waterflooding schemes

Georesursy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 70-78
Author(s):  
Konstantin A. Potashev ◽  
Alexander B. Mazo
Keyword(s):  
Numerical Modeling ◽  
Two Phase Flow ◽  
Flow Problem ◽  
Constant Thickness ◽  
Oil Reservoir ◽  
Phase Flow ◽  
Two Dimensional ◽  
Petroleum Reservoir ◽  
Local Effects ◽  
Two Phase

The difficulty of numerical modeling of areal methods of flows redistribution in the oil reservoir is the need for detailed resolution of local hydrodynamic effects and the fine geological structure of the reservoir, which are centimeter-wide, at inter-well distances of the order of several hundred meters. The dimension of computational grids of traditional 3D models of such resolution, even for impact areas containing a small number of injection and production wells, turns out to be excessively large for design calculations. To overcome these limitations, it is proposed to perform a detailed simulation of the flow in two-dimensional cross sections of the reservoir along fixed streamtubes of variable width between each pair of interacting injector and producer wells. Reducing the dimension of the problem allows the use of high-resolution grids to simulate short-term local effects. In this paper, we present an algorithm for constructing a single fixed streamtube between injector and producer, which provides a minimum error in calculating of flow rate and water cut using a two-phase flow problem of reduced dimension along the streamtube. The algorithm is demonstrated by the example of the two-dimensional two-phase flow problem neglecting capillary and gravitational forces in a homogeneous reservoir of constant thickness for three waterflooding elements corresponding to seven vertical well flooding patterns – standard and inverted four-spot, five-spot and seven-spot, as well as staggered line drive. For these waterflooding elements, efficient streamtubes have been constructed, the relative width of which is approximated by piecewise linear functions. On the example of a staggered line drive or five-spot well patterns, the width of the effective streamtube was parameterized for an arbitrary ratio of the sides of the waterflood element. Presented streamtubes can be used as ready templates for subsequent modeling of geological and technical treatments in the relevant elements of the water flooding of the oil reservoir.

An Exact Sensitivity Analysis of a Simplified Transient Two-Phase Flow Problem

1985 ◽  
Vol 89 (1) ◽  
pp. 1-35 ◽  
Author(s):  
E. Wacholder ◽  
S. Kaizerman ◽  
N. Tomerian ◽  
D. G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Two Phase Flow ◽  
Flow Problem ◽  
Phase Flow ◽  
Two Phase

A note on the two-phase Hele-Shaw problem

2000 ◽  
Vol 409 ◽  
pp. 243-249 ◽  
Author(s):  
SAM D. HOWISON
Keyword(s):  
Two Phase Flow ◽  
Schwartz Function ◽  
Explicit Solutions ◽  
Well Posedness ◽  
Phase Flow ◽  
Two Phase ◽  
Hele Shaw Cell

We discuss some techniques for finding explicit solutions to immiscible two-phase flow in a Hele-Shaw cell, exploiting properties of the Schwartz function of the interface between the fluids. We also discuss the question of the well-posedness of this problem.

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