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In order to analyze the microscopic theory of viscous-elastic fluid flooding residual oil, the flow equation of polymer solution in the micro pore can be derived by selecting upper-convected Maxwell constitutive equation, continuity equation and motion equation. Then, the flow velocity field and stress field can be calculated under the boundary condition, and with the theory of stress tensor, the horizontal stress difference of polymer solution acting on the residual oil can be calculated. The results show that the greater the elasticity of viscous-elastic fluid is, the wider the flow channel is, the greater the horizontal stress difference is. The force acting on residual oil by viscous-elastic fluid can be increased by increasing the concentration of the polymer solution.

The practice of enhanced oil recovery shows that the recovery can be improved by the viscous-elastic polymer solution flooding. The conclusion that the greater the elasticity of viscous-elastic fluid is, the higher the sweep efficiency is, which has been derived through using the modified upper-convected Maxwell constitutive model by Yin Hongjun [

In this paper, the microscopic force acting on the residual oil of viscous-elastic fluid has been calculated quantitative. And the microscopic force which made the residual oil deform is the horizontal stress difference acting on the residual oil at the same level, which lays the basis for the further analysis of deformation and separation of residual oil.

In order to analyze the force of the residual oil in micro pore of different flow channel width, the calculation model has been established in

The viscous-elastic fluid has complicated rheological characteristics. After the practical research, it is suitable for upper-convected Maxwell constitutive equation to describe the rheological characteristics of the viscous- elastic fluid. And the continuity equation, motion equation and constitutive equation are as follows:

Continuity equation:

where: u, v is the velocity in the x, y direction respectively, m/s;

Motion equation:

Upper-convected Maxwell constitutive equation [

where:

where: A is the First Rivlin-Ericksen deformation tensor, the expression is

Constitutive equation:

Calculation model

Make the motion equation and constitutive equation dimensionless and introduce the dimensionless parameters as follows: take U (the average velocity of inlet) as the characteristic velocity; take h (the width of inlet) as the characteristic length.

For the sake of simplicity, “_{*}” in the lower right corner is omitted.

1) The solid boundaries are all in the no-slip condition. And the boundary condition of wall is

2) The inlet and outlet are in the same pressure difference. The pressure gradient is 0.02 MPa/m. And the boundary condition of the inlet is

The boundary condition of outlet is: normal stress is 0, tangential velocity is 0.

The oil micro pore of different permeability is calculated with the change of We, the variation curves of the horizontal stress difference are all shown in

From

Three conclusions can be got from

1) The wider the flow channel is, the greater the permeability is. The horizontal stress difference acting on

The horizontal stress difference of residual oil on the surface of oil wet rock. (a) The flow channel width H = 20 μm; (b) The flow channel width H = 40 μm; (c) The flow channel width H = 60 μm

The relationship curve of the maximum of horizontal stress difference and We

the residual oil will be greater.

2) The greater We (namely, the greater the elasticity of polymer solution) is, the greater the horizontal stress difference acting on the residual oil is.

For class II reservoirs, the concentration of polymer solution can be increased, and the We of the polymer fluid will be increased. Then the force of residual oil can be increased. That is in favor of the deformation of residual oil in low permeability reservoir, which lays the basis for the analysis of residual oil deformation and the separation of the small oil drop from the residual oil.