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Based on the mathematical model of one dimension transient flow of the polymer foam in porous media, the numerical calculation method of the flow mentioned above by using the finite difference method is given. Through the experiments of one dimension transient flow of HPAM (Hydrolytic Polyacrylamide) foam in the artificial sandstone core, the HPAM foam generation and coalescence coefficient of the mathematical model mentioned above are determined. The profiles of the liquid phase saturation, the pressure drop and the number density of one dimension transient flow of HPAM foam with the dimensionless time in artificial sandstone core are numerically calculated and analyzed by using the numerical calculation method.

The researches about the flow of aqueous foam in porous media are published more in literatures and reports. Kovseck [

By using the finite difference method, one dimension transient flow of the polymer foam in porous media will be numerically calculated. In this paper, the profiles of the liquid phase saturation, the pressure drop and the number density of one dimension transient flow of HPAM foam with the dimensionless time in artificial sandstone core will be analyzed.

1) The porous media is incompressible;

2) Polymer foam liquid phase is considered as the incompressible power-law fluid. The concentration of surfactant is constant. Gas phase obeys the ideal gas law;

3) Extensive Darcy law is adaptable, foam only influence on the gas phase relative permeability and viscocity;

4) Bubbles of the flow of the polymer foam in porous media are in the same size;

5) The effects of convection, diffusion, adsorption and gravitation of the polymer foam liquid phase in porous media are neglected;

6) The foam relative permeability is characterized by the gas relative permeability model.

The liquid and gas phase mass balance equations of one dimension transient flow of the polymer foam in porous media are [

where

where

The population balance equation of one dimension transient flow of the polymer foam in porous media is [

where

where [

where

where

where

The mass balance Equations (1) and (2), the bubble population balance Equation (8), the assistant equations (14), (16), (17), the definite condition (18)-(29) mentioned above consist of the mathematical model of one dimension transient flow of the polymer foam in porous media.

It is generally considered that the polymer foam generation coefficient

The mathematical model mentioned above is numerically calculated by using the finite difference method.

The mass balance Equations (1) and (2) of the mathematical model mentioned above are solved by using IMPES (Implicit Pressure Explicit Saturation) method. And the bubble population balance Equation (8) is solved by using TVD (Total Variation Diminish) three order methods [

Through the laboratory experiments, with measuring the time-average pressure drop

The main experiment meters include: DV-II + Pro viscometer, produced by American Brookfield Company, the measurement error is ±1%; TX -500C Spining interfacial tension meter, produced by American Bowing Company, the measurement error is 0.001 mm.

HPAM: foam liquid phase is the aqueous solution of 0.045 wt% HPAM, 0.200 wt% FL-605 and 0.830 wt% NaCl, gas phase is air. The core is the homemade artificial sandstone core of 0.045 m × 0.045 m × 0.30 m.

The experiment programme shows in

“1” D -250L liquid pump; “2” D -250L gas pump; “3” PMQ-2 foam performance measurement apparatus; “4” the liquid can; “5” the gas can; “6” digital manometer; “7” back-pressure valve; “8” the homemade artificial sandstone; “9” digital manometer; “10” cylinder.

Shut the back-pressure valve “ 7” of the outlet of the artificial sandstone core “8” of PMQ-2 foam performance measurement apparatus “3” and set the backpressure; Start D -250L liquid pump “ 1” and the liquid can “4” and set the liquid injection velocity

The experimental parameters of one dimension transient flow of the HPAM foam of 0.045 wt% HPAM, 0.200 wt% FL-605 and 0.083 wt% NaCl in the artificial sandstone core show as

1000.24 | 0.28 | ||
---|---|---|---|

n | 0.7872 | 11.03 | |

0.5126 | 0.18 | ||

0.30 | 0.01 | ||

0.51 | 1.00 | ||

0.25 | 0.90 | ||

2.30 | 6.00 | ||

0.72 | 0.33 | ||

1.00 | 4.80 | ||

2.99 | 4.80 | ||

3.02 | 0.10 | ||

0.33 | 0.046 | ||

1.00 | 0.430 | ||

0.26 | 1129.42 |

By using the mathematical model, the relevant numerical calculated method,

By using the mathematical model mentioned above, the relevant numerical calculated method,

The profiles of the liquid phase saturation

In

The profiles of the pressure drop

In

The profiles of the number density

In

By using the mathematical model, the relevant numerical calculated method,

In ^{ }that the mathematical model of one dimension transient flow of polymer foam in porous media and the relevant numerical calculation method in the paper are correct [

1) Based on the mathematical model of one dimension transient flow of the polymer foam in porous media, the numerical calculation method of the flow mentioned above by using the finite difference method is given;

2) Through the experiments, the generation coefficient and the coalescence coefficient of the transient flow of HPAM foam of 0.045 wt% HPAM, 0.200 wt% FL-605 surfactant and 0.830 wt% NaCl in the artificial sandstone core are determined;

3) The profiles of the liquid phase saturation ,the pressure drop and the number density of one dimension transient flow of HPAM foam of 0.045 wt% HPAM, 0.200 wt% FL-605 and 0.830 wt% NaCl with the dimen- sionless time in the artificial sandstone core are numerically calculated and analyzed.

4) Through the experiments, the mathematical model of one dimension transient flow of polymer foam in porous media and the relevant numerical calculation method are verified.

5) Based on the research results mentioned above, it needs the future study to continue working and researching for the polymer concentration influencing on the transient flow of the polymer foam in porous media.

WeiZhao,HaiqingCui,KeliangWang, (2015) Numerical Calculation of Transient Flow of Polymer Foam in Porous Media. Open Journal of Fluid Dynamics,05,215-223. doi: 10.4236/ojfd.2015.53024