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The mathematical models of the flow of polymer foam in porous media under three injection modes are established and the relevant numerical calculation methods are given. The profiles of the liquid phase saturation, the pressure drop and the number density of the flowing HPAM foam in artificial sandstone cores with the dimensionless distance under three injection modes are numerically calculated and analyzed. The results show that, compared with the injection mode 2 and 3, HPAM foam flows in a piston-like fashion in the artificial sandstone core under the injection mode 1 and produces the biggest pressure drop. Obviously, the flood efficiency is the highest under the injection mode 1.

It can provides the necessary theoretical foundation for polymer flooding engineering design through researching the flow of the polymer foam in porous media under different injection modes. Shan, et al. [_{2} foam injection and the details of the CO_{2} foam injection schedule and design criteria in the East Vacuum Grayburg San Andres Unit. Hou, et al. [

There are three injection modes for the porous media filled with polymer-surfactant aqueous solution,that is, the injection mode 1 which is the co-injection of polymer surfactant aqueous solution and air into the porous media, the injection mode 2 which is the injection of air into the porous media and the injection mode 3 which is the injection of polymer surfactant aqueous solution into the porous media.

According to the mass and the population balance principles, the mathematical models of polymer foam flow in porous media under different injection modes can be obtained.

The mathematical model of the flow of polymer foam in porous media under the injection mode 1 is as follows [^{ }

The mass balance equations

the population balance equations

the assistant equations

the initial conditions

the boundary conditions

where

Under the injection mode 2, where the Formula (19) of the mathematical model of the flow of the polymer foam in porous media under the injection mode 1 changes as follow

the mathematical model of the flow of the polymer foam in porous media consists of Formula (1)-(18), (25), (20)-(24).

Under the injection mode 3, the mathematical model of the flow of the polymer foam in porous media consists of Formula (1), (13), (15), (19) and (21).

The mathematical models of the flow of polymer foam in porous media under three injection modes are numerically calculated by the finite difference method [

For the Injection mode 1 and the injection mode 2, the mass balance Equations (1) and (2) are solved by IMPES (Implicit Pressure Explicit Saturation) method, and the population balance Equation (3) is solved by TVD (Total Variation Diminish) three order method. For the Injection mode 3, the mass balance Equation (1) is solved by IM (Implicit Method).

The flow of the foam of the 0.015 wt% HPAM, 0.200 wt% FL-605 and 0.830 wt% NaCl HPAM solution and the air under different injection modes in the artificial sandstone core are numerically calculated and analyzed.^{ }

The basic data of the three injection modes are shows as

Under the injection mode 1, the profiles of the liquid phase saturation

In

In

In

Injection mode 1 | Injection mode 2 | Injection mode 3 | |
---|---|---|---|

1000.09 | 1000.09 | 1000.09 | |

n | 0.9316 | 0.9316 | 0.9316 |

0.1359 | 0.1359 | 0.1359 | |

11.03 | 11.03 | 0.00 | |

0.30 | 0.30 | 0.30 | |

0.66 | 0.66 | 0.66 | |

0.26 | 0.26 | 0.26 | |

2.30 | 2.30 | 2.30 | |

0.70 | 0.70 | 0.00 | |

1.00 | 1.00 | 0.00 | |

3.01 | 3.01 | 0.00 | |

3.03 | 3.03 | 0.00 | |

0.29 | 0.29 | 0.29 | |

0.26 | 0.26 | 0.00 | |

0.33 | 0.33 | 0.00 | |

0.18 | 0.18 | 0.00 | |

0.01 | 0.01 | 0.01 | |

6.00 | 6.00 | 0.00 | |

0.33 | 0.33 | 0.00 | |

4.80 | 4.80 | 4.80 | |

4.80 | 4.80 | 4.80 | |

0.10 | 0.10 | 0.00 | |

0.046 | 0.000 | 0.046 | |

0.431 | 0.431 | 0.000 | |

10.08 | 10.08 | 0.00 | |

57.84 | 57.84 | 0.00 |

number density

Under the injection mode 2, the profiles of the liquid phase saturation

In

In

downstream of flow front decreases slowly, which is due to the fine foam texture of flow front under injection mode 2.

In

Under the injection mode 3, the profiles of the liquid phase saturation

In

In

In

Among the three injection modes mentioned above, the pressure drop

1) The mathematical models of the flow of the polymer foam in porous media under the three injection modes are established and the relevant numerical calculation methods are given.

2) The profiles of the liquid phase saturation, the pressure drop and the number density of the flowing HPAM foam with the dimensionless distance in the artificial sandstone core under the three injection modes are numerically calculated and analyzed.

3) Compared with the injection mode 2 and 3, HPAM foam flows in a piston-like fashion in the artificial sandstone core under the injection mode 1 and shows the biggest pressure drop. Obviously, flood efficiency is highest under the injection mode 1.

4) Based on the research results mentioned above, it can choose the better injection mode to reach the best flood efficiency in the polymer flooding engineering design according to the actual situation. Especially, in the injection mode 1, it also needs the future study to continue working and researching for what factor influencing the flood efficiency most, such as the polymer type, concentration and so on.

WeiZhao,HaiqingCui,KeliangWang, (2015) Polymer Foam Flow in Porous Media under Different Injection Modes. Energy and Power Engineering,07,365-374. doi: 10.4236/epe.2015.78034