# Numerical Investigation on EOR in Porous Media by Cyclic Water Injection with Vibration Frequency

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, CO

_{2}) flooding, surfactant injection, micro/nanoparticle injection, polymer injection, microorganism injection and fracturing development [3,4,5,6]. Though higher EOR has been achieved via the enhanced oil recovery techniques than the water flooding, these techniques required the oil companies to append the gas compressor investment, update the surface pipe network system and pump stations and re-consider the compatibility of surfactants, polymers and microorganisms with the original equipment [7,8,9]. In addition, the residual surfactants, polymers and microorganisms in reservoirs after the enhanced oil recovery probably contaminated the groundwater [10,11,12]. Meanwhile, the injected micro/nanoparticles plug the reservoir pores, which is not conducive to the recycling and sustainability of the reservoir for CO

_{2}capture, utilization and underground storage and hydrogen underground storage [13,14]. Nevertheless, by optimizing the water flooding techniques, it is able to achieve EOR, maintain, and even reduce, the investment and operation costs of the oil field, and eliminate the pollution of groundwater and the destruction of reservoirs simultaneously.

## 2. Model and Methodology

#### 2.1. Problem Description

^{3}and the water viscosity ${\mu}_{w}$ is 1 mPa·s. The number of grids in the three directions of x, y, and z is 590 × 185 × 1.

#### 2.2. Mathematical Models

^{3}; $\mu $ is viscosity, Pa·s; ∇ is the Hamiltonian operator; ${\mathit{F}}_{s}$ is the continuous surface force (CSF) applied on the interface [34],

^{−1}; n is the normal vector of the interface.

#### 2.3. Numerical Scheme

## 3. Model Benchmark

#### 3.1. Problem Definition

#### 3.2. Simulation Results

## 4. Results and Discussion

#### 4.1. The Critical Frequency

#### 4.2. The Effect of Interfacial Tension

#### 4.3. The Effect of Viscosity of Oil

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The schematics of the simulation for the cyclic water injection stimulated two-phase displacements in porous media. The computational domain and initial fluid distributions.

**Figure 3.**The threshold pressure difference $\Delta {P}_{A,t}$ required for the elastic wave to successfully squeeze droplets under different frequencies: comparisons between the simulation results and theoretical predictions by Deng et al. [41].

**Figure 4.**The effect of wave frequency on EOR. (

**a**) The relationship between the frequency and the final remaining oil saturation. (

**b**) The final remaining oil saturation of three typical frequencies.

**Figure 5.**Comparison of residual oil saturation affected by various interfacial tensions $\gamma $ in different frequencies.

**Figure 6.**Schematic diagram of a single trapped oil droplet in the pore, where the yellow area represents trapped oil droplet, the blue area is water, and the black area is grain.

**Figure 7.**Comparison of residual oil saturation affected by various viscosities of oil ${\mu}_{o}$ in different frequencies.

Parameters (Unit) | Baseline Value | Discussed Value |
---|---|---|

$\mathrm{The}\text{}\mathrm{interfacial}\text{}\mathrm{tension}\text{}\gamma $ (N/m) | 0.02 | 0.01, 0.03 |

$\mathrm{The}\text{}\mathrm{viscosity}\text{}\mathrm{of}\text{}\mathrm{the}\text{}\mathrm{oil}\text{}{\mu}_{o}$ (Pa·s) | 0.01 | 0.005, 0.015 |

$\mathrm{The}\text{}\mathrm{frequency}\text{}f$ (HZ) | 0 | 50, 80, 100, 120, 150, 200 |

Parameters (Unit) | Value |
---|---|

The minimum radius of the throat ${R}_{min}$ (mm) | 0.5 |

The maximum radius of the pore ${R}_{max}$ (mm) | 2 |

The inlet position ${L}_{in}$ (mm) | −20 |

The outlet position ${L}_{o\mathit{u}t}$ (mm) | 20 |

The length of the sinusoidal part of the channel 2$L$ (mm) | 20 |

The density of the wetting phase ${\rho}_{w}$ (kg/m^{3}) | 1000 |

The viscosity of the wetting phase ${\mu}_{w}$ (Pa·s) | 0.001 |

The droplet density ${\rho}_{o}$ (kg/m^{3}) | 1000 |

The droplet viscosity ${\mu}_{o}$ (Pa·s) | 0.01 |

The interfacial tension $\sigma $ (N/m) | 0.05 |

The static contact angle $\theta $ (°) | 0 |

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**MDPI and ACS Style**

Yang, H.; Lao, J.; Tong, D.; Song, H. Numerical Investigation on EOR in Porous Media by Cyclic Water Injection with Vibration Frequency. *Water* **2022**, *14*, 3961.
https://doi.org/10.3390/w14233961

**AMA Style**

Yang H, Lao J, Tong D, Song H. Numerical Investigation on EOR in Porous Media by Cyclic Water Injection with Vibration Frequency. *Water*. 2022; 14(23):3961.
https://doi.org/10.3390/w14233961

**Chicago/Turabian Style**

Yang, Hongen, Junming Lao, Delin Tong, and Hongqing Song. 2022. "Numerical Investigation on EOR in Porous Media by Cyclic Water Injection with Vibration Frequency" *Water* 14, no. 23: 3961.
https://doi.org/10.3390/w14233961