# Analysis of Controlling Factors at Separate Imbibition Stages for Ultra-Low-Permeability Reservoirs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Geologic Features of the Study Area

#### 2.2. Experimental Preparation

^{3}. The viscosity of surface crude oil is 4.28~8.89 mPa·s (the average is 5.22 mPa·s), and the freezing point is −6~22 °C (the average is 7.4 °C). Therefore, No. 5 white oil, which has similar properties to crude oil in Chang 6 formation, is selected as the experimental oil. The formation water in the study area is calcium chloride (CaCl

_{2}) water type, with a total salinity of 91.3384 g/L and PH value of 6.53~7.37 (the average is 6.85). Based on the above properties, the formation water is prepared in the laboratory. The salinity is measured as 91 g/L. The core samples are selected from Chang 6 formation in Zichang area. The cores are processed by cutting flat, washing oil, drying, weighing, etc., for experimental use.

#### 2.3. Experimental Cases

#### 2.4. Experimental Results

#### 2.4.1. Effects of the Core Length

#### 2.4.2. Effects of the RQI (Reservoir Quantity Index)

#### 2.4.3. Effects of Salinity

#### 2.4.4. Effects of the Interfacial Tension and Contact Angle

**Figure 6.**Displacement efficiency curve of imbibition for investigating the interface characteristics.

#### 2.4.5. Effects of the Initial Oil Saturation

#### 2.4.6. Effects of Oil Viscosity

## 3. Discussion of Controlling Factors at Different Imbibition Stages

#### 3.1. Dimensionless Time Scale Model

^{4}).

_{c}is the characteristic length of core samples. For fully immersed cylindrical cores, the equation of characteristic length is shown below.

#### 3.2. Analysis of Controlling Factors at Different Imbibition Stages

## 4. Discussion with a Comparative Analysis Model

#### 4.1. Analytic Hierarchy Process

#### 4.1.1. Construction of Judgement Matrix

#### 4.1.2. Calculate the Weight of Each Parameter and Check the Procedure Consistency

#### 4.1.3. Establishment and Discussion of the Comparative Model

#### 4.2. Analysis of the Controlling Factors at Different Stages of Imbibition Processes in a Field

## 5. Conclusions

- By calculating the standard deviation of the dimensionless time and oil displacement efficiency for each controlling factor, the imbibition processes can be divided into three stages (i.e., the early stage, middle stage, and late stage) according to the strength of the main control factors.
- By using the analytic hierarchy process, the importance weights of controlling factors are quantitatively calculated for the three imbibition stages. The most significant controlling factor at the early imbibition stage and middle imbibition are both interfacial characteristics. For the later stage, the most significant controlling factor is initial oil saturation.
- Based on the experiments, the theoretical model is established to evaluate the controlling factors during the imbibition process for dual-porosity formation in the Chang 6 reservoir.
- From the field case study, it can be concluded that at the early imbibition stage of imbibition, the interfacial tension and contact angle play an important role. In consideration of reducing reservoir damage, the salinity of water injection should be reduced. At the middle imbibition stage, the interfacial characteristics should be given priority. At the late imbibition stage, oil displacement with a high initial oil saturation should be selected as the priority for imbibition processes.
- This study provides theoretical support to guide the water injection in ultra-low-permeability reservoirs during different imbibition processes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$\sigma $ | interfacial tension between oil and water. |

$\varphi $ | reservoir porosity. |

$k$ | reservoir permeability. |

${\mu}_{w}$ | water viscosity. |

$t$ | time. |

$L$ | length of a core sample. |

$\alpha $ | unit transformation factor (3.16 × 10^{4}). |

${\mu}_{o}$ | oil viscosity. |

${L}_{c}$ | characteristic length of core samples. |

$r$ | radius of a core sample or average value of samples. |

$N$ | degree of freedom. |

${x}_{i}$ | value of the i sample. |

${\overline{W}}_{i}$ | normalization processing. |

$CI$ | consistency index of the judgment matrix. |

$CR$ | random consistency ratio. |

$RI$ | consistency index. |

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**Figure 2.**The process of spontaneous imbibition in the tests investigating salinity effects after 4 h (

**a**), 8 h (

**b**), 18 h (

**c**) and 28 h (

**d**).

**Figure 10.**Importance weights of the controlling factors at the early stage (

**a**), middle stage (

**b**) and late stage (

**c**).

Core# | Length cm | Diameter cm | Porosity % | Permeability ×10 ^{−3} μm^{2} | Controlling Factors | |
---|---|---|---|---|---|---|

Z-17 | 3.39 | 2.53 | 8.01 | 0.081 | Core length (cm) | 3.39 |

Z-18 | 5.00 | 2.53 | 8.19 | 0.081 | 5.00 | |

Z-19 | 6.01 | 2.53 | 8.04 | 0.084 | 6.01 | |

Z-20 | 8.11 | 2.52 | 8.20 | 0.076 | 8.11 | |

Q-9 | 8.05 | 2.45 | 11.02 | 0.812 | RQI (μm) | 0.0858 |

Z-12 | 8.08 | 2.53 | 9.57 | 0.503 | 0.0725 | |

Z-13 | 8.07 | 2.54 | 8.53 | 0.212 | 0.0499 | |

Z-14 | 8.09 | 2.53 | 7.56 | 0.110 | 0.0381 | |

Z-15 | 8.06 | 2.54 | 5.22 | 0.052 | 0.0316 | |

Z-16 | 7.95 | 2.54 | 3.54 | 0.011 | 0.0176 | |

Z-10 | 7.98 | 2.54 | 9.68 | 0.041 | Salinity (g/L) | 0 |

Z-24 | 8.29 | 2.53 | 7.94 | 0.016 | 30 | |

Z-21 | 8.16 | 2.54 | 8.06 | 0.012 | 60 | |

Q-22 | 8.14 | 2.54 | 7.92 | 0.011 | 91 | |

Q-23 | 8.00 | 2.53 | 7.91 | 0.015 | 120 | |

Q-5 | 7.95 | 2.54 | 9.62 | 0.035 | 182 | |

Q-1 | 8.03 | 2.43 | 10.60 | 0.179 | Interfacial tension (mN/m) and contact angle | 11.64 mN/m; 58.3° |

Q-2 | 8.04 | 2.45 | 10.42 | 0.151 | 3.27 mN/m; 38.5° | |

Q-3 | 8.04 | 2.42 | 11.33 | 0.243 | 2.24 mN/m; 30.3° | |

Q-4 | 8.10 | 2.42 | 11.36 | 0.266 | 1.68 mN/m; 28.7° | |

Q-5 | 8.10 | 2.42 | 11.27 | 0.186 | 1.23 mN/m; 18.8° | |

Q-6 | 8.07 | 2.42 | 10.72 | 0.182 | 1.02 mN/m; 14.3° | |

Q-7 | 8.02 | 2.45 | 10.60 | 0.191 | 0.77 mN/m; 11.2° | |

Q-8 | 8.13 | 2.43 | 10.68 | 0.157 | 0.70 mN/m; 10.8° | |

T-1 | 5.21 | 2.52 | 10.70 | 0.33 | Initial water saturation (%) | 0 |

33.0 | ||||||

42.0 | ||||||

61.0 | ||||||

T-15 | 4.53 | 2.50 | 14.06 | 0.55 | Oil viscosity (mPa·s) | 0.82 |

T-16 | 4.50 | 2.48 | 13.22 | 0.53 | 2.50 | |

T-17 | 4.52 | 2.50 | 13.48 | 0.51 | 5.00 | |

T-18 | 4.50 | 2.51 | 13.29 | 0.58 | 10.00 |

Core# | RQI, µm | Final Imbibition Efficiency |
---|---|---|

Q-9 | 0.0858 | 27.49% |

Z-12 | 0.0725 | 25.80% |

Z-13 | 0.0499 | 23.22% |

Z-14 | 0.0381 | 21.15% |

Z-15 | 0.0316 | 16.40% |

Z-16 | 0.0176 | 5.61% |

Core# | Salinity, g/mL | Final Imbibition Efficiency |
---|---|---|

Z-10 | 0 | 26.29% |

Z-24 | 30 | 25.76% |

Z-21 | 60 | 24.79% |

Z-22 | 91 | 23.43% |

Z-23 | 120 | 23.13% |

Q-5 | 182 | 22.76% |

Controlling Factors (The Corresponding Tests Can Refer to Table 1) | Time Scale Model |
---|---|

Core length | t_{D} = 4.893 t |

RQI | t_{D} = 7.598 t |

Salinity test | t_{D} = 2.305 t |

Interfacial characters | t_{D} = 0.660 t |

Initial oil saturation | t_{D} = 10.919 t |

Oil viscosity | t_{D} = 4.893 t |

Scale | Meaning |
---|---|

1 | The ith factor has the same effect as the jth factor |

3 | The influence of the ith factor is slightly stronger than that of the jth factor |

5 | The influence of the ith factor is stronger than that of the jth factor |

7 | The influence of the ith factor is significantly stronger than that of the jth factor |

9 | The influence of the ith factor is absolutely stronger than that of the jth factor |

2, 4, 6, 8 | Represents the intermediate value of the above adjacent judgment |

a_{ij}: a_{ii} = 1, a_{ij} = 1/a_{ij} |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

RI | 0.00 | 0.00 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 |

Cube Side Length/m | Early Stage/Years | Middle Stage/Years | Later Stage/Years | |
---|---|---|---|---|

1 | <0.27 | 0.27~0.99 | >0.99 | |

2 | <1.10 | 1.10~5.06 | >5.06 | |

3 | <2.46 | 2.46~11.35 | >11.35 | |

4 | <4.39 | 4.39~20.24 | >20.24 | |

5 | <6.94 | 6.94~31.95 | >31.95 | |

Weight of the controlling factor | Salinity | 20.0% | 12.2% | 8.5% |

Interfacial characteristics | 68.3% | 55.8% | 27.1% | |

Initial oil saturation | 11.7% | 32.0% | 64.4% |

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## Share and Cite

**MDPI and ACS Style**

Dang, H.; Jiang, H.; Hou, B.; Wang, X.; Gao, T.; Wang, C.; Lu, C.
Analysis of Controlling Factors at Separate Imbibition Stages for Ultra-Low-Permeability Reservoirs. *Energies* **2021**, *14*, 7093.
https://doi.org/10.3390/en14217093

**AMA Style**

Dang H, Jiang H, Hou B, Wang X, Gao T, Wang C, Lu C.
Analysis of Controlling Factors at Separate Imbibition Stages for Ultra-Low-Permeability Reservoirs. *Energies*. 2021; 14(21):7093.
https://doi.org/10.3390/en14217093

**Chicago/Turabian Style**

Dang, Hailong, Hanqiao Jiang, Binchi Hou, Xiaofeng Wang, Tao Gao, Chengjun Wang, and Chunhua Lu.
2021. "Analysis of Controlling Factors at Separate Imbibition Stages for Ultra-Low-Permeability Reservoirs" *Energies* 14, no. 21: 7093.
https://doi.org/10.3390/en14217093