# Analysis and Application of Horizontal Well Test in Low Permeability Porous Carbonate Reservoir

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## Abstract

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## 1. Introduction

## 2. Geologic Reservoir Characteristic

## 3. Horizontal Well Test Mathematical Model

- ${K}_{V}$ = Vertical permeability, mD
- ${K}_{H}$ = Horizontal permeability, mD
- $\overline{K}$ = Permeability anisotropy ratio
- L = Half length of horizontal wells, ft
- ${L}_{D}$= Dimensionless half length of horizontal wells
- $\chi $= Horizontal pressure diffusivity
- ${\chi}_{V}$= Vertical pressure diffusivity
- $h$= Reservoir thickness, ft
- ${h}^{*}$= Normalized h, from uniform anisotropic medium to uniform isotropic medium
- ${h}_{D}^{*}$= Dimensionless normalized h
- $p$ = Pressure, psi
- ${p}_{i}$ = Initial pressure, psi
- ${p}_{D}$ = Dimensionless pressure
- $Q$ = Flow rate, stb/d
- ${r}_{wD}$ = Dimensionless wellbore radius
- ${r}_{w}$ = Wellbore radius, ft
- $s$ = Laplace transform variable
- $S$ = Skin
- $t$ = Time, h
- ${t}_{D}$ = Dimensionless time
- $x$ = Coordinate, ft
- ${x}_{w}$ = Midpoint coordinates in horizontal segment, ft
- ${x}_{D}$ = Dimensionless coordinate
- $y$ = Coordinate, ft
- ${y}_{w}$ = Midpoint coordinates in horizontal segment, ft
- ${y}_{D}$ = Dimensionless coordinate
- $z$ = Coordinate, ft
- ${z}_{D}$ = Dimensionless coordinate
- ${z}_{w}$ = Height of horizontal section above bottom surface, ft
- ${z}_{wD}$ = Dimensionless height of horizontal section above bottom surface, ft
- ${z}^{\ast}$= Normalize z, from uniform anisotropic medium to uniform isotropic medium
- $\varphi \varnothing $ = Porosity, dimensionless
- $\mu $ = Fluid viscosity, cp
- $c$ = Composite compressibility, 1/psi
- $B$ = Formation volume coefficient
- ${C}_{D}$ = Dimensionless wellbore storage coefficient,
- ${\overline{p}}_{wD}\left(s\right)$ = Image function of bottom hole pressure
- $erf$= error function

## 4. Well Test Curve Characteristics of Low Permeability Carbonate Reservoir

#### 4.1. Typical Horizontal Well Test Curve

- Wellbore storage stage;

- Initial radial flow stage;

- Linear flow stage;

- Later quasi-radial flow stage;

#### 4.2. Influencing Factors of Well Test Curve Characteristics

#### 4.3. Well Test Curve Characteristics of Low Permeability Carbonate Reservoir

- There is no radial flow stage in the well test curves:The permeability of the main reservoir in the study area is low, and the permeability is 10 mD. At the same time, the development of the white spot section in the reservoir hinders the migration of the fluid, resulting in low pressure conductivity of the reservoir, slow water injection efficiency, and inability to achieve radial flow during the test time.
- Characteristics of variable well storage:The characteristics of changing wellbore storage mainly appear in the well test curve of production wells. Low permeability reservoirs generally have the characteristics of variable well storage. In the water injection development area, there is a multiphase flow in the wellbore. Shutdown for a period of time will redistribute the phase in the wellbore, resulting in a decrease in the fluid compression coefficient and a decrease in the wellbore storage coefficient.
- Double logarithmic curve opening is small:Reservoir A has good formation conditions and no pollution blockage exists. Reflected in the well test curve, the explanatory skin coefficient parameter is negative, and the opening of the double logarithmic curve is small.

- Well trajectory:Well trajectory is mainly A-3; the average permeability of this layer is slightly lower. At the same time, the well trajectory slants through the formation as shown in Figure 10 or shows bending shape in the formation. The fluid flow direction in the formation intersects with the fluid flow direction in the production well or the injection well, which is inconsistent with the theoretical model, leading to the abnormality of the field well test curve.
- Reservoir properties:Combined with geological understanding, reservoir properties around the well with bilinear flow are poor. Combined with a series of well test curves under different formation permeability conditions established by PTA in KAPPA, we can see that when the formation permeability is low, the slope of the linear flow section becomes lower, the linear flow occurs late, and does not reach the radial flow stage, as shown in Figure 11.

- Other factors:The possible influencing factors also include the transition between radial flow and stable linear flow and the existence of white spots. Due to well test time constraints, the transition between initial radial flow and 1/2 slope linear flow may not be observed. The main production layers of reservoir A developed discontinuous white spots, which hindered the fluid flow to a certain extent. However, due to its horizontal discontinuous distribution, its influence is limited.

## 5. Dynamic Analysis of Typical Horizontal Well Pattern

#### 5.1. Well Test Result

#### 5.2. Reservoir Pressure

#### 5.3. Well Water Cut

#### 5.4. Well Production

## 6. Discussion

## 7. Conclusions

- The well test curves of low permeability carbonate reservoirs in the study area are generally characterized by no radial flow stage, changing wellbore storage effect and small openings of the double logarithmic curve.
- Most horizontal wells show a linear flow with a slope of 1/2, and there are also a few linear flow stages with a slope of 1/3 and a slope of 1/4. This anomalous feature is less affected by the difference in inter-layer permeability, and the influencing factors are well trajectory and reservoir properties. The transition between radial flow and stable linear flow and the existence of white spots also have certain effects on the characteristics of well test curves.
- Based on the above dynamic and static data and the analysis of well test interpretation results, it can be obtained that there is no pollution in the formation of the study area, and the development effect is overall good. However, there are still differences among various injection wells and production wells, and the main control factors are reservoir properties.
- Further injection-production optimization measures include:
- The injection parameters of 9-3H and 9-4H need to be adjusted to improve the pressure build-up condition.
- It is necessary to detect production parameters such as yield, water cut and pressure in time to prevent rapid increase of water cut and ensure stable production.
- The water injection volume of injection wells around reopened production wells should be adjusted according too a time frame designed to prevent flooding.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Comparison figure of average daily oil production between vertical wells and horizontal wells in A reservoir.

**Figure 3.**Comparison figure of average water cut between vertical wells and horizontal wells in A reservoir.

**Figure 6.**Schematic diagram of different flow stages in horizontal well test [21]: (

**a**) Wellbore storage stage; (

**b**) Initial radial flow stage; (

**c**) Linear flow stage; (

**d**) Later quasi-radial flow stage. The arrow represents liquid flow, the blue strip represents horizontal well, and the blue circle represents horizontal well cross section.

**Figure 13.**Permeability distribution map of injection-production area in a horizontal well. The circles represent wellhead positions.

**Figure 21.**Numerical well test grid of 8-5H well. Tested well represents 9-1H well and Well #1 represents 8-5H well. Lines and arrows. The lines form a grid, and the arrows represent directions.

**Table 1.**Proportion table of well test curves with different characteristics of water injection wells.

Liner Flow Stage Slope | 1/2 | 1/3 | 1/4 |
---|---|---|---|

Total | 8 | 2 | 2 |

Proportion | 66.67% | 16.67% | 16.67% |

Production Well | Corresponding Injection Well |
---|---|

8-5H | 9-1H |

8-6H | 9-2H |

8-7H | 9-2H, 9-3H |

8-10H | 9-4H, 9-5H |

8-11H | 9-5H |

10-1H | 9-1H |

10-4H | 9-3H, 9-4H |

10-5H | 9-4H, 9-5H |

Well | Time | Skin | Permeability (mD) | Effective Length (m) | Injectivity Index (bbl/d/psia) | Interpretation Model |
---|---|---|---|---|---|---|

9-1H | August 2019 | −0.12 | 2.58 | 575 | −1.65 | Horizontal and Homogeneous |

June 2020 | 0.00 | 4.06 | 518 | −1.97 | Horizontal and Homogeneous | |

9-2H | January 2019 | −0.08 | 4.66 | 616 | −3.06 | Horizontal and Radial Composite |

May 2020 | −0.13 | 3.43 | 591 | −1.92 | Horizontal and Radial Composite | |

9-3H | June 2019 | −0.14 | 4.65 | 628 | −2.29 | Horizontal and Homogeneous |

January 2020 | −0.12 | 3.41 | 656 | −1.90 | Horizontal and Homogeneous | |

9-4H | April 2019 | −0.16 | 4.32 | 520 | −2.22 | Horizontal and Homogeneous |

February 2020 | −0.11 | 2.47 | 811 | −1.84 | Horizontal and Homogeneous | |

9-5H | April 2020 | −0.17 | 2.80 | 610 | −1.63 | Horizontal and Homogeneous |

Well | Time | Skin | Permeability (mD) | Effective Length (m) | Production Index (bbl/d/psia) | Interpretation Model |
---|---|---|---|---|---|---|

8-5H | December 2020 | −6.96 | 2.31 | 317 | 0.80 | Horizontal and Homogeneous |

10-1H | December 2022 | −7.30 | 7.29 | 513 | 1.22 | Horizontal and Homogeneous |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Z.; Li, Y.; Jiang, T.; Hu, D.; Zhang, L.; Ma, R.
Analysis and Application of Horizontal Well Test in Low Permeability Porous Carbonate Reservoir. *Processes* **2022**, *10*, 1545.
https://doi.org/10.3390/pr10081545

**AMA Style**

Zhao Z, Li Y, Jiang T, Hu D, Zhang L, Ma R.
Analysis and Application of Horizontal Well Test in Low Permeability Porous Carbonate Reservoir. *Processes*. 2022; 10(8):1545.
https://doi.org/10.3390/pr10081545

**Chicago/Turabian Style**

Zhao, Zeqi, Yong Li, Tongwen Jiang, Dandan Hu, Lixia Zhang, and Ruicheng Ma.
2022. "Analysis and Application of Horizontal Well Test in Low Permeability Porous Carbonate Reservoir" *Processes* 10, no. 8: 1545.
https://doi.org/10.3390/pr10081545