# Diagnostic Fracture Injection Tests Analysis and Numerical Simulation in Montney Shale Formation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{w}(t) is the bottom-hole pressure at t time, MPa. pi is the initial reservoir pressure, MPa. ${V}_{inj}$ is the cumulative injection fluid volume, m

^{3}. h is the formation thickness, m. μ is the fluid viscosity, mPa.s. φ is the porosity, %. C

_{t}is the formation compressibility. ${x}_{f}$ is the fracture half length, m. k is reservoir permeability. ∆t is the testing duration. KL is the slope between ∆P and time in Pseudolinear flow regime, while KR is the slope between ∆P and time in Pseudoradial flow regime.

## 3. Results

#### 3.1. Background of Montney Shale Formation

#### 3.1.1. General Information of Montney

#### 3.1.2. Development of Wapiti Field

#### 3.1.3. Summaries of Key Reservoir Parameters

#### 3.2. Application of Diagnostic Fracture Injection Tests

#### 3.2.1. Selection of Experimental Well

^{3}and 342.60 m

^{3}, respectively, and this well is predicted to be economically viable based on the predicted EUR, operating cost, and capital investment.

#### 3.2.2. DFIT Data Analysis and Interpretation

^{3}/min, and the total injected volume is about 4.0 m

^{3}. After 10 min, pump is shut down and the surface pressure is monitored and recorded for 10 days. It should be noted that the pressure in Figure 7 refers to the surface pressure.

#### 3.2.3. Results Discussion

#### 3.2.4. DFIT Numerical Simulation

## 4. Conclusions

- The general pressure Gdp/dG responses’ results for Well-A show a signature of pressure-dependent leak-off behavior, which occurs when the fluid-loss rate varies significantly with the pressure-dependent permeability in a dual-porosity system. A characteristic height recession/transverse storage trend has been identified.
- The net pressure of DFIT on Well-A in the Wapiti Montney formation is about 5.137 MPa, based on the determined fracture closure pressure.
- Based on DFIT data, the closure pressure is estimated to be 34.367 MPa, contributing to a stress gradient of 14.09 kpa/m; 39.344 MPa contributing to 16.13 kpa/m by the Compliance method; and 37.163 MPa contributing to 15.23 kpa/m by the Variable Compliance method.
- Based on the pressure transient analysis, the pore pressure ranges from 20.82 to 24.58 MPa, which is equivalent to a pore pressure gradient of 8.54 to 10.07 KPa/m for the Wapiti Montney formation.
- Using the DFIT’s numerical simulation and history matching, the reservoir permeability is 0.024 md, fracture length is 13.44 m, and fracture geometries analyzed by different models are summarized in Table 3.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Fracture surface area |

C | A constant relevant to leak-off coefficient and comprehensive compressibility |

C | Closure |

${C}_{L}$ | Carter’s leak-off coefficient |

${C}_{t}$ | Total compressibility |

${E}^{\prime}$ | Plane strain for Young’s modulus |

h | Formation thickness |

${h}_{f}$ | Fracture height |

${K}_{L}$ | Linear flow regime |

${K}_{R}$ | Radial flow regime |

k | Permeability |

${p}_{i}$ | Reservoir initial pressure |

${p}_{net}$ | Net pressure |

${p}_{w}\left(t\right)$ | Bottom hole pressure at generic time |

$S{h}_{min}$ | Minimum principal stress |

${S}_{f}$ | Fracture stiffness |

t | Generic time |

${t}_{e}$ | Shut-in time |

${t}_{p}$ | Pumping time |

$\Delta {t}_{D}$ | Dimensionless time in G-function |

${V}_{inj}$ | Cumulative pumped fluid volume |

${W}_{f}$ | Average fracture width |

${X}_{f}$ | Fracture half-length |

φ | Formation porosity |

μ | Fluid viscosity |

AC | After Closure |

BC | Before Closure |

DFIT | Diagnostic fracture injection tests |

BL | End linear flow |

BR | Begin radial flow |

FBP | Formation breakdown pressure |

FO | Fissure opening |

FPP | Fracture propagation pressure |

ISIP | Instantaneous shut-in pressure |

LOP | Leak-off point |

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**Figure 1.**Typical DFIT data and relevant physical phenomena in region of Before Closure and region of After Closure.

**Figure 2.**Type of pressure vs. G-function, dP/dG vs. G-function, and GdP/dG vs. G-function trends: (

**a**) normal leak-off behavior and (

**b**) non-ideal leak-off behavior (I) that depicts a signature of height recession/transverse storage. (

**c**) Non-ideal leak-off behavior (II) that depicts a signature of pressure-dependent leak-off behavior, which occurs when the fluid-loss rate varies significantly with the pressure-dependent permeability in a dual-porosity system (usually micro-cracks and natural fractures exist in these cases). (

**d**) Non-ideal leak-off behavior (III) that demonstrates a signature of fracture tip extension, which occurs in low-permeability reservoirs.

**Figure 3.**(

**a**) Depositional environment of Montney Formation; (

**b**) Montney conventional vs. unconventional plays.

**Figure 6.**Wapiti Montney engineering information: (

**a**) stimulated length (m); (

**b**) injection rate (m

^{3}/min); (

**c**) proppant per SL (kg /m); (

**d**) fluid per SL (m

^{3}/min); (

**e**) total stage count.

**Figure 7.**Well-A DFIT pressure and pump schedule. The inserted images show pressure vs. time in semi-log plot.

**Figure 11.**Before Closure (BC) and After Closure (AC) analyses by pressure derivative log–log plot. Signatures of linear and radial flow regimes are slopes of −0.5 and −1, respectively, after the fracture closure time.

**Figure 12.**Pore pressure is estimated by pressure transient analysis. The main image shows pore pressure determination by linear flow regime, and the inserted image shows pore pressure determination by radial flow regime.

**Figure 13.**Bottom hole pressure field-smoothed vs. simulation results; pressure derivative field-smoothed vs. simulation results.

Age | Triassic (240 ma) |

Lithology | Siltstone |

Sedimentary Environment | Marine shoreface/shelf |

Depth (m) | 2200–2900 |

Area (km^{2}) | 3500 |

Thickness (m) | >200 |

Pressure Gradient (kPa/m) | 12–14.5 |

Production Since | 2005 |

Porosity | 3–6% |

Permeability (mD) | 0.005–0.05 mD |

Water Saturation | <20% |

**Table 2.**Expression to calculate the Sf by three different fracture geometries [23].

Fracture Geometry | PKN | KGD | Radial |
---|---|---|---|

Fracture Stiffness Sf | $\frac{2{E}^{\prime}}{\pi {h}_{f}}$ | $\frac{{E}^{\prime}}{\pi {x}_{f}}$ | $\frac{3\pi {E}^{\prime}}{16{R}_{f}}$ |

Estimated Fracture Half-Length by PKN Model, m | 13.44 |

Estimated Fracture Average Width by PKN Model, m | 0.00671 |

Estimated Fracture Half-Length by Radial Geometry, m | 12.25 |

Estimated Fracture Average Width by Radial Geometry, m | 0.00583 |

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**MDPI and ACS Style**

Liao, L.; Li, G.; Liang, Y.; Zeng, Y.
Diagnostic Fracture Injection Tests Analysis and Numerical Simulation in Montney Shale Formation. *Energies* **2022**, *15*, 9094.
https://doi.org/10.3390/en15239094

**AMA Style**

Liao L, Li G, Liang Y, Zeng Y.
Diagnostic Fracture Injection Tests Analysis and Numerical Simulation in Montney Shale Formation. *Energies*. 2022; 15(23):9094.
https://doi.org/10.3390/en15239094

**Chicago/Turabian Style**

Liao, Lulu, Gensheng Li, Yu Liang, and Yijin Zeng.
2022. "Diagnostic Fracture Injection Tests Analysis and Numerical Simulation in Montney Shale Formation" *Energies* 15, no. 23: 9094.
https://doi.org/10.3390/en15239094