# Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Models

- ${a}_{1}=\left[\frac{RT}{M}-\left(\frac{1}{3}\left[\frac{1+\nu}{1-\nu}\right]-1+f\right)\gamma RT\right]$: macropore compression;
- ${a}_{2}=\left(\frac{1}{3}\left[\frac{1+\nu}{1-\nu}\right]-1\right){K}^{\prime}d]$: shrinkage/swelling due to gas dissolution;
- ${a}_{3}=\left[\left(\frac{1}{3}\left[\frac{1+\nu}{1-\nu}\right]-1\right){\epsilon}_{l}\right]$: desorption-induced matrix deformation effect.

## 3. Numerical Simulation

- Depth: 7971 ft;
- TOC: 12.4;
- Temp: 148 F;
- As received moisture: 0.75%.

## 4. Results and Discussion

_{1}(macropore compression), a

_{2}(shrinkage and swelling) and a

_{3}(desorption-induced matrix deformation). Organic porosity defined using Equation (7) was then coupled with the reset of the governing equations through Equations (1) and (4). The main parameters affecting the poroelastic effect in organic materials were the Young’s modulus, Poisson’s ratio and desorption constant.

_{1}, a

_{2}and a

_{3}terms, as defined in Equation (7). Due to the low TOC content, the matrix swelling and shrinkage effect were negligible in the case of shale gas reservoirs. The pore compressibility effect also showed a minimal impact on the ultimate recovery and pressure response; however, gas desorption-induced matrix deformation showed the greatest impact on both pressure and ultimate recovery, as shown in Figure 5. The effect was pronounced at an early stage, when the pressure gradient was larger. A greater pore pressure drop accelerated the desorption process, which led to an increase in desorption-induced matrix deformation. This effect was also reported by [23], using a finite element method and the dual permeability model. In Figure 5, without a poroelastic effect, the curve is associated with the case where constant porosity and permeability in both organic and inorganic matrices were assumed. The poroelastic effect curve includes both porosity and permeability pressure dependent on both organic and inorganic materials. The desorption-induced matrix deformation only curve corresponds to the case where inorganic porosity and permeability were assumed constant and there was no macropore compression or shrinkage and swelling effect $({a}_{1}={a}_{2}=0,{a}_{3}\ne 0)$.

_{1}(organic macropore compression), a

_{2}(shrinkage and swelling) and a

_{3}(desorption-induced matrix deformation) on pressure response and ultimate recovery. As discussed earlier, the organic macropore compression and shrinkage and swelling showed a minimal impact, while the desorption-induced matrix deformation showed a major impact on both pressure and ultimate recovery.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Pressure decay (

**bottom**) and ultimate recovery (

**top**) comparisons of models with and without poroelastic effect.

**Figure 5.**Pressure decay (

**bottom**) and ultimate recovery (

**top**) comparisons of models with desorption-induced matrix deformation only.

**Figure 6.**Comparisons of the effects of ${a}_{1}$ (organic macropore compression), ${a}_{2}$ (shrinkage and swelling) and ${a}_{3}$ (desorption-induced matrix deformation) on pressure decay (

**bottom**) and ultimate recovery (

**top**).

**Figure 7.**Impact of changes in Poisson’s ratio on pressure decay (

**bottom**) and ultimate recovery (

**top**).

**Figure 8.**Impact of changes in Biot’s coefficient on pressure decay (

**bottom**) and ultimate recovery (

**top**).

**Table 1.**Summary of Langmuir adsorption parameters courtesy of Schlumberger Reservoir Laboratory 20 July 2020.

Sample | PL (Langmuir Pressure) | VL (Langmuir Volume) | ||
---|---|---|---|---|

Psia | MPa | scf/ton | scc/gm | |

Raw basis | 670.7 | 4.62 | 239.3 | 7.5 |

Dry basis | 670.7 | 4.62 | 241.1 | 7.5 |

Core Depth | As-Received Bulk Density | Effective Confining Pressure | Young’s Modulus Normal to Bedding | Young’s Modulus Parallel to Bedding | Poisson’s Ratio Normal to Bedding | Poisson’s Ratio Parallel to Bedding |
---|---|---|---|---|---|---|

FT | g/cc | psi | psi | psi | unitless | unitless |

7940.38 | 2.409 | 2150 | 2.451 × 10^{6} | 5.108 × 10^{6} | 0.15 | 0.19 |

Reservoir Parameters | Values | Unit | Reservoir Parameters | Values | Unit |
---|---|---|---|---|---|

Matrix initial pressure | 5136 | psi | Pore diffusion organic | 5 × 10^{−6} | cm^{2}/s |

Matrix half length | 100 | ft | Solid diffusion organic | 5 × 10^{−8} | cm^{2}/s |

Reservoir Temperature | 148 | °F | Pore diffusion inorganic | 1 × 10^{−7} | cm^{2}/s |

Inorganic initial porosity | 7% | fraction | Fracture permeability | 0.001 | mD |

Matrix initial permeability | 400 | nD | Biot’s coefficient | 0.7 | dimensionless |

Organic initial porosity | 1% | fraction | Shape factor ${\tau}_{m}$ | 0.3 | dimensionless |

Henry’s constant | 0.28 | dimensionless | Shape factor ${\tau}_{f}$ | 0.5 | dimensionless |

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**MDPI and ACS Style**

Fathi, E.; Belyadi, F.; Jabbar, B. Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs. *Fuels* **2021**, *2*, 130-143.
https://doi.org/10.3390/fuels2020008

**AMA Style**

Fathi E, Belyadi F, Jabbar B. Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs. *Fuels*. 2021; 2(2):130-143.
https://doi.org/10.3390/fuels2020008

**Chicago/Turabian Style**

Fathi, Ebrahim, Fatemeh Belyadi, and Bahiya Jabbar. 2021. "Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs" *Fuels* 2, no. 2: 130-143.
https://doi.org/10.3390/fuels2020008