# A New Approach for Production Prediction in Onshore and Offshore Tight Oil Reservoir

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Model Development

- The reservoir is homogeneous, thick uniformly and isothermal.
- Fluid flow is single phase and 1D linear in each region.
- The whole production process is under constant bottom-hole pressure.
- The entire flow system follows symmetry and continuity.
- The effect of gravity and capillary forces are neglected.

- Model 1: Based on Brown’s conceptual model

_{e}.

_{0}.

- Model 2: Based on Stalgorova and Matter’s conceptual model

_{2}.

_{wf}is the bottom-hole pressure and remains constant.

## 3. Model Derivation

_{Dn}

_{1}, q

_{Dn}

_{2}and q

_{Dn}

_{3}are the dimensionless production rate from the n-th mode in Region 1, Region 2 and Region 3, respectively. q

_{1}, q

_{2}and q

_{3}and $\overline{{p}_{1}}$, $\overline{{p}_{2}}$ and $\overline{{p}_{3}}$ are the initial production rate and average pressure in Region 1, Region 2 and Region 3, respectively. The productivity index is represented by J and the transmissibility between two regions are represented by T

_{21}and T

_{32}, which can be defined as $J=\frac{{\pi}^{2}}{4}\frac{{q}_{1}}{{p}_{i}-{p}_{wf}}$, ${T}_{21}=\frac{{\pi}^{2}}{4}\frac{{q}_{2}}{{p}_{i}-\overline{{p}_{1}}}$ and ${T}_{32}=\frac{{\pi}^{2}}{4}\frac{{q}_{3}}{{p}_{i}-\overline{{p}_{2}}}$.

_{1}, τ

_{2}and τ

_{3}indicate the linear flow time in Region 1, Region 2 and Region 3, respectively, which can be defined as ${\tau}_{1}=\frac{{({c}_{t}{V}_{p})}_{1}}{J}$, ${\tau}_{2}=\frac{{({c}_{t}{V}_{p})}_{2}}{{T}_{21}}$ and ${\tau}_{3}=\frac{{({c}_{t}{V}_{p})}_{3}}{{T}_{32}}$.

_{1}, λ

_{2}and λ

_{3}are three eigenvalues and r

_{1}~r

_{9}represent the nine elements in three eigenvectors. And β

_{1}, β

_{2}and β

_{3}are the combination of parameters, which can be expressed as ${\beta}_{1}=\frac{{r}_{1}({r}_{1}{r}_{5}-{r}_{2}{r}_{4})}{({r}_{1}{r}_{9}-{r}_{3}{r}_{7})({r}_{1}{r}_{5}-{r}_{2}{r}_{4})-({r}_{1}{r}_{6}-{r}_{3}{r}_{4})({r}_{1}{r}_{8}-{r}_{2}{r}_{7})}$, ${\beta}_{2}=\frac{{r}_{1}{r}_{8}-{r}_{2}{r}_{7}}{{r}_{1}{r}_{5}-{r}_{2}{r}_{4}}{\beta}_{1}$, ${\beta}_{3}=\frac{{\beta}_{2}{r}_{4}{r}_{7}}{{r}_{1}}{\beta}_{1}$.

_{1}is the summation of all production rate terms. After many mathematical manipulations, the analytical solution can be obtained by simplifying Equation (66).

_{1}, τ

_{2}, τ

_{3}) in Region 1, Region 2 and Region 3, productivity index J, two transmissibility T

_{21}and T

_{32}and initial production rate q

_{i}. By fitting Equation (67) to the target data, the several variables can be obtained when the desired match is achieved. In addition, the analytical solution with output variables can be further used for production prediction.

## 4. Model Validation

## 5. Application to Field Cases

- Make a log–log plot of oil rate versus production time.
- Diagnose the flow regimes.
- Apply analytical solution to the production data.
- Output the six parameters after obtaining the desired matching.
- Predict the future production rate with the obtained parameters.

## 6. Conclusions

- Through bypassing the complex Laplace transform solution, the analytical solution is derived in real-time space and directly presents the oil-rate-versus-production-time relationship. Therefore, it is more convenient in field applications.
- The derived analytical solution is not only applicable to unconventional reservoirs without the region beyond the hydraulic fractures, but can also consider the contribution from the region beyond the hydraulic fractures because of the excellent agreement with two numerical models.
- The diagnosis of transient linear flow in offshore and onshore tight oilfields is critical for production data analysis. The same slope straight line may represent the different fluid-transfer mechanism, and the linear flow in unstimulated region cannot be ignored, which represents a significant contribution to long-term production.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic of a multi-stage fractured horizontal well based on two conceptual models. (

**a**,

**b**) 3D schematic. (

**c**,

**d**) Plan view.

**Figure 4.**Production analysis in Well O. (

**a**) Actual oil rate on the log–log plot; (

**b**) the history matching and forecasting results on the log–log plot.

**Figure 5.**Production analysis in Volve oil field. (

**a**) Actual oil rate on the log–log plot; (

**b**) the history matching and forecasting results on the log–log plot.

Model 1 | Model 2 | |
---|---|---|

Parameter | Value | |

Model dimension (X × Y × Z) (ft) | 150 × 400 × 10 | 150 × 400 × 10 |

Initial pressure (psi) | 2500 | 2500 |

Bottom-hole pressure (psi) | 500 | 500 |

Viscosity (cp) | 0.0174 | 0.0174 |

Compressibility (10^{−5} psi) | 9.75 | 9.75 |

Porosity | 0.06 | 0.06 |

Permeability of hydraulic fracture | 5000 | 5000 |

Permeability in Region 3 (mD) | 0.003 | 0.005 |

Permeability in Region 2 (mD) | 0.3 | 0.5 |

**Table 2.**Output parameters obtained from the analytical solution for validation against two numerical models.

Model 1 | Model 2 | |
---|---|---|

Parameter | Value | |

τ_{1} (days) | 1.2 × 10^{−4} | 1.4 × 10^{−4} |

τ_{2} (days) | 418 | 244 |

τ_{3} (days) | 1869 | 1389 |

T_{21}/J | 0.012 | 0.01 |

T_{32}/T_{21} | 0.022 | 0.065 |

q_{i} (STB/day) | 10.96 | 12.02 |

**Table 3.**Output parameters obtained from the analytical solution for application in two field cases.

Well O | Volve Field | |
---|---|---|

Parameter | Value | |

τ_{1} | 0.003 (days) | 5 × 10^{−6} (Months) |

τ_{2} | 197(days) | 14 (Months) |

τ_{3} | 2100 (days) | 460 (Months) |

T_{21/}J | 0.203 | 0.0729 |

T_{32/}T_{21} | 0.049 | 0.0045 |

q_{i} | 1200 (STB/day) | 1780 (MSTB/month) |

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## Share and Cite

**MDPI and ACS Style**

Qiu, K.; Fan, K.; Chen, X.; Lei, G.; Wei, S.; Navik, R.; Li, J.
A New Approach for Production Prediction in Onshore and Offshore Tight Oil Reservoir. *J. Mar. Sci. Eng.* **2023**, *11*, 2079.
https://doi.org/10.3390/jmse11112079

**AMA Style**

Qiu K, Fan K, Chen X, Lei G, Wei S, Navik R, Li J.
A New Approach for Production Prediction in Onshore and Offshore Tight Oil Reservoir. *Journal of Marine Science and Engineering*. 2023; 11(11):2079.
https://doi.org/10.3390/jmse11112079

**Chicago/Turabian Style**

Qiu, Kaixuan, Kaifeng Fan, Xiaolin Chen, Gang Lei, Shiming Wei, Rahul Navik, and Jia Li.
2023. "A New Approach for Production Prediction in Onshore and Offshore Tight Oil Reservoir" *Journal of Marine Science and Engineering* 11, no. 11: 2079.
https://doi.org/10.3390/jmse11112079