# Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs

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## Abstract

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## 1. Introduction

## 2. Multilayer Reservoir Commingling Production Waterflood Model

#### 2.1. Multilayer Water Flooding Model under One-Dimensional Linear Seepage Flow

#### 2.1.1. Assumptions

- The left boundary is the supply boundary with constant injection, and the right boundary is the production ends, which creates a balance between injection and production.
- The media is rigid and porous, and the fluid is incompressible.
- There are stable interlayers between layers, regardless of inter-layer cross flow.
- Non-piston water displacement oil is present, and there are two phases of oil and water.

#### 2.1.2. Modeling

#### 2.2. Multilayer Water Flooding Model under Planar Radial Flow

#### 2.2.1. Assumptions

- The boundary is the supply boundary with constant injection and creates a balance between injection and production.
- The media is rigid and porous, and the fluid is incompressible.
- There are stable interlayers between layers, regardless of inter-layer cross flow.
- Non-piston water displacement oil is present, and there are two phases of oil and water.

#### 2.2.2. Modeling

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## 3. Model Solving

## 4. Model Validation

## 5. Model Application and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${r}_{fi}$ | position of waterflood front in layer i, m; |

${R}_{o}$ | initial oil edge radius, m; |

${h}_{i}$ | thickness of layer i, m; |

${\varphi}_{i}$ | porosity of layer i, dimensionless; |

${s}_{wfi}$ | water saturation of the waterflood front of layer i, dimensionless; |

${f}_{w}^{\prime}\left({s}_{wfi}\right)$ | the derivative of the fractional flow corresponding to the water saturation of the waterflood front in layer i, dimensionless; |

${Q}_{i}$ | liquid production rate in layer i, m^{3}/d; |

${Q}_{l}$ | total liquid production rate, m^{3}/d; |

${K}_{i}$ | the permeability of layer i, 10^{−3}µm^{2}; |

${K}_{ro}$ | relative permeability of oil, fraction; |

${K}_{rw}$ | relative permeability of water, fraction; |

${r}_{w}$ | wellbore radius, m; |

$\Delta P$ | displacement pressure in layer i, MPa; |

${\mu}_{oi}$ | oil viscosity in layer i, mPa·s; |

${V}_{p}$ | total pore volume of the reservoir, m^{3}; |

${R}_{i}$ | resistance of layer i, mPa·s/(d·m); |

$\eta $ | reservoir recovery percent of the multilayer commingling production, dimensionless; |

${E}_{v}$ | sweep efficiency of the multilayer commingling production, dimensionless; |

${\overline{s}}_{w}$ | average water saturation in two-phase region, fraction; |

${s}_{wc}$ | irreducible water saturation, fraction; |

M | number of water-breakthrough layers, dimensionless; |

N | total number of model layers, dimensionless; |

i, j | serial number of layers. |

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**Figure 4.**Comparison of our calculated model and Zhang’s model [34] for the daily oil production rate in different permeability layers. Red dots denote Zhang’s model; blue dotted line denotes the calculated model. (

**a**) High permeability layer; (

**b**) Middle permeability layer; (

**c**) Low permeability layer.

**Figure 5.**Comparison of the seepage resistance with different permeability in each layer of the planar radial flow model ranging from 0 to 5 pore volume (PV).

**Figure 6.**Comparison of recovery percentage in the reservoir ranging from 0 to 5 PV (

**a**) separated and commingling production; (

**b**) each different permeability layer (solid line, commingling production; dotted line, separated production).

**Figure 7.**Ratio of liquid production between high and low permeability layers (best to the worst) as the water cut ranging from 0 to nearly 100%.

**Figure 8.**Comparison of the liquid production rate with a permeability-to-viscosity ratio ranging from 0 to 5 PV. (

**a**) Permeability ratio = 5; (

**b**) Viscosity ratio = 5.

**Figure 9.**Recovery degree increase of separate production with a permeability ratio ranging from 1 to 10.

**Figure 10.**Comparison of the single well production index after separated production for nine months.

Model Parameters | Value | Model Parameters | Value |
---|---|---|---|

Reservoir radius (m) | 350 | Layer 1 permeability (10^{−3} µm^{2}) | 3000 |

Reservoir thickness (m) | 5 | Layer 2 permeability (10^{−3} µm^{2}) | 1800 |

Reservoir porosity (%) | 25 | Layer 3 permeability (10^{−3} µm^{2}) | 600 |

Water injection rate (m^{3}/d) | 500 | Oil viscosity (mPa·s) | 50 |

Model Parameters | Value | Model Parameters | Value |
---|---|---|---|

Reservoir radius (m) | 350 | Oil viscosity in Layer 1 (mPa·s) | 17 |

Reservoir thickness (m) | 5 | Oil viscosity in Layer 2 (mPa·s) | 50 |

Reservoir porosity (%) | 25 | Oil viscosity in Layer 3 (mPa·s) | 85 |

Water injection rate (m^{3}/d) | 500 | Layers’ permeability (10^{−3} µm^{2}) | 1800 |

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**MDPI and ACS Style**

Shen, F.; Cheng, L.; Sun, Q.; Huang, S.
Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs. *Energies* **2018**, *11*, 2428.
https://doi.org/10.3390/en11092428

**AMA Style**

Shen F, Cheng L, Sun Q, Huang S.
Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs. *Energies*. 2018; 11(9):2428.
https://doi.org/10.3390/en11092428

**Chicago/Turabian Style**

Shen, Fei, Linsong Cheng, Qiang Sun, and Shijun Huang.
2018. "Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs" *Energies* 11, no. 9: 2428.
https://doi.org/10.3390/en11092428