### Abstract

Capillary imbibition is one of the main recovery mechanisms of naturally fractured reservoirs where fracture fluid imbibes, by capillary forces, in the matrix and the matrix fluid is transferred to the fracture. Simulating counter-current imbibition in dual-medium models is a challenging task. The semi-steady state approach has been used in Warren and Root based transfer functions for the past forty years. However, it eliminates the speed of early time recovery and assigns average property values in matrix and fracture. In this paper, we eliminate the semi-steady state approach in matrix capillary imbibition by making the transfer function depend on time, space and two recovery periods (early and late time). We make it depend on space by dividing the invaded face into two equal sub-faces, each with its own capillary pressure, relative permeability and location. Then, the two contributions are summed up to equal one mass conservation equation for each matrix cell. In early time recovery, the saturation front moves laterally in the matrix, until it reaches the no-flux boundary. The distance of invasion is calculated using an integral of the inverse capillary pressure curve, the saturation values of previous time step, and the distance between the invaded face and the no-flux boundary. Then, new capillary pressure, relative permeability and location values are assigned to each subface; where the transfer of fluid is calculated. When the saturation front reaches the no-flux boundary, at start of late time, it moves vertically until the Pc at the no-flux boundary equals the Pc at the invaded face. The capillary pressure and relative permeability of the sub-faces are calculated using integral of the inverse of capillary pressure curve and the saturation value of previous time step. Our approach matched the results of fine-grid single-porosity models under various parameters of capillary pressure, matrix shape and mobility. It also outperformed the results of three transfer functions: Gilman & Kazemi, Quandalle & Sabathier, and the General Transfer Function proposed by Hu & Blunt.

Original language | English |
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Title of host publication | ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery |

Publisher | European Association of Geoscientists and Engineers, EAGE |

Publication status | Published - 2008 |

Event | 11th European Conference on the Mathematics of Oil Recovery, ECMOR 2008 - Bergen Duration: 8 Sep 2008 → 11 Sep 2008 |

### Other

Other | 11th European Conference on the Mathematics of Oil Recovery, ECMOR 2008 |
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City | Bergen |

Period | 8/9/08 → 11/9/08 |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geotechnical Engineering and Engineering Geology
- Energy Engineering and Power Technology

### Cite this

*ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery*European Association of Geoscientists and Engineers, EAGE.

**Matrix-fracture transfer function in dual-medium flow simulation - Improved model of capillary imbibition.** / Abushaikha, Ahmad; Gosselin, O. R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery.*European Association of Geoscientists and Engineers, EAGE, 11th European Conference on the Mathematics of Oil Recovery, ECMOR 2008, Bergen, 8/9/08.

}

TY - GEN

T1 - Matrix-fracture transfer function in dual-medium flow simulation - Improved model of capillary imbibition

AU - Abushaikha, Ahmad

AU - Gosselin, O. R.

PY - 2008

Y1 - 2008

N2 - Capillary imbibition is one of the main recovery mechanisms of naturally fractured reservoirs where fracture fluid imbibes, by capillary forces, in the matrix and the matrix fluid is transferred to the fracture. Simulating counter-current imbibition in dual-medium models is a challenging task. The semi-steady state approach has been used in Warren and Root based transfer functions for the past forty years. However, it eliminates the speed of early time recovery and assigns average property values in matrix and fracture. In this paper, we eliminate the semi-steady state approach in matrix capillary imbibition by making the transfer function depend on time, space and two recovery periods (early and late time). We make it depend on space by dividing the invaded face into two equal sub-faces, each with its own capillary pressure, relative permeability and location. Then, the two contributions are summed up to equal one mass conservation equation for each matrix cell. In early time recovery, the saturation front moves laterally in the matrix, until it reaches the no-flux boundary. The distance of invasion is calculated using an integral of the inverse capillary pressure curve, the saturation values of previous time step, and the distance between the invaded face and the no-flux boundary. Then, new capillary pressure, relative permeability and location values are assigned to each subface; where the transfer of fluid is calculated. When the saturation front reaches the no-flux boundary, at start of late time, it moves vertically until the Pc at the no-flux boundary equals the Pc at the invaded face. The capillary pressure and relative permeability of the sub-faces are calculated using integral of the inverse of capillary pressure curve and the saturation value of previous time step. Our approach matched the results of fine-grid single-porosity models under various parameters of capillary pressure, matrix shape and mobility. It also outperformed the results of three transfer functions: Gilman & Kazemi, Quandalle & Sabathier, and the General Transfer Function proposed by Hu & Blunt.

AB - Capillary imbibition is one of the main recovery mechanisms of naturally fractured reservoirs where fracture fluid imbibes, by capillary forces, in the matrix and the matrix fluid is transferred to the fracture. Simulating counter-current imbibition in dual-medium models is a challenging task. The semi-steady state approach has been used in Warren and Root based transfer functions for the past forty years. However, it eliminates the speed of early time recovery and assigns average property values in matrix and fracture. In this paper, we eliminate the semi-steady state approach in matrix capillary imbibition by making the transfer function depend on time, space and two recovery periods (early and late time). We make it depend on space by dividing the invaded face into two equal sub-faces, each with its own capillary pressure, relative permeability and location. Then, the two contributions are summed up to equal one mass conservation equation for each matrix cell. In early time recovery, the saturation front moves laterally in the matrix, until it reaches the no-flux boundary. The distance of invasion is calculated using an integral of the inverse capillary pressure curve, the saturation values of previous time step, and the distance between the invaded face and the no-flux boundary. Then, new capillary pressure, relative permeability and location values are assigned to each subface; where the transfer of fluid is calculated. When the saturation front reaches the no-flux boundary, at start of late time, it moves vertically until the Pc at the no-flux boundary equals the Pc at the invaded face. The capillary pressure and relative permeability of the sub-faces are calculated using integral of the inverse of capillary pressure curve and the saturation value of previous time step. Our approach matched the results of fine-grid single-porosity models under various parameters of capillary pressure, matrix shape and mobility. It also outperformed the results of three transfer functions: Gilman & Kazemi, Quandalle & Sabathier, and the General Transfer Function proposed by Hu & Blunt.

UR - http://www.scopus.com/inward/record.url?scp=84896347920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896347920&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84896347920

BT - ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery

PB - European Association of Geoscientists and Engineers, EAGE

ER -