### Abstract

Steady, one-phase, 2D Darcian seepage in a homogeneous pay from one horizontal isobar to another with a tilted fracture intersecting the two isobars is studied by the methods of complex analysis. The shortcut through the fracture is foiled by an impermeable seal of a constant length which is placed at the fracture-isobar intersection with an objective to minimise either the total flow rate from the fracture or the travel time of marked particles moving along the seal. Conformal mappings of the slanted-face half-strip in the physical domain onto a half-strip in the complex potential domain give explicit expressions of the seepage rate and travel time through hypergeometric functions. The optimal seal position is found by computer algebra routines for any given distance between isobaric horizons, tilt angle, pressure drop between isobars and hydraulic conductivity of the rock.

Original language | English |
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Pages (from-to) | 140-147 |

Number of pages | 8 |

Journal | Applied Mathematical Modelling |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2009 |

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### Keywords

- Complex variables
- Fracture
- Horizontal well
- Optimisation
- Seepage

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Control and Optimization

### Cite this

**Optimal placement of a wellbore seal impeding seepage from a tilted fracture.** / Kacimov, Anvar; Marketz, Franz; Pervez, Tasneem.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 33, no. 1, pp. 140-147. https://doi.org/10.1016/j.apm.2007.10.027

}

TY - JOUR

T1 - Optimal placement of a wellbore seal impeding seepage from a tilted fracture

AU - Kacimov, Anvar

AU - Marketz, Franz

AU - Pervez, Tasneem

PY - 2009/1

Y1 - 2009/1

N2 - Steady, one-phase, 2D Darcian seepage in a homogeneous pay from one horizontal isobar to another with a tilted fracture intersecting the two isobars is studied by the methods of complex analysis. The shortcut through the fracture is foiled by an impermeable seal of a constant length which is placed at the fracture-isobar intersection with an objective to minimise either the total flow rate from the fracture or the travel time of marked particles moving along the seal. Conformal mappings of the slanted-face half-strip in the physical domain onto a half-strip in the complex potential domain give explicit expressions of the seepage rate and travel time through hypergeometric functions. The optimal seal position is found by computer algebra routines for any given distance between isobaric horizons, tilt angle, pressure drop between isobars and hydraulic conductivity of the rock.

AB - Steady, one-phase, 2D Darcian seepage in a homogeneous pay from one horizontal isobar to another with a tilted fracture intersecting the two isobars is studied by the methods of complex analysis. The shortcut through the fracture is foiled by an impermeable seal of a constant length which is placed at the fracture-isobar intersection with an objective to minimise either the total flow rate from the fracture or the travel time of marked particles moving along the seal. Conformal mappings of the slanted-face half-strip in the physical domain onto a half-strip in the complex potential domain give explicit expressions of the seepage rate and travel time through hypergeometric functions. The optimal seal position is found by computer algebra routines for any given distance between isobaric horizons, tilt angle, pressure drop between isobars and hydraulic conductivity of the rock.

KW - Complex variables

KW - Fracture

KW - Horizontal well

KW - Optimisation

KW - Seepage

UR - http://www.scopus.com/inward/record.url?scp=51949109314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51949109314&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2007.10.027

DO - 10.1016/j.apm.2007.10.027

M3 - Article

AN - SCOPUS:51949109314

VL - 33

SP - 140

EP - 147

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 1

ER -