### Abstract

Standard compositional simulators use composition-dependent cubic equations-of-state (EoS), but saturation-dependent relative permeability (kr). This discrepancy causes discontinuities, increasing computational time and reduced accuracy. To rectify this problem, kr has been recently defined as a state function, so that it becomes compositional dependent. Such a form of the kr EoS can significantly improve the convergence in compositional simulation, in that time step sizes are near the IMPEC stability limit and flash calculation convergence is improved. This paper revisits the development of kr EoS by defining relevant state variables and deriving functional forms of the state function via a methodical approach. The state variables include phase saturation, phase connectivity, wettability, capillary number, and pore topology. The developed EoS is constrained to physical boundary conditions. The model coefficients are estimated through linear regression on data collected from a pore-scale simulation study that estimates kr based on micro-CT image analysis. The results show that a simple quadratic expression gives an excellent match with simulation measurements from the literature. The goodness of fit (R2) value is 0.97 for kr at variable phase saturation and phase connectivity, and constant wettability, pore structure, and capillary number (∼10-4). The quadratic response for kr also shows excellent predictive capabilities.

Original language | English (US) |
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Title of host publication | 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018 |

Publisher | European Association of Geoscientists and Engineers, EAGE |

ISBN (Print) | 9789462822603 |

State | Published - Jan 1 2018 |

Event | 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018 - Barcelona, Spain Duration: Sep 3 2018 → Sep 6 2018 |

### Publication series

Name | 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018 |
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### Other

Other | 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018 |
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Country | Spain |

City | Barcelona |

Period | 9/3/18 → 9/6/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018*(16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018). European Association of Geoscientists and Engineers, EAGE.

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*16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018.*16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018, European Association of Geoscientists and Engineers, EAGE, 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018, Barcelona, Spain, 9/3/18.

**On the development of a relative permeability equation of state.** / Purswani, P.; Tawfik, M. S.; Karpyn, Zuleima; Johns, Russell Taylor.

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

TY - GEN

T1 - On the development of a relative permeability equation of state

AU - Purswani, P.

AU - Tawfik, M. S.

AU - Karpyn, Zuleima

AU - Johns, Russell Taylor

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Standard compositional simulators use composition-dependent cubic equations-of-state (EoS), but saturation-dependent relative permeability (kr). This discrepancy causes discontinuities, increasing computational time and reduced accuracy. To rectify this problem, kr has been recently defined as a state function, so that it becomes compositional dependent. Such a form of the kr EoS can significantly improve the convergence in compositional simulation, in that time step sizes are near the IMPEC stability limit and flash calculation convergence is improved. This paper revisits the development of kr EoS by defining relevant state variables and deriving functional forms of the state function via a methodical approach. The state variables include phase saturation, phase connectivity, wettability, capillary number, and pore topology. The developed EoS is constrained to physical boundary conditions. The model coefficients are estimated through linear regression on data collected from a pore-scale simulation study that estimates kr based on micro-CT image analysis. The results show that a simple quadratic expression gives an excellent match with simulation measurements from the literature. The goodness of fit (R2) value is 0.97 for kr at variable phase saturation and phase connectivity, and constant wettability, pore structure, and capillary number (∼10-4). The quadratic response for kr also shows excellent predictive capabilities.

AB - Standard compositional simulators use composition-dependent cubic equations-of-state (EoS), but saturation-dependent relative permeability (kr). This discrepancy causes discontinuities, increasing computational time and reduced accuracy. To rectify this problem, kr has been recently defined as a state function, so that it becomes compositional dependent. Such a form of the kr EoS can significantly improve the convergence in compositional simulation, in that time step sizes are near the IMPEC stability limit and flash calculation convergence is improved. This paper revisits the development of kr EoS by defining relevant state variables and deriving functional forms of the state function via a methodical approach. The state variables include phase saturation, phase connectivity, wettability, capillary number, and pore topology. The developed EoS is constrained to physical boundary conditions. The model coefficients are estimated through linear regression on data collected from a pore-scale simulation study that estimates kr based on micro-CT image analysis. The results show that a simple quadratic expression gives an excellent match with simulation measurements from the literature. The goodness of fit (R2) value is 0.97 for kr at variable phase saturation and phase connectivity, and constant wettability, pore structure, and capillary number (∼10-4). The quadratic response for kr also shows excellent predictive capabilities.

UR - http://www.scopus.com/inward/record.url?scp=85054597377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054597377&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85054597377

SN - 9789462822603

T3 - 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018

BT - 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018

PB - European Association of Geoscientists and Engineers, EAGE

ER -