Abstract
Oil–water relative permeability curve constitutes important basic data in reservoir engineering. Given the influence of dead volume on experimental apparatus, the actual oil–water relative permeability curve cannot be obtained when the unsteady-state method is adopted to measure oil–water relative permeability. In this paper, on the basis of the analysis of the influence of dead volume on oil–water relative permeability, we summarize the conventional methods used to overcome dead volume and then propose the use of relationship theory between resistivity and water saturation to calibrate the oil–water relative permeability curve. This method mainly aims at to measure the resistance values at both ends of the core by using a resistance-measuring instrument. Meantime, the Archie formula is used to calibrate the relational expression of core resistivity and water saturation based on the steady-state experimental method. Therefore, the core of the actual cumulative oil production and the average water saturation can be calculated, and then oil–water relative permeability can be accurately computed without the influence of dead volume. By comparing the oil displacement process of dead volume calculated through two different methods (probability subtraction and resistivity methods), the crude oil in dead volume is found to be displaced at the beginning of the displacement. The oil–water relative permeability curve corrected through resistivity method can eliminate the influence of dead volume and iterative error in calculation, and is consistent with the law of the actual development of oilfield, which has certain theoretical and practical application values.
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Abbreviations
- \(\overline{V_{o} } \) :
-
Dimensionless cumulative oil production
- \(\overline{V} \left( t \right) \) :
-
Dimensionless cumulative water injection
- \(\overline{V_{\mathrm{core}} } \) :
-
Dimensionless cumulative oil production of the core
- \(\overline{V_{\mathrm{dead}} } \) :
-
Dimensionless cumulative oil production of the dead volume
- \(V_{\mathrm{dead}}\) :
-
Cumulative oil production of the dead volume
- \(V_{\exp }\) :
-
Cumulative oil production obtained from the experiment
- \(\overline{V_{\exp } }\) :
-
Dimensionless cumulative oil production obtained from the experiment
- \(f\left( {S_{w}} \right) \) :
-
The core endpiece oil cut
- \(\overline{S_w} \) :
-
Average water saturation in the core
- \(K_{ro} \) :
-
Oil-phase relative permeability
- \(K_{rw} \) :
-
Water-phase relative permeability
- \(K_{ro} \) (resistivity):
-
Oil-phase relative permeability obtained through resistivity method
- \(K_{rw} \) (resistivity):
-
Water-phase relative permeability obtained through resistivity method
- \(K_{ro} \) (probability subtract):
-
Oil-phase relative permeability obtained through probability subtract method
- \(K_{rw} \) (probability subtract):
-
Water-phase relative permeability obtained through probability subtract method
- \(\mu _o \) :
-
Viscosity of the oil-phase
- \(\mu _w \) :
-
Viscosity of the water phase
- \(S_{wi} \) :
-
Immobile water saturation
- \(S_{we} \) :
-
The core endpiece water saturation
- \(\alpha \) :
-
Dead volume output coefficient
- \(Q_{\mathrm{readings}} \) :
-
Oil production of each test tube
- \(Q_{\mathrm{correct}}\) :
-
Oil production of each test tube corrected through the probability subtraction method
- I :
-
Injectability ratio at the time t with the injectability at the initial time
- \(Q_o\) :
-
The core endpiece oil flow at the initial time
- \(Q\left( t \right) \) :
-
The core endpiece liquid flow at the time
- \(t \Delta p_o\) :
-
Displacement pressure difference at the initial time
- \(\Delta p\left( t \right) \) :
-
Displacement pressure difference at the time t
- \(I_A\) :
-
Resistivity index
- \(R_o\) :
-
Resistivity at a water saturation of 100 %
- \(R_t\) :
-
Resistivity of oil-bearing rock
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Acknowledgments
The authors would like to thank CNPC and Huabei oilfield of their kind permission to publish this paper. Thanks also extended to Research Institute of Petroleum Exploration and Development, Petro-China, Beijing, for their support and encouragement.
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Hu, W., Yang, S., Liu, G. et al. A New Correction Method for Oil–Water Relative Permeability Curve on the Basis of Resistivity and Water Saturation Relationship. Transp Porous Med 109, 527–540 (2015). https://doi.org/10.1007/s11242-015-0543-4
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DOI: https://doi.org/10.1007/s11242-015-0543-4