Abstract
The relative permeability is the ratio of the effective permeability to the absolute permeability. Due to the importance of relative permeability in reservoir simulation, there is a dominant need to upscale it. So, several models were introduced to modeling the relative permeability. Some correlation models were dependent on capillary pressure measurements, while other models did not require such measurements. In this study, four relative permeability correlation models were chosen to apply them on two sandstone reservoir (labeled A and B) data sets. The two reservoirs belong to different ages and depositional environments. Both reservoirs are located in the Southern Gulf of Suez, Egypt. Reservoir A is the Nubian sandstone of Cambrian age. Reservoir B is the Nukhul clastic of Early Miocene age. The data sets include laboratory measurements of unsteady-state gas–oil relative permeability and steady-state water–oil relative permeability tests. The results indicate that the practical and modified Corey models were the most applicable model for the studied reservoirs. Additionally, prediction of relative permeability at saturation end points was carried out based on using routine core porosity and permeability by introducing new empirical equations. The relative permeability was used to identify rock wettability, water cut, water cutoffs and the areal and vertical sweep efficiencies.
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Abbreviations
- A, B, L and M :
-
Positive numbers
- \({E_{{\rm ABT}}}\) :
-
Efficiency at breakthrough
- \({E_{{\rm D}}}\) :
-
Displacement efficiency
- \({E_{{\rm R}}}\) :
-
Overall waterflood oil-recovery efficiency
- \({E_{\rm v}}\) :
-
Vertical efficiency
- \({f_{{\rm w}}}\) :
-
The fractional flow of water (water cut)
- \({k_{{\rm rg}}}\) :
-
Relative permeability to gas
- \({k_{{\rm rg}}@{{\rm S}}_{{\rm org}}}\) :
-
Relative permeability to gas at residual oil Saturation in gas–oil system
- \({k_{{\rm rnw}}}\) :
-
Relative permeability for nonwetting phase
- \({k_{{\rm rog}}}\) :
-
Relative permeability to oil in the two phase Gas–oil system
- \({k_{{\rm row}}}\) :
-
Relative permeability to oil in the two phase Oil–water system
- \({k_{{\rm ro}}@{{\rm S}}_{{\rm wc}}}\) :
-
Relative permeability to oil at connate water saturation
- \({k_{{\rm ro}}@{{\rm S}}_{{\rm gc}}}\) :
-
Relative permeability to oil at critical gas saturation
- \({k_{{\rm ro}}^{\ast}}\) :
-
Normalized relative permeability to oil
- \({k_{{\rm rw}}}\) :
-
Relative permeability for wetting phase
- \({k_{{\rm rw}}@{{\rm S}}_{{\rm orw}}}\) :
-
Relative permeability to oil at residual oil saturation
- \({k_{{\rm rw}}^{\ast}}\) :
-
Normalized relative permeability to water
- \({M}\) :
-
The mobility ratio
- \({M_{{\rm w}}}\) :
-
The molecular weight
- no, nw, ng, ngo:
-
\({\square}\) Exponents on relative permeability curves
- P :
-
The pressure, psi
- \({P_{\rm b}}\) :
-
Rhe bubble—point pressure, psi
- \({P_{\rm c}}\) :
-
Capillary pressure, psi
- \({P_{\rm d}}\) :
-
Displacement pressure, psi
- \({R_{\rm g}}\) :
-
The normalized saturation
- \({R_{\rm s}}\) :
-
The solubility of the gas–oil ratio SCF/STB
- S :
-
The salinity (%)
- \({S_{\rm g}}\) :
-
\({\square}\) Gas saturation
- \({S_{\rm gc}}\) :
-
\({\square}\) Critical gas saturation
- \({S_{\rm o}}\) :
-
Oil saturation
- \({S_{{\rm oe}}}\) :
-
Normalized wetting phase saturation
- \({S_{{\rm or}}}\) :
-
Residual oil saturation
- \({S_{{\rm org}}}\) :
-
\({\square}\) Residual oil saturation in the gas–oil system
- \({S_{\rm orw}}\) :
-
Residual oil saturation in the water–oil system
- \({S_{\rm w}}\) :
-
Water or wetting phase saturation
- \({S_{{\rm w}^\ast}}\) :
-
Normalized water saturation
- \({S_{\rm wc}}\) :
-
\({\square}\) (Irreducible) water saturation
- \({S_{{\rm wir}}}\) :
-
Irreducible water saturation
- \({T}\) :
-
Temperature (\({^{\circ}}\)F)
- \({V}\) :
-
Permeability variation
- \({\mu_{{\rm o}}}\) :
-
The oil viscosity (cp)
- \({\mu_{{\rm obd}}}\) :
-
The dead oil viscosity above bubble point pressure (cp)
- \({\mu_{{\rm od}}}\) :
-
The dead oil viscosity (cp)
- \({\mu_{{\rm w}}}\) :
-
The water viscosity (cp)
- \({\mu_{{\rm w1}}}\) :
-
The water viscosity at atmospheric pressure and reservoir temperature (cp)
- \({\gamma g}\) :
-
The specific gas gravity
- \({\rho_{{\rm o}}}\) :
-
The oil density (API)
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El Sharawy, M.S. Modeling of Two-Phase Relative Permeability in Cambrian and Early Miocene Sandstone Reservoirs: A Case Study, Egypt. Arab J Sci Eng 41, 2751–2770 (2016). https://doi.org/10.1007/s13369-016-2186-3
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DOI: https://doi.org/10.1007/s13369-016-2186-3