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Investigation of Dynamic Effect of Capillary Pressure in Ultra-Low Permeability Sandstones

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Abstract

Generally, an empirical relationship between capillary pressure and saturation obtained by means of laboratory experiments is used to describe capillary pressure. However, this relationship assumes equilibrium in the distribution of the phases in the porous medium. This assumption is valid in cases where saturation varies slowly, however it may not be appropriate for application in faster processes. In such cases, dynamic effects may have an influence on the system. In this study, an extended relationship of capillary pressure that includes the dynamic effect is chosen to be implemented into the percolation model of two-phase flow in ultra-low permeability (K is less than 1 × 10−3 μm2) sandstones. This model is used for the numerical simulation. The purpose of this study is to examine the influence of the inclusion of the extended relationship on two-phase flow. Firstly, the dynamic effect was investigated through laboratory tests and then the factors influencing on the dynamic capillary pressure were analyzed. Secondly, the percolation model of two-phase flow considering the dynamic effect was established. Finally, the influences of dynamic capillary pressure on two-phase flow were investigated. The results reveal that the dynamic effect of capillary pressure is obvious in ultra-low permeability reservoir. The inclusion of the dynamic capillary pressure relationship has a different influence compared to the cases without capillary pressure. The existence of dynamic effect has a significant influence on the water saturation distribution and oil production. The moisture content rises faster for water-wetting sandstones but the rising velocity is reduced for oil-wetting sandstones considering the dynamic effect.

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Abbreviations

α s :

Empirical constant, which is equal to 0.1

φ :

Porosity (%)

μ w :

Viscosity of the wetting phase (mPa s)

P e and λ :

Factors of capillary pressure–saturation relationships in the Brook–Corey model

τ s or τ :

The coefficients of dynamic capillary pressure (kg m−1 s−1)

P ec :

The static capillary pressure (MPa)

P dc :

The dynamic capillary pressure (MPa)

P w :

The capillary pressure of wetting phase (MPa)

P o :

The capillary pressure of non-wetting phase (MPa)

K :

Absolute permeability (10−3 μm2)

K w :

Absolute permeability of wetting phase (10−3 μm2)

ρ w :

Density of the wetting phase (kg/m3)

g :

Gravity acceleration (m/s2)

L :

Characteristic length (cm)

D :

Diameter (cm)

q w :

Injection velocity of water phase (ml/min)

S oi :

Initial oil saturation (%)

S or :

Residual oil saturation (%)

S wc :

Connate water saturation (%)

K rw (S or):

Relative permeability to water under residual oil saturation (dimensionless)

K ro (S wc):

Relative permeability to oil under connate water saturation (dimensionless)

K ro :

Relative permeability to oil (dimensionless)

K rw :

Relative permeability to water (dimensionless)

u w :

Flow velocity of the wetting phase (cm/s)

u z :

Injection velocity of the wetting phase at the inlet end of core (cm/s)

K air :

Absolute permeability to air (10−3 μm2)

K wat :

Absolute permeability to water (10−3 μm2)

EOR :

Oil recovery (%)

S we :

Water saturation at the core outlet (%)

S wi :

Initial water saturation (%)

f o :

Oil ratio at the core outlet (%)

f w :

Water ratio at the core outlet (%)

I :

Injection ability at some time/the initial injection ability

\( \bar{V}_{o} \,(t) \) :

Dimensionless cumulative oil production volume

\( \bar{V}_{(t)} \) :

Dimensionless liquid production volume

V f :

The volume of core sample (cm3)

S Hg :

The mercury saturation (%)

V Hg :

The volume of injected mercury (ml)

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Acknowledgments

This article was supported by the National Natural Sciences Foundation (No. 51204193) in China.

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Authors and Affiliations

  1. School of Petroleum Engineering, China University of Petroleum, Beijing, China

    Haiyong Zhang, Shunli He, Shaoyuan Mo & Gang Lei

  2. PetroChina Petroleum Safety and Environmental Protection Institute of Technology, Beijing, China

    Guohua Luan

  3. Langfang Branch of PetroChina Research Institute of Petroleum Exploration and Development, Langfang, China

    Chunyan Jiao

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  1. Haiyong Zhang
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  2. Shunli He
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  3. Chunyan Jiao
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  4. Guohua Luan
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  5. Shaoyuan Mo
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  6. Gang Lei
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Correspondence to Haiyong Zhang.

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Zhang, H., He, S., Jiao, C. et al. Investigation of Dynamic Effect of Capillary Pressure in Ultra-Low Permeability Sandstones. Indian Geotech J 45, 79–88 (2015). https://doi.org/10.1007/s40098-014-0109-3

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  • DOI: https://doi.org/10.1007/s40098-014-0109-3

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