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Journal of Petroleum Exploration and Production Technology

, Volume 4, Issue 4, pp 443–455

First Online: 20 January 2014Received: 05 September 2013Accepted: 06 January 2014


Forced oil–water displacement is the crucial mechanisms of secondary oil recovery. The knowledge of relative permeability is required in the simulation of multiphase flow in porous media. Obvious dynamic effect of capillary pressure occurs in that the formation of ultra-low permeability reservoir the permeability is <1 × 10μm is tight and the pores and throats are very small. In addition, the significant capillary end effect causes serious errors when calculating relative permeabilities. For these reasons, the JBN method neglecting capillary pressure does not apply. Therefore, the dynamic capillary pressure and capillary end effects should be taken into account. This work focuses on calculating two-phase relative permeability of ultra-low permeability reservoir through considering the dynamic capillary pressure and eliminating the influence of capillary end effects. Firstly, laboratory core scale measurements of in situ water phase saturation history based on X-ray CT scanning technique were used to estimate relative permeability. Secondly, a mathematical model of two-phase relative permeability considering the dynamic capillary pressure was established. The basic problem formulations, as well as the more specific equations, were given, and the results of comparison using experimental data are presented and discussed. Results indicate that the dynamic capillary pressure measured at laboratory core scale in ultra-low permeability rocks has a significant influence on the estimation of unsteady-state relative permeability. The mathematical calculating method was compared with the history matching method and the results were close, suggesting reliability for ultra-low permeability reservoirs. Importantly, the proposed methods allow measurement of relative permeability from a single experiment. Potentially this represents a great time savings.

KeywordsDynamic capillary effect X-ray CT Ultra-low permeability Relative permeability List of symbolsαsEmpirical constant, which is equal to 0.1

φPorosity %

φCTThe CT-measured porosity %

μwViscosity of the wetting phase mPa s

Peand λFactors of capillary pressure–saturation relationships in the Brook–Corey model

pcThe dynamic capillary pressure MPa

pcThe steady-state capillary pressure MPa

poThe capillary pressure of oil phase MPa

pwThe capillary pressure of water phase MPa

τs or τThe coefficient of dynamic capillary pressure kg ms

KAbsolute permeability 10μm

ρwDensity of the wetting phase kg m

gGravity acceleration m s

LCharacteristic length cm

DDiameter cm

SoiInitial oil saturation %

SorResidual oil saturation %

SwcConnate water saturation %

Krw SorRelative permeability to water under residual oil saturation, dimensionless

Kro SwcRelative permeability to oil under connate water saturation, dimensionless

KroRelative permeability to oil, dimensionless

KrwRelative permeability to water, dimensionless

uwFlow velocity of the wetting phase cm s

uzInjection velocity of the wetting phase at the inlet end of core cm s

KairAbsolute permeability to air 10μm

KwatAbsolute permeability to water 10μm

EOROil recovery %

SweWater saturation at the core outlet %

SwiInitial water saturation %

foOil ratio at the core outlet %

fwWater ratio at the core outlet %

IInjection ability at some time-the initial injection ability

V ¯ o t Dimensionless cumulative oil production volume

V ¯ t Dimensionless liquid production volume

CTDryThe CT number for the dry core sample

CTAirThe CT number for air

CTPhase1The CT number for phase1

CTPhase2The CT number for phase2

CTSaturatedThe CT number for the core saturated by one single phase

CTTwoThe CT number for two-phase liquids

CTGrainThe CT number for the grain of core sample

CTowThe CT number for the oil–water two phases

CTwThe CT number for the water phase

CToThe CT number for the oil phase

CTorThe CT number for the core sample saturated by oil phase

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Autor: Haiyong Zhang - Shunli He - Chunyan Jiao - Guohua Luan - Shaoyuan Mo - Xuejing Guo


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