Investigation of Two-Phase and Three-Phase Relative Permeability in Different Rocks with Similar Pore Size Distribution

2013 ◽  
Author(s):  
H. Shahverdi ◽  
M. Sohrabi ◽  
S. M. Fatemi ◽  
S. Ireland
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Relative Permeability ◽  
Two Phase ◽  
Three Phase

Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties

1968 ◽  
Vol 8 (02) ◽  
pp. 149-156 ◽  
Author(s):  
Carlon S. Land
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Relative Permeability ◽  
Empirical Relation ◽  
Phase Flow ◽  
Three Phase ◽  
Phase Saturation ◽  
Phase Systems ◽  
Relative Permeability Curves

Abstract Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water-wet rocks for both two- and three-phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. Introduction Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. and by Osaba et al. Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems. Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by Snell as II, ID, DI and DD. I refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis published three-phase curves for unconsolidated sand, and Snell reported results of several English authors for both drainage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et al. for increasing water and gas saturations (ID). Corey et al. reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean and Sarem calculated three- phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three - phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (II) are those of Naar and Wygal. These curves are based on at theoretical study of the model of Wyllie and Gardner as modified by Naar and Henderson. Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids. Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term. SPEJ P. 149ˆ

SOIL HYDRAULIC PROPERTIES DETERMINED WITH WATER AND WITH A HYDROCARBON LIQUID

1970 ◽  
Vol 50 (1) ◽  
pp. 79-84 ◽  
Author(s):  
J. C. VAN SCHAIK
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Relative Permeability ◽  
Hydraulic Properties ◽  
Direct Transfer ◽  
Soil Hydraulic Properties ◽  
Distribution Index ◽  
Wetting Fluid ◽  
Hydrocarbon Oil

Hydraulic properties of three soils were compared using either water or a hydrocarbon oil as the wetting fluid. Equations relating various properties for oil were also valid for water when appropriate values for water were used. As differences in saturated permeability were not consistent, a direct transfer of data obtained with oil to those of water was not possible. The relative permeability for both fluids showed better agreement because bubbling pressures were similar. However, the pore-size distribution index for water was somewhat lower than that for oil.

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