Three-Phase Oil Relative Permeability Models

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract Two variations of an indirect technique for predicting three-phase oil relative permeability are described in this paper. permeability are described in this paper. Relative permeabilities and the dependence of waterflood residual oil saturation on trapped gas saturations predicted by these two models are compared with the three-phase experimental data available in the literature. Both models provide acceptable schemes for interpolating in the three-phase region, and qualitatively match the curvature of isoperms generated in the more carefully conducted (and previously published) threephase experiments. Limitations of each model are described, including the need for establishing derivative constraints to prevent calculation of relative permeabilities greater than unity. Guidelines are also presented for determining which model should be used in specific applications. Introduction Thorough analysis of a displacement process in which three-phase flow predominates process in which three-phase flow predominates (viz. steam drive and alternate gas/water) requires three-phase relative permeability data. The effort involved in determining these data experimentally suggests that indirect methods should be investigated. The difficulty in direct experimental work lies mainly in determination of saturation distributions along the length of the core. Electrical resistance circuits and either gamma-ray or x-ray absorption techniques are required to measure two of the three saturations in a three-phase system. Only nine experiments concerning three-phase relative permeability have been found in the literature. As an alternative to the direct methods, Stone has suggested that more easily measured two-phase data can be used to predict relative permeability to both the predict relative permeability to both the wetting and nonwetting fluids in three-phase flow. Then an indirect approach involving a technique which uses two sets of two-phase data-water/oil and gas/liquid - can be used to predict the relative permeability of the predict the relative permeability of the intermediate wettability phase. THE TWO RELATIVE PERMEABILITY MODELS Two variations of the indirect technique are described here. The first is a three-phase oil relative permeability expression developed by Hirasaki. This is a modification of a model originally proposed by Stone in 1970. The second model was presented in a paper by Stone during 1973, as a revision paper by Stone during 1973, as a revision of his first technique. Model I It has been observed experimentally in water-wet systems that the water relative permeability is approximately only a function of permeability is approximately only a function of the water saturation, and that the gas relative permeability is approximately only a function of permeability is approximately only a function of the gas saturation.

Comparison of the three-phase oil relative permeability models

“…Manjnath and Honarpour [20] have also presented a review of experimental and mathematical methods to predict three-phase oil relative permeabilities. In their review paper, they have discussed three-phase relative permeability models proposed by Corey et al [8], Naar and Wygal [24], Land [18], Stone [33,34], normalized Stone's Model II by Dietrich and Bonder [12] and by Nolen [11]. However, they compared only Corey's equation against Donaldson and Dean's three-phase data [13].…”

Novel Three-Phase Compositional Relative Permeability and Three-Phase Hysteresis Models

“…We tested the proposed model with the relative permeability data of Donaldson (1966), Oak (1990Oak ( , 1991, Maini et al (1990), andBaker (1993). In general, the UTKR3P model captures the relative permeability trends for water-and oil-wet rocks even in saturation range where phase relative permeability is a function of its own saturation.…”

Mapping of Reservoir Properties and Facies Through Integration of Static and Dynamic Data

“…This result, however, is simply a peculiarity of Stone's Model II. For example, if one used the Dietrich and Bonder (1976) modification of Stone's model, then it is possible to obtain identical effective permeabilities under three-phase flow conditions for two different absolute permeability fields. The Dietrich-Bonder model, however, has other disadvantages; see Aziz and Settari (1979).…”