Three-Phase Relative Permeability of Petroleum Reservoirs

Abstract

This paper presents a critical review of recent experimental and theoretical developments in the area of three-phase relative permeability along with a comparative evaluation of several models for estimating the oil relative permeability under three-phase flow conditions. Reported experimental data on three-phase relative permeability were screened for reliability and completeness and three representative data sets were selected for use in evaluation of the prediction techniques. Eight different prediction models were selected for evaluation. Each model was tested with the three selected data sets for its ability to match the experimentally determined oil relative permeability under three-phase flow conditions. It was found that none of the models predicted all of the tested data sets with high accuracy. However, there are models that give significantly more reliable predictions of three-phase oil relative permeability compared to the other models. Introduction When studying a production from an oil reservoir, an investigator can sometimes successfully limit the scope of his research on one or two flowing phases. However, there are many situations where the flow of all three phases - oil, gas and water must be considered. The water drive, steam drive, underground combustion, solution gas drive and gas cap drive often involve simultaneous flow of all three phases. Application of enhanced oil recovery techniques that utilize injection of gas or light hydrocarbon are frequently accompanied with three-phase flow. Analyzing relative permeabilities and hysteresis effects in a flowing oil-water-gas system, numerous investigators have pointed out that gas always behaves as a non-wetting phase and oil and water could be wetting or intermediate wetting. It was also noted (Leverett 1941, Corey 1956, Saraf 1966) that the relative permeability of the wetting and non-wetting phase is primarily a function of its own saturation and relative permeability of the intermediate-wetting phase is strongly affected by the saturation history and the saturations of other two phases. Conducting three-phase flow experiments is a tedious task and only a limited number of such experiments dealing with three-phase relative permeability measurements have been reported. Most of the reservoir engineering calculations for processes involving three-phase flow are based on predictive models that attempt to estimate the three-phase relative permeability from more easily obtained two-phase oil-water, oil-gas and/or water-gas relative permeability measurements. Review of Recent Experimental Data This review focusses on the data reported in the ninties and later. Oak (1990) presented several sets of steady-state experimental data for both two-phase and three-phase relative permeabilities of water-wet Berea sandstone. Three different cores having 200 md, 800 md and 1000 md permeability were tested. X-ray absorption method was used for measurement of liquid saturations; gas saturation was calculated as complement. Eight cases of saturation history were considered. The agreement between the experimental data and the Stone's models I and II was not good. Oak suggested that the difficulty was in using the two-phase saturation history to model the much more complex three-phase one. He also pointed out that displacement of trapped oil by gas can not be neglected in a water-wet medium. The critical oil saturation needed to initiate oil flow was not always the same for the two-phase and three-phase data. He observed that the three-phase relative permeability to water was dependant only on its own saturation and the relative permeability to gas was a function of gas saturation and the saturation history. Oil relative permeability was dependent on saturation of all phases as well as on the saturation history.

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

“…It is a homogeneous reservoir and replicates the high-permeability, intermediate-wet sample (Sample 15) of Oak (1991). Eight components were used to represent light oil with the Peng-Robinson equation of state (Peng and Robinson 1976). The simulation model has two wells, an injector and a producer, which are at the opposite ends of the reservoir model.…”

“…It implies that the saturation-averaged interpolation method is a common choice in more-recent models in place of other mathematical models, such as capillary models, statistical models, and network models. Several investigators (Fayers and Matthews 1984;Delshad and Pope 1989;Baker 1988;Oak 1990Oak , 1991Hustad and Holt 1992;Skjaeveland and Kleppe 1992;Balbinski et al 1999;Pejic and Maini 2003;Spiteri et al 2008;Ahmadloo et al 2009) have identified various limitations of classical three-phase relative permeability models such as Stone I (Stone 1970) and Stone II (Stone 1973), especially for nonwater-wet rocks and/or at low oil saturation. Although the majority of three-phase relative permeability models found in Table 1 are applicable only to water-wet conditions, many oil reservoirs are not strongly water-wet and their wettability may be altered in various ways (Treiber and Owens 1972;Morrow 1990).…”

Modeling and Simulation of WAG Injection Processes - The Role of Counter-Current Flow

“…The Stone I model suggests that, in a water-wet medium, relative permeabilities of gas and water (non-wetting and wetting phases) are the same as their two-phase counterparts as observed in gas-oil and oil-water displacements, respectively. Relative permeability of the intermediate wetting phase, oil in this case, depends on the phaseconfiguration within the pore space, which in turn depends on both water and gas saturations (Pejic and Maini, 2003). The modified Stone I model is defined by the following set of equations.…”

The Role of Counter-Current Flow in Simultaneous Water and Gas Injection Processes

“…Relative permeability of the intermediate wetting phase, oil, depends on the phase configuration within the pore space, which in turn depends on both water and gas saturations (Pejic and Maini, 2003 where is the three-phase residual oil saturation, and is the maximum oil relative permeability in a two-phase oilwater displacement process.…”