An Improved Method for Estimating Oil Reserves in Oil/Water Transition Zones

The amount of recoverable oil in an oil-water transition zone depends on the distribution of oil saturation as a function of depth, and the relationship between initial oil saturation in the transition zone (Soitz) and residual oil saturation in the transition zone (Sortz). Traditionally, it is assumed that Sortz is the same as the residual oil saturation in the oil column (Sor) above the transition zone. However, data in the literature show that residual oil saturation depends on initial oil saturation. So, residual oil saturation in the transition zone (Sortz) should be a function of initial oil saturation in the transition zone (Soitz). The relationship between Sortz and Soitz is referred to as a trapped oil relationship. The purpose of this paper is to show recent experimental corroboration of the trapped oil relationship and to demonstrate the impact of the trapped oil relationship on reserves determination in oilwater transition zones. Details of the experimental work may be found in a companion paper (Christiansen et al., 1999), which discusses in depth the appropriate rock-fluid properties for characterizing transition zones. In this paper, the effect of the trapped oil relationship on reserves determination is shown in two ways: first, with an analytical model that shows the maximum possible incremental benefit of including the trapped oil relationship; and second, with an extended black oil simulation that incorporates the effects of relative permeabilities on reserves determination. Introduction Transition zones may vary in thickness from a few feet to a few thousand feet (Bradley, 1992). The size of the transition zone affects estimates of original hydrocarbons in place and the distribution of recoverable reserves. It is important to accurately characterize transition zones because of their potentially large effect on reservoir economics. In one example from the literature (Heymans, 1997), a 90 foot thick transition zone, in an edge-water drive reservoir with nearly a 1000 foot oil column, contributed more than 30% of the estimated original oil in place. Rigorous volumetrics and material balance calculations were within 2% agreement. In other words, the volume of hydrocarbons in a seemingly relatively thin transition zone that formed a ring around the example reservoir with edge-water drive had a significant consequence on original oil in place estimates. An oil-water transition zone is generally described from the perspective of oil recovery as a zone in which both oil and water are produced. The top of a transition zone in a reservoir is the elevation at which water-free oil can be produced. It corresponds to the depth at which mobile water first appears. The bottom of an oil-water transition zone is the shallowest depth at which oil-free water is produced. Initial oil saturation at this depth is equal to residual oil saturation. Additional oil is not recoverable from waterflooding once the residual oil saturation to waterflooding is attained. For a more detailed discussion with graphs of conventional methods used for determining hydrocarbon recovery from a transition zone, see Christiansen et al. (1999). Data in the literature show that residual oil saturation in the transition zone (Sortz) is a function of initial oil saturation in the transition zone (Soitz). The relationship between Sortz and Soitz is referred to as a trapped oil relationship and is illustrated in Figure 1 using a trapped gas relationship from Pickell et al. (1966). (See also Schowalter and Hess, 1982.) Trapped oil relationships can be measured in experiments with partial saturation of a sample with oil. However, such measurements of trapped oil saturations and the associated oil-water relative permeabilities are rarely reported in the literature. Hysteresis effects provide a significant obstacle to measurement of trapped oil relationships. An experiment must be carefully designed and operated to avoid flow reversals that would complicate the interpretation of the results. Such reversals could be detected if saturation profiles in a rock sample are monitored throughout any experiments. These difficulties are considered further by Christiansen et al. (1999). In this paper, we briefly describe the procedure and the results of recent experiments for measuring the trapped oil relationship for water-wet media as reported in detail by Christiansen et al.(1999). (Results for oil-wet media are not yet available.) Then, the effect of the trapped oil relationship on estimates of oil reserves is demonstrated using a simple analytical method and a numerical simulator. The analytical method provides a formula for estimating oil reserves in an oil-water transition zone. A numerical simulation example illustrates a relatively arduous procedure for including the trapped oil relationship in existing simulators. Experimental Measurement of the Trapped Oil Relationship In the discussion below, first, results and methods of previous experimental efforts are reviewed. Then, the apparatus and procedures for our tests are briefly described. Finally, a summary of results of the tests is given. For details of the experiments, see Christiansen et al. (1999). Previous Measurements. Although there are many papers on trapped gas relationships, the literature on measurements of trapped oil relationships is sparse (see Morrow, 1987). Indeed, the only paper that reports measurements of trapped oil relationships is that of Pickell et al. (1966). Pickell et al. used porous-plate methods to saturate their sandstone samples to initial oil saturation; then, the samples were waterflooded to residual oil saturation. This method is satisfactory, yet one should be concerned that the initial saturation procedure could impart a combination of drainage and imbibition cycles on portions of the rock sample. As mentioned above, local flow reversals within the sample complicate the interpretation of the experiment. Measurements of trapped gas saturation have been reported by many (Pickell et al., 1966; Land, 1968; Keelan and Pugh, 1973; Yuan and Swanson, 1989). The trapped gas relationship could be a good estimate of the trapped oil relationship for a rock sample, particularly if the sample is strongly water wet. Land (1968) shows six trapped gas relationships, taken from previous literature. These relationships were obtained from displacements with oil, water, and gas through rock samples. Pickell et al. (1966) demonstrated a simpler method for measuring the trapped gas relationship, involving evaporation and re-saturation with a hydrocarbon liquid. Several groups have used that method since. Again, flow reversals may complicate interpretation of these experiments. One can easily imagine that evaporation could dry completely the external portion of the rock, while the internal rock is still saturated with liquid. So, careful experimental design and operation is needed to obtain trapped gas relationships. y = -0.509x + 0.8302x R = 0.9983 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 Initial Oil Saturation Fi na l O il Sa tu ra tio n Pickell et al. Poly. (Pickell et al.) Figure 1. A trapped oil relationship, as estimated from a trapped gas relationship in Figure 7 of Pickell et al. (1966).