Chemical tracers flowing with oil and brine in a reservoir follow a characteristic oil saturation under certain conditions. The theory of tracer movement is combined with the well-known Buckley-Leverett theory of two-phase flow to establish these conditions.
Two potential applications of this result are described. The first, in laboratory core floods, provides a means of detecting and correcting for provides a means of detecting and correcting for permeability stratification in non-homogeneous samples. permeability stratification in non-homogeneous samples. The second application is an extension of the single-well chemical tracer test for measuring residual oil saturation. Using multiple tracers, the new method gives points on the fractional flow vs. saturation function. Water-wet and oil-film systems are used as examples to show the different types of fractional flow functions which can be measured near residual oil saturation.
The standard mathematical formulations of two-phase flow in porous media require a functional relationship between fractional flow of one phase and its saturation. Buckley and Leverett revealed how this fractional flow function completely determines one-dimensional incompressible flows with negligible capillary effects. Even in more complex situations when capillarity and compressibility are included, production behavior still depends strongly on how fractional production behavior still depends strongly on how fractional flow varies with saturation. The region near residual oil saturation is particularly important.
This paper considers methods using chemical tracers to determine fractional flow vs. saturation in this critical region. The work is basically theoretical, although the important results have been confirmed by computer simulations. Theory leads to an extension of the single-well tracer method for determining residual oil saturation in-situ, which has been used extensively in the field. Examples are given to show the importance of tracers in both laboratory and field experiments.
The computer-simulated tests require as input the relative permeability functions for the two phases and a viscosity ratio. Two rather different types of oil relative permeability curves are used in the examples. The first, typical of a water-wet system, is shown in Figure 1 along with the companion brine curve. The semi-log plot of, vs. shows a very definite approach to near 27%. The polynomial approximation of used in the computer simulation gives a non-zero value of at.
The second type of function, shown in Figure 2, is characteristic of "oil-film" or mixed-wettability systems. The approach to residual oil is much more gradual, extending over more than 20 saturation percent after decreases below 0.01. The curves in Figures 1 and 2 are hypothetical, representing composite rather than single-reservoir characteristics.
Richardson et al. reported and Salathiel later quantified the observation that East Texas Field Woodbine cores could show either type of behavior, depending on the laboratory procedure used. Extracted cores tested with refined oils and brine gave type one (water wet) curves. When equilibrated with live crude at reservoir conditions for extended periods, the same cores reverted to oil-film behavior. Oil saturations below 10% could be attained with continued flooding, in agreement with field tests in this reservoir.
It can be assumed that media with these two types of curves will behave quite differently, especially if gravity drainage is an important factor during an extended waterflood. As potential candidates for enhanced recovery projects, reservoirs of the second type may have to be rejected because of low oil saturation in the brine-accessible strata. The importance of making a positive identification beforehand is evident. Considering the difficulty of representative laboratory tests, in-situ measurements are clearly preferable.