Foam diversion is used worldwide in acid matrix-stimulation treatments. Gas trapping is a crucial component of foam mobility and diversion. Previous studies have estimated trapped-gas saturation from a fit of coreflood effluent profiles of one or more gas tracers to a one-dimensional (1D) model for tracer mass transfer. A major factor in these experiments is diffusion of tracer between flowing and trapped gas.
We previously reported x-ray computed tomography (CT) images of Xe tracer injected during steady-state foam flow, which for the first time allowed direct visualization of the location of tracer in the core throughout the experiment. Here we extend the study by analyzing the diffusion of tracer through trapped foam in 3D. Cross-sectional CT images show that in this experiment tracer did not flow through the core evenly, but mostly along the top and sides of the core. Within these regions, tracer flowed in pathways separated by distances of a few mm. Modeling suggests that tracer diffused through trapped gas between the flowing gas pathways quickly, while mass transfer between the larger region and foam in the rest of the core was slower.
A three-dimensional (3D) model of flow and diffusion of tracer can fit the effluent data from the previous experiment quantitatively and fit CT images qualitatively. Moreover, the model fits the data well with values of flowing-gas fraction that differ by a factor of 2 (0.25 and 0.51).
We test four published methods of inferring flowing-gas fraction against our synthetic data: the method of Friedmann et al., based on early breakthrough of tracer; fitting effluent data with a 1D mass-transfer model, using one or two tracers; and the method of Nguyen et al. (2007), based on a break in a plot of average tracer concentration in a given cross-section as a function of time. None of these methods were able to distinguish between the two cases with different flowing-gas fractions. Using the 1D model fitted to results for two tracers with different diffusion coefficients gave less-accurate results than a fit using the slower-diffusing tracer alone.
Applications of foam in porous media to matrix acidization (Zerhboub et al., 1994) and improved oil recovery (Kovscek and Radke, 1994; Rossen, 1996) depend on large part on trapping of gas by foam. As foam flows, gas trapping reduces gas mobility by up to 1000-fold (Kovscek and Radke, 1993); when liquid injection follows foam it is entirely responsible for the low mobility of liquid (Zhou and Rossen, 1994).
Therefore various studies have attempted to quantify the amount of gas trapped in foam during foam flow. Laboratory measurements of the fraction of gas that is trapped during foam flow usually involve injecting foam until steady-state is reached, and then substituting a tracer for some of the gas in the foam (Radke and Gillis, 1990; Friedmann et al., 1991; Nguyen, 2004; Nguyen et al., 2005, 2007; Tang and Kovscek, 2006). In an ideal tracer experiment the paths of the flowing gas do not fluctuate with time; gas moves with equal velocity along all paths; there is no exchange of tracer between flowing and trapped gas; and there is no dispersion of tracer concentration in the flowing gas. Then the pore volume of flowing gas in the core is simply the pore volumes of gas with tracer injected before tracer breaks through at the outlet. In reality, tracer in the moving bubbles in the core diffuses through foam lamellae into nearby trapped bubbles, and, eventually, through all the trapped gas in the core. No model yet allows for fluctuations in flow paths over the time of the experiment.