Foam is used worldwide to improve acid placement in matrix acid treatments and redirect gas flow in improved oil recovery. Gas trapping is a major factor in foam processes: it affects foam mobility and controls diversion of liquids such as acid injected after foam. Most previous studies of gas trapping have relied on fitting effluent gas tracer profiles to a one-dimensional (1D) model for transport of tracer in the presence of trapped gas, including mass transfer between flowing and trapped gas. We present new experiments where X-ray computed tomography (CT) directly determines the gas tracer distribution in situ. The key is using a gas-phase tracer (Xe) visible in CT. The CT images show clearly that the standard 1D model used to interpret tracer effluent profiles is incorrect in its assumptions. For the first time here we compare the in situ tracer distribution from CT images to the trapped-gas saturation estimated from fitting the effluent tracer profile to the 1D model, augmented here for the effect of pressure variation along the core. The effluent profile is determined indirectly from the CT images in two ways: by imaging the tracer concentration in the flow line downstream of the core, and using a mass balance on tracer in the core. Estimates of trapped-gas fraction using the 1D model vary by as much as 0.2 among reasonable fits to the effluent data, and flowing gas fraction by as much as a factor of 1.5 or 2.The experiments span a range of foam qualities and injection rates in Bentheim sandstone. Model-derived estimates of trapped-gas fraction decrease with increasing gas injection rate and increase weakly with increasing liquid injection rate in our experiments. The CT images show a shift to a wider variety of fluctuating flow paths as liquid or gas injection rate increases.
Foam applications in improved oil recovery and near-wellbore treatments (e.g., matrix acidizing) have been extensively studied on both laboratory and field scales [1–5]. The success of foam in controlling gas mobility as well as blocking or diverting fluids (gas or liquid) is determined by two constituents of foam rheology: effective gas viscosity and effective yield stress. The latter property accounts for the fact that foam flow in a porous medium is often associated with a large fraction of trapped gas, which significantly reduces gas relative permeability. Attempts to represent gas mobility in foam mechanistically [5–8] estimate that effective gas relative permeability varies with the flowing-gas fraction in foam raised to a power of between 1 and 3, depending on the model. A flowing gas fraction of 0.1 then reduces gas mobility by a power of between 10 and 1000. Thus characterization of the gas-trapping process is crucial for understanding foam rheology. This has been a challenging task.
Injection of gas-phase tracers with the foam and measurement of tracer concentration in the effluent have been used to estimate trapped-gas fraction during steady-state foam flow in porous media. Previous studies using this technique have employed different gas tracers and methods of interpretation, always with nitrogen as the main constituent of the foam. Friedmann et al.  used krypton gas as a tracer to estimate the trapped-gas fraction during steady-state flow of 95%-quality foam in a vertically mounted Berea sandstone core (30 cm long and 5 cm diameter). The trapped-gas fraction was estimated as the ratio of the times at which effluent tracer concentration was 10% of the injected tracer concentration in two cases: co-injection of gas and surfactant solution, and co-injection of gas and brine without surfactant and at the same gas volume fraction. The authors state that effect of mechanical dispersion was the rationale for the use of 10% (instead of 50%) tracer concentration in the effluent. Using brine-gas flow as a reference in the calculation assumes that water saturation is the same in brine-gas flow as in foam flow, a dubious assumption. In fact, the breakthrough time in pore volumes PV of 10% of injected tracer concentration gives a good estimate of the saturation of flowing gas in foam under certain conditions, as described below. The authors concluded that 85% of the gas in the pore space was trapped during foam injection, a value which increased weakly with superficial gas velocity in the range 25–130 m/day. The authors attributed the asymmetric shape of the effluent tracer profiles to diffusion of tracer into trapped gas.