In this study, we conducted experiments to measure the pressure drop across different points in a porous medium while injecting surfactant solutions to create foam. We tested two different surfactant concentrations and two different permeabilities. The pressure drop was used to estimate the average bubble density, which in turn was used to calculate part of the source term. We used a model with four equations (pressure, water saturation, bubble density, and surfactant transport-adsorption) to describe the pressure drop during the experiments. The viscosity coefficient in the equation was estimated based on the surfactant concentration. The difference between the simulated and experimental pressure drop was within 10%, indicating that our estimates were accurate. We also looked at the individual contributions of accumulation, convection, and dispersion to the source term. By considering water saturation and the flowing fraction of foam, we were able to calculate the rate of change of bubble density during the transient state.
Foam can be used to improve the effectiveness of water or gas for displacing fluids in a reservoir. This is because foam can decrease the mobility of the fluid being displaced. To properly model how foam behaves in a porous medium, experiments are used to validate the models. These experiments involve injecting a gas and a surfactant solution together, creating foam. The results of the experiment, such as the saturation and surfactant concentration profiles, the amount of water in the effluent, and the pressure drop, can be used to validate the models. Most modeling efforts have focused on situations where the concentration of surfactant is much higher than the critical micelle concentration (CMC). However, there are some experimental data available for concentrations close to the CMC. When using surfactants with concentrations close to the CMC, the pressure drop may take some time to stabilize. Models that consider the development of foam bubbles over time are needed to understand these delayed pressure drops.
The bubble population model combines the density of bubbles in multiphase flow equations to understand the movement of foam in porous media. These equations include the water equation, an equation for foam as a gas with increased viscosity, a bubble density equation, and sometimes a surfactant transport equation. The IMPES method is used to solve these equations. The bubble density is assumed to be the same in both flowing and non-flowing conditions. The flow of foam in porous media with the injection of gas and surfactant water can be seen as a flow of two phases, described by Darcy’s law. The viscosity of foam is not constant and is affected by the density of bubbles and the movement of the bubbles in the pores. The resistance to foam flow is due to the lamellae separating the bubbles from the pore walls and the surface tension gradient across the moving bubbles. The bubble density and local interstitial velocity are used to calculate the apparent viscosity of the foam.
The bubble density equation is used to describe the number of bubbles in a foam. It includes a term, known as the bubble generation-coalescence function, which represents the difference between the rates at which bubbles are created and merged together. This function is often based on assumptions about how bubbles are formed and merged, such as through capillary snap-off or mass transfer between bubbles. However, it can be difficult to accurately measure the bubble generation-coalescence function in experiments, especially when the saturation and flowing fraction of the foam are unknown. In this study, the authors propose a method for approximating the bubble generation-coalescence function from experimental pressure drop data, without prior knowledge of the foam’s saturation and flowing fraction. They do this by estimating the bubble density from the pressure drop data and assuming that the source term (bubble generation-coalescence function) is the derivative of the bubble density with respect to time. Once the bubble density has been estimated, the authors can use it to calculate the flowing fraction of foam and the water saturation. They then compare the simulated pressure drop history to the experimental pressure drop data to refine their estimate of the bubble generation-coalescence function.
We conducted experiments to study the flow of foam made from a mixture of AOS and N2 at two different concentrations. One concentration was 0.0375% in double distilled water and the other was 0.075% in brine. These experiments were conducted in order to compare the results with experiments using nanoparticles. The optimal stability for the particles was found at pH 3, so we used pH 3 for the experiments using double distilled water. We also conducted a single-phase adsorption test using the same conditions as the foam flow experiments to determine the adsorption parameters. The main results of the experiments were the pressure drop and the time required to reach a stable value. We used a model to analyze the results, considering the downward vertical flow of the foam. The model included equations for the flow of water and foam, the bubble density, and the adsorption and transport of surfactants. We used a commercial software program to implement the model and simulated the results in terms of the water saturation and flowing fraction of the foam. We also analyzed the importance of different terms in the bubble density equation and compared the experimental and simulated pressure drop results. Overall, we reached some conclusions about the procedure used and the foam generation-coalescence function.