Foam Flow Experiments. I. Estimation of the Bubble generation-Coalescence Function

Gas injection leads to foam formation in porous media in the presence of surfactant solutions, which is used for flow diversion and enhanced oil recovery. We present here laboratory experiments of co-injecting nitrogen and sodium C14-16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{14-16}$$\end{document} alpha olefin sulfonate with two concentrations: 20×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$20 \times $$\end{document} the critical micelle concentration (CMC) in an unconsolidated sandpack of 1860 Darcy and at the CMC for a Bentheimer sandstone of 3 Darcy. The steady state profile for the unconsolidated sandpack is achieved after 1.3 pore volumes, whereas for Bentheimer sandstone, steady state is obtained after injection of 12–15 pore volume. A model that leads to four equations, viz., a pressure equation, a water saturation equation, a bubble density equation and a surfactant transport–adsorption equation, is used to explain the experimental pressure drop. It is asserted that the experimental pressure drop across the measurement points can be used to obtain a first estimate of the average bubble density, which can be further used to obtain part of the source term in the bubble density equation. If we consider flowing fraction of foam, the rate of change of bubble density during transient state can be equated to the bubble density generation-coalescence function plus the terms accounted for bubble transport by convection and diffusion divided by porosity and saturation.