A Graphical Interpretation Technique to Evaluate Strength and Stability of Foam in Porous Media Based on Mobile-Trapped Foam Ratio

Abstract

Trapped foam saturation (Sgt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\\text{g}}}^{{\\text{t}}}$$\\end{document}), apparent viscosity (μappf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu { }_{{{\\text{app}}}}^{{\\text{f}}}$$\\end{document}), and the limiting capillary pressure of foam (Pc∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{{\\text{c}}}^{*}$$\\end{document}) are the common indices used to describe foam strength in porous media. They are linearly intercorrelated when they are obtained from a single porous medium. However, Pc∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{{\\text{c}}}^{*}$$\\end{document} is inversely correlated with Sgt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\\text{g}}}^{{\\text{t}}}$$\\end{document} and μappf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu { }_{{{\\text{app}}}}^{{\\text{f}}}$$\\end{document}, when obtained from porous media with different pore structures. This paper investigates these contradictions and presents a new insight. Here, the three indices were obtained from 12 different rock samples with multiple steady-state foam injection coreflood experiments. The pore properties of the rock samples were measured with high-resolution synchrotron X-ray microtomography 3D imaging, pore network analysis, and nuclear magnetic resonance (NMR) relaxometry. Pore aspect ratio was found to offer opposing effects on Pc∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{{\\text{c}}}^{*}$$\\end{document} relative to Sgt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\\text{g}}}^{{\\text{t}}}$$\\end{document} and μappf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu_{{{\\text{app}}}}^{{\\text{f}}}$$\\end{document}, resulting in an inverse relationship between them. Hence, Sgt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\\text{g}}}^{{\\text{t}}}$$\\end{document} or μappf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }_{{{\\text{app}}}}^{{\\text{f}}}$$\\end{document} may not be an absolute index of foam strength. Rather, mobile-trapped foam ratio (ranging from 0 to 1) appears to be a more appropriate index as it correlates linearly with Pc∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{{\\text{c}}}^{*}$$\\end{document}. A mobile-trapped foam ratio near zero indicates a very weak foam while a ratio of unity indicates a very strong foam. The ratio also correlates strongly with NMR relaxation time, making NMR log a promising tool for predicting foam strength in reservoir rocks. The graphical interpretation technique used to obtain these ratios is presented. This technique also allowed foam stability to be evaluated based on the ability of the trapped lamellae to withstand shear force during prolonged liquid flow. Based on these, different combinations of strength and stability of foam in porous media were identified namely strong and stable; strong and unstable; weak and stable, and weak and unstable foam.