Modelling flow in a pressure-sensitive, heterogeneous medium

摘要: Modeling ow in a pressure-sensitive, heterogeneous medium D. W. Vasco 1 and Susan E. Minkoff 2 Berkeley Laboratory, University of California, Berkeley, California 94720 Maryland, Department Mathematics Statistics, 1000 Hilltop Circle, Baltimore, 21250 SUMMARY Using an asymptotic methodology, including expansion inverse powers ω, where ω is the frequency, we derive solution for flow with pressure dependent properties. The valid smoothly varying That is, scale length heterogeneity must be significantly larger then over which increases from it initial value to its peak value. resulting expres- sion similar form properties are not functions pressure. Both expression pseudo-phase, related ’travel time’ transient disturbance, amplitude contain modifications due dependence medium. We apply method synthetic observed variations deforming In test model one- dimensional propagation pressure-dependent Comparisons both analytic self-similar results numerical simulation indicate general agreement. Fur- thermore, able match during pulse at Coaraze Laboratory site France. Key words: fluid flow, permeability, methods, INTRODUCTION introduction volume into Earth will induce some degree deformation within geologic material compris- ing subsurface. most cases significant, or even observable, may safely ignored. How- ever, situations, such as poorly consolidated sediments, fractured media (Gale 1975, Jones Noorishad et al. 1992, Cappa 2008), large changes rates (Fatt 1958, Raghavan 1972, Rutqvist 1998), matrix impact important ways. For ex- ample, can modify porosity permeability. Also, transmission stress medium, lead non-local effects. A comprehensive approach this problem involves coupled modeling deformation. Such mod- eling complicated, making methods attractive. While utility well established (Noor- ishad 2002, 2003, 2004, Dean al.2006), solutions aid our un- derstanding factors, parameters, contributing calculated Thus, provide valuable insight, complementing existing purely nu- merical approaches. To date, studies prob- lem have been restricted relatively simple cases, ho- mogeneous do change function classic example homogeneous poroe- lastic (Booker Carter 1986, Rudnicki 1986) exhibit effects noted above (Segall 1985). Recently, semi-analytic was developed poroelastic also contained coupling diffusive Biot wave ’fast’ elastic (Vasco 2008, 2009). provides more complete satis- factory understanding deformable useful examine particular aspects problem. fact, just mentioned focused on between neglecting effective stress. paper alternative situation, neglect throughout As such, complement cited above. Allowing leads non-linear diffusion equation (Wu Pruess 2000). non- linear has used flu- ids (Barenblatt 1952), rock joints openings (Murphy 2004), tempera- ture waves saturated (Natale Salusti 1996), compaction sedimentary basins (Audet Fowler 1992) among other things (Newman 1983). diffu- studied rather extensively mathe- matical perspective (Crank Hayashi 2006), particularly case that permeability proportional raised power. instance one exact