Fluid flow through branched channels in a fracture plane in an enhanced geothermal system

Abstract

<jats:p>Fluid flow in Enhanced Geothermal Systems (EGS) occurs primarily through fractures which are embedded in an almost impermeable granite rock matrix. Experimental and numerical studies have shown that flow in fractures exhibits channeling effects; this means that flow occurs along preferred pathways, most likely the paths of least resistance. There has been evidence to date of dendritic and star-like patterns in granite and as a result, authors have used fractal theory in order to address flow phenomena in these patterns. The application of Bejan’s Constructal theory to this problem however has never been attempted. We base our model on dendritic patterns of flow paths in heterogeneous rock fractures. Flow enters into a main channel which bifurcates into daughter channels of unique dimensions of length and height. We study these parameters for consecutive channels in the flow path and show that for minimization of resistance to flow within a plane using area and volume constraints for a T-shaped channel, a simple relationship holds for the ratios of lengths and heights which will enable maximum flow for this configuration.</jats:p>