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Where is a function of . Substituting into yields From further simplification it is shown that since where is a constant, from it is seen that the velocity profile is parabolic. The stress field is finally determined from the following: Solutions show that . The only other two non-zero components are Hence the stress on the plates is: Figure [6] : Geometry of a discrete fracture represented by COMSOL Multiphysics 4.0 2.1 Model Definition, coefficients and parameters The block of porous material illustrated by Figure 7[b] can be considered to have a 1m measurement on each side. The fracture thickness has a standard value of 0.1mm, with the fracture being more permeable than the matrix block. Ideally the walls of the block are impermeable except for the fracture edges, hence the fluid flows along the fracture path with minimum to no leakage to the matrix block. Darcy’s law governs velocities in the system from which the velocity paths (arrow heads) can be shown to be ideally perpendicular to the fluid field. Coefficient and parameters include: porosity of the matrix block , compressibility of the fluid and of the solid , permeability of the matrix block , thickness , storage coefficient and permeability of the fracture , viscosity , fluid density , inlet and outlet , pressures. Within the matrix block the fluid flow is described time-dependently (simulation period), through Darcy’s law as shown below: where the linearized storage model In the matrix block, the predefined velocity variable, , gives the Darcy velocity, which can be described as the volume flow rate per unit area of the porous material: Parallel to all faces of the block the zero flow boundary is applied where The outward-pointing normal to the boundary is given as , hence this means no flow across the boundary. (COMSOL Multiphysics 4.0 Model library) For the lower plate For the upper plate . Hence , yielding 2.0 Representation of the Physical Geometry A conceptual model can be used to simplify the understanding and prediction of physical processes occurring in a complex fractured geological system. With the use of COMSOL Multiphysics software, it provides solutions for multiphysics modeling. A clear representation of the geometry and conceptualized models of the different processes within the fractured system can be achieved using COMSOL Multiphysics 4.0. The model represented in this paper is the discrete fracture model. Fluids travel through tiny pores within the rock matrix and the fracture; furthermore, fluid exchange can occur between them. Hence with this method the fractures are represented as boundaries between adjacent matrix blocks, and are considered as an interior boundary. This model takes into account that the fractures may not be perfectly parallel to each other, hence some vertical variation or inclination is possible for the path of the fracture. A representation of such a fracture is shown below.PDF Image | CONCEPTUAL MODEL FOR GEOTHERMAL ENERGY CARIBBEAN
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