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• Conceptual representation of the structure. • Selection of relevant physical processes • Conceptual representation of the physical processes. It is essential to note when model results are being interpreted, that model is merely an approximation of nature. A hydrothermal system or reservoir can be considered as one in which the rock matrix is highly fractured, to facilitate the ease of fluid flow throughout the system. Fractured porous rock is generally divided into three components, these include: (1) a fractured network - a system of partially intersecting single fractures. Its hydraulic properties are typically characterized by the distribution of fracture size, permeability, orientation, distance and density, (2) fractured filled networks - filling material consisting of mineral deposits can be found at these fractures, and (3) the matrix blocks between the fractures – these have a spatially varying texture and porosity. The permeability contrast between fractures and matrix is important for the flow and transport processes. It is not possible to generate a model that is an exact representation of reality; however, conceptual models are developed to describe the relevant structures and physical processes of a problem. The choice of a model concept for the description of fractured media strongly depends on the scale of the problem, the geological characteristics of the area of investigation, and the purpose of the simulation. It is a necessity to have different model concepts of varying characteristics, in order to generate models of systems. According to Helmig (1993), two principal approaches are possible: 1. Provided that the scale of the investigation area is sufficiently large and that the concept of representative elementary volume (REV) is valid the model can then be described as a heterogeneous, anisotropic continuum. 2. If shear zones dominate the flow and transport processes in the fractured media, the rock matrix can be neglected and the features specifically described, using a discrete fracture network model. (Dietrich P . et al., 2005) The size of a potential REV is linked to the reliability of hydraulic properties of fractured reservoirs (Bear, 1972; De Marsily, 1986), and is fundamental to the mathematical description of fluid flow and transport in porous media. It is the smallest volume over which a measurement can be made yielding a value representative of the whole (Blocher, M. G. 2010). 1.1 Mathematical considerations of fluid flow The main concepts of the stress and strain tensor are fundamental in approaching more useful forms of the Navier-Stokes equation, continuity equation, parallel plate concepts of fractured systems, and Darcy’s law. The fluids under discussion can be assumed to have no internal forces between the fluid particles, therefore for these inviscid fluids, the equation of motion is given by Euler’ s equation where the external force , the density, pressure and rate of fluid flow are represented by , , and respectively . The associated fluids are known as Newtonian or viscous fluids. A further property of these inviscid fluids is the stress tensor , sometimes referred to as the traction or Cauchy stress tensor. A general case where S can be any surface with unit normal, , ( and are the direction cosines of ) can be considered. The traction can be represented by Hence the traction on any surface with unit normal can be expressed as a linear combination of the three basic tractions and . In addition by considering an infinitesimal part of a fluid as a cuboid the stress components can be observed: where ; is a second order tensor as shown below is called the normal component of If then the stress tensor i.e. , when then is called the shear stress component of the stress tensor i.e. . Furthermore, a useful form of Euler’s equation is shown below: Using, and, , equation (2) can be written as 1.2 Strain Tensor The strain tensor, otherwise known as the Rate of Deformation tensor, is established when the stressPDF Image | CONCEPTUAL MODEL FOR GEOTHERMAL ENERGY CARIBBEAN
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