FINITE ELEMENT MODELS Sample Clauses

FINITE ELEMENT MODELS. The laws that describe the physics of a system are usually expressed in the form of partial differential equations (PDEs) that are differential equations containing more than one variable. In most of the cases, they are non-linear equations, and they cannot be solved analytically. However, it is possible to approximate these non-linear equations with the linear equation by applying a discretization of the domain in finite element. A typical discretization of a system, called mesh, consists of defining components called elements that are connected in points called nodes. The solution of the complete system corresponds to the assembly of each small domain. Finite element method (FEM) is used to compute the solution of the complete system by applying the linear approximation of the equations in the small elements of the domain. In this way, it is possible to describe the behaviour of an engineering system modelling physics such as heat transfer, mass transport, fluid flow, kinetics of the reactions. The convergence and accuracy of the solution depend on the hypothesis done in the model and numbers of element used in the domain. Computing a very fine mesh can be difficult for high computational time. For this reason, it is usually applied to a refinement of the mesh. After computing the first solution, it is created a denser mesh in the zone of the domain with higher error. FEM method can be applied to model the fixed bed reactor and study the performance of the catalyst. The typical modelling approaches widely used for an accurate description of the reactor are shown in (Figure 25). The main difference is in the types of assumption used in pseudo-homogeneous model and heterogeneous model. The pseudo-homogeneous model is applied if the heat and mass transfer limitations between the fluid phase and the solid phase are negligible. Thus, it is assumed that the bulk fluid and the surface of the catalyst are at the same temperature and the diffusion effect inside the pore of the catalyst are ignored. The heterogeneous model is more complicated because it considers heat and mass transfer limitation and it is applied when these effects carry out considerable resistance to the reaction rate which is not uniform inside the catalyst particles. Figure 25 - models commonly used for describing catalytic FBR [17] In this work, it is developed a pseudo-homogeneous model using as software COMSOL Multiphysics