Numerical methods

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Numerical methods

  1. 1. MATHEMATICALMODELS<br />Lizeth Paola Barrero Riaño<br />PetroleumEnginnering<br />Industrial University of Santander<br />2010<br />
  2. 2. Definition<br /> A mathematical model can be defined broadly, as a formulation or an equation that expresses the essential characteristics of a physical system or process in mathematical terms. Its variables are obtained by studying the physical laws that are involved in the process.<br />
  3. 3. Characteristics<br />
  4. 4. Components<br />Overall, the model can be represented by the functional relationship of the form:<br />Dependent = f (independent variables, parameters, forcefunctions )<br />variables<br />
  5. 5. Darcy’s law<br /> Darcy's Law is a generalized relationship for flow in porous media. It shows the volumetric flow rate is a function of the flow area, elevation, fluid pressure and a proportionality constant. It may be stated in several different forms depending on the flow conditions..<br />
  6. 6. One-Dimensional Flow<br />Where:<br />Q = Volumetric flow rate (m3/s or ft3/s),<br />A = Flow area perpendicular to L (m2 or ft2),<br />K = Hydraulic conductivity (m/s or ft/s),<br />l = Flow path length (m or ft),<br />h = Hydraulic head (m or ft), and<br />D = Denotes the change in h over the path L.<br />
  7. 7. Thehydraulic head at a specificpoint, histhesum of thepressure head and theelevation, or<br />h = (p/r g + z) Normal SI form of the equation__<br />h = (p/g + z)Usual form used with English units<br />Where:<br />p = waterpressure (N/m2, lb/ft2),r = waterdensity (kg/m3),g = waterspecificweight (lb/ft3),g = acceleration of gravity (m/s2or ft/s2), andz = elevation (m or ft).<br />
  8. 8. Bibliography<br />CHAPRA, Steven. Métodos números para ingenieros. Thirdedition. McGraw-Hill Editorial. 2000<br />Article: Conceptos básicos de modelación matemática y simulación computacional de sistemas biológicos una herramienta útil para la docencia y la investigación. Authors: Alejandro Pelaez and Sergio Mejia. CES Odontología Magazine Vol. 3 No 1.2000<br />http://bioen.okstate.edu/Darcy/LaLoi/basics.htm<br />

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