The document discusses mathematical modeling and Darcy's Law. It provides definitions of a mathematical model and its variables. Darcy's Law expresses the volumetric flow rate through porous media as a function of the flow area, elevation difference, fluid pressure, and a proportionality constant. It then gives the specific equations for Darcy's Law in terms of hydraulic head and its components of pressure head and elevation.

1. Lizeth Paola Barrero Riaño Petroleum Enginnering Industrial University of Santander 2010

2. 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.

4. Overall , the model can be represented by the functional relationship of the form: Dependent = f (independent variables, parameters, force functions ) variables

5. 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..

6. Where: Q = Volumetric flow rate (m3/s or ft3/s), A = Flow area perpendicular to L (m2 or ft2), K = Hydraulic conductivity (m/s or ft/s), l = Flow path length (m or ft), h = Hydraulic head (m or ft), and D = Denotes the change in h over the path L.

7. The hydraulic head at a specific point, h is the sum of the pressure head and the elevation, or Where: p = water pressure (N/m 2 , lb/ft 2 ), r = water density (kg/m 3 ), g = water specific weight (lb/ft 3 ), g = acceleration of gravity (m/s 2 or ft/s 2 ), and z = elevation (m or ft). h = (p/ r g + z) N ormal SI form of the equation __ h = (p/ g + z) Usual form used with English units

8. CHAPRA, Steven. Métodos números para ingenieros. Third edition . McGraw-Hill Editorial. 2000 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 http://bioen.okstate.edu/Darcy/LaLoi/basics.htm