TABLE OF CONTENTS The fluid flow equations that are used to describe the flow behavior in a reservoir can take many forms depending upon the combination of variables presented previously (i.e., types of flow, types of fluids, etc.). By combining the conservation of mass equation with the transport equation (Darcy s equation) and various equations of state, the necessary flow equations can be developed. Since all flow equations to be considered depend on Darcy s law, it is important to consider this transport relationship first.
The fundamental law of fluid motion in porous media is Darcy s law. The mathematical expression developed by Darcy in 1956 states that the velocity of a homogeneous fluid in a porous medium is proportional to the pressure gradient, and inversely proportional to the fluid viscosity. For a horizontal linear system, this relationship is:
v is the apparent velocity in centimeters per second and is equal to q/ A, where q is the volumetric flow rate in cubic centimeters per second and A is the total cross-sectional area of the rock in square centimeters. In other words, A includes the area of the rock material as well as the area of the pore channels. The fluid viscosity, ?, is expressed in centipoise units, and the pressure gradient, d p/d x, is in atmospheres per centimeter, taken in the same direction as v and q. The proportionality constant, k, is the permeability of...
