Page 448 - Petrophysics

41 6 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

throughout the reservoir becomes a linear function of time and 6p/6t =
constant. When this flow regime occurs, it is referred to as pseudosteady
state or semi-steady state.
Natural reservoir systems do not ordinarily conform to any simple
geometrical shape. The two most practical geometries are the linear flow
system and the radial flow system. In the linear system, the flow occurs
through a constant cross-sectional area and the flow lines are parallel. In
the radial system, the flow occurs between two concentric cylindrical
surfaces, the well being the inner cylinder and the reservoir boundary
the outer cylinder. Another flow system of interest is the spherical
geometry. Finally, reservoir fluids are classed either as incompressible
or slightly compressible liquid, or gas. A compressible liquid is defined
as one whose change of volume is small with respect to the change of
pressure.

DARCY’S LAW

To express the quantity of fluid that will flow through a porous rock
system of specified geometry and dimensions, such as the one shown in
Figure 7.1, it is necessary to integrate Darcy’s law over the boundaries of
the porous system. This law, in its simple differential form, is:

where: v = apparent fluid flowing velocity, cmJs.
k = permeability of the porous rock, darcy.
p = viscosity of the flowing fluid, centipoise.
dP
- = pressure gradient in the direction of flow, atm/cm.
dx
x = distance in the direction of flow, always positive, cm.

This one-dimensional empirical relationship was developed by French
engineer Henry Darcy in 1856 while he was investigating the flow of

Pin pout

-L-
Figure 7.1. Typical linearpow system in a core sample.