Page 466 - Petrophysics

434 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

RADIAL FLOW SYSTEMS

Figure 7.6 illustrates a single producing well located in a radial reservoir
system. Flow in this system converges from the external boundary of
radius re and pressure pe to the well of radius r, and pressure p,. The
flow rate at any radius r and pressure p, according to Darcy’s law for
radial incompressible fluid flow, is:

(7.52)

In radial flow, the minus sign in Darcy’s law is no longer required as
the radius r increases (from r, to re) in the same directions as pressure.
Combining Darcy’s law, the law of conservation of mass, and
the equation of state, the following general mathematical expression
describing the flow of fluids in porous media, known as the diffusivity
equation, can be derived:

(7.53)

The ratio k/@pct is called the hydraulic diffusivity constant. Equation
7.53 is for the case of unsteady-state flow because it is time dependent.
This flow regime is beyond the scope of this book and, therefore, will
not be discussed. The solution of differential Equation 7.53, of interest to
the development of steady-state and pseudosteady-state flow equations,
is for the case of a centrally located well producing at a constant

.
Direction of Flow
.
F
.
_____,
.

P

.....................

Figure 7.6. Ideal radial flow system [47J,