Page 447 - Petrophysics

CHAPTER 7

APPLIC~TIONS OF

s
DARCY LAW

This chapter describes the characteristics of the flow of fluids through
porous geological materials. The pores, or flow conduits, are complex,
inter-connected capillaries and channels of variable sizes as described in
previous chapters. The flow of compressible and incompressible fluids
through porous rocks is described by Darcy’s Law and its derivatives. The
simplest case of fluid flow through porous media is the linear flow of a
single-phase fluid under a constant pressure gradient, which is known as
linear steady-state flow. When two fluids are present in a porous medium,
steady-state flow occurs under a constant pressure gradient only when
the fluid staturations remain constant. If the saturations change with
respect to time (for example, if the water saturation is increasing while
the oil saturation is decreasing), the flow of fluids is characterized as
unsteady-state flow.
Steady-state and pseudosteady-state flow rate equations, based on
Darcy’s law for linear and radial flow of compressible and incompressible
fluids, can be used to predict the production performance of porous
and permeable flow systems of simple geometry. In steady-state flow
systems, the pressure and fluid velocity at every point throughout the
porous system adjust instantaneously to changes in pressure or flow rate
in any part of the system [l]. This flow condition occurs only when
the rock is 100% saturated with a fluid and the pressure of the porous
media is effectively maintained constant by either an active aquifer or
the injection of a displacing fluid, Le., fluid withdrawal from the porous
rock is exactly balanced by fluid entry across the open boundary and
6p/6t = 0. If there is no flow across the reservoir boundary and the well
is produced at a constant flow rate for a long time, the pressure decline

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