Page 449 - Petrophysics

LINEAR FLOW OF INCOMPRESSIBLE FLUIDS 41 7

water through sand filters for water purification [2]. The experimental
variation in this investigation is the type of sandpack, which had the
effect of changing the value of the permeability. All of the experiments
were carried out with water; therefore, the effects of fluid density
and viscosity on Equation 7.1 were not investigated [3,4]. In addition,
Darcy’s law holds only for conditions of viscous flow, i.e., the rate of
the flowing fluid is sufficiently low to be directly proportional to the
potential gradient. Another requirement of this law is that the flowing
fluid must not react chemically with the porous medium. Such a reaction
can alter the permeability of the sand body as flow continues. The
sandpack in Darcy’s original experiment was always maintained in the
vertical position. Subsequent researchers repeated this experiment under
less-restrictive conditions and found that:

(1) Darcy’s law could be extended to fluids other than water,
(2) the constant of proportionality is actually the mobility ratio Up, and
(3) Darcy’s law is independent of the direction of flow in the Earth’s
gravitational field.

The gradient dp/dx is the driving force, and may be due to fluid
pressure gradients and/or hydraulic (gravitational) gradients [ 51. Gener-
ally, the hydraulic gradients are small compared with the fluid pressure
gradients, and are, therefore, negligible. In oil reservoirs with a large
expanding gas cap and considerable gravity drainage characteristics,
however, the gravitational gradients are important and must be taken
into account when analyzing reservoir performance.

LINEAR FLOW OF INCOMPRESSIBLE FLUIDS

The following assumptions are necessary to the development of the
basic equations describing linear flow of incompressible or slightly
compressible fluids through porous media:

(1) steady-state flow conditions exist;
(2) the porous rock is 100% saturated with the flowing fluid; however, a
fixed and immobile phase may be present and often is, as is the case
for oil flow in a porous rock containing irreducible water saturation,
or in the case of oil flow with an immobile gas phase of saturation
less than critical gas saturation [5];
(3) the viscosity of the flowing fluid is constant;
(4) isothermal conditions prevail;
(5) the porous rock is homogeneous and isotropic;
(6) porosity and permeability are constant, i.e., independent of pressure;