The Well / Aquifer Model (Initial Test Results) - 12
5.0 THEORETICAL CONSIDERATIONS
5.1 General
One of the primary objectives of the initial series of tests was to
understand the qualitative and quantitative hydraulic relationships that exist between
the parameters that contribute to efficient gravel envelope water well design; these
are the well screen, gravel pack, and aquifer materials. To understand these
interrelationships requires utilizing the principles of fluid mechanics and the flow
of fluids through porous media.
One advantage of using a model of this type is that qualitative and
quantitative relationships may be developed from experimental observations alone, and
rigorous mathematical theory is not absolutely necessary. However, a certain amount
of mathematical background analysis should be done to understand the basic principles
of hydraulics which result in the physical observations observed. This is not to say
that these observations will necessarily conform to theory. On the contrary, the
purpose of this research is to find out what significant relationships might occur,
and to understand them. Mathematical analysis serves as a foundation upon which
experimental observations and resulting analysis may be laid. It also is a tool used
to confirm the validity of model analogy and test procedures.
Flow through well screens can be thought of as analogous to flow
through a series of orifices. As water enters, there is a conversion of potential
energy to kinetic energy which is necessary in order to develop the jet velocity that
drives the water through the individual screen openings. Once through the screen,
the energy developed by the jet is completely dissipated and not recoverable either
as kinetic or potential energy. The water then rotates in a direction parallel to
the axis of the screen and accelerates toward the pump intake. This acceleration
results in a change of the momentum flux. Here the flow resembles flow through a
pressurized pipe conduit.
Figure 13
In conjunction with this movement of water into and along the well
screen, a loss of hydraulic head occurs between the inside and outside of the well
screen (see Figure 13). Quantitatively, this concept for the
loss of head through a well screen can be expressed as
Where:
L = length of screen section [L]
D = screen diameter [L]
= pressure difference between inside and outside of screen [F/L2]
n = roughness coefficient of screen [Lo]
= mass density of the fluid [M/L3]
= dynamic viscosity of the fluid [FT/L2]
V = fluid velocity in well screen [L/T]
Ap = percentage open area of well screen [Lo]
Cc = coefficient of contraction of well screen openings [Lo]
By using principles of dimensional analysis and hydraulic similitude
and choosing D, , and V as the
repeating variables, equation (1) can be reduced to
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