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Chapter 17: Subsurface Flow Measurements
rate through the conductive medium (i.e., pipe or other conveyance) few accurate,
total flow rate methods that do not impede the flow have been devised. It is usually
necessary to balance the need for accuracy with the need for unimpeded flow, as
well as the need for reasonable cost, and the technology practical for the desired flow
range.
Sometimes an approximate flow rate measurement is all that is needed for subsur-
face systems. A simple total flow rate measurement can be made in many gas flow
systems using a lightweight plastic (or similar) bag of known volume and a timer.
The flimsy bag is compressed then attached to the flow system and filled until the bag
begins to present significant backpressure to the flow system. The time to fill the bag to
the measured volume is a direct measure of the flow rate of the system. This method
has obvious limitations and sources of error (e.g., accurate volume measurement,
backpressure significance, leak-free attachment to the flow system, etc.) however the
accuracy and precision of the method may be acceptable for specific applications.
This method is analogous to the “calibrated bucket” method often used in the field
to verify liquid flow meters or as the primary measurement technique. Obviously
this method has many disadvantages with respect to accuracy, time resolution, and
repeated monitoring applications; however, it is often accurate enough and simple
to apply for first order and scoping measurements. More sophisticated total flow
measurements generally rely on physical displacement or flow narrowing/changing
devices to make their measurements.
If a total flow measurement is not possible, methods to infer the total flow in a
system are used. Techniques that measure the flow at very small sampling points in
the flow profile are selected to minimize the effect of the measurement on the system.
Many point measurements are made in a particular plane in the flow field and these
measurements are used to calculate the total flow through the system (Pesarini et al.,
2002). Pitot tubes and thermal mass flow measurements are often used for this method.
The behavior and characteristics of the flowing fluid may also determine the best
choice for a flowmeter. Under a uniform force, an ideal frictionless fluid (one with
viscosity = 0) will move through a conduit as a uniform planar front. The movement
of real fluids deviates from the ideal planar front, however, because they are affected
by internal friction (viscosity > 0). At lower velocities, fluids move in layers or
laminae as they slide past the conveying structure (which is at rest with respect to the
moving fluid), and other fluid layers subsequently affected by the frictional forces.
Although gases generally have much lower viscosity than liquids they still are affected
by these frictional forces and exhibit a non-uniform velocity profile perpendicular to
the vector of motion. Poiseuille’s law is an expression that describes the total flow
rate of a viscous fluid traveling in laminae through a cylindrical conduit that accounts
for the non-uniform velocity of the different fluid laminae.
The Reynolds number of a fluid moving in a physical structure provides a descrip-
tion of the type of flow that is occurring in the system. The two main types of
flow are laminar, which occurs at lower flow velocities and is identified as a more
homogeneous movement of packets of fluid in an ordered procession, and turbulent
flow signified by more chaotic patterns where the individual packets of fluid do not