Page 407 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-11
where V t3 is the terminal velocity of the particle in turbulent flow (m/sec).
Note that Equations 9-3a to 9-5a and 9-3b and 9-5b were originally developed in
field units [11, 12]. To be consistent with most of the other equations in this
treatise, these equations have been re-stated in consistent English system units
(Equations 9-3a to 9-5a) and consistent SI units (Equations 9-3b to 9-5b).
The non-dimensional Reynolds number, N R, is defined as
DV
N R (9-6)
where D is the inside diameter (or hydraulic diameter) of the pressure conduit (ft),
V is average velocity of the fluid in the pressure conduit (ft/sec),
2
is the kinematic viscosity of the flowing fluid (ft /sec).
The above non-dimensional Reynolds number equation above can be used with any
consistent of units.
9.3.2 Engineering Practice
Engineering practice is to design the incompressible drilling fluid to have
minimum, but adequate, cleaning, lifting, and suspension capabilities to drill a
planned openhole interval. Modern aerated drilling operations utilize a variety of
incompressible drilling fluids. These can be fresh and salt water drilling muds, oil
based drilling muds, fresh waters, formation waters, and formation crude oils. In the
initial design of the aerated drilling fluid, the compressed gas contributions are
neglected.
The minimum volumetric flow rate of the incompressible drilling fluid will be
determined using Equations 9-1, 9-2, 9-3a,. 9-4a, 9-5a, and 9-6 above. When
assessing the cleaning, lifting, and suspension capabilities of Newtonian
incompressible drilling fluids (e.g., waters and oils), analysis should include the
possibility of laminar, transition, and turbulent flow conditions. Traditionally, non-
Newtonian incompressible drilling fluids (e.g., drilling muds) have been analyzed
assuming that no transition flow conditions exist and that turbulent flow conditions
begin at the Reynolds number of approximately 2,000.
Once the incompressible drilling fluid minimum volumetric flow rate has been
determined, an optimum volumetric flow rate of injected compressed gas can be
determined using the basic equations derived in Chapter 6.
It should be noted that for follow-on aerated drilling fluids analyses, even those
that have a non-Newtonian incompressible fluid component like a water based
drilling mud, transition flow conditions will be considered along with laminar and
turbulent flow conditions.
Illustrative Examples 9.1 describes the implementation of the basic planning
steps Nos. 1 through 8 in Section 9.1.
Illustrative Example 9.1 The borehole to be used in this illustrative example
is the basic example used in Chapter 8. The 7 7/8 inch diameter borehole is to be
drilled out of the bottom of API 8 5/8 inch diameter, 28.00 lb/ft nominal, Grade H-
40, casing set to 7,000 ft (see Figure 9-4 for well casing and openhole geometric
configuration). The drill bit to be used to drill the interval is a 7 7/8 inch diameter