Page 134 - Chemical Process Equipment - Selection and Design

106 FLOW OF FLUIDS
PIPELINE DESIGN
The sizing of pipelines for non-Newtonian liquids may be based on
scaleup of tests made under the conditions at which the proposed
line is to operate, without prior determination and correlation of
rheological properties. A body of theory and some correlations are
available for design with four mathematical models:
T, = Kj.", power law, (6.45)
z, = zy + pBp, Bingham plastic, (6.46)
zw = zy + Kj", Generalized Bingham or
yield-power law, (6.47)
z, = K'(8vJD)"' Generalized power law
(Metzner-Reed) (AZChE J. 1,434,1955).
I
0
W (6.48)
c
cn PArnbino Crude Oil,
Temperature 44.5'F In the last model, the parameters may be somewhat dependent on
the shear stress and deformation rate, and should be determined at
I , I I l n l d n I , I I
magnitudes of those quantities near those to be applied in the plant.
The shear stress z, at the wall is independent of the model and
is derived from pressure drop measurements as
z, = DAP/4L. (6.49)
Friction Factor. In rheological literature the friction factor is
defined as

DAP (6.50)
= 4LpV2/2gc
(6.51)

This value is one-fourth of the friction factor used in Section 6.3.
For the sake of consistency with the literature, the definition of Eq.
(6.50) will be used with non-Newtonian fluids in the present section.
Table 6.2 lists theoretical equations for friction factors in
laminar flows. In terms of the generalized power law, Eq. (6.48),

0.0004 I I I111111 I I I111111 I I illllll I I IIII
IO 100 1000 l0,OOO
(b) Length, L, ff
(6.52)
Figure 6.4. Shear and pipeline flow data of a thixotropic Pembina
crude oil at 44.5"F. (a) Rheograms relating shear stress and rate of By analogy with the Newtonian relation, f = 16/Re, the
shear at several constant durations of shear (Ritfer and Govier,
Can. J. Chem. Eng. 48,505 (1970)]. (b) Decay of pressure gradient denominator of Eq. (6.52) is designated as a modified Reynolds
of the fluid flowing from a condition of rest at 15,000 barrelslday in number,
a 12 in. line [Riffer and Batycky, SPE Journal 7, 369 (1967)].
Re, = D"'V2-"' p /g, K '8'"'. (6.53)
and that of relaxation time (sec) is
The subscript MR designates Metzner-Reed, who introduced this
Water 3 x lo-= form.
Castor oil 2 x
Copal varnish 2x10 Scale Up. The design of pipelines and other equipment for
Colophony (at 55°C) 5X 10 handling non-Newtonian fluids may be based on model equations
Gelatine, 0.5% solution 8 x 10'
Colophony (at 12°C) 4X lo6 with parameters obtained on the basis of measurements with
Ideal solids m viscometers or with pipelines of substantial diameter. The shapes of
plots of z,,, against j. or WID may reveal the appropriate model.
Examples thus appear to exist of gradations between the properties Examples 6.9 and 6.10 are such analyses.
of normally recognized true liquids (water) and true solids. In critical cases of substantial economic importance, it may be
Elastic properties usually have a negligible effect on resistance advisable to perform flow tests-Q against AP-in lines of
to flow in straight pipes, but examples have been noted that the moderate size and to scale up the results to plant size, without
resistances of fittings may be as much as 10 times as great for necessarily trying to fit one of the accepted models. Among the
viscoelastic liquids as for Newtonian ones. effects that may not be accounted for by such models are time