Page 141 - Chemical Process Equipment - Selection and Design

6.8. LIQUID-GAS FLOW IN PIPELINES
particular flow pattern is subjective and all the pertinent variables 64, 193-200 (1942)] is popular:
apparently have not yet been correlated, boundaries between
+
regions are fuzzy, as in (d). l/kwo-phase = x/k - x)/@L. (6.97)
I is to be: expected that the kind of phase distribution will
affect such phenomena as heat transfer and friction in pipelines. For The specific volumes are weight fraction additive,
the most part, however, these operations have not been correlated
yet with flow patterns, and the majority of calculations of two-phase Vtwo-phase = XVG + (1 - X)VL (6.98)
flow are made without reference to them. A partial exception is
annular flow which tends to exist at high gas flow rates and has been so that
studied in some detail from the point of view of friction and heat
transfer. l/Ptwo-phase = x/P~ +
The usual procedure for evaluating two-phase pressure drop is - x)/pL, (6.99)
to combine pressure drops of individual phases in some way. To this
end, multiplieris $i are defined by where x is the weight fraction of the gas. Pressure drops by this
method tend to be underestimated, but are more nearly accurate at
higher pressures and higher flow rates.
(6.94) With the Blasius equation (6.96), the friction factor and the
pressure gradient become, with this model,
In the following table, subscript L refers to the liquid phase, G to
the gas phase, and LO to the total flow but with properties of the . f = 0 32 x 1 -x 0.25

liquid phase; x is the weight fraction of the vapor phase. (DG)0.25 (E + ’ (6.100)
Subscript e AP/L +2 (6,101)
G DGx~PG fGG2x2/2gcDpG (APIL)I(APIL),
L DG(1 - X)i’p, CG2(1 - X)~/~S,DPL (AP/L)/(Af/L),
LO DGIy, iFLo~2/2&DP,L (APIL)I(APIL),, A particularly simple expression is obtained for the multiplier in
terms of the Blasius equation:
In view of the many other uncertainties of two phase flow
correlations, the friction factors are adequately represented by
46.102)
e < 2000, Poiseuille equation, (6.95)
.0.32/Re0-”, We > 2000, Blasius equation. (6.96)
Some values of +io from this equation for steam are
OGENEOUS MODEL x P = 0.689 bar P = 10.3 bar
The simplest ?way to compute line friction in two-phase flow is to 0.01 3.40 1.10
adopt some kiinds of mean properties of the mixtures and to employ 0.10 12.18 1.95
the single phlase friction equation. The main problem is the 0.50 80.2 4.36
assignment of a two-phase viscosity. Of the number of definitions
that have been proposed, thzt of McAdams et al. [Trans. ASME High values of multipliers are not uncommon.

EXAMPLE 5.13 ’ -0.0369 + 5.52W4) + 0.0272
Isothermad Flow of a Nonideal Gas = [(V - 0.00169)2 V3
The case of Example 6.12 will be solved with a van der Waals
equation of steam. From the CRC Handbook of Chemistry and The integration is performed with Simpson’s rule with 20
Physics (CRC Press, Boca Raton, FL, 1979), intervals. Values of V2 are assumed until one is found that makes
+ = 0. Then the pressure is found from the v dW equation:
Q = 5.464 atm(m3/kg mol)’ = 1703.7 Pa(m3/kg)’,
b = 0.03049 m3/kg mol = 0.001692 m3/kg, P- 2.276(105) -- 1703.7
RT = 831,4(493.2)/18.02 = 2.276(105) N m/kg. ’ - (V, - 0.00169) V;

Equation (6.93) becornies Two trials and, a linear interpolation are shown. The value
P2 = 18.44 bar compares with the ideal gas 17.13.
4 +
0.120 -0.0540
+ 0.0187(410.07)2(305) - 0.117 +0.0054
- 0,
2(0.0777) 0.1 173 0 18.44 bar