Page 144 - Chemical Process Equipment - Selection and Design

116 FLOW OF FLUIDS

EXAMPLE 6.14 4(39.11)
- 157,100
Pressure Drop and Void Fraction in Liquid-Gas Flow Re = n(32.2)(0.2557)3.85(10-5) -
A mixture of an oil and hydrogen at 500psia and 200°F enters a
3 in. Schedule 40 steel line. Data are: f= 0.0202,
Oil: 140,000 Ib/hr, 51.85 Ib/cuft, 2700 cfh, viscosity 15 cP.
Hydrogen: 800 lb/hr, 0.142 lb/cuft, 5619 cfh, viscosity
2.5(10-7) Ibf sec/sqft. compared with 53.0 by the LMC method.
Voidfraction by Eq. (6.104):
The pressure drop in 1OOft of line will be found, and also the
=
voidage at the inlet condition. E~ = 1 - 1/GL = 1 - l/m 0.413,

Re,=-- 4k - 4(140,000/3600) compared with input flow condition of
nDg,,u n(0.2557)(32.2)0.15 ’
4(800/3600) E=-- QG 5619 =0.675.
Re - 7 = 137,500, Q, + QL - 5619 + 2700
- n(0.2557)(32.2)(2.5)(10- )
E
- = 0.00059. Method of Premoli [Eqs. (6.105) and (6.106)]:
D
Surface tension u = 20 dyn/cm, 0.00137 lbf/ft,
Round equations:
1.6434 0.0272, liquid,
f=[ln(0.135~/D + 6.5/ReI2= { 0.0204, gas,
- - 16(38.89)’ = 64,118,
n2(32.2)(0.2557)’(51.85)(0.00137)
= 18.27 psf/ft, Re = 19,196,
E, = 1.578(19196)-0~’9(51.85/0.142)0-22 0.8872,
=
E, = 0.0273(6411.8)(19196)-0~51(51.85/0.142)-0~08 7.140,
=
Xz = 18.27/0.1633 = 111.8. y = 5619/2700 = 2.081,
Lockhart-Martinelli-Chisholm: YE, = 2.081(7.140) = 14.86.
c = 20 for TT regime (Table 64, Clearly, this term must be less than unity if Eq. (6.105a) for S is to
c1 be valid, so that equation is not applicable to this problem as it
x xz-
& 1 + - + - - 2.90, stands. If YE, is replaced by y/E, = 0.2914, then
:. (APIL) two phase = &(AP/L), = Z.gO(18.27)
2.081
=
= 53.0psf/ft, 36.8 psi/lOO ft. S = 1 + 0.8872(~ 0.2914)~.~ 2.02,
-
Check with the homogeneous model: and the voidage is
8oo 5619
X= 140,000 -I- 800 = 0.0057 wt fraction gas, E = 5619 + 2.02(2700) = 0.51’
’= [m 3.13(1OW4) 1 sqft ’ which is a plausible result. However, Eqs. (6.105) and (6.105a) are
0.0057
+ 0.9943
-1=3.85(10-5)- lbf sec
quoted correctly from the original paper; no numerical examples
are given there.

Hewitt (1982). A procedure for stratified flow is given by 17-26 (1971); cited by Hewitt, 19821 gives the void fraction in terms
Cheremisinoff and Davis [AZChE J. 25, 1 (1979)]. of the incoming volumetric flow rates by the equation
Voidage of the holdup in the line is different from that given by
the proportions of the incoming volumetric flows of the two phases, EG = Qc/(Qc + SQJ, (6.105)
but is of course related to it. Lockhart and Martinelli’s work where S is given by the series of equations
indicates that the fractional gas volume is
S = 1 + El[y/(l +YE,) YE,]"^,
E = 1 - l/4L, (6.104) E, = 1.578 Re-0.’9(pL/pG)0.22, (6.105’)

where +L is defined in Table 6.8. This relation has been found to E, = 0.0273 We Re-o.5i(p~/p~)-o.08,
give high values. A correlation of Premoli et al. [Termotecnica 25, y = QG/QL, Re = DG/p,, We = DG2/apL.