Page 184 - Applied Process Design For Chemical And Petrochemical Plants Volume III

66131_Ludwig_CH10E 5/30/2001 4:33 PM Page 147

Heat Transfer 147

Calculate LMTD: 9. For each selected temperature interval, calculate a bal-
ance on fundamental relation:
t 1 → t 2 (cool and condense)
h o (t g t c ) K g M (p v p c ) h io (t c t w ) U (t g t w )
t 4 ←t 3 (water temperature rise)
(10-118)
Assume gas cooling and condensing coefficients, then
h io inside film coefficient corrected to outside, plus out-
q gas cooling q cond. side condensing film coefficient clean basis,
Trial area (10-115) Btu/hr (ft ) (°F)
2
U gas cool 1LMTD2 U cond. 1LMTD2
2
h o dry gas coefficient, on shell side, Btu/hr (ft ) (°F)
2
K g diffusion coefficient, lb-mol/(hr) (ft ) (atm)
5. Determine the gpm tube-side flow rate and
M v average molecular weight of vapor, dimensionless
temperature rise for the overall unit to be certain that p c partial pressure of vapor at the condensate film, °F
they are reasonable and consistent with heat load. p v partial pressure of vapor in gas body, atm
6. Calculate the tube-side film coefficient, h i , and t c temperature of condensate film, °F
reference it to the outside of the tube, h io . Calculate the t g temperature of dry gas (inerts), °F
condensing film coefficient: t w temperature of water, °F
latent heat of vaporization, Btu/lb
1 1 1
Then This procedure involves the following:
h io ¿ h cond. h io
a. Establish
t g inlet temperature of interval, °F.
This value will remain constant throughout the design.
p v vapor pressure of condensate at t g , psia or atm
7. Calculate the shell-side dry-gas film coefficient, h g or h o , P inlet gas-vapor mixture absolute pressure to interval,
for outside tube conditions. Assume a baffle spacing or allowing for estimated pressure drop where neces-
about equal to one shell diameter. Use the shell-side sary, psia or atm
method described in Equation 10-48 and Figure 10-54. p g P p v , psia or atm
This is necessary for inlet conditions and then must be q i
t w ¿ t wo , °F (10-119)
checked and recalculated if sufficient change occurs in
W t 1c p 2 t
the mass flow rate, G, to yield a change in h g .
t w temperature of inlet water to interval, °F
8. Calculate mass transfer coefficient, K g using h o :
t wo temperature of outside tube wall, °F
W t tube side flow rate, lb/hr
h o 1c >k a 2 2>3 1Expression2 (c p ) t tube side specific heat, Btu/lb (°F)
K g (10-116)
cp gf M a 1 > k d 2 2>3 p gf q i heat load of previous interval, Btu/hr
b. Assume:
Gilliland 285 correlation for one gas diffusing through t c temperature of condensate film, °F
another: p c vapor pressure of condensate at t c , psia or atm
c. Calculate: p g P p c , psia or atm.
3>2 1>2
T k 1 1 p g ¿ p g
k d 0.0166 a b (10-117) p gf , psia or atm. (10-120)
1>3
1>3 2
p t ¿1V A V B 2 M A M B p g '
2.3 log
p g
where d. Substitute in balance equation and try for as close a
V A molecular volume for component A, diffusing gas balance as reasonable, depending upon the magni-
V B molecular volume for component B, diffused gas tude of the heat load and significance of changes in
(See chapter on “Packed Towers,” Volume 2, 3rd Ed. t c . Usually
5% is acceptable. If check is not
for further discussion.) Compute from atomic volumes: obtained, reassume t c and continue as per (b), (c),
2
k d diffusivity, ft /hr and (d).
p t total pressure, atm e. Calculate U t average of the value of the two
T k absolute temperature, ° Kelvin sides of equation of (d).
M A and M B molecular weights of the gases
3h o 1t g t c 2 K g M v 1p v p c 24 h io 1t c t w 2
U t (10-121)
2
relating K g to the change in logarithmic difference in
f. Calculate U:
inerts in the main gas body and at the condensate film.
This value of K g may have to be recalculated each time U U t U t (10-122)
a new h o is determined, these values being re-evaluated t g t w t
with physical properties at the interval temperatures. g. Summarize results of the intervals