I
R. S. SCHECHTER and T. L. KANG University of Texas, Austin, Tex.
Design Considerations in
...
Cross-Flow Air-Water Contactors A simple method of analyzing cross-flow air-water contactors is presented. The recommended design or evaluation procedures are based on the application of generalized curves
PREDICTISG
changes in water temperature a n d air enthalpy in air-water contactors is complicared considerably if the two streams flow perpendicular to one another as in natural draft cooling towers. T h e purpose of this work was to evolve a series of charts, which encompass a wide range of inlet conditions, to facilitate cross-flow cooling tower design and evaluation. Formulation of the Problem T h e following set of partial differential equations which describe the relationship betwetn air enthalpy and water temperature as a function of position have been presented by Zivi and Brand (4):
ai
BtL
Numerical Solution
-L C p~ =GBr BX
and
Bi
G-
BX
= k gQ ( 2 * -
2)
An analytical solution of the set of partial differential equations can be developed, if the relationship between i* and t L is assumed to be linear. Klinkenberg (2) has given a n excellent discussion and survey of the solution of the linearized set of equations. Zivi and Brand have presented a numerical solution for the set of partial differential equations for a particular inlet water temperature and inlet air wet-bulb temperature. This discussion extends the work of Zivi and Brand to encompass a wide range of inlet conditions.
(2)
As the problem was treated numerically, there was no incentive to restrict the results to a linear relationship. Instead, a n empirical expression which was developed by Butcher (7) was employed.
with the boundary conditions (for most practical problems) t~ = t ~ at,
I
= 0
i = i,atx = 0
(3)
(4)
These equations are subject to the following restrictions :
A steady state has been attained. T h e liquid flow rate, the liquid heat capacity, and the humid heat are independent of position. Diffusional processes are negligible compared to convective transport. T h e use of a n over-all mass transfer coefficient independent of position is valid.
Equation 5 is applicable over a range of water temperatures from 40' to 130' F. (7).
To decrease the numerical labor, the set of equations being considered were put into a dimensionless form and the number of parameters is reduced to one. T h e following dimensionless variables were defined:
+ O.OZjfL, = 0.025 ( t ~ t
I,* e1.77
T h e Lewis relationship ( 3 ) is valid.
V
~
~
)
Z = i/ZOak
I , = iJZ,?* Using the empirical equilibrium relationship, Equations 1 and 2 become
with boundary conditions V
=
0 at Z = 0
I = I, at
x=0
(8)
Equations 7 and 8 are dimensionless (the units of the constant 0.025 are ' F.-l) and the only parameter is the relative inlet air enthalpy, I,. T h e problem is then to perform the necessary computations which yield values of V and I for various values of the distance variables, Z and for a given value of I,. Figures 1 to 5 represent the numerical solutions of Equations 7 and 8 for I, .= 0.125, 0.25, 0.375, 0.50 and 0.75, respectively. These plots were generated by approximating the partial differmtial equations by the following pair of difference equations :
x,
k,aZ,*r z =(0.025) C,LL ' y -k,ax
G
VOL. 51,
NO. 11
NOVEMBER 1959
1373
and
20
I
,
I
l
l
-X=O
-x=
I , = O 25
5
I0
10 9
-V
where subscripts m and n denote the value of the function a t the lattice point ( m A X , nLZ). T h e general method of computation involved evaluating the dependent functions column by column. T o determine the value of V and I a t a n interior point ( m 4-1, n I), the values of these functions a t rn 1, n and m,n 1 are required. The procedure then entailed assuming a value of V,,+ I , ~ 1+ and I,+ I , " + 1. These assumed values are denoted by the superscript zero, that is, the assumed values are Vm+,, and I$: ,,n + l. Corrected esti1 are obmates of Vm+I.,,+ 1 and I,, tained by applying the following iteration scheme. which is a rearrangement v of Equations 3 and 10:
+ +
+
Z Figure 2. The distribution of outlet water temperatures can be visualized by constructing a vertical line at the appropriate value of Z
(0)
+
(11)
and
T h e iteration was continued until the percentage differences between succes1 were sive values of V,+ I,"+ 1 and Im+ less than 0.0001. T h e computation of a point on the boundary is somewhat simpler, in that the iteration of both Equations 11 and 12 (depending on the boundary being considered) is unnecessary because the water temperature is specified a t Z = 0 and the inlet air enthalpy a t X = 0. These computations were performed using a n IBM 650 computer.
Error Considerations
(I2)
Figure 1.
+
s
s
+
This design chart should be used when the inlet relative air enthalpy
is 0.1 25 1 374
+
In the interval ( m 1, n) and ( m 1. n I), V m + ~ , n +(k0 k 1) can be written as
INDUSTRIAL AND ENGINEERING CHEMISTRY
v,,+
I. n
+ k = L-rn + 1.
112
+
where the asterisk denotes funstions evaluated a t points called for by Taylor's remainder theorem. From Equation 13 we can write
CROSS-FLOW A I R - W A T E R C O N T A C T O R S Hence V m + l . n + l
-
-
Vm+1.n
AZ
+ gm+
(-zz-)
dVm+1.n+1/2
Lchcre g,,L 1 , ,,,. I / ? is of order Similarly
I, n + I / ?
(iz)?. -V -070
where h,, 113, *+ 1 is of order (AX).' From Equation 7
7 Figure 4. is 0.50
This design chart should be used when the inlet relative air enthalpy
and
I,+,~,. n + 1
(20) A z (k
Expanding e v m + l , n + k into a Taylor Series about m + l , n yields eP.rn+I
n+k
= eVm+l,n
-
q
+
(k
1)
A similar analysis yields
(aevmi2
zm+l n+1/2
lyeV,*+, (7) (22) n+1
-
1)2
Setting k = i12and adding ~~~~~i~~~ 21 and 22, we obtain
Expanding the same function about latrice point m 1, n 1, we get
+
+ eVrn.1,
eVm+l, n+l
+
n
2
+
~
jo*
n
(24)
+ eVm+i. n -
2
- Ln. n t 1
Irndl, n + l
AX
I,=O 375 I,+
-V
- J m + I.
Similarly, we can prove
09
A0 5
n
where J,+ I , is~ of order (AX)'. Substituting Equations 13, 23, and 24 into Equation 17 gives
(23)
li
+ Im.1.
2
eVm+i, n + l Fm.1.
=
I ~ + nI +.
1. n + 1
=
+ I,, - + n+ 1
2
I
terms of order (AX)'
+ (AZ)2
(26)
1 04
Thus the maximum truncation error 7 in the new value of V,,,+I.~+I or Zm+i,
1:
-'O 3
l
0
5
10
15
20
l
,
,
I
,
25
I
1
,oo
30
Z Figure 3. The variation of air enthalpy of particular horizontal position can easily be determined b y following the appropriate x line
%+
is of the order of
AZ[(AX)2
+ (.lZ)2]or A X [ ( A x ) z+ ( A Z ) * 1 .
Rather large unequal space steps (AZ = 0.43 and AX = 0.1) were used in the computations because of limited machine time. To make a quantitative estimate of the errors, the space steps were reduced by a factor of 4 and the VOL. 51, NO. 11
NOVEMBER 1959
1375
Then, average water temperature a t outlet - 1 ,043 = 78.2' F. t~ = 120
1.00
h
+ (&)
I,= 0.75
0.3
0.95
0.90
I
-V 0.85
Average air enthalpy a t outlet i = (117.85) (0.427) = 50.32 B.t.u./lb. of dry air. As a check, over-all heat balance can be written as Heat removed from water = ( L ) ( x ) ( A t ) = (1500) (15) (120-78.2) = 9.41 X 105 B.t.u./hr.-ft. o f j H e a t removed by air = (C) ( 2 ) (Ai) = (1500) (30) (50.32-29.50) = 9.37 X 105 B.t.u./hr.-ft. ofy These values are fairly close to each other. The discrepancy is due to inaccuracies in graphical integration. Nomenclature = surface of contact between phases, sq. ft./cu. ft. of apparatus CpL = heat capacity of water a t constant pressure, B.t.u./(lb.) ( O F . ) G = mass velocity of air, lb./(hr.) (sq. ft. cross section) Z = relative enthalpy of air a t any point, dimensionless, I = i,/Zo* le = relative enthalpy of entering air, dimensionless, le = ie/Zo* lo*= saturation air enthalpy, B.t.u./lb. o f d r y air, Io* = e1.77 f 0 . 0 2 5 i ~ e i = enthalpy of air a t any point, B.t.u./lb. of dry air ie = enthalpy of entering air, B.t.u./ lb. of dry air i* = saturation air enthalpy, B.t.u./lb. o f d r y air, i* = ,1.77 -I-0 . 0 2 5 t ~ k , = over-all mass transfer coefficient, lb./(hr.)(sq. ft.) (unit Ai) L = mass velocity of water, lb./(hr.) (sq. ft. cross section) t L = water temperature, ' F. tLc = entering water temperature, ' F. P' = temperature difference, dimensionless, V = 0.025 ( t ~ the) X = width of cooling tower, dimensionless, X Koax/G x = width of cooling tower, feet 2' = length of coolinE tower, feet = height of cooligg tower, dimenZ (0.025)k0aZo*t sionless, Z = a
0.80
0.75 0
2
4
6
IO
8
12
14
16
Z Figure 5. grations
Design based on these charts would entail a series of graphical inte-
values of V and Z recalculated for a particular value of the relative inlet air enthalpy. T h e maximum percentage difference between values of the dependent functions a t corresponding lattice points was 1%. This maximum error was observed in the regions where the greatest changes in I.'and I occurred a n d the error diminished as m or n increased. This analysis would seem to indicate that the values presented in this article are accurate to three significant figures.
lb./hr.-sq. ft.; Dry bulb temperature Wet of atmospheric air = 80.5'F.; bulb temperature = 64.5'F.; C,L = 1 B.t.u./lb.-'F. SOLUTION.From psychrometric chart, i, = 29.5 B.t.u./lb. I,*
=e1.77
+ ( O . O W ( 1 2 0 ) = 117.85 B.t.u./lb. I,
CZlL
29.5 117.85
__ = 0.25
So Figure 2 should be used.
Uses of Generalized Curves T h e generalized curves are very useful either in evaluating the performance of existing cross-flow towers or in designing new ones. T h e use of the curves in solving practical problems is illustrated by the following example. Example. Find the outlet water temperature and air enthalpy for a n atmospheric cross-flow cooling tower of dimensions, x = 15 feet and z = 30 feet. DATA. tLc = 120'F.; L = 1500 lb./hr.-sq. ft.; k,a = 100 B.t.u.--cu. ft./hr.-sq. ft.-unit (Ai); G = 1500
1 376
z
= height of cooling tower, feet
SUBSCRIPTS m, n = coordinates of lattice point, rn andn 2 1 k = increment in coordinates: 0 5 k I
1 (117.85) (30) = 5.89 z =(0.025) (100) (1) (1500) From Figure 2, a t Z = 5.89 X
v
0 0.5
- 1.200 - 1.056 - 0.846
1.0
T h e average V as obtained by graphical integration is -1.045. Also, for X = 1.0 and Z = 5.89 the average value of Z is 0.427.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
SUPERSCRIPTS o
j
= assumed value = number of interation, j
>=
1
literature Cited (1) Fuller, A. L.: Petrol. R e j n e r 35, No. 12, 211 (1956). (2) Klinkenberg, A, IND. EXG. CHEM. 46,2285 (1954). (3) Lewis, W. K., Trans. Am. Soc. Mech. Engrs. 44, 329 (1922). (4) Zivi, S. M., Brand, B. B., Refrig. Eng. 64, No. 8, 31 (1956). RECEIVED for review January 23, 1959 ACCEPTED June 8, 1959
I
W . E. GARWOOD, W. 1. DENTONI1 R. B. BISHOP,2 S. J. LUKASIEWICZ, and J. N. MlALE Research and Development Laboratory, Socony Mobil Oil Co., Inc., Paulsboro, N. J.
Cleaning Up Petroleum Stocks with Hydriodic Acid Hydriodic acid effectively removes nitrogen and metals from California crudes and coker stocks. Iodine and nonhydrocarbon products are recovers ble from precipitated tar
Tm
advantages of removing nitrogen and metal constituents from petroleum fractions and crudes have become more pronounced \vith improved catalytic conversion processes. Present hydrogenation processes efficiently remove nitrogen and metals (729, but high hydrogen consumptions may restrict unit size in refineries with limited hydrogen availability.
Literature Background Coal reduced to petroleumlike material with HI at 540° F. in closed tube Porphyrin complexes exist in shale oil and in petroleum crudes, as in California area Porphyrin-type compounds totally destroyed by prolonged action of H1 in acetic acid Extraction with HI and AcOH recovers most of vanadium and lesser amounts of other metals in petroleum distillates Nitrogen compounds inhibit Si-Al?Os cracking catalysts Acid sites of Pt on A12Od reforming catalysts poisoned by N compounds Nitrogen compounds deactivate acid and Pt sites of platinumoxide isomerization catalysts Nickel and vanadium, in gas oil stocks, contaminate cracking catalysts and are chief metallic offenders in poisoning fluid cracking catalysts Vanadium attacks protective film of alloys during combustion in gas turbine engines Petroleum ashes containing V destroy fireclay brick on high temperature contact
(9)
(4, 7, 8f, 22)
Charge Stock Properties S P . gr. Boiling range, F., ASTM IBP 10% 30% 50% 70% 90% EP Toresidue Nitrogen, wt. yo Sulfur, wt. % Ni, p.p.m. V, p.p.m. Fe, p.p.m. a
(8)
380 445 481 521 564 615 652 1.5 0.26 1.39 0.03 0.04
Crude 0.9065 170 324 536 695"
... ... ...
50 0.49 1.21 47 52 28
...
+
+
Cracking. 100 1
I
I
(1)
(18, 19)
(10) (14 )
( 6 , I S , 15)
I
I
I
1-0-0
were heated and held for the desired residence time. Pressures were autogenous 80 and depend on temperature and charge stock-1000 to 1400 p.s.i.g. at 700' F. At the end of the runs, the autoclaves c z 60 were allowed to cool to room temperaw V ture, and then opened. Products were cs a n oil layer, aqueous layer, and tarry W 40 precipitate. T h e liquid products were decanted. T h e oil products were waterCALIFORNIA COKER G A S O I L washed after separation from the aqueous 5 0 . 5 % HI I N HO , 20 layer. T h e tarry precipitates, containM O L E S HI ing hydriodic acid, iodine, trace metals, G. ATOMS ( N t 5 ) 700 OF. sulfur, and nitrogen compounds, were 0 scraped from the bottom of the autoclave, 0 2 4 6 8 and the autoclave was rinsed with aceTIME, HOURS tone. T h e Kjeldahl method was used for niFigure 2. The reaction is essentially trogen, a colorimetric procedure for complete in 2 hours metals (76), and dry combustion followed IO0 by alkalimetric titration for sulfur. ,
'*'
(20)
(11)
Materials and Equipment. Aqueous: 5 0 . 5 7 ~ (J. T. Baker) containing 27, HsP02 oxidation inhibitor; 557, (Eastman Kodak Co.) containing no inhibitor, as received, or diluted with distilled water. Two California petroleum stocks, mixed Wilmington-Kettleman crude and coker gas oil derived from crude. All experiments were made in American Instrument Co. stainless steel rocking-type autoclaves. A glass liner was used in one run. Procedure. T h e autoclaves were charged, pressured to 1000 p.s.i.g. with nitrogen, and vented, and the contents
80 I-
w
Present address, Olin Mathieson Chemical Gorp., New Haven, Conn. 2 Present address, Foster Grant Go., Leominster, Mass.
60
U I "OL
Y r
a
2
40
20 48-55 X HI IN HIO 1.6 RATIO
G.ATOMS(N~ 2 HR. REACTION TIM1
0
400 1
Coker 0.8838
Sulfur is removed from the charge stocks with nitrogen and trace metals. Thiophene reacts with hydriodic acid to give hydrogen sulfide, iodine, carbon, and other products (77). With aqueous hydriodic acid solutions a secondary reaction takes place quantitatively: H,S I9 + 2 HI S. This reaction also takes place in the present work; hence, the process is catalytic. Nitrogen Removal. At 700' F., 77 weight yo of nitrogen (and 68 weight yo of sulfur) were removed from the coker gas oil (Figure 1). Above 700' F., cracking started, indicated by rapid drop of oil recovery below 9070, with little
500
600 700 T E M P E RAT UR E,
800
'
OF.
Figure 1. Denitrogenation occurs more rapidly than desulfurization
.
SrcOIlsl
> *IlsOCI*sr.o"lL f .IYLIYR 311Ill.L
-
P"'
CALIFORNIA COKER GAS O I L MOLES H I G. ATOMS ( N t S ) 700 'F. 2 H R . REACTION TIME
0
I
~
0 20 40 60 CONCENTRATION OF HI IN H,O,
80
WTX
Figure 3. Nitrogen and sulfur removals are directly related to concentration of HI in HzO VOL. 51, NO. 11
NOVEMBER 1959
1377
