A. GENERAL
As the first vapor reheat plant is still in the experimental design stage, precise estimates of capital and operating costs are impossible, but some approximations may be useful.
In most distillation plants, sulfuric acid is added to sea water to convert bicarbonate into C 02 , which is then removed in the deaerator.
Feed to the evaporators is maintained at a pH of about 7.5, to prevent scale formation. Sea water having a pH of less than about 9 is quite corrosive to concrete. In the vapor reheat process, scaling presents only a minor problem, and it is proposed to remove C 02 by adding lime and converting bicarbonate into carbonate, which precipitates as C a C 03 . This method is used by several plants that produce M g O from sea water.
The treated sea water has a pH of 10 to 10.5 and is not corrossive to concrete, at least not at ambient temperatures. Concrete tanks which have contained alkaline sea water for 2 0 years are still in excellent condition.
Another advantage of lime treatment is that the precipitated calcium
carbonate removes other suspended solids and any organic material (plankton) that may be present. Some concern has been expressed that organic matter in sea water might contaminate the hydrocarbon heat-exchange liquid. Although extensive tests at high temperatures have not been made, it is the opinion of some experts that prestressed concrete can be used for heat-exchange columns and evaporator shells. The cost of large vessels with a working pressure of 100 psig has been estimated at
$2.00/ft3 (Lyn, Τ . Y., 1957).
B. FLASH CHAMBERS AND CONDENSERS
The open channels used for condensers can be made from inexpensive materials, possibly plastics, for the low-temperature stages. They are subject to very little stress. A cost of $0.50/ft2 channel area installed will be used for estimating purposes. For each 1000 gal/day installed capacity, 30 ft3 of flash chamber1 and 106 ft2 of condenser will be assumed.
($2.00)(30) + ($0.50)(106) = $ 1 1 3 . If we refer the combined flash chamber and condenser investment to condenser surface only, we have
$113/106 = $1.07/ft2 of condensing surface.
C. HEAT EXCHANGERS
L Shells
If heat-exchanger sections are stacked as suggested (Fig. 4.16), they must be separated by an estimated 4 ft. This adds 4 0 % to the cost of the column.
2. Oil-Dispersion Plates
Ceramic is probably the best material for oil-dispersion plates. It is hydrophylic, noncorrosive, and practically indestructible. Plates might be cast or "drilled" by a hydrofluoric acid etching process developed by Corning. One manufacturer has suggested a price of $10/ft2 (in quantity).
The cost of plate holders, water distribution system, and connecting pipes has been estimated at $7/ft2.
Although oil holdup in the column is only about 70 % , an additional quantity will be needed to fill connecting pipes and collecting areas. A n inventory which will fill the entire column appears to be ample. Cost is estimated on the basis of a recent quotation, but it is expected to be less in quantity.
1 Size of flash chambers in original Point L o m a Plant of the Office of Saline Water, U . S . Department of the Interior.
A n oil storage tank large enough to contain all the oil must be provided.
Estimated cost, $0.25 ft3. Approximate cost of heat exchangers for each 1000 gal/day production is then:
Shells (21.9)(2)(1.4)($2.00) $123 Dispersion plates (0.365)(2)($10.00)(6) 44 Plate holders, water distributors, and
piping (0.365)(2)($7.00)(6) 31 Oil(21.9)(2)(1.4)($1.37) 84 Oil storage (21.9)(2)(1.4)(0.25) 15
Total $297
$297/43.8 = $6.78/ft3 of effective heat-transfer volume.
D . C O S T COMPARISON OF V A P O R REHEAT AND MULTISTAGE FLASH
The Bechtel Corporation (1963) has recently made a study of large-size saline-water conversion plants using the flash distillation method. Their
T A B L E 4.7
C O S T D A T A FOR 1 4 χ 1 0β GAL/DAY F L A S H D I S T I L L A T I O N PLANT**
Amortization6 (includes taxes and insurance) 9 . 4 % per a n n u m Operating days per year 3 3 0 Amortized capital cost per day = (capital cost)(2.8$ X 10~4)
Amortized capital cost per hour = (capital cost)(1.187 X 10~5) Cost of steam
Fuel 400/10° Btu Amortization (boilers & accessories) 30/1O6 Btu
Total 4 3 0 / 1 0e Btu = 0.150/kw-hr Cost of pumping with steam turbines
Amortization 0.1360/kw-hr Steam ( 5 0 % efficiency) 0.3000/kw-hr
Total 0.4360/kw-hr Capital cost of heat-transfer surfaces (includes tubes and flash chamber)
$3.18/ft2
Heat-transfer coefficient flashing brine to tube side brine. Based on log mean At. Corrected for boiling-point elevation
4 0 0 Btu/ft2/hr/°F
a Bechtel Corporation ( 1 9 6 3 ) .
b Amortized cost includes taxes and insurance. It is designated C*_ by T r i b u s and Evans ( 1 9 6 2 ) . See Chapter 2.
figures may be used as a basis for estimating cost of water production by vapor reheat. Table 4.7 gives cost data taken from Bechters estimate for a 14-million-gal/day plant. Table 4.8 gives assumed conditions for the vapor reheat plant. Table 4.9 gives cost of unit conductance calculated by the method of Tribus and Evans (1962) (see also Chapter 2).
T A B L E 4.8
Brine blowdown temperature 75 °F.
˜ = 7°F.
Open-channel condenser
Cost (includes concrete flash chamber) $1.07/ft2 of condensing surface Heat-transfer coefficient 1 0 0 0 ( B t u X f t ) -3^ ) -1^ )- 1
Liquid-liquid heat exchangers Cost $6.78/ft3
Heat-transfer coefficient 8 0 0 0 ( B t u X f t ) -3^ ) "1^ ) -1
Energy to p u m p oil and water through heat exchangers: 1 kw-hr/1000 gal product 7 0 % of energy developed by inlet fresh-water stream recovered in water turbine.
7 0 % of energy developed by exit fresh-water stream recovered in water turbine.
Labor cost 70/1000 gal ( 4 0 % higher than multistage flash).
α These conditions are somewhat different from those shown in Fig. 3.
T A B L E 4.9
Amortized capital cost of unit area,
( t f X f t ) -2^ ) -1 a 3.77 χ 1 0 -3 1.27 χ 1 0 "3 Amortized capital cost of unit volume,
( t f X f t ) -3^ ) -1 8.05 x 1 0 -3
In a multistage flash system, heat is transferred only once. A t an approach temperature of 1°F it costs 9.42 X 1O~60 to transfer each Btu.
In a vapor reheat system heat must be transferred three times. Assuming approach temperature of 1/3°F for the condenser and both heat exchangers, it will cost 3(2 X 1.01 + 1.27) 1O~60 = 9.87 Χ 10"6<£ to transfer each Btu. Conditions may be optimized by using a slightly smaller condenser (At = 0.36°F) and slightly larger heat exchanger (At = 0.32°F). This will result in a cost of 9.84 X lO"60/Btu transferred.
Except for pumping, costs are about the same in the two systems, but absence of scaling problems will permit operating vapor reheat systems at a higher maximum temperature with lower fuel costs. Table 4 . 1 0 gives the estimated cost of producing fresh water for several values of tx . It is assumed that all costs except steam and pumping remain constant.
T A B L E 4 . 1 0
"Based on information developed by the Bechtel Corporation ( 1 9 6 3 ) .
L I S T OF S Y M B O L S
A A r e a (ft2) Q Heat flow (Btu/hr) C Heat capacity ( B t u X l b ) "1^ ) -1 t T e m p e r a t u r e ( ° F ) 8 Mass flow (lb/hr) t’ t - δ ( ° F )
G Mass velocity (lb)(hr)-Hft)-2 log mean At’ ( ° F ) h Length or height (ft) ı Mass-transfer coefficient2 k Heat-transfer coefficient o b x f t r ^ h o - v F ) -1
(Btu)(ftcol. v o L J - T F ) -1 X lb product/lb sea-water feed m Mass (lb) A T e m p e r a t u r e difference ( ° F )
Stage n u m b e r δ Boiling-point elevation ( ° F ) Pressure (ft of water), dyne/cm2 Ł T i m e (hr)
2 Mass-transfer coefficient refers to condensation; ° F is the temperature difference between brine and condensate.
Σ
Specific gravity Summation
Approximately equals Fixed gas (% by volume)
m M e a n ( )m Log mean
Oil (hydrocarbon) or base tempera
ture w W a t e r
1, 2, 3, Designation of some specific loca-etc. tion or quantity
Subscript
´ Brine
REFERENCES
Bechtel Corporation (1963). Office of Saline W a t e r Res. Develop. Rept. 72.
Christianson, R. M . and A . N. Hixson (1957). Ind. Eng. Chem. 49, 1 0 1 7 . Fluor Corporation (1959). Office of Saline W a t e r Res. Develop. Rept. 34.
F M C Corporation (1962). Office of Saline W a t e r Res. Develop. Rept. 63.
F M C Corporation (1963). Office of Saline W a t e r Res. Develop. Rept. 78.
Gastaldo, Charles (1962). Univ. California (Los Angeles) Dept. Eng. Rept. 6 1 - 8 0 . Griswold, J . , and J . E. Kasch (1942). Ind. Eng. Chem. 34, 804.
Hayworth, C. B. and R. E. Treybal (1950). Ind. Eng. Chem. 42, 1 1 7 4 . K n u t h , E. L. (1964). Ind. Eng. Chem. Process Design Develop. 3, 55.
L y n , Τ . Y., and Associates ( 1 9 5 7 ) . Private communication, 1 4 6 5 6 Oxnard St., V a n Nuys, Calif.
Othmer, D . F., R. F. Benenati, and G. C. Goulandris ( 1 9 6 1 ) . Chem. Eng. Progr. 57, 4 7 . Othmer, D . F., R. F. Benenati, and G. C. Goulandris ( 1 9 6 3 ) . Chem. Eng. Progr. 59, 63.
Tribus, M y r o n , and Robert Evans (1962). Univ. California (Los Angeles) D e p t . Eng.
Rept. 6 1 - 8 0 .
W o o d w a r d , Η. T . ( 1 9 6 1 ) . Chem. Eng. Progr. 57, 52.