- Email: [email protected]
Engineering analysis of pumping cold deep nutrient-rich seawater for mariculture and nuclear power plant cooling
Ocean Engng. Vol. 7, pp. 501-520. Pergamon Press Ltd. 1980. Printed in Great Britain
ENGINEERING ANALYSIS OF PUMPING COLD DEEP NUTRIENT-RICH SEAWATER FOR MARICULTURE AND NUCLEAR POWER PLANT COOLING CHAO-HSIN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG Department of Oceanography, National Taiwan College of Marine Science and Technology, Keelung, Taiwan, Republic of China Al~tract--The engineering feasibility of pumping deep seawater has been achieved by using a simplified mathematical model. It was proved that the pumping power required to draw seawater from deep sea is always less than 100 kW (134 h.p.) for pipe diameters below 15 cm and mass flowrate lower than 100 tons/hr, which is suitable for mariculture farmings, and the replacement of warm surface seawater by cold deep seawater as nuclear power plant coolant is technically feasible for pipes with diameters larger than 150 cm and intake levels below 600 m. This model can be further extended to study the performance of the Ocean Thermal Energy Conversion (OTEC) system onshore. Continuationof this study should be the design of deep seawater prototype pumping system, the construction of pilot plants of cooling applications and mariculture experiments, and the feasibility analysis of the Ocean Thermal Energy Conversion power plants.
INTRODUCTION
THE IDF.Aof using the temperature difference between the warm surface water of the tropical oceans and the deep cold layer originating from the pole regions to run a Rankine-cycle heat engine to generate electricity was first proposed by D'Arsonval in 1881 and was first demonstrated by Georges Claude in 1929. However, not too many research activities have been stimulated all over the world until the energy crisis. In addition to its low-temperature characteristic, ocean deep water is the largest nutrient reservoir for marine life. Warmed seawater coming from a depth below 700 m could be used for the growth of algae, shellfish, crustacea and seaweed. The growth rate has been proved to be much faster than that in nature (Othmer and Rods, 1974). An experimental station has been operated on the north coast of St. Croix, one of the U.S. Virgin Islands, near Puerto Rico (Othmer and Roels, 1973). Three polyethylene pipe lines, each 1,800 m long, 6.9 cm inside diameter, pumped water from a 870 m depth in an amount of 159 l./min. This water was warmed by being drawn up through the small pipes, so that it is satisfactory for the growth of hard clam, Pacific and European oyster, bay scallop and spiny lobster cultures. The combined applications utilizing cold deep seawater were proposed by Othmer in 1976. He suggested a number of engineering alternatives using warmed cold deep seawater from OTEC system to grow seafoods. In the present project, we intend to pump cold deep seawater from the offshore areas of the eastern coast of Taiwan to the seashore, first for nuclear power plant cooling to promote the thermal efficiency, and then the warmed nutrient-rich deep seawater will be used for seafoods growth. A lot of theoretical works have been conducted recently to study the technical and economical feasibility of extracting 501
502
CHAO-HSIN WEI,
BXN-JtJINEHUANGand MING-SHENGKONG
cold deep seawater for power generation (Grit~n, 1975; Zener, 1977; Watt, Mathews and Hathaway, 1977). However, little has been mentioned in details about the engineering aspects of pumping cold deep seawater for OTEC, mariculture, and other applications. When pumping cold seawater from deep sea through a long pipeline, a great portion of pumping power is consumed in overcoming the flow friction losses and the density-gradientheat losses. The latter results from the density different between the seawater in the pipe and the seawater outside the pipe, because the water in the pipe is all approximately at the density of the intake level and the water outside the pipe decreases in density all the way to the sea surface. On the other hand, when drawing the cold seawater from the ocean depths up through the warmer water to the surface, the cold seawater will be warmed and the rise in temperature will cause a large impact on system performance. Only few rough estimations have been given on this subject up to date (Watt et al., 1977). To investigate the engineering feasibility of pumping cold, deep nutrient-rich seawater for mariculture and nuclear power plant cooling, the present work is divided into two parts. In the first part, a simple analytical model is developed for the evaluations of pumping power and temperature rise of cold deep seawater, and then for the second part a simulation will be carried out to study the engineering feasibility of nuclear power plant cooling. PUMPING DEEP SEAWATER THROUGH PIPELINES For the steady and incompressible fluid flow through a pipeline, the momentum balance can be represented by the celebrated Bernoulli equation: A(v2/2) + gAh + I dP/p -- Wp ÷ Z(f(L/Rh)vZ/2)i ~- E(evv~/2)i : 0 i
(1)
i
where v is the average velocity of the fluid, h is the gravitational height, P is the fluid pressure, 9 is the fluid density inside the pipe, W~ is the pumping work to the fluid, g is the gravitational acceleration, L is the pipe length. The fifth term of Equation (1) represents the summation on all sections of straight conduits, and the last term represents the summation on all fittings, valves, and bends etc. f i s the friction factor depending on Reynolds' number and can be expressed as, according to Moody (1944), for smooth pipe:
~16/Re f----- ]0.0791/R¢ °.2~ ~0.046/Re °'2
R e < 2,100 2,100 < Re <__ 20,000 20,000 < R e ~ 107
(2)
where Re is defined as vD/v, D is the pipe inside diameter, and v is the kinematic viscosity of the fluid. R h is the mean hydraulic radius, and for circular pipe ,R h = 0 / 4 . e v is the friction loss factor due to fittings, valves, and bends etc. To simplify the analysis, the following assumptions are made: (1) Seawater is incompressible. The cross-section of pipeline is uniform and the pipe is straight all the way from seashore down to offshore deep sea, as shown in Fig. 1. Therefore the average velocities of the seawater at the intake and at the outlet of the pipeline are the same, i.e. Av = 0, and the friction loss factor can be neglected, i.e. ev = 0. (2) The seawater in the pipeline is all at the same density as the intake level. Therefore, P = Pa -----PH = constant, and
Engineering analysis of pumping cold deep nutrient-rich seawater 2_"~,,=
Seo sur foce
% 1 " ~
X.L
503
Y =0
-
H
"X
J
×=0 FIG. I.
Schematic diagram of the basic pipeline configuration. 2
I
2
de/p = I dP/pn -----(Pz -- Pa)/Pn.
1
(3)
1
(3) The outlet of the pipe is at sea level, and the pipe is circular. (4) Only one straight pipe is considered in the present analysis, so that Z (f(L/Rh)v2/2)i = f(L/Rh)v2/2.
(4)
i
From preceding assumptions, Equation (1) then can be written as: Wp = gH + (P2 -- PO/Pn + f(L/Rh)v~/2.
(5)
Since the seawater is pumped into the atmosphere at the outlet, the outlet pressure is equal to the ambient pressure Pa, i.e. P2 = Pa. Thus the intake pressure P1 can be evaluated by the hydrostatic relation: el = Pa -~- Ilg Psgd Y -----P2 + I~ Psgd Y
(6)
where p~ is the seawater density distribution outside the pipe, and Y represents the depth from sea surface. Substituting Equation (6) into Equation (5), we get Wp = gH -- ~noo(p( Y)/Pn)gd Y + f(L/Rh)v2/2.
(7)
Normalization of Equation (7) gives wp = 1 -- f0l p ' d r + (vO'/2g) (L/H)f/Rh where wp ==- Wp/gH, y ~
(8)
Y/H, p*(y) = p(Y)/pn, and Z = 1 -- j"01p*dy.
Here, Z represents the density-gradient-head loss depending on the density distribution. Since there exists thermohaline circulation at deep sea region, the variation of density with depth is generally not so uniform that a single profile p(Y) can be approximated. Therefore, instead of direct integration, a finite difference summation is used to calculate the densitygradient-head loss, i.e.
504
QttAo-HSIN WEI, BIN-JUINE [-'IUANGa n d MING-SHENG KONG
Z
=
1 --
(9)
Y~'pi*L.~yi
i
where ~ i * = (Pfl + p~_,*)/2, and Ay; = Y i - )'r r Since the density distributions are different at various oceans and in different seasons, Z is a regional and seasonal function determined from actual measurement. Substituting Equation (2) for friction factor f into Equation (8), we obtain
wp =
Z -F 32 nRe, Z -k 0.1582 nRe 7/4, LZ + 0.092 nRe 9!s,
R e ~ 2,100 2,100 < R e ~ 20,000 20,000 < Re ~ 10~
f
(10)
where n, (v2/gD a) (L/H). Equation (10) shows that the required pumping work is a function of Z, n and Re as plotted in Fig. 2, and n is a factor depending on the viscosity of the seawater and the geometry of the pipeline. =
IO2
.g
o
0-1
i
0-2
IO3
104
105
106
Re
FIG. 2. Specific pumping work (Wp) vs. Reynolds number (Re).
The variations of Z value in eastern coast of Taiwan ranges from 0.001 to 0.002 for depth down to 1,000 m. It is small, but cannot be arbitrarily ignored. If the flowrate is very small such as in mariculture applications, Z becomes dominant. For high ttowrate such as in
Engineering analysis of pumping cold deep nutrient-rich seawater
505
nuclear power plant cooling application, it can be neglected as compared with the friction loss. From Equation (10), the total pumping power I~'p for a given mass flowrate of deep seawater mc from depth H can be evaluated by the relation: ff/p = wp g H m¢.
(11)
HEAT LOSS DURING PUMPING When pumping the cold deep seawater through pipeline, the water will be warmed due to the heating by the outside warmer seawater through the pipe wall. A simple analytical model is developed here to predict the thermal loss. By energy balance to a differential volume of seawater inside the pipe dL, the following equation can be derived: r n c C p d T - = U n D ( T , -- T ) d X
02)
where Cp is the specific hcat of seawater, T is the mean bulk seawater temperature at L, U is the overall heat transfer coefficient across the pipe wall, T, is the temperature distribution of seawater with respect to depth, and L is the position from the intake. From Fig. 28, the transformation of the coordinate gives d L = -- ( L / H ) d Y.
(13)
Substituting (13) into (12) and rearranging, we obtain d T / d Y = - - ( 4 L / k P r R e ) ( L / H ) (T,( Y)) -- T ( Y )
(14)
where k is the thermal conductivity of seawater inside the pipe, and Pr is the Prandtl number. Equation (14) can be solved if the temperature distribution of seawater, T~(Y), was known. In many oceans, the temperature distributions along depth are so uniform that an exponential function, Equation (15), can be used to fit the measured temperature. T,(Y) = To~ + (L(O) -- T~) exp (-- ~ Y)
05)
where [3 is a constant depending on location and season, and T® is the temperature at infinite depth. Normalization of Equation (14), in conjunction with Equation (15) will give: d t / d y - - ¢t = -- ¢t~
where t = t~ ~
[TA0)
--
T(Y)]/[T~(O)
ITs(0) - - T ~ ( r ) ] / [ L ( 0 )
= E [1 -- exp (-- $Hy)]
--
L(H)]
-- rs(H)]
(16)
506
CHAO-HSIN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG
3,-~ Y/H e = 4LU/kPrR~ = 4LU/kP~
Pe -- Peclet n u m b e r -- P~Re E ~ IT,(0) -- T•]/[L(0)
-- T,(H)].
Solving Equation (16) with b o u n d a r y condition, t(l) --= 1, we obtain the fluid temperature distribution inside the pipe, tO') = E - -
[eEl(1~ ÷ e)] exp ( - - Fy) 4- [1 -- E -t- eE exp (-- r ) / ( I ' 4- e)] exp [e O, -- 1)]
(17)
where F = [3H. F r o m Equation (17), the outlet temperature of cold deep seawater drawn through a straight pipeline can be determined: t(0) = to = E + (1 -- E) exp (--~) -- eE {1 -- exp [ - - ( P ÷ e)]}/(r + e).
08)
The unity of t o means no thermal loss during pumping which takes place for perfectly insulated pipe, i.e. U ~ 0, or ~ -----0. The value of t o is always less than one, and thus indicates that the a m o u n t of heat of the deep seawater is being remained after p u m p i n g out of sea surface. Therefore, the thermal loss during p u m p i n g can be readily examined from the values of t o. The factor ~ has the physical meaning of the overall heat transfer across the pipe wall, and I' represents the effect of seawater temperature distribution on the thermal loss. [3 or I" is zero for constant-temperature sea and approaches infinite for a b r u p t change of temperature from sea surface. Equation (18) is plotted in Fig. 3 to illustrate the trend. 1.0
t
b
I
"1
i
i
i'
i
'f'
I
I
I
I
1
E--1.2
-\\\\ 0.5
2.0
_
_
1.5
I 0
I
I
I
I I0
l
-
I
i
I
I
I
I
)
20
FIG, 3. Deep seawater temperature at pipeline outlet.
I
Engineering analysis of pumping cold deep nutrient-rich seawater
507
COOLING OF NUCLEAR POWER PLANT BY COLD DEEP SEAWATER In drawing cold deep seawater through long pipeline, power is needed to compensate the friction and density-gradient losses and the seawater is warmed up by the warmer seawater outside the pipe all the way up to the sea surface. The possibility of using this warmed deep seawater as a cooling agent for a power plant depends upon the flowrate and the pipeline design such as length, diameter, and material of the pipe. Power plants were originally cooled by the surface seawater. According to the principle of thermodynamics, the replacement of cold deep seawater as coolant would reduce the condensation temperature of the power cycle, and thus promote the thermal efficiency. As a first order approximation, assume that the thermal efficiency rI is proportional to Carnot efficiency, i.e. (19)
1] = I'Vn,t/QH o~ 1 - - T e / T .
where ffznet is the net power output of the power plant, QH is the heat added to the boiler, Tc is the condensation temperature, and T n is the boiling temperature. For simplicity, we assume that the replacement of cold deep seawater as coolant will lower the condensation temperature by an amount of Tso - - To, where Tso is the surface seawater temperature, and To is the deep seawater temperature at the outlet of pipeline which can be evaluated by Equation (18). The new condensation temperature To* then becomes T:
(20)
= Tc - - (7",0 - - To)
and the new thermal efficiency 1]* becomes q * = (F,,t/QI-I ~ 1 - - T~*/T H
(21)
where Wn~t* is the new output power. Here, we also assume that the higher new output power can be generated by a properly renewed turbine generator, and all the components in the power plant can be rebuilt to meet the power output increase due to lowering the condensation temperature. Therefore, the ratio of power outputs is
~.o,*/ff'.,,
= l +
(T,o
7"0)/(7:. T3.
-
-
(22)
The net power gain by deep seawater cooling G is the difference between the power increase, l)¢,et* -- Whet, and the seawater pumping power, Pgp. Therefore,
G-- (wo:-
z&,,)
-
w,.
(23)
Whet- ~rp.
(24)
Substituting Equation (22) into (23), we obtain G = E(r~o- r o ) / ( r . -
rc)l
From Equation (24), it can be seen that the net power gain by deep seawater cooling is dependent on the outlet temperature of pipeline, the highest and the lowest temperatures and the net power output in original power cycle, and the pumping power consumed in drawing deep seawater through pipeline.
508
CItAO-HSlN WEI, BIN-JUINE H U A N G and MING-SHENG KONG
APPLICATIONS FOR NUCLEAR POWER PLANT COOLING AND MARICULTURE ON THE EASTERN COAST OF TAIWAN Taiwan is a small spindle-shaped island located in the western Pacific ocean. Preliminary investigation indicates that the eastern coast of Taiwan is very similar to the Virgin Islands in both meteorological and oceanographic conditions. Therefore, the applications of cold deep seawater on the eastern coast for nuclear power plant cooling and mariculture will be investigated according to the previous modelling. Two locations on the eastern coast were selected for the present study. The results of the physical oceanographic measurements in spring season at these two locations are shown in Tables 1 and 2 (Chen and Lien, 1977). The temperature distributions are first least-square fitted to Equation (15) with the assumption that Too is I°C. The values of the exponents [3 are then determined and shown in Figs. 4 and 5. The density distributions are plotted in Fig. 6.
1. Pumping power evaluations From Equations (10) and (11), we know that the pumping power required for drawing deep seawater through pipelines depends on the intake level, the total length and the diameter of the pipeline, and the flowrate. The simulation is carried out for pipe diameters D = 7.5, 10, 15, 50, 100, 150 cm. The first four diameters are suitable for mariculture application and the rest are suitable for power plant coolant conduits. The intake levels H are taken as 400, 600, 800 and 1,000 m for the present calculation. The results are shown in Figs. 7-12.
Temperature,
°C 27.2
20
I0
0
30
--TStotion
3 0 : 2 2 ° 4 5 ' N, 121° 17'E
IOO 200
-
o Measured
300T , Tco ¢ ( To_Too)e- ¥# 400 E T¢o= I o c =
500 --
0
--
TO, 27.2°C = 0.00249
m"1
600--
7OO 8OO
900
I000
Fla. 4. Temperature distribution at Station No. 30.
Engineering analysis of pumping cold deep nutrient-rich seawater
509
TABLE I. OCEANOGRAPHIC DATA AT STATION NO. 30 (121°17'E, 22°45'N) WITH OFFSHOREDISTANCE 19 km.
Depth
Temperature
Density
(m)
(°C)
(g/L)
0 10 20 30 50 75
27.16 26.92 25.88 25.80 24.38 23.45 21.03 20.43 18,81 15.85 14.31 12.82 10.27 8.53 7.34 6.25 5.58 3.96
1022.08 1022.29 1022.58 1022.57 1023.09 1023.39 1024.14 1024.33 1024.72 1025.39 1025.67 1025.92 1026.34 1026.62 1026.82 1026.97 1027.06 1027.23
I00 125 150 200 250 300 400 500 600 700 800
1000
TABLE 2. OCEANOGRAPHIC DATA AT STA~ON NO. 31 (121°46'E, 23°45'N) WITH OFFSHOREDISTANCE 10 kin.
Depth
Temperatur¢
Density
(m)
(°C)
(g/L)
0 10 20 30 50 75
25.48 25.27 25.17 24.74 23.89 22.28
1022.92 1023.02 1023.09 1023.21 1023.48 1024.00
I00
20.31
1024,57
125 150 200 250
18.97 17.65 15.62 14.07 12.89 12.78
1024.92 1025.23 1025.67 1025.90 1026.08 1026.59
300 400
5O0
8.51
1026.88
600 700
6,97 5.96
1026.95 1027.15
800 I000
5.25 4.33
1027.23 1027.39
It can be seen from the calculations that the required pumping power is lessthan 100 kW for pipe diameter below 15 cm and mass flowrate lower than 100 tons/hr which is just in the range of mariculture application. To reduce the pumping power in nuclear power plant cooling application, it is necessary that the pipeline diameter has to be larger than 50 cm.
510
CHAo-HsIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
0
Temperoture, I0
"T-T -
100
Stati
=C 20
25.5
30
:5L23° 45' N, 121° 4 6 ' E
-
200 -
o Meosured
300--
400
-
E
500( To - Too I ¢ ,a'r 6OO
TGo-- I°C To = 2 5 . 5 °C ~ =0 . 0 0 2 3 3 m "t
700
8OO
11300 FIG. 5.
Temperature distribution at Station No. 31.
Density
0
1022
1023
1024
g/L
1025
1026, 1 0 2 7
1028
X
:
I00
200
300
4OO E
500 --. 0 Station 3 0 ( 2 2 * 4 5 ' N t 121= 17'E) t ~ _ ~ Station 31 (23=45 , N, 121° 4 6 " E )
6OO 700 8O0 9OO
l
_ I000 ~ FIG. 6. Density distributions at Stations No. 30 and 31.
Engineering analysis of pumping cold deep nutrient-rich seawater IO"I ~
-
~
II ~
10"2
lilt~ill" /#77I .,2"i4"//
,~.
~2~'17'E
~ ' ~ ,
off-shore distonce19 km)
,~.~",'// /#.~.~//
•~
511
~ ....
H =400 m 600 m
----....
.ooo ,.
800,. D,: ~.S ~m ok ,o c~
ildYl
.//,;7
°;" '~ c~
7
D4: SOcrn
Ds--I00 cm 10"4 I02 Fio. 7.
'°'r ~-
i
r , ll,,,I
D~ I50cm , , t .... I , , 104 Flowrofe me, k g / h r
i
IO3
" ....' Station30
'
1 ' 7 "Ii
///
i roo
/
0
tO4
" 7
I I
~ ~/
103
,
,
, I,,,,
IO6
Pumping power vs. Mass Flowrate at Station No. 30 (I~p: 10-4-10 -I kW).
,,o,
i
I IO5
, I ....
I
/d# ~4 ,~
1
/ 'I 7
I
,
,A,~,;I
-.
~ I0,~
Flowrate me,
106
iO7
kg/hr
FIG. 8. Pumping power vs. Mass Flowrate at Station No. 30 (/~'~,: 10-1-101 kW).
512
CHAO-HSlN WEI, BIN-JUINE HUANG and MING-SHENG KONG
r
i
:1,
ii
,
i,
,
,,i
i
Station 30
/ 8 .& ~ m
103
I0 2 104
L
I
]
105
I
106 Flowrote
Fla. 9.
I I
, i
L
,
i
J i
107
me,
1
I() ~q
kg/hr
Pumping power vs. Mass Flowrate at Station No. 30 (l+'p: 102-106 kW).
i(~ I ......
,-
,
,
°tY V II
,,
io-~ S t a t i o n 5 1 : 2 5 ° 4 5 ' N , 121° 4 6 ' E ( o f f - s h o r e distance I0 k m )
E 7# Z l I -
a. ~.
~ a_
t6 ~
-
H= 400
...... -----
600 800
.....
I000 m
m
m m
,
Di = 7 . 5 c m D2 = I0 c m D3:15
c m
134= 5 0 c m D5 = I 0 0 c m D e = 150 c m
10-4
~
IO2
j
,
L
iO3
104 FIowrate m c ,
FIG. lO.
,
,
I
ILL,I
L
i0 5
I.
,
J
I~I
106
kg/hr
Pumping power vs. Mass Flowrate at Station No. 31 (l~v: 10-4-10 -x kW).
Engineering analysis of pumping cold deep nutrient-rich seawater
513
io2
io I
& 0~ [00
~
~0 -L
103
i
'
~
'
7
.
104
.
- -
/ ~ / z //,~/~/4 ,/ ~//,~ .
Flowrofe
.
....... -----
.....
.
105 mc, kg/hr
, ,,,I
H=400 m 600 m 800 m I000 m
I06
i/
107
Pumping power vs. Mass Flowrate at Station No. 31 (g/p: 10-1-10 s kW).
F I G . 11. io 5
, [frr, I
d
l04 '5 (D o t:. c {:L 103
IO:
104
j/ f
J
t
/
i! / ro5
: j t
/
/ ill/
Ftowrofe
ill
ro6 me,
107
[ r r T, t
106
kg/hr
FIG. 12. Pumping power vs. Mass Flowrate at Station No. 31 (I~V~,:IOt-105 kW).
2. Heat loss during pumping Equation (18) gives the outlet temperature of cold deep seawater through the pipeline if the overall heat transfer coefficient U is determined. In general, the overall heat transfer coefficient can be evaluated by the following equation:
514
CHAO-HSIN WE1, BIN-JUINE HUANG and MINO-SHENG KONG
U ~ ll[lfh i ~ I. (rolri)12~ k,. + 11170]
(25)
where h,- -----convection heat transfer coefficient at pipe inner wall, ho = convection heat transfer coefficient at pipe outer wall, ri inside radius of pipe, r o = outside radius of pipe, and k w -- thermal conductivity of pipe material. =
Since the deep seawater is pumped through the pipeline, the heat transfer at the inner wall is forced-convection and can be evaluated by (Dittus and Boetler, 1930) [4.36, Re ~ 2,100. N,, = ~0.023 R 2 .8 Pr0"4 2,100 < R e
(26)
The heat transfer at the outside wall is determined by the tide current which varies from location to location in the sea and is very difficult to measure. However, the pipeline is usually laid out along the sea bottom so that the effect of tide current can be neglected and the heat transfer at the outside wall is dominated by free convection. The following empirical equation for free convection then can be used (Churchill and Chu, 1975): N, ½ ---- 0.60 + 0.387 (G,P,/[I + (0.559/P,)9118]1~19)ls~
(27)
for 10 _5 < G,Pr < l0 n, where Gr = Grashof number based on the average temperature difference between the wall and outside seawater temperatures and the outside diameter of the pipe. If the pipe is not well insulated, such as using bare metal pipe, the thermal resistance through the wall is negligible compared with convective heat transfer. Therefore
v ~ h,ho/(h, + ho).
(28)
With the previous data, the simulation is carried out for pipe diameters D ---- 7.5, 10, 15, 50, 100 and 150 cm, and intake level H = 600, 800 and 1,000 m. The results are shown in Figs. 13-18. For well-insulated pipes, the heat resistance through the insulation layer is so high that the overall heat transfer coefficient U approaches zero, and the outlet temperature of the deep seawater is just the intake temperature as shown in Figs. 13-18. 3. Feasibility of nuclear power plant cooling application Using Equation (24) and previous simulation results, the feasibility of nuclear power plant cooling application can be determined. The nuclear power plant selected for the present simulation is the unit now located at Chinshan in northern Taiwan. This power plant delivers a net generator output (li/~t) of 635 MW with the highest cycle temperature T H of 288°C, the condensation temperature Tc of 47°C, and the cooling water flowrate mr of 3.3 X 107 kg/hr.
Engineering analysis of pumping cold deep nutrient-rich seawater
28
'
' 'J .... i
'
''1
.... I
'
''1 .... I
'
' '1 .... J
515
''1 ....
D~ISOcrn
2O H=600 rn
1 ~ 0 ~ ~ 7 .
e~
E I0
Intoke fempereture
7.3
0105
104
IO5
Flowrote
FIG. 13.
106
I0 7
108
rnc, kg/hr
O u t l e t t e m p e r a t u r e o f s e a w a t e r vs. F l o w r a t e
at S t a t i o n N o .
30 (H =- 600 m).
28
o
2o
H,8OOm
d E o
~
~50crn
~0 Intake tern~rature
5.6
IO3
104
105
IO 6
Flowrotem=, FIG. 14.
Outlet t e m p e r a t u r ~
IO7
10 8
kg/hr
o f s e a w a t e r vs. F l o w r a t ¢
at Station
No. 30 (H = 800 m).
The net power gain by deep seawater cooling (G) is calculated for two limiting cases: the well-insulated pipeline and the bare metal pipeline. Tables 3 and 4 show the variations of net gain with pipe diameters and intake levels. It is seen that positive gain can be obtained only for pipes with diameters larger than 150 cm. FURTHER
DEVELOPMENT
OF STEPWISE PIPELINE
A simple theoretical model is developed in the present research work to study the technical feasibility of pumping cold deep nutrient-rich seawater for nuclear power plant cooling and mariculture. The model assumes that the pipeline is straight and directly stretched into the intake level in deep sea. However, the bathymetrical map of Taiwan
516
CHAo-HSIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
28
TIIILT
I
' E''''''
I11~
'T']
d ~ntake t e m p e r a t u r e 4.0
, ,J,,,,I 103
t
~ ,,,,,,I
104
,
L ,,,ql[
iO 5 Flowrate me,
FIG. 15.
Outlet
28
temperature
'
'
'1 ....
of seawater
I
'
"
~I'""1
L I II~L~l[ Io 7
10s
~ tili~l 10 o
kg/hr
vs. F l o w r a t e
i
t
at Station
I , i .....
i
No.
~ ,llL,,i
30 (H
1
,
=
I000
m).
,111,
2O 0)
I0 0
7.0
103
104
105 F ] o w r a t e m c,
FIG. 16.
106
i0 7
~0fl
kg/hr
Outlet temperature of seawater vs. Flowrate at Station No. 31 (H = 600 m).
shows that there is a very narrow shelf along the eastern coast. Generally the continental slope drops off to 1,000 m within 10 km from the coast. At several points off the coast, the 1,000 m contour is even closer, within two km. Therefore, an underwater straight pipe line can hardly be constructed to reach the deep sea region. Instead, a stepwise pipeline as shown in Fig. 19 is more likely to be built in practical applications. Thus the previous mathematical model should be modified by a successive stepwise calculations using the similar forms of the equation. Under this circumstance, the total pumping work equation becomes, from Equation (1),
Engineering analysis of pumping cold de¢p nutrient-rich seawater 28
'
r
'1'"'1
'
'
'l""f
'
'
\\\
H=SOOm
e:
' ']""l
~ ~
'
'1
....
E
kO\;50c
'
'
517
' ....
m
E ,o 5.3 . . . . . . . . .
Z_o,_ok.,,_m_~r._otur,,_ _ _
l0 3
l0 4
l0 5
_
_
10 6
Flowrote me,
~
10 ?
l0 8
kg/hr
FIG. 17. Outlet temperature of seawater vs. Flowrate at Station No. 3! (H = 800 m).
28
'
'
'~
....
I
'
'
'~t'"l
¢
..,ooo
#
'
'1
. . . . . . . . . . . . .
I
. . . . . . . .
\\\ \\,%°° \ \ \ , : o \ \X,°°
i Intoke temperoture
4,3
l
T 11111ii
010 3
I04
k
I I I~I,I[
i
i ii,ill[
I
I I
I0 5 I0 6 Fk>wrote me, kg/hr
I0 7
I0 8
FIe, 18.
Outlet temperature of seawater vs. Flowrate at Station No. 31 (H = I000 m).
w, =
[gAh, + / d ? / O , +:
/. i=1
(29)
.ILl
a n d the t e m p e r a t u r e rise at the i-th section becomes d T i / d X i = (Ui~D,/mcCp) (T~ - - Tt)
i = 1, 2, 3 , . . .
with the b o u n d a r y c o n d i t i o n s : for i ---- l, 7'1(0) = T~ at X1 = 0 Pz(O) =
PH a t X z =
0.
(30)
518
CHAo-HSlN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG
TABLE 3.
D (cm)/H
NET POWER GAIN (MW) BY DEEP SEAWATER COOLING AT STATION NO, 30
(m)
7.5 10 15 50 100 150
400
-- 1.1850 --2.9787 --4.2540 - - 1.2756 - - 8.9888 30.294
x x x ×
600
107MW 10" 10 ~ 10 a
Bare - - 1.1852 --2.9787 --4.2540 - - 1.2684 - - 1.6730 37.580
800
metal pipe x 107MW x 10 ~ x 105 × 10 :~
-- 1.1864 --2.9816 --4.2582 -- 1.2655 2.5100 41.879
x x × ×
1000
107MW l0 s lO s I0 a
- - 1.1881 --2.9865 --4.2640 -- 1.2634 6.3890 45.833
× x × x
107MW l0 s 10 ~ 10 a
Well insulated pipe D(cm) / H(m) 7.5 10 15 50 100 150
400
600
- - 1.1851 × 1 0 7 M W -- 2.9787 x 10 ~ - - 4 . 2 5 4 0 x 10 ~ -- 1.2741 × 10 :~ -- 6.1697 34.300
TABLE 4.
:~ x × ×
107MW 106 IO t 10 ~
- 1.1864 -- 2.9816 --4.2582 -- 1.2641 5.1560 45.667
× z × ~
1000 107MW 10 n 10 '~ I0 :~
-- 1.1881 -- 2.9865 --4,2640 -- 1.2620 9.0150 49.588
x x x ×
107MW l0 s 10 ~ 10 :~
NET POWER GAIN (MW) BY DEEP SEAWATER COOLING AT STATION NO, 31
D(cm) / H(m) 7.5 10 15 50 100 150
- - 1.1852 - - 2.9787 --4.2540 - - 1.2669 1.1780 41.647
800
Bare metal pipe 600
400 --2.2493 --5.6539 --8.0756 --2.4629 - - 58.205 16,893
× x x x
107MW l0 s 10 ~ 10:5
--2.2487 --5.6513 --8.0705 --2,4533 -- 49.673 25.077
x × x x
800
107MW 106 l0 s 10 :~
1000
- - 2 . 2 4 7 7 x 107MW - 5.6503 x 106 - - 8 . 0 6 9 8 ~ l0 t - - 2 . 4 4 8 3 × 10 ;~ - - 45.273 29.515
--2.2487 --5.6516 --8.0705 -2.4466 -- 42,641 32,329
x × x ×
107MW 10 ~ l0 t 10 ;~
Well i n s u l a t e d p i p e D(cm) / H(m) 7.5 10 15 50 100 150
The
400 ------
detailed
the pumping
2.2493 5.6539 8.0756 2.4609 53.884 22.919
x × x x
computations station
600 107MW 106 105 10 ~
can
------
2.2487 5.6513 8.0705 2.4506 44.598 32.182
800 x × 7" x
107MW l0 s l0 s 103
be completed
when
------
2.2477 5.6503 8.0698 2.4456 40.418 36,349
× x ~'< x
1000 107MW 10 e l0 s 10 :~
the bathymetrical
------
2.2487 5.6516 8.0705 2.4439 38,204 38.576
information
× × × x
107MW 108 10 ~ 10 :~
around
is p r o v i d e d . CONCLUSION
From
the analytical
to the engineering and tions
nuclear
results, a number
feasibility
power
are summarized
plant
of pumping
cooling
as follows:
of conclusions cold
applications.
deep These
can be drawn
nutrient-rich encouraging
that have implications
seawater and
for mariculture
constructive
deduc-
Engineering analysis ol pumping cold deep nutrient-rich seawater v
519
~ 0 SUrfcIce n
H
FIG. 19. Real piping configuration.
(1) The pumping power required to draw seawater from deep sea is always less than 100 kW (134 h.p.) for pipe diameters below 15 cm and mass flowrate lower than 100 tons/hr which is suitable for mariculture operations. (2) Replacing warm surface seawater by cold deep seawater as nuclear power plan coolant is technically feasible and, hopefully, economically worthwhile for pipes with diameters larger than 150 cm and intake levels below 600 m. The present model can be extended to study the performance of the Ocean Thermal Energy Conversion (OTEC) system onshore. (3) For further practical development, more intensive investigations should be conducted on marine conditions at selected sites and on the economical and technical feasibility of seawater pumping, air-conditioning, fresh water production, and power generation. It is highly recommended to build a pilot plant onshore at Taitung for the purposes of cooling applications and mariculture experiments, and all possibly related works. The simplified model used here to assess the engineering feasibility of pumping cold deep nutrient-rich seawater for nuclear power plant cooling and mariculture is worth enlarging to design the deep seawater prototype pumping system. Acknowledgements--The work presented in this report was fully supported by the National Science Council
under contract NSC-66M-0407-20(01). We are grateful to Dr. C. T. Sieh, president of National Taiwan College of Marine Science and Technology, for his hearty encouragement. Thanks are extended to Drs. Shin Wang, Ju-Chin Chen, and Min-Pen Chert, Prof. Tsu-Chang Hung, and the crew of R/V Chiu-Lien for their valuable comments and substantial assistance in various ways. The authors are also deeply indebted to Misses Shui-Giin Huang, Wei-ShingChow, and Yih-Chyr Wang and Messrs Cheng-Long Kuo, Shang-Long Lia, Gung-Rong Chen, and Teng-Wei Yau for their conscientious effort in the conduction of this study. REFERENCES CHEN,W. C. and LIEN,S. L. 1977. Oceanographic Data of the Sea Surrounding Taiwan. Special Pub. No. 15, Institute of Oceanography, National Taiwan University. CHURCHILL,S. W. and CHU, H. H. S. 1975. Correlating Equations for Laminar and Turbulent Free Convectiort from A Horizontal Cylinder. Int. J. Heat Mass Transfer 18, 1049. CLAUDE,G. 1930. Power from Tropical Seas. Mech. Engng 52, 1039.
520
CHAo-HsIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
DITTUS, F. W. and BOELTER, L. M. K. 1930. Univ. Calif. Pubs. Engng 2, 443. GRrelqN, O. M. 1975. The Ocean as a Renewable Source of Energy. J. Engng Ind. Trans. ASME 897. MOODY, L. F. 1944. Trans. ASME66, 671. OTHMER, D. F. 1976. Power, Fresh Water and Food from the Sea. Mech. Engng 27. OTHMER, D. F. and REELS, O. A. 1973. Power, Fresh Water and Food from Cold Deep-Sea Water. Science, N. Y. 182 (4108), 121. OTHMER, D. F. and REELS, O. A. 1974. Mar. Tech. Soc. J. 8, 40, WATT, A. D., MATHEWS, F. S. and HATHAWAY, R. E. 1977. Open Cycle Ocean Thermal Energy Conversion. A Preliminary Engineering Evaluation, U.S. Department of Energy, ALO/3723.76/3. ZENER, C. 1977. Solar Sea Power. Mech. Engng 27.
ENGINEERING ANALYSIS OF PUMPING COLD DEEP NUTRIENT-RICH SEAWATER FOR MARICULTURE AND NUCLEAR POWER PLANT COOLING CHAO-HSIN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG Department of Oceanography, National Taiwan College of Marine Science and Technology, Keelung, Taiwan, Republic of China Al~tract--The engineering feasibility of pumping deep seawater has been achieved by using a simplified mathematical model. It was proved that the pumping power required to draw seawater from deep sea is always less than 100 kW (134 h.p.) for pipe diameters below 15 cm and mass flowrate lower than 100 tons/hr, which is suitable for mariculture farmings, and the replacement of warm surface seawater by cold deep seawater as nuclear power plant coolant is technically feasible for pipes with diameters larger than 150 cm and intake levels below 600 m. This model can be further extended to study the performance of the Ocean Thermal Energy Conversion (OTEC) system onshore. Continuationof this study should be the design of deep seawater prototype pumping system, the construction of pilot plants of cooling applications and mariculture experiments, and the feasibility analysis of the Ocean Thermal Energy Conversion power plants.
INTRODUCTION
THE IDF.Aof using the temperature difference between the warm surface water of the tropical oceans and the deep cold layer originating from the pole regions to run a Rankine-cycle heat engine to generate electricity was first proposed by D'Arsonval in 1881 and was first demonstrated by Georges Claude in 1929. However, not too many research activities have been stimulated all over the world until the energy crisis. In addition to its low-temperature characteristic, ocean deep water is the largest nutrient reservoir for marine life. Warmed seawater coming from a depth below 700 m could be used for the growth of algae, shellfish, crustacea and seaweed. The growth rate has been proved to be much faster than that in nature (Othmer and Rods, 1974). An experimental station has been operated on the north coast of St. Croix, one of the U.S. Virgin Islands, near Puerto Rico (Othmer and Roels, 1973). Three polyethylene pipe lines, each 1,800 m long, 6.9 cm inside diameter, pumped water from a 870 m depth in an amount of 159 l./min. This water was warmed by being drawn up through the small pipes, so that it is satisfactory for the growth of hard clam, Pacific and European oyster, bay scallop and spiny lobster cultures. The combined applications utilizing cold deep seawater were proposed by Othmer in 1976. He suggested a number of engineering alternatives using warmed cold deep seawater from OTEC system to grow seafoods. In the present project, we intend to pump cold deep seawater from the offshore areas of the eastern coast of Taiwan to the seashore, first for nuclear power plant cooling to promote the thermal efficiency, and then the warmed nutrient-rich deep seawater will be used for seafoods growth. A lot of theoretical works have been conducted recently to study the technical and economical feasibility of extracting 501
502
CHAO-HSIN WEI,
BXN-JtJINEHUANGand MING-SHENGKONG
cold deep seawater for power generation (Grit~n, 1975; Zener, 1977; Watt, Mathews and Hathaway, 1977). However, little has been mentioned in details about the engineering aspects of pumping cold deep seawater for OTEC, mariculture, and other applications. When pumping cold seawater from deep sea through a long pipeline, a great portion of pumping power is consumed in overcoming the flow friction losses and the density-gradientheat losses. The latter results from the density different between the seawater in the pipe and the seawater outside the pipe, because the water in the pipe is all approximately at the density of the intake level and the water outside the pipe decreases in density all the way to the sea surface. On the other hand, when drawing the cold seawater from the ocean depths up through the warmer water to the surface, the cold seawater will be warmed and the rise in temperature will cause a large impact on system performance. Only few rough estimations have been given on this subject up to date (Watt et al., 1977). To investigate the engineering feasibility of pumping cold, deep nutrient-rich seawater for mariculture and nuclear power plant cooling, the present work is divided into two parts. In the first part, a simple analytical model is developed for the evaluations of pumping power and temperature rise of cold deep seawater, and then for the second part a simulation will be carried out to study the engineering feasibility of nuclear power plant cooling. PUMPING DEEP SEAWATER THROUGH PIPELINES For the steady and incompressible fluid flow through a pipeline, the momentum balance can be represented by the celebrated Bernoulli equation: A(v2/2) + gAh + I dP/p -- Wp ÷ Z(f(L/Rh)vZ/2)i ~- E(evv~/2)i : 0 i
(1)
i
where v is the average velocity of the fluid, h is the gravitational height, P is the fluid pressure, 9 is the fluid density inside the pipe, W~ is the pumping work to the fluid, g is the gravitational acceleration, L is the pipe length. The fifth term of Equation (1) represents the summation on all sections of straight conduits, and the last term represents the summation on all fittings, valves, and bends etc. f i s the friction factor depending on Reynolds' number and can be expressed as, according to Moody (1944), for smooth pipe:
~16/Re f----- ]0.0791/R¢ °.2~ ~0.046/Re °'2
R e < 2,100 2,100 < Re <__ 20,000 20,000 < R e ~ 107
(2)
where Re is defined as vD/v, D is the pipe inside diameter, and v is the kinematic viscosity of the fluid. R h is the mean hydraulic radius, and for circular pipe ,R h = 0 / 4 . e v is the friction loss factor due to fittings, valves, and bends etc. To simplify the analysis, the following assumptions are made: (1) Seawater is incompressible. The cross-section of pipeline is uniform and the pipe is straight all the way from seashore down to offshore deep sea, as shown in Fig. 1. Therefore the average velocities of the seawater at the intake and at the outlet of the pipeline are the same, i.e. Av = 0, and the friction loss factor can be neglected, i.e. ev = 0. (2) The seawater in the pipeline is all at the same density as the intake level. Therefore, P = Pa -----PH = constant, and
Engineering analysis of pumping cold deep nutrient-rich seawater 2_"~,,=
Seo sur foce
% 1 " ~
X.L
503
Y =0
-
H
"X
J
×=0 FIG. I.
Schematic diagram of the basic pipeline configuration. 2
I
2
de/p = I dP/pn -----(Pz -- Pa)/Pn.
1
(3)
1
(3) The outlet of the pipe is at sea level, and the pipe is circular. (4) Only one straight pipe is considered in the present analysis, so that Z (f(L/Rh)v2/2)i = f(L/Rh)v2/2.
(4)
i
From preceding assumptions, Equation (1) then can be written as: Wp = gH + (P2 -- PO/Pn + f(L/Rh)v~/2.
(5)
Since the seawater is pumped into the atmosphere at the outlet, the outlet pressure is equal to the ambient pressure Pa, i.e. P2 = Pa. Thus the intake pressure P1 can be evaluated by the hydrostatic relation: el = Pa -~- Ilg Psgd Y -----P2 + I~ Psgd Y
(6)
where p~ is the seawater density distribution outside the pipe, and Y represents the depth from sea surface. Substituting Equation (6) into Equation (5), we get Wp = gH -- ~noo(p( Y)/Pn)gd Y + f(L/Rh)v2/2.
(7)
Normalization of Equation (7) gives wp = 1 -- f0l p ' d r + (vO'/2g) (L/H)f/Rh where wp ==- Wp/gH, y ~
(8)
Y/H, p*(y) = p(Y)/pn, and Z = 1 -- j"01p*dy.
Here, Z represents the density-gradient-head loss depending on the density distribution. Since there exists thermohaline circulation at deep sea region, the variation of density with depth is generally not so uniform that a single profile p(Y) can be approximated. Therefore, instead of direct integration, a finite difference summation is used to calculate the densitygradient-head loss, i.e.
504
QttAo-HSIN WEI, BIN-JUINE [-'IUANGa n d MING-SHENG KONG
Z
=
1 --
(9)
Y~'pi*L.~yi
i
where ~ i * = (Pfl + p~_,*)/2, and Ay; = Y i - )'r r Since the density distributions are different at various oceans and in different seasons, Z is a regional and seasonal function determined from actual measurement. Substituting Equation (2) for friction factor f into Equation (8), we obtain
wp =
Z -F 32 nRe, Z -k 0.1582 nRe 7/4, LZ + 0.092 nRe 9!s,
R e ~ 2,100 2,100 < R e ~ 20,000 20,000 < Re ~ 10~
f
(10)
where n, (v2/gD a) (L/H). Equation (10) shows that the required pumping work is a function of Z, n and Re as plotted in Fig. 2, and n is a factor depending on the viscosity of the seawater and the geometry of the pipeline. =
IO2
.g
o
0-1
i
0-2
IO3
104
105
106
Re
FIG. 2. Specific pumping work (Wp) vs. Reynolds number (Re).
The variations of Z value in eastern coast of Taiwan ranges from 0.001 to 0.002 for depth down to 1,000 m. It is small, but cannot be arbitrarily ignored. If the flowrate is very small such as in mariculture applications, Z becomes dominant. For high ttowrate such as in
Engineering analysis of pumping cold deep nutrient-rich seawater
505
nuclear power plant cooling application, it can be neglected as compared with the friction loss. From Equation (10), the total pumping power I~'p for a given mass flowrate of deep seawater mc from depth H can be evaluated by the relation: ff/p = wp g H m¢.
(11)
HEAT LOSS DURING PUMPING When pumping the cold deep seawater through pipeline, the water will be warmed due to the heating by the outside warmer seawater through the pipe wall. A simple analytical model is developed here to predict the thermal loss. By energy balance to a differential volume of seawater inside the pipe dL, the following equation can be derived: r n c C p d T - = U n D ( T , -- T ) d X
02)
where Cp is the specific hcat of seawater, T is the mean bulk seawater temperature at L, U is the overall heat transfer coefficient across the pipe wall, T, is the temperature distribution of seawater with respect to depth, and L is the position from the intake. From Fig. 28, the transformation of the coordinate gives d L = -- ( L / H ) d Y.
(13)
Substituting (13) into (12) and rearranging, we obtain d T / d Y = - - ( 4 L / k P r R e ) ( L / H ) (T,( Y)) -- T ( Y )
(14)
where k is the thermal conductivity of seawater inside the pipe, and Pr is the Prandtl number. Equation (14) can be solved if the temperature distribution of seawater, T~(Y), was known. In many oceans, the temperature distributions along depth are so uniform that an exponential function, Equation (15), can be used to fit the measured temperature. T,(Y) = To~ + (L(O) -- T~) exp (-- ~ Y)
05)
where [3 is a constant depending on location and season, and T® is the temperature at infinite depth. Normalization of Equation (14), in conjunction with Equation (15) will give: d t / d y - - ¢t = -- ¢t~
where t = t~ ~
[TA0)
--
T(Y)]/[T~(O)
ITs(0) - - T ~ ( r ) ] / [ L ( 0 )
= E [1 -- exp (-- $Hy)]
--
L(H)]
-- rs(H)]
(16)
506
CHAO-HSIN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG
3,-~ Y/H e = 4LU/kPrR~ = 4LU/kP~
Pe -- Peclet n u m b e r -- P~Re E ~ IT,(0) -- T•]/[L(0)
-- T,(H)].
Solving Equation (16) with b o u n d a r y condition, t(l) --= 1, we obtain the fluid temperature distribution inside the pipe, tO') = E - -
[eEl(1~ ÷ e)] exp ( - - Fy) 4- [1 -- E -t- eE exp (-- r ) / ( I ' 4- e)] exp [e O, -- 1)]
(17)
where F = [3H. F r o m Equation (17), the outlet temperature of cold deep seawater drawn through a straight pipeline can be determined: t(0) = to = E + (1 -- E) exp (--~) -- eE {1 -- exp [ - - ( P ÷ e)]}/(r + e).
08)
The unity of t o means no thermal loss during pumping which takes place for perfectly insulated pipe, i.e. U ~ 0, or ~ -----0. The value of t o is always less than one, and thus indicates that the a m o u n t of heat of the deep seawater is being remained after p u m p i n g out of sea surface. Therefore, the thermal loss during p u m p i n g can be readily examined from the values of t o. The factor ~ has the physical meaning of the overall heat transfer across the pipe wall, and I' represents the effect of seawater temperature distribution on the thermal loss. [3 or I" is zero for constant-temperature sea and approaches infinite for a b r u p t change of temperature from sea surface. Equation (18) is plotted in Fig. 3 to illustrate the trend. 1.0
t
b
I
"1
i
i
i'
i
'f'
I
I
I
I
1
E--1.2
-\\\\ 0.5
2.0
_
_
1.5
I 0
I
I
I
I I0
l
-
I
i
I
I
I
I
)
20
FIG, 3. Deep seawater temperature at pipeline outlet.
I
Engineering analysis of pumping cold deep nutrient-rich seawater
507
COOLING OF NUCLEAR POWER PLANT BY COLD DEEP SEAWATER In drawing cold deep seawater through long pipeline, power is needed to compensate the friction and density-gradient losses and the seawater is warmed up by the warmer seawater outside the pipe all the way up to the sea surface. The possibility of using this warmed deep seawater as a cooling agent for a power plant depends upon the flowrate and the pipeline design such as length, diameter, and material of the pipe. Power plants were originally cooled by the surface seawater. According to the principle of thermodynamics, the replacement of cold deep seawater as coolant would reduce the condensation temperature of the power cycle, and thus promote the thermal efficiency. As a first order approximation, assume that the thermal efficiency rI is proportional to Carnot efficiency, i.e. (19)
1] = I'Vn,t/QH o~ 1 - - T e / T .
where ffznet is the net power output of the power plant, QH is the heat added to the boiler, Tc is the condensation temperature, and T n is the boiling temperature. For simplicity, we assume that the replacement of cold deep seawater as coolant will lower the condensation temperature by an amount of Tso - - To, where Tso is the surface seawater temperature, and To is the deep seawater temperature at the outlet of pipeline which can be evaluated by Equation (18). The new condensation temperature To* then becomes T:
(20)
= Tc - - (7",0 - - To)
and the new thermal efficiency 1]* becomes q * = (F,,t/QI-I ~ 1 - - T~*/T H
(21)
where Wn~t* is the new output power. Here, we also assume that the higher new output power can be generated by a properly renewed turbine generator, and all the components in the power plant can be rebuilt to meet the power output increase due to lowering the condensation temperature. Therefore, the ratio of power outputs is
~.o,*/ff'.,,
= l +
(T,o
7"0)/(7:. T3.
-
-
(22)
The net power gain by deep seawater cooling G is the difference between the power increase, l)¢,et* -- Whet, and the seawater pumping power, Pgp. Therefore,
G-- (wo:-
z&,,)
-
w,.
(23)
Whet- ~rp.
(24)
Substituting Equation (22) into (23), we obtain G = E(r~o- r o ) / ( r . -
rc)l
From Equation (24), it can be seen that the net power gain by deep seawater cooling is dependent on the outlet temperature of pipeline, the highest and the lowest temperatures and the net power output in original power cycle, and the pumping power consumed in drawing deep seawater through pipeline.
508
CItAO-HSlN WEI, BIN-JUINE H U A N G and MING-SHENG KONG
APPLICATIONS FOR NUCLEAR POWER PLANT COOLING AND MARICULTURE ON THE EASTERN COAST OF TAIWAN Taiwan is a small spindle-shaped island located in the western Pacific ocean. Preliminary investigation indicates that the eastern coast of Taiwan is very similar to the Virgin Islands in both meteorological and oceanographic conditions. Therefore, the applications of cold deep seawater on the eastern coast for nuclear power plant cooling and mariculture will be investigated according to the previous modelling. Two locations on the eastern coast were selected for the present study. The results of the physical oceanographic measurements in spring season at these two locations are shown in Tables 1 and 2 (Chen and Lien, 1977). The temperature distributions are first least-square fitted to Equation (15) with the assumption that Too is I°C. The values of the exponents [3 are then determined and shown in Figs. 4 and 5. The density distributions are plotted in Fig. 6.
1. Pumping power evaluations From Equations (10) and (11), we know that the pumping power required for drawing deep seawater through pipelines depends on the intake level, the total length and the diameter of the pipeline, and the flowrate. The simulation is carried out for pipe diameters D = 7.5, 10, 15, 50, 100, 150 cm. The first four diameters are suitable for mariculture application and the rest are suitable for power plant coolant conduits. The intake levels H are taken as 400, 600, 800 and 1,000 m for the present calculation. The results are shown in Figs. 7-12.
Temperature,
°C 27.2
20
I0
0
30
--TStotion
3 0 : 2 2 ° 4 5 ' N, 121° 17'E
IOO 200
-
o Measured
300T , Tco ¢ ( To_Too)e- ¥# 400 E T¢o= I o c =
500 --
0
--
TO, 27.2°C = 0.00249
m"1
600--
7OO 8OO
900
I000
Fla. 4. Temperature distribution at Station No. 30.
Engineering analysis of pumping cold deep nutrient-rich seawater
509
TABLE I. OCEANOGRAPHIC DATA AT STATION NO. 30 (121°17'E, 22°45'N) WITH OFFSHOREDISTANCE 19 km.
Depth
Temperature
Density
(m)
(°C)
(g/L)
0 10 20 30 50 75
27.16 26.92 25.88 25.80 24.38 23.45 21.03 20.43 18,81 15.85 14.31 12.82 10.27 8.53 7.34 6.25 5.58 3.96
1022.08 1022.29 1022.58 1022.57 1023.09 1023.39 1024.14 1024.33 1024.72 1025.39 1025.67 1025.92 1026.34 1026.62 1026.82 1026.97 1027.06 1027.23
I00 125 150 200 250 300 400 500 600 700 800
1000
TABLE 2. OCEANOGRAPHIC DATA AT STA~ON NO. 31 (121°46'E, 23°45'N) WITH OFFSHOREDISTANCE 10 kin.
Depth
Temperatur¢
Density
(m)
(°C)
(g/L)
0 10 20 30 50 75
25.48 25.27 25.17 24.74 23.89 22.28
1022.92 1023.02 1023.09 1023.21 1023.48 1024.00
I00
20.31
1024,57
125 150 200 250
18.97 17.65 15.62 14.07 12.89 12.78
1024.92 1025.23 1025.67 1025.90 1026.08 1026.59
300 400
5O0
8.51
1026.88
600 700
6,97 5.96
1026.95 1027.15
800 I000
5.25 4.33
1027.23 1027.39
It can be seen from the calculations that the required pumping power is lessthan 100 kW for pipe diameter below 15 cm and mass flowrate lower than 100 tons/hr which is just in the range of mariculture application. To reduce the pumping power in nuclear power plant cooling application, it is necessary that the pipeline diameter has to be larger than 50 cm.
510
CHAo-HsIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
0
Temperoture, I0
"T-T -
100
Stati
=C 20
25.5
30
:5L23° 45' N, 121° 4 6 ' E
-
200 -
o Meosured
300--
400
-
E
500( To - Too I ¢ ,a'r 6OO
TGo-- I°C To = 2 5 . 5 °C ~ =0 . 0 0 2 3 3 m "t
700
8OO
11300 FIG. 5.
Temperature distribution at Station No. 31.
Density
0
1022
1023
1024
g/L
1025
1026, 1 0 2 7
1028
X
:
I00
200
300
4OO E
500 --. 0 Station 3 0 ( 2 2 * 4 5 ' N t 121= 17'E) t ~ _ ~ Station 31 (23=45 , N, 121° 4 6 " E )
6OO 700 8O0 9OO
l
_ I000 ~ FIG. 6. Density distributions at Stations No. 30 and 31.
Engineering analysis of pumping cold deep nutrient-rich seawater IO"I ~
-
~
II ~
10"2
lilt~ill" /#77I .,2"i4"//
,~.
~2~'17'E
~ ' ~ ,
off-shore distonce19 km)
,~.~",'// /#.~.~//
•~
511
~ ....
H =400 m 600 m
----....
.ooo ,.
800,. D,: ~.S ~m ok ,o c~
ildYl
.//,;7
°;" '~ c~
7
D4: SOcrn
Ds--I00 cm 10"4 I02 Fio. 7.
'°'r ~-
i
r , ll,,,I
D~ I50cm , , t .... I , , 104 Flowrofe me, k g / h r
i
IO3
" ....' Station30
'
1 ' 7 "Ii
///
i roo
/
0
tO4
" 7
I I
~ ~/
103
,
,
, I,,,,
IO6
Pumping power vs. Mass Flowrate at Station No. 30 (I~p: 10-4-10 -I kW).
,,o,
i
I IO5
, I ....
I
/d# ~4 ,~
1
/ 'I 7
I
,
,A,~,;I
-.
~ I0,~
Flowrate me,
106
iO7
kg/hr
FIG. 8. Pumping power vs. Mass Flowrate at Station No. 30 (/~'~,: 10-1-101 kW).
512
CHAO-HSlN WEI, BIN-JUINE HUANG and MING-SHENG KONG
r
i
:1,
ii
,
i,
,
,,i
i
Station 30
/ 8 .& ~ m
103
I0 2 104
L
I
]
105
I
106 Flowrote
Fla. 9.
I I
, i
L
,
i
J i
107
me,
1
I() ~q
kg/hr
Pumping power vs. Mass Flowrate at Station No. 30 (l+'p: 102-106 kW).
i(~ I ......
,-
,
,
°tY V II
,,
io-~ S t a t i o n 5 1 : 2 5 ° 4 5 ' N , 121° 4 6 ' E ( o f f - s h o r e distance I0 k m )
E 7# Z l I -
a. ~.
~ a_
t6 ~
-
H= 400
...... -----
600 800
.....
I000 m
m
m m
,
Di = 7 . 5 c m D2 = I0 c m D3:15
c m
134= 5 0 c m D5 = I 0 0 c m D e = 150 c m
10-4
~
IO2
j
,
L
iO3
104 FIowrate m c ,
FIG. lO.
,
,
I
ILL,I
L
i0 5
I.
,
J
I~I
106
kg/hr
Pumping power vs. Mass Flowrate at Station No. 31 (l~v: 10-4-10 -x kW).
Engineering analysis of pumping cold deep nutrient-rich seawater
513
io2
io I
& 0~ [00
~
~0 -L
103
i
'
~
'
7
.
104
.
- -
/ ~ / z //,~/~/4 ,/ ~//,~ .
Flowrofe
.
....... -----
.....
.
105 mc, kg/hr
, ,,,I
H=400 m 600 m 800 m I000 m
I06
i/
107
Pumping power vs. Mass Flowrate at Station No. 31 (g/p: 10-1-10 s kW).
F I G . 11. io 5
, [frr, I
d
l04 '5 (D o t:. c {:L 103
IO:
104
j/ f
J
t
/
i! / ro5
: j t
/
/ ill/
Ftowrofe
ill
ro6 me,
107
[ r r T, t
106
kg/hr
FIG. 12. Pumping power vs. Mass Flowrate at Station No. 31 (I~V~,:IOt-105 kW).
2. Heat loss during pumping Equation (18) gives the outlet temperature of cold deep seawater through the pipeline if the overall heat transfer coefficient U is determined. In general, the overall heat transfer coefficient can be evaluated by the following equation:
514
CHAO-HSIN WE1, BIN-JUINE HUANG and MINO-SHENG KONG
U ~ ll[lfh i ~ I. (rolri)12~ k,. + 11170]
(25)
where h,- -----convection heat transfer coefficient at pipe inner wall, ho = convection heat transfer coefficient at pipe outer wall, ri inside radius of pipe, r o = outside radius of pipe, and k w -- thermal conductivity of pipe material. =
Since the deep seawater is pumped through the pipeline, the heat transfer at the inner wall is forced-convection and can be evaluated by (Dittus and Boetler, 1930) [4.36, Re ~ 2,100. N,, = ~0.023 R 2 .8 Pr0"4 2,100 < R e
(26)
The heat transfer at the outside wall is determined by the tide current which varies from location to location in the sea and is very difficult to measure. However, the pipeline is usually laid out along the sea bottom so that the effect of tide current can be neglected and the heat transfer at the outside wall is dominated by free convection. The following empirical equation for free convection then can be used (Churchill and Chu, 1975): N, ½ ---- 0.60 + 0.387 (G,P,/[I + (0.559/P,)9118]1~19)ls~
(27)
for 10 _5 < G,Pr < l0 n, where Gr = Grashof number based on the average temperature difference between the wall and outside seawater temperatures and the outside diameter of the pipe. If the pipe is not well insulated, such as using bare metal pipe, the thermal resistance through the wall is negligible compared with convective heat transfer. Therefore
v ~ h,ho/(h, + ho).
(28)
With the previous data, the simulation is carried out for pipe diameters D ---- 7.5, 10, 15, 50, 100 and 150 cm, and intake level H = 600, 800 and 1,000 m. The results are shown in Figs. 13-18. For well-insulated pipes, the heat resistance through the insulation layer is so high that the overall heat transfer coefficient U approaches zero, and the outlet temperature of the deep seawater is just the intake temperature as shown in Figs. 13-18. 3. Feasibility of nuclear power plant cooling application Using Equation (24) and previous simulation results, the feasibility of nuclear power plant cooling application can be determined. The nuclear power plant selected for the present simulation is the unit now located at Chinshan in northern Taiwan. This power plant delivers a net generator output (li/~t) of 635 MW with the highest cycle temperature T H of 288°C, the condensation temperature Tc of 47°C, and the cooling water flowrate mr of 3.3 X 107 kg/hr.
Engineering analysis of pumping cold deep nutrient-rich seawater
28
'
' 'J .... i
'
''1
.... I
'
''1 .... I
'
' '1 .... J
515
''1 ....
D~ISOcrn
2O H=600 rn
1 ~ 0 ~ ~ 7 .
e~
E I0
Intoke fempereture
7.3
0105
104
IO5
Flowrote
FIG. 13.
106
I0 7
108
rnc, kg/hr
O u t l e t t e m p e r a t u r e o f s e a w a t e r vs. F l o w r a t e
at S t a t i o n N o .
30 (H =- 600 m).
28
o
2o
H,8OOm
d E o
~
~50crn
~0 Intake tern~rature
5.6
IO3
104
105
IO 6
Flowrotem=, FIG. 14.
Outlet t e m p e r a t u r ~
IO7
10 8
kg/hr
o f s e a w a t e r vs. F l o w r a t ¢
at Station
No. 30 (H = 800 m).
The net power gain by deep seawater cooling (G) is calculated for two limiting cases: the well-insulated pipeline and the bare metal pipeline. Tables 3 and 4 show the variations of net gain with pipe diameters and intake levels. It is seen that positive gain can be obtained only for pipes with diameters larger than 150 cm. FURTHER
DEVELOPMENT
OF STEPWISE PIPELINE
A simple theoretical model is developed in the present research work to study the technical feasibility of pumping cold deep nutrient-rich seawater for nuclear power plant cooling and mariculture. The model assumes that the pipeline is straight and directly stretched into the intake level in deep sea. However, the bathymetrical map of Taiwan
516
CHAo-HSIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
28
TIIILT
I
' E''''''
I11~
'T']
d ~ntake t e m p e r a t u r e 4.0
, ,J,,,,I 103
t
~ ,,,,,,I
104
,
L ,,,ql[
iO 5 Flowrate me,
FIG. 15.
Outlet
28
temperature
'
'
'1 ....
of seawater
I
'
"
~I'""1
L I II~L~l[ Io 7
10s
~ tili~l 10 o
kg/hr
vs. F l o w r a t e
i
t
at Station
I , i .....
i
No.
~ ,llL,,i
30 (H
1
,
=
I000
m).
,111,
2O 0)
I0 0
7.0
103
104
105 F ] o w r a t e m c,
FIG. 16.
106
i0 7
~0fl
kg/hr
Outlet temperature of seawater vs. Flowrate at Station No. 31 (H = 600 m).
shows that there is a very narrow shelf along the eastern coast. Generally the continental slope drops off to 1,000 m within 10 km from the coast. At several points off the coast, the 1,000 m contour is even closer, within two km. Therefore, an underwater straight pipe line can hardly be constructed to reach the deep sea region. Instead, a stepwise pipeline as shown in Fig. 19 is more likely to be built in practical applications. Thus the previous mathematical model should be modified by a successive stepwise calculations using the similar forms of the equation. Under this circumstance, the total pumping work equation becomes, from Equation (1),
Engineering analysis of pumping cold de¢p nutrient-rich seawater 28
'
r
'1'"'1
'
'
'l""f
'
'
\\\
H=SOOm
e:
' ']""l
~ ~
'
'1
....
E
kO\;50c
'
'
517
' ....
m
E ,o 5.3 . . . . . . . . .
Z_o,_ok.,,_m_~r._otur,,_ _ _
l0 3
l0 4
l0 5
_
_
10 6
Flowrote me,
~
10 ?
l0 8
kg/hr
FIG. 17. Outlet temperature of seawater vs. Flowrate at Station No. 3! (H = 800 m).
28
'
'
'~
....
I
'
'
'~t'"l
¢
..,ooo
#
'
'1
. . . . . . . . . . . . .
I
. . . . . . . .
\\\ \\,%°° \ \ \ , : o \ \X,°°
i Intoke temperoture
4,3
l
T 11111ii
010 3
I04
k
I I I~I,I[
i
i ii,ill[
I
I I
I0 5 I0 6 Fk>wrote me, kg/hr
I0 7
I0 8
FIe, 18.
Outlet temperature of seawater vs. Flowrate at Station No. 31 (H = I000 m).
w, =
[gAh, + / d ? / O , +:
/. i=1
(29)
.ILl
a n d the t e m p e r a t u r e rise at the i-th section becomes d T i / d X i = (Ui~D,/mcCp) (T~ - - Tt)
i = 1, 2, 3 , . . .
with the b o u n d a r y c o n d i t i o n s : for i ---- l, 7'1(0) = T~ at X1 = 0 Pz(O) =
PH a t X z =
0.
(30)
518
CHAo-HSlN WEI, BIN-JUINE HUANG a n d MING-SHENG KONG
TABLE 3.
D (cm)/H
NET POWER GAIN (MW) BY DEEP SEAWATER COOLING AT STATION NO, 30
(m)
7.5 10 15 50 100 150
400
-- 1.1850 --2.9787 --4.2540 - - 1.2756 - - 8.9888 30.294
x x x ×
600
107MW 10" 10 ~ 10 a
Bare - - 1.1852 --2.9787 --4.2540 - - 1.2684 - - 1.6730 37.580
800
metal pipe x 107MW x 10 ~ x 105 × 10 :~
-- 1.1864 --2.9816 --4.2582 -- 1.2655 2.5100 41.879
x x × ×
1000
107MW l0 s lO s I0 a
- - 1.1881 --2.9865 --4.2640 -- 1.2634 6.3890 45.833
× x × x
107MW l0 s 10 ~ 10 a
Well insulated pipe D(cm) / H(m) 7.5 10 15 50 100 150
400
600
- - 1.1851 × 1 0 7 M W -- 2.9787 x 10 ~ - - 4 . 2 5 4 0 x 10 ~ -- 1.2741 × 10 :~ -- 6.1697 34.300
TABLE 4.
:~ x × ×
107MW 106 IO t 10 ~
- 1.1864 -- 2.9816 --4.2582 -- 1.2641 5.1560 45.667
× z × ~
1000 107MW 10 n 10 '~ I0 :~
-- 1.1881 -- 2.9865 --4,2640 -- 1.2620 9.0150 49.588
x x x ×
107MW l0 s 10 ~ 10 :~
NET POWER GAIN (MW) BY DEEP SEAWATER COOLING AT STATION NO, 31
D(cm) / H(m) 7.5 10 15 50 100 150
- - 1.1852 - - 2.9787 --4.2540 - - 1.2669 1.1780 41.647
800
Bare metal pipe 600
400 --2.2493 --5.6539 --8.0756 --2.4629 - - 58.205 16,893
× x x x
107MW l0 s 10 ~ 10:5
--2.2487 --5.6513 --8.0705 --2,4533 -- 49.673 25.077
x × x x
800
107MW 106 l0 s 10 :~
1000
- - 2 . 2 4 7 7 x 107MW - 5.6503 x 106 - - 8 . 0 6 9 8 ~ l0 t - - 2 . 4 4 8 3 × 10 ;~ - - 45.273 29.515
--2.2487 --5.6516 --8.0705 -2.4466 -- 42,641 32,329
x × x ×
107MW 10 ~ l0 t 10 ;~
Well i n s u l a t e d p i p e D(cm) / H(m) 7.5 10 15 50 100 150
The
400 ------
detailed
the pumping
2.2493 5.6539 8.0756 2.4609 53.884 22.919
x × x x
computations station
600 107MW 106 105 10 ~
can
------
2.2487 5.6513 8.0705 2.4506 44.598 32.182
800 x × 7" x
107MW l0 s l0 s 103
be completed
when
------
2.2477 5.6503 8.0698 2.4456 40.418 36,349
× x ~'< x
1000 107MW 10 e l0 s 10 :~
the bathymetrical
------
2.2487 5.6516 8.0705 2.4439 38,204 38.576
information
× × × x
107MW 108 10 ~ 10 :~
around
is p r o v i d e d . CONCLUSION
From
the analytical
to the engineering and tions
nuclear
results, a number
feasibility
power
are summarized
plant
of pumping
cooling
as follows:
of conclusions cold
applications.
deep These
can be drawn
nutrient-rich encouraging
that have implications
seawater and
for mariculture
constructive
deduc-
Engineering analysis ol pumping cold deep nutrient-rich seawater v
519
~ 0 SUrfcIce n
H
FIG. 19. Real piping configuration.
(1) The pumping power required to draw seawater from deep sea is always less than 100 kW (134 h.p.) for pipe diameters below 15 cm and mass flowrate lower than 100 tons/hr which is suitable for mariculture operations. (2) Replacing warm surface seawater by cold deep seawater as nuclear power plan coolant is technically feasible and, hopefully, economically worthwhile for pipes with diameters larger than 150 cm and intake levels below 600 m. The present model can be extended to study the performance of the Ocean Thermal Energy Conversion (OTEC) system onshore. (3) For further practical development, more intensive investigations should be conducted on marine conditions at selected sites and on the economical and technical feasibility of seawater pumping, air-conditioning, fresh water production, and power generation. It is highly recommended to build a pilot plant onshore at Taitung for the purposes of cooling applications and mariculture experiments, and all possibly related works. The simplified model used here to assess the engineering feasibility of pumping cold deep nutrient-rich seawater for nuclear power plant cooling and mariculture is worth enlarging to design the deep seawater prototype pumping system. Acknowledgements--The work presented in this report was fully supported by the National Science Council
under contract NSC-66M-0407-20(01). We are grateful to Dr. C. T. Sieh, president of National Taiwan College of Marine Science and Technology, for his hearty encouragement. Thanks are extended to Drs. Shin Wang, Ju-Chin Chen, and Min-Pen Chert, Prof. Tsu-Chang Hung, and the crew of R/V Chiu-Lien for their valuable comments and substantial assistance in various ways. The authors are also deeply indebted to Misses Shui-Giin Huang, Wei-ShingChow, and Yih-Chyr Wang and Messrs Cheng-Long Kuo, Shang-Long Lia, Gung-Rong Chen, and Teng-Wei Yau for their conscientious effort in the conduction of this study. REFERENCES CHEN,W. C. and LIEN,S. L. 1977. Oceanographic Data of the Sea Surrounding Taiwan. Special Pub. No. 15, Institute of Oceanography, National Taiwan University. CHURCHILL,S. W. and CHU, H. H. S. 1975. Correlating Equations for Laminar and Turbulent Free Convectiort from A Horizontal Cylinder. Int. J. Heat Mass Transfer 18, 1049. CLAUDE,G. 1930. Power from Tropical Seas. Mech. Engng 52, 1039.
520
CHAo-HsIN WEI, BIN-JUINE HUANG and MING-SHENG KONG
DITTUS, F. W. and BOELTER, L. M. K. 1930. Univ. Calif. Pubs. Engng 2, 443. GRrelqN, O. M. 1975. The Ocean as a Renewable Source of Energy. J. Engng Ind. Trans. ASME 897. MOODY, L. F. 1944. Trans. ASME66, 671. OTHMER, D. F. 1976. Power, Fresh Water and Food from the Sea. Mech. Engng 27. OTHMER, D. F. and REELS, O. A. 1973. Power, Fresh Water and Food from Cold Deep-Sea Water. Science, N. Y. 182 (4108), 121. OTHMER, D. F. and REELS, O. A. 1974. Mar. Tech. Soc. J. 8, 40, WATT, A. D., MATHEWS, F. S. and HATHAWAY, R. E. 1977. Open Cycle Ocean Thermal Energy Conversion. A Preliminary Engineering Evaluation, U.S. Department of Energy, ALO/3723.76/3. ZENER, C. 1977. Solar Sea Power. Mech. Engng 27.