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re: using brine solutions to generate heat & electricity
3 sep 2001
toby  wrote:

>hi nick,

hi toby,

>sounds like a cool idea...

right. 

>> say it's 90 f outdoors (a cold spell in phoenix :-) we want to make our
>> r16 2' cube (g = 24ft^2/r16 = 1.5 btu/h-f) 70 f inside, using downstairs
>> evaporation and a 40% 90 f licl attic pond under a transparent roof. say
>> no heat flows downstairs from the attic via air circulation (when moist air
>> flows up and dry air flows down through a good sensible heat exchanger.)

we might not need a heat exchanger if the upward latent heatflow
is a lot larger than the downward sensible heatflow... 

>> we need (90f-70f)g = 30 btu/h of cooling. say the downstairs pond (or
>> a large plant) evaporates 24hx30/1000 = 0.72 pounds of water per day.
>
>so far, i understand.
>
>the "1000" is because it takes about 1000 btu's to evaporate 1 lb of water.

right.

>> at 40% and 90 f, the licl pond keeps the indoor vapor pressure 0.3096 "hg,
>> vs exp(17.863-9621/(460+70)) = 0.748 for 70 f air at 100% rh, making the
>> indoor rh = 100x0.3096/0.748 = 41%. comfy.
>
>i'm a awful lost here. it looks like you are dealing with the
>saturation pressures at the 2 different temperatures.

this structure is warmer upstairs than downstairs because of solar
attic heating during the day and attic water absorption at night...

>what are, and where'ld you get, the numbers 17.863 and 9621?

they are constants derived from two pairs of temperatures
and water vapor pressures in a psychrometric table. 

>where did you get the following equation from?
>
>    exp(17.863-9621/(460+70)) = pp (?)

that's a clausius-clapeyron approximation kindly donated by
local p chem prof ray schultz. a way to avoid using tables.

>it looks like 0.748"hg is the vapor pressure for 70f air at 100% rh
>---- the point at which condensation occurs. right?

right.

>460 + 70 is the rankine temperature right?

right.

here's a program that estimates the equilibrium concentration of a licl
solution after keeping it for a long time at a high temperature in phila
in july (w= 0.0133 and pa = 0.626 "hg) , and its vapor pressure after it
cools to 25 c... 

10 a1=12.7409'licl vapor pressure constants from the 1993 hawlader paper
20 a2=-.065536
30 a3=-8.2416e-04
40 b1=-4675.4
50 b2=+29.31
60 b3=+.66911
70 c1=372690!
80 c2=-1689.8
90 c3=-187.1
100 a11=1.002'specific heat constants...
110 a12=-.012505
120 a13=7.575e-05
130 a21=-.0005554
140 a22=-1.5178e-05
150 a23=+6.8248e-07
160 a31=5.2266e-06
170 a32=3.6623e-08
180 a33=-3.8345e-09
190 w=.0133'humidity ratio for phila air in july
200 pv=25.4*29.921/(1+.62198/w)'vapor pressure for phila air in july (mmhg)
210 for tc=20 to 100 step 20'solution temp (c)
220 tf=1.8*tc+32
230 tk=273.1+tc
240 c=a1+b1/tk+c1/tk^2-log(pv)/log(10)
250 b=a2+b2/tk+c2/tk^2
260 a=a3+b3/tk+c3/tk^2
270 conc=(-b-sqr(b^2-4*a*c)/(2*a))'equilibrium soln conc (wt%)
280 sg=(1.681+conc/100)/1.682'specific gravity
290 tk=298.1
300 ap=a1+a2*conc+a3*conc^2
310 bp=b1+b2*conc+b3*conc^2
320 cp=c1+c2*conc+c3*conc^2
330 pvc=10^(ap+bp/tk+cp/(tk^2))/25.4'vapor pressure at 25 c (mmhg)
340 t=25'c
350 as1=a11+a21*conc+a22*conc^2
360 as2=a21+a22*conc+a23*conc^2
370 as3=a31+a32*conc+a33*conc^2
380 cpp=4186*(as1+as2*t+as3*t^2)'specific heat (j/kgc)
390 print tc;tab(6);conc;tab(16);sg;tab(26);pvc;tab(40);cpp
400 next

temp  conc.    specific    vap.press    specific 
(c)   (wt%)    gravity     (" hg)       heat (j/kgc)

20    1.65099  1.009221    .736024      4143.615
40   27.70661  1.16413     .503139      4042.507
60   42.06722  1.249508    .163317      3985.536
80   54.91183  1.325873    .034401      3933.83
100  67.06037  1.3981      .004884      3884.274

looks like heating a licl solution to 60 c (140 f) makes it 42% by weight,
and its vapor pressure is 0.163 "hg after it cools to 25 c, so 1 ft^2 might
absorb 100(0.626-0.163) = 46.3 btu/h (0.0463 lb/h) of water vapor from 25 c
july air in phila, if it acts like an ashrae swimming pool, eventually
leaving the air with 100x0.163/0.948 = 17% humidity...

nick




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