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a thermal design for midland, tx
15 oct 2001
1. weather statistics and responses

nrel data show january is the worst-case month for solar house heating
in midland, when 1040 btu/ft^2 of sun falls on a horizontal surface on
an average 42.5 f day. 

july is the worst-case month for cooling, with an 82 f average temp and
a 68.5 f average daily min. the 0.0119 (pounds of water per pound of dry 
air) humidity ratio makes the partial pressure of water vapor in air
29.921/(1+0.62109/0.0119) = 0.562 "hg, vs exp(17.863-9621/(460+70)) = 1.119
"hg for 82 f air at 100 rh, so the rh is 100(0.0562/1.119) = 50.2% at 82 f
(using a clausius-clapeyron approximation.) the partial pressure of 100%
70 f air is 0.748 "hg, so cooling outdoor air to 70 f with a roofpond or
night ventilation would raise the rh to 75% on an average july day.
it looks like dehumidification is required for comfort.

if a house can heat and cool itself in the worst-case months using nrel's 
30-year averages, it can do so in the other months of an average year.
with some backup for less-likely non-average weather, it can do so over
a typical meteorological year, as evidenced by a spreadsheet simulation
using nrel's tmy2 weather data for midland.

we might heat and cool a structure with a "high-bandwidth," fast-charging
heat store on average days, assisted by a larger but slower-to-charge heat
store (a "trickle-charged heat battery") during less-likely strings of
non-average days, eg a cloudy week.

if the sun shines 50% of the time, and nature flips coins, the likelihood
of 2 cloudy days in a row is 25%, with 12% for 3, 6% for 4, 3% for 5, and
so on, so a cloudy-week heat store would be non-empty 99.78% of the time.
it might take a long time to recharge, and still be useful. long recharge
times mean lower heat transfer rates, ie smaller collectors and less heat
transfer area and less fluid flow needed for charging, so long-term heat
stores can be cheap, if they supply no energy on an average day. 

it is also useful to be able to suddenly raise or lower the fluid temp
in a heat delivery system once in a while to increase its heat transfer
rate on very cold or very hot days. this can reduce the required flow
rates and heat transfer area and cost of a heat distribution system.

we might store long-term heat and coolth in a concentrated lithium chloride 
solution. licl is a salt, like nacl. it is a desiccant, ie it has a great
affinity for water and releases heat when accepting water or water vapor.
i put an $85 h08-007-02 hobo data logger and 10 g of dry licl in a small
spice jar with holes in the top into a sealed jar with 400 g of damp
cookies (de ruiter's "het gouden speculaasje"), and sampled the rh every
6 minutes. it dropped exponentially from 72% to 37% in 3 days.

cyprus-foote mineral sells anhydrous licl powder for $4/lb in 55 gallon
drums. it has been used for air conditioning (see "unglazed collector/
regenerator performance for a solar assisted open cycle absorption cooling
system" by m. n. a. hawlader, k. s. novak, and b. d. wood of the center
for energy system research, college of engineering and applied sciences,
arizona state university, tempe, az 85287-5806 usa, in solar energy, v. 50,
pp 59-73, 1993.) licl is relatively non-toxic: ingesting 1 gram per day may
increase birth defects, but it was once used as a table salt substitute.

desiccants can store long-term heat in a very small volume compared to
hot water (tom lawand of brace research institute recalls a canadian paper 
describing a 1 m^3 zeolite _seasonal_ heat store with no loss of heat over
time and no insulation :-) the crc chem/phys handbook says licl's heat of 
solution is 8,850 cal/mole (with infinite dilution) and a calorie (capital
c) raises 1 kg of water 1 c (1.8 f), so it's about 4 btu, and a mole of
licl weighs 42 grams, vs 454 grams/lb, so we can store about 8.8x4x454/42
= 379 btu/lb of licl.

when i mixed equal weights of 70 f dry licl and water in a styrofoam cup
to make a 50% solution, the temperature initially jumped to 187 f (measured
with a raytek ir thermometer with a 500 ms sampling time), so the heat of
solution to 50% dilution is about 187-70 = 117 btu/lb (a conservative
estimate, ignoring the licl's heat capacity), so the 50% solution would
release another 379-117 = 262 btu/lb on further dilution to 0%. a solution
absorbing water vapor from air (vs liquid water) would also release the
heat of condensation, about 1000 btu per pound of water. hawlader's appendix
a has data for more accurate calcs.

it is very nice to be able to store 200-1200 btu/lb of solution with
no loss of heat over time...

2. system design

suppose we want to heat and cool a well-insulated space with a transparent
roof. we might put some thermal mass (eg large water-filled pipes) in the
space and control the room temp by controlling room airflow past the pipes. 

we could keep the mass warmer than room air in wintertime and cooler in
summertime with some "solar collectors" (how big?) in the attic. we might
use 2 shallow ponds, an open one containing licl that can evaporate water
to attic air during the day and condense water vapor from attic air at
night, and a water pond with a transparent cover that can heat water under
the cover or evaporate water above the cover. warm water rises, so the
water pipes in the conditioned space could naturally supply warm water
that flows over the water pond cover and cools and sinks back into the pipes
via a thermosyphon loop. water heating would require a small low-head,
low-energy pump (maybe a 4 watt pv-powered fountain pump, or a zomeworks
solar "teeter-totter" rocking beam pump with a shade so it oscillates :-)
is that an unacceptable complication?

on a very cold winter day, or during a cloudy week, we add heat to the
water pipe by adding some concentrated licl solution to the pipe water,
releasing 262 btu per pound of 50% licl. 

the sun would concentrate the licl pond all year. heating a solution to
about 160 f should make a 50% equilibrium concentration. with a short
time constant (rc~3h) it could get hot and evaporate water during the
day, and the vapor might condense on the underside of the attic glazing
and run back into the downstairs pipes in a "single-effect solar still." 
steve baer might devise a "multiple-effect humidification still" that
works a lot more efficiently.

at night, the licl pond would cool and accept water vapor (if any) from
attic air. we could cool the downstairs pipes by pumping some water up
onto the water pond cover (one time) and letting it evaporate. cooler
water would sink back down through the pipes.

for dehumidification, we might keep the water pond dry and open a damper
(a simple attic-floor skylight?) or turn on a fan to circulate conditioned-
space air through the attic at night. herbach and rademan near phila
(800-848-8001) sell fine navy surplus humidistats with 7.5 a spdt switches
in attractive brass boxes for $4.95 as cat #tm89hvc5203. we might also use
increased humidity as a signal for more ventilation, if the indoor humidity 
is adjusted back to 50% after adding fresh outdoor air.

licl is not happy accepting water vapor when it is hot and its vapor
pressure is high, so cooling control can become predictive: on a hot
sunny day, the licl pond in the attic will nto be able to accept much
water vapor from the water pond, so we need to store enough cool water
downstairs to get through a hot day, before we are sure how hot it
will be. ditto humidity. some way to store dryness downstairs (eg a
licl fountain or concrete slab) would be helpful.

3. sizing

suppose we want to heat and cool a 24'x24'x8' tall space in midland.
with 48 ft^2 of shaded r4 windows (8.3% of the floorspace) and the rest
of the walls and ceiling made from 7 8'x24'x12" structural insulated
panels (r48 sips), with 0.2 air changes per hour (15 cfm) and no 
internal heat gain. its thermal conductance would be about 476ft^2/r48
for the ceiling plus 48/4 for the windows plus 720/48 for the walls
plus 15 for air leaks, a total of 54 btu/h-f. 

with 2 4'x24' shallow ponds in the attic, under a transparent south roof,
it might look like this (in courier font):

            clear roof      |           .              4'
      water    dark    licl |
---- ~~~~~~~~--------~~~~~~~~------------------------
   ||p      |                            r48         |
r4 ||p      |                                        | 8'
   ||p      |   r48  (the ps are vertical water-     |
    |p      |         filled pipes in a closet.)     |

        4'      4'      4'         "... it needs more je ne sais quoi."

     ------------------------------------------------   "...formulaic 
    |       |       |       |                        |      contextularity?"
    |       |       |       p                        |
    |       |       |       a                        |
    |       |       |       r                        |
    |       |       |       a r                      |
 ---|       |       |       b e                      |
|   |       |       |       o f                      |
|  ||       |       |       l l                      |
|  || water | dark  | licl  i e                      |
|  || pond  | floor | pond  c c                      | 24'
|  ||       |       |       | t                      |
|   |       |       |       t o                      |
 ---|       |       |       r r                      |
    |       |       |       o                        |
    |       |       |       u                        |
    |-------|       |       g                        |
    |p      |       |       h                        |
    |p      |       |       |                        |

the south attic roof could be clear corrugated dynaglas polycarbonate
greenhouse roofing. the ponds could be a layer of epdm rubber draped
over a 2x4 perimeter berm with a single 4'x24'x0.020" layer of clear
flat replex polycarbonate as a water pond cover.

on an average january day, the space needs (65-42.5)54 = 1215 btu/h or
29.2k btu of heat. with 90% roof and cover solar transmission, the water 
pond gains 0.9x0.9x1040 = 842 btu/ft^2. it loses 6h(120-42.5)/r2 = 232
btu/ft^2 at 120 f with an r1 roof and cover and a 6h collection day.

the net gain is 610 btu/ft^2, so we need at least 29.2k/610 = 48 ft^2
of water pond, so the 4'x24' pond should work, with extra hot water for
showers, especially if the licl pond is mostly concentrated and the
4'x24' dark attic floor strip between the ponds raises the attic air
temp as a "parasitic heater" (see "khanh's radically new approach..."
on page 118 of "new inventions in low-cost solar heating," by william
a. shurcliff, brick house, 1979.)

the downstairs water pipes (vertical, in a closet) need enough thermal
capacitance to keep the space warm over an average day. if c pounds of
water cool from 120-80 f, c >= 29.2k/(120-80) = 730 lb, assuming the
space contains no other thermal mass. 

if the space is 70 f at dusk and 60 f at dawn on an average jan day,
the pipes need enough surface to supply 1215 btu/h with an 80-60 = 20 f
pipe-to-room air temperature difference. say the pipe closet has a 1'x4'
motorized damper at the top (honeywell's $50 6161b1000 damper actuator
has a motor the size of a ping-pong ball that uses 2 watts when moving
and 0 watts when stopped :-)

one empirical chimney formula gives cfm = 16.6asqrt(hdt) = 188sqrt(dt)
with a = 4 ft^2 and h = 8'. the heatflow out of the closet would be
about 188dt^1.5 = 1215 btu/h, which makes dt = 3.5 f, as 60 f air
enters the closet through a 4 ft^2 opening at the bottom and 63.5 f
air leaves via the top damper at 350 cfm. 

the average closet air temp near the pipes is about 62 f, so an 80-62
= 18 f pipe-air temp difference drives the pipe cooling at dawn. with
slowly-moving air and a 1.5 btu/h-f-ft^2 film conductance, we need about
1215/18f/1.5 = 45 ft^2 of pipe surface. we might use n d" diameter x
8' tall pipes, with 45 = 8npid/12 and 730 = 8n64pi(d/24)^2, eg 4 8" or
2 12" x 8' thinwall pvc pipes.

norman saunders says a properly designed solar house is as likely to need
cooling as heat on an average winter day, when ashrae's upcoming adaptive
comfort standard says this midland house should be 54+0.31(42.5) = 67.2
+/- 4.5 f for 90% satisfaction. this comfort band is less than the 3.5 f
difference above, and the space is well insulated, so more uniform air
temps may not be needed for comfort.

during swing seasons when indoor and outdoor temps are about the same,
we might open a window (gasp :-) or keep the pipes warm and the room air
dry or vice-versa, using humidity to extend hysteresis in each direction
before changing the pipe temp, which is expensive, energy-wise. it would
be easy to change the humidity in the space with a licl fountain next to
a water fountain, adding about 2 pounds of water to raise the interior rh
from 30% to 70%. alternatively, we could just keep the pipes at 54+0.31(68)
= 75 f (like harry thomason's "dead battery.")

as another alternative, we might vary the air velocity with a ceiling fan
or keep one set of pipes cool and another warm, and use 2 motorized dampers.
what's the range of outdoor temps consistent with ashrae's adaptive indoor
comfort standard, given a constant pipe temp with lower humidities and
higher ceiling fan speeds up to say, 130 fpm, accompanying higher indoor
dry bulb temps?

the space requires 5x29.2k = 146k btu over 5 42.5 f cloudy days in a row,
so we need to add 146k/262 = 557 lb or 69 gallons or 8.7 ft^3 of 50% licl
solution at 0.01 gpm over that time. this defines the minimum licl pond
depth for cloudy-day heating: 8.7 ft^3 = 4x96d/12 makes d = 0.27". we
might use a 1" pond with rc = 64 btu/f-ft^3(1"/12"/ft/1.5btu/h-f-ft^2)
= 3.6 hours (notice how nicely the units cancel) that cools from say,
130 to 90 f in -3.6ln((90-68)/(130-68)) = 3.7 hours on an average 68 f
july night. and we might store some extra concentrated licl in a separate
closed container with a "turbo-valve" for cold spells. we could easily
store some summer heat for winter this way. 

on a 0 f night, the space needs (65-0)54 = 3510 btu/h of heat, ie 3510
= 188dt^1.5, so dt = 7 f and the average closet air temp is 63.5 and the
t(f) pipe-air temp diff is t-63.5 f... 4 8"x8' pipes have 67 ft^2 of
surface, so they can supply 3510 btu/h of heat with a 3510/67/1.5 = 35 f
temp diff, so we need to raise the water temp to 35+63.5 = 98.4 f on a
0 f night, suddenly adding (98.4-80)730 = 13.4k btu of heat in the form
of 51 lb or 6.4 gallons of 50% licl solution. 

the rate of water vapor diffusion into the licl pond (vs evaporation from
the water pond) appears to be the limiting factor in cooling capacity.
the data in hawlader's appendix indicate that a 50% licl solution at 90 f
would have a vapor pressure of 0.109 "hg, which corresponds to a dew point
of 19 f and an rh of 7.5%. a 60 f water pond with a 60 f saturated layer
of air with 0.528 "hg of vapor pressure near the surface would lose
100(0.528-0.109) = 42 btu/h-ft^2 of latent heat to the 0.109 "hg attic air,
according to one ashrae swimming pool formula, ie 4021 btu/h for the 4'x24'
pond, but i only got about half that rate in a recent crude closed cooler
experiment with a pan of water downstairs and a pan of licl upstairs and
no control of humidity. however, this midland space only needs (84-65)54
= 1026 btu/h of cooling on an average july day, ie half of the 4'x24' 90 f
licl pond's capacity, so this system may suffice. if not, the licl pond 
could be bigger, and we might use a fan in the attic to make it cooler
and increase its cooling capacity.

evacuated latent heat exchangers (as in hawlader's paper or german fridges
and railroad ac systems) have dramatically larger heat transfer rates than
those that operate in free air with non-condensibles, but are they worth
the extra complexity? we might produce the mild vacuum required by (rarely)
boiling some water and letting the steam condense, as in a high-school
collapsing can experiment, or run some pressurized house water through
a simple aspirator. we could use a vacuum gauge or some measurement of
performance to determine when this is needed. 

does licl obey bowen's 1926 equation (qe/qc = 100(pw-pa)/(tw-ta), p. 664
of duffie and beckman's 1991 "solar engineering of thermal processes")?
if so, how do the diffusion coefficients change with temperature and
concentration? a little more research would be helpful.


here's a program that calculates the equilibrium licl concentration
after a long high-temperature bake, and the vapor pressure, dew point
and rh of nearby air after the solution cools to 90 f...

10 a1=12.7409'licl vapor pressure constants from 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
190 w=.0119'humidity ratio for midland air in july
200 pv=25.4*29.921/(1+.62198/w)'vapor pressure in july (mmhg)
210 for tf=120 to 300 step 20'solution temp (f)
220 tc=(tf-32)/1.8
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%)
340 tsf=90'soln temp after cooling (f)
350 ts=(tsf-32)/1.8'soln temp (c)
360 tk=ts+273.1'soln temp (k)
370 ap=a1+a2*conc+a3*conc^2
380 bp=b1+b2*conc+b3*conc^2
390 cp=c1+c2*conc+c3*conc^2
400 pvc=10^(ap+bp/tk+cp/(tk^2))/25.4'vapor pressure at tk ("hg)
410 td=9621/(17.863-log(pvc))-460'dew point (f)
420 rh=100*pvc/(exp(17.863-9621/(tsf+460)))
430 print tf,conc,pvc,td,rh
440 next

bake             vapor        dew        
temp   conc      press        point      rh
(f)    (%)       ("hg)        (f)        (%)

120    35.62    .4452         55.26      30.74
140    43.17    .2296         37.61      15.86
160    50.35    .1048         18.21       7.238
180    57.28    .04254        -2.30       2.938
200    64.02    .01543       -23.36       1.066
220    70.61    .005037      -44.48        .3478
240    77.05    .001492      -65.22        .1030
260    83.32    .0004051     -85.25        .02798
280    89.41    .0001022    -104.3         .007059
300    95.30    .00002432   -122.3         .001679

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