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Economic analysis of some solar energy systems
Energy Convers. Mgmt Vol. 24, No. 2, pp. 131-135, 1984
0196-8904/84 $3.00+0.00 Copyright C) 1984 Pergamon Press Lid
Printed in Great Britain. All rights reserved
ECONOMIC
ANALYSIS OF SOME SOLAR ENERGY SYSTEMS
GOVIND and G. N. T I W A R I Centre of Energy Studies, Indian Institute of Technology, Hauz Kha~ New Delhi 110 016, India (Received 7 April 1983) ~ct--An analysis of the savings in energy costs that accrue from use of solar energy in place of conventional fuels with special reference to the effect of inflation on unit costs of conventional fuels is crudal to the decision making process for installation of various solar energy systems. Because of the energy crisis, various kinds of solar energy gadgets have been developed and marketed in different parts of the world with varying degrees of thermal performance. In this paper, cost analyses of three types of solar energy systems, viL, solar dryers, solar water heating systems and solar distillation units (brief descriptions of the systems have been discussed in the Appendix) has been described. A uniform cost analysis procedure has been adopted. No such cost analysis has been done heretofore in solar energy systems taking into account the various factors. Economic analysis
Solarsystems
Solar energy
COST ANALYSIS
Annual cost method This is given by the expression (as described in the previous section)
Considering the initial investment on any solar energy system to be P, with an annual interest rate on such capital being r% and ifn is the number of useful years up to which the given system will perform, then the capital recovery factor (CRF)--
annual cost (C) = annual first cost + maintenance c o s t - annual salvage value.
r ( l + r)" (1 + r)"-- 1"
Annual cost per unit mass of the product
(1) Hence, the first annual cost of the system ffi (CRF) P.
(2)
Depending on the capacity of the dryer, if M is the mass of the product which has been dried in time z, and T is the harvesting time, then, the annual product yield is given by
Again, if the salvage value of the system is taken as S and since the sinking fund factor (SFF) is given by SFF ffi
r
(1 + r ) " - - 1
then, the annual salvage value - (SFF) S.
annual product yield ( Y ) =
T
(6)
(3)
Now, the cost of the drying per unit mass of the .product is given by
(4)
annual cost C annual product yield = Y"
As the system will also require some annual maintenance, the annual cost of the system, incorporating the annual maintenance cost, will be given by
(7)
Annual cost per unit useful energy If M,. is the fractional moisture content on a wet basis, and d is the dry weight, then the weight of the moist product w can be calculated from
annual cost = first annual cost + annual maintenance c o s t - a n n u a l salvage value.
MxT
(5)
Taking this cost analysis as a model for the various systems described above, we will be giving here the cost analysis of these systems (A, B and C) for typical locations in India, U.S.A. and Colombia. (A) SOLAR DRYING SYSTEMS
w-d W
If h/g is the latent heat of vaporisation, then, the heat utilised to dry the product is (w - d) h/r If the available insolation on the dryer's collector area is H kWh, then, the efficiency can be written as
Three types of economic analysis have been carried out for solar dryers: 131
r/---
f., - d) h:, HT
(9)
132
GOVIND and TIWARI: ECONOMIC ANALYSIS OF SOLAR SYSTEMS
The annual useful energy gain is,then, given by the expression Q = = ( w - d)
hlgT = ~HT.
number of days required for drying = 12 days total harvesting day = 210 days
(10)
annual product yield
The annual cost of energy is obtained by dividing the annual cost given in equation (5) by Q=, i.e. cost per unit energy =
C Q---~.
(11)
=
18.75 x 210 12
=
328 kg.
(b) Annual cost of drying/kg of coffee (1970 [l]) Annual cost of drying/kg of
Now, we will calculate the annual cost per m 2, per kg and per kWh useful energy for a paseras dryer which is used to dry coffee beans in Colombia.
coffee = $0.423 328
= $0.0013]kg-m 2
(a) Annual cost of the product (1970, [1])
given efficiency of drying = 22.56%
Initial investment per m 2 of the drying system average incident solar energy = 4.19 ~
P = $2. l 0/m 2
kWh
during
harvesting days
salvage value S = $ (0.35 x 2.10)
annual energy used for drying = 0.2256 x 4.19 x 210 = 198.5 kWh/m 2
= $0.735/m 2 life time n = 8 years interest rate r = 12%
annual cost per kWh =
C R F = 0.2013 S F F = 0.0813
$0.42 198.5
= $0.0021 ]kWh.
first annual cost/m 2 = $ C R F x P
Cost calculations for various types of dryers and for various types of product can be calculated in a similar way. Costs per m 2, per kg and per unit energy have been given in Table 1 (cost is updated for year 1980 by considering a 5% inflation rate). The last column of the table shows the unit cost of electricity rate in these countries.
= 0.2013 x 2.10 = $0.42/m 2 first annual salvage value/m 2 = $ SFF x S = $0.0813 x 0.735 = $0.06/m 2 maintenance charge/m 2 = O. 15 x 0.42
(B) SOLAR WATER HEATING SYSTEM
= S0.063/m 2
Cost analyses of two types of water heating system, viz. (1) built in storage type, (ii) conventional type have been taken here to study the relative economics of the two types.
hence, annual cost/m 2 = $ (0.42 + 0.063 - 0.06) = $0.423/m 2 amount of coffee which may be dried by the d r i e r = 18.75 kg (dry weight)
(i) Built in storage (100 litre capacity) (a) Initial costs per m 2 of the materials used are given in Table 2. Table I
S. No.
Country
Product
1. 2.
Colombia Coffee India Prunes
3.
Brazil
Banana
4.
U.S.A.
Apricots
Total Life cost (year) (U.S. $)
Type of dryer
Capacity (kg)
Paseras Cabinet dryer Chamber type
106 75
8 10
200 (total number) 27.5
5
Chamber type
20
4 20
Cost/
Unit
Annual unit Cost/m 2 ¢ost/m = CosUproduct energy
electricity cost
OJ.s. s) (u.s.$) Co.s.S/kg) (kWh)
(S/kWh)
2.10 0.15
64.10
32.5
34.0
27.2
0.684 5.16 I l .$8
5.998
0.0013 0.028
0.0021 0.011
0.055
O.OOl I
--
0.023
0.015
0.0056
0.073
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS a n n u a l m a i n t e n a n c e c o s t = 0.15 (156.55)
Table 2 Cost in
Materials Steel structure (for box and cover material) Glass Insulation Paint Stand, bucket, frame etc. Labour
133
= Rs23.48/m 2
Indian Rs
a n n u a l cost = 156.55 + 23.48 - - 18.06
350 60 50 50 175 200
Total cost in Rs
885
= ILs161.97/m 2. Hence, a n n u a l c o s t / m 2 = Rs161.97/m 2. A v e r a g e daily i n s o l a t i o n ( = 5 . 8 7 6 8 k W h / m 2 day) at 45 ° inclination o f the a b s o r b e r a n n u a l total i n s o l a t i o n = 5.8768 x 365
(b) Salvage values: after t h e useful fives o f the solar system, t h e usable materials are structures, glass cover, frame, insulation, etc. T h e salvage value is e s t i m a t e d at half t h e initial cost. Salvage value o f built in s t o r a g e w a t e r h e a t i n g s y s t e m = Rs317.5/m 2. (c) M a i n t e n a n c e cost: this has been t a k e n as follows a n n u a l m a i n t e n a n c e c o s t = 0.15 x a n n u a l first cost. H e n c e we can calculate the a n n u a l cost by using expressions (1)-(5). Useful life o f the system is a s s u m e d at = 10 years interest rate = 12% per a n n u m CRF
= 0.1769
SFF =0.0569
P = Rs885/m 2 S = Rs317.5/m 2
= 2145 k W h / m 2. Useful energy (as the efficiency o f built in s t o r a g e is 70%)
= 2 1 4 5 x 0.7 = 1501 k W h / m 2 a n n u a l c o s t / k W h = gs0.1 I / m 2.
(ii) Conventional type water heating system: (100 litre ) A s in the previous case, the cost break up o f various materials used is given in Table 3. M a i n t e n a n c e cost: this has been taken as in the previous case a n n u a l m a i n t e n a n c e cost = 0.15 x (first a n n u a l cost) useful life o f the system is a s s u m e d as = 10 years interest rate = 12% p e r a n n u m . Hence, by using expressions (1)--(5), we can calculate the a n n u a l cost
a n n u a l first cost = ( C R F ) P = 0.1769 (885)
C R F = 0.1769 S F F = 0.0569
= Rs156.55/m 2 a n n u a l salvage value = ( S F F ) S
(a)
(c)
S = Rs782.50 a n n u a l first cost = ( C R F ) P
= (0.0569) 317.5
= 0.1769 (1940)
= R s l 8.06/m ~
= Rs343.2
Table 3 Materials Collector part (for 1.5 m: collector area) Steel and aluminium structures Insulation
(b)
P = (1265 + 675) = Rs1940
Cost in Indian Rs 475 50
Glass cover Plywood, frame etc. Paint Stand, socket etc. Labour Total cost
90 125 75 200 250 1265
Storage tank Steel structure Stand etc. Insulation stant etc. Labour Total cost
400 1.50 75 150
Salvage values Salvage value of collector
470.00
Salvage value of storage tank Total cost
312.05 782.50
675
134
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS a n n u m , the cost calculations o f the t w o stills can be d o n e as follows.
a n n u a l salvage value = ( S F F ) S = (0.0569) 782.50
(i) Mounted single basin solar still
ffi Rs44.52
C R F -- 0.1769
P -- Rs695/m s
a n n u a l m a i n t e n a n c e cost ffi (0.15) 343.2 S F F -- 0.0569
ffi Rs51.48
a n n u a l first cost ffi ( C R F ) P
.'. a n n u a l cost for 1.5 m s collector area = 343.2 + 51.48 -
S = Rs227.5/m s
= 0.1769 (695) = Rs122.95/m s a n n u a l salvage value ffi ( S F F ) S
44.52
= Rs350.16
-- 0.0569 (227.5)
hence, a n n u a l c o s t / m 2 = Rs233.44/m s
= Rs12.95/m 2
a v e r a g e daily insolation at 45 ° inclination o f the a b s o r b e r = 5.8768 k W h / m s d a y
a n n u a l m a i n t e n a n c e cost = 1 5 ~ ( a n n u a l first = 0 . 1 5 x 122.95
a n n u a l total insolation = 5.8768 x 365 = 2145 k W h
= Rs 18.44/m 2
Useful energy (as the efficiency o f w a t e r h e a t i n g system is 6 0 ~ ) = 2145 x 0.6 = 1287 k W h / m s. annual cost/kWh = Rs0.18/kWh (C) SOLAR DISTILLATION UNITS T w o types o f solar stills, viz. (i) m o u n t e d single basin solar still a n d (ii) multiple wick solar still, have been c o n s i d e r e d here for their relative e c o n o m i c p e r f o r m a n c e . A b r i e f description o f systems have been given in the A p p e n d i x . T h e cost b r e a k - u p p e r m 2 o f the t w o stills has been given in Table 4. T h e yearly average yield o f the two types o f stills
are as follows: (a) mounted single basin solar stillffi2 I/day (b) multiple wick solar still= 3 I/day.
a n n u a l c o s t / m 2 -- 122.95 + 1 8 . 4 4 - 12.95 -- R s 128.44/m 2 a n n u a l yield o f the 1st still = 2 x 365 = 7301 a n n u a l useful energy = 730 x 0.65 = 474.5 k W h (0.65 k W h / k g is the latent h e a t o f v a p o r i z a t i o n ) a n n u a l c o s t / k g --
a n n e a l cost a n n u a l yield
= Rs0.18/kg a n n u a l c o s t / k W h = Rs0.27/kWh.
(ii) Multiple wick solar still C R F = 0.1769 S F F = 0.0569
P = Rs460 S = Rs127.50
a n n u a l first cost = ( C R F ) P Salvage value o f solar 455 still (i) ffi h a l f o f initial cost = 2 = Rs227.5/m s.
-- 0.1769 (460) = Rs81.37/m: a n n u a l salvage value = ( S F F ) S
Salvage value o f solar 255 still (ii) ffi half o f initial cost ffi n 2 ffi Rs127.5/m 2. A s s u m i n g the useful life o f the t w o stills as 10 years a n d c o n s i d e r i n g the m a i n t e n a n c e cost at 1 5 ~ o f the a n n u a l c o s t a n d taking the interest rate as 1 2 ~ p e r
Still (i) materials Steel and aluminium
cost)
= 0.0569 (127.50) -- Rs7.25/m 2 annual maintenance cost -- 0.15 x 81.37 Rsl2.20/m 2
Table 4 Cost in Still (ii) Indian Rs materials 380 Steel and aluminium
structures
Cost in Indian Rs 195
structures
Glass Rubber material Paint Insulation Labour
60 15 25 15 200
Glass Polyethene .lute cloth Foam and solution Labour
60 15 35 30 125
Total cost
695
Total cost
460
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS
a n n u a l cost/m 2 = 81.37 + 12.20 - 7.25 = Rs86.32/m 2 a n n u a l yield of the 2nd still = 3 x 365 iitres = 1095 1 a n n u a l useful energy -~ 1095 x 0.65 -- 711.75 k w h a n n u a l cost/kg = Rs0.08/kg a n n u a l c o s t / k W h = Rs0.12/kWh. CONCLUSIONS Since the interest in solar drying has been rather recent, the data on the performance o f solar dryers is rather scanty. Due to this reason, a definite conclusion a b o u t the economics of solar dryers c a n n o t be reached. Parsera dryers for coffee are found to be more economical t h a n other types o f dryers. F r o m the cost analyses o f two types o f water heating systems, viz. built in type a n d conventional type water heater, as the cost per unit useful energy are Rs0.11 and Rs0.18, respectively, the built in storage water heater is more economical t h a n the conventional type water heater. Lastly, cost analyses of solar stills ( m o u n t e d type a n d multiple wick type) indicate that, for a small requirement of distilled water, the multiple wick solar still is more economical than the m o u n t e d type solar still.
.4cknowledgement--The authors are grateful to Professor M. S. Sodha, I. I. T. Delhi for fruitful discussions. REFERENCES 1. Brace Research Institute, Survey of Agricultural Dryers. McGill University, Quebec (1978). 2. J. K. Nayak, G. N. Tiwari and M. S. Sodha, Energy Reg. 4, 41 (1980). 3. M. S. Sodha, A. Kumar, G. N. Tiwari and R. C. Tyagl, Solar Energy 26, 127 (1981). 4. M. S. Sodha, J. K. Nayak, S. C. Kaushik, S. P. Sabbarwai and M. A. S. Malik, Energy Convers. Mgmt 19, 41 (1979). 5. M. S. Sodha, G. N. Tiwari and S. N. Shukla, Thermal Model of Hot Water System. Eastern Wiley, Delhi (1982). APPENDIX
(.4) Solar dryers (i) Paseras dryers (Colombia). These are open sun dryers. For construction of the trays, or "Paseras", wood is used. During the drying process, the coffee beans are directly exposed to solar radiation, and during rainy periods and at night time, they are stored under a cover. (ii) Chamber dryers (Brazil and U.S.A.). This small scale solar dryer is essentially a wooden rectangular box covered by two layers of glass separated by an air gap. The bottom of the dryer is insulated with glass wool sandwiched between an underside plywood sheet and an innerside blackened metallic collector surface. The fruits are spread on the
E.C.M. 24/2---.C
135
collector surface for drying. The drying chamber is mounted on an upright wood structure and tilted 7* northward. Only natural convection air circulation is used. The collector heats the inside air which flows over the drying fruits and escapes at the top of the dryer, allowing fresh air to enter at the dryer air inlet. (fii) Cabinet dryer (lnd/a). The dryer is essentially a solar hot box, in which fruit, vegetables or other matter can be dehydrated on a small scale. It consists of a rectangular container, insulated at its base and preferably at the sides and covered with a transparent roof. Solar radiation is transmitted through the roofand absorbed on the blackened interior surfaces. Owing to the insulation, the internal temperature is raised. Holes are drilled through the base to permit fresh ventilating air entry into the cabinet.
(B ) Solar distillation units (i) Mounted single basin solar still (2). The system consists of a single sloped still, made up of G.I. sheet (24 gauge) and encased in a wooden box. The vertical heights of the still are 29 and 15 em with a slope of 10° along the breadth of the still. The space between the steel and wooden box is filled with glass wool insulation to reduce conduction losses. The inner side of the still is painted black by black board paint. A 3 mm thick glass cover is fixed on the top with the help of a frame made up of Iron "1"', and the assembly is made air tight with the help of rubber gaskets. A V-drain of aluminium is used for drainage of distillate water. A slight slope has been given to the drainage system so as to enable the distillate water to come out without difficulty. (i) Multiple wick solar still (3). In this design of the still, blackened wet jute cloth forms the liquid surface which can be oriented to intercept maximum solar radiation and attain high temperatures on account of low thermal capacity. The wet surface consists of a series of jute cloth pieces of increasing length separated by black polythene sheet. One end of the jute cloth is dipped in a saline water reservoir made up of G.I. sheet attached to the reseroir. A 3 mm thick window glass cover is placed above 5cm high wall of insulated foam (of thickness 3-5 crn) with the help of a rubber gasket and a frame made up of aluminium "L" tightens the glass to make the assembly airtight. A V-drain of aluminium is used for drainage of the distillate with slight slope so as to enable the distillate to flow without difficulty. To drain the extra saline water from the still, another drainage made of copper pipe is attached at the bottom. By the capillary action of the cloth fibre, water goes up and rolls along the length under gravity, thus the whole cloth pieces form a layer of water. The system is oriented towards south and is kept at an inclination of 10° (in summer) to receive maximum solar radiation. (C) Solar water heating systems (i) Built in storage water heater (4). The system consists of a rectangular box made up of galvanized iron sheet and is insulated from all sides with glass wool insulation. The top of the tank is blackened to absorb solar radiation. A 3 mm thick window glass is placed at a distance of 5 em with the help of rubber gasket and wooden frame. The system has one inlet at the bottom and one outlet at the top of the tank. (ii) Conventional water heater (5). In this system, the absorber consists basically of galvanized iron pipe attached to an aluminium sheet with the help of wire mesh to have good contact. The pipes are joined at the ends by another galvanized iron pipe header. The entire plate is painted black and placed inside a wooden box insulated at the bottom. The top of the box is glazed with 3 mm thick window glass plate. The absorber unit is placed at an angle of 45 ° facing south and is connected to an insulated double cylindrical storage tank.
0196-8904/84 $3.00+0.00 Copyright C) 1984 Pergamon Press Lid
Printed in Great Britain. All rights reserved
ECONOMIC
ANALYSIS OF SOME SOLAR ENERGY SYSTEMS
GOVIND and G. N. T I W A R I Centre of Energy Studies, Indian Institute of Technology, Hauz Kha~ New Delhi 110 016, India (Received 7 April 1983) ~ct--An analysis of the savings in energy costs that accrue from use of solar energy in place of conventional fuels with special reference to the effect of inflation on unit costs of conventional fuels is crudal to the decision making process for installation of various solar energy systems. Because of the energy crisis, various kinds of solar energy gadgets have been developed and marketed in different parts of the world with varying degrees of thermal performance. In this paper, cost analyses of three types of solar energy systems, viL, solar dryers, solar water heating systems and solar distillation units (brief descriptions of the systems have been discussed in the Appendix) has been described. A uniform cost analysis procedure has been adopted. No such cost analysis has been done heretofore in solar energy systems taking into account the various factors. Economic analysis
Solarsystems
Solar energy
COST ANALYSIS
Annual cost method This is given by the expression (as described in the previous section)
Considering the initial investment on any solar energy system to be P, with an annual interest rate on such capital being r% and ifn is the number of useful years up to which the given system will perform, then the capital recovery factor (CRF)--
annual cost (C) = annual first cost + maintenance c o s t - annual salvage value.
r ( l + r)" (1 + r)"-- 1"
Annual cost per unit mass of the product
(1) Hence, the first annual cost of the system ffi (CRF) P.
(2)
Depending on the capacity of the dryer, if M is the mass of the product which has been dried in time z, and T is the harvesting time, then, the annual product yield is given by
Again, if the salvage value of the system is taken as S and since the sinking fund factor (SFF) is given by SFF ffi
r
(1 + r ) " - - 1
then, the annual salvage value - (SFF) S.
annual product yield ( Y ) =
T
(6)
(3)
Now, the cost of the drying per unit mass of the .product is given by
(4)
annual cost C annual product yield = Y"
As the system will also require some annual maintenance, the annual cost of the system, incorporating the annual maintenance cost, will be given by
(7)
Annual cost per unit useful energy If M,. is the fractional moisture content on a wet basis, and d is the dry weight, then the weight of the moist product w can be calculated from
annual cost = first annual cost + annual maintenance c o s t - a n n u a l salvage value.
MxT
(5)
Taking this cost analysis as a model for the various systems described above, we will be giving here the cost analysis of these systems (A, B and C) for typical locations in India, U.S.A. and Colombia. (A) SOLAR DRYING SYSTEMS
w-d W
If h/g is the latent heat of vaporisation, then, the heat utilised to dry the product is (w - d) h/r If the available insolation on the dryer's collector area is H kWh, then, the efficiency can be written as
Three types of economic analysis have been carried out for solar dryers: 131
r/---
f., - d) h:, HT
(9)
132
GOVIND and TIWARI: ECONOMIC ANALYSIS OF SOLAR SYSTEMS
The annual useful energy gain is,then, given by the expression Q = = ( w - d)
hlgT = ~HT.
number of days required for drying = 12 days total harvesting day = 210 days
(10)
annual product yield
The annual cost of energy is obtained by dividing the annual cost given in equation (5) by Q=, i.e. cost per unit energy =
C Q---~.
(11)
=
18.75 x 210 12
=
328 kg.
(b) Annual cost of drying/kg of coffee (1970 [l]) Annual cost of drying/kg of
Now, we will calculate the annual cost per m 2, per kg and per kWh useful energy for a paseras dryer which is used to dry coffee beans in Colombia.
coffee = $0.423 328
= $0.0013]kg-m 2
(a) Annual cost of the product (1970, [1])
given efficiency of drying = 22.56%
Initial investment per m 2 of the drying system average incident solar energy = 4.19 ~
P = $2. l 0/m 2
kWh
during
harvesting days
salvage value S = $ (0.35 x 2.10)
annual energy used for drying = 0.2256 x 4.19 x 210 = 198.5 kWh/m 2
= $0.735/m 2 life time n = 8 years interest rate r = 12%
annual cost per kWh =
C R F = 0.2013 S F F = 0.0813
$0.42 198.5
= $0.0021 ]kWh.
first annual cost/m 2 = $ C R F x P
Cost calculations for various types of dryers and for various types of product can be calculated in a similar way. Costs per m 2, per kg and per unit energy have been given in Table 1 (cost is updated for year 1980 by considering a 5% inflation rate). The last column of the table shows the unit cost of electricity rate in these countries.
= 0.2013 x 2.10 = $0.42/m 2 first annual salvage value/m 2 = $ SFF x S = $0.0813 x 0.735 = $0.06/m 2 maintenance charge/m 2 = O. 15 x 0.42
(B) SOLAR WATER HEATING SYSTEM
= S0.063/m 2
Cost analyses of two types of water heating system, viz. (1) built in storage type, (ii) conventional type have been taken here to study the relative economics of the two types.
hence, annual cost/m 2 = $ (0.42 + 0.063 - 0.06) = $0.423/m 2 amount of coffee which may be dried by the d r i e r = 18.75 kg (dry weight)
(i) Built in storage (100 litre capacity) (a) Initial costs per m 2 of the materials used are given in Table 2. Table I
S. No.
Country
Product
1. 2.
Colombia Coffee India Prunes
3.
Brazil
Banana
4.
U.S.A.
Apricots
Total Life cost (year) (U.S. $)
Type of dryer
Capacity (kg)
Paseras Cabinet dryer Chamber type
106 75
8 10
200 (total number) 27.5
5
Chamber type
20
4 20
Cost/
Unit
Annual unit Cost/m 2 ¢ost/m = CosUproduct energy
electricity cost
OJ.s. s) (u.s.$) Co.s.S/kg) (kWh)
(S/kWh)
2.10 0.15
64.10
32.5
34.0
27.2
0.684 5.16 I l .$8
5.998
0.0013 0.028
0.0021 0.011
0.055
O.OOl I
--
0.023
0.015
0.0056
0.073
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS a n n u a l m a i n t e n a n c e c o s t = 0.15 (156.55)
Table 2 Cost in
Materials Steel structure (for box and cover material) Glass Insulation Paint Stand, bucket, frame etc. Labour
133
= Rs23.48/m 2
Indian Rs
a n n u a l cost = 156.55 + 23.48 - - 18.06
350 60 50 50 175 200
Total cost in Rs
885
= ILs161.97/m 2. Hence, a n n u a l c o s t / m 2 = Rs161.97/m 2. A v e r a g e daily i n s o l a t i o n ( = 5 . 8 7 6 8 k W h / m 2 day) at 45 ° inclination o f the a b s o r b e r a n n u a l total i n s o l a t i o n = 5.8768 x 365
(b) Salvage values: after t h e useful fives o f the solar system, t h e usable materials are structures, glass cover, frame, insulation, etc. T h e salvage value is e s t i m a t e d at half t h e initial cost. Salvage value o f built in s t o r a g e w a t e r h e a t i n g s y s t e m = Rs317.5/m 2. (c) M a i n t e n a n c e cost: this has been t a k e n as follows a n n u a l m a i n t e n a n c e c o s t = 0.15 x a n n u a l first cost. H e n c e we can calculate the a n n u a l cost by using expressions (1)-(5). Useful life o f the system is a s s u m e d at = 10 years interest rate = 12% per a n n u m CRF
= 0.1769
SFF =0.0569
P = Rs885/m 2 S = Rs317.5/m 2
= 2145 k W h / m 2. Useful energy (as the efficiency o f built in s t o r a g e is 70%)
= 2 1 4 5 x 0.7 = 1501 k W h / m 2 a n n u a l c o s t / k W h = gs0.1 I / m 2.
(ii) Conventional type water heating system: (100 litre ) A s in the previous case, the cost break up o f various materials used is given in Table 3. M a i n t e n a n c e cost: this has been taken as in the previous case a n n u a l m a i n t e n a n c e cost = 0.15 x (first a n n u a l cost) useful life o f the system is a s s u m e d as = 10 years interest rate = 12% p e r a n n u m . Hence, by using expressions (1)--(5), we can calculate the a n n u a l cost
a n n u a l first cost = ( C R F ) P = 0.1769 (885)
C R F = 0.1769 S F F = 0.0569
= Rs156.55/m 2 a n n u a l salvage value = ( S F F ) S
(a)
(c)
S = Rs782.50 a n n u a l first cost = ( C R F ) P
= (0.0569) 317.5
= 0.1769 (1940)
= R s l 8.06/m ~
= Rs343.2
Table 3 Materials Collector part (for 1.5 m: collector area) Steel and aluminium structures Insulation
(b)
P = (1265 + 675) = Rs1940
Cost in Indian Rs 475 50
Glass cover Plywood, frame etc. Paint Stand, socket etc. Labour Total cost
90 125 75 200 250 1265
Storage tank Steel structure Stand etc. Insulation stant etc. Labour Total cost
400 1.50 75 150
Salvage values Salvage value of collector
470.00
Salvage value of storage tank Total cost
312.05 782.50
675
134
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS a n n u m , the cost calculations o f the t w o stills can be d o n e as follows.
a n n u a l salvage value = ( S F F ) S = (0.0569) 782.50
(i) Mounted single basin solar still
ffi Rs44.52
C R F -- 0.1769
P -- Rs695/m s
a n n u a l m a i n t e n a n c e cost ffi (0.15) 343.2 S F F -- 0.0569
ffi Rs51.48
a n n u a l first cost ffi ( C R F ) P
.'. a n n u a l cost for 1.5 m s collector area = 343.2 + 51.48 -
S = Rs227.5/m s
= 0.1769 (695) = Rs122.95/m s a n n u a l salvage value ffi ( S F F ) S
44.52
= Rs350.16
-- 0.0569 (227.5)
hence, a n n u a l c o s t / m 2 = Rs233.44/m s
= Rs12.95/m 2
a v e r a g e daily insolation at 45 ° inclination o f the a b s o r b e r = 5.8768 k W h / m s d a y
a n n u a l m a i n t e n a n c e cost = 1 5 ~ ( a n n u a l first = 0 . 1 5 x 122.95
a n n u a l total insolation = 5.8768 x 365 = 2145 k W h
= Rs 18.44/m 2
Useful energy (as the efficiency o f w a t e r h e a t i n g system is 6 0 ~ ) = 2145 x 0.6 = 1287 k W h / m s. annual cost/kWh = Rs0.18/kWh (C) SOLAR DISTILLATION UNITS T w o types o f solar stills, viz. (i) m o u n t e d single basin solar still a n d (ii) multiple wick solar still, have been c o n s i d e r e d here for their relative e c o n o m i c p e r f o r m a n c e . A b r i e f description o f systems have been given in the A p p e n d i x . T h e cost b r e a k - u p p e r m 2 o f the t w o stills has been given in Table 4. T h e yearly average yield o f the two types o f stills
are as follows: (a) mounted single basin solar stillffi2 I/day (b) multiple wick solar still= 3 I/day.
a n n u a l c o s t / m 2 -- 122.95 + 1 8 . 4 4 - 12.95 -- R s 128.44/m 2 a n n u a l yield o f the 1st still = 2 x 365 = 7301 a n n u a l useful energy = 730 x 0.65 = 474.5 k W h (0.65 k W h / k g is the latent h e a t o f v a p o r i z a t i o n ) a n n u a l c o s t / k g --
a n n e a l cost a n n u a l yield
= Rs0.18/kg a n n u a l c o s t / k W h = Rs0.27/kWh.
(ii) Multiple wick solar still C R F = 0.1769 S F F = 0.0569
P = Rs460 S = Rs127.50
a n n u a l first cost = ( C R F ) P Salvage value o f solar 455 still (i) ffi h a l f o f initial cost = 2 = Rs227.5/m s.
-- 0.1769 (460) = Rs81.37/m: a n n u a l salvage value = ( S F F ) S
Salvage value o f solar 255 still (ii) ffi half o f initial cost ffi n 2 ffi Rs127.5/m 2. A s s u m i n g the useful life o f the t w o stills as 10 years a n d c o n s i d e r i n g the m a i n t e n a n c e cost at 1 5 ~ o f the a n n u a l c o s t a n d taking the interest rate as 1 2 ~ p e r
Still (i) materials Steel and aluminium
cost)
= 0.0569 (127.50) -- Rs7.25/m 2 annual maintenance cost -- 0.15 x 81.37 Rsl2.20/m 2
Table 4 Cost in Still (ii) Indian Rs materials 380 Steel and aluminium
structures
Cost in Indian Rs 195
structures
Glass Rubber material Paint Insulation Labour
60 15 25 15 200
Glass Polyethene .lute cloth Foam and solution Labour
60 15 35 30 125
Total cost
695
Total cost
460
GOVIND and TIWARI:
ECONOMIC ANALYSIS OF SOLAR SYSTEMS
a n n u a l cost/m 2 = 81.37 + 12.20 - 7.25 = Rs86.32/m 2 a n n u a l yield of the 2nd still = 3 x 365 iitres = 1095 1 a n n u a l useful energy -~ 1095 x 0.65 -- 711.75 k w h a n n u a l cost/kg = Rs0.08/kg a n n u a l c o s t / k W h = Rs0.12/kWh. CONCLUSIONS Since the interest in solar drying has been rather recent, the data on the performance o f solar dryers is rather scanty. Due to this reason, a definite conclusion a b o u t the economics of solar dryers c a n n o t be reached. Parsera dryers for coffee are found to be more economical t h a n other types o f dryers. F r o m the cost analyses o f two types o f water heating systems, viz. built in type a n d conventional type water heater, as the cost per unit useful energy are Rs0.11 and Rs0.18, respectively, the built in storage water heater is more economical t h a n the conventional type water heater. Lastly, cost analyses of solar stills ( m o u n t e d type a n d multiple wick type) indicate that, for a small requirement of distilled water, the multiple wick solar still is more economical than the m o u n t e d type solar still.
.4cknowledgement--The authors are grateful to Professor M. S. Sodha, I. I. T. Delhi for fruitful discussions. REFERENCES 1. Brace Research Institute, Survey of Agricultural Dryers. McGill University, Quebec (1978). 2. J. K. Nayak, G. N. Tiwari and M. S. Sodha, Energy Reg. 4, 41 (1980). 3. M. S. Sodha, A. Kumar, G. N. Tiwari and R. C. Tyagl, Solar Energy 26, 127 (1981). 4. M. S. Sodha, J. K. Nayak, S. C. Kaushik, S. P. Sabbarwai and M. A. S. Malik, Energy Convers. Mgmt 19, 41 (1979). 5. M. S. Sodha, G. N. Tiwari and S. N. Shukla, Thermal Model of Hot Water System. Eastern Wiley, Delhi (1982). APPENDIX
(.4) Solar dryers (i) Paseras dryers (Colombia). These are open sun dryers. For construction of the trays, or "Paseras", wood is used. During the drying process, the coffee beans are directly exposed to solar radiation, and during rainy periods and at night time, they are stored under a cover. (ii) Chamber dryers (Brazil and U.S.A.). This small scale solar dryer is essentially a wooden rectangular box covered by two layers of glass separated by an air gap. The bottom of the dryer is insulated with glass wool sandwiched between an underside plywood sheet and an innerside blackened metallic collector surface. The fruits are spread on the
E.C.M. 24/2---.C
135
collector surface for drying. The drying chamber is mounted on an upright wood structure and tilted 7* northward. Only natural convection air circulation is used. The collector heats the inside air which flows over the drying fruits and escapes at the top of the dryer, allowing fresh air to enter at the dryer air inlet. (fii) Cabinet dryer (lnd/a). The dryer is essentially a solar hot box, in which fruit, vegetables or other matter can be dehydrated on a small scale. It consists of a rectangular container, insulated at its base and preferably at the sides and covered with a transparent roof. Solar radiation is transmitted through the roofand absorbed on the blackened interior surfaces. Owing to the insulation, the internal temperature is raised. Holes are drilled through the base to permit fresh ventilating air entry into the cabinet.
(B ) Solar distillation units (i) Mounted single basin solar still (2). The system consists of a single sloped still, made up of G.I. sheet (24 gauge) and encased in a wooden box. The vertical heights of the still are 29 and 15 em with a slope of 10° along the breadth of the still. The space between the steel and wooden box is filled with glass wool insulation to reduce conduction losses. The inner side of the still is painted black by black board paint. A 3 mm thick glass cover is fixed on the top with the help of a frame made up of Iron "1"', and the assembly is made air tight with the help of rubber gaskets. A V-drain of aluminium is used for drainage of distillate water. A slight slope has been given to the drainage system so as to enable the distillate water to come out without difficulty. (i) Multiple wick solar still (3). In this design of the still, blackened wet jute cloth forms the liquid surface which can be oriented to intercept maximum solar radiation and attain high temperatures on account of low thermal capacity. The wet surface consists of a series of jute cloth pieces of increasing length separated by black polythene sheet. One end of the jute cloth is dipped in a saline water reservoir made up of G.I. sheet attached to the reseroir. A 3 mm thick window glass cover is placed above 5cm high wall of insulated foam (of thickness 3-5 crn) with the help of a rubber gasket and a frame made up of aluminium "L" tightens the glass to make the assembly airtight. A V-drain of aluminium is used for drainage of the distillate with slight slope so as to enable the distillate to flow without difficulty. To drain the extra saline water from the still, another drainage made of copper pipe is attached at the bottom. By the capillary action of the cloth fibre, water goes up and rolls along the length under gravity, thus the whole cloth pieces form a layer of water. The system is oriented towards south and is kept at an inclination of 10° (in summer) to receive maximum solar radiation. (C) Solar water heating systems (i) Built in storage water heater (4). The system consists of a rectangular box made up of galvanized iron sheet and is insulated from all sides with glass wool insulation. The top of the tank is blackened to absorb solar radiation. A 3 mm thick window glass is placed at a distance of 5 em with the help of rubber gasket and wooden frame. The system has one inlet at the bottom and one outlet at the top of the tank. (ii) Conventional water heater (5). In this system, the absorber consists basically of galvanized iron pipe attached to an aluminium sheet with the help of wire mesh to have good contact. The pipes are joined at the ends by another galvanized iron pipe header. The entire plate is painted black and placed inside a wooden box insulated at the bottom. The top of the box is glazed with 3 mm thick window glass plate. The absorber unit is placed at an angle of 45 ° facing south and is connected to an insulated double cylindrical storage tank.