MEDIUM-TEMPERATURE SOLAR PROCESSES

MEDIUM- TEMPERA TURE SOLAR PROCESSES

5 There is no gamble in solar energy use. It is sure to work. F. Daniels

This c h a p t e r describes the four principal medium-tem­ p e r a t u r e solar p r o c e s s e s which h a v e b e e n engineered a n d / o r built at the p r o t o t y p e level. T h e four system types are (a) distributed p o w e r genera­ tion, (b) industrial p r o c e s s heat, (c) shaft w o r k production, (d) solar to­ tal energy s y s t e m s . E a c h concept is described in this c h a p t e r , perform­ ance characteristics given, and an example system described. D a t a from existing facilities are given w h e r e available. The emphasis is on systems (b) and (c) for which there is field e x p e r i e n c e . In the final sections of this c h a p t e r a m e t h o d of performance estimation is described in detail. T h e m e t h o d c a n be used to predict average annual performance of all c o n c e n t r a t o r - b a s e d s y s t e m s .

/.

DISTRIBUTED PRODUCTION

SOLAR POWER SYSTEMS

Solar-thermal p o w e r production can be accomplished by two generic types of s y s t e m s . The first, called the central receiver con-

161

162

5.

Medium-Temperature

Solar

Processes

cept, uses large arrays of sun-tracking mirrors which reflect solar flux onto a central boiler atop a tall tower. In the central receiver system, therefore, energy t r a n s p o r t from the collector field to the p o w e r plant o c c u r s by optical m e a n s . Concentration ratios of the o r d e r of 10 are used along with turbines operating a b o v e 550°C. This concept is therefore a high-temperature solar-thermal p r o c e s s for the p u r p o s e s of this b o o k and will be treated in C h a p t e r 6. T h e second c o n c e p t , using relatively small collectors (a few tens of m ) spread over a large area, is called the distributed n e t w o r k con­ cept. Energy transport to the p o w e r plant turbine occurs through a net­ w o r k of pipes i n t e r c o n n e c t i n g the dispersed collector units. T h e s e systems use line-focus collectors and o p e r a t e at t e m p e r a t u r e s within the scope of this chapter. O n e distributed system idea uses dispersed c o m p o u n d - c u r v a t u r e (dish) collectors with small turbine generators inte­ gral with each collector. Energy transport o c c u r s by buried electrical cables. H o w e v e r , very high collector t e m p e r a t u r e s are required; there­ fore, this generation m e t h o d will be treated in C h a p t e r 6. T h e r e are m a n y types of distributed systems for p o w e r pro­ duction. F a c t o r s differentiating a m o n g the many generic types include 3

2

(1) point of solar heat input to p o w e r s y s t e m — p r e h e a t e r , boiler, superheater or combination; (2) storage size, if a n y ; (3) transport fluids—gas, liquid, chemical r e a c t a n t s ; (4) type of heat e n g i n e — R a n k i n e , B r a y t o n , Stirling; (5) baseload, intermediate load, peak load; (6) s i z e — 1 0 - , 100-, 1000-MW scales; (7) collector t y p e . e

It is the p u r p o s e of this section to describe some of the m o r e promising system c o n c e p t s and to outline the major design determinants for such s y s t e m s . A c o m p r e h e n s i v e t r e a t m e n t of all p r o p o s e d systems would be repetitive. All projected distributed solar-thermal p o w e r systems con­ sist of a collector field ( 0 . 5 - 1 . 0 mile per 100 M W ) , a fluid distribution n e t w o r k , a heat engine generator plant, and a control system. Most systems also include s o m e form of short-term storage (see Fig. 5.1). O t h e r than p o w e r plant control systems and steam generators [see (W4) for an overview] w h o s e design is not the subject of this b o o k , these major c o m p o n e n t s will be described in this section. Since no solar p o w e r plants now exist, detailed c o s t s , design criteria, and test data cannot be presented. 2

e

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Distributed

Solar Power Production

163

Systems

S o l a r heat col l e c t o r / c o n c e n t r a t o r system

Receiver heat t r a n s f e r system

Heat t r a n s p o r t system Energy storage system Heat rejection system

Prime mover system

Electric generator

F I G U R E 5.1

A.

The Collector

Conceptual block diagram of solar-thermal power s y s t e m s .

Subsystem

C h a p t e r 4 described several solar collectors usable for p o w e r production. A m o n g t h e s e are parabolic and circular troughs, Fresnel reflectors, and Fresnel lenses. T w o generic receiver types can be u s e d — e v a c u a t e d tubular or n o n e v a c u a t e d c a v i t y — a n d several tracking m o d e s are possible including n o r t h - s o u t h , e a s t - w e s t , and polar. T h e s e various line-focus s y s t e m s o p e r a t e at t e m p e r a t u r e s from 350 to 450°C at good efficiency. Parabolic troughs with tubular re­ ceivers are near the lower limit and Fresnel mirrors with small rim angles and cavity receivers n e a r the u p p e r . Associated p o w e r plant efficiencies of 1 2 - 1 8 % are achievable (F2). Figure 5.2 s h o w s a typical line-focus thermal p o w e r system with storage. Preliminary d a t a indicate that collector efficiencies of 4 0 - 4 5 % are achievable with parabolic troughs at 400°C w h e r e a s 5 0 - 5 5 % can be achieved with Fresnel reflector/cavity t y p e s at 4 5 0 - 5 0 0 ° C . T h e s e t e m p e r a t u r e s c o r r e s p o n d to the p e a k system conversion efficiency (not

5.

164

Medium-Temperature

Sensible thermal storage F I G U R E 5.2

Solar

Processes

Central steam rankine plant

Distributed solar-thermal system using steam transport and

thermal storage.

peak collector efficiency) including the steam Rankine cycle. Although the Fresnel mirror collector s h o w s higher efficiency, the mechanical mirror segment drive device and cavity receiver add about one-third more to the cost. Winston (W5) has suggested a c o n c e p t for p o w e r production using fixed collectors of the C P C t y p e . This c o n c e p t had formerly been dismissed in solar p o w e r feasibility studies and projections without careful study. A state of the art C P C with CR = 1.45, optical effciency of 0.76, and a selective, e v a c u a t e d receiver w a s s h o w n to be capable of col­ lecting about 5 3 % of the incident flux in a sunny climate. Collector outlet t e m p e r a t u r e w a s specified at 225°C to give an overall p o w e r plant effi­ ciency of ~ 10%. Although 4 0 - 5 0 % below efficiencies noted a b o v e , the less expensive fixed collectors would m a k e this p o w e r plant c o n c e p t via­ ble. Since no moving parts are involved in the collector field, field mainte­ n a n c e costs should be below those for tracking devices. A detailed study of the fixed-field idea is required prior to a final j u d g m e n t o n its economic feasibility. It is likely that the 225°C t e m p e r a t u r e may find application in solar total energy systems described later rather than in only p o w e r pro­ duction. Cavity receivers are attractive for several r e a s o n s . Evacua­ tion is not required to control convection. Therefore, the reflectance and a b s o r p t a n c e losses of a glass envelope are avoided. Similarly, radiation losses are small since the heat loss area is small although the effective emittance of the cavity is approximately unity. Selective surfaces need not be used and a b s o r b e r surfaces are not critical since the cavity effect assures an a b s o r p t a n c e value d ~ 1 even if the actual surface absorp­ tance is only 0.5. Therefore, optical efficiency of these collectors is lims

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Distributed

Solar Power Production

165

Systems

ited only by mirror reflectance. High a b s o r b e r heat fluxes need not be a problem since a cavity may use any internal dimensions b e c a u s e the cav­ ity size is quite i n d e p e n d e n t of the cavity a p e r t u r e . A n u m b e r of collector cooling fluids can be used. Pres­ surized w a t e r has excellent heat transfer characteristics but requires high-pressure piping and significant p u m p w o r k to circulate. S t e a m is also an excellent t r a n s p o r t fluid and seems to h a v e the e c o n o m i c edge over liq­ uid w a t e r (F2). Organic fluids and most gases such as helium are also tech­ nically feasible. Liquid m e t a l s — s o d i u m and p o t a s s i u m — c o u l d be used; h o w e v e r , stainless steel a b s o r b e r conduits and fittings are n e c e s s a r y . Collector fluid flow rate is an important design variable for several r e a s o n s . T h e collector t e m p e r a t u r e rise A J is inversely propor­ tional to flow rate and determines heat engine efficiency for a given con­ densing t e m p e r a t u r e . T h e higher A J , the higher the heat engine effi­ ciency. F o r very high flow rates A J is small but p u m p p o w e r require­ ments are h i g h — a s described later, the fluid loop pipe diameter could be increased to r e d u c e h o r s e p o w e r but increased heat losses would o c c u r from the pipe n e t w o r k . Therefore, an e c o n o m i c analysis is n e c e s s a r y to find the best mix of cycle efficiency, p u m p h o r s e p o w e r , pipe cost and pipe heat loss (see C h a p t e r 7). In general, h o w e v e r , the cost of energy trans­ port increases with decreasing AT . C

C

C

C

B.

Distribution

Subsystem

High-temperature fluid heat transfer media described above are all practical m e t h o d s of heat t r a n s p o r t by m e a n s of fluid internal en­ ergy. A promising alternative transport is by chemical reactants which are dissociated in the collector and recombined at the central plant to release their heat of reaction. T h e reactants are p u m p e d at near ambient tempera­ ture and p r e s s u r e thereby obviating the need for insulation and highpressure piping. A n example of this c o n c e p t is given below. A pipe n e t w o r k for any type of working fluid can be sized using m e t h o d s described in C h a p t e r 4. Collector field shape and piping layout are variables which can be determined in such a w a y that p u m p h o r s e p o w e r is a minimum for given constraints on pipe size. Figure 5.3 shows a typical layout for a square collector field. N u m b e r s s h o w n are in units of single-collector flow r a t e . It is seen that both diagonal and cross­ wise h e a d e r s carry the same exit flow rate but different rates at entry ports along the h e a d e r s . Multiples of the array shown can be added in an obvious fashion. A trade-off involved in field layout involves collector

166

5.

.1.2

Medium-Temperature

Solar

Processes

3 4 16 24 32 40 48 56

64^

24 Squares (1126 ft)

64

8 Squares (376 ft) Power plant

47 ft

A 47 ft -

F I G U R E 5.3 Piping network for 512 collectors to ensure equal flow at each header exit at the power plant. Numbers shown are in units of single collector flow rate.

shading at low sun angles. If collectors are spaced so that no shading o c c u r s , pipe runs will be longer than if some shading is tolerated for a few w e e k s a year. G r o u n d c o v e r ratios (ratio of collector aperture area to ground area) of 4 0 - 5 0 % seem a good c o m p r o m i s e (C5). C a r b o n steel is usable below 430°C for noncorrosive fluids w h e r e a s m o r e expensive alloys are required for the same fluids at higher t e m p e r a t u r e s . Liquid metals require stainless steel pipes, p u m p s , and heat exchangers at substantial cost (12 x c a r b o n steel pipe). T h e r m a l ex­ pansion in long pipe runs must be a c c o m o d a t e d by expansion loops of the sawtooth or semicircle t y p e s . Pipe wall thickness is proportional to in­ ternal p r e s s u r e as s h o w n below in a s u m m a r y field design calculation pro­ cedure. Pipe insulation to control parasitic heat loss was described in Chapter 4. F o r high-temperature s y s t e m s e x p o s e d to the w e a t h e r , cal­ cium silicate with an aluminum j a c k e t can be used to 900°C. E v a c u a t e d , multilayer foil insulations c a n achieve higher R values but are delicate and costly. Array design can be accomplished in a stepwise process by selecting a pipe size and then calculating first the p u m p w o r k , then the pipe thickness, and finally the insulation t h i c k n e s s . T h e s e p a r a m e t e r s all have an associated cost, the minimization of which is the goal of the op-

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Distributed

Solar Power Production

167

Systems

timal design. Of c o u r s e , t h e pipe material t h i c k n e s s m u s t be greater than that required by the boiler code which applies. P u m p w o r k W is calculated from E q . (5.1). F o r various lengths of pipe L t h r o u g h o u t a collector field with flow rates (see Fig. 5.3) the total p u m p w o r k is t

w h e r e p is the fluid density (usually c o n s t a n t unless a chemical reaction takes place) in a pipe element of length L , and inside diameter d . Pipe thickness f can be calculated from a force balance on a pipe element: t

{

{

p

f

p

= d /2cr,

(5.2)

iP

w h e r e p is the internal gage p r e s s u r e , d is t h e pipe inside diameter, and ois the allowable stress depending on the material in a c c o r d a n c e with the applicable c o d e , for e x a m p l e the A S M E Standard C o d e for P r e s s u r e Piping. In o r d e r to a c c o u n t for threading and o t h e r effects, in practice E q . (5.2) is modified to the form used by the piping industry (B2) as suggested by the A S M E c o d e : {

U = [doP/(2cr + yp)] + C,

(5.3)

w h e r e d is the outside diameter. P a r a m e t e r s y and C (the allowance for t h r e a d s , mechanical strength, and corrosion) are given in (B2). F o r ex­ a m p l e , at T < 525°C, y = 0.4 for steel pipe and C, e x p r e s s e d in i n c h e s , is zero for plain end pipe and related to thread d e p t h and pipe size for t h r e a d e d pipe. Pipe wall thickness is not a major cost determinant (how­ e v e r , diameter is) but m u s t be k n o w n to find the insulation t h i c k n e s s . Insulation thickness t c a n be calculated by requiring that a given total v o l u m e of system insulation V be distributed so that the heat loss p e r unit area o v e r the entire s y s t e m is uniform (K2). This m e t h o d is b a s e d o n an a s s u m e d uniform fluid t e m p e r a t u r e in e a c h part of the net­ w o r k . T h e total v o l u m e of insulation on cylindrical pipes elements of length L is 0

i n s

t

V

i n s

= 2

irLfrtdo

- t]

(5.4)

2

t

w h e r e ti is the thickness of insulation on pipe element of length L and out­ side diameter d . Finally the total cost C of the t h r e e major n e t w o r k c o m p o ­ nents discussed a b o v e is found by summing: t

0

n

C

n

= W x ( h / y r x cost of p u m p p o w e r ) / i 7 + S UCM)

+ ^insCms + <2 C L

n

m

(5.5)

5.

168

Medium-Temperature

Solar

Processes

w h e r e i q is the p u m p m o t o r efficiency, C (di) the present w o r t h (refer to Chapter 7) of pipe cost p e r unit length of diameter d C the present worth insulation cost per unit v o l u m e , Q t h e heat lost through the insula­ tion, and C its present w o r t h . If fluid costs are significant, the cost of the fluid volume used to fill the pipe n e t w o r k should be a d d e d to this cost equation. N e t w o r k cost C is then minimized by selecting the c o s t optimal pipe d i a m e t e r / i n s u l a t i o n thickness pairs by an iterative p r o c e s s . Minimum C is technically only a system suboptimization for a given fluid t e m p e r a t u r e , p r e s s u r e , flow r a t e , and central heat engine. T h e complete system optimal design requires exercising of all first-order design vari­ ables simultaneously. Typical optimal n e t w o r k designs result in 5 - 1 0 % parasitic heat loss from the pipe field. m

pA

i9

i n s

L

h

n

n

Network Transients An additional consideration in sizing the distribution n e t w o r k is the morning starting time required to bring the fluid to t e m p e r a t u r e . A simple energy balance can be used to estimate this effect. During the night the internal energy rate of change E is given by ^

[

=

Q

m

^

f

f

+

c

P

m

p ^ p

+

(5.6)

^iCif(ri,r )T ] 0

{

where mc, m c , and m c are fluid, pipe, and insulation mass-specific heat p r o d u c t s , and f{r r ) is a function relating mean insulation tempera­ ture to the fluid t e m p e r a t u r e in which r and r are the pipe insulation outer and inner radii. It is given by (B5) f

{

p

p

x

i9

x

0

0

Since most of the

fluid-to-ambient

x

t e m p e r a t u r e gradient o c c u r s across the

insulation, J ~ T ; then E q . (5.6) can be e x p r e s s e d as f

p

E = [CM](dT /dt)

(5.8)

f

w h e r e CM is the quantity in b r a c k e t s in E q . (5.6) divided by J , i.e., it is the thermal capacitance of the distribution n e t w o r k . An energy balance on the n e t w o r k of total length L is then f

It is a s s u m e d that the major resistance to heat transfer occurs across the insulation. Solving for T , f

Tf(0) - r

C a

X

P

L

CM\n{rJry

J

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Distributed

Solar Power Production

169

Systems

The energy E lost overnight for a period of t from the pipe n e t w o r k is given by n

E =

P" CM dT

t

Jo - CMiUO)

-

{exp [ c ^

% ] - l \

r

(5-10)

T h e heat loss E is the nighttime c o m p o n e n t of the total loss Q in E q . (5.5). T h e daytime c o m p o n e n t is [27r/c L/ln(r /r )]/( J - T ) dt. Generally ( J - T ) is not a c o n s t a n t so simple integration is not possible. T h e pre­ ceding expression a s s u m e s that fluid t e m p e r a t u r e fluctuations are small and d a y t i m e transients after s t a r t u p , negligible. h

i

f

0

i

f

a

a

Chemical Transport O n e w a y of eliminating nearly all para­ sitic heat leaks from a distribution s y s t e m is to u s e ambient t e m p e r a t u r e reactive fluids which are capable of releasing their heat of reaction at the p o w e r plant turbine site. T h e reactive fluids, usually g a s e o u s , are pro­ d u c e d by e n d o t h e r m i c dissociation at the collector. All transport lines can then be uninsulated and n o e x p a n s i o n loops are n e e d e d . F o r chemical t r a n s p o r t and storage to be successful, the r e a c t a n t s must be (1) free of side p r o d u c t s and the reaction completely reversible (most organic reactions are therefore disqualified), (2) compati­ ble with all collector, t r a n s p o r t , and r e a c t o r materials, and (3) simple to integrate into t h e solar s y s t e m . M a n y chemical s y s t e m s could be used for this t y p e of p o w e r plant. F o r e x a m p l e , m e t h a n e and steam can be dissociated at 700°C to hy­ drogen and c a r b o n m o n o x i d e . T h e r m a l energy left in the outlet stream is e x c h a n g e d with the collector inlet fluid s t r e a m . At the central site the hy­ drogen and c a r b o n m o n o x i d e can be reacted in the p r e s e n c e of a catalyst to release the heat of reaction at a b o u t 550°C. T h e hot gas stream pro­ d u c e s s t e a m in a boiler to o p e r a t e the p o w e r plant and is then r e t u r n e d to the collector as c o n d e n s a t e and g a s e o u s C H for redissociation. Since en­ ergy is t r a n s p o r t e d as chemical energy (26 k c a l / m o l e or 109 k J / m o l e ) and not sensible heat, the mass flow rates required are relatively smaller. A second reaction p r o p o s e d for p o w e r p r o d u c t i o n is the 2 S O + 0 2 ^ 2 S 0 oxidation reaction (C8). Dissociation o c c u r s at 800°C or a b o v e and r e c o m b i n a t i o n in the p r e s e n c e of a catalyst (e.g., platinum or vanadium) c a n o c c u r at 5 0 0 - 6 0 0 ° C . T h e chemical energy involved is 23 k c a l / m o l e (96 k J / m o l e ) . A working p r e s s u r e in the pipe n e t w o r k of only 3 - 4 a t m ( 3 0 0 - 4 0 0 kPa) is required and less than 1% of the electric p o w e r p r o d u c e d is n e e d e d for pumping (C8). G a s e o u s reactions are subject to the constraints of chemical 4

z

3

170

5.

Medium-Temperature

Solar

Processes

kinetics, which specifies both rate and completion fraction for any reac­ tion. Using the S 0 reaction as an e x a m p l e , the free energy of reaction A F ( J ) at t e m p e r a t u r e T is given by 3

AF( T) = AF(Jo) + RT \n[Pl P /Pl ] 02

02

(5.11)

0s

w h e r e the partial p r e s s u r e s are d e n o t e d by P. At equilibrium AF(T) = 0. If N moles of S 0 are initially involved in a reaction and x moles of 0 are p r o d u c e d , then (N - 2x) moles of S 0 and 2x moles of S 0 remain after the reaction. Using the ideal gas law to relate x and the partial p r e s s u r e s it is easy to show at equilibrium that 3

2

3

ln[(N + x)(N - 2x) /4x ] 2

where

3

= In P

2

T 0 T

+ [&F{T )/RT] 0

9

(5.12)

is the total p r e s s u r e . E q u a t i o n (5.12) s h o w s the effect of p r e s s u r e and tempera­ ture on the extent of dissociation of the reaction as m e a s u r e d by x. F o r ex­ ample, at 1 atm 9 0 % of the S 0 will h a v e dissociated at 1200 K; at 10 a t m , about 7 3 % will h a v e dissociated (D7). F u r t h e r details of reaction kinetics are contained in various chemical engineering t e x t s . Problems with the chemical t r a n s p o r t system include cata­ lyst decomposition and coking, corrosion, suitable reaction r a t e , low con­ version ratios, and the need for large heat exchangers to t r a n s p o r t large a m o u n t s of sensible heat b e t w e e n inlet and outlet streams at both the col­ lector and boiler. If reactants are stored, the t a n k s for gaseous compo­ nents must be quite large. Depending on the r e a c t a n t s , toxicity may be a problem and environmental impacts of an accident releasing C O , S 0 , or S 0 could be disastrous. P

T

O

T

3

2

3

C.

Storage

Subsystem

Storage media for solar p o w e r plants are usually liquid or a combined l i q u i d - s o l i d b e c a u s e of the simplicity and ease of heat transfer using a liquid. Large a m o u n t s of storage of the o r d e r of days or more for solar p o w e r plants are rarely e c o n o m i c (F2,F4). A m a x i m u m of about 6 h seems to b e the conclusion of several investigators using the standard 1-day outage p e r 10 yr criterion for the p o w e r grid. T h e physical proper­ ties of storage fluids h a v e b e e n given in C h a p t e r 4 along with tank costs. Since storage volume V for a given a m o u n t of energy storage is inversely proportional to the allowable t e m p e r a t u r e swing A J , it is important to re­ late A J to the p r o c e s s t e m p e r a t u r e . Allowable t e m p e r a t u r e swing is de­ termined by the storage material, t e m p e r a t u r e differences required for heat transfer, and the operating t e m p e r a t u r e of the p r o c e s s . Figure 5.4 s

S

S

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Distributed

Solar Power Production

111

Systems

s h o w s the design storage A J for a n u m b e r of solar-thermal p r o c e s s e s in­ cluding p o w e r p r o d u c t i o n (B7). It is seen that an approximately linear re­ lation exists b e t w e e n the m a x i m u m storage t e m p e r a t u r e and t h e allowable swing. A linear e x p r e s s i o n for the d a t a s h o w n is r e p r e s e n t e d by S

AJ = 0.65(J S

m a x

- 204)

(5.13)

in °C. Storage v o l u m e for a given a m o u n t of stored heat as p o w e r plant r e s e r v e c a n be calculated from the e x p e c t e d value of A J and the cost can be estimated from E q . (4.56). Since the fluid cost is proportional to volume directly with no e c o n o m i e s of scale usually available, the total cost of a tank and its c o n t e n t s C will usually be r e p r e s e n t e d by an equa­ tion of the form S

T K

C

T K

= K F V»(K x

m

+ K p)

2

3

+ KV, 4

(5.14)

S

w h e r e p is the p r e s s u r e and the K are c o n s t a n t s ; n ( < 1) and F are from Tables 4.5 and 4.4, respectively. T h e storage cost per unit energy c = C / ( V A J c ) is {

m

TK

T K

S

S

y

c

T K

= {[K[F (K m

+ K p)]/AT»}

2

3

+ (tfJ/AT,),

(5.15)

a decreasing function of A J . H e n c e , e c o n o m i e s of scale c a n be e x p e c t e d for the storage s u b s y s t e m for p o w e r plants using liquids confined in metal tanks. S

Two-Phase Storage A n o t h e r effect of decreasing unit costs of storage s h o w n a b o v e is the possibility of mixing rock with the working 500

Ol 300

I 400

I

I

I

I

I

500 600 700 800 900 Maximum storage temp. ( T ) (°F)

I 1000

m Q X

F I G U R E 5.4 Thermal storage maximum temperature v s . temperature swing AT for various high-temperature solar p r o c e s s e s . Legend: • , 1 0 - M W pilot plant systems; O, total energy s y s t e m s . [From (B7).] S

e

172

5.

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Solar

Processes

fluid to r e d u c e cost. Since rock is c h e a p e r than m o s t heat transfer fluids it can offer cost a d v a n t a g e s . T h e volumetric specific heat of a r o c k - l i q u i d mix c is v

c = (1 - € )c„, + e c v

v

f

v

(5.16)

VtT

w h e r e € is the rock void fraction, c is the fluid heat capacity, and c the rock heat capacity ( k J / m °C). Since c and c h a v e roughly the s a m e values for rock and organic fluids, storage volume V is u n c h a n g e d . H o w e v e r , in the cost equation, the second t e r m is r e d u c e d since the mix­ ture price is lower than that of the p u r e fluid. Solid media o t h e r than rock can be used. F o r cast iron c i > c so c is larger and V smaller, t h e r e b y reducing both the first and second t e r m s of E q . (5.14). In its simplest form the s o l i d - l i q u i d storage s u b s y s t e m con­ sists of a bed of inexpensive, uniformly sized particles contained in a tank. T h e high-temperature storage liquid fills the voids and circulates through the bed as heat is a d d e d or extracted from the tank. Charging is d o n e by removing fluid from the b o t t o m of the t a n k — t h e lowest tempera­ ture s t r a t u m — a n d returning it after heating to the top of the tank. B e t w e e n the high- and low-temperature z o n e s a relatively sharp t h e r m o cline is naturally p r e s e n t . As energy is added or subtracted, the t h e r m o cline m o v e s d o w n w a r d or u p w a r d , respectively. (This is c o n t r a r y to storage with high throughput rates which destroy the local thermocline and spread the t e m p e r a t u r e gradient o v e r the full length of the bed.) In ad­ dition to the cost advantage of this storage m e t h o d noted a b o v e , the bed a p p r o a c h permits storage of hot and cold fluid in o n e tank. At all times en­ ergy of m a x i m u m t h e r m o d y n a m i c availability is used as o p p o s e d to avail­ ability loss in well-mixed t a n k s . v

vA

V)V

3

VtV

v>{

s

VtC

Vti

v

s

T e s t s c o n d u c t e d on biphase storage h a v e s h o w n that a reli­ able thermocline can be initiated and maintained in a natural steel tank using granite and an organic heat transfer oil (M3). Typical d a t a showed that a 100°C t e m p e r a t u r e difference w a s maintained for e x t e n d e d periods. A b o u t 20% of the storage volume is c o n s u m e d by the thermocline. Flow channeling with uniformly sized gravel w a s not o b s e r v e d . It w a s also found that the effect of parasitic heat losses from the tank surface pene­ trated into the tank only a short distance. If w a s h e d gravel is used, pro­ vision must be m a d e for releasing steam producing during the first few charging cycles. Removal of solid residue must also be d o n e by filtration. In s u m m a r y , the s o l i d - l i q u i d storage c o n c e p t has the same capacity per unit volume as all-liquid storage (if it could be stratified), is less costly, is easily stratified, and is chemically stable. It is e x p e c t e d that this storage m o d e will be used in t h e first solar p o w e r plant in the U . S . — a 10-MW facility to be completed in the mid-1980s. O t h e r variations of e

//.

Industrial

Process

173

Heat

two-phase storage showing p r o m i s e include (1) the use of liquid metals and molten salts for the liquid p h a s e , (2) i m p r o v e d tank aspect ratios, (3) use of t w o immiscible liquids, and (4) use of metal, c e r a m i c , or metal ores for the solid p h a s e . Fluid Decomposition Storage cost is a decreasing function of m a x i m u m t e m p e r a t u r e via the A J d e p e n d e n c e on r m a x s h o w n a b o v e if the d e c o m p o s i t i o n limit is not r e a c h e d . B e y o n d the decomposition limit, fluid r e p l a c e m e n t b e c o m e s quite costly and will adversely affect s y s t e m economies (B7). A n o t h e r high-temperature effect, if w a t e r is u s e d , is the rapid increase of p r e s s u r e p in E q . (5.15) with r m a x . In that c a s e , the ATj (i.e., Tmax) and A J ^ (i.e., J m ) unit cost reduction can b e o v e r w h e l m e d by the rapidly increasing p t e r m and cost can begin to increase with J eliminating any e c o n o m i e s of scale. Most organic oils d o not require high-pressure confinement and the d e c o m p o s i t i o n effect o c c u r s prior to the high-vapor p r e s s u r e effect. T h e r m a l degradation of organic oils has b e e n studied by Morgan et al. (M3). It w a s found that the decomposition rate ra for H T 4 3 ® (see C h a p t e r 4) in w t % / h is S

n

1

a x

m a x

d

m

d

= 5.38 x 1 0

10

e x p [ - 17650/(7 + 273)]

(5.17)

e x p [ - 3 9 5 8 0 / ( J + 273)],

(5.18)

and for Therminol 6 6 ® is m

d

= 1.93 x 1 0

27

w h e r e T = [290,340°C]. It w a s also found that viscosity d e c r e a s e d with increasing fluid decomposition r a t e . Additional d a t a on high-temperature degradation and its effects o n e c o n o m i e s are given in (B7). Unit storage costs for all materials listed in Table 4.3 lie in the range of $ 3 - 6 / M J (B7) w h e n fluid, tank pressurization, and fluid r e p l a c e m e n t are c o n s i d e r e d if a mixture of 7 5 % rock and 2 5 % fluid is u s e d . Insulation cost is not included. A d v a n c e d storage c o n c e p t s and costs for solar p o w e r plants are discussed in (D7).

//.

INDUSTRIAL

PROCESS

Industrial goods in manufacturing direct firing as in a kiln, in the U . S . c o n s u m e s

HEAT

p r o c e s s heat is the thermal energy used to p r e p a r e p r o c e s s e s . P r o c e s s heat c a n be supplied as steam hot air, or hot w a t e r (or other hot liquid). Industry about 4 0 % of the national energy budget and

174

5.

Medium-Temperature

Solar

Processes

Table 5.1 s h o w s the U . S . use of heat by standard industrial classification (SIC) c o d e . It is seen that nine sectors a c c o u n t for the majority of heat u s a g e — m i n i n g , food, textiles, lumber, paper, chemicals, petroleum p r o d u c t s , s t o n e - c l a y - g l a s s , and primary metals. The b r e a k d o w n of industrial energy usage type is as follows (II): p r o c e s s steam, 4 1 % ; direct p r o c e s s heat, 2 8 % ; shaft drive, 19%; feedstock (chemical), 9%; other, 3%. Although the quantity of energy used by industry has been well k n o w n for m a n y y e a r s , the t h e r m o d y n a m i c quality or t e m p e r a t u r e TABLE

5.1

Summary of U.S. Industrial Heat Usage with Projections to 1985 and 2000

by SIC Category

for

1971

a

SIC group

11 12 * Mining 13 Subtotal 20 F o o d and kindred products 21 T o b a c c o products 22 Textile mills 23 Apparel 24 Lumber and w o o d products 25 Furniture 26 Paper and allied products 27 Printing and publishing 28 Chemicals 29 Petroleum products 30 Rubber 31 Leather 32 Stone, clay and glass 33 Primary metals 34 Fabricated metal products 35 Machinery 36 Electrical equipment 37 Transportation 38 Instruments 39 Miscellaneous Subtotal Grand total a

From (II).

Quantities in 1 0

12

Btu

1971

1985

2000

41 0.2 6 971 55 1,073 738 13 254 21 178 35 1,901 15 2,404 2,442 150 18 1,461 3,287 280 268 202 294 50 68 14,079 15,152

59 0.1 10.7 1,353 78 1,501 974 28 440 28 204 71 3,119 15 3,764 3,148 220 18 2,530 4,972 484 477 347 415 86 127 21,467 22,968

87 0?05 19.8 1,932 113 2,152 1,310 68 792 37 237 152 5,301 15 6,400 4,132 333 18 4,556 7,746 871 884 624 601 155 235 34,467 36,619

//.

Industrial

Process

175

Heat

level has only been determined recently (II, B5). Figure 5.5 shows the cu­ mulative distribution of p r o c e s s heat u s e by t e m p e r a t u r e . If p r e h e a t from 15°C is c o n s i d e r e d and the p r o c e s s t e m p e r a t u r e requirement (may differ from c u r r e n t practice in the field) is used to d e t e r m i n e heat d e m a n d , it is seen that 5 0 % of the p r o c e s s heat usage occurs at or below 260°C (500°F) and 6 0 % below 370°C (700°F). Therefore, b e t w e e n 50% and 6 0 % of all U . S . p r o c e s s heat could be delivered by single-curvature concentrating systems which are the subject of this c h a p t e r . (Table 5.3 at the end of this section s h o w s p r o c e s s t e m p e r a t u r e requirements by SIC code.) Currently, m u c h heat from fossil sources with high avail­ ability levels is used for applications at 300°C or below. The w a s t e of availability is e n o r m o u s . Table 5.2 below indicates second law effi­ ciencies for the p r o c e s s heat sectors below 260°C (500°F) if fossil fuels are c o n s u m e d at 8 0 % first law efficiency. Also s h o w n are r} values for the 2

100.0

50.0

-

20.0 lb)/ -

°

IO.O

ya> ac

5.0

/(a)

/

2.0

1.0

0.5

0.2 0.1 ' 20

.

i t 11

I

50

100

i 200

i

i

I

500

i

i i 11

1000

2000

Application temperature T (°C) F I G U R E 5.5

Distribution of U . S . process heat use by required tempera­

ture level: (a) heat requirements; (b) IPH requirements plus preheat from 15°C. [From (II).]

176 TABLE Second

5.

Medium-Temperature

Solar

Processes

5.2 Law Efficiencies

for U.S. Industrial

Processes

below 260°C

{500°F)

Fraction of U . S . process heat

Fossil fuel

Solar

Temperature

(T? )

(T? )

85°F 120°F 150°F 175°F 210°F 250°F 300°F 370°F 460°F Total/averages

10% 5% 5% 5% 5% 5% 5% 5% 5% 50%

<1% 6% 10% 13% 16% 20% 25% 30% 35% 16%

12% 52% 65% 71% 72% 77% 83% 85% 85% 61%

2

2

same p r o c e s s e s if performed by a solar energy system (without storage) with 10% parasitic losses and a 20°C driving force for heat transfer from collector to load device. Storage and additional heat exchangers degrade this second law efficiency as described in C h a p t e r 4. T h e n u m b e r s in Table 5.2 may not be precise in detail, nor need they be to vividly d e m o n s t r a t e the potential for i m p r o v e m e n t . Solar energy could increase the efficiency of energy use by a factor of m o r e than three by using available technology. Solar applications a b o v e 260°C may be s o m e w h a t m o r e difficult but the 50% of industrial heat below 260°C represents m o r e than 2 0 % of U . S . energy c o n s u m p t i o n . T h e benefits from the use of solar heat to c o n s e r v e high quality fossil fuels for higher priority u s e s are o b v i o u s . Industrial p r o c e s s heat (IPH) systems are quite simple from a h a r d w a r e viewpoint. T h e y consist mainly of a collector field, fluid con­ duits, a heat exchanger, and a controller. In s o m e cases storage for an hour or t w o to buffer short-term insolation outages is used. T h e size of storage must be evaluated for each process using a c o s t - b e n e f i t analysis. Sun-following I P H s y s t e m s without storage are basically fuel savers and can be added to existing plants if land is available. In the industrial N o r t h ­ east of the U . S . , land availability m a y be the critical constraint acting on I P H systems in that area. Since I P H s y s t e m s use c o m p o n e n t s already described for other m e d i u m - t e m p e r a t u r e applications this section will be d e v o t e d to the descriptions of generic types of systems. T h e prediction of the long-term performance of these systems is described in the final section of the chapter.

//.

Industrial

A.

Example

Process Process

111

Heat Heat

System

Prior to the discussion of generic industrial p r o c e s s heat (IPH) s y s t e m s , one of the first I P H , steam-based s y s t e m s in the U . S . will be described to provide the reader with a feel for system sizes and config­ urations. T h e J a c o b s - D e l Solar S y s t e m C o m p a n y (JD) collaborated with the H o m e L a u n d r y C o m p a n y in 1978-1979 to design and build a solar steam system for laundry and dry cleaning p u r p o s e s . A b o u t 600 m* of P T C collectors are used to p r o d u c e 170°C steam. The system will furnish 2 5 % of the steam r e q u i r e m e n t s of a laundry in P a s a d e n a , California (E2). Figure 5.6 shows the major c o m p o n e n t s of the J D system. The solar loop consists of the collector field, a steam generator (heat ex­ changer), p u m p , and control valves. T r e a t e d city w a t e r is used as the loop working fluid and is pressurized by a nitrogen bottle to operating pres­ sure. N o boiling takes place in the collector loop. T h e collector fluid can be used in three m o d e s — s t e a m p r o d u c t i o n , w a t e r heating, or short-term storage depending upon the t e m p e r a t u r e . S t e a m is p r o d u c e d in unit SG-1 c o n n e c t e d in parallel with the fossil-fuel boiler (200 hp). As solar heat is added to SG-1 its tube-side p r e s s u r e rises to slightly a b o v e the boiler set point (105 psig, 0.72 MPa) and solar-produced steam is used in the laundry s y s t e m . If solar steam p r e s s u r e falls, the boiler is brought on to pick up the load. Since this I P H s y s t e m is of the fuel saver t y p e , the a m o u n t of storage is small and a m o u n t s to a b o u t 15 min heat d e m a n d . T h e role of storage is to buffer solar flux transients during daylight but not to extend solar heat use into nighttime h o u r s . The relatively low, 2 5 % solar load fraction also indicates that storage is not required. T h e control system has several functions. First, w h e n fluid leaving the collector is 215°C, the steam generator control valves C V 6 and CV8 modulate to p r o d u c e 170°C steam (110 psig, 0.76 M P a ) . If collector fluid t e m p e r a t u r e d r o p s below 182°C, the b a c k u p boiler is used to provide the full load. Buffer storage is used for short solar outage periods only. Storage is recharged up to the 215°C level w h e n e v e r collector outlet tem­ perature is greater than storage t e m p e r a t u r e . A n o t h e r control feature in­ verts the trough collectors for overnight storage or for a loss of coolant episode or for p o w e r or p u m p failure. F r e e z e control is achieved by circu­ lating storage fluid through the collectors w h e n the ambient t e m p e r a t u r e is less than 1°C. Collector cleaning with w a t e r sprays is also d o n e periodi­ cally. This sample system includes all features of an I P H in a simple and reliable configuration. A solar s u b s y s t e m , fossil-fuel b a c k u p

178

5.

Medium-Temperature

Solar

Processes

O

6

G

'5

t o
>, a c/3

O

OH

£

to

c

^ gp SO

in'

^

X!

C

* a

E

i

a,s <03u 5

1

S

//.

Industrial

Process

179

Heat

and controls are c o m b i n e d together in logical fashion to achieve the de­ sign goal. All c o m p o n e n t s o t h e r t h a n the collectors (and sun tracker) are off-the-shelf, chemical p r o c e s s industry, standard items.

B.

Liquid Heating

Systems

Figure 5.7 s h o w s a schematic diagram for a liquid heating I P H s y s t e m . T h e liquid to be heated m a y be p a s s e d through the collectors or may be h e a t e d indirectly in a heat e x c h a n g e r (not s h o w n ) . Collector p u m p P I is activated for T > 7\ + A w h e r e A is selected to provide ade­ quate hysteresis to suppress cycling of P I . H e a t is delivered to the p r o c e s s by p u m p P3 which m a y use a c o n s t a n t or variable flow rate de­ pending on the relative cost effectiveness of e a c h . If w a t e r or other freezing collector liquid is u s e d , a d r a i n d o w n s y s t e m , activated by operating valves V I and V2 w h e n p u m p P I ceases to o p e r a t e , is required. If a nonfreezing organic fluid is u s e d , n o collector d r a i n d o w n is required but the fluid must be maintained a b o v e its p o u r point in the collectors overnight. If liquid m a k e u p is required to replace fluid c o n s u m e d in the p r o c e s s , it is provided through p u m p P2 and valve V3 b o t h operated by a level controller in t h e storage tank. T h e series b a c k u p heater is of the rapid r e s p o n s e type and can b e gas, oil, or steam fired. Fluid stream t e m p e r a t u r e T is controlled 2

3

{Sun,

! ! P

P3

Auxiliary heating

T l V4

F I G U R E 5.7 Direct, liquid-based IPH system schematic diagram. LIC denotes level indicator controller. [From ( I I ) . ]

180

5.

Medium-Temperature

Solar

Processes

by a feedback controller along with a feedforward signal from the storage tank. T h e auxiliary heat rate is modulated by t e m p e r a t u r e signal J . If solar heat collection is higher than instantaneous p r o c e s s d e m a n d , a tem­ pering or mixing v a l v e — V 4 , for e x a m p l e — c a n be used to maintain process inlet t e m p e r a t u r e at its desired point. Normally, industrial pro­ cesses have uniform loads and a system controller using a system mathe­ matical model on a minicomputer will give very precise p r o c e s s control. H o t w a t e r is c o n s u m e d directly in many industries such as food, p a p e r , leather, textiles, and some chemicals. O t h e r systems do not c o n s u m e hot w a t e r directly but use only its internal energy; for e x a m p l e , feed p r e h e a t in a petrochemical plant u s e s only the heat from the hot fluid. A modification of the direct heating system of Fig. 5.7 is shown in Fig. 5.8. H e r e the p r o c e s s fluid is heated indirectly by m e a n s of a heat exchanger placed b e t w e e n the solar collection loop and the p r o c e s s . This type of system would be used if the liquid to be heated is unsuitable for a solar collector working and storage fluid. T h e control methodology for the indirect system is slightly different. If p r o c e s s return t e m p e r a t u r e J > 7 \ , valve V5 b y p a s s e s storage and the auxiliary source supplies the full p r o c e s s d e m a n d . This control feature is needed to pre­ vent auxiliary heat from partially heating a fully depleted storage tank (T < T ). During p e a k insolation p e r i o d s , 7\ may exceed the desired process t e m p e r a t u r e T . T h e usual industrial practice in this case is to use p r o c e s s return fluid at T to t e m p e r fluid at T if T > T . Valve V7 is a p r e s s u r e balancing valve b e t w e e n the two inlet streams to the tempering valve V6. F o r solar system m a i n t e n a n c e , b y p a s s valve V5 can be locked 3

3

t

3

5

3

FIGURE [From (II).]

5.8

4

4

5

Indirect, liquid-based IPH system schematic

diagram.

II.

Industrial

Process

181

Heat

in the full auxiliary m o d e and process operation can continue without interruption.

C.

Gas Heating

Systems

H o t gases are used in industry for several p u r p o s e s in­ cluding curing, drying (minerals, food, paint, textiles, lumber), baking, preheating, chemical reaction, and moisture stripping in a stripping col­ u m n . Figure 5.9 shows a schematic diagram of a solar, indirect gas heater which could be used in m a n y industrial installations. T h e solar collection loop and its control are similar to those described a b o v e for liquid-based I P H s y s t e m s . H e a t delivery to the gas stream is controlled by the entering gas t e m p e r a t u r e T which causes the p r o c e s s p u m p P2 to operate if storage t e m p e r a t u r e T > T + A; the extra t e m p e r a t u r e increment A is determined by the heating coil effectiveness. If the storage t e m p e r a t u r e is greater than that n e e d e d to supply hot gas at the p r o c e s s design t e m p e r a t u r e , valve V I t e m p e r s the heating coil inlet 3

x

gas heater

S

v

3

P3

F I G U R E 5.9 (II).]

Indirect gas heating IPH system schematic diagram. [From

182

5.

Medium-Temperature

Solar

Processes

t e m p e r a t u r e to provide a p r o p e r T value. T e m p e r a t u r e T must be mea­ sured with an averaging probe to c o m p e n s a t e for r a t h e r c o m m o n nonuni­ form distribution of t e m p e r a t u r e d o w n s t r e a m of an air heating coil. The b a c k u p unit functions in the series m o d e as is the case for previous liquid h e a t e r s . If the b a c k u p heater has an appreciable time constant, feedforward control from the storage tank may be n e e d e d . Given the usual m a s s of storage used, it is unlikely, h o w e v e r , that storage t e m p e r a t u r e would d r o p at a rate exceeding the w a r m u p rate of the b a c k u p device. 4

D.

Steam IPH

4

Systems

S t e a m is the most c o m m o n fluid used for process heat end uses in the U . S . In this section t w o steam systems compatible with solar heat are d e s c r i b e d — t h e steam flash c h a m b e r and the series solar-backup boilers m e t h o d s . Steam Flashing Systems T h e design of steam accumulators was described earlier in C h a p t e r 4. Figure 5.10 shows one way of using an accumulator in a solar I P H s y s t e m . Although the flash tank c o n c e p t is

{Sun) Steam

F I G U R E 5.10 Steam accumulator or flash chamber IPH system sche­ matic. Legend: F C , flow controller; T C , temperature controller; P R C , pressure regulator controller; D T C , differential temperature controller; PR, pressure regulator. [From (II).]

II.

Industrial

Process

Heat

183

simple, control is rather complex since most boilers c a n n o t act as rapid r e s p o n s e b a c k u p d e v i c e s . In addition, a minimum flow must be main­ tained in most boilers to avoid tube d a m a g e owing to hot s p o t s . T h e rate at which saturated steam is p r o d u c e d at the flash c h a m b e r is determined by the t e m p e r a t u r e of storage and the minimum flow required by the boiler. In principle, if solar storage w e r e sufficiently hot, the boiler could be b y p a s s e d . H o w e v e r , minimum boiler flow must be maintained as specified by the manufacturer to avoid tube b u r n o u t be­ cause of inadequate flow rate and low convection rates in the t u b e s . O n e m e t h o d of accomplishing this is to use flow controller F C 2 to direct p r o c e s s c o n d e n s a t e to the flash c h a m b e r directly via V 5 . This fluid b y p a s s e s solar storage and r e d u c e s the solar heat input to the flash tank. Since c o n d e n s a t e return has a lower enthalpy than flash tank output, the boiler injects steam into the c h a m b e r , through valve V 3 , b a s e d on a signal from controller T C I . Auxiliary steam is provided to maintain flash c h a m b e r de­ sign conditions based on the level control signal. Since c h a m b e r tempera­ ture correlates with liquid volume in the c h a m b e r , the fluid level c a n be used to determine boiler heat addition a b o v e the minimum continuous flow level. If solar storage is completely depleted, i.e., T C 3 > T C 2 , the valves V4 and V6 close and 100% flow o c c u r s through the boiler and valves V5 and V2. T h e major p r o b l e m with the flash tank a p p r o a c h is the limited steam rate which can b e achieved efficiently. Solar Boiler-Auxiliary Boiler System Figure 5.11 s h o w s a solar b o i l e r - a u x i l i a r y boiler s y s t e m . The solar boiler is a kettle evap-

F I G U R E 5.11 Solar boiler-auxiliary boiler IPH s y s t e m schematic dia­ gram. Legend: L C , level controller; L L S D , low-level shutdown; H L S D , high level shut down (other flow symbols defined in Fig. 5.10). [From (II).]

184

5.

Medium-Temperature

Solar

Processes

orator with its solar fluid throughput via p u m p P2 continuously at a max­ imum level. Only the boiler minimum flow criterion can override this solar fluid flow rate. If boiler minimum flow is being a p p r o a c h e d , flow con­ troller F C 2 modulates solar flow control valve V4. Since solar firing of the solar boiler is thereby r e d u c e d , the p r o c e s s loop liquid level rises in the kettle. Level controller L C then opens valve V2 increasing the boiler flow as required. In normal operation w h e n the boiler base flow rate criterion does not override m a x i m u m solar flow to the solar boiler, it is possible for the solar heat rate to e x c e e d the p r o c e s s d e m a n d s on a sunny day. As a re­ sult, the solar boiler could boil dry. This is to be avoided to p r e v e n t scale buildup and can be accomplished by m e a n s of a low-level s h u t d o w n ( L L S D ) on the solar delivery p u m p P2. As solar storage b e c o m e s depleted, the solar boiler ceases to o p e r a t e and the kettle p r o c e s s fluid level rises. A high-level s h u t d o w n ( H L S D ) switch then closes valve V3 preventing any further fluid buildup in the kettle. Full auxiliary heat is used to operate the p r o c e s s although the solar boiler continues to act as a p r e h e a t e r until T C I > T C 2 , at which point solar delivery p u m p P2 is deactivated. This system is quite flexible and can even o p e r a t e a batch p r o c e s s while continuously collecting solar heat since P3 o p e r a t e s inde­ pendently of the p r o c e s s . T h e control strategy for this system is quite simple and extracts as m u c h solar heat as possible since solar heat is used for boiling or fluid p r e h e a t depending on storage t e m p e r a t u r e . T h e t w o steam systems described a b o v e are only examples of m a n y c o n c e p t s p r o p o s e d for solar p r o c e s s steam s y s t e m s . E a c h pro­ posal must be examined for controllability, m a x i m u m solar usage and flexibility. E.

Possible

Field

Problems

Although less than a d o z e n solar I P H s y s t e m s w e r e built prior to J a n u a r y 1, 1979, several problems have been o b s e r v e d which should be avoided in future s y s t e m s . Controls require careful design regarding hysteresis or dead band size, m o d e switch criteria, and sensor location. Controls can m a k e or break a system and therefore must be ana­ lyzed for function in all possible m o d e s including normal collection, tran­ sient w a r m u p in the morning, daytime solar outage, nighttime storage, loss-of-coolant fail-safe m e a s u r e s , dust storm and hail e p i s o d e s , high winds, e t c . Sensor placement and reliability at high t e m p e r a t u r e w a s found to be a particular problem in the early s y s t e m s . T r a c k e r s must a c c o m m o -

//.

Industrial

Process

Heat

185

date any vibration caused by wind or reciprocating p r o c e s s machinery and sluggishness c a u s e d by low t e m p e r a t u r e of t r a c k e r lubricants. Possible piping problems include leaking rotary j o i n t s , fit­ tings, use of plastic pipe for high t e m p e r a t u r e s and p r e s s u r e s for which it is not suited, and use of control valves which do not fully seal. In addition, dirt and o t h e r refuse can be left in lines to foul collectors and damage valves. Manifold design must be d o n e carefully to a s s u r e good flow balance in all collectors (See C h a p t e r 4). Although collector roof mounting is usu­ ally more e x p e n s i v e than ground mounting (if ground is available) a longer w a r m u p period will be needed in the morning owing to larger fluid volume in e x t e n d e d pipe runs to and from a r e m o t e collector field. High viscosity of heat transfer oils w h e n cold is also a potential problem. Retrofit mounting of collectors on a roof may be impossible if the building structure is not designed to carry the extra dead load. A m e t h o d for cleaning the collector reflectors or lenses is a necessity in an industrial e n v i r o n m e n t . Airborne pollutants should be identified prior to selection of the collector reflector material and col­ lectors should b e sited to minimize particulate pollutant fallout. M o s t col­ lectors of the reflecting type are shipped disassembled. During field as­ sembly, therefore, a m e t h o d of aligning and leveling the absorber relative to the m i n o r m u s t be used. Special jigs seem to be an effective w a y to ac­ complish alignment. Long-term average efficiencies of 4 0 - 4 5 % are typi­ cal for line-focus c o n c e n t r a t o r s , irrespective of specific collector designs, operating in p r o c e s s heat s y s t e m s below 250°C. T h e preference of I P H designers of early systems w a s to avoid the cost and complexity of long-term storage, using only short-term buffer storage. F.

Projected

Technical

Readiness

T h e m a r k e t penetration of solar I P H systems d e p e n d s u p o n cost, performance, and reliability of the solar system vis-a-vis the non­ solar system. A recent study (B5) has projected the state of technical readiness of solar s y s t e m for m a n y major I P H sectors. A s e x p e c t e d , those systems using simple collectors—flat plates or solar p o n d s — a t low tem­ perature are technically viable t o d a y . T h o s e p r o c e s s e s operating at higher t e m p e r a t u r e and requiring concentrating collectors will be technically tested and developed in the m o r e distant future. Table 5.3 lists the major I P H SIC sectors with estimates of technical readiness and the type of solar collector s u b s y s t e m which seems most suitable. Of c o u r s e , tech­ nical and e c o n o m i c viability are t w o distinct questions and the latter is considered in C h a p t e r 7.

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Shaft Work

III.

SHAFT

Production

WORK

189

PRODUCTION

The conversion of solar heat to shaft w o r k in a heat engine w a s d e m o n s t r a t e d more than a c e n t u r y ago. Since that time several d o z e n experimental s y s t e m s , most based on the Rankine cycle, h a v e b e e n operated successfully from a technical viewpoint. T h o s e s y s t e m s w e r e used to p r o d u c e shaft w o r k for w a t e r pumping, air conditioning, industrial shaft drive, and electric p o w e r production. This section will describe the design of intermediate sized solar-powered heat engines which operate below 300°C. A simplified schematic diagram of a solar-powered Rankine type heat engine is s h o w n in Fig. 5.12 and an energy flow diagram is shown in Fig. 5.13. The Rankine engine system shown schematically in Caloria H T 4 3 p u m p - electric

Sti

valve

Separator

i

vw-

Solar heat storage reservoir

Burst disk

-A/W-A/W-

-AA/V•AMr

Boiler

Preheater

Torque meter

Pulley M

N

To water pump

Check ,

Regenerator

Float tank Filter drier

Boost p u m p - e l e c t r i c

F I G U R E 5.12 Schematic diagram of 25-hp example solar-powered Ran­ kine cycle system. (Courtesy of Barber-Nichols Engineering, Arvada, Colorado.)

5.

190

Medium-Temperature

Losses

Temperatures

Solar i r r a d i a n c e varies w i t h t i m e and m e t e o r o l o g i c a l conditions

Q

0

c

a

Concentration onto receiver of area A ,

V c

Processes

Notes

Solar f l u x on c o l l e c t o r aperture A

(1-77 )I A

Solar

A

C o n c e n t r a t i o n r a t i o ranges from 2 to 1 0 3

a Collector e f f i c i e n c y Receiver temperature T

Collector receiver area A r

r

[See (Eq. 4 - 4 3 ) ]

^cVc Work o u t p u t Heat engine M a x i m u m -q^

7

?c a c( - 7E^ A

Condenser

Ambient environmental heat sink

I

1

7

L = p a r a s i t i c losses

L

Condenser temperature T

-

cond temperature

T

c o n (

j

m

u

s

t

D e

above T

ambient

a

Overall efficiency Ambient sink temperature T

W a

" ^ c ^ E

F I G U R E 5.13 Schematic diagram of a solar-powered heat engine system. Optical and thermal losses to the environment as well as heat rejection to the environmental sink are shown. Efficiencies of each step are shown to the right.

Fig. 5.12 contains t w o fluid loops. T h e solar heat supply loop uses H T - 4 3 ® (See C h a p t e r 4) as the working fluid from which heat is extracted in a boiler and preheater. The heat engine fluid passes from the boiler through a l i q u i d - v a p o r separator to the turbine w h e r e shaft w o r k is pro­ duced. Sensible heat remaining in the turbine exhaust is transferred to the c o n d e n s a t e u p s t r e a m of the p r e h e a t e r by m e a n s of a regenerator. After this step the turbine e x h a u s t gas is c o n d e n s e d in a water-cooled con­ denser and piped to the fluid tank. Prior to its return to the preheater, the

///.

Shaft Work

Production

191

liquid working fluid is passed through a filter. T h e main fluid p u m p is driven by the turbine o u t p u t shaft. T h e start-up p u m p s h o w n in Fig. 5.12 is used to initiate fluid circulation prior to turbine start-up. After the main p u m p begins operation, the start-up p u m p is shut off. T w o counteracting p h e n o m e n a are present in solar-powered engine s y s t e m s . A s s h o w n in C h a p t e r 3, the efficiency of heat engines in­ creases as the input fluid t e m p e r a t u r e i n c r e a s e s , w h e r e a s the efficiency of a solar collector d e c r e a s e s with outlet t e m p e r a t u r e as s h o w n in Chapter 4. A system first law efficiency T 7 can be defined as the p r o d u c t of collector and engine efficiency as shown in Fig. 5.13. T h e value of i7sys first in­ creases with collector t e m p e r a t u r e , then d e c r e a s e s as collector heat losses o v e r w h e l m t h e r m o d y n a m i c gains owing to progressively higher engine inlet t e m p e r a t u r e . Using relations d e v e l o p e d earlier, the efficiency of a solar-powered Carnot engine can be e x p r e s s e d by sys

Vsys

= { %

" U (T e

t0

- T )/I]}

[1 -

x

a

(TjTtJl

(5.19)

w h e r e T is the environmental t e m p e r a t u r e , T the collector fluid outlet t e m p e r a t u r e (same as engine inlet t e m p e r a t u r e if no heat e x c h a n g e r is used and conduit heat losses are small), and other t e r m s are as defined previously. E q u a t i o n (5.19) can be differentiated with respect to fluid t e m p e r a t u r e to find the t e m p e r a t u r e corresponding to m a x i m u m system efficiency. It is easy to show that the peak efficiency is achieved for a value of T given by a

t0

f>0

r,.o:max =

F o r e x a m p l e , if

V o

= 0.7,

MwJTjU*) + V P ' . 2

U = 0.2 W / m e

2

(5.20)

°C, T = 280 K , and / = a

900 W / m , then T , :max = 700°C and the m a x i m u m system efficiency is 39%. T o i m p r o v e performance it is clear from E q s . (5.19) and (5.20) that 2

f

0

high optical efficiency r} , very low U values requiring high concentra­ tion, and high insolation are all required. Of c o u r s e , E q . (5.20) applies only for the idealized Carnot and Stirling cycles with second law efficiency of unity. H o w e v e r , all heat engine systems have an efficiency curve which exhibits a m a x i m u m de­ pending u p o n collector p r o p e r t i e s , cycle p a r a m e t e r s , and w e a t h e r condi­ tions. Real engines h a v e lower efficiency values than the theoretical limit for several r e a s o n s : (1) real fluids must be used with associated t h e r m o d y ­ namic penalites as described shortly; (2) turbines and p u m p s are not per­ fect, and (3) thermal and mechanical losses o c c u r in piping and all c o m p o ­ nents of the system. T h e s e important effects are described in this chapter by describing their impacts on the performance of a c o m m o n heat e n g i n e — t h e Rankine cycle described in general in C h a p t e r 3. 0

c

5.

192

A.

Working

Medium-Temperature

Solar

Processes

Fluids

T h e most c o m m o n fluid used in Rankine cycles is w a t e r since its heat of vaporization is high, its cost low, and its supply plentiful. H o w e v e r , from a t h e r m o d y n a m i c viewpoint other fluids m a y be m o r e de­ sirable, owing to vapor density, phase-change o c c u r r e n c e conditions, or transport properties at intermediate t e m p e r a t u r e s . In the ideal Rankine cycle all heat addition occurs at con­ stant t e m p e r a t u r e equal to the collector outlet t e m p e r a t u r e . H o w e v e r , the real collector fluid cannot provide heat at a constant t e m p e r a t u r e since sensible heat removal is associated with a t e m p e r a t u r e d e c r e a s e in the collector fluid. Since a heat e x c h a n g e r is used b e t w e e n the collector and heat engine, s o m e additional t h e r m o d y n a m i c availability is lost in accord­ ance with E q . (4.80). Vaporization of cycle fluid directly in the collector is usually not practical b e c a u s e of flow b a l a n c e , control, and piping problems. T h r e e types of cycle fluids can be identified as s h o w n in Fig. 5.14. Fluid type A has a relatively large latent heat addition occurring at the m a x i m u m cycle t e m p e r a t u r e ; therefore, cycle efficiency is good. H o w e v e r , the collector outlet t e m p e r a t u r e must be relatively high to avoid a zero pinch point t e m p e r a t u r e . (The pinch point t e m p e r a t u r e is that t e m p e r a t u r e at which the difference b e t w e e n stream t e m p e r a t u r e s in a heat exchanger is smallest.) T y p e A fluids have a high critical point tem­ perature relative to cycle t e m p e r a t u r e and high collector fluid flow rates are needed.

L

i

0

i

50

i

100

i

i

1

i

1

0

50

100

0

50

1 100

Percent heat addition

F I G U R E 5.14 Temperature characteristics of three types of fluids as they pass through the boiler of a Rankine cycle. Solar collector and engine fluid temperature pro­ files are shown for the same values of cycle fluid inlet temperature T and outlet temperature T . The slope of the collector fluid (upper) T curve is determined by the collector fluid flow rate constrained by the pinch point A7\ c

0

col

Shaft Work

Production

193

T y p e B fluids have a smaller a m o u n t of latent heat addition than type A fluids. Therefore, the cycle efficiency is lower but the col­ lector fluid exits the boiler at a lower t e m p e r a t u r e and as a result collector efficiency is higher than for type A fluids since the average collector tem­ perature is lower. T h e critical t e m p e r a t u r e of type B fluids is of the same order as the collector outlet t e m p e r a t u r e . T y p e C fluids are operated in the supercritical range and do not experience constant t e m p e r a t u r e heat addition. Therefore, cycle effi­ ciency is low. H o w e v e r , the collector fluid experiences a large tempera­ ture drop in the boiler and collector efficiency can be quite good for a spe­ cific design outlet t e m p e r a t u r e T . Collector fluid flow rates are small rel­ ative to those for type A fluids. E a c h of the three real fluid classes imposes a t h e r m o d y n a m i c penalty on the ideal cycle efficiency since heat addition c a n n o t be d o n e isothermally. Although the t h e r m o d y n a m i c characteristics of fluids are important, other properties m u s t be considered. F o r e x a m p l e , for the same cycle t e m p e r a t u r e conditions t w o different fluids m a y require vastly different p u m p and e x p a n d e r designs with major cost effects. Operating p r e s s u r e s also effect p r e s s u r e vessel and p u m p and turbine seal designs and c o s t s . Various fluids have widely varying cost, durability, flammability, toxicity, and chemical reactivity with other cycle c o m p o n e n t s . Typi­ cal practical cycle fluids include the halocarbon r e f r i g e r a n t s — R l l , R12, R22, R113, R114, R 1 1 5 — p y r i d i n e , w a t e r , and a n u m b e r of stable organic fluids with appropriate p r o p e r t i e s . Uo

B.

The Expander

or Turbine

T h e e x p a n d e r of a heat engine is the c o m p o n e n t which con­ verts kinetic and internal energy in the vaporized working fluid to shaft w o r k . Piston- or turbine-type e x p a n d e r s are used depending u p o n the size of the engine and its speed. T h e performance of e x p a n d e r s has b e e n thoroughly analyzed in the engineering literature and it has b e e n found that similarity p a r a m e t e r s can be used to p r e p a r e generalized perform­ ance m a p s for the broad range of sizes. T h e similarity p a r a m e t e r s which are most useful are the Reynolds n u m b e r , the M a c h n u m b e r , the specific speed N , and the spe­ cific diameter D . T h e specific speed is defined by s

s

N s

NQ^/m,

(5.21)

w h e r e N is the rotation rate in r p m , Q is the inlet flow rate in f t / s e c , and 3

194

5.

Medium-Temperature

Solar

Processes

/ / is the enthalpy d r o p in ft l b / l b across the e x p a n d e r for adiabatic (no heat loss) conditions. It is seen that N is a dimensional m e a s u r e of turbine speed (but with a consistent set of units will be dimensionless). Specific diameter D , a dimensional similarity m e a s u r e of e x p a n d e r size, is defined by a d

s

s

D = DH %/Q ,

(5.22)

112

s

a

w h e r e D is the diameter in feet. F o r most e x p a n d e r s used in solar systems the M a c h n u m b e r is low ( < 0 . 7 ) so that compressibility effects are of sec­ ond order. T h e Reynolds n u m b e r is usually sufficiently high ( > 10 ) so that fluid inertial forces dominate viscous forces and performance effects are independent of Reynolds n u m b e r . Therefore, of the four similarity p a r a m e t e r s , only t w o — D and N —are of first order. It is possible to plot turbine efficiency as a function of the t w o p a r a m e t e r s for all geometrically similar devices (B3). Turbine efficiency is defined as the w o r k output divided by the fluid enthalpy change in the turbine. Figure 5.15 is a general N -D m a p for many c o m m o n e x p a n d e r t y p e s . The figure shows that certain generic ex­ p a n d e r types are best for certain applications. Selecting an e x p a n d e r type is a major use of the N -D m a p . F o r e x a m p l e , if the specific speed is low, the m a p indicates that piston engines are the e x p a n d e r of choice. As speed increases piston e x p a n d e r s would be replaced by rotary e x p a n d e r s for smaller sizes and by axial turbines in larger sizes. At very high speed only small diameter axial turbines are useful. F o r e x a m p l e , if a specific speed of 3.0 is specified, a partial-admission axial turbine with specific diameter of about 10 will have higher efficiency than either a drag turbine or a rotary piston e x p a n d e r . Figure 5.16 s h o w s the c o m p o n e n t s of a 250-hp axial flow turbine designed for an intermediate t e m p e r a t u r e system. 6

s

s

s

s

C.

s

s

Pumps

T h e p u m p used to pressurize the c o n d e n s e d cycle fluid prior to boiling can be of the positive displacement or rotary t y p e . The perform­ ance of p u m p s can be analyzed using the same similarity p a r a m e t e r s as are used for e x p a n d e r analysis. An additional p a r a m e t e r , the suction spe­ cific speed, is frequently introduced as an indicator of possible cavitation at the p u m p inlet. Figure 5.17 is a performance m a p for all c o m m o n types of p u m p s and c o m p r e s s o r s . It is seen that specific types of p u m p s are most suitable for specific subsets of N -D values. s

s

///.

Shaft Work

Production

195

5.

196

Medium-Temperature

Solar

Processes

F I G U R E 5.16 Components of a 250-hp axial flow turbine for solar or other intermediate temperature applications. The rotor diameter is 5.5 in and the design speed is 66,000 rpm. (Courtesy of Barber-Nichols Engineering, Arvada, Colorado.)

D.

Other

Components

H e a t exchangers are used to transfer heat from the collector or storage fluid to the cycle working fluid. Both preheating and boiling are generally required and separate exchangers are used for each function. The p r e h e a t e r adds sensible heat, the boiler, latent heat. T h e design of heat exchangers is described earlier in C h a p t e r 4 and follows standard industrial practice. Rankine cycle c o n d e n s e r s (either air- or water-cooled) are also designed using conventional m e t h o d s . A fourth heat e x c h a n g e r is used in some Rankine cycles to transfer heat remaining in the turbine e x h a u s t to the boiler (or preheater) inlet liquid stream. This exchanger is called the regenerator and can be used if the turbine e x h a u s t contains appreciable superheat. That is, the exhaust t e m p e r a t u r e at the condensing p r e s s u r e is greater than the con­ densing t e m p e r a t u r e at the condensing p r e s s u r e . Fluids which have cycle characteristics of this type are called " d r y i n g " fluids and can be identified by the relation, on a p r e s s u r e - e n t h a l p y diagram, of isentropic lines to the saturated vapor line. If the isentropic lines diverge from the saturation

Shaft Work

Production

197

5.

198

Medium-Temperature

Solar

Processes

line with decreasing p r e s s u r e , the fluid is of the drying t y p e . T h e regen­ erator is sized using the e - N T U m e t h o d described in Chapter 4. Controls for heat engines can be relatively complex and are designed for a specific application. The controller must perform several major tasks including: (1) operation of the solar collection loop, (2) tur­ bine subsystem cold start-up, (3) turbine speed and heat rate control, (4) fail-safe system m o d e control. The second function is particularly impor­ tant for systems which use the cycle fluid as the lubricant for e x p a n d e r and p u m p . Complete lubrication must be established before heat addition to the boiler begins. Storage for solar shaft drive systems can be either thermal or mechanical. Thermal storage is discussed in detail elsewhere in this chapter and in Chapter 4. Mechanical storage in flywheels or in water reservoirs for solar p u m p systems is completely available from a second law viewpoint since it is stored as kinetic or potential, i.e., organized en­ ergy. The technology of h y d r o p u m p storage is well developed and w a t e r turbine first and second law efficiencies of the order of 8 0 % can be achieved with commercial e q u i p m e n t . Flywheel storage has b e e n used only for small-scale devices and requires additional d e v e l o p m e n t . A third type of mechanical storage involves pressurized gas storage in large un­ derground reservoirs; h o w e v e r , c o m p r e s s e d gas is not completely avail­ able in the second law sense.*

E.

System

Performance

Long-term performance of intermediate t e m p e r a t u r e solar systems is analyzed in the final section of this chapter. S o m e instanta­ neous performance m e a s u r e m e n t s are presented in this section. Fig.ure 5.18 shows the losses m e a s u r e d in a small Rankine engine (3 hp) de­ signed to operate on R113 heated by a flat-plate collector at 100°C. The * Compressed air storage is not completely available thermodynamically since a heat loss from the warm, compressed gas to the underground storage reservoir occurs. The entropy change of the gas at T plus the environment at T during cooling is g

0

given by

and the loss of availability A A = T AS. The value of T 0

sure ratio r , p

T /T in

= r%~ , vly

0

in

depends on the compression pres­

where y is the specific heat ratio.

Shaft Work

Production

199

25.

ol 170

i

i

i

i

I

180

190 200 210 220 Collector water temp. (°F) F I G U R E 5.18 Measured l o s s e s in a Rankine engine owing to thermody­ namic and parasitic mechanical inefficiencies in major c o m p o n e n t s . D o e s not include feed pump (ideal pump work = 0 . 0 5 hp). Cooling water temperature = 85°F; condensing temper­ ature = 95°F. [From (B4).]

cycle losses s h o w n include c o n d e n s e r and boiler available energy con­ sumption owing to the requirement of finite t e m p e r a t u r e differences b e t w e e n fluid s t r e a m s . T h e effect of using a real fluid is also s h o w n and has b e e n described a b o v e . T h e cycle losses include e x p a n d e r and p u m p inefficiencies as well as p r e s s u r e losses throughout the fluid c o n d u i t s . The final loss s h o w n is that associated with the output drive s u b s y s t e m . In larger s y s t e m s , parasitic mechanical losses would be relatively smaller.

F.

Example

System

Figure 5.19 s h o w s the major c o m p o n e n t s in a Rankinep o w e r e d irrigation system located n e a r Gila B e n d , Arizona. A 5,500-ft (46-m ) field of P T C collectors heats w a t e r to 300°F (150°C) to o p e r a t e the heat engine rated at 50 hp (37 k W ) . A halocarbon working fluid is used in the engine as described a b o v e . T h e p u m p lifts w a t e r 14 ft (4.3 m) at a flow rate of 10,000 gpm (630 1/s). Control valves, heat e x c h a n g e r s , p u m p s are shown in the foreground of Figure 5.19. T h e turbine and gearbox are lo­ cated behind the u p p e r fluid tank. A global and s h a d o w - b a n d diffuse p y r a n o m e t e r are s h o w n at the u p p e r right. 2

2

200

5.

Medium-Temperature

Solar

Processes

F I G U R E 5.19 Photograph of the 50-hp Rankine engine used for the Gila Bend pumping s y s t e m . (Courtesy of Northwestern Mutual Life Insurance Co. and Battelle Memorial Institute.)

G.

Second

Law

Analysis

T h e second law provides a m e t h o d of calculating the ther­ m o d y n a m i c losses in p o w e r cycles and gives insight into their possible re­ duction. The availability AA contained in a constant p r e s s u r e fluid stream at t e m p e r a t u r e T can be calculated from the definition f

AA = A / / - T AS.

(5.23)

0

In the case of a liquid stream AA - c [(T p

f

- T ) - J ln(7V7o)] 0

(5.24a)

0

and for a saturated v a p o r stream

AA =

h JL\ f

- (T /T )] 0

f

+ [(r - r ) " To ln(J /J )], Cp

f

0

f

0

(5.24b)

///.

Shaft Work

201

Production

w h e r e T is the environmental t e m p e r a t u r e and h is the latent heat. Phys­ ically, E q . (5.24a) states that an ideal heat engine can extract c (T - T ) heat from the liquid stream. Part is c o n v e r t e d to work and c J l n ( J / J ) is rejected as w a s t e heat. Equation (5.24) s h o w s that a reduction of T will increase the available work m o r e than an equal increase in 7 . T h e second law efficiency can be written for the fluid stream as Q

fg

p

p

{

0

0

f

0

0

f

7)2

W T ) - 7oln(r /7o)]'

m c [(T -

=

f

p

{

0

( 5 > 2 5 )

f

w h e r e W is the useful work p r o d u c e d at a flow rate ra . The first law effi­ ciency is f

Th = W/(m c AJ ), f

p

(5.26)

f

w h e r e A 7 is the fluid t e m p e r a t u r e d r o p required to p r o d u c e work W. Usually A J < (T - T ). Combining (5.25) and (5.26), f

f

{

0

7)2

= vi

{

T

-

{

A T

o

j in(r /r )0

)

f

( 5

0

'

2 7 )

It is seen that high values of r) require both high cycle efficiencies rjx and high fluid t e m p e r a t u r e d r o p s . In a real cycle such as a Rankine cycle additional losses are incurred above those noted above for an idealized extraction of heat from a liquid stream. E a c h c o m p o n e n t of the p o w e r cycle-fluid p u m p , h e a t ex­ changer, turbine, and c o n d e n s e r — h a s an associated t h e r m o d y n a m i c irre­ versibility I analogous to the last t e r m of E q . (5.23). F o r the fluid p u m p 2

t

A.P = [(1 - vJ/VvMToMp],

(5.28)

w h e r e 7 j is the p u m p efficiency, Vi(T ) the liquid specific volume at T , and Ap the p u m p p r e s s u r e rise. (The small effect of fpdv w o r k is ignored in the liquid phase.) F o r small values of 7 small p r e s s u r e rises and high p u m p efficiencies are n e e d e d . T h e boiler t h e r m o d y n a m i c irreversibility I is given by p

0

0

t ) P

uh

A , = A.s + 4 t f ,

(5.29)

b

w h e r e the second subscripts s and tf refer to the solar-heated and turbine fluid s t r e a m s , respectively. T h e values are ks=

-

I

\ m

£ s

-

f

~ l s

J boiler L t,tf =

l

To,

\m ^A T .

J boiler L

it

* tf J

(5.30)

J 0

(5.31)

5.

202 Recalling that m c ibility is s

p

dT = - m s

t f

Medium-Temperature

Solar

Processes

dh from the first law, the total irrevers­ t{

Kb = rhsC»T

hp -

c/T ,

J J boiler L^tf

0

(5.32)

s

^ s.

w h e r e J is usually c o n s t a n t in t h e boiler. O n a per unit working fluid mass basis (using the overall energy balance m c /m = AH /AT ) t f

s

i

uh

= (T A / / / A r ) f 0

s

tf

( J s

J boiler

p

t{

~/

t f )

tf

^

•* t f s

s

(- > 5

33

1

w h e r e A / / is the turbine fluid enthalpy increase in t h e boiler and AT is the t e m p e r a t u r e d r o p in the solar-heated fluid. T o minimize the boiler irreversibility the solar-heated fluid-to-turbine fluid t e m p e r a t u r e dif­ ference must be minimized. Turbine irreversibility I arises from the nonisentropic ex­ pansion of fluid in the blading. T h e turbine irreversibility / is tf

S

Ui

u

/u

= T

^ P ,

0

W

T

ideal)

(5.34)

^

w h e r e T is the turbine exhaust t e m p e r a t u r e . Since the real and ideal tur­ bine exhaust t e m p e r a t u r e s are about the same for a well-designed turbine, ^tecreai) T i ) , denoted as T hereafter. T h e turbine irreversibility is then te

=

te

m i d e a

A,t -

( r / r ) [ ( i - )/vti 0

t e

m

A//

(5.35)

t

w h e r e AH is the turbine enthalpy d r o p . Small values of I can be achieved with large turbine efficiencies. If the turbine e x h a u s t contains superheat which is rejected in t h e d e s u p e r h e a t e r region of the c o n d e n s e r , s o m e availability is lost unless a regenerator is used and this additional irreversibility is given by t

ut

A,C

~~

^

Htt

desuperheater

~~

^0

J

desuperheater d

* tf

(5.36)

To minimize / small values of sensible heat rejected to t h e desuper­ heater A / / f are needed along with low values of turbine e x h a u s t tempera­ ture. T h e final reversibility source is the finite t e m p e r a t u r e dif­ ference across the c o n d e n s e r . An expression similar to that for the boiler, E q . (5.32), is used to calculate the c o n d e n s e r irreversibility. Evaluation of the several irreversibilities requires the use of an equation of state for the turbine working fluid. Values of enthalpy and t ) C

t

IV.

Solar Total Energy Systems

(STESs)

203

specific volume are calculated from the equation of state. Milora and Tester (M5) h a v e tabulated equations of state for fluids useful up to 300°C. F o r subcritical cycles (fluids type A and B , Fig. 5.14) the heat exchanger, d e s u p e r h e a t e r , and c o n d e n s e r irreversibilities are the largest of the five terms described a b o v e . As cycle p r e s s u r e is increased for a supercritical cycle, the p u m p and turbine shaft w o r k levels increase for most fluids. H o w e v e r , the boiler irreversibility is smaller since the solar and cycle fluid t e m p e r a t u r e profiles are nearly parallel (type C fluid). Milora and T e s t e r , using the principle of corresponding states, have developed an a c c u r a t e but simple m e t h o d for screening tur­ bine fluids. T h e y s h o w e d that for m a x i m u m r) (minimum cycle irrevers­ ibility), the critical t e m p e r a t u r e of the fluid r c r i t should be related to the solar collector (or storage) outlet t e m p e r a t u r e T (°C): 2

{i0

T .o = T t

crit

+ 790[(y - l ) / y ] ,

(5.37)

w h e r e y is the specific heat ratio c /c for the cycle fluid. A survey of fluids gives a value of T which can then be m a t c h e d to a solar concen­ trator design. F o r e x a m p l e , R113 gives a peak cycle T} value at 299°C w h e r e a s isobutane (R600a) is best for near 200°C operation. F u r t h e r d a t a are given in (M5). p

v

Uo

2

IV.

SOLAR

TOTAL

ENERGY

SYSTEMS

(STESs)

Solar total energy s y s t e m s are designed to provide electric p o w e r (or shaft w o r k for other purposes) with associated use of turbine exhaust heat to provide hot w a t e r , space heating, a n d / o r cooling and other thermal l o a d s . T h e principle reason for considering an S T E S is to use the t h e r m o d y n a m i c availability p r e s e n t in solar heat p r o d u c e d by con­ centrators in the most efficient way by insuring a close second law m a t c h to the various tasks to be performed. The several p r o c e s s e s are usually c a s c a d e d in o r d e r of increasing e n t r o p y with w o r k production occuring first and low-temperature heating last. Figure 5.20 s h o w s a typical S T E S , this example being a proposal for the Solar E n e r g y R e s e a r c h Institute in Golden, C o l o r a d o . This section will describe the first-order variables in the de­ sign of an S T E S and give the results of performance estimates for several locations in the U . S .

204

5.

Medium-Temperature

Solar

Processes

*2 o*

6 o o

U e -a 3

a o o c o C

o o

o a o W 1/3

W

a E

a> 03

IV. A.

Solar Total Energy Systems Load

(STESs)

205

Type

A n S T E S exists b e t w e e n t w o application l i m i t s — a n electric p o w e r plant w h o s e sole output is electricity (or other shaftwork) and a thermal plant w h o s e sole output is heat. A convenient p a r a m e t e r to de­ scribe the nature of the S T E S load is the thermal to electrical load ratio T/E: T/E = end u s e thermal d e m a n d / e n d u s e electrical d e m a n d

(5.38)

w h e r e the total S T E S load L = T + E. T and E values for nonsolar systems include conversion efficiencies at the boiler or c o m b u s t o r and p o w e r plant, respectively. A second important design characteristic of an S T E S is the load phasing for a given T/E ratio. Figure 5.21 shows three generic types of phasing p a t t e r n s which can be e n c o u n t e r e d in an S T E S . Idealized pat­ tern I is found in office buildings, schools or other institutions, and single shift industrial plants. This pattern has a uniform T/E ratio for the h o u r s of o c c u p a n c y and T = E ~ 0 o t h e r w i s e . Generic pattern II r e p r e s e n t s the idealized load phasing which might be found in r e s i d e n c e s , some industries, shopping c e n t e r s , and hospitals. Pattern III is found in larger industries continuously operating on t h r e e shifts and is characterized by a fixed T/E ratio for 24 h. T h e third major characteristic of an S T E S is its thermal per­ formance as m e a s u r e d by its energy delivery, which is some fraction of the total load L depending o n the solar s y s t e m size relative to the value of L. Since few such s y s t e m s have b e e n built, most performance estimates are p r o d u c e d from short-time scale c o m p u t e r simulations carried out for periods of the order of y e a r s . A convenient dimensionless ratio for exPattern I

Pattern II

Pattern III

Thermal

Thermal

Thermal

Electric

Electric u

b

Time^

20

24

Near ideal case Office buildings School Industrial F I G U R E 5.21 for an S T E S .

0

Time -

Residential Industrial Hospital

Electric 22 24

Time —*•

24

Industrial

Three idealized thermal and electric load phasing patterns

5.

206

Medium-Temperature

Solar

Processes

pressing thermal performance is / , the solar load fraction or percent of annual d e m a n d carried by solar energy. T h e solar load fraction d e p e n d s upon the T/E ratio and load phasing for a given system configuration. In addition, the local solar climate determines the response of an S T E S to various load profiles. T h e quantity / refers to end uses of energy and in­ cludes both p o w e r and heat requirements and deliveries by the S T E S or utility. The fraction of thermal load carried is f and of electrical load / , . Typical T/E ratios are shown in Table 5.4. for major U . S . industries. Since the incentive to use an S T E S is primarily e c o n o m i c in industrial e c o n o m i e s , a c o s t - b e n e f i t ratio C/B is an alternative w a y of measuring the performance of an S T E S . The details of C/B calculation s

s

sA

s

e

TABLE 54 T/E Ratios for Some U.S. Standard Industrial Classification {SIC) Code

a

Purchased fuels and electric energy

Name

(kWh eq x 10 )

(cost x $10 )

$ per 1000 kWh

(kWh eq x 10 )

(cost x $10 )

Tobacco products Cigarettes Tobacco stemming/drying Textile mill products Knitting mills Textile finishing, except wool Floor covering mills Yarn and thread mills Misc. textile goods Apparel, other textile prod. Men's, boys' furnishings Women's, misses' outerwear Women's, children underwear Hats, caps, millinery Children's outerwear Misc. apparel Misc. fabricated text. prod. Lumber and wood products Sawmills, planing mills Sawmills, planing gen. Mill work, plywood Hardwood veneer Softwood veneer Wood containers Wood bldgs. and mobile homes Misc. wood products

5.9 3.8 1.5 94.5 16.5 21.8 8.8 12.0 8.0 19.0 4.2 4.2 1.1 0.3 0.6 0.8 5.8 79.6 26.9 24.0 15.9 2.3 9.4 1.7 2.6 16.1

38.6 22.8 11.7 692.1 121.6 117.3 45.6 116.3 62.3 171.0 37.0 45.9 11.7 2.9 6.5 7.6 40.4 482.4 180.0 160.1 94.9 15.0 48.1 13.3 16.5 94.4

6.54 6.00 7.80 7.32 7.37 5.38 5.18 9.69 7.79 9.00 8.81 10.93 10.64 9.87 10.83 9.50 6.97 6.06 6.69 6.67 5.97 6.52 5.12 7.82 6.35 5.86

4.8 3.2 1.2 67.6 12.6 19.9 7.8 5.5 5.9 12.6 7.7 S 0.6 0.2 0.3 0.5 4.4 64.7 17.5 17.2 12.4 1.8 7.6 1.3 2.2 13.2

20.2 12.1 6.5 286.1 59.0 85.1 29.2 21.2 26.2 47.3 9.6 S 2.1 1.1 1.3 2.1 16.6 274.7 85.8 76.9 45.2 6.6 26.8 6.2 8.4 50.8

SIC 21 2111 2141 22 225 226 227 228 229 23 232 233 234 235 236 238 239 24 242 2421 243 2435 2436 244 245 249

Purchased fuels

a

error. [From (B7).]

9

6

9

6

D = data withheld to avoid disclosure. S = data inconsistent or large standard

IV.

Solar Total Energy Systems

207

(STESs)

are given in C h a p t e r 7 b u t , stated simply, C/B is the ratio of annual S T E S c o s t s — c a p i t a l , interest, m a i n t e n a n c e , insurance, and o p e r a t i n g — t o the dollar value of the annual fuel savings. In equation form, C/B = S T E S c o s t / ( / , r C + A e £ C ) , s

t

t

(5.39)

e

w h e r e C and C are the annual w o r t h of unit fuel prices ( $ / G J , for ex­ ample) over the system useful life including taxes and inflation in fuel prices. F o r C/B < 1 there is an e c o n o m i c incentive to use an S T E S ; if C/B > 1, an S T E S is not economically viable. A convenient m e t h o d of finding the lower b o u n d of C/B at a given site for a given p r o c e s s is to de­ termine the performance of an S T E S for the best possible set of T/E and phasing values. If C/B > 1 for this best c a s e , no possible S T E S configu­ ration will be viable. t

e

Purchased electric energy $

$

per 1000 kWh

(kWh x 10 )

(cost x $10 )

per 1000 kWh

4.21 3.78 5.42 4.23 4.68 4.28 3.74 2.98 4.53 3.75 3.56

1027.9 624.8 265.6 26908.4 3923.0 1943.7 1013.5 6458.8 2092.0 6357.0 1490.2 c o 544.6 74.3 268.6 271.5 1441.9 14790.7 7345.4 6777.7 3452.6 512.9 1827.1 370.8 408.9 2902.3

18.4 10.7 5.2 406.0 62.6 32.2 16.4 94.4 35.6 123.7 27.4 Q 9.6 1.8 5.2 5.5 23.8 207.7 94.2 83.2 49.7 8.4 21.3 7.1 8.1 43.6

17.92 17.13 19.58 15.09 15.% 16.57 16.18 14.62 17.02 19.46 18.39

3.50 5.50 4.33 4.20 3.77 4.25 4.40 4.47 3.65 3.67 3.53 4.77 3.82 3.85

6

6

17.63 24.23 19.36 20.26 16.51 14.04 12.82 12.28 14.39 16.38 11.66 19.14 19.81 15.02

Electric energy generated less sold (kWh x 10 )

Total elec energy used E (kWh x 10 )

(kWh x 10 )

Ratio (E /E )

D D S 374.6 S 150.7 D D D S 1.9 c D

1.028 0.625 0.266 27.283 3.923 2.094 1.014 6.459 2.092 4.357 1.492

4.8 3.2 1.2 66.776 12.6 19.448 7.8 5.5 5.9 12.6 2.694

4.67 5.12 4.51 2.44 3.21 9.29 7.7 0.85 2.82 1.98 1.81

0.545 0.0743 0.269 0.272 1.442 15.291 7.662 7.026 3.576 0.513 1.827 0.371 0.409 2.902

0.6 0.2 0.3 0.5 4.4 63.199 18.609 16.274 12.030 1.8 7.6 1.3 2.2 13.2

1.10 2.63 1.12 1.84 3.06 4.13 2.42 2.30 3.36 3.51 4.16 3.50 5.38 4.55

6

— S S

s

500.5 316.9 308.5 123.3 D D D S D

Net therm energy used

T

9

9

TH

r

208

5.

Medium-Temperature

Solar

Processes

The A e r o s p a c e Corporation ( B 7 - B 9 ) has c o n d u c t e d a study of S T E S s in several U . S . locations to determine w h e t h e r C/B < 1 for the optimum d e m a n d profile. A central receiver collector was a s s u m e d (see C h a p t e r 6 for a description of the collector) but the results are similar for any high performance c o n c e n t r a t o r . S o m e of the reported results of this study will be summarized below. It w a s found that the ideal load phasing occurred if the electrical load E occurred for a time period slightly longer than daylight and the ideal T/E ratio (3.64) w a s such that all turbine ex­ haust heat could be used, subject to limits imposed by finite heat ex­ c h a n g e r s , and no turbine throttling required. The ideal T/E ratio is calcu­ lated from (1 - T7t)r?th/T7t, w h e r e rj is the turbine efficiency and 17th is the heat use efficiency of the thermal p r o c e s s . F o r a line-focus p o w e r e d heat engine y] ~ 0.18 at 400°C (see previous section on p o w e r production) and for commercial thermal p r o c e s s e s rj ~ 0.8. F o r a 400°C turbine inlet, most thermal applications (i.e., those operated by the turbine exhaust) would be limited to 260°C and below. The cost-benefit ratio for the ideal case is a minimum for all possible cases and is denoted by C/B in the discussion below. T h e major variables in a given solar conversion s u b s y s t e m of an S T E S are collector area and storage size. T h e s e variables are impor­ tant in all solarthermal applications and are also first-order variables for an S T E S as e x p e c t e d . t

t

th

min

B.

General Performance

Characteristics

of STESs

Using the results of c o m p u t e r simulations (B7), it is possible to d r a w several general conclusions about the performance of S T E S s in various parts of the U . S . F o r this p u r p o s e it is useful to define a set of standard e c o n o m i c a s s u m p t i o n s , each of which can be later varied for sensitivity studies. T o assign a cost to the results of this section, solar col­ lectors at $ 1 5 0 / m , high-temperature storage (up to 400°C) at $4265/GJ and low-temperature storage at $950/GJ are used along with a turbine cost of $ 4 0 0 / k W . T h e factor used to annualize all costs (see Chapter 7 for details) is 15% of the initial cost per year. Competitive energy is a s s u m e d to cost 4 . 4 0 / k W h for electricity and $6.90/GJ for thermal energy. These costs include a small inflation factor ( 1 . 5 - 3 % per year, real rate) over a 30-yr period. 2

e

Phasing, TIE, and Solar Flux Level Effects Figure 5.22 s h o w s the effect of load T/E ratio on the c o s t - b e n e f i t ratio C/B. It is seen that for T/E > 2, the c o s t - b e n e f i t ratio is near its asymptotic and min-

IV.

Solar Total Energy Systems

(STESs)

209

3

2

-

[ = Phasing pattern

i n \

-

0

i 1

I

I

2

3

1 4

I 5

6

T / E d e m a n d ratio

F I G U R E 5.22 Effect of load phasing and J / E ratio on the c o s t - b e n e f i t ratio C/B for an S T E S in Albuquerque. [From (B7).]

imum value. Therefore the conclusion is that relatively high thermal loads result in the best economic performance of an S T E S . Table 5.4 shows that most industrial users of c o n s e q u e n c e have T/E > 2. Figure 5.22 also s h o w s that the load phasing (see Fig. 5.21) is important only for systems w h e r e the electrical load is relatively large and e v e n then the m a x i m u m effect is only 2 0 % . F o r larger T/E ratios the phasing effect can be ignored. It is seen that the ideal S T E S described above (T/E = 3.64) is on the a s y m p t o t i c portion of the c u r v e s . Figure 5.22 was p r e p a r e d by choosing a phasing p a t t e r n and T/E ratio followed by performance simulations of several d o z e n system configurations capable of providing the specified T/E. The lowest C/B configuration of all con­ sidered is plotted in Fig. 5.22. T w o s y s t e m s exist for the production of a cooling effect— absorption and v a p o r c o m p r e s s i o n — t h e former using a heat input, the latter, shaft w o r k . If cooling loads are high it m a y be efficacious to shift to absorption to increase the T/E ratio, h e n c e improve the c o s t - b e n e f i t ratio C/B. H o w e v e r , the C O P of absorption units is in the range of 0.6 ~ 0.8 and for vapor c o m p r e s s i o n units 2.0 or a b o v e . This C O P disadvantage tends to offset possible higher T/E ratio benefits. T h e best strategy for cooling in an S T E S is not yet u n d e r s t o o d . S T E S performance for several locations is s h o w n in Fig. 5.23 for various T/E ratios. The same asymptotic behavior is seen for all sites with the p o o r e s t solar radiation sites showing the highest values of C/B. In generating these results, high t e m p e r a t u r e storage (used for

5.

210

Medium-Temperature

Solar

Processes

T/E demand ratio

F I G U R E 5.23 C o s t - b e n e f i t v s . T/E ratio for various locations. Blue Hill has the lowest solar flux and Albuquerque the highest on the average. [From (B7).]

p o w e r production) w a s increased with decreasing T/E and lowt e m p e r a t u r e storage (for thermal end uses) has b e e n d e c r e a s e d propor­ tionately. T h e results of S T E S studies for 34 locations show a strong cor­ relation b e t w e e n C/B ratio and the yearly a v e r a g e d , daily b e a m radiation 7 . It is therefore e x p e c t e d that S T E S feasibility at any site could be ana­ lyzed using this information. F o r the ideal S T E S with costs as defined a b o v e , the relationship b e t w e e n C/B and 7 is (B9) b

b

[2.5 - 0 . 2 8 / + 0 . 0 0 9 / 2.4 - 0 . 2 5 / + 0.007J [2.6 - 0 . 3 0 / + 0.01 l / b

C/B

=

b

b

2 b 2 b

b

2

(phasing pattern I) (phasing p a t t e r n II) , (phasing p a t t e r n III)

(5.40)

w h e r e 7 is in units of k W h / m d a y . L i k e w i s e , the solar load fraction f in p e r c e n t can be estimated from (B9) 2

b

s

[32.5 + 0 . 9 8 / + 0 . 4 6 / = 57.6 - 9.2/ _+ 1.27/ _ [58.4 - 1 0 . 9 / + 1.32/ b

/

2

b

2

g

b

b

b

2 b

(phasing p a t t e r n I) (phasing p a t t e r n II) . (phasing pattern III)

(5.41)

If fuel costs differ from those a s s u m e d or T/E # 3.64, adjustments in C/B and f can be m a d e . E q u a t i o n s (5.40) and (5.41) are based on an electrical load E of 500 k W . s

e

Competing Energy Cost Effects Previous results based on 4 . 4 0 / k W h p o w e r and $ 6 . 9 0 / G J fuel can be generalized to any cost struc­ ture and T/E ratio very simply. E q u a t i o n (5.39) defined the C/B ratio. T h e d e n o m i n a t o r of the equation contains cost and T/E effects, therefore: C/B

(C/B)

min

_

[fs,tTC

+ /sje^^e]ideal

t

f , (T/E)TC s t

t

/c

+ f JT/E)EC s

y

e

D e n o m i n a t o r values for solar load fractions f ,t(T/E) s

and f , (T/E) s e

'

Aj) }

are cal-

IV.

Solar Total Energy Systems

211

(STESs)

culated from the performance model. Fuel costs C and C are local costs including the effect of real inflation in fuel price o v e r a 30-yr period. Figure 5.24 s h o w s minimum achievable C/B ratios for the ideal S T E S s in various parts of the U . S . Fuel costs are based on data col­ lected in 1977 with net price escalation of 3 % for fuel and 1.5% for elec­ tricity. Although the ideal S T E S has a T/E ratio of 3.64, most industrial applications require T/E > 2 for which the C/B versus T/E c u r v e is near its asymptotic minimum value. H e n c e , t h e C/B ratios for ideal S T E S s should be approximately correct for the range of real T/E ratios encoun­ tered in industry. If residential and commercial S T E S s have relatively high T/E ratios, the m a p should apply as well. H o w e v e r , s o m e commer­ cial s y s t e m s have high electrical d e m a n d s (E > T) and the values given on the m a p would not apply. D a t a overlaid on the m a p show the dramatic effect of local fuel prices. It will be recalled that the highest insolation areas of the c o u n t r y had low C/B ratios according to Fig. 5.23 and E q . (5.40) if con­ stant prices w e r e u s e d . H o w e v e r , the effect of locally high energy prices in the N o r t h e a s t and South are seen to give S T E S C/B ratios less than one and equivalent or less than those in the sunny S o u t h w e s t . T h e s e conclu­ sions are b a s e d on solar system prices given earlier which w e r e estimated for m a s s p r o d u c t i o n . Current prices of solar c o m p o n e n t s are s o m e w h a t higher and m a y shift C/B ratios calculated as slightly below unity to the infeasible range C/B > 1. t

e

F I G U R E 5.24 Minimum c o s t - b e n e f i t ratios C/B for S T E S s in the U . S . based on local fuel prices. C/B < 1 implies e c o n o m i c feasibility. [From (B7).]

5.

212

Medium-Temperature

Solar

Processes

T h e earliest date for any appreciable penetration of S T E S s into the U . S . energy mix is ~ 1995 (B9) assuming nominal energy inflation rates. After 1995 the largest impact is speculated to be in California, Hawaii, and T e x a s . By the year 2000 some 500 applications in 44 states could displace 4.7Q (IQ = 1 0 Btu) of energy. Any projection of this type is subject to e c o n o m i c decisions by industry, political decisions by g o v e r n m e n t , and the prevailing costs and efficiencies of solar system and fossil fuels. 15

C.

Second

Law Efficiencies

of STES

T h e fundamental t h e r m o d y n a m i c r e a s o n for the use of an S T E S is to m a t c h the decreasing quality of energy in collector fluid stream, as available energy is e x t r a c t e d , to a set of tasks which can use a progressively lower t e m p e r a t u r e source of heat. If the matching is d o n e properly, the second law efficiency can be increased over that which could be achieved if the p r o c e s s e s were not c a s c a d e d but o p e r a t e d in par­ allel from the same heat s o u r c e . T h e outputs of the p r o c e s s are obviously the same for either a p p r o a c h . An example illustrates this p h e n o m e n o n . Example Find the second law efficiencies of an S T E S con­ sisting of a turbine and space heating system operating from a solar col­ lector field at T = 400°C and in a S T E S operating for the same field. The turbine exhaust vapor is supplied at T = 50°C to the condensing space heater which delivers heat at T = 30°C. T h e T/E ratio is 3.0, turbine effi­ ciency 7? = 18%, and the environmental t e m p e r a t u r e T = 0°C. Ignore heat exchanger and p u m p irreversibilities. c0

uo

h

t

0

Solution Second law efficiencies can be calculated from ex­ pressions given in Table 3 . 1 . F o r the turbine superheated vapor assume that an effective constant specific heat applies. F o r a variable t e m p e r a t u r e heat source such as the turbine vapor, the availability c o n s u m e d is given by the fluid enthalpy change multiplied by 1 - [ J ln(T /T )/(T 0

c0

t0

-

c0

J )] t0

[see E q . (5.24a)]. The various process efficiencies are calculated below. Turbine V*

= n. [l L

^H^r J- co

J- to

= 0.42 J

V.

Performance

of Medium-Temperature

Space Heater [Eq. r)2 = i j i i l

Solar Processes

(3.2)]

(r /r )]/[l -

-

213

0

h

(T /T )] 0

c0

= 0.17

f ° Vi.h = 1 . 0 for simplicity. r

STES „ m

1 + (T/E)[\

=

(i/r?Mi - [ r i n ( r / j ) / ( r o t

0

c0

to

c

-

- (T /T )] 0

T )]} t0

h

+ r/E(i - r /r )(i/7 , ) 0

t 0

h

h

by analogy with the preceding t w o e x p r e s s i o n s . F o r r/E = 3, 7}

2

= 0.46

greater than the second law efficiency of either c o m p o n e n t taken alone. N o t e that the S T E S does not use the entire heat rate provided by the col­ lector field since T/E = 3.0. T o do so, the T/E ratio would need to be (i - m)/m = 4.56.

D.

Example

System

Most S T E S s are quite complex and are specific to the process and T/E ratio to be met. H e n c e , no example system is described herein. References (E3), (G7), and (W8) contain detailed engineering de­ signs of S T E S s for federal d e m o n s t r a t i o n projects in the South.

V.

LONG-TERM PERFORMANCE OF MEDIUM-TEMPERATURE SOLAR

PROCESSES

In order to assess the economic viability of any solar p r o c e s s , its cumulative energy delivery over its economic life of the order of years or d e c a d e s , must be k n o w n . It is very difficult to calculate this n u m b e r in detail since (1) solar systems and their energy delivery are sub­ j e c t to the vagaries of local microclimate which can change on a time scale on the order of h o u r s , and (2) future w e a t h e r cannot be predicted at this level of detail. T h e standard a p p r o a c h used to estimate future perform­ ance of a solar system is to use a typical year of past w e a t h e r d a t a and as­ sume that it will represent the future on the average, to engineering accu-

5.

214

Medium-Temperature

Solar

Processes

racy. The first difficulty a b o v e can be avoided by using long-time scale calculations instead of hourly or smaller scales. In order to use long-term m e a n s of solar and w e a t h e r data, the statistical distribution of these data must be k n o w n . A long-term calculation m e t h o d based on these ideas is the subject of this section. A.

Critical Solar Intensity

Ratio X

T h e instantaneous efficiency equation for m a n y solar col­ lectors has been s h o w n to be of the form Vc = F(Vo ~ U A r / / ) , c

(r) > 0)

C

(5.43)

c

w h e r e A J is the value of a collector to ambient t e m p e r a t u r e difference if positive and r) is zero otherwise and F is a heat exchanger factor the ex­ pression for which d e p e n d s on the definition of AT [see E q s . (4.43)-(4.47)]. It is technically correct but not always economical to operate the solar collector system if r) > 0. In practice r) > T7 > 0 is usually the system turn-on criterion since it is not worthwhile to operate collector loops for cases w h e r e r) is very small. E q u a t i o n (5.43) can be used to determine the solar intensity level a b o v e which useful energy collection can take place. Solving E q . (5.43) for / , +

c

+

c

c

min

c

c

I > U A J / ( T , O " VmJF).

(5.44)

+

c

c

A dimensionless critical intensity ratio X is generally used and since T?min « 1 > for c o n v e n i e n c e the second t e r m in the d e n o m i n a t o r above is dropped: X=

U AT /r) I ^

1.0.

+

c

0

c

(5.45)

X is seen to be the ratio of collector heat loss to absorbed solar flux at rjc = 0, i.e., at the no-net-energy-delivery condition. In m a n y cases the daily or monthly averaged daily critical intensity ratio X is of m o r e inter­ est and is defined as* X=

U AT

+

(5.46)

AfcAjo/c,

c

w h e r e V) is the daily averaged optical efficiency and A J is the daily mean t e m p e r a t u r e difference during collection. These can also be expressed +

0

i

rto+At

c

AT =

(T

c

^ ' C

-

r) a

dt,

(5.47)

J to

* N o t e that U can be defined to include piping heat loss per collector c

arrays (BIO).

V.

Performance

of Medium-Temperature

Solar

Processes

215

(5.48)

and (5.49) T h e collector cut-in time t and cut-off time t + Ar are described shortly. The time t = [0,24] h and is related to the solar hour angle h by / = (180 - h )/\5; Ar is the collection period in h o u r s . In E q . (5.47) T can be collector surface, average fluid, inlet fluid, or outlet fluid t e m p e r a t u r e de­ pending u p o n the efficiency d a t a basis. 0

0

c

s

s

B.

The

c

c

Utilizability

Utilizability (the c o m m o n but, unfortunately, r a t h e r cum­ b e r s o m e w o r d ) (f> has b e e n used to describe the fraction of solar flux ab­ sorbed by a collector which is delivered to the working fluid. O n a monthly time scale j> = QJF^h

< 1.0,

(5.50)

w h e r e the o v e r b a r s d e n o t e monthly m e a n s and Q is the monthly averaged daily total useful energy delivery. is the fraction of the ab­ sorbed solar flux which is delivered to the fluid in a collector operating at a fixed temperature T . T h e c o n c e p t d o e s not apply to a system com­ prised of collectors, storage, and other c o m p o n e n t s wherein the value of T varies continuously. T h e fixed t e m p e r a t u r e m o d e will occur if the col­ lector is a boiler, if very high flow rates are u s e d , if the fluid flow rate is modulated in r e s p o n s e to flux variations to maintain a uniform T value, or if the collector provides only a minor fraction of the thermal d e m a n d . H o w e v e r , if the flow is m o d u l a t e d , note that the value of F (i.e., F ' , F ) may not remain c o n s t a n t to engineering a c c u r a c y . W h e n T is not c o n s t a n t in time as in the case of a collector coupled to storage, the c o n c e p t cannot be applied directly. H o w e v e r , for m o s t c o n c e n t r a t o r s for C R > 10, the value of U is small and the col­ lector is relatively insensitive to & small range of operating t e m p e r a t u r e s . To check this a s s u m p t i o n for a particular p r o c e s s , values of at the ex­ t r e m e s of the e x p e c t e d t e m p e r a t u r e excursion can be c o m p a r e d . T h e value of <£> d e p e n d s u p o n m a n y s y s t e m and climatic u

c

c

c

R

c

c

216

5.

Medium-Temperature

Solar

Processes

p a r a m e t e r s . H o w e v e r , Collares-Pereira and Rabl (CI) have shown that only three are of first o r d e r — t h e clearness index K (See Chapter 2), the critical intensity ratio X [Eq. (5.46)], and the ratio r /r (See Chapter 2). The first is related to insolation statistics, the second to collector p a r a m e ­ ters and operating conditions, and the last to collector tracking and solar geometry. Empirical expressions for $ have b e e n developed for sev­ eral collector types (CI). F o r nontracking collectors, T

6

= e x p { - [ Z - (0.337 - U6K

+ 0.55rJr )X ]} 2

T

for 0 > 0.4, K

T

T

(5.51)

= [0.3,0.5], and X = [0,1.2]. Also,

T

(j> = 1 - X + (0.50 - 0.67K + 0.25rJr )X

(5.52)

2

T

for (/> > 0.4, K

T

= [0.5,0.75], and X = [0,1.2]

T

T h e expression for tracking collectors (CR > 10) is 0 = 1.0 - (0.049 + \MR )X

+ 0.341 K X

2

T

for 0 > 0.4, K

T

(5.53)

= [0,0.75], and X = [0,1.2]. Also

T

4> = 1.0 - X (5.54) > 0.75 (very sunny climate), and X = [0,1.0] for any col­

for 4> > 0.4, K lector type. E q u a t i o n s (5.51)—(5.54) w e r e developed using curve-fitting techniques emphasizing large 0 values since this is the region of interest for most practical designs. H e n c e , they should be considered accurate to ± 5 % only for 0 > 0.4. T

C.

Example

Calculation

T o illustrate the use of the long-term m e t h o d an example will be w o r k e d in stepwise fashion. The several steps used are (1) Evaluate data. (2) Calculate m o d e for the collector. (3) Calculate using a long-term optical collector-plane insolation.

K

from terrestrial H data and extraterres­

T

h

trial H

0th

rJr

T

for the concentration ratio and tracking

the critical intensity ratio X from E q . (5.46) efficiency value T) and monthly average 0

I = (r - r D /H )H . c

T

d

h

h

h

(5.55)

V.

Performance

of Medium-Temperature

Solar

111

Processes

The collection time At may need to be d e t e r m i n e d in s o m e cases for nontracking, low-concentration collectors by an iterative method as described in the next section. c

Example Find the energy delivery of a polar-mounted, par­ abolic trough collector operated for 8 h per day (Af = 8) during March in K a b u l , Afghanistan (L = 34.5°N). T h e collector has an optical efficiency T) of 60%, a heat loss coefficient U = 0.5 W / m C , CR - 20, and heat removal factor F = 0.95. T h e collector is to be operated at 150°C. The m e a n , horizontal solar flux is 450 L y / d a y (5.23 k W h / m day) and the am­ bient t e m p e r a t u r e is 10°C. c

2 o

0

c

R

2

Solution Following the three-step p r o c e d u r e a b o v e , the clearness index is calculated: H

= 8.15

0th

kW h / m

(Table 2.9);

2

K

T

= 5.23/8.15 = 0.64.

The geometric factors r and r are calculated from expressions in Table 2.11: d

r = (ah T

T

+ b sin h )/d

coU

cos L;

coU

>d' = (/icoiiAOU/cos L

+ cos h (a sr

= 0)/(CR)) - sin

h /d(CR), coU

where ^coll

hja

= 0) a b d

—

= = = =

60° = 1.047 rad (h = ( A f / 2 ) x 15° if the collection period is centered about solar noon), 90° = 1.571 rad, 0.409 4- 0.5016 sin 30° - 0.66, 0.6609 - .4767 sin 30° = 0.42, sin 90° - 1.571 cos 90° = 1.0, coll

c

in which case r = (0.66 x 1.047 4- 0.42 x sin 60°)/1.0 cos 34.5° = 1.28, r = ( 1 . 0 4 7 / 1 . 0 ) [ l / c o s 34.5° 4- cos 90°/20] - sin 60°/1.0 x 20 = 1.31. T

d

Finally the critical intensity ratio is X=

U

c

A7+

Af /77o/c c

and the collector plane insolation 7 is from E q . (2.51) C

I

c

= (1.28 -

1.31

x

0.34)

x

5.23 = 5.4

kW h / m

so X = 0.5 x (150 - 10) x 8/0.6 x 5400 - 0.173. The utilizability from E q . (5.53) is

2

5.

218

Medium-Temperature

Solar

Processes

<> j = 1.0 - (0.049 + 1.44 x 0.64)(0.173) + 0.341 x 0.64 x (.173) = 0.84. 2

Finally, the useful energy is Qu = FRVOIC = 0.95

x 0.6

x 5.4

x 0.84

= 2.58

kW

h/m

2

day.

for the m o n t h of March on the a v e r a g e .

D.

Collection

Period

(A/ ) c

T h e collection period A/ can be dictated either by optical or thermal constraints. F o r e x a m p l e , with a fixed collector, the sun may pass beyond the a c c e p t a n c e limit or be blocked by a n o t h e r collector and col­ lection would then c e a s e . Alternatively, a high efficiency, solar-tracking c o n c e n t r a t o r operating at relatively low t e m p e r a t u r e might be able to col­ lect from sunrise to sunset. A third scenario would be for a relatively low concentration device operating at high t e m p e r a t u r e to c e a s e to have a positive efficiency during daylight at the time that heat losses are equal to absorbed solar flux. In this c a s e , the cutoff time is dictated by thermal properties of the collector and the operating conditions. c

Collares-Pereira and Rabl (CI) h a v e suggested a simple pro­ c e d u r e to find the p r o p e r value of At . Useful collection Q is calculated using the optical time limit first, i.e., A/ = 2 min [h (a = 0), h (i = 90)]/15. S e c o n d , Q is calculated for a time period slightly shorter, say by one-half h o u r , than the optical limit; if this value of Q is larger than that for the first, optically limited c a s e , the collection period is shorter than the optical limit. T h e time period is then further reduced until the m a x i m u m Q is r e a c h e d . T h e a b o v e m e t h o d a s s u m e s that collection time is s y m m e ­ tric about solar n o o n . This is almost n e v e r the case in practice since the heat collected for an h o u r or so in the morning is required to w a r m the fluid and o t h e r m a s s e s to operating t e m p e r a t u r e . A symmetric p h e n o m e ­ non does not o c c u r in the afternoon. If the time c o n s t a n t of the thermal mass in the collector loop is k n o w n , the collection period may be assumed to begin at t , Af / 2 h (from a b o v e symmetric calculation) before noon de­ creased by t w o or t h r e e time c o n s t a n t s . A n o t h e r a s y m m e t r y can o c c u r if solar flux is obstructed during low sun angle periods in winter. It is suggested that r and r from Table 2.11 u n d e r a s y m m e t r i c collection con­ ditions be calculated from c

u

c

sr

ST

u

u

u

0

c

T

d

r

T

= [r (/2 , r

s

s t o p

)

+ rj
(5.56)

V.

Performance

of Medium-Temperature

Solar

Processes

219

>*d = l>d(As,stop) + >d(/! tart)]/2,

( 5

SfS

5 7

)

w h e r e t h e collection starting a n d stopping h o u r angles a c c o u n t for tran­ sients, shading, e t c . , as described a b o v e : / * , s t a r t = 180 -

15f ,

/*s,sto = 180 -

15(f

s

P

(5.58)

0

0

+ A/ ).

(5.59)

c

Example Calculations in t h e previous e x a m p l e w e r e based on A / = 8 h. R e p e a t for 10 h to see the effect of collection time if a sym­ metric collection period about n o o n is used. c

Solution

T h e values of r a n d r for h T

d

coU

= 75° = 1.31 rad

are r = (0.66 x 1.31 + 0.42 x sin 75°)/1.0 c o s 34.5° - 1.98 r = ( 1 . 3 1 / 1 . 0 ) l / c o s 34.5° - sin 75°/20 = 1.54. T

d

T h e collector plane insolation is then

7 = (1.98 - 1.54 x 0.34) x 5.23 = 7.6 k w h / m

2

C

and X = [0.5 x (150 - 10) x 10J/0.6 x 7600 = 0.154. T h e n is 0.86 from E q . (5.53) and the useful energy delivery is 3.7 k W h / m d a y . H e n c e , it is worthwhile operating the collector for at least 10 h. T h e calculation can b e repeated by t h e r e a d e r for an a s y m m e t r i c case 4 h before noon a n d 6 h after t o determine t h e effect of w a r m u p . I 2

E.

Long-Term

Performance

of Collector

Systems

with

Storage

T h e previous section of this c h a p t e r described a m e t h o d of predicting long-term performance of a solar collector operated at a tem­ porally constant t e m p e r a t u r e . This situation is a good approximation of the operating conditions experienced by several t y p e s of generic thermal s y s t e m s . O t h e r s y s t e m s , h o w e v e r , d o not o p e r a t e at constant t e m p e r a t u r e and t h e m e t h o d c a n n o t be used. Although there is n o simplified per­ formance m e t h o d n o w extant for varying t e m p e r a t u r e s y s t e m s , Klein and B e c k m a n ( K l l ) have correlated some modeling results o n c o l l e c t o r - h e a t e x c h a n g e r - s t o r a g e s u b s y s t e m s coupled t o a uniform, processlike load operating a b o v e some t e m p e r a t u r e r c- T h e m e t h o d is called t h e ,/ chart by t h e a u t h o r s a n d is described below. Although t h e method w a s developed for flat-plate collectors and u s e s a different $ calculation pr0

5.

220

Medium-Temperature

Solar

Processes

method than used a b o v e , it can be applied equally well to c o n c e n t r a t o r s (K12). T h e calculation m e t h o d requires first the determination of the utilizability 0 f r o m E q s . (5.51)—(5.54) a b o v e . This represents the max­ imum energy deliverable to a load at T . W h e n storage is p r e s e n t and collected solar heat is greater than the d e m a n d , the t e m p e r a t u r e of storage and h e n c e the collector inlet t e m p e r a t u r e will rise. (The ,/ m e t h o d ap­ plies only to well-mixed, sensible heat storage with liquid heat transfer fluids and storage media.) H e n c e , the monthly averaged, daily useful en­ ergy collected Q will be less than Fr) I ^) but storage m a y permit a greater fraction of the d e m a n d to be met by solar since the m a x i m u m a m o u n t of heat Fi) I (j) collectable may be m o r e than can be u s e d , de­ pending on the d e m a n d a m o u n t . The ,/method can be employed to find Q in a system with storage. T h e technical basis for the J m e t h o d lies in the nondimensionalization of governing energy equations for a solar thermal system. Dimensionless g r o u p s , so identified, are used to correlate monthly thermal energy delivery-to-load for various systems simulated in various climates by an hourly time-scale c o m p u t e r model. The t w o dimensionless groups identified for use in the ,/method, in addition to ( $ is defined in this context relative to the minimum t e m p e r a t u r e acceptable to the process r p r o c not relative to the collector t e m p e r a t u r e as in the previous section) are a solar p a r a m e t e r P , a m e a s u r e of long-term solar gain by the collector receiver, and a collector heat loss p a r a m e t e r P , a m e a s u r e of long-term heat loss at a fixed collector-to-ambient t e m p e r a t u r e difference of 100°C. This 100°C value does not restrict the generality of the results, h o w e v e r . In equation form, proc

u

0

0

c

c

u

s

L

P = Fr)J A NjL,

(5.60)

P

(5.61)

s

L

c

c

= FU A N \00/L, c

c

h

in which F ( F ' , F , etc.) is given in E q s . (4.44)-(4.47), L is the monthly thermal d e m a n d , and N and N are the n u m b e r of days and h o u r s in a m o n t h . T h e ,/ chart predicts the monthly solar load fraction R

d

m,P*,PJ

h

= QjL.

(5.62)

Figure 5.25 is one chart and is entered with values of $ P and P to give a monthly value o f / . T h e calculation of P and P is done once for e a c h m o n t h of an average year and the totals added to give annual performance. An example below shows how the method is used. It is noted that P , the ordinate, is the ratio of m a x i m u m possible energy S

L

s

s

s

L

V.

Performance 1.6

0.

of Medium-Temperature 2.

4.

6.

8.

10.

Solar Processes 12.

14. 16. " — — — —

18.

221 20.

1.4 1.2

1.0

•6- 0.8 0.6

0.4

0.2 0.0 0.

2.

4.

6.

8.

10. P

12.

14.

16.

18.

20.

L

F I G U R E 5.25 The chart used to calculate average, monthly solar fraction / ( / ) of solar-thermal s y s t e m s . [From ( K l l ) . ] s

delivered by a collector operating at fixed r p r o c , (Pr} / A ), to the monthly load L. At values of / > 0.4, the ,/curves are not indepen­ dent of X since at progressively higher load fractions the average storage and collector t e m p e r a t u r e s are higher and collected solar heat p e r unit area smaller b e c a u s e collector efficiency is lower at higher t e m p e r a t u r e . This
C

s

s

(a) The load L is distributed uniformly over the m o n t h b e t w e e n the hours of 6:00 and 18:00. (b) Storage a m o u n t is fixed at 350 k J / ° C m (about 2 gal of H 0 / f t or 84 l / m ) . See second equation in footnote p . 222 for a storage correction. (c) N o energy is rejected from storage; therefore, the vessel is a s s u m e d to be designed for the peak t e m p e r a t u r e and pressure expected. (d) Storage is well mixed and no storage-to-load heat ex­ changer is used. (e) T h e load device uses solar heat at t e m p e r a t u r e independent efficiency to meet the load L. Therefore, the load device cannot be a turbine, for e x a m p l e . (f) N o parasitic heat losses from storage occur. 2

2

2

c

2

c

5.

222

Medium-Temperature

Solar

Processes

Some of these restrictions can be relaxed using w o r k on the $J method conducted by Klein and his c o - w o r k e r s ( K l l ) . U s e r s of the meth­ ods must exercise caution in the p r o p e r choice of the time scale. In the method p r e s e n t e d here and 7 are calculated over the collection period Af , not over all daylight h o u r s . The m e t h o d developed by Klein uses and 7 for all daylight h o u r s . Although the Collares-Pereira $ value can be used with the chart, the t w o m e t h o d s of finding itself must not be confused.* C

c

C

Example R e p e a t the first example from the previous section for K a b u l , Afghanistan, for a monthly averaged load of 260 k W h / d a y using a collector of 100 m . F r o m the previous example recall that F tj = 0.57. F U = 0.475 W / m °C, 7 = 5.4 k W h / m , and = 0.84. What is the effect of storage on energy delivery p e r unit collector a r e a ? 2

r

2

R

0

2

C

C

Solution First calculate P and P , then use the ,/chart to find the solar fraction. s

L

^ = F rj I A N /L = 0.57 x 5.4 x 100 x 31/260 x 31 = 1.18, Pl = F U A N \00/L = 0.475 x 100 x (31 x 24) x 100/(260 x 31) x 1000 = 0.44. s

R

0

c

c

d

R

c

c

h

The value of / from the chart with P = 0.44 and 0 F = 0.99 is / = 0.97. Therefore, the energy delivery per unit area is 0.97 x 260/100 = 2.52 k W h / m d a y , nearly identical to the result using the m e t h o d . This is a result of the low value of U for the c o n c e n t r a t o r and its resulting insensitivity to t e m p e r a t u r e fluctuations a b o v e T . T h e reader may repeat the calculations for a 200-m collector with U = 2.0 W / m °C to show that 0 = 0.43, P = 1.75, P = 2.37, / = 0.85. T h e energy delivery per unit area is then 1.11 k W h / m day c o m p a r e d with 1.32 k W h / m d a y predicted by the m e t h o d . H e n c e the effects of storage reduce the unit energy de­ livery by 16% for the m o r e lossy collector. I s

L

S

s

2

c

proc

2

2

c

L

s

s

2

2

* The data from which Fig. 5.25 was constructed can be represented the empirical equation ( K l l ) / = P - [ e - ^ - 1][1 - - ° ^ ] where a = r Mr "I 0.015 355*3-1 in which m = (kg), c = (kJ/kg °C), and A = (m ). by

3

s

- 0

s

l 5 P

8

e

a

7 6

2

p

c