Efficiency and Costing - American Chemical Society

3 Reversibility of Combustion Processes HORST J. RICHTER

Downloaded by UNIV OF ARIZONA on December 21, 2012 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch003

Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 KARL F. KNOCHE Lehrstuhl für Technische Thermodynamik, RWTH Aachen, D-5100 Aachen, Federal Republic of Germany Technical combustion processes are highly irreversible. Theoretical considerations show that the irreversible entropy production of combustion can be decreased i f immediate contact of fuel with oxygen is prevented and intermediate chemical reactions are supported. Therefore, the potential for mechanical work output can be increased. Metal oxides can be used as reactants for these intermediate reactions. In many of our energy conversion processes, like in conventional power plants, we rely on chemical energy being released i n a combustion process. The combustion of f o s s i l fuels, usually employed as an intermediate step, is in common practice highly irreversible. This is the main reason for the overall low efficiency of these energy conversion processes. It i s known that the less irreversible the chemical reactions, the closer they occur to the thermodynamic equilibrium. Unfortunately, the equilibrium of technical combustion processes i s usually at such high temperatures that the materials which enclose the reaction volume cannot withstand these temperatures. Therefore, the development of high temperature materials i s a way to improve such efficiency. Technical combustion i s usually performed by crude mixing of fuel and oxygen, thus the reaction is allowed to occur in a very disorderly way, inevitably resulting in irreversible entropy production. The human body, as an example, produces mechanical energy from chemical energy by allowing many intermediate chemical reactions of the "fuel" and the "oxygen" separately before one molecule of "fuel" i s united with the stoichiometric number of oxygen molecules i n the muscle c e l l s , where the mechanical energy i s produced. Not a l l of these intermediate reactions are known, but physiological studies by Lehmann (1) indicate that the total efficiency of the human body i s surprisingly high, for some labor i t i s in the range of 30 to 35%, thus exceeding the Carnot efficiency substantially. Therefore, i t seems advantageous to 0097-6156/83/0235-0071$06.00/0 © 1983 American Chemical Society In Efficiency and Costing; Gaggioli, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

SECOND LAW ANALYSIS OF PROCESSES

72

t r y t o i m i t a t e nature and search f o r p o s s i b i l i t i e s t o improve the t e c h n i c a l combustion by preventing immediate contact of oxygen with f u e l and r a t h e r support intermediate r e a c t i o n s . The intermediate r e a c t i o n s i n the l i v i n g organism are h i g h molecular organic r e a c t i o n s . But f o r t e c h n i c a l purposes anorganic substances l i k e metal oxides are probably more favorable as oxygen c a r r i e r s . T h i s was s t u d i e d e x t e n s i v e l y by Knoche and R i c h t e r ( 2 ) .


T e c h n i c a l Background The maximum work output of any thermodynamic system or process can be obtained, i f the m a t e r i a l i n the system or the working f l u i d i n the process i s brought i n t o e q u i l i b r i u m w i t h the environment r e v e r s i b l y . The a c t u a l work output of a t e c h n i c a l process with combustion i s much s m a l l e r because the combustion i s h i g h l y i r r e v e r s i b l e . The work l o s s e s i n a continuous comb u s t i o n can be evaluated i f the exergy (or a v a i l a b l e energy) before and a f t e r the r e a c t i o n i s c a l c u l a t e d . T h i s exergy i s described by the equation: e = (h- - h ) - T (s- - s ) 1 o o 1 o

(1)

In the above equation the exergy i s w r i t t e n as an i n t e n s i v e property, e.g. per mol of f u e l . The s u b s c r i p t "1" represents the o r i g i n a l thermodynamic s t a t e , the s u b s c r i p t "o" describes the s t a t e when thermodynamic e q u i l i b r i u m with the environment i s e s t a b l i s h e d . In these c o n s i d e r a t i o n s i t i s a r b i t r a r i l y assumed that any r e a c t i o n product i s i n e q u i l i b r i u m with the environment when i t has a temperature of T = 300K and a pressure of P = l b a r . As was shown by Baehr (3) the a v a i l a b l e energy or exergy can be represented g r a p h i c a l l y very e a s i l y i n an enthalpy, entropy diagram (see F i g u r e 1 ) . Knoche (4) p l o t t e d the r e a c t a n t s and r e a c t i o n products i n one enthalpy, entropy diagram by s u p e r p o s i t i o n , thus he was able t o evaluate immediately the i r r e v e r s i b l e entropy p r o d u c t i o n , r e s p e c t i v e l y the exergy l o s s e s o f the combustion (see F i g u r e 2 ) . For an a d i a b a t i c combustion process at constant pressure, the enthalpy stays constant. F i g u r e 2 shows the exergy of the r e a c t a n t s , e^, and the exergy of the r e a c t i o n products, e^* a f t e r t h i s r e a c t i o n has taken p l a c e . The l o s s i n exergy i s : F

L

=

e

e

l- 2

=

T

o

(

8

S

l " 2>

(2)

In t e c h n i c a l combustion processes, t h i s l o s s of exergy can be as high as 50%. I f the combustion process i s a d i a b a t i c , but at constant volume, then the i n t e r n a l energy stays constant. U s u a l l y the exergy l o s s e s are somewhat s m a l l e r than i n the previous case (see F i g u r e 3 ) . A t h i r d way of combustion would be i s o t h e r m a l , i s o b a r i c as i n d i c a t e d i n F i g u r e 4. T h i s r e a c t i o n r e q u i r e s a heat r e s e r v o i r

In Efficiency and Costing; Gaggioli, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


RICHTER AND KNOCHE

Reversibility of Combustion Processes

ENTROPY

S

F i g u r e 1. Enthalpy, entropy diagram w i t h g r a p h i c a l p r e s e n t a t i o n of exergy (3)•

ENTROPY S

F i g u r e 2* Enthalpy, entropy diagram with exergy f o r reactants e^ and r e a c t i o n products ^ a f t e r an a d i a b a t i c , i s o b a r i c combustion (4).




ENTROPY S

F i g u r e 3. Enthalpy, entropy diagram with exergy f o r r e a c t a n t s e-^ and r e a c t i o n products &2 a f t e r adiabatic combustion at constant volume . a

n

A

a.

ENTROPY S

F i g u r e 4. Enthalpy, entropy diagram w i t h exergy f o r reactants e^ and r e a c t i o n products e£ a f t e r an i s o t h e r m a l , i s o b a r i c combustion ( 4 ) The change of s t a t e from 1 t o l a i s a r e l e a s e of heat at constant temperature, t h e r e f o r e the entropy decreases. 0


3.

75


RICHTER AND KNOCHE

at the combustion temperature thus i s not an a d i a b a t i c process. T h i s case u s u a l l y shows the smallest i r r e v e r s i b l e entropy production. From these b r i e f c o n s i d e r a t i o n s an e x e r g e t i c e f f i c i e n c y of the combustion process can be d e f i n e d : r

=

l -

exergy l o s s during combustion exergy of reactants

or T As Downloaded by UNIV OF ARIZONA on December 21, 2012 | http://pubs.acs.org Publication Date: November 11, 1983 | doi: 10.1021/bk-1983-0235.ch003

C

-

1 -

2 reactants

W_ =

h reactants

x _

(3a)

where i s the work l o s s . T h i s e x e r g e t i c e f f i c i e n c y w i l l be the measure of performance f o r the f o l l o w i n g c o n s i d e r a t i o n s . Combustion with Intermediate

Reactions

As was i n d i c a t e d above, the l o s s e s i n exergy can e v e n t u a l l y be diminished i f intermediate r e a c t i o n s a r e employed r a t h e r than immediate contact between f u e l and oxygen, A schematic o f such a r e a c t i o n scheme i s shown i n Figure 5, In " r e a c t o r " A the f u e l i s o x i d i z e d , an appropriate c a r r i e r provides the oxygen. The c a r r i e r w i l l be c i r c u l a t e d between " r e a c t o r " A and r e a c t o r B . In r e a c t o r B i t w i l l be recharged with oxygen. The mass balance performed at the s u r f a c e of the c o n t r o l volume of the process i s i d e n t i c a l t o a normal combustion. Only f u e l and oxygen or a i r a r e t r a n s f e r r e d i n t o the c o n t r o l volume and combustion products and n i t r o g e n are exhausted from i t ; the l a t t e r one only i f a i r i s used f o r o x i d a t i o n i n s t e a d of pure oxygen. The chemical energy r e l e a s e d i n a normal combustion process i n c r e a s e s only the i n t e r n a l energy of the combustion products. According t o the second law of thermodynamics only p a r t of t h i s energy can be harnessed. An improvement of the process should enable us t o o b t a i n a l a r g e r f r a c t i o n of the a v a i l a b l e energy as u s e f u l work, thus the i r r e v e r s i b l e entropy production should become s m a l l e r . In the f o l l o w i n g c o n s i d e r a t i o n s , methane w i l l be used as f u e l . For intermediate r e a c t i o n s we could use the f o l l o w i n g p o s s i b i l i t i e s f o r improvement: f|

a)

M

The o x i d a t i o n of f u e l s occurs by r e d u c t i o n of s o l i d metal ("Me") oxides. T h i s takes place such that the number of gaseous moles i s increased s u b s t a n t i a l l y . As an example, the o x i d a t i o n of methane: CH

4

+ 4"Me"0 -> C 0 + 2H 0 + 4"Me" 2

2

In t h i s r e a c t i o n the number of gaseous moles i s t r i p l e d . At higher pressures the r e a c t i o n occurs c l o s e r t o the


(4)

76


b)

SECOND LAW ANALYSIS OF PROCESSES e q u i l i b r i u m , thus the i r r e v e r s i b l e entropy production and consequently the work l o s s e s are s m a l l e r . But t h i s i s u s u a l l y only a very s m a l l improvement, Metal oxides are used as oxygen c a r r i e r s which r e a c t w i t h the f u e l at r e l a t i v e l y low temperatures endothermally. In t h i s case heat has t o be provided to the " r e a c t o r " A i n F i g u r e 5 to keep the temperature constant. Therefore, i n the r e o x i d a t i o n of the oxygen c a r r i e r i n " r e a c t o r " B more heat has t o be r e l e a s e d , s i n c e the o v e r a l l energy balance has to be the same as f o r the u s u a l combustion process. Work producing c y c l i c processes (Carnot heat engines) could be employed between a heat source, represented by the constant temperature r e o x i d a t i o n of the oxygen c a r r i e r , the heat s i n k of the endothermic f u e l o x i d a t i o n , and the heat s i n k of the environment (see F i g u r e 6 ) . In the i d e a l case, i f the chemical r e a c t i o n s i n both r e a c t o r s are r e v e r s i b l e , the work producing devices (heat engines) should t h e o r e t i c a l l y d e l i v e r the maximum a v a i l a b l e energy or exergy of the f u e l as mechanical work.

Both processes d e s c r i b e d above can be u t i l i z e d at l e a s t partially. Only the i d e a l cases of an i s o t h e r m a l - i s o b a r i c combustion process w i l l be assumed. T h i s combustion i s s u p e r i o r to the usual i s o b a r i c - a d i a b a t i c process. Such an assumption can be v e r i f i e d more e a s i l y than i n a normal combustion process, s i n c e i n the cases s t u d i e d here the chemical r e a c t i o n s take p l a c e at the s u r f a c e of the oxygen c a r r i e r s . I f , f o r the methane combustion, copper oxide i s used as an oxygen c a r r i e r , the chemical r e a c t i o n i n the " r e a c t o r " A (see F i g u r e 5) i s : CH

4

+ 4Cu0 -> C 0

2

+ 2H 0 + 4Cu

(5)

2

and the r e o x i d a t i o n i n " r e a c t o r " B i s : Cu + 0.5

0

2

+ 0.5

•

N

2

•> CuO + 0.5

•

N

£

(6)

The o x i d a t i o n r e a c t i o n of CH^ with CuO i s shown i n F i g u r e 7 and the r e o x i d a t i o n of Cu i n F i g u r e 8. In t h i s case, both the r e d u c t i o n and r e o x i d a t i o n are i r r e v e r s i b l e ; the only improvement i s due to the i n c r e a s e i n the number of gaseous moles, i n c r e a s i n g the e f f i c i e n c y at higher p r e s s u r e s . The e v a l u a t i o n of the i r r e v e r s i b l e entropy production i s very e a s i l y performed i n these enthalpy, entropy diagrams as was shown by Knoche ( 4 ) . I t i s simply f o r one mole methane: W

L

=

T (As. + 4As_J o A a

(7)

As. i s the i r r e v e r s i b l e entropy production during the copper r e a u c t i o n i n r e a c t o r A and As~ i s the i r r e v e r s i b l e entropy pro-


RICHTER AND KNOCHE



NITR06EN

t

t OXYGEN OR AIR

FUEL

F i g u r e 5, Schematic mediate r e a c t i o n .

of a combustion

COMBUST I ON

W

PRODUCTS

.

Q

\ CONTROL VOLUME

process with i n t e r -

ENV IRONMENT NITROGEN 4

A

A

r-f—kt-— EXOTHERM

F i g u r e 6. Schematic of a combustion mediate r e a c t i o n s and heat engines.

process w i t h i n t e r -







RICHTER AND KNOCHE



80

d u c t i o n i n the subsequent r e o x i d a t i o n process i n r e a c t o r B, both at the d e s i r e d process temperatures. Another p o s s i b l e oxygen c a r r i e r i s n i c k e l oxide,the chemical r e a c t i o n i n r e a c t o r A i n F i g u r e 6 would be: CH

4

+ 4Ni0 + C 0 + 2H 0 + 4Ni 2

(8)

2

and i n r e a c t o r B


N i + 0.5 0

2

+ 0.5 •

N

2

+ NiO + 0.5 •

N

2

(9)

The d i f f e r e n c e to the copper process i s , that the r e d u c t i o n of n i c k e l oxide with methane i s an endothermic process, thus a heat engine could be employed. F i g u r e s 9 and 10 show the enthalpy, entropy diagrams of the r e a c t i o n s o u t l i n e d i n equations (8) and (9). (A m e t a l l u r g i s t w i l l not favor the r e o x i d a t i o n of n i c k e l s i n c e i t i s very d i f f i c u l t , but e q u i l i b r i u m thernodynamic cons i d e r a t i o n s do allow i t . ) Another very i n t e r e s t i n g oxygen c a r r i e r i s cadmium. For the methane combustion the f o l l o w i n g r e a c t i o n s are o c c u r r i n g i n r e a c t o r s A and B (see F i g u r e 6 ) : CH^ + 4Cd0 -> C 0 + 2H 0 + 4Cd 2

(10)

2

and Cd + 0.5 0

2

+ 0.5 • ^ —

N

2

-v CdO + 0.5 •

N

£

(11)

At a temperature of about 1050K and a pressure of 1 bar, the cadmium v a p o r i z e s , thus i n the r e d u c t i o n process o f CdO, (equation 10), the number o f gaseous moles i n c r e a s e s from one mole of CH^ t o 7 moles. I n the i d e a l case the cadmium oxide r e d u c t i o n i s r e v e r s i b l e at a temperature of about 800K at a pressure of 300 b a r (see F i g u r e 11). The subsequent r e o x i d a t i o n of Cd i s r e v e r s i b l e at a temperature of about 1600K, i n which s o l i d i f i c a t i o n occurs (see F i g u r e 12). Thus the t o t a l process with cadmium oxide as an oxygen c a r r i e r i s r e v e r s i b l e i f the r e o x i d a t i o n could be handled at t h i s r e l a t i v e l y high temperature. (Cadmium i s probably not a p o t e n t i a l oxygen c a r r i e r i n a r e a l design due to i t s hazardous p r o p e r t i e s . ) The i r r e v e r s i b l e entropy production f o r i s o t h e r m a l , i s o b a r i c chemical r e a c t i o n s i s p l o t t e d i n each diagram f o r an i s o t h e r m a l i r r e v e r s i b l e process a t 1200K, but can be evaluated as e a s i l y f o r any other temperature. The e x e r g e t i c e f f i c i e n c y of the t o t a l process can then be evaluated with equations (3a) and (7) as a f u n c t i o n of the maximum process temperature. F i g u r e 13 shows the e x e r g e t i c e f f i c i e n c y v s . the maximum temperature f o r d i f f e r e n t combustion processes with and without intermediate r e a c t i o n s . As a comparison, the a d i a b a t i c , i s o b a r i c




3. RICHTER AND KNOCHE


81






RICHTER AND KNOCHE




F i g u r e 13. E x e r g e t i c e f f i c i e n c y of methane combustion f o r d i f f e r e n t processes as a f u n c t i o n of maximum process temperature.


3.

RICHTER AND KNOCHE


85

combustion of methane i s plotted for an i n i t i a l temperature of = 300K and different excess a i r ratios. The exergetic efficiency of combustion processes with intermediate reactions is theoretically higher than combustion i n usual practice. For a maximum process temperature of 1600K a reversible combustion can be obtained theoretically with cadmium as the oxygen carrier.


Conclusions These basic thermodynamic considerations show that intermediate reactions i n combustion processes can be very advantageous and that i n some cases most or a l l of the chemical energy could be harnessed as mechanical energy at least theoretically. Important questions of reaction kinetics, actual design and applicability of such a device of the selected oxygen carriers have not been included i n these fundamental thermodynamic equilibrium studies. Yet there i s indication from the production of synthetic fuels that the reduction reactions are reasonably fast, see Terisawa and Sakikawa (5), and Lewis and G i l l i l a n d (6). Literature Cited 1. 2. 3. 4. 5. 6.

Lehmann, G. "Praktische Arbeitsphysiologie"; Thieme Verlag: Stuttgart, 1953. Knoche, K.F.; Richter, H . J . Brennstoff-Wärme-Kraft. 1968, 5, 205-210. Baehr, H.D. "Thermodynamik"; 2nd E d . , Springer-Verlag. Berlin, 1966. Knoche, K . F . Brennstoff-Wärme-Kraft. 1967, 1, 9-14. Terasawa, S.; Sakikawa, N . ; Shiba, T. B u l l . Jap. Petrol. Inst. 1963, 3, 20-26. Lewis, W.K.; G i l l i l a n d , E . R . ; Reed, W.A. Ind. Engng. Chem. (1949), 6, 1227-1237.

RECEIVED July 7, 1983


Efficiency and Costing - American Chemical Society

Recommend Documents