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A theoretical and experimental study of the energy harvest efficiency of an energy crop
Solar Energy Vol. 39, No. 4, pp. 291-295, 1987 Printed in the U.S.A.
0038-092X/87 $3.00 + .00 © 1987 Pergamon Journals Ltd.
A THEORETICAL AND EXPERIMENTAL STUDY OF THE ENERGY HARVEST EFFICIENCY OF AN ENERGY CROP K. T E N N A K O N E * , S . WICKRAMANAYAKE and S. PLINCHIHEWA Institute of Fundamental Studies, Hantana, Kandy, Sri Lanka and K. L. WEERASENA Department of Physics, University of Ruhuna, Matara, Sri Lanka Abstract--It is shown that growth kinetics of a plant community determine the maximum rate at which biomass can be extracted continously while maintaining a quasistatic equilibrium. The floating hydrophyte Lemna major is studied as a model system. It is shown that the measurements on this system are in agreement with the theoretical model and that the optimum energy harvest efficiency of Lemna major is -4%.
I. INTRODUCTION
Development of plant species with high photosynthetic capabilities is one of the m o s t promising methods of harnessing solar power[ 1-4]. It is hoped that the search among existing species, selective breeding or genetic manipulation will eventually succeed in finding plants suitable for conversion of solar energy. A n ideal energy crop must admit continous biomass (energy) extraction while maintaining quasistatic equilibrium with the growth process. In a short communication published in this journal[5], we defined a parameter termed "energy harvest efficiency" ('qnE) as a measure of the suitability of such species for conversion o f solar energy. In this paper we elaborate on this idea and present experimental results on measurements of "qnE for the floating hydrophyte Lemna major, which was studied as a model system. 2. "I'HEORY
The photosynthetic efficiency (ripE) of a plant or a plant community can be defined as
where N is the total biomass per unit area at time t. If b is the calorific value of biomass, which in general is a slow varying function of t (especially true for biomass from fast growing species[8]), we obtain
f(N)b ri~,e =
(3)
I
When biomass is extracted at a constant rate, C, eqn (2) modifies, i.e., dN dt
--
=
f(N)
-
C,
and a quasistatic equilibrium is possible if
C = f(N).
(5)
The function f ( N ) could have a maximum for some value of N ( = N) and the maximum biomass extraction rate is,
CMax = f ( N ) . "qP~ = 1 (dE/dt),
where E = energy stored in biomass per unit area (Jm -2) as measured at time t, I = intensity of solar radiation (Wm-2). Even if the external conditions (e.g., COz concentration, I, temperature) are kept fixed, rive cannot be regarded constant, but depends on time t referred to the growth. The growth process is described by a rate equation of the form[6-7]
Thus the maximum energy harvest rate can be written as follows: (ritte)~i~x -
f(N),
I
(7)
N = N
(8)
dt
(2)
* Postal address is Department of Physics, University of Ruhuna, Matara, Sri Lanka.
f(N) b
The equilibrium points of a differential equation of the form (4) are known to be stable iti9]
df(N._.....~)_< 0 =
(6)
(1)
1
dN -dt
(4)
Hence it follows form (3) and (7) that, provided (8) is satisfied, energy can be extracted at a rate nearly same as the maximum storage rate. 291
292
K. TENNAKONEet al.
N'k/o
N __ ~ 2 o NO lcm Fig. 2. Fronds of Lemna major. t
Fig. 1. Plot of the solution of eqn (3) for different values of C, when f ( N ) is the logistic function (1) C = 0, (2) C = CM~x, (3) C > CM~x. The function f ( N ) has to be determined from experiment. It is known that in many instances f ( N ) approximates quite well to the logistic form[6, 7, 10], i.e., f(N) = kN -
aN 2
(9)
where k = growth constant, a = coefficient of seifintefa6tion, and both are constants. The value of CM~x, ('qilE)M~ and N corresponding to (9) are
/fi CMax = - - .
4a
/fib ('qHE)M~x = 4"-~-"
(10)
k 2a
duce lateral buds, which themselves become fronds and separate. Known weights of Lemna ( - 0 . 5 g -~ 20 fronds) were inoculated into a series of glass vessels (crosssectional area - 90 cm 2, outside surface painted black to minimize the growth of algae and other photosynthetic organisms) containing sterilized water supplemented with mineral nutrients (nitrate nitrogen = 0.02 gl -~, ammonical nitrogen ---- 0.02 gl - I , K20 = 0.1 gl - I , P205 --- 0.1 g l - l ) . The concentration of the nutrients were kept constant throughout the entire period of growth. Solar intensity was monitored using an Eppley Pyranometer and Electronic Integrator. Temperature and humidity were also recorded. Contents of two vessels of the set were weighed at regular intervals, and the mean of the two measurements was taken to calculate N. The saturation was reached in a period o f - 5 0 days. Biomass harvested at different stages of growth were dried in an oven at I05°C and the calorific value determined by bomb calorimetry. Significant variations were not seen and the average of 5 measurements gave b = 4050 cal/g dry wt.
Also, f ( N ) given by (9) satisfies the condition (8), i.e., it guarantees a stable quasistatic equilibrium at the maximum biomass extraction point. Instability occurs only if C exceeds CM~x (Fig. 1). It is interesting to note that N is half the saturation concentration that would be reached in absence of harvesting.
4. RESULTS
The plot o f N vs t is shown in Fig. 3. The curve has a logistic shape with a saturation concentration = 3.8 k g m - : . Fig. 4 shows a plot of In N vs t, the initial phase of growth approximates to a straight line whose gradient gives k = 0.40 d a y - L Again
3. EXPERLMENTAL PROCEDURE
Floating aquatic plants have high productivities and are probably the most promising class of plants for conversion processes based on utilization of whole biomass. We have studied Lemna major as a model system for measurementt of growth parameters and determination of ('q~l~)M~. Lemna major (Fig. 2) is a monocot consisting of fronds (2-4 leaves)J11-12]. The linear dimensions of a frond are - 0 . 8 cm. Although Lemna major is a flowering plant, flowers are rarely formed, and the propagation is almost entirely vegetative. Fronds pro-
Table 1. Experimental conditions and values of different parameters for Lemna major I Av. Temperature Av. Rel. Humidity k a dry wt/wet wt N b Cmax (711tz),~
1.41 x 104 KJ day - l 28°C 76% 0.40 d a y 0.10 m2 kg -1 day - ! 0.81 1.9 kgm -2 4050 cal/g dry wt 396 gm2 d a y - I 3.8%
The energy harvest efficiency of an energy crop
293
O
% Z
2
20
I
4O t/days
6O
Fig. 3. Plot of N vs t.
O
O
O
0
O
zt-2 -
I
I
20
I
I
40
t/days Fig. 4. Plot of In N vs t, showing the exponential phase of growth.
K. TENNAKONE et al.
294
0.4 "T :=,., {3
-lo
Zl. --Iz 0.20
I
1
2
3
4
N / K g m -z Fig. 5. Plot o f llN(dNIdt) vs N.
0.4 (M
'E 3E
0.2-
I
2
t
N / K g m -2
Fig. 6. Plot o f dNIdt vs N.
4
The energy harvest efficiency of an energy crop the plot of 1/N(dN/dt) vs N fits into a straight line proving that the logistic approximation is valid (Fig. 5). This is also evident from Fig. 6, where dN/dt is plotted against N, the curve has the expected parabolic shape with a maximum at N = N = 1.85 kgm -2. The values of a, k, N, (rlHe)M~x and other relevant parameters are given in Table 1. 5. CONCLUSION Experimental results are in good agreement with the theory we have outlined. An optimum energy harvest efficiency of ~ 4 % for Lemna major is an encouraging result. It is possible that other floating hydrophytes (e.g., Water hyacinth, Salvinia) have higher energy harvest efflciencies. L o w e r plants, e.g., microalgae, would perhaps agree even more closely with the theoretical model. Continous biomass extraction requires rapid propagation without irreversible changes. In higher plants the presence of irreversible phases lasting for long intervals of time prevent continous biomass extraction. Even in such cases growth generally approximates to logistic form[7-10] and (rlHE).~i~xgiven b y (9) still defines a useful parameter. In a process that consumes whole biomass, the energy economy is higher when the crop is harvested at the maximum growth point to start the second crop. I n t h i s sense (rlltE)x~x is also the optimum efficiency at which energy could be extracted in a discontinous harvesting process. Another factor that needs consideration is the energy spent in the harvesting process. In this re-
295
spect floating plants are superior to algae, because the harvesting process does not involve energy costly operations such as centrifuging. Again the recycling o f mineral nutrients and CO2 is easier in a culture of floating plants. REFERENCES I. H. Mislin and R. Bachofen, New Trends in Research and Utilization o f Solar Energy through Biological Systems, Experimentia Supplementum, Vol. 43. Birk hauser, Verlag, Basel (1982). 2. O. P. Vimal and P. D. Jyagl, Energy From Biomass. Agricole Publishing Academy, New Delhi (1984). 3. G. Porter, Photosynthesis, in Light Chemical Change and Life (Edited by J. D. Coyle, R. R. Hill and D. R. Roberts). Open University Press, Milton Keynes (1982). 4. I(. K. Rao and D. O. Hall, A 1983 View of Non-Conventional Energy Sources. (Edited by G. Furlan, N. A. Mancini and A. A. M. Sayigh) World Scientific, Singapore (1983). 5. K. Tennakone, Solar Energy (in press) (1986). 6. K. E. Watt, Ecology and Resource Management, A Quantative Approach. McGraw Hill, New York (1968). 7. Yu. M. Svirezhev and D. O. Logofet, Stability o f Biological Communities, Translated from Russian by Alexy Voinov. Mir Publishers, Moscow (1983). 8. G. loss and D. D. Joseph, Elementary Stability and Bifurcation Theory. Springer, Berlin (1980). 9. E. P. Odum, Fundamentals of Ecology. Saunders College Publishing, Philadelphia (1971). 10. W. S. Hilman and D. D. Culley, Am. Sci. 66, 442 (1978). 11. M.A. Murry and J. R. Benemann, Fresh water plants, in CRC Handbook of Biosolar Resources Vol. H (Edited by O. R. Zaborsky, T. A. McClure and E. S. Lipinsky). CRC Press, Florida (1979).
0038-092X/87 $3.00 + .00 © 1987 Pergamon Journals Ltd.
A THEORETICAL AND EXPERIMENTAL STUDY OF THE ENERGY HARVEST EFFICIENCY OF AN ENERGY CROP K. T E N N A K O N E * , S . WICKRAMANAYAKE and S. PLINCHIHEWA Institute of Fundamental Studies, Hantana, Kandy, Sri Lanka and K. L. WEERASENA Department of Physics, University of Ruhuna, Matara, Sri Lanka Abstract--It is shown that growth kinetics of a plant community determine the maximum rate at which biomass can be extracted continously while maintaining a quasistatic equilibrium. The floating hydrophyte Lemna major is studied as a model system. It is shown that the measurements on this system are in agreement with the theoretical model and that the optimum energy harvest efficiency of Lemna major is -4%.
I. INTRODUCTION
Development of plant species with high photosynthetic capabilities is one of the m o s t promising methods of harnessing solar power[ 1-4]. It is hoped that the search among existing species, selective breeding or genetic manipulation will eventually succeed in finding plants suitable for conversion of solar energy. A n ideal energy crop must admit continous biomass (energy) extraction while maintaining quasistatic equilibrium with the growth process. In a short communication published in this journal[5], we defined a parameter termed "energy harvest efficiency" ('qnE) as a measure of the suitability of such species for conversion o f solar energy. In this paper we elaborate on this idea and present experimental results on measurements of "qnE for the floating hydrophyte Lemna major, which was studied as a model system. 2. "I'HEORY
The photosynthetic efficiency (ripE) of a plant or a plant community can be defined as
where N is the total biomass per unit area at time t. If b is the calorific value of biomass, which in general is a slow varying function of t (especially true for biomass from fast growing species[8]), we obtain
f(N)b ri~,e =
(3)
I
When biomass is extracted at a constant rate, C, eqn (2) modifies, i.e., dN dt
--
=
f(N)
-
C,
and a quasistatic equilibrium is possible if
C = f(N).
(5)
The function f ( N ) could have a maximum for some value of N ( = N) and the maximum biomass extraction rate is,
CMax = f ( N ) . "qP~ = 1 (dE/dt),
where E = energy stored in biomass per unit area (Jm -2) as measured at time t, I = intensity of solar radiation (Wm-2). Even if the external conditions (e.g., COz concentration, I, temperature) are kept fixed, rive cannot be regarded constant, but depends on time t referred to the growth. The growth process is described by a rate equation of the form[6-7]
Thus the maximum energy harvest rate can be written as follows: (ritte)~i~x -
f(N),
I
(7)
N = N
(8)
dt
(2)
* Postal address is Department of Physics, University of Ruhuna, Matara, Sri Lanka.
f(N) b
The equilibrium points of a differential equation of the form (4) are known to be stable iti9]
df(N._.....~)_< 0 =
(6)
(1)
1
dN -dt
(4)
Hence it follows form (3) and (7) that, provided (8) is satisfied, energy can be extracted at a rate nearly same as the maximum storage rate. 291
292
K. TENNAKONEet al.
N'k/o
N __ ~ 2 o NO lcm Fig. 2. Fronds of Lemna major. t
Fig. 1. Plot of the solution of eqn (3) for different values of C, when f ( N ) is the logistic function (1) C = 0, (2) C = CM~x, (3) C > CM~x. The function f ( N ) has to be determined from experiment. It is known that in many instances f ( N ) approximates quite well to the logistic form[6, 7, 10], i.e., f(N) = kN -
aN 2
(9)
where k = growth constant, a = coefficient of seifintefa6tion, and both are constants. The value of CM~x, ('qilE)M~ and N corresponding to (9) are
/fi CMax = - - .
4a
/fib ('qHE)M~x = 4"-~-"
(10)
k 2a
duce lateral buds, which themselves become fronds and separate. Known weights of Lemna ( - 0 . 5 g -~ 20 fronds) were inoculated into a series of glass vessels (crosssectional area - 90 cm 2, outside surface painted black to minimize the growth of algae and other photosynthetic organisms) containing sterilized water supplemented with mineral nutrients (nitrate nitrogen = 0.02 gl -~, ammonical nitrogen ---- 0.02 gl - I , K20 = 0.1 gl - I , P205 --- 0.1 g l - l ) . The concentration of the nutrients were kept constant throughout the entire period of growth. Solar intensity was monitored using an Eppley Pyranometer and Electronic Integrator. Temperature and humidity were also recorded. Contents of two vessels of the set were weighed at regular intervals, and the mean of the two measurements was taken to calculate N. The saturation was reached in a period o f - 5 0 days. Biomass harvested at different stages of growth were dried in an oven at I05°C and the calorific value determined by bomb calorimetry. Significant variations were not seen and the average of 5 measurements gave b = 4050 cal/g dry wt.
Also, f ( N ) given by (9) satisfies the condition (8), i.e., it guarantees a stable quasistatic equilibrium at the maximum biomass extraction point. Instability occurs only if C exceeds CM~x (Fig. 1). It is interesting to note that N is half the saturation concentration that would be reached in absence of harvesting.
4. RESULTS
The plot o f N vs t is shown in Fig. 3. The curve has a logistic shape with a saturation concentration = 3.8 k g m - : . Fig. 4 shows a plot of In N vs t, the initial phase of growth approximates to a straight line whose gradient gives k = 0.40 d a y - L Again
3. EXPERLMENTAL PROCEDURE
Floating aquatic plants have high productivities and are probably the most promising class of plants for conversion processes based on utilization of whole biomass. We have studied Lemna major as a model system for measurementt of growth parameters and determination of ('q~l~)M~. Lemna major (Fig. 2) is a monocot consisting of fronds (2-4 leaves)J11-12]. The linear dimensions of a frond are - 0 . 8 cm. Although Lemna major is a flowering plant, flowers are rarely formed, and the propagation is almost entirely vegetative. Fronds pro-
Table 1. Experimental conditions and values of different parameters for Lemna major I Av. Temperature Av. Rel. Humidity k a dry wt/wet wt N b Cmax (711tz),~
1.41 x 104 KJ day - l 28°C 76% 0.40 d a y 0.10 m2 kg -1 day - ! 0.81 1.9 kgm -2 4050 cal/g dry wt 396 gm2 d a y - I 3.8%
The energy harvest efficiency of an energy crop
293
O
% Z
2
20
I
4O t/days
6O
Fig. 3. Plot of N vs t.
O
O
O
0
O
zt-2 -
I
I
20
I
I
40
t/days Fig. 4. Plot of In N vs t, showing the exponential phase of growth.
K. TENNAKONE et al.
294
0.4 "T :=,., {3
-lo
Zl. --Iz 0.20
I
1
2
3
4
N / K g m -z Fig. 5. Plot o f llN(dNIdt) vs N.
0.4 (M
'E 3E
0.2-
I
2
t
N / K g m -2
Fig. 6. Plot o f dNIdt vs N.
4
The energy harvest efficiency of an energy crop the plot of 1/N(dN/dt) vs N fits into a straight line proving that the logistic approximation is valid (Fig. 5). This is also evident from Fig. 6, where dN/dt is plotted against N, the curve has the expected parabolic shape with a maximum at N = N = 1.85 kgm -2. The values of a, k, N, (rlHe)M~x and other relevant parameters are given in Table 1. 5. CONCLUSION Experimental results are in good agreement with the theory we have outlined. An optimum energy harvest efficiency of ~ 4 % for Lemna major is an encouraging result. It is possible that other floating hydrophytes (e.g., Water hyacinth, Salvinia) have higher energy harvest efflciencies. L o w e r plants, e.g., microalgae, would perhaps agree even more closely with the theoretical model. Continous biomass extraction requires rapid propagation without irreversible changes. In higher plants the presence of irreversible phases lasting for long intervals of time prevent continous biomass extraction. Even in such cases growth generally approximates to logistic form[7-10] and (rlHE).~i~xgiven b y (9) still defines a useful parameter. In a process that consumes whole biomass, the energy economy is higher when the crop is harvested at the maximum growth point to start the second crop. I n t h i s sense (rlltE)x~x is also the optimum efficiency at which energy could be extracted in a discontinous harvesting process. Another factor that needs consideration is the energy spent in the harvesting process. In this re-
295
spect floating plants are superior to algae, because the harvesting process does not involve energy costly operations such as centrifuging. Again the recycling o f mineral nutrients and CO2 is easier in a culture of floating plants. REFERENCES I. H. Mislin and R. Bachofen, New Trends in Research and Utilization o f Solar Energy through Biological Systems, Experimentia Supplementum, Vol. 43. Birk hauser, Verlag, Basel (1982). 2. O. P. Vimal and P. D. Jyagl, Energy From Biomass. Agricole Publishing Academy, New Delhi (1984). 3. G. Porter, Photosynthesis, in Light Chemical Change and Life (Edited by J. D. Coyle, R. R. Hill and D. R. Roberts). Open University Press, Milton Keynes (1982). 4. I(. K. Rao and D. O. Hall, A 1983 View of Non-Conventional Energy Sources. (Edited by G. Furlan, N. A. Mancini and A. A. M. Sayigh) World Scientific, Singapore (1983). 5. K. Tennakone, Solar Energy (in press) (1986). 6. K. E. Watt, Ecology and Resource Management, A Quantative Approach. McGraw Hill, New York (1968). 7. Yu. M. Svirezhev and D. O. Logofet, Stability o f Biological Communities, Translated from Russian by Alexy Voinov. Mir Publishers, Moscow (1983). 8. G. loss and D. D. Joseph, Elementary Stability and Bifurcation Theory. Springer, Berlin (1980). 9. E. P. Odum, Fundamentals of Ecology. Saunders College Publishing, Philadelphia (1971). 10. W. S. Hilman and D. D. Culley, Am. Sci. 66, 442 (1978). 11. M.A. Murry and J. R. Benemann, Fresh water plants, in CRC Handbook of Biosolar Resources Vol. H (Edited by O. R. Zaborsky, T. A. McClure and E. S. Lipinsky). CRC Press, Florida (1979).