This article was downloaded by: [Florida Institute of Technology]On: 20 August 2014, At: 23:11Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Environmental Technology LettersPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tent19

Optimisation of sludge anaerobic digestionby separation of hydrolysis‐acidification andmethanogenesisC. Perot a & D. Amar aa Laboratoire Central de la Lyonnaise des Eaux , 38, rue du Président Wilson, 78230, Le Pecq,FrancePublished online: 17 Dec 2008.

To cite this article: C. Perot & D. Amar (1989) Optimisation of sludge anaerobic digestion by separation ofhydrolysis‐acidification and methanogenesis, Environmental Technology Letters, 10:7, 633-644

To link to this article: http://dx.doi.org/10.1080/09593338909384780

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in thepublications on our platform. However, Taylor & Francis, our agents, and our licensors make no representationsor warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions and views of the authors, and are not theviews of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor and Francis shall not be liable for any losses,actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoevercaused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Environmental Technology Letters, Vol. It), pp. 633-644©Publications Division Selper Ltd., 1989

OPTIMISATION OF SLUDGE ANAEROBIC DIGESTIONBY SEPARATION OF HYDROLYSIS-ACIDIFICATION

AND METHANOGENESIS

C. Perot* and D. Amar

Laboratoire Central de la Lyonnaise des Eaux,38, rue du Président Wilson - 78230 Le Pecq (France)

(Received 24 April 1989; in final form 12 June 1989)

ABSTRACT

In the following study, a two-phase anaerobic digestion with an optimisedhydrolysis-acidification reactor was studied in comparison with a single-stepdigestion of municipal mixed sludge. The results of the two processes were comparedby using the statistical test of BEHRENS-FISHER. The advantages of the two-phasedigester were the following : -Faster steady-state conditions, they were reachedafter 45 days instead of 75 days for the single-stage process. - Greater eliminationof volatile suspended solids (degradacion of 60 % instead of 40 % ) . - Decrease ofthe retention time by a factor two (11,6 days instead of 25 days).

INTRODUCTION

In order to provide better environmental protection, wastewater treatment methodshave become increasingly effective. However, for a given volume of effluent, sludgeproduction is gradually increasing. Consequently, sludge treatment costs are alsorising. As a result it has become necessary to improve organic matter degradationefficiency. One commonly used treatment method that can be applied to achieve thisaim is sludge anaerobic digestion. It stabilises the sludge while degrading 40 % ofthe organic matter and produces methane gas that can be used as a local source ofenergy. It is a relatively slow process that generally takes 20 to 40 days in asingle step at 37 °C.

The limiting step in this process is the hydrolysis of complex organicmacromolecules (1). Some authors have already demonstrated the advantages to bederived from separating the digestion into two phases : hydrolysis-acidification andmethanogenesis. Through this separation, it is possible to :

- increase the degradation of volatile matter and produce a greater quantity of gas(2) as well as better stabilisation of the sludge ;

- reduce digestion time (3), and so reduce the size of reactors.

However, the limiting factor in organic matter hydrolysis has never been optimisedin the case of wastewater treatment sludge.

The aim of this study was to compare the efficiency of the anaerobic digestion ofmixed municipal sludge in two steps : hydrolysis-acidification and methanisation,with a single-step digester under conventional operating conditions. Each step inthe two-step digester was operated under optimum conditions. A previous study haddetermined the most favourable conditions for the hydrolysis-acidification step (4).

633

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

They were the following : 50°C, pH 6.8, agitation speed : 545 rpm. During thefollowing test, the start-up-periods for the two processes were compared and theirefficiency analysed according to the various conventional parameters used formonitoring anaerobic digesters.

MATERIAL AND METHODS

1. Reactors

This study was carried out in completely mixed laboratory-scale reactors.

The two-step process (Figure 1) had two reactors connected in series :

- a fermenter with a net volume of 1.6 litres for the hydrolysis-acidification step.The pH was set at 6.8 by the automatic addition of NaOH IM, the temperature wasset at 50°C and the mixing speed at 545 rpm. Retention time was 1.6 days ;

- a fermenter with a net volume of 5 litres for the mèthanisation step. The pH wascontinuously measured but not adjusted, the temperature was set at 37°C and themixing speed at 300 rpm. Retention time was 10 days.

The single-step process (Figure 2) had a 10 litre net volume reactor. Theexperimental conditions were the same as those for the mèthanisation reactor exceptthat the retention time was 25 days. This latter retention time is the one which isusually used for the single-step anaerobic digester of sludge (5).

Figure 1 - Two-step process

Agitation speed :300 rpm

pH regulation" (pH:6.8)pH meter

Agitationspeed

545 rpm

pH meter

Inlet—>

Temperatureregulation(50TJ

h <

oo

pulse-melerfor gas

production

Retention time1.6 days

OO

CO

do

_ Temperature regulation37'C

pulse-meter(or gas

production

Outlet

Retention time:10 days

Hydrolysis - acidification step(net volume : 1.6 1)

Methanogenesis stepNet volume : 5 litres

634

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Figure 2 - Single-step process

Agitation speed : 300 rpm

IpH meter—i

Inlet v

Temperature—regulation

|(37-C)| OO

ooCO

-»Outletpulse-meter I

Retention time :25 days

| Net volume : 10 litres [

2. Substrate

Each reactor was supplied once a day with mixed sludge (mixture of primary andactivated sludge), for 130 days. The feed sludge came from the "LES MUREAUX"municipal wastewater treatment plant.The feeding and the withdrawing were realized manually with a peristaltic pump.The hydrolysis-acidification reactor was fed with 1000 ml of mixed sludge per day.The methanisation reactor was supplied once a day with the half of the hydrolysedsludge volume which came out from the first reactor : 500 ml.day-1.The single-step digester was fed with 400 ml.day-1 of mixed sludge.

3. Analytical methods

Every day or every second day, 20 ml of the sludge in each fermenter and the rawsludge were sampled and centrifuged (13 000 rpm) for 10 minutes.

Total suspended solids (S5) and volatile suspended solids (VSS) determination

The layer of centrifuged sludge was dried in a silica crucible at 105°C for 24 hoursand then weighed (suspended solids). The sample was then burned at 550°C for twohours. The concentration in volatile suspended solids or volatile matter wasobtained by calculating the difference between the total suspended solids and theweight after incineration.

Measurement of total organic carbon (TOC)

The TOC was measured usingcentrifuged sludge.

a TOCmeter (BECKMAN 915 B), in the liquid phase of the

635

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Determination of volatile fatty acids (VFA)

The VFA concentration was determined by gaseous-phase chromatography (CARLO ERBAVEGA 6300) of the soluble phase of the centrifuged sludge. The two-metre glasscolumn was filled with Chromosorb. The vector gas was helium. The flame ionisationsensor and the injector were at a temperature of 250°C. The temperature of the ovenincreased during the analysis from 120°C to 140°C at the rate of 2°C min"1.

The VFA measured were acetic, propionic, butyric and valeric acids.

In order to differentiate the fraction of VFA from the total organic carbon, theTOCvfa was calculated for each sample by adding the various concentrations of VFAmultiplied by their respective percentages in carbon.

Gas volume and composition

The volume of gas produced during 24 hours was measured using a pulsemeter, eachpulse corresponding to a given quantity of gas and its composition was determined bygaseous-phase chromatography (PACKARD 627). The 2-metre stainless steel column wasfilled with Porapak R. The vector gas was argon. The temperature of the oven and theinjector was maintained at 30°C. The detector, a catharometer, was maintained at atemperature of 400°C.

The various measurements were used to compare the two systems of digesters. In orderto check their efficiency, the mean figures for each parameter were processed instatistical form.

4. Statistical processing of the results

The means (m) of the parameters measured at the steady state were calculated fromthe last 20 to 50 days operation of both systems. In order to highlight thesignificant differences between the means obtained in these two tests, theBEHRENS-FISHER law as tabulated by DARMOIS was used (6). It is possible with thistest to compare samples with large variations. For this test, the hypothesis thatthe mean for each statistical group is the same is given. The reduced variable is asfollows :

m. — nu

where :

120nP

V

single-step digestertwo-step digesterthe reduced variablethe number of experimental pointsthe level of the testthe variationthe number of freedom degrees

The limits of acceptance interval for 0 at the level P = 0.10 and Vj =» 25,V2 = 10, are +/- 2.74.

RESULTS1. Start-up period

Two-step digester

At the end of five times the retention time, the steady state of the hydrolysisreactor was reached. Hence, at the end of a week, it was possible to start supplyinghydrolysed sludge to the methanisation fermenter. The latter was first seeded withtwo litres of sludge from a municipal sludge digester.

636

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

It can be seen in the curve showing the VFA degradation in the methanisation reactor(Figure 3), that the concentrations in acetic, butyric and valeric acid decreasevery rapidly In twenty jdays operation, these three acids represent a totalconcentration of 285 mg.l . In the other hand, the concentration of propionic acidincreased up to the thirtieth day of testing and then decreased to a stable level of50 mg 1 at the end of 45 days. A reduction in the pH to 6.0 in the methanisationreactor was observed at the same time as a decrease in degradation of the propionicacid (Figure 4). Then the pH increased again to an average of 6.9, obtained after 30days testing.

The steady state of the two-step digester was reached after 45 days operation.

Figure 3 - VFA degradation during methanogenesis step

2000

ActtlcPrtploifc tcMBitirtc tcUYtltric tcU

20 50 40Time (da?*)

Figure 4 - pH value and propionic acid concentration during start-up periodof methanogenesis fermenter

2000

Xa

10TIME (days)

637

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Single-step digester

Figure 5 shows that the VFA are fairly quickly transformed in this reactor (20 days)with the exception of propionic acid, the quantity of which did not exceed theincoming flow for up to 75 days operation. Then, the concentrations of VFA stabiliseat an average level of 122 mg of C.I-1. The pH measured periodically stabilised at.about 7.0.

Figure 5 - VFA degradation during one-step digestion

2000

"". 1000 -

Acttic »ci4Prtpitiic »cidBwtjric »cUYtlerie « id

20 30 40 SO 60 70 80 90 100 110 120 130TIME (days)

The steady state for the single-step digester was reached after 75 days operation.

2. Comparison between incoming substrate in both processes

The mean values and the standard deviations obtained for each of the parametersmeasured at the inlet to the single-step digester and the hydrolysis-acidificationfermenter are listed in Table 1. The calculation of the' reduced variable has made itpossible to determine whether these values were significantly different.

The concentration of volatile matter in the sludge as well as the means for thepropionic and valeric acids were signicantly different at the inlet to the twoprocesses. This is due to the fact that the means were not calculated with the samenumber of experimental points.

The soluble TOC concentrations were, however, similar at the inlet to bothdigesters.

The standard deviations are sometimes quite high because of the considerabledifferences in the quality of the sludge used.

638

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Table 1. Average values and standard deviations for the various parametersmeasured at the inlet to the two different digesters

Concentration ofvss (g.l-1)

Concentration ofTOC (mg.I-1)

Concentration ofTOCvfa (mg.l-1)

Concentration ofacetic acid(mg.l-1)

Concentration ofpropionic acid(mg.l-1)

Concentration ofbutyric acid(mg.l-1)

Concentration ofvaleric acid(mg.l-1)

1-step cMean

15.7

1022

809

517

814

186

179

ligesterStandarddeviation

2.2

450

407

185

502

69

113

2-step cMean

22.2

844

659

626

488

230

89

îigesterStandarddeviation

3.7

131

105

106

96

50

17

3. Comparative efficiency for the two processes

Table 2 gives the mean values and the standard deviations for the various parametersmeasured at the outlet from the two types of digesters as well as from the outletfrom the hydrolysis-acidification reactor.

The reduced variable was calculated in order to compare the means obtained at theoutlet from the two processes.

Degradation of volatile matter

According to the reduced variable calculated from the average concentrations of VSS,the latter does not differ significantly at the outlet from the two reactors. Theretention time is shorter in the two-step reactor and the concentration of volatilematter at the inlet is higher than in the single-step process. The two-step processtherefore is more efficient and faster than the single-step one.

639

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Table 2. Mean figures and standard deviations for the various parametersmeasured at the outlet from the two types of digesters

Concentration ofVSS (g.l-1)

Concentration ofTOC . (mg.I-1)

Concentration ofTOCvfa (mg.I-1)

Concentration ofacetic acid(mg.l-1)

Concentration ofpropionic acid(mg.l-»)

Concentration ofbutyric acid(mg.l-1)

Concentration ofvaleric acid(mg.l-1)

Gas production(ml)

COj content (%)

CH4 content (%)

Total gas yield(1.kg-»VSS at inlet)

Total CH. yield(1.kg-1 VSS at inlet)

1-step c

Mean

8.4

175

122

123

97

25

24

2491

ligester

Standarddeviat.

1.1

37

45

50

52

19

13

961

30

70

395

277

FirstMean

18.2

2366

1820

1453

1027

867

454

537

2-step c: stepStandarddeviat.

3.0

472

409

358

226

193

120

126

65

35

24

8

iigesterSeconc

Mean

9.0

378

113

89

84

42

23

3904

i stepStandarddeviat.

1.0

55

49

34

61

13

9

792

26

74

429

317

The VSS degradation yield obtained from the respective concentrations are given inTable 3. These yields are significantly different in the two processes. They- showthat the two-step digestion results in a greater level of organic matter removal inhalf the time required in a single-step digester.

The hydrolysis-acidification reactor only removes 20 % of the incoming VSS, but thisstep promotes their degradation later in the process : 50 % of the VSS is degradedin the methanisation reactor.

640

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Table 3. VSS degradation yields obtained at the outlet from the various reactors

Degradation yield (%)

Hydrolysisacidification

20

Methanisation

50

2-stepprocess

60

1-stepprocess

40

TOC and VFA degradation

The reduced variable calculated from the results given in Table 2 show that the TOCconcentrations are not the same at the outlet from the two processes. At the outletfrom the two-step digester, the soluble TOC concentration is about twice that at theoutlet from the single-phase digester.Hence a part of the soluble TOC produced during the first phase is not degraded inthe methanisation reactor.

If the mean VFA concentrations are taken into account at the outlet from the twoprocesses, only the concentration of butyric acid is higher at the outlet from thetwo-step system. The other VFA are present at the same concentration in the twooutflows. However, no significant difference was observed between the meanconcentrations of TOCvfa at the outlet from both processes.Whether the digestion takes place in one or two steps, the efficiency in thedegradation of VFA is similar. However, this degradation can be achieved in 10 daysinstead of 25 in the two-phase system.

The hydrolysis-acidification step promoted the production of 1.5 g.l-^d-1 ofsoluble TOC. A fraction of the soluble TOC is used in the methanisation reactor. Atthe outlet from the acid-generating reactor, VFA account for 75 % of the TOC. TheseVFA are then degraded during methane production and the soluble TOC at the outletfrom the two-step process then only contains 30 % of VFA whereas it was 77 % of thesoluble TOC at the outlet from the single-step digester. As the various VFAconcentrations at the outlet from the two processes are very or totally similar, theexcess TOC measured at the outlet from the methanisation reactor must be largelycomprised of the soluble products of hydrolysis not transformed into VFA. Theseproducts were not determined in this study.

Gas production • • • •

The total production of gas at the outlet from the two-step digester issignificantly higher than that from the single-phase digester (35 % more). However,if this production is expressed as yield (function of the incoming VSS content),, thequantity of gas is virtually not different from one system to the other and theproportion of methane gas produced is virtually the same (see Table 2).

The hydrolysis-acidification reactor provides a low emission of gas composed largelyof carbon dioxide. However, 35 % of the gas produced is methane. The methanogenicbacteria are the only ones with the coenzyme F 420 in their cell wall. The latterdevelops a blue-green fluorescence when subjected to UV rays (7). Observation undera microscope of a sample of sludge taken from the hydrolysis-acidification reactorrevealed a large quantity of fluorescent methanogenic bacilli. The bacilli are thespecies that can utilise a mixture of VFA and hydrogen as a substrate (8). As thepercentage of hydrogen detected in the acid-producing reactor gas was always lessthan 1 %, the methane produced during this step was essentially due to the activityof hydrogenophilic bacteria.

641

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

4. Partial conclusions

- An adaptation period is required in both digesters for the propionic acid to bedegraded. However, a two-step digester reaches its steady state faster than asingle-step digester.

- Considerable solubilisation of the VSS is observed in the two-step process andtakes only half the time required in the single-step digester.

- The production of gas is virtually the same in both processes even though agreater proportion of the VSS is degraded in the two-step system. Theconcentration of soluble TOC is therefore slightly higher at the outlet from thelatter system.

INTERPRETATION - DISCUSSION

During the start-up phase for both processes, certain difficulties were encounteredin the degradation of propionic acid.Hydrogen was not responsible for this accumulation as it was never detected in thegas from these reactors.The pH measured in the methanisation reactor dropped at the same time. This decreaseis not due to an excessively high concentration of the other volatile fatty acids inthe fermenter. Their concentration, in particular that of acetic acid (3 mmoles),never reached a level that would inhibit the degradation of propionic acid. Kasparet al (9) quote 80 mmoles of acétate as being an inhibiting level. This decrease ofthe pH does not, however, disrupt the acetoclastic bacteria that continue to degradethe acetate and the gas production is not interrupted. .Only a decrease in the buffering power in the hydrolysis-acidification reactor couldhave caused a reduction of the pH in the methanisation reactor. This hypothesis has,however, not been verified.

Propionic acid is only efficiently degradad after a more or less lengthy period ofadaptation of the methanogenic bacteria in both types of reactors. This start-upperiod is however shorter when the methanisation is separated from the hydrolysis-acidification step.

The limiting factor in the first step of anaerobic digestion of sludge is thedegradation of the complex organic macromolecules (1,10). Eastman et al (11) hadsuggested placing this step under optimum operating conditions so as to improve thedegradation of organic matter. Lawler et al (12) demonstrated that the first phasein a two-step process fostered a decrease in the size of organic particles and sotheir hydrolysis. The improvement of VSS degradation obtained in two-step anaerobicdigestion of sludge is 40 to 55 % (2,13). The two-step process presented in thispaper promotes degradation of 60 % of the VSS. This higher value was obtained fasterthan in the single-step digester. The first step placed under optimal operationconditions made it possible to reduce digestion time while rendering the organicmatter in the sludge more accessible to the methanogenic bacteria in themethanisation reactor.

After the two-step treatment, the sludge liquid phase has a higher concentration ofsoluble carbonaceous products than in single-phase digestion. The hydrolysis of theorganic matter in the first step produces soluble compounds only part of which aretransformed into VFA. This is due to the operating conditions in the hydrolysis-acidification reactor (4).The higher soluble TOC content at the outlet from the two-step system explains whythe production of gas is hardly any greater despite the improved degradation in thisprocess.

642

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

Table 4. Gas production according to various authors

4a. Gas production (ml.g VSS at inlet-1)

1-step digestion

2-step digestion

Ghosh (2)

320

592

Demharteret al (14)

496

428

Speece (15)

460

Test results

395

453

4b. Methane production (ml.g VSS at inlet-1)

1-step

2-step

digestion

digestion

Ghosh (2)

225

410

Lawler et al

440

510

(12) Test results

277

325

The results obtained for gas production in this study are quite similar to thosereported by various authors (Table 4). Only Ghosh (2) noted a distinctly higherproduction of gas from sludge digestion in two mesophilic steps. Overall, thequantity and the quality of the gas produced is not affected by the separation ofthe acidogenic and methanogenic phases : the production of gas is linked to thequantity of biodegraded organic matter.

CONCLUSIONS

In comparison to a single-phase digester, anaerobic digestion of mixed sludge in twooptimised steps presents several advantages :

- the start-up period is not as long (45 days instead of 75 for a single-stepprocess),

- the volatile matter degradation yield is higher (60 % instead of 40 % ) ,- the retention time can be half as long without modifying the effectiveness inchanging volatile fatty acids into methane. However, the production of this gas isvirtually no greater than that in a conventional reactor.

The anaerobic digestion of sludge in two separate reactors makes it possible totreat a larger volume of sludge in a shorter time and therefore the structures neednot be as big.

Despite the need for greater heat in the first reactor, it is still advantageous todegrade an extra 20 % of the organic matter. This study has, therefore, demonstratedthe advantages to be gained from optimising the limiting step in anaerobic digestionof sludge in order to increase the degradation efficiency.

REFERENCES

1. L. DE BAERE and A. ROZZI, Trib. Cebed., 484, 37, 75-81 (1984).2. S. GHOSH, J. Envir. Engng. Div., 113, 6, 1265-1284 (1987).3. N.J. DICHTL, Wat. Sci. Technol., 19, 7, 1247-1250 (1987).

643

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014

4. C. PEROT, M. SERGENT, P. RICHARD, R. PHAN TAN LUU and N. MILLOT, Envir. Technol.Lett., 9, 741-752 (1988).

5. W.W. ECKENFELDER, Tec. et Doc. Lavoisier, 1-503 (1982).6. A. VESSEREAU, Tec. et Doc. Lavoisier, 1-539 (1988).7. M. TAYA, N. AOKI and T. KOBAYASHI, Appl. Microbial. Biotechnol., 23, 342-347

(1986).8. C.Y. LIN, K. SATO, T. NOIKE and J. MATSUMOTO, Water Res., 20, 3, 385-394 (1986).9. H.F. KASPAR and K. WUHRMANN, Microbial Ecology, 4, 241-248 (1978).10. S.G. PAVLOSTATHIS and J.M. GOSSETT, J. Envir. Engng., 114, 3, 575-592 (1988).11. J.A. EASTMAN and J.F. FERGUSON, J. Wat. Pollut. Control. Fed., 53, 3, 352-366

(1981).12. D.F. LAWLER, Y.J. CHUNG, S.I. HWANG and B.A. HULL, J. Wat. Pollut. Control.

Fed., 58, 12, 1107-1117 (1986).13. S. GHOSH, J.R. CONRAD and D.L. KLASS, J. Wat. Pollut. Control. Fed., 47, 1,

30-45 (1975).14. W. DEMHARTER and W. PFEIFFER, Fifth International Symposium on Anaerobic

Digestion, May 22-26, Bologna, 699-701 (1988).15. R.E. SPEECE, Water Res., 22, 3, 365-372 (1988).

644

Dow

nloa

ded

by [

Flor

ida

Inst

itute

of

Tec

hnol

ogy]

at 2

3:11

20

Aug

ust 2

014