p.1 

OAR Box 1413 

Prepped by Ollie Stewart 

Document Number: 

111)11-1-112 

Docket Number: 

A-94-52 

Printed 7/9/2008 3:11:25 PM Sheet 111 of 114 
7W":\ 

try wr 

BS96-58 

Evaluation of Source Reduction 

Through Modeling of Batch Production Processes 

In the Coatings and Composite Plastics Industries 

David J. Lipiro 

SeanM. Hays 

EdmundS. Golpashin 

- MoLioron/IUit JStiEvhomuautid Eiigiiiegrhig Cuipotai}ion 

•29225 Chogrih Boulevard, Suite 300 

Ctovcloiid, Ohio AMtlMW 

6^ ^«cWl1 ^ CouCe/e-AC^

 ; ^WH ^ t°7?^ 

< & 

EPA-AfRQOCKET * . 

ABSTRACT 

Many companies have implemented or are considering various methods to

 vclosen

 processes 

or othenvise suppress the generation of VOC emissions, rather' tbaii install expensive back-end 

controls. Producers of solvent'laden coatings and styrenated composite plastic molding compounds 

have adopted sueh measures as^ covering open mix tanks, modifying material transfer systems, and 

modifying vapor collection systems to minimize swept gas volume. 

One impediment to the use of these measures is the difficulty in predicting the rate of VOC 

generation in the highly variable batch processes that typify these industries. Such information is 

needed to optimize tlie design of modifications, and to document the associated emission reductions 

with sufficient rigor to satisfy regulatory agencies. 

This paper will present models of VQC emission generation from batch mixing and 

subsequent operations. Realistic examples will be presented illustrating the application of these 

models to the production of paints and the production and use of composite plastic molding 

compounds. The need for additional field verification data will berdiscussed. 

INTRODUCTION 

Pollution prevention (source reduction), whereby the-generation of air emissions is reduced at 

the source, is widely touted as more desirable than the control of resulting emissions downstream of 

the source. Indeed, many companies in the coatings and composite plastics industries have 

implemented a variety of source reduction methods in lieu of or in conjunction 'with downstream 

devices to control air emission bf volatile organic compounds (VOCs) and hazardous ait-pollutants 

(HAPs); 

One impediment to die use of such methods is the difficulty: in predicting $he*ate of VOC 

generation from the highly variable batch processes that typify thes*e industries. Without such data, 

it is difficult to properly optimize the design of process modifications. It is also impossible.to 

document the associated emission reductions to regulators. 

The latter problem is particularly crucial to sources in the coatings and composite industries. 

Both are potentially subject to the technology-based emission standards, which are typically imposed 

after consideration of the cost expended per ton of reduction achieved. 

For example, major VOG sources (potential emissions exceed IOO tons/year) may be 

required to implement Reasonably AvailableControfTechnology (RACT), RACT 4s Customarily 

defined as the most effective emission reduction measure costing less than $3,000/ton of pollutant 

reduced. If process emissions are estimated-based upon "guesstimates" or published "average" 

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emission factors, RACT could be mistakenly imposed, or the wrong reduction optioti Selected as 

RACT: '. r^ryl''-' 

This problem is compounded dueto upcoming regulations requiring Maximum Achievable 

Control Technology (MACT) for major sources of HAPs. MACT standards wi|l; $£:i&$$d• iipon the 

average level of emission reductions provided by the top ;12% ^controlled sources^|^^d1aist;ry 

(source category) for which the standard will beissued. Companies nustakem^E%,|^f^^;i^CT 

controls or installing RACT controls that do not optimize cost--efficiency wiU ady^ply:^ia!s;Ethe 

MACT •determination. • ••:;'^••%:•••: 

This paper summarizes work dpne by the authors for various private comp^ei in the 

coatings and composite plastics production industries, and for the Society of Plarti^Indusiries (SPI) 

Composites Institute. The process models presented herein were developed to p^yi^ffeettei::; 

engineering estimates of VOC emissionsE Due to project scope limitations, they:|h^sjn;otbeen 

calibrated or verified. The authors proposesto conduct calibration/verification st^mfs^liic^i^ 

described in .this paper. • ''•r^jyrr '•?•".]".- ' •,.''' 

PROCESSES CONSIDERED 

Production of coatings (paints, colorants, and adhesives) typically involyeSl^Jhigh^hear 

mixing of solvent-laden polymer resin mixtures with other ingredients, includingis^ivihtssuch as 

toluene, xylene, and hexane. Production of composite molding compound simil^^a^oryes^nighshear mixing (blending) of monomer-laden polymer resin mixtures withi other ing^^iiti iaiid 

additional mpnpmet. The most widely used monomer is styrene. y i££ 

Coatings and paints generally:require little or no additional processing beyond ^ mixing 

operation. Further processing is; required in the composites industry: For instance^Cprtj^ianies that 

produce parts in closed molds must combine the paste resulting from the blenduiig^j^^io'^;'iivith 

the composite fiber (usually chopped fiberglass), form the mixture into a sheet ojr ^fc:shariJe;, and 

wrap it in a carrier film to retard the loss of styrene. This process is termed coW^^^ing:VThe 

resulting sheet (SMC) or bulk molding compound (BMC) is unwrapped, cut to fii'0tm$t.and: either 

injection- or compression-molded. During molding the styrene crosslinks with r^sirifpiSly/m^^ 

forming a matrix within which the fibers are embedded. Prior to molding, the wrap|»e| compound is 

often allowed to age (mature) in storage,! during which partial crosslinking occurSi^i; ;>: s ^ : 

—^ Storage Tank Emissions 

In both industries, VOC liquids are typically stored in bulk and dispense^^^^t o the 

shop floor. Emission occur when the v^por space of the tank is displaced, eithet;:'^h^.j^<gli'it£khk'.. 

filling (working losses) or thermal expansion (breathing losses).. &$•&.%.'*'•'•', 

A common source reduction method in both industries isthe installation of t^ri^e^atipn 

vents on storage tanks. A conservation vent is analogous to a low-pressure reUef ^v^E^^ese ' 

relatively inexpensive devices are installed Pn the tank vent, and are set tp releasie;^^%h^-tank 

pressure exceeds a low value (often no more than 25 mmHg oriO^Epsig). This dpe^^t:ifl&jtfere 

with tank operation, but eliminates thermal expansion losses associated With tempeiatiiife increases of 

:.: ' up to io°c (i9°F). -,yr;'

:

y..t: 

The source reduction can be calculated based upon the widely used empirical model •; 

developed by USEPA and published in AP-42 (Reference 1). As ^ri example, con^&ir^^tfttshly 

painted 10,000 white vertical tanks, one containing toluene; and the other styrene;: JV^ * 

'••l 

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ES96-58 

The breathing losses eliminated can be calculated as follows: 

.Breathing lasses = 2.26 % KT2 Mv 

t p \o,« 

,P. -P. 

^1.73 #0.51 jO.5 pp&K \ (D 

Where: 

Mv = . Molecular Weight, 92.1fpr toluene*.104.2 fbr styrene ; ' -

P = Atmospheric Pressure* 760 mmHg 

Ptt = True Vapor Pressure, 20 mm/Hg for toluene, 5mmHg for .^yjrtSrie . 

D = Diameter, assume 9.75 ft E \ 

H = Height, assume 18 ft 

T = Diumal Temperature Ran^e, assume 10 C 

FP = Tank Paint Factor, 1.0 for whitetanks 

C = Adjustment Factor forSmall Tanks, 049for this size tank 

Kc = Product Factor, 1.0 fbr toluene and styrene 

The source reduction attributable to the installation of a conservation vent oni-10,000 gallon 

tank of toluene is 20 kg/yr (44 lbs/yr). For a 10,000 tank of styrehe, the corresponding source 

reduction is 8.6 kg/yr (19 lbs/yr). «—"r>us'''V* «icto<clU <* sU<jU*f o^reSTitMitfe ; 

Stirvce tovxy^o^iiJ^ \Rc»i$ cio iA:oEt"el**o»v*.'t<«? 

Mixing (Blending) Emissions b^-eutfi.^j l^5e s ^.e^h^ly * <- ^•U^j*¥rq't/i*'/t>&. 

Mixing of coatings and compound paste isbest envisioned as a three step process;.;\ 

1) Mix vessel filling 

2) High-shear mixing 

3) Batch transfer to next process : • ^ 

In the coatings industry, mix vessels (often referred tP as Aspereers) may .hoHoVer several 

thousand gallons. Such stationary vessels may be manifolded to one or more letdown tanks, from 

which product is dispensed to filling stations. In the composites industry, such mbcgrs aire smaller; 

often the mix vessel is carried by lift truck to the compounding lines, where the folefltjed paste is 

consumed. .

 : " 

Because the composite compound paste operation is more complex, it hasibeen used as an 

example. Emission estimates before source reduction are derived for each operationi ^id the impact 

of potential source reduction methods is described. Based upon thei authors' experience, the process 

cycle times and other operating assumptions used in this paper are reasonably typica^, ^ . 

M i * Yftfffil ffin

g Consider open cylindrical mix vessel 1.22m"(48") in^JS^tr and 

1.22 m high, that can be filled within 6:6 minutes to 1 ;0m. The volatile ingredient^..styrene, is 30 

% by weight of the mix. 

We assume that the styrene in displaced air from the vesselis weti-mixed aricSI uustatic 

equilibrium with the styrene in the underlying liquid. This is conservative but intuitively 

reasonable, considering that raw materials are often splash-loaded. 

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On this basis, vessel filling emissions can be calculated as; 

c NAP VAW <yr</:

 •.,-,.•• ,, . 

E r = — •-• 1— : •• •-•••••:•%•:•::.::.•••. . . W 

'••• * r yr.y- rr . 

Where: 

Er == Emission Rate g of Styrene /Batch ofPaste yj-i yfN - Number of Effective Vapor Spaces Removed Per Batch, ' as^ta&<;%E fc 

A ='• ActivityCoefficient of Styrene in Paste Mixtures, assume :#^s" ; 

P = Vapor Pressure (5,0 mm Hg) '.-.. ; i.yySj:i'.-E 

V = Displaced Volume (1.168 ni3) • ''l :^ y y 

MW = Molecular Weight of Styrene (104l2 g/g^moi) vE^s';;:' 

R .=. Gas constant (6,0624mm Hg m3/g-molK) -':y

:

yy

:

'-••''' 

T ' = Temperature (298 K) '}$»%?:?:'•+•'' 

The factors N and A are seldom considered. For example, Reference 2 oririitSvj$thvtfctiris in 

its formula for calculation of filling emissions, implyingthat the vapor space is ^j^i^tedi(A«sl) and 

the emitted volume consists entirely of a single displaced" vapor space (N=l). Giv ^ EtKese • 

assumptions, resulting batch emissions would be 32,7 g (0.672 lbs). Assummg-^fi|i^jfc;hies: 

produced per shift (48 batches per day) total filling emissions would be 3.46 Ibi^i^jf^^i^listi c 

are these predictions?" • s:;E;''!R

:

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'4': 

The assumption that A« l holds for ideal gases in equilibrium with ideafl^isttifls^ •Mixtures 

of resin polymers with a miscible, reaclive monomer (styrene) and relatively hi^|^ire1iS;6fSplids 

are at face value norHdeal, which could markedly lower A. Lab data should b^oH^cte|(I:id;' 

determine A, or it should be estimated based upon solution thermodynamic conoj^^y^UpH assthe 

Flory-Huggins theory (Reference 6). 'rr.h: 

For covered, unswept vessels, the assumption that N- 1 is invalid if air fro^n: oiitsid*e the 

vessel is dragged inside (induced) by the liquid stream being loaded. Tightly seale^orEliaril-'piped 

charging lines would eliminate induction: Fpr highly yehtilated open or swept c.io^^ssets^'N > 1 

and the static equilibrium assumption becomes untenable.Hather, a new dynamics^ui|ibnum may 

be attained, at an exhaust gas concentration lower that the static equilibrium concehtiatibn, such that 

the mass transport of organic eompouncbacross the liquid-vappr interface in theiv¥^pis((^ua | to the 

mass transport of organic compound out of the vessel. 

A simplistic view of this process would relate liquid/vapor mass transport ^^i % residence 

time of introduced air in the vessel. The mass transport race function could be ini^i^ti^^y^ r the 

residence to determine the vapor mass released to the introduced air by the time it ^ejfl^usted from 

the vessel. The mass transport rate function must be derived to apply this approach Several methods 

to do so are proposed in later sections of this report i-°L:^y 

Whatever their magnitude, mix vessel filling emissions could be «limina^:^itni^ry^biy 

tightly closing the vessel and providing vapdr return (balance) lines from the vess^lb^]|^;tli e raw 

material storage tanks. This method is unworkable in practice if the mixed vapo^!nf;3|i^s^eturii line 

would contaminate any of the raw materials separately stored. s ••$:; i-s 

Mixing. Assume thatthe resulting batch must be mixed for 18 minutes. J$S< ^ 

mixing is required, we conservatively assume that the displaced vapor styrene cohee^ti^tion' will be 

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ES96-58 

near static equilibrium levels, which we further assume to be full saturation.as lbrig^the"': 

superficial velocity of ventilation air is not excessive: Based upon the authors' ob-ie^^phs/it is 

possible for mixing to increase the temperature of the paste by 20' C, which woiil|^iiTC?ea5e::the 

vapor pressure by a factor of four.. •• .-:••.:•'£*.'*,'•'•• 

Reference 2 provides guidance that for swept vessels, saturation can be c.^se^^tiyely: 

assumed if the ventilation flow rate does npt exceed 100 acfm, where the the vejs^yiipDr; spajce 

displacement rate is assumed to be equivalent to the ventilation rate. This is an e^t-fetniiiiy 

conservative assumption for an open mixer with nearby spot yentilktion, wMch fe ikvf^ical s 

equipment configuration in this industry. Only a fraction of the ventUation streamiis|E^wn 

(entrained) frpm the vapor space; the remainder is drawn from; surrounding air.iE ^ ^th e 'i 

entrained vapor space is; nearlyE saturated, the ventilation exhaust is substantially-'Ediiuted;; , 

Using the mixer configuration previously given, the vapor space above the Eliquid;ls:'; 

approximately 0.2 m3. If one vapor space is removed (entrained) per minute, :3;6i||^^^wrate d 

vapor will be removed per batch, or roughly 400 g Of styrene: (see eq.2). At 48.i^^^'-.':jpeEf:'.day , 

total emissions would be 19.2kg (42.2 lbs/day). .•.•Y-Y^>':V .:'•''•.•• ' 

This result is an example, not an estimate. The assumption that the vapor^^die- is saturated 

is subject to the same objections described in the previous section. Furthennore,sd^;on;iy*ipor space 

entrainment were not available for this study. The accuracy of this method dependsseritically on 

such data, which could be obtained through carefully designed field;studies. -

:

r-y

:

r 

Mixing emissions could be reduced by closing miji vessels. During mixing*;t^pnly'••.,' 

emissions would be then be the organic mass in the vapor space displaced due to:,ti|e'ii|^f 

expansion. ' r-iiyy?-:. ''*.' 

Batch Transfer Emission*!. During this step, opeiv mix vessels are moveid^cbiifipqunding 

lines, and puitiped out gradually to feed the lines. Assume that this process tak^krMs ^ 

batch. Emissions could be calculated Using either of twb independently derived.ih^ESiEtfaiispoirt rate 

functions.'

 i •';•;'"":• ^v-E;; ^ >-, 'E. 

Funcition I is derived from a mPdificat ion of the Mackay-Matsugu empirical'procedure 

(Reference 3) to estimate of emissions from ai quiescent pool of volatile liquid, adapted1 perE, ' 

Reference 2. Emissions can be calculated as follows: •/^yyy^r-r 

Er=QM5 MWV U°-n D1^ vH^-^' • (3)' 

, . ; RT :. ••:,; ''•yyy-'^-' 

Where : .••-.; • • •'# $ '•/•':; •';"••• 

Er = . . Emission Rate ^ g/hr ' ;' Y 1 •ivss'';-v'': • 

MW • =» Molecular Weighty 104.2 for styrene 

V . = Vapor Pressure, 5 mm Hg for styrene :''->'sv';T '(y•'•'••.'• 

R =. Gas Constant, 0.0623 mm Hg m3/gTm6fKs ;;;••••-••.< 

' T • ••=.• Temperature , 29 8 K /••l^ff--}]7rS 

U ' - . Gas Velocity at the Liquid Surface, 50 m/ht 

D = Vessel Diameter, 1.22 m ,2^i ^ 

FOr the vessel configuration previously considered, assume that U is 50 m/hpi $iisminimal 

surface airflow is considered conservatively realistic, because high capacity spot^i^Sibn Is 

generally not provided over these vessels. On this basis, styrene emissions would^e'f^attiiv; At 48 

batehes/day, emissions would total 336g, or 0.74 lbs/day. 

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Function 2 is derived based on a mass transfer model of the diffusion of s^ren ^ through 

stagnant air within the vessel, and into a pool of air with infinite capacity to ab,spr^s^yretie, but. 

without convective mass transfer. The air at the liquid surface is assumed to beVs^irated.; 

Emissions can be calculated as follows: i'.-:*'..'. • 

Er = 3.6£7» MW :» A-. *

 Da P * In 

RTdtvmf (f - ^|fES'S> : -: ;(4), 

Where: 

Er = Emission Rate, g/hr .':Vs.v }^:y 

A' .• = • Liquid Surface Area, m2 . sEE'VsE: ;;,;*'. 

Da = Diifiisivity of styrene in air, 75E-2 cm? / sec 

P = Atmospheric Pressure,. 1atm 

R = Gas constant, 82:057 cm3 atm / g-mol K '-'$.0X?.'',:';[-' 

T = Temperature, 298 K i^ f; ; 

Psat = Saturation Pressure ,0.0065 atm for styrene ••'•'.!;<>••r). 

Hv = Height of mixing vessel , 122 cm -

:

' yr 

HI = Height of liquid within the niixing vessel, 100 cm -'sv;V*;>:£ '•;.,;,*,•'• 

This method yields styrene emissions of 0.75 g/batch. At 48 batches/day, emission^ are;e5tiraated 

to be 36-g or ; 08 lbs/day. ."• 7yj'r'^: • ^ ' 

Field data are not available tp enable an informed choice between these fwo-appi^^s^ciwever, 

based uppn either method, eraissions are predicted to be quite low. They cpuld be^ti^inated;at 

minimal cost by covering the mix vessels during this operation with nylon fUm.-*E.'.;;:fi^:.E^'.-;'.;\.:;."; 

Sheet Molding Compounding Emissions . 

During this prpceiss, paste is fed into an open doctor bpx, from which it i^^tfibuted across 

and flows through a narrow slit extending the width of the sheet (3-4 ft widths ^^|^^l);;'.*lii this 

way the paste is evenly spread onto a plastic qairier, film in thicknesses that typicallE^i^g^fitjm 1/4 

to 1/2 inches (0.32 to 0.64 cm). Chopped fiberglass roving is shaken onto the surface of the paste, 

and then.a top layer of film is applied. The resulting sandwich of carrier film, fib^aiitfpaste is 

compressed, and either pulled off onto rolls or folded (festooned) into cartons. Fiipfjtp use,.the 

resulting sheet molding compound (SMC) is commonly allowed to inature in storag;^ during Which 

time the styrene in the paste begins to crosslink with the resin polymers. High-flowr^Wvyeiitilatibn 

is often provided at and around the doctor box to remove styrene fumes. ; sss ;• 

Emissions are generated at two sources, the open doctor box itself and the $h^^d^ r 

process. For the sheet under process, methods similar to those presented in the next s^tionE could be 

employed to estimate emissions. Once carrier: film is in place, sheet emissions w^!||^>i^Uced, If 

the process uses nylon carrier films, which are essentially impervipus to styrene, Jstyi^ehe emissions 

will be generated only from the sheet prior to application of the top film. 

Emissions from open doctor boxes are difficult to characterize. Assume a dd-e%r,box:4 ft 

wide and 2 ft across. If the open vapor space depth in the doctor box averages Q;5^:thevstpor 

space volume is 4 ft3 (O.Um3). From equation (1), each saturated vapor space Wui|;pOfltain 3.1 g 

of styrene. If spot ventilation entrains saturated vapor at a rate,20 cfm, in one miiiutfj'^V9.iS grams of 

90 3Stfd S3HWS 310 £UZ.Z9t70E£ St>:91 0102/61/60 
P.8 

ES96-58 

styrene: would be emitted, or 930 g/hr (2.05 ibs/hr). The accuracy of this approach-is directly 

related to the accuracy of estimates pf entrainment, and of the assumption that entrained vapor will 

be saturated. Further research is required to support predictive modeling of doctorbox,emissions. 

Fugitive Emissions From SMC Handling 

Whenever fresh SMC surfaces are exposed to air, styrene is released; It ^reasonable to 

assume that emissions are limited by diffusional mass transfer through the SMC. Pick's Second Law 

of Diffusion describes the diffusion of a chemical from the surface of a plane sttefet/as; -

K = D t£ (5) 

' ar-':.:- ' Bx* • " -

Where:-.' .'.•'• ; V, ' ' 

C = Concentration pf diffusing substance 

D = Diffusivity 

x '.'•== Distance across which cpncentratipn gradient is measured <..'..:, -. 

Reference 4 gives tbefollbwing nunierical solution to this equation, to calculate percent tost per 

unit surface area as a function of time: .'--' . 

lost - 100 (1 -;-A £ ^

 l

. expf-D (2*+l)2 *2.r I Lh) (6) 

7t2 ^ (2X + 1)2 

Where: 

D = Diffusivity, cm2/see 

t = Time, sec '•„'"_-'. 

L = Sheet Thickness, cm 

Consider twp.SMC samples, both 18% by weight styrene; with thicknesses Of.174" (0.635 

cm) and 1/8" (0.318 cm). Assume the diffusivity,of styrehe in SMC is the same as ^polystyrene, 

9.57E^8 as reported in Reference 5. The thin solid and dashed lines on Figure .1:stow'the results of 

this calculation. If SMC is uncovered fbr two minutes prior to closure of the mol<i press, predicted 

styrene losses are 1 % for the thick sheet and 2.2% for the thin sheet. This reflects tiie fact th^t the 

surface area -to- volume ratio is greater for the thin sheet, • •'" 

It is possible that the diffusivity of styrene in SMC is substantially higher than in 

polystyrene. The thick solid line on Figure I shows the impact of a tenfold increa§e;in diffusivity on 

the thick sheet. Over the same two-minute period, predicted; styrene loss is now 3,5 %:' 

It is also possible that this method overestimates styrene emissions, because:exposed styrene 

quickly develops a surface skin which may suppress emissions. Data collected undet:c0ntrolled 

conditions were not available at the time Of this study to test the predictive ability ofthis method. 

Fugitive SMC emissions can be reduced by minimizing the time during which SMC is-:, 

7 

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P.9 

ES96-58 

uncovered, and by emplpying impervious.nylon carrier films. The latter essentially eliminate styrene 

emissipris from wrapped SMC; 

CONCLUSIONS 

The authors have presented a variety pf methods that can be used to model emissions from 

processes, so that the effectiveness of source reduction methods can be evaluated. Iiy most cases, 

these methods cannot yet be reliably applied because critical variables are poorly characterized in 

the field. Research should focus on two issues: the rate of mass transfer across susbstrgte/air 

interfaces, and the rate of vessel vapor space entrainment by spot ventilation system's: 

5 

80 39tfd S3~ws ana EILLLSPBEZ 9P=9T 0T0e;/6i/60 
P.10 

ES96-58 

REFERENCES 

1. Compilalion of Air Pollution Emission Factors (AIM2) Fourth Edition. U.SJ2PA, 1985 

2. Guideline Series - Control of Volatile Orgamc Compound Emission From Batch Processes^ 

U.S.EPA Office of Air Quality Planning and Standards, November, 1993. 

3. Mackay, D., and R. S. Matsugu; "Evaporation Rates of liquid Hydrocarbon. Spills ori Land and 

Water." Can. J. Chemical Engineering, 51:434 (1973)-

4 J. Crank, The Mathematics -of Diffusion. Oxford UniversityPress, Inc., N2w York, 1975 

5. Peev, G.i Trifonova, M., Peeva, L., and P.Miehailov,: "Kinetics of Sryrene-Removal in 

Polystyrene tty Thermal Treatment in Air." Journal of Applied Polymer Scieffci, 33:283-287 

(1987). , . . 

6. Grulke, Eric A., Polymer Process Engineering. Prentice H^ll; Inc., 1994 ^ l 

" 6 0 listf d •'"' ' " S31tfS ai a £U^9t>0EE SP:9I 0102/61/60 
Styrene Loss from Sheet Molding Compound 

p.11 

2.5 3.5 7

-

5

 • y:m 9.5 

L « 0.635 cm, , D = 9.57E-8 • 

*5

 5

-

5

 6.5 E 

Time (minutes) s v 

• • L = 0.3175 cm, D =:9.57E-8 - • ~L = O^i^ b ^9;57E-7 

IO 

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