ENGINEERING DATA TRANSMITTAL Pa.* Of 619205/67531/metadc... · WHC-SD-WM-CN-068, Rev. 0 Calculation Notes in Support of Ammonia Releases from Waste Tank Ventilation Systems L. F

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WHC-SO-WM-CN-068 Rev 0

DATA TRANSHITTI

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(El ' W e or Dsicriptian of Data Tranrmittsd

Calculation notes in support of ammonia releases from waste tank ventilation systems

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WHC-SD-WM-CN-068, Rev. 0

Calculation Notes in Support of Ammonia Releases from Waste Tank Ventilation Systems

L. F. Wojdac Westinghouse Hanford Co., Richland, WA 99352 U.S. Department o f Energy Contract DE-AC06-87RL10930

EDT/ECN: 619205 Org Code: 8M400 B&R Code: EW3130010

uc: 2000 Charge Code: NE602 Total Pages: 1 1

Key Words: Diffusion, toxic, TWRS, dose

Abstract: nitrogen compounds. mechanism which is dependent on temperature, pH, ionic strength and ammonia concentration. The release o f ammonia to the environment occurs via diffusion o f ammonia through a stagnant air mass and into the ventilation system.

Ammonia is generated in waste tanks via the degradation of The ammonia is released from the liquids by a

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of America. .O. Box 1970,

To obtain copies of t h i s docunent, contact: WHClBtS Mailstop H6-08, Richland UA 99352, Phone ( 5 0 9 ) 372-2420;

Approved for Public Release

A-6400-073 (10 /95 ) CEF321


Diameter (m)

23 m

23 m

1

Diffusion of Ammonia into The Head Spaces for both Single and Double Shelled Tanks

Total Height (m) Depth of Head Space Height Li quid (m) (diffusion length)

11.3 m 5.2 m 6.1 m (nominal (nominal operation) operation)

11.3 m 9.4 m 1.9 m (Maximum (Maximum operation) operation)

Purpose: the concentration of ammonia in forced ventilation exhaust gases under normal operating conditions. All data and tank specific information was obtained from document number WHC-SD-BIO-001 REV A.

Methodology: manner such that ventilation flow enters the tank through ventilation headers and exits through an exhaust manifold which is maintained at a reduced pressure. highly turbulent with the possible exception of entrance and outlet effects. Assuming nonturbulent flow, diffusion of ammonia from the surface o f the tank waste can be represented by a diffusion cell model.

This document reports the results of analyses designed to predict

Actively vented single and double shell tanks are vented in a

Stream lines for this type of flow typically are smooth and are not - *_ ' ' -

The basis for this analysis is the Arnold diffusion cell. The diffusion height is defined to be the space between the top of the waste surface and the top of the tank. shel 1 tanks.

Table 1 lists the critical tank dimensions for the single

TABLE 1 TABLE OF VARIABLES (sing1 e shel 1 tanks)

1-3000-723 (01/95> GET014 2


Table 2 lists the critical tank dimensions for the double shell tanks. Data on the heights and nominal capacities for the double shell tanks were taken from Table 2-20 of document WHC-SD-WM-810-001, The highest and lowest values were used to calculate the upper and lower bounds for the nominal and maximum capacity cases.

Depth of Li quid(m)

TAI

Head Space Height (diffusion length)

TABLE 2 E OF VARIABLES le shell tanks)

I

9.1 m (nominal low operation)

10.6 m (nominal high operation)

9.2 m (maximum low operation)

10.7 m (maximum high operation)

5.15 m (nominal operation)

3.65 m (nominal operation)

5.05 m (maximum operation)

3.55 m (maximum operation)

Background:

The basic relation describing the unidirectional diffusion o f a gas describes the molar flux relative to a molar-average velocity, J,. An empirical relation, which is the basis for all, one directional analyses is Fick's law of diffusion (Fick's First Law). For isothermal, isobaric conditions, the Fick rate equation can be stated as:

where J, average 'velocity, DAB is the diffusion coefficient and c, is the molar concentration.

is the molar average flux in the z direction relative to the molar

For nonisobaric, noTisotherma1 conditions a more general flux relation was proposed by de Groot . The de Groot relation i s stated as:

A-3000-723 (01195) GEF014 3

....... - .....

WHC-SO-WM-CN-068, Rev. 0

o v e r a l l d i f f u s i o n concentra t ion = - ( d e n s i t y ) ( c o e f f i c i e n t ) ( gradient ) ( 2 )

expressed in mathematical terms

JA = - C D = 5% d z ( 3 )

where yA is the mole fraction o f component A. 1

direction relative to the molar average flux can be defined as - - -- . - i .e. “1- For a binary system the unidirectional flux o f component A in the z JA,z = C A ( V A , , - V,) (4 )

where vA , is the velocity of component A in the z direction and V, is the molar av’erage velocity .

Equating equations 3 and 4 yields the expression

JA,Z = cA ( v A , z - vZ)

solving for yields

d y A CA VA,z = -C Dna - dz +eA V, (6)

for a binary system the molar average velocity can be expressed as

‘A vz = YA vA,z + v B , z ) (7)

The molar flux of component A can then be written as

C A V A , g = -C Dm dYA/dz + YA ( C A V A , g + C B Va,g) ( 8 )

considering the diffusion relative to a stationary set o f axes define

and N, = cAvA

N, = C,V,

A-3000-723 (01195) GEFO14 4


The molar d i f f u s i o n express ion can then be w r i t t e n as

For d i f f u s i o n i n t o a s tagnant system, N B z i s taken t o be 0. Rearranging equat ion 9 and s o l v i n g f o r NA,z t h e d e f i n i n g e'quation f o of a gas A i n t o B ( a i r ) i s

..- - 1 .- .I(- NA,z = -C - DAB - dyA (10) - ._- 1 1 - y, dz -

i n t e g r a t i n g

evaluated a t t h e l i m i t s

Where yAl and yA2 a re mole f r a c t i o n s o f component A a t p o i n t s z, and z r e s p e c t i v e l y . For a two component system, component B can be expressed i n terms o f component A as:

- Y A 1 = YE1 - YA2 = YE2

so t h a t t h e l o g term can be expressed i n terms o f component B ( a i r ) as

The l o g - mean average concen t ra t i on i s de f i ned by t h e r e l a t i o n

A-3000-723 (01/95) tEfOl4 5


the term 1n(yB2/yB1) then can be expressed as

~. _-.-. 8- - . . . . . - * Equation 15 can be stated in terms of the partial pressure of component A (p ), component 8 (ps) and the system pressure by making the following s uts t i tu t i on s :

YA = PA/'

Ye = PB/'

c = n/V

n = PV/RT

On making the above substitutions, the system pressure cancels out of the partial pressure terms and the expression for the steady state diffusion (molar flux), of component A into a stagnant gas (B) reduces to

z2 - z1 is the diffusion length, which in this analysis is taken to be the length of the vapor space above the liquid. vapor pressure of component A at the liquid/air interface and P is the system pressure, taken to be one atmosphere in this analysis. and p are the partial pressures of air in this analysis and are obtained !ram t6e ammonia values pA using the relation

Pressure pAl is the equilibrium

The values of p

p , = 1 - pAl where the partial pressures are expressed in atmospheres.

The diffusion constant, DAB has units of cm2/sec and was calculated

The value for pB2 is obtained in a similar manner.

based on an empirical estimation method presented by Fuller, Schettler and Giddi ngs2.

MA and M, are the molecular weights o f ammonia and air respectively, P is the system pressure in atmospheres and T is the temperature in O K

A-3000-723 (01195) GEF014 6


The terms ( 1 ~ ) ~ and (Iv) are defined as diffusion volumes y d were obtained from Table 3-342 of berry's Chemical Engineers Handbook . for air and ammonia are listed below

The values

(Iv), - 14.9 (NH3) ( 1 ~ ) ~ - 20.1 (air)

~

of ammonia in air is f o r T = 372'K (210 O F ) and one atmosphere pressure the diffusion constant-. --".I ----W.

3721.75 (17.03 + 28.84) U2 (17.03) (28.84) (18) Dns =

(1) [(14.9)~/~ + ( 2 0 . 1 ) ~ / ~ ] ~

Dae = 0.3571cm2/sec

System Specific Calculations:

the single and double shell tanks. The tank parameters required for the calculations were the diameter and diffusion length, these parameter are listed in tables 1 and 2 of this document.

Assumptions: The concentration of ammonia in the headspace air was calculated for both

It is reported in section 5.3.3.9.1 of document number WHC-SD-WM-BIO-001 that the equilibrium vapor concentration of ammonia in waste tanks is 0.4mg/liter of headspace volume. It is further stated that the concentration of ammonia in the headspace does not change with pH at pH's above 9.27. At a cqncentration of 0.4 mg/L, the partial pressure of ammonia is 0.00072 Atm. at 372 OK.

Calculations:

* 22.4 0.4 mg/l * 2 1 1000 * g'mg * 17 g/g-mole

l i t e r hW3 l i t e r headspace volume

= 0.00072

t/g-mole * 372 27 3

(19)

Letting pA = plH3 = 0.00072 atm. pB = 1 - pA = 1 - 0.00072 = 0.9993 atm.

A-3000-723 (01195) GEFOl4 7


pt * 3 = p m , (20) vtot

- 0.00072 In 1.0007

p B I m =1.029 (21)

- .. __. _. -.-..- _. *

0 . 3 5 7 d sec

(372 O K ) (610 cm) 1.029 a t m * 1000 1 a t m * 0.00072 a t m

N*z =

P (0.08205)

a K-mol e

= 1.43 x10-11 g-mole (22) cm2 sec

Using t h e d a t a from Table 1 (nominal opera t ion) :

The molar d i f f u s i o n w i l l then be

f o r a s u r f a c e a r e a of 4 . 1 5 x IO6 cm2 t h e mass r e l e a s e r a t e of ammonia i n the vented headspace a i r will be

1.43 x 10-11 g-mole * 4.15 x 106 em2 * 17 9 = 1.01 x 10-3 9 cm2 sec g-mol e sec (3.6 (23)

All headspace concent ra t ions were c a l c u l a t e d i n a s i m i l a r manner, only the d i f f u s i o n length d i f f e r e d . The results a r e t a b u l a t e d i n Table 3.

A-3000-723 (01195) CEF014 a


TABLE 3 Concentration of A m n i a in the

Headspace for Selected Dcuble she l l and

A-3000-723 (01195) GEFDl4 3

f


Turbulent flow considerations:

Because of momentum considerations, the flow across the top of tank is never truly streamlined. The incoming air mass tumbles into the tank for a certain distance before flowing toward the exit port, which is maintained at a reduced pressure. Although it is technically possible to calculate the free volume of a tank that is swept by the incoming air mass the uncertainties in such a calculation would be quite high.

Using engineering judgement, it is reasonable to assume that there is some fraction of the free volume of a waste tank that is stagnant. be assumed that at least one meter of tank atmosphere above the liquid surface is stagnant the maximum release rate of ammonia into the vent gas system for the forced ventilation case is approximately 16 grams per hour per tank for

If it can

any double or single shell tank. -i .*L

REFERENCES

1. S. R. de Groot, Thermodynamics of Irreversible Processes, North-

2. E. N. Fuller, P. D. Schettler, and J. C. Giddings, Ind. Eng.

3. R. H. Perry, D. W . Green, Perry's Chemical Engineers' Handbook, 6th

Holland, Amsterdam, 1951.

Chem.,58(5), 18 (1966).

edition, McGraw-Hill Book Co., 1984. WHC-SD-WM-BIO-001 REV A, Tank Waste Remediation System, "Basis' for Interim Operation", (Draft).

, 4 .

A-3000-723 ( 0 1 1 9 5 ) GEFOl4 10

CHECKLIST FOR TECHNICAL PEER REVIEW

Document Reviewed: WHC-SD-WM-CN-068 REV 0

Scope of Review: ?J.N ra\i;ed entire d o c u w w k t

Yes No NA [I[lW Previous reviews complete and cover analysis, up to scope o f

this review, with no gaps. Problem completely defined. Accident scenarios developed in a clear and-logical manner. Necessary assumptions explicitly stated and supported. Computer codes and data files documented. Data used in calculations explicitly stated in document. Data checked for consistency with original source information as applicable. Mathematical derivations checked including dimensional consistency of results. Models appropriate and used within range of validity or use outside range of established validity justified. Hand calculations checked for errors. should be treated exactly the same as hand calculations. Software input correct and consistent with document reviewed. Software output consistent with input and with results reported in document reviewed. Limits/criteria/guidelines applied to analysis results are appropriate and referenced. Limits/criteria/guidelines checked against references. Safety margins consistent with good engineering practices. Conclusions consistent with analytical results and applicable limits.

Spreadsheet results

[XI [ ] [ 3 Results and conclusions address all points required in the

Dc] [ ] [ ] Format consistent with appropriate NRC Regulatory Guide or

UQ [ ] Review calculations, comments, and/or notes are attached.

problem statement.

other standards

[ ] [ ] [ ] Document approved.

D. L . Scott 6\,2 A sew- S/a 9 h 6 Reviewer (Printed Name and Signature) Date

Any notes and/or comments should be attached.

Documents

ENGINEERING DATA TRANSMITTAL Pa.* Of 619205/67531/metadc... · WHC-SD-WM-CN-068, Rev. 0 Calculation Notes in Support of Ammonia Releases from Waste Tank Ventilation Systems L. F