API BULLETIN 2518 19.1D.pdf

API

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Date of Issue: June 1994 Affected Publication: API Chapter 19.1D,Documentation File for APl Manual of Petroleum Measurement Standards Chapter 19.lD-EvaporativeLossfrom Fixed Roof Tanks [MI Builelin 2.5181, Fust Edition, March 1993 (first printing)

ERRATUM

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The corrected Table of Contents is shown on the following page:

Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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A P I PUBLICATION 2518 DOCUMENTATION FILE

CONTENTS SECTION

DESCRIPTION INTRODUCTION..

...............................................

PAGE -

1

!STANDING STORAGE LOSS

A

Development o f Vapor Space Expansion Factor, KE

............. A l

E

......... B1 Development o f Vapor Space Temperature Factor, KT.. ......... C 1 Development o f Solar I n s o l a t i o n Parameters.. ................ D1 Development o f Paint Solar Absorptance, ................. El

F

Development o f L i q u i d Surface Temperature Equations..

G

S e n s i t i v i t y Analysis of Standing Storage Loss Equation..

H

Comparison o f Standing Storage Loss Equation w i t h Test Data..

B C

D

Development of Vented Vapor Saturation Factor, Ks..

Q..

....... F1

.... G 1

......................................... i . . ..... H1.

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REFERENCES..

................................................

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R1

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Documentation File for API Manual of Petroleum Measurement Standards Chapter 19.1-Evaporative Loss From Fixed Roof Tanks [API Bulletin 25181 API PUBLICATION CHAPTER 19.1D FIRST EDITION, MARCH 1993

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American Petroleum Institute 1220 L Street, Northwest Washington, D.C. 20005

4’


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API MPMS*LS.LD 93

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Documentation File for API Manual of Petroleum Measurement Standards Chapter 19.1-Evaporative From Fixed Roof Tanks [API Bulletin 25181

Loss

Measurement Coordination

API PUBLICATION CHAPTER 19.1D FIRST EDITION, MARCH 1993

American Petroleum Institute

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A P I MPMS*L9*LD 93

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Copyright O 1993 American Petroleum Institute


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FOREWORD API publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for the violation of any federal, state, or municipal regulation with which this publication may conflict. Suggested revisions are invited and should be submitted to the director of the Measurement Coordination, Industry Services Department, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005.

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iii


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API MPMS*:LS.LD 93 W 0732290 0533442 433

API

MPMS*LS*LD 93

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API PUBLICATION 2518 WCUMENTATION FILE --```,``-`-`,,`,,`,`,,`---

CONTENTS SECTION

PAGE -

DESCRIPTIûN INTRODUCTION..

..............................................

1

‘STANDING STORAGE LOSS A

B

............. A l Development o f Vented Vapor Saturation Factor, KS ........... B1 Development o f Vapor Space Temperature Factor, KT ........... CI Deve1opment o f Sol a r Insol a t ion Parameters. ................. D1 Development o f Paint Solar Absorptance, ................... El Development o f Vapor Space Expansion Factor, KE

Q

....... F1 Equation.. .... G1

Development o f Liquid Surface Temperature Equations.. S e n s i t i v i t y Analysis o f Standing Storage Loss

Comparison o f Standing Storage Loss Equation w i t h Test Data............................................

.......

H1.

WORKING LOSS

........................ I1 Deveìopment o f Turnover Factor, Q .......................... 31 Development of Product Factor, Kp...........................K1 Comparison of Working Loss Equation with Test Data .......... L1 REFERENCES.. ................................................ R1 Development o f Working Loss Equation


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API MPMS*LS.LD 93 m 0732290 05LL444 204 m

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3

API PUBLICATION 2518

DOCUMENTATION FILE

INTRODUCTION

This document is the Documentation File to API Publication 2518, Second Edition [A7]*. The purpose of the Documentation File is to present detailed technical infomation related to the development of A N . Publication 2518 that includes: ( I ) the development o f theoretical equations; (2) comparisons with test data; (3) a sensitivity analysis of the loss equation; and (4) other pertinent information that was developed during the preparation of API Publication 2518. The Documentation File is divided into two main parts: Sections A through H pertain to the standing storage loss, and Sections I through L pertain to the worki ng 1 oss. The standing storage loss equation in the Second Edition [A71 is different then that in the First Edition [A6]. Sections A through H present the development of the new standing storage loss equation. The working loss equation in the Second Edition [A71 is the same as that in the First Edition [A6]. Sections I through L contain development information that originally appeared in the First Edition. Section R contains a list of important References that were reviewed in developing the Second Edition. These references are cited in various sections of the Documentation File.

t

Numbers in brackets refer to the numbered references listed at the end o f this Documentation File. 1


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API PUBLICATION 2518 ûûCUMENTATION F I L E

SECTION A

DEVELOPMENT OF VAPOR SPACE EXPANSION FACTOR, KE

Al Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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CONTENTS

DESCRIPTION --```,``-`-`,,`,,`,`,,`---

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A P I W6LICATION 2518 DOCUMENTATION FILE SECTION A

PAGE -

........................................... A3 INTRODUCTION.. ................................ .......... A4 VAPOR SPACE VOLUME CHANGE.. ... ........................ A4 VAPOR SPACE EXPANSION FACTOR. ............................. A9 SIMPLIFIED EQUATIONS FOR THE VAPOR SPACE EXPANSION FACTOR.. ....................................... A9 Neglecting the Term PBp................................ A9 Replacement o f T y l With TM. ........................... A9 Replacement o f Py2 With PvA.. .......................... A10 Use o f a-Simplified Equation for the Vapor Pressure .... A10 Range, APy ..... ................................... Neglecting the Term APB ................................ A l l CONCLUSION. ........ ................ ............. .... A12 NOMENCLATURE..

A l .O A2.0

A3.0 A4.0 A4.1 A4.2 A4.3 A4.4 A4.5 A5.0

i..

i..

TABLES Al

Value o f the Variables a t the Maximum and Minimum Conditions..

................. ........................... A5

FI6üRES Al

Schematic o f the Tank Vapor Space Heating Process and the Resulting Volume Expansion Due t o the Thermal Breathing.. ... ..

................................... . ..... A13


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API W B L I C A T I W 2518 DOCUMENTATION FILE SECTION A NOMENCLANRE UNITS -

DESCRIPTION A

B KE

n

P AP R T

AT V AV Y

Vapor pressure function constant Vapor pressure function constant Vapor space expansion factor Number of mol es Pressure Pressure change Ideal gas constant (10.731) TemperatUre Temperature change Vol Ume Vol Ume change Mole fraction in the vapor phase

dimens i on1 es s OR

dimensionless mol e psi psi psia ft3/l bmole

OR

OR OR

ft3 ft3

mol e fracti on

A ATM 8

BP BV L LA T

V VA 1 2

Air Atmospheric Breather Vent Breather Vent Pressure Setting Breather Vent Vacuum Setting Liquid Liquid Average Total Stock Vapor Vapor Average Initial Condition or Minimum Condition Final Condition or Maximum Condition

A3

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SUBSCRIPTS

A l -0 INTRODUCTION

This section of the Documentation File t o API Publication 2518, Second Edition, contains a derivation of the equation for the vapor space expansion factor, KE. This equation i s derived from the ideal gas law and from the pressure, temperature and volume conditions that exist in the vapor space of a fixed-roof tank containing a volatile liquid stock. Section A2 presents a derivation o f the vapor space volume change due to thermal breathing. This derivation closely follows that originally derived' by Boardman [i]* and that. presented at the API "Symposium on Evaporation Loss' of Petroleum from Storage Tanks" November 10, 1952 [2]. Section A3 defines the vapor space expansion factor, KE, and develops the equation that may be used to calculate this factor. Section A4 describes various simplifications that can be made to the equation for the vapor space expansion factor to permit ease of calculation with little loss i n accuracy. A2-O VAPOR SPACE VûLWE CHANGE Figure Al is a schematic illustrating the tank vapor space thermal breathing process i n a fixed-roof tank that is partially filled with a volatile liquid stock and equipped with a pressure-vacuum vent. During the thermal breathing process, the pressure, volume. and temperature vary from minimum condition 1 t o maximum condition 2. At conditions 1 and 2, the total absolute pressure in the vapor space is Pl and P2, respectively, where:

~~~

~~~

~-

Numbers in brackets refer to the numbered references listed at the end of this Documentation File. A4

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A P I MPMS*Lî-LD 9 3

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0 7 3 2 2 9 0 0533449 B9b

=,

During the thermal breathing process, the pressure, volume and temperature vary from a certain combination of values at the minimum condition to be certain combination o f values at the maximum condition. At the minimum condition 1, it is assumed that all o f the variables are simultaneously at their minimum values; and at the maximum condition 2, it is assumed that all o f the variables are simultaneously at their maximum values. lhe value o f the variables at the minimum condition i and maximum condition 2 are listed in Table Al.

- Value of

the Variables at the Hinimupi and iíaximm Conditions

Variable

Units

Gas space total pressure

psia

Atmospheric pressure

psia

Gas space gage pressure

Psig

Stock vapor pressure

psi a

Ai r part i al -pressure

PJ i

6as volume

ft3

Gas temperatUre

OR

Liquid surface temperature

OR

Minimum Condition 1

Maximum Condition 2

I

From the ideal gas law, the total number o f moles o f gas, nT, in an enclosed volume, V, at temperature, T, and pressure, P, is given by:

-P V

nT

(A-3

RT

1

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Assume that the gas mixture in the tank vapor space is a two-component mixture consisting air and stock vapor. The mole fraction of air, YA, and the mole fraction o f stock vapor, yv, may be determined by Eqs (A-4) through (A-7):

AS Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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Table Al

A P I flPflS*LT.lD

YA =

93 W 0732290 05LL450 508 W

nA -

"T

Yy =

"V -

nT

Yy =

pV P

The mole f r a c t i o n of air, YA, may be expressed i n terms o f the mole f r a c t i o n of vapor, yy, as follows: (A-8)

During the thermal breathing process o f the tank vapor space, the number o f

moles o f a i r , nA, i n the volumes, V i and Vp, i s assumed t o remain the same. This assumption may be expressed as follows:

We may substitute Eq (A-4) i n t o Eq (A-9) t o yield:

(A- 10)

YA1 nT1 = YA2 n12 We may substitute Eq (A-3) i n t o Eq (A-10) to y i e l d :

[cl

p2v2

plVI

yA1

=

yA2

]-&i[

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(A-11)

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Solving for ‘2 and using Eq

v2

=

v1

(A-8),

we may write:

k]I;[ k]

(A- 12)

(A-13)

We may substitute Eq (A-7) into Eq (A-13) to yield:

v2

= v1

[;;: k]

(A- 14)

p”] pv2

Using Eq (A-14), the volume change due to thermal breathing, AV, may be determined as follows: AV = V2

-

V1

(A-15)

(A-16)

We may substitute Eqs (A-1) and (A-2) into Eq (A-16) to yield:

A7 --```,``-`-`,,`,,`,`,,`---


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A P I MPMS*LS.LD

93

0732290 05LL452 380

(A-17)

[I

+ (‘V2

AV = V1

- ‘Vi) p~~~

+

- ‘BV)]

(‘BP

p~~

-

[1

2 (‘

ilTl)] 1]

(A-18)

pv2

It .is a convenient to define the terms APy, APg and ATy as follows: APV = QV2

- QVl

(A-19)

APB = PBP

-

(A-20)

ATv = 1 2

PBV

- T 1 = Tv2 - TV1

(A-21)

AV = V1 [[l

- APB

APV

+ ’ATM

+

(A-22)

’BP .-

(A-23)

-

Since the terms (ATV/Tyl) and (APy A P B ) / ( P A ~ + PBP - Pyp) are small, their product can be considered negligable. Thus, the product term in Eq (A-23) can.be neglected. Eq (A-23) then simplifies t o the following:

AV = \Il

k

APV

- APB

t

P~~~

+

p~~

-

Ï

(A-24)

pv2

A8 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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We may substitute Eqs (A-19), (A-20) and (A-21) into Eq (A-18) and expand the terms to yield:

I

API flPflS*:LS-LD 93 U 0732290 0511453 217 m

A3.0 VAPOR SPACE EXPANSION FACTOR

The vapor space expansion factor, KE, i s defined as the r a t i o of tile vo urne change, AV, t o the i n i t i a l volume, V i , as follows:

KE

AV -

(A-25)

v1

Substituting Eq (A-24) i n t o (A-25) we obtain: --```,``-`-`,,`,,`,`,,`---

-TV1 A4.0

‘ATM

’ ‘BP

(A-26)

-

‘Y2

SIMPLIFIED EQUATIONS FOR

THE

VAPOR SPACE

EXPANSION FACTOR

Eq (A-26) m a y be simplified f o r ease o f calculation. Sections A4.1 through A4.4 present various simp1 i.fications t h a t can be made. A4.1

Neqlectincr the Term P w

I t should be noted that PBP is small (about 0.03 psi) compared t o PATH (about 14.7 psia) and can be neglected i n the denomination of Eq (A-26) t o yield:

(A-27)

A4.2

Replacement of T v i With TI

A

In the f i r s t tem o f Eq ( A - 2 7 ) , the minimum vapor space tmperature, TV1, i s close t o the daily average l i q u i d surface ,temperature, TLA, since both are absolute temperatures. Thus, f o r ease o f calculation, we can replace TV1 w i t h TLA i n Eq (A-27) t o yield:


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API RPRS*L9*1D 93'- 0732290 0511454 153 H

KE

=

-+

AT"

APV

T~~

p~~~

Replacement of

A4.3

For compared pressure pressure

-

APS

-

(A- 28)

pv2

Pv7 With

Pvq

low vapor pressure stocks, the stock vapor pressure, Pv, is small t o atmospheric pressure, PA^. Thus, we may replace the stock vapor -at the minimum l i q u i d surface temperature, Pvp, w i t h the 'stock vapor a t the daily average liquid surface temperature, PVA, i n Eq (A-28) t o

yield:

A4.4

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Eq (A-29) appears as Eq 4 i n Ref. A7.

Use of a Simplified Equation for the Vapor Pressure Range, APy

The vapor pressure of the stock may be determined from Eq (A-30), where the vapor pressure function constants A and B must be selected f o r the particular stock [see Tables 4 and 5 i n Ref. A7]. (A-30)

We can determine the slope of the vapor space pressure function by taking i t s derivative w i t h respect to the l i q u i d surface temperature, TL, as follows: dP, -t-

6 Py (A-31)

'>

Eq (A-31) can be written i n differential form as follows:


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(A- 29)

A P I MPMS*19=1D 9 3

0732290 0511455 09T

(A-32)

Eq (A-32) gives the vapor pressure range, APv, in terms o f the liquid surface

temperature range, ATL. For most hydrocarbon liquids, the liquid surface temperature range, ATL , may be related to the vapor temperature range, ATy, as follows (see Eq (F-16) in Section F): (A-33)

Substituting Eq (A-33) into Eq (A-32), equation for the vapor pressure range:

[

]

we obtain the following simplified

0.50 8 Py

=

T t

--```,``-`-`,,`,,`,`,,`---

ATL = 0.50 ATy

(A-34)

ATy

Eq (A-34) may be substituted into Eq (A-29) to yield:

A4.5

Neglecting the Term APg

For most atmospheric storage tanks, the breather vent pressure and vacuum settings are typically +0.03 psi and -0.03 psi, respectively. Thus, the term APB/(PATM - PYA) is small (about 0.002 for low vapor pressure stock) compared to the term ATv/TLA (about 0.040 for ATy = 2OOF and TLA = 5200R). For these cases, the last tern in Eq (A-35) may be neglected to yield:

Al 1 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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(A-35)

API MPMSULS.LD 9 3 H 0732290 05LL45b T2b

KE

- El

[~l[p*T:.p"j] 0.50

[I

+

=

B

(A-36)

In comparing fq (A-36) to Eq (A-26), we can see that the calculation process is greatly simplified because it is not necessary to determine all o f the variables, T U , 1 ~ 2 ,TM, Pyl, Pyp and PYA, but only the variables TLA and PYA.

coNcLusIoN

Equation (A-29) was selected for use in calculating the vapor space expansion factor, KE, in API Publication 2518, Second Edition [A7]. This equation was derived from the ideal gas law and from the pressure, temperature, and volume conditions that exist in the vapor space o f a fixed-roof tank containing a volatile liquid stock. Equation (A-29) was developed from a more complete expression, Eq (A-26) , by incorporating several simp1 ifications that make the calculations more user friendly, with little loss in accuracy. --```,``-`-`,,`,,`,`,,`---

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AS.0

m:

Thi8 documnt i8 part o f the API mtandudi developerkt procems and is intendecl for use by API cooraittwm M. I t ahall not bo rmproguced or circulated or quoted, i n whole or i n part, outmide of t h e cognizant APT conmittee(8) except with t h e written approval o f A P X . Thio draft API mtandard w i l l be formatted and edited prior to APT publication. Copyright@1990.


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Pressure-Vacuum

b

Av{

Heat

0

Figure Al

- Schematic of

T2

the Tank Vapor Space Heating Process and the Resulting Volume Expansion Due to Themal Breathing


p2

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. A P I MPMS*39-3D 93

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API PUBLICATION 2518 DOCUMENTATION FILE

SECTION B

DEVELOPHENT OF VENTED VAPOR SATURATION FACTOR,

Ks

B1 --```,``-`-`,,`,,`,`,,`---


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API

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API PUBLICATION 2518 00CUnEKTATION FILE ‘SECTION 8

CONTENTS PAGE .

DESCRIPTION

SECTION

NOMENCLATURE ............................................. 83 81 .o

82.0 82.1

B2.2 82.3 82.4 B3.0 63.1 B3.2 B3.3

84.0

.............................................BS VENTED VAWR SATURATION FACTOR HODEL ..................... B5 Model Description ...................................... 85 Vented Vapor Saturation Factor D e f i n i t i o n ............... 87 Saturation Parameter ...................................88 Vented Vapor Saturation Factor Deve1opment ............. B10 VENTED VAPOR SATURATION FACTOR CORRELATION............... 811 INTROWCTIûN

.

................. .

Sumnary o f API. €PA and UOGA Test Data B12 Saturation Factor Correlation of A P I and €PA Test Data 813 Saturation Factor Correlation o f API. €PA and WOGA Test Data 813

.............................................. CONCLUSION...............................................815 TABLES Saturation Sumnary o f Saturation Sunriiary o f Saturation Sumnary o f Saturation

81 82 B3 84 B5 86

............. 816 ....................... 817 ............ 818 ...................... 619 ........... 821 ............................ 823

Factor. KS. f o r A P I Test Data [38] €PA Tests [20] Selected Factor. Ks. f o r EPA Test Data [20] UOGA Tests [17] Selected Factor. Ks. f o r UOGA Test Data [17] Test Data Used t o Develop the Vented Vapor Factor Corre1a t ion

FIGURES Schematic o f the Tank Vapor Space f o r the Vented Vapor Saturation Factor Analysis Saturation Factor. Ks. Versus PVAHV f o r the A P I and €PA Test Data Saturation Factor. Ks. Correlation Saturation Factor. Ks. Versus PVAHV f o r the API. EPA and WOGA Test Data

81

............................... 824 ................................................ ....................... 825 826

82 83 84

.......................................

I

62 --```,``-`-`,,`,,`,`,,`---


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API PUBLICATION 2518 DOCUMENTATION FILE SECTION B NûMENCUTURE

SYMBOL

WITS -

DESCRIPTION Constant i n the vapor pressure equation Area of the stock liquid surface Defined by Eq (8-15) Constant in the vapor pressure equation Defined by Eq (8-16) Average vapor concentration i n the vented gas Tank diameter Evaporation loss Evaporati on 1oss cal cul ated Evaporation loss measured Tank vapor space o u t age Overall mass transfer coefficient between the l i q u i d surface and the vented vapor

A

AL

a

B b CV D

E EC EM HV

K

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Vapor space expansion factor Vented vapor' saturation factor Stock vapor molecul a r weight Moles o f stock vapor vented Atmospheric pressure Stock vapor pressure detemined a t TLA Vented gas volume outflow Ideal gas law constant, (10.731)

Re id Vapor Pressure Saturation parameter, defined by Eq (6-4) Average daily ambient temperature Average daily 1iquid surface temperature Average daily vapor space temperature Daily ambient temperature range Daily vapor space temperature range Time o f a daily period Vol urne o f the tank vapor space

RVP S

TAR

*LA TVA ATA

ATV

t0 "V

--```,``-`-`,,`,,`,`,,`---


Not for Resale

psia

ft2 dimensionless OR

dimensionless lbm/sft3 ft 1WdaY 1h / d a y 1bm/day ft 1bmol e ft2 hr mole frac. dimens i on1ess d imens i on1 ess 1bm/l bmol e 1h o l e psi a psia sft3/day

psi dimensi on1ess OF or OR OF o r OR OF or OR OF or OR OF o r OR hr ft 3

A P I MPMS*LS.LD

93

0732290 0 5 LLYbL 393

API PUBLICATION 2518 DOCUMENTATION FICE SECTION B NfflENCLATURE (Continued)

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

UNITS -

DESCRIPTION

SYMBOL AV

Volunie of gas vented during a single daily thermal breathing cycle

ft3

YV

Daily average stock vapor concentration i n the vented vapor

mole fraction

YVO

Daily average saturated stock vapor concentrat ion Gat density

mole fraction 1 kn01 e/ft3

P6

64 --```,``-`-`,,`,,`,`,,`---


Not for Resale

81 .O

INTROûüCTIûN

This section o f the Documentation F i l e t o API Publication 2518, Second Edition, contains the development o f the vented vapor saturation factor, Ks. The 'Vented Vapor Saturation Factor',

Ks, i s defined as the r a t i o o f the

d a i l y average stock vapor concentration i n the vented gas, yv, t o the stock vapor concentration, yvo, i n equilibrium with the stock l i q u i d surface a t the d a i l y average 1i q u i d surface temperature. Section B2 presents the derivation of a theoretical equation f o r estimating t h e vented vapor saturation factor t h a t i s based on an analytical model of the d a i l y thermal breathing process.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Section B3 presents the development of a c o r r e l a t i o n f o r estimating the vented vapor saturation factor t h a t s based on t e s t data. 82.0

VENTU) VAWR SANRATION FACTOR MODEL

82.1

Model Description

Figure 61 i s a schematic o f a f;xed-roof tank that i s p a r t i a l l y f i l l e d w i t h a v o l a t i l e l i q u i d stock and equipped with a pressure-vacuum vent. During the d a i l y thermal breathing cycle, the gas mixture i n the tank vapor space i s i n i t i a l l y heated from i t s minimum condition t o i t s maximum condition (see Section A o f t h i s Documentation F i l e f o r additional d e t a i l ) . Vapor i s vented from the tank vapor space when the pressure increases t o t h e pressure s e t t i n g o f the pressure-vacuum vent. As the gas mixture i n the tank vapor space i s cooled from i t s maximum condition back t o i t s minimum condition, a i r i s admitted t o the tank vapor space when the pressure decreases t o the vacuum s e t t i n g o f the pressurevacuum vent. Evaporation o f stock occurs f r o m the l i q u i d surface as the stock t r i e s t o saturate the a i r t h a t was admitted t o the tank vapor space. Test data indicates t h a t there i s a region a t the top o f the tank vapor space under the pressurevacuum vent where there i s a s i g n i f i c a n t concentration gradient.

B5 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

--```,``-`-`,,`,,`,`,,`---

A P I MPMSJLCI-LD 93

0732290 05124b3 I b b

During the daily thermal breathing cycle, the moles o f stock vapor t h a t are expelled from the tank vapor space, my, may be estimated by Eq (8-1):

The vented gas contains less stock vapor per u n i t volume than the gas near the liquid surface. The daily average stock vapor concentration i n the vented vapor is yy (unsaturated), and the daily average stock vapor concentration near the 1iquid surface is yvo (saturated). DÚring the daily thermal breathing cycle, stock vapor evaporates and rises upward from the area near the l i q u i d surface t o replace the stock vapor lost as gas i s vented from the tank vapor space. Stock will continue t o evaporate as it t iies t o establish. a saturati.on condition a t the top o f the tank vapor space. The moles o f stock that evaporate during a daily thermal breathing cycle may be estimated by Eq (B-2):

where K i s the overall nass transfer coefficient between the l i q u i d surface and the vented vapor.

After a series of repeated daily thermal breathing cycles where the same meteorological conditions occur, the stock vapor concentration i n the vented vapor will vary during each thermal breathing cycle i n a repeated manner, and the daily average stock vapor concentration i n the vented vapor, yy, will achieve a steady value. This concentration value depends upon the rate a t which the stock vapor lost from the tank vapor space i s replaced by stock evaporated from the 1iquid surface.

86 --```,``-`-`,,`,,`,`,,`---


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

where the tern AV represents the volume vented during a single themal breathing cycle (see Section A2, Eq (A-24)).

A P I MPMS*lS*lD 93 W 0732290 0511464 O T 2 W

The steady value of the daily average stock vapor concentration in the vented vapor, yv, may be determined by equating Eq (B-1) with Eq (6-2) and

solving for yv as follows:

yy

[

=- (Yyo

pG

- Yy)

It is useful to define the saturation parameter, S, as follows:

s

3

[

p6 Aval

K AL t

--```,``-`-`,,`,,`,`,,`---

Using this defined saturation parameter, Eq (B-3) may be written as: Yy s = (Yyo

- Yy)

Eq (8-5) may now be solved for yy to yield:

Yy = Y+

1 ' 1 + s

82.2 Vented Vapor Saturation Factor Defini tion

The vented vapor saturation factor, Ks, is defined by Eq (6-7) as the ratio o f the daily average stock vapor concentration in the vented vapor, yv, to the daily average saturated stock vapor concentration, yyo.

87 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

0732290 0511465 T39

-

ühen KS 1, the vented gas is completely saturated; when KS = O, the vented gas contains no stock vapor. 62.3

Saturation Parameter

lhe saturation parameter, S, as defined by Eq (8-4) may be written in terms o f other evaporation loss parameters. First, note Eqs (8-8) threugh (B-11) as follows: .

];I[

*L

AV = Vy

--```,``-`-`,,`,,`,`,,`---

VV'

(B-9)

t

KE

,

(see Eq (A-25) in Section A)

r ":"1

-

(8-10)

(8-11)

Substituting Eqs (B-8) through (8-11) into Eq (B-4), we obtain: (B-12)


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*IjS*LD 9 3

0732290 05LL4bb 975

A P I MPflS*LS-LD 9 3

The vapor space expansion factor, KE,

may be expressed in the following

simplified form (see Eq (A-36) in Section AS):

(B-13)

Substituting Eq (8-13) into Eq (8-12) and replacing TVA with TM (since both are absol Ute temperatures), we. obtain:

(B-14)

It is convenient to define the following dimensionless parameters a and b:

a

E

r""" "LI R tD

K TM

0.50

B

(8-15)

(B- 16)

We also know that the daily average saturated stock vapor concentration, yvo, can be expressed as follows: (B-17)

B9 --```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS+LS.LD

93

0732290 05LL4b7 B O L M

Substituting Eqs (8-15), (B-16) and (B-17) into Eq (B-14), we obtain:

(B- 18)

82.4 Vented Vapor Saturation Factor Deve1 opment

Substituting yv from Eq (6-6) into Eq (8-7) we obtain:

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

(B-19)

Equation (B-19) shows that as the saturation parameter, S, increases, the vented vapor saturation factor, KS, decrease toward O. Conversely, as S decreases, the value of KS increases toward 1.

i

1

(8-20) --```,``-`-`,,`,,`,`,,`---

=

Equation (B-20) shows that the vented vapor saturation factor, Ks, depends upon only 3 parameters: a, b and yyo. Inserting the expressions for a, b and yvo from Eqs (B-15). (8-16) and (817), we obtain the following final expression which contains all of the vari ab1 es :


Not for Resale

API

M P M S * L q = L D 93

0732290 0511468 748

1 K, = 4

I 1 t

1

[a[a

(B-21)

-

I t should be noted that KS will tend toward 1 as Hy tends toward O. Also, KS w i l l tend toward O as PYA tends toward PATH.

Insufficient information is currently available t o determine the overail mass transfer coefficient, K, and thus Eq (8-21) was used only as a guide t o show t h e dependancy o f KS on PYA, Hy and the other variables. Although i t is possible t o improve the above simplified analysis t o develop a theoretical relation for the vented vapor saturation factor, Ks, i t was decided instead t o develop a correlation for KS based on actual t e s t ' d a t a , as described i n Section 83. However, the above Simplified analysis was used a s a guide i n selecting the analytical form for the correlation equation and i n selecting the parameters t o include i n the correlation. B3.0

VENTED VAPOR SATURATION FACTOR CORRELATION

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

This section sumarizes the development of a correlation for estimating the vented vapor saturation factor, Ks.

Section 83.1 summarizes the saturation factors that were calculated from the API[38]*, EPA[20] and üOGA[lI) test data. The API t e s t data showed that t h e vented gas was near saturation conditions a t a l l times. lhe €PA and UOGA lest Data, however, showed that the vented gas was not saturated, w i t h the degree of saturation being less w i t h increasing product vapor pressure, PYA, and increasing vapor space outage, Hy.

t

Numbers i n brackets refer t o the numbered references l i s t e d a t the end of this Documentation File. 611 --```,``-`-`,,`,,`,`,,`---


Not for Resale

The fact that the vented gas is not saturated w i t h stock vapor reflects the effect of mass transfer'rate limitations from the liquid surface t o the area below the pressure-vacuum vent. As the vapor space outage increases, the distance that the stock vapor must travel from the l i q u i d surface t o the vent is lengthened. This lengthened distance decreases the mass transfer r a t e and t h u s the concentration i n the vented gas. For high vapor pressure stocks, since the amount o f stock vapor lost i n each daily thermal breathing cycle is larger, a higher rate of evaporation from the liquid surface is required to replenish the stock vapor that i s lost. Mass transfer r a t e limitations, however, limit the ability o f the stock t o replenish the vented vapor a t these higher vapor pressures and t h u s reduce the degree of saturation i n the vented gas. Section 83.2 presents the -development of a correlation for the vented vapor saturation factor based on only the A P I and ÊPA test data. T h i s correlation showed trends that are similar t o those predicted by the theoretical analysis (see Eq (6119)) i n that the saturation factor approaches 1 as the vapor pressure o r the outage approach O, and the saturation factor becomes small as the vapor pressure or outage increase. Section 3.3 presents the development of a correlation for the vented vapor saturation factor based on the combined set o f A P I , EPA and UOGA test data. T h i s correlation showed the same trends as the correlation that was based on only the A P I and EPA test data, but there was more scatter of the WOGA test data from the corre1 a t i on.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

63.1 Sumnary of API, €PA and WOGA Test Data

Table 82 summarizes the IS €PA tests [20]. I t was found t h a t a l l of the €PA test data was suitable for use i n calculating a saturation factor, w i t h the exception of Tests EPA-IA, EPA-4B and EPA-4C. The reason for rejecting these t e s t s i s stated a t the bottom of Table 62.


Not for Resale

--```,``-`-`,,`,,`,`,,`---

Table 81 sumnarires the 10 A P I tests [38) along w i t h the calculated saturation factor, Ks. The saturation factor for the API test data are very close to 1, with an average value for the 10 tests of 0.964.

API flPMS*LS=LD

73

0732290 0511970 3Tb

Table 83 summarizes the EPA t e s t data along w i t h the calculated saturated factor, Ks, for those t e s t s which were selected i n Table 62. Since the average l i q u i d surface temperature was n o t measured during the EPA t e s t s , the equation indicated i n Note 5 at the bottom of Table B3 was used t o estimate the average 1i q u i d surface temperature. Table 84 summarizes the 44 WOW t e s t s (171. O u t of the total of 44 t e s t s , 21 were found suitable t o calculate a saturation factor. The reasons for rejecting the other tests is noted a t the bottom o f Table 84. Table BS summarizes the suitable UOGA test data and the calculated saturation factor, Ks. Only the crude o i l t e s t s were used t o calculate a saturation factor. The vapor pressure a t the daiTy average l i q u i d surface temperature was calculated u t i l i z i n g the equations noted a t the bottom of Table BS. No such relationships were available for t h e d i s t i l l a t e and fuel o i l products used i n the WOGA t e s t program.

63.2 Saturation Factor Correlation of A P I and EPA Test Data I n general, i t was found t h a t there was a higher quality i n t h e A P I t e s t data [38] and EPA test data [20] than i n the WOGA t e s t data [17]. The combined set of A P I and EPA test data were used t o develop a saturation factor corre1 a t i on'.

Figure 82 presents the correlation, where the saturation f a c t o r , Ks, was found t o be related t o the product o f the vapor pressure, PYA, and the vapor space outage, Hy. The vapor pressure characteristics of the stock used i n the €PA t e s t s were readily known because they were single component stocks. 63.3

Saturation Factor Correlation of A P I , EPA and WOGA Test Data

The correlation of the A P I and EPA t e s t data shown i n Figure 82 i s satisfactory, but i s based only on t e s t data from fuel o i l (API test data) and single component l i q u i d stocks (EPA t e s t data).

--```,``-`-`,,`,,`,`,,`---


813 Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Table 66 sumnarizes the 34 data points which were used to develop the saturation factor correlation from the combined set o f API, €PA and WOGA test data.

-

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

1) versus P ~ A H vfor the A P I , EPA and WOGA Figure 63 i s a plot of ((l/Ks) test data. The test data were fit with a least squares linear correlation, as noted on Figure 83. The correlation coefficient, r2, was 0.76. Eq (6-22) is the resul ti ng corre1 at ion. (6- 22)

Figures B3 and B4 illustrate that the WOGA test data has nore scatter in comparison to the API and EPA test data. Part o f this scatter is believed to be due to the more uncertain vapor pressure characteristics of the stocks used in the WOGA tests and the fact that only a few vapor samples were taken during each YOGA test. Figure 84 Illustrates the results o f the correlation developed in Figure 83, where the saturation factor is plotted. versus PVAHV. The correlation indicates that the saturation factor approaches 1 as the vapor pressure or the vapor space outage approach O. The correlation also shows that the saturation factor becomes small as the vapor pressure or the vapor space outage increase. These trends are in agreement with those that are predicted by Eq (8-21) o f the theoretical analysis.


Not for Resale

--```,``-`-`,,`,,`,`,,`---

Although it was found that, in general, the API and €PA test data were of higher quality than the UOGA test data, it was decided to develop a single Correlation which was fit to the combined set o f API, €PA and UOGA test data. This combined data set includes 34 data points that extend up to a PVAHV value of about 78 psia ft. and include WOGA test data on crude oil.

API MPMS*39=3D 93

I

84.0

m

0732290 0533472 377

m

CONCLUSION

I

Equation (8-22) was selected f o r use i n c a l c u l a t i n g the vented vapor saturation 'factor, Ks, i n A P I Publication 2518, Second Edition [A7]. This equation was developed from a c o r r e l a t i o n o f the A P I , ?PA and WOW t e s t data, and e x h i b i t s the same trends with varying PYA and Hvo t h a t were exhibited by Eq (8-

--```,``-`-`,,`,,`,`,,`---

21) o f the theoretical analysis.

//^:^^#^~^^""~:@":^*^~$~


Not for Resale

A P I MPMS*tLS=LD 9 3

0732290 O511473 005

-

i

t

8

ci

m

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Y

(1

x

O

t;:

ro! 4 Y

A

a

L

ai* O

E

c -

e

U

1

u m O c

oL


Not for Resale

--```,``-`-`,,`,,`,`,,`---

(Co

.

A P I MPMS*:LS=LD 93

Table B2

I-

-

m

0732290 0511474 T4L D

Sumaary o f €PA Tests f20] Selected

Product Type

Insu1ated Tank (Yes/No)

Selected

EPA- 1A

Isopropanol

N

Y

€PA- 18

I sopropanol

N

Y

€PA-PA

Ethanol

N

Y

EPA-PB

Ethanol

N

Y

EPA-2C

Ethanol

N

Y

€PA-3A

Glacial Acetic Acid

N

Y

€PA-38

Glacial Acetic Acid

N

Y

EPA-4A

Formaldehyde

Y

N

€PA-4B

Formaldehyde

Y

N

€PA-IC

Formaldehyde

Y

N

€PA- 5A

Ethyl Benzene

N

Y

€PA-5B

Ethyl Benzene

N

Y

EPA-6A

Cyclohexane

N

Y

EPA-6B

Cyclohexane

N

Y

€PA-6C

Cyclohexane

N

Reasons for Rejection

Reasons f o r Rejection: (1) Tank i s insulated.

--```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

93 W 0732290 0511475 988

--```,``-`-`,,`,,`,`,,`---

A P I MPMS*LS.LD

I

B Q)

c

9 c

I

- 1

n

u

d

L O


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Table B4

- Summary o f UOGA

Tests [17] Selected ~~

--```,``-`-`,,`,,`,`,,`---

Product TYPe

Test No.

RV P

Selected

Insu1 ated Tank

(Psi 1

(Yes/No)

(Y es/No) -

YOGA- 1A

YOGA-18

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

YOGA- 1c UOGA-2A

UOGA-26

UOGA- 3A WûûA-38

UOGA-4A UOGA-4B UOGA-5 WOGA-6 UOGA 7A WOGA-7B WOGA- 7c WOW-8A

-

UOGA-88 UOGA-8C UOGA- 9A WOGA-98

YOGA-9c

UOGA- 1OA UOGA- 106 UOGA- 1OC WOGA- 11A UOGA-11B UOGA- 12 UOGA- 13A UOGA- 138 WOGA-14 UOGA- 15

Crude Oil Crude Oil Crude Oil Crude Oil Crude O i l Di sti 11ate Di sti 11ate Crude Oil Crude Oil Fuel Oil Di s t i 11ate Crude Oil Crude Oil Crude Oil Crude Oil Crude Oil Crude O i l Crude Oil Crude Oil Crude Oil D i s t i l l ate Distillate Distillate Crude Oil Crude Oil Crude Oil Crude Oil Crude Oil D i s t i11ate Crude Oil

1.8 1.8 1.8 0.8 0.0 - 0 -

- 0 -

1.3 1.3

----3.4

3.4 3.4 1.2 1.2 1.2 5.3 5.3 5.3

-----

N

N N Y Y Y Y N N Y

O O O O 1,030 O 15,300

29,200 15,800 14,930 19,220 19,300 4 ,740 5 ,800 5,800 O O O 33

N N N N N

0.1 15.1 0.5 0.5

Y Y N N N

3.0

42

N N N N

---

---

31

N

N N N

o. 1

O O O

7 430 18,300 18,320 7,675 1,800

N N

BI 9 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

Y Y Y N N N N Y Y

N N Y Y Y Y Y Y

N N N N N N

N N N N

N N Y

Reasons

for Reject i on

API MPflS*Lq=LD 93 --```,``-`-`,,`,,`,`,,`---

Table 94

- Sitmaiary of

0732290 0511477 750

Tests 1171 Selected (Continued)

YOGA

~

Test No.

Product Type

RVP

(Psi 1

~

Selected

Insu1ated Tank

(Y es/No)

(Yes/No)

Reasons for Reject i on

YOGA- 16A YOGA- 168

yoGA-16C WGA-17A W-17B

wOGA-18A YOGA- 18B YOGA- 18C YOGA- 19A WûA- 198 WOGA-ZOA WOU- 206

UOGA-ZIA UOûA- 2 1B

Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l Crude O i l D i st il 1ate D i still ate

5.2 5.2 5.2

N N

4,029 5 857 5 454

N

5.5

N

17,058

5.5 0.4 O. 4 0.4 3.0 3.0 4.1 4.1

N N N

16,059

N N N

284

N

---

N N

---

O O O

N

173

O O 27,210 25,680

Y Y Y Y Y N N N Y Y Y Y

.

4 4 4

N

2

N

2

Reasons for Rejection:

( I ) Tank i s insulated. (2) Product i r a distillate or fuel o i l . The vapor pressure versus temperature behavior of these stock types was not well established i n these tests. (3) The l i q u i d sample may not be representative of the t a n k stock during the test. (4) lhe RVP was less than 1.0 psi and the stock vapor pressure i s , theretherefore, questionable. (5) The vented gas volume outflow, Q, appears t o be i n error.


Not for Resale

.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

~~

A P I MPMS+LS.LD

0 7 3 2 2 9 0 0 5 1 1 4 7 8 b97

i

u c

c

93

I

--```,``-`-`,,`,,`,`,,`---

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\


Not for Resale

API MPMS*19.1D 93

0732290 0511479 523

n

z

Y

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

L

. Y

&E

i

c

zeì 4J S t - 4 J

L

O

&

::

Y

e

O c &

a

L

3 c,

a

v) I

rn m

I

ü

..

. I

o

U

L O --```,``-`-`,,`,,`,`,,`---


Not for Resale

=

A P I MPMS*37.3D

Table B6

-

93

Sumnary o f Test Data Used t o Develop the Vented Vapor Saturation Factor Corre1 a t i o n

Test

PVAHV (psia ft)

No.

------

--```,``-`-`,,`,,`,`,,`---

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API- 1 API- 2 API- 3 API- 4 API- 5 API- 6 API- 7 API- 8 API- 9 API-10

1.025 O. 958 O. 967 O. 983 O. 965 O. 963 O. 866 O. 884 O. 958 1.O33

€PA- 1A EPA- 1B EPA-.ZA EPA-2B EPA-2C EPA-3A EPA-38 €PA- 5A EPA- 5B €PA-6A EPA-6B EPA-6C

O. 553 O. 547 o. 551 0.521 O. 506 O. 779 O. 737 1.062 O. 933 O. 240 O. 204 O. 178

o. ao9

WOW-IA WOûA- 1B WOU- 1c WOU-4A UOGA-48 WOU-7A UOGA-78 UOGA-7C UOGA-8A WOûA-8B WOU-ac WOGA- 15 WOGA- 161 WOGA- 16E WOGA- 16( UOûA- 171 WOGA- 171 WOGA- 191 WOGA- 191 WOGA- 201 WOGA-201

1.416 1.976 1.842 0.725 O. 763 0,211 o. 218 O. 214 0.815 O. 834 0.826 1.522 O. 666 0.661 O. 685 o. 959 O. 943 1.456 1.406 O. 775 O. 780

---------

O. 0434 O. 0338 0.0177 O. 0363 o. 0380 0.154 O. 131 O. 0442

------

O. 827 0.816 0.918 O. 975 o. 284 0.356

-----

O. 0716 3.17 3.90 4.62

-----

O .379 0.311 3.74 3.59 3.67 O. 227 0.199 0.211

-----

O. 502 O. 513 O. 460 O. 0428 O. 0604

---------

O. 290 O. 282


0732290 0 5 3 3 4 8 0 245

Not for Resale

~

O. 0474 O. 0504 0.0531 O. 0539 O. 0521 O. 0467 O. 0865 O. 126

o. 111 0.106

18.26 19.11 11.63 11.81 10.00 7.29 8.32 2.77 2.69 34.79 33.15 33.39 9.11 7.65 6.72 6.65 6.29 78.26 75.53 76.80 21.11 20.60 20.80 5.18 7.43 7.49 7.20 26.36 26.85 4.20 4.37 11.22 11 .o2

API MPMS*LS*LD 73 m 0732270 OSLLLt8L L B L m

Vented Vapor

Heat

0

Figure 81

- Vented Schematic o f the Tank Vapor Space f o r t h e Vapor Saturation Factor Analysis

--```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

m 0732290 05LLq82 018 m

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I M P M S + L S = L D 93

0.8 O. 7

0.6 O. 5

. . ..

c ul

VI

aJ

w C O

.

0.4

...

.

,

.

.

..

<

:T.'d

_-.

.

.

,

:

. . . . .. ..

I _ .

.

'

'

..

.

I

'I

.. .

!.

.

.

.

................. _____-__._ .

.r

VI

C

a E

O. 3

u

Y

* ul

0.2

. .

. .

. .

. . . . . . . . . . ,!. ,..

.

1

O. 1

.

.

.

...

..l. !

.

.

i'

i

I

40

10

O

I

50 i,;.'. .

-

Saturation Factor, Ks, Versus PVAHV for the API and €PA Test Data

--```,``-`-`,,`,,`,`,,`---

Figure B2


Not for Resale

93

= 0732290

0511483 T 5 4

--```,``-`-`,,`,,`,`,,`---

A P I MPMS*ltS.LD


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API MPMS+19.LD 93 W 0732290 0511484 990 M '

--```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API MPMSt19.1D

93

0732290 0511485 8 2 7

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API PUBLICATION 2518 ûûCUMENTATION FILE

SECTION C

DEVELOPHENT OF VAPOR SPACE TEMPERATURE FACTOR, KT

--```,``-`-`,,`,,`,`,,`---


CI Not for Resale

--```,``-`-`,,`,,`,`,,`---

API PUBtICATION 2518 DOCUMENTATION FILE SECTION C

TABLE OF CONIENTS

PAGE .

DESCRIPTI ON

SECTION

............................................. C4 C6 INTRODUCTION............................................. HEAT TRANSFER MODEL DESCRIPTION.......................... C8 HEAT BALANCES............................................ CO Roof Heat Balance ....................................... C9 C9 North Shell Heat Balance............................... South Shell Heat Balance............................... C10 fias Space Heat Balance ................................. C10 Heat Transfer Equations ................................ C10 Tank Element Temperature Equations ..................... C11 VAPOR SPACE TEMPERATURE FACTOR........................... C13 Gas Space Temperature Equation ......................... C13 Maximum 6as Space Temperature .......................... C15 Minimum Gas Space Temperature .......................... C15 Average Gas Space Temperature ........................... C15 C16 Gas Space Temperature Change ........................... C16 Ambient Temperature Range Factor ....................... Area Equations ......................................... C18 Gas Space Temperature Change Equation .................. C19 Vapor Space Temperature Factor .........................C20 NOMENCUTURE

c1

.o

c2.0 C3.0

C3.1 C3.2 c3.3 c3.4 c3.5 C3.6 C4.0 C4.1 C4.2 c4.3 c4.4 c4.5 C4.6 c4.7 c4.a c4*9 cs.0 C6.0 C7.0

C8.0 c9.0 c10.0

.

............................................ C20 TYPICAL SOLAR INSOLATION PARAHETERS...................... C23 ONE COLOR TANK ...........................................C26 TWO COLOR TANK

TYPICAL HEAT TRANSFER COEFFICIENTS AND TYPICAL VAPOR SPACE ASPECT RATIO

C27

TYPICAL METEOROLOGICAL PARAMETERS AND TYPICAL PAINT SOLAR ABSORPTANCE

C29

.......................................

........................................ CONCLUSION...............................................

C30

TABLES

c1

Annual Average Meteoro1ogical Data f o r Selected U.$. Locations [22. 351

.................................... c2


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

C31

.

API?MPMS*LS-LD 9 3 m 0732290 0533487 bTT m

API WBLICATION 2518 DOCUMENTATION FILE SECTION C

TABLE OF CONTENTS (Continued) SECTION

PAGE -

DESCRIPTION FIMIRES

c1 c2

c3 c4

cs

............... C33 Sinusoidal D a i l y Ambient Temperature Variation.. ......... C34 Schematic o f Energy Flows and Temperatures

Vapor Space Temperature Factor, KT, f o r a Heat Transfer Coefficient Ratio, 6, o f 0.1

C35


C36

Vapor Space Temperature Factor, KT, f o r a Heat Transfer Coefficient Ratio, G, o f 0.5

C37

............................. ............................

.............................

C6


c7

E f f e c t o f Heat Transfer Coefficient Ratio, hI/hO, on the ? Average Oifference o f Estimated Emissions.. C39

C8

E f f e c t o f Heat Transfer Coefficient Ratio, hI/ho, on the Standard Deviation i n Average Difference o f Estimated C40 ?mi ssions

c9

..............

................................................ ATA Versus HH f o r Selected U.S. Locations................ C41 ?/ATA Versus HH f o r Selected U.S. Locations............. C42

--```,``-`-`,,`,,`,`,,`---

c10

............................. C38

c3 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*LS.LD

93

= 0732290 0511488 536

API PUBLICATION 2518 DOCUMENTATION FILE SECTION C . NOMENCLATURE

A B

C C

D

E e F f

G 9 H

HH h

I J KSN KT m

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

q rG0 rH T AT t

U 6 d 7

Area Defined by Eq (C-35) Ambient temperature range factor, defined by Eq (C-44) Heat capacity D i ameter Vapor space aspect r a t i o , defined by Eq (C-77) Defined by Eqs (C-19), (C-20) and (C-21) Solar insolation factor, defined by Eq (C-78) Defined by Eqs (C-22), (C-23) and (C-24) Heat transfer c o e f f i c i e n t r a t i o , defined by Eq (C-79) Defined by Eqs (C-25), (C-26) and (C-27) Height Daily t o t a l solar i n s o l a t i o n on a horizontal surf ace Heat transfer c o e f f i c i e n t Solar insolation i n t e n s i t y Solar absorptance r a t i o , defined by Eq (C-80) Defined by Eq (C-68) Vapor space temperature factor, defined by Eq (C-60) Hass Heat transfer r a t e Solar r e f l e c t i v i t y o f the ground Ratio o f IH t o HH, defined by Eq (C-71) Temperature Temperat Ure change lime Overall heat transfer c o e f f i c i e n t Zenith angle, o r the angle between the sun and the normal t o a horizontal surface Sol a r absorptance Atmospheric s o l a r transmittance c4


UNITS

DESCRI PTIo)(

Not for Resale

ft 2 B/hr ft2 d i mension1 B/lbm OF ft dimensionl eso dimension1ess d imens ion1ess dimensionless

d i mens i on1ess OF

ft

B/day ft2 B/hr ft2 OF B/hr ft2 dimensionl ess dimensionless d i mension1ess

lbm B/hr d i mension1ess day/hr OF

OF

hr B/hr f t 2 OF deg . dimens ion1ess dimensionless

--```,``-`-`,,`,,`,`,,`---

SYMBOL

API MPMS*LS.LD 9 3 m 0732290 05LL489 472 m

SUBSCRIPTS

A AV

B 0

G GD H

I L . MN MX N

NI NO O . R

RI RO S

SI SN

so

--```,``-`-`,,`,,`,`,,`---

T

Ambient (or air) Average Beam component of sol ar i nsol at i on Diffuse component o f solar insolation Gas Ground Horizontal surface solar insolation Inside Liquid Minimum Max i mum North shell (or the half of the tank shell facing away from the sun) North shell inside North shell outside Outside Roof Roof i ns i de Roof outside South shell (or the half o f the tank shell facing toward the sun) Sourn shell inside Sol ar noon South shell outside TemperatUre


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

___

A P I MPMS*L9*1D 93

m

0732290 0511490 194

m

--```,``-`-`,,`,,`,`,,`---

This section of the Documentation File to API Publication 2518, Second Edition, presents the development of the equation for the vapor space temperature factor, KT, which is defined as the ratio o f the gas space temperature range, ATg, to the ambient temperature range, ATA. Section C2 describes the heat transfer model. The major assumptions used in the model development are:

o

Assumtion 1 The gas space i s fully mixed (i.e. it is at a uniform temperature and compos'iti on).

o

Assumption 2 The liquid space is fully mixed (i.e. it is at a uniform temperature and composition), and remains at a constant temperature during the daily cycle.

o

Assumption 3 The tank wall in the gas space can be treated as three (3) separate elements: (1) the roof; (2) the half of the tank wall facing away from the sun; and (3) the half of the tank wall facing the sun. Each tank wall element can be characterized by a single temperature, which varies during the daily cycle.

o

Assumption 4 The affects of rain and snow precipitation are not included in the model.

These assumptions are the same as those upon which the API Computer Model i s based [ 3 0 , 38]*. .

Numbers in brackets refer to the numbered references listed at the end of this Documentation File. C6 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

INTROWCTION

C1.0

O732290 05Ll49L O20 //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*LS=LD 93

Section C3 presents the heat balance differential equations f o r each of the tank wall elements and the gas space (see Eqs (C-i),. (C-3), (C-5) and (C-7)). These ordinary differential equations are essentially the same as those used i n t h e A P I Computer Model [30, 381, where they are solved by stepwise numerical integration

.

A sensitivity analysis 1301 of the API Computer Model showed that the gas and tank wall heat capacity terms i n the differential equations have a negligible

a f f e c t on the computed results. Thus, the following additional assumption was made:

o

Assumption 5 The heat capacity terms i n the energy balance equations can be neglected i n comparison t o the other heat transfer terms.

Section C4 presents the solution t o these simultaneous equations by. solving for the gas temperature, TG (see Eq (C-36)). and gas temperature range, Al6 (see Eqs (C-58) and (C-59)). Section CS presents the vapor space temperature factor equation for the general case of a two color fixed-roof tank, where the roof and shell -are painted different colors (see Eqs (C-74) through (C-80)). Section C6 presents the vapor space temperature factor equation f o r the simplified case of a two color fixed-roof tank where typical solar insolation parameters are used (see Eqs (C-89) through (C-94)). Sections C7, Cû and C9 present the vapor space temperature factor equation f o r progressively simplified cases where more typical information is used instead o f detail information f o r a particular tank (see Eqs (C-97), (C-106), (C-110) and (C-115)). As less detail information is used for the calculation o f Ki, the estimation equations become simpler, b u t the estimated value o f KT becomes less accurate for a specific tank.


c7 Not for Resale

--```,``-`-`,,`,,`,`,,`---

Y i t h this assumption, the differential equations reduce t o a s e t of four (4) simultaneous algebraic equations (see Eqs (C-16), (C-17), (C-18) and (C-29)).

HEAT TRANSFER MOOEL DESCRIPTION

C2.0

--```,``-`-`,,`,,`,`,,`---

Figure C1 i s a schematic of the energy f l o w s and temperatures f o r a fixedr o o f tank. The gas space tank w a l l i s divided i n t o three (3) tank w a l l e l entents:

o o

o

.

the roof, the h a l f (referred the h a l f (referred

o f the gas space tank s h e l l t h a t faces away from t h e sun t o herein as the "north shell"), and o f the gas space tank s h e l l t h a t faces toward the sun t o herein as the "south s h e l l " ) .

Each o f these tank wall elements i s characterized by a single, different temperature, TR, TN and Ts, respectively. The temperature o f each wall element varies with time over the course o f the d a i l y cycle i n response t o a heat balance on the wall element. The elements exchange heat on both t h e i r i n s i d e and outside surfaces. The inside o f each element exchanges heat with the gas, which i s characterized by a single temperature, 16, by natural convention heat transfer. Heat transfer on the inside surface by long wave length thermal radiation, however, i s neglected because the magnitude o f t h i s heat t r a n s f e r r a t e i s small i n comparison t o the natural convection heat transfer rate. The outside of each element exchanges heat w i t h the ambient a i r by convection due t o the wind. I n addition, the outside o f each element receives solar insolation due t o beam solar i n s o l a t i o n (except the north shell), d i f f u s e solar insolation, and ground reflected s o l a r i n s o l a t i o n . Each wall element also exchanges heat by long wave length thermal r a d i a t i o n with the tank surroundings. This l a s t mode o f heat t r a n s f e r i s incorporated i n the outside heat t r a n s f e r c o e f f i c i e n t f o r each element, hRO, hNO and hso, respectively. I t should be noted t h a t the thermal resistance o f any thermal i n s u l a t i o n material applied t o the outside surface o f the r o o f and shell elements can be incorporated i n the outside heat t r a n s f e r c o e f f i c i e n t s hRO, hNO and hSO.


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*:LS-LD 9 3

m

0732290 0511493 9T3

m

The gas space exchanges heat by natural convection w i t h the wall elements and the l i q u i d surface, which i s assumed t o be a t a constant liquid temperature, TL, during the daily cycle. The gas space i s assumed t o be fully mixed, so t h a t i t can be characterized by a single temperature, 76. (3.0

HEAT BALAHCES

Sections C3.1 through C3.4 describe the heat balances t h a t can be written for each o f the four elements. C3.1

Roof Heat Balance

--```,``-`-`,,`,,`,`,,`---

lhe term on the r i g h t hand side o f Eq (C-1), which represents the heat capacity effect o f the roof, will be neglected because i t s magnitude a t most times during the course of the d a i l y heating cycle i s small i n comparison t o the other terms. Eq.(C-1) then reduces t o :

C3.2

North Shell Heat Balance

The tern on the r i g h t hand side o f Eq (C-3) will again be neglected because its magnitude is small i n comparison t o the other terns. Eq (C-3) then reduces to:


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API flPflS*:LS-LD 9 3

0732290 0511494 83T

South Shell Heat Balance

%o

+

%I

mscs

=

p]

The term on the right hand side of Eq (C-5) will again be neglected because its magnitude i s small i n comparison t o the other terms. Eq (C-5) then reduces to: 9SI = O

qso

Gas Space Heat Balance

The term on the r i g h t hand side of Eq (C-7) wi-ll again be neglected because its magnitude is small i n comparison t o the other terms. Eq (C-7) then reduces to:

4121

C3.5

+

QI

+

qSI

+

QL

0

Heat Transfer Equations

qNO

hNO AN (TA -.TN)

+ ali(

[i

1

ANID

+ 2 ANrGD


Not for Resale

(IgCOS 8 +

ID)

1

(C-il)

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

C3.4

--```,``-`-`,,`,,`,`,,`---

C3.3

-

A P I MPMS*LS.LD

93

= 0732290 05LL495

776

(C-12)

1

DHGIB Sin 8

t

- AsIo

t

2

(C-14)

(C-15)

C3.6

Tank E l ement Temperature Equations

Eqs (C-9)

through (C-15) can be substituted i n t o the tank element energy balance relations, Eqs (C-2), (C-4), and (C-6), t o r e s u l t i n the f o l l o w i n g tank element temperature equations, Eqs (C-16) through (C-18).

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

TN

(C-17)

= eNTG + fNTA + 9N

(C-19)


Not for Resale

--```,``-`-`,,`,,`,`,,`---

(C-13)

API MPMS*LS-LD 93

0732290 0533496 602 D

(C-20)

(C-21)

(C-22)

fR

(C-23)

fN

(C-24) --```,``-`-`,,`,,`,`,,`---

fS

(C-25)

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

(C-26)


Not for Resale

A P I MPMS*Lq.LD

93

m 0732290 0511497 549 m

1

r

9s =

(C-27) hSI

+

hSO-

C4.0 VAPOR SPACE TEIIPERATURE FACTOR --```,``-`-`,,`,,`,`,,`---

C4.1

Gas Space Temperature Equation

The gas space temperature equation can be developed from the gas space energy balance equation, Eq (C-8). Substituting Eqs (C-io), (C-12), (C-14) and (C-15) into Eq (C-8), we obtain:

(C-28) Eq (C-28) may be rewritten as follows:

(C-29) Eqs (C-16), (C-17) and (C-18) may now be substituted into Eq (C-29) for the terms TR, TN and Ts, respectively. The resulting equation may be rearranged by factoring out the temperatures TG, TA and TL to obtain:

Substituting the expressions for eR, eN, es, fR, fN, fS, gR, gN and gs found i n Eqs (C-19) through (C-27), the above Eq (C-30) becomes:

C13 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API MPMS*I,S.LD

TG (URAR

+

UNAN

+ UsAs +

hLAL)

TA WRAR + UNAN + USAS) + TL

93

0732290 0 5 3 3 4 9 8 4 8 5

=

(WL)+

(C-31)

BAL

where UR, UN, Us and B are defined by Eqs (C-32) t h r o u g h (C-35).

(C-32)

(C-33)

(C-34)

B =

Eq (C-31) may now be solved f o r TG t o obtain:

(C-36)


--```,``-`-`,,`,,`,`,,`---

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Maximum Gas Space Temperature

The maximum gas space temperature, Noon. Eq (C-36) then becomes:

TG,MX, will generally occur a t Solar

where BSN represents Eq (C-35) w i t h the terms Ig, ID and 8 evaluated a t Solar Noon. C4.3

Minimum Gas Space Temperature

.

The minimum gas space temperature, TG,", w i l l occur i n the n i g h t a t the t i m e o f minimum ambient temperature, TA,^, when there i s no s o l a r i n s o l a t i o n (i .e. when B

-

O).

Eq (C-36) then becomes:

(C-38)

C4.4

Averaqe Gas Space Temperature The average gas space temperature, T ~ , A v , i s defined by Eq (C-39):

T

TG,MX + TG,MN ~= , ~ 2 ~

Substituting Eqs (C-37) and (C-38) i n t o - E q (C-39), we obtain:

(C-40)

c15

//^:^^#^~^^""~


Not for Resale

--```,``-`-`,,`,,`,`,,`---

C1.2

API MPMS*
0732290 0533500 963 D

Gas Space Temperature Change

C4.5

The gas space temperature change, ATG, may be determined by subtracting Eq (C-38) from Eq (C-37) t o yield:

AT- = *~A,sN("R~R

+

u ~ A N+ "9s)

+

BsNA~

(C-42)

where ATA,SN i s are defined as follows: ATA,SN

(TA,SN

.. TA,MN)

(C-43)

Ambient Temperat Ure Range Factor

C4.6

It i s convenient t o define the ambient temperature range factor, C, as f 011ows : CIE

AT^, SN

(C-44)

ATA

or (C-45)

ATA,SN = C ATA

where

ATA i s defined as follows:

ATA

=

(TA,MX

-

(C-46)

TA,MN)

Figure C2 depicts a sinusoidally varying d a i l y ambient temperature. The ambient temperature varies from i t s minimum value, TA,MN, a t time tMN t o i t s Eaximum value, TA,MX, a t t i m e tm. This sinusoidal v a r i a t i o n i s described by Eq (C-47).

C16 --```,``-`-`,,`,,`,`,,`---


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

(C-41)

A P I FlPHS*:LS-LD 9 3

-

t ATA S i n

T~

T

~

,

~

0732290 05LLSOL 8 T T

[EI

(t-- tMX+ 611

~

=

(C-47)

I t is coranon for the maximum ambient temperature t o occur about 2 hr after Solar Noon, or a t 14:OO hrs. For this reason, we will select:

tm

=

(C-48)

14 hr (or 14:OO hrs)

With this value for

tm,

E q (C-47) becomes: ~

TA * T

~

ATA Sin +, ~

(C-49)

~

Solar Noon occurs a t tSN: (C-50)

tSN = 12 h r (or 12:OO hrs)

The ambient temperature a t Solar Noon, TA,SN, from Eq (C-49) is:

~

T,

~

T

~

T,

~ t 0.433013 ~, ~ ~ATA

(C-51)

can now calculate C from Eq (C-44) using Eqs (C-43) and (C-51) as follows:


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

Ye

ATA S i n +,~ ~ ~

T

API MPMS*LS-LD 93

-

TA,SN

T

~

,

~

0732290 05LL502 73b

~ //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

C =

-

ATA

C

C4.7

=

(C-52)

0.933013

Area Equations

For a fixed-roof tank with a f l a t roof, the areas AR, AN, AS and AL may be determined from Eqs (C-53) through (C-56). (C-53)

AS =

sOHG 2

(C-54)

2

(C-55)

nwG

nD2

--```,``-`-`,,`,,`,`,,`---

A,, =

(C-56)

'


Not for Resale

'

API MPMS*LS=LD 73 W 0732270 0511503 b72 W

Gas Space Temperature Chanqe Equation

C4.8

Using the area relationships o f Eqs (C-53) through (C-56) and Eq (C-45), we r a y rewrite Eqs (C-40), (C-42) and (C-35), respectively as follows:

(C-57)

T

~

,

~

r

~

7

(C-58) --```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*19=1D 93

The SN a t the end o f Eq (C-59)

0732290 0511504 509 W

indicates t h a t the terms Ig, io and 8 are

evaluated a t Solar Noon. CI.9

Vapor Space Temperature Factor

The vapor space temperature factor, K i , is defined.as the r a t i o of AT6 t o ATA, as follows:

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

(C-60)

Using Eq (C-58), KT becomes:

[

['Dl

c uR t u N -

+

]I?[%

:t

(C-61)

KTæ

1

where BSN i s determined from Eq (C-59). CS.0

TüO COLOR TANK

I f t h e tank roof i s painted a different color than the tank shell, then the s o l a r absorptance of the roof i s aR and the solar absorptance o f the shell is US,

where : QN

(C-62)

aS

--```,``-`-`,,`,,`,`,,`---


c20 Not for Resale

A P I MPMS*LS*LD 93

To s i m p l i f y Eqs (C-57),

O732290 0511505 445

=

(C-59) and (C-61), we w i l l assume t h a t :

(C-63) (C-64) (C-65) Using these simplifications, Eqs (C-57) and (C-61) reduce to:

(C-66)

K, =

(C-67)

æ

AV

r

1

where:

KSN

BSN u ATA

--```,``-`-`,,`,,`,`,,`---


(C-68)

c21 Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMSJLSmLD 93

m

0732290 05LL50b 381

m

It is convenient to rewrite Eq (C-69) in terms of IH and Io instead of 18 and ID. Note the following relation, Eq (C-70), between IH, Ig and ID, and the re1 ation, Eq (C-72), between IH and HH.

(C-71)

IH

=

rH HH

(C-72)

Using Eqs (C-70) and (C-72), Eq (C-69) may be rewritten as follows:

[i-

-

t] t] Tan 8

+

'

(C-73)

SN

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

It i s convenient to define the dimensionless parameters E, F, G and 3 as described by Eqs (C-77), (C-78), (C-79) and (C-ûO), respectively. Using these defined parameters, Eqs (C-66), (C-67) and (C-73) may be rewritten as follows for the case of a two color fixed-roof tank.

--```,``-`-`,,`,,`,`,,`---


c22 Not for Resale

MPMS*LS-LD 9 3 . M 0732290 0533507 23B

APT

=

Two Color Fixed-Roof Tank

C(1 KT

t

4E) t KSN

(2 t 4E

T

T

~

,

~

~

(J

KSN

I

where:

t

(C-74)

t 6)

( 1 t 4E)

,

~

~ (2

+

~

1

TL(I

+ 4E

t

2rGoE) + 2 E [ S

+ 6) t -KSN 2

6)

-

ATA

(C-75)

3 :]

(C-76)

Tan 8 +

SN

.

(C-77) I

(C-78)

[g

G =

J C6.0

=

(C-79)

(C-80)

U

TYPICAL

SOLAR INSOLATION PARAMETERS

The expression for KSN, Eq (C-76), may be simplified for the case o f the typical solar insolation parameters used t o generate the API Computer Data Base (391. These typical solar insolation parameters are developed in Section O of t h i s Documentation File and are based on the following assumed conditions:

--```,``-`-`,,`,,`,`,,`---


C23 Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*19=1D 93

m 0732290

0511508 154

m

Ground reflectivity, rGD, o f 0.1, Tank s i t e latitude i s 35 deg. north, Tank s i t e elevation i s 2000 f t . above sea level, and 'The year day number i s 105 (April 15).

o

o o

o

For the entire API Computer Data Base, parameters rg, rg, rH and following constant parameters (see Table 02) : TO

are the

(C-81)

= 0.0767938

T B = 0.660790

(C-82.)

rH

(C-83)

= 25.5848

(C-84)

deg.

The ratio I g / l ~ an be express d in terms of

70

and

7B

--```,``-`-`,,`,,`,`,,`---

e

= 0.133277

as follows:

(C-85)

Using the values of 70 and 7B listed by Eqs (C-81) calculate the r a t i o I ~ I H from Eq (C-85) as follows:

and (C-82),

we can

O. 0767938 O. 660790

+

O.

* 0.104115

(C-86)

Substituting the above values for IO/IH, rGD, rH and B i n t o Eqs (C-76) and (C-78), we obtain:


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMSt39.3D 93

KSN

=

F (J

0732290 0 5 3 3 5 0 9 O90

(C-87)

t 0.954378 E)

F = r.133277

HH]

Q~

ATA

Eqs (C-52) and (C-87) may be substituted into Eqs (C-74) and (C-75) t o yield the following result of KT and TG,AV for the case o f a two color fixed-roof tank with typical soi ar insolat ion parameters: --```,``-`-`,,`,,`,`,,`---

Two Color Fixed-Roof lank With Typical Solar Insolation Parameters:

0.933(1

KT =

T

+ 4E) (2

~

T

~

,

~

(1

t

i

,

~

i

4E

4E) ~

+

F (J

+

0.954E)

(C-89)

6)

+ TL ~

(1

+

1

6)

+ -ATAF 2

(3 + 0.954E)

(2 + 4E + 6)

(C-90)

where:

(C-91)

F =

G =

O. 133 as

HH

(C-92)

[y

(C-93)

(C-94)


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMSr
0732290 05LL5LO 802

m

ONE COLOR TANK

C7.O

I f the r o o f and shell of the fixed-roof tank are painted the same color, the

s o l a r absorptance of the roof and shell paint can be represented by the same value, Q: p

Q

as =

(C-95)

QR

Substituting these values i n t o Eq (C-94), we see that:

J = l

(C-96)

Eqc (C-95) and (C-96) may be substituted i n t o Eqs (C-89) and (C-90) t o give the following result of KT and TG,AV for the case of a one color fixed-roof tank w i t h typci al sol ar insol a t i on parameters : --```,``-`-`,,`,,`,`,,`---

One Color Fixed-Roof Tank With Typical Sol a r Insol ation Parameters: 0.933(1

t

KT

T

(2

~

T

~

,

~

4E)

+

+

4E

F(l

~

(C-97)

+ 6)

(1 t 4E)

,

0.954E)

t

~

+ TL ~

(2

1 (1 t 6) t -ATAF (1 . 2 t

4E

+

0.954E) (C-98)

+ 6)

where:

E

=

[>]

I

0.133

=

(C-99)

Q

1

HH

hg AT*

( c - 100)

(C-101) I


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I NPNS*19.1D

93 H 0732290 0511511 749

the vapor space temperature factor, KT, dimensionless parameters, E, F and 6. Thus,

~

depends only on the

three

figures C3 through C6 illustrate the dependency of KT on E, F and G. NPICAL HEAT TRANSFER COEFFICIEHTS AND TYPICAL VAPOR SPACE ASPECT RATIO

c8.0

Figures C7 and C8 show the effect of heat transfer coefficient r a t i o , 6, on the average percent difference of estimated emissions compared t o the A P I Computer Data Base [39] and the A P I Test Data [33]. These figures show that the following average value may be selected for 6:

G

=

0.45

(C-102)

value of G corresponds t o the following average values for t h e inside and outside heat transfer coefficients, h I and ho, respectively: This

--```,``-`-`,,`,,`,`,,`---

hI = 0.65 B/hr ft2

OF

( G-103 )

ho = 1.45 B/hr ft2

OF

(C-104)

Figure CS, which i s for a value of G

-

0.50, shows t h a t KT depends l i t t l e on the value o f the vapor space aspect ratio, E, as the insolation factor, F, varies from 1 t o 10. An average value of E may be selected as follows:

E = 1.0

(C- 105)

Substituting the typical values o f G, h i , ho, and E listed i n Eqs (C-102) through (C-105) into Eqs (C-89) through (C-94) for a two color fixed-roof t a n k , we obtain the following results for KT, ATy and TG,AV:


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I M P M S * L S = L D 93

0732290 05L25L2 6 8 5 D

Two Color Fixed-Roof Tank With Typical Solar Insolation Parameters, Typical Heat Transfer Coefficients, and Typical Vapor Space Aspect Ratio:

KT = 0.723 t û . 0 2 7 9 p j

(C-106)

ATy = 0.723AT~t 0.0273oH~

(C-107) (C-108)

where: S'

a =

+

*R

(C- 109)

2

Substituting the typical values of 6, h I , ho and E listed i n Eqs (C-102) through (C-105) into Eqs (C-97) through (C-101) f o r a one color fixed-roof tank, we obtain the following results f o r K i , ATy and TG,AV:

KT

= 0.723

+

0.0279

E]

(C-110)

--```,``-`-`,,`,,`,`,,`---

One Color Fixed-Roof Tank With Typical Sol ar Insolation Parameters, Typical Heat Transfer Coefficients, and Typical Vapor Space Aspect Ratio:

(C-ill)


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

(C-112)

C9.0

93

= 0732290 0511513 511 m

I

TYPICAL METEOROLOGICAL PARAMETERS AND TYPICAL PAINT SOIAR ABSORPTANCE

Figure C9 i s a p l o t o f the ambient temperature range, ATA, as a function o f the daily. t o t a l solar i n s o l a t i o n on a horizontal surface, HH, f o r the selected U.S. locations l i s t e d i n Table C 1 [the meteorological data are from Table 6 i n Ref. A7]. Figure C10 i s a p l o t o f the r a t i o (“/ATA) as a function o f ATA for the same locations presented i n Figure C9. For these locations, the average is: annual value o f (“/ATA)

” = 66.0

(C-113)

B / f t 2 day OF

ATA I f specific information i s not available on the tank paint c o l o r and paint condition, a white shell and white roof, w i t h the p a i n t i n good condition, may be assumed. For t h i s assumed condition, the f o l l o w i n g value o f p a i n t solar absorptance may be used: a = 0.17

(C- 114)

Substituting the t y p i c a l values f o r (“/ATA) and a from Eqs (C-113) and (C-114) i n t o Iqs (C-110) through (C-112), we obtain the following t y p i c a l r e s u l t f o r KT, ATy and TG,AV. --```,``-`-`,,`,,`,`,,`---

One Color Fixed-Roof Tank With Typical Sol ar Insol ation Parameters, Typical Heat Transfer Coefficients, Typical Vapor Space Aspect Ratio, Typical Meteorological Conditions, and Typical Paint Solar Absorptance:

KT

(C- 115)

= 1.04

(C- 116)

ATy = 1.04 ATA

(C-117)


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^

A P I MPMS*lS.lD

A P I MPMS*17-1D 93

C10.0

m

0 7 3 2 Z 9 0 0511514 458

m

CONCLUSION

In sumnary, Equations (C-61), (C-74), (C-89). (C-97), (C-1061, (C-110) or (C-115) may be used to estimate KT, depending upon the level o f detail in the information available for a specific tank. As less infomation i s available, the equation used f o r the calculation of KT becomes simpler, but the calculated value of KT will be less accurate for the specific tank. Equation (C-107) was selected for use in calculating the daily vapor temperature range, ATy, in API Publication 2518, Second Editibn [A7]. T h i s equation is based on a comprehensive analytical heat .transfer model o f the tank vapor space during a daily heating cycle. Equation (C-107) was developed from a more complete expression, Eq (C-58), by incorporating several simp1 ifications that make the calculations more user friendly, with little loss in accuracy. --```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

I

API MPMS*LS=LD 93

Table C 1

Location Birmingham, AL Hontgomery, AL Homer, AK Phoenix, AZ Tucson, Aï Fort Smith, AZ l i t t l e Rock, AR Bakersfield, CA long Beach, CA Los Angeles, CA Sacramento, CA San Francisco, CA Santa Maria, CA Denver, CO Grand Junction, CO Yilmington, DE Atlanta, GA Savannah, 6A Honolulu, HI Chicago, I L Springfield, Il Indi anapol is, I N Wichita, KS Louisville, KY . Baton Rouge, LA Lake Charleston, LA New Orleans, LA Detroit, HI Grand Rapids, MI H i nneapol i s , MN

- Annual

0732290 0533535 394

Average Meteorological Data for Selected &S.- Locations [22,35]

TA,MX

TA,MN

(OF)

(OF)

73 20 75.90 43.20 85.10 81.70 72.50 72.90 77.70 74.20 70.10 73.40 64.90 68.30 64.30 65.70 63.50 71.30 76.70 84 + 20 58.70 62.6G 62.00 67.60 66.10 78.00 77.60 77.70 58.20 57.20 54.20

51.10 53.90 29.50 57.30 54.20 49.00 50.80 53.30 53.50 55.00 47.80 48.30 45.30 36.20 39.60 44.50 51.10 55.10 69.70 39.70 42.50 42.20 45.10 46.20 57.00 58.30 58.70 38.90 37.70 35.20

HH

TA,AV

(B/day ft2) (OF) 1345 1388 838 1869 1872 1404 1404 1749 1598 1594 1643 1553 1608 1568 16591208 1345 1365 1639 1215 1302 1302 1502 1216 1379 1365 1437 1120 1135 1170

62.15 64.90 36.35 71.20 67.95 60.75 61.85 65.50 63.85 62.55 60.60 56.60 56.80 50.25 52.65 54.00 61.20 65.90 76.95 49.20 52.55 52.10 56.35 56.15 67.50 67.95 68.20 48.55 47.45 44.70

ATA

(3

(OF)

(B/day f t 2 OF)

22.10 22.00 13.70 27.80 27. SO 23.50 22.10 24.40 20.70 15.10 25.60 16.60 23.00 28.10 26.10 19.00 20.20 21.60 14.50 19.00 20.10 19.80 22.50 19.90 21 .o0 19.30 19.00 19.30 19.50 19.00

60.860 63.091 61.168 67.230 68.073 59.745 63.529 71.680 77.198 105.563 64.180 93.554 69.913 55.801 63.563 63.579 - 66.584 63.194 113.034 63.947 64.776 65.758 66.756 61.106 65.667 70.725 75.632 58.031 58.205 61.579

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

I

C3 1

--```,``-`-`,,`,,`,`,,`---


Not for Resale

Table C 1

- Annual

Average Heteorological Data f o r Selected U.S. Locations [22,35] (Continued)

-

Jackson, MS Billingsw, MT Las Vegas, NV Newark, NJ Roswell, NM Buffalo, NY New York, NY C1eve1and, OH Columbus, OH Toledo, OH Oklahoma City, OK Tulsa, OK Astoria, OR Portland, OR Phi1adel phia, PA Pittsburg, PA Providence, R I Columbia, SC Sioux Falls, SD Memphis, TN Corpus Ch., TX Houston, TX Midland-Od., TX Salt Lake, UT Richmond, VA Seattle, UA Charleston, Mi Hungtinton, UV Cheyenne , WY

TA, MN

"li

(OF) -

(OF)

(B/day ft2)

52.90 35.40 52 A O 45.90 47.50 39.30 47.50 40.70 41.80 38.30 48.60 49.20 43.10 44.00 45.10 40.70 41.20 51.20 33.90 51.90 62 50 57.40 49.90 39.30 46.50 43.90 44.00 45.00 33.10

1409 1325 1864 1165 1810 1034 1171 1091 1123 1133 1461 1373 1O00 1067 1169 1069 1112 1380 1290 1366 1521 1351 1802 1603 1248 1053 1123 1176 1491

76.30 57.90 79.60 62.50 75.30 55.80 61.00 58.50 61.50 58.80 71.20 71.30 58.10 62.00 63.40 59.50 59.30 75.30 56.70 71.60 81.60 79.10 77.00 64.00 68.80 58.90 65.50 65.30 58.30

TA,AV

- 23.40 (OF)

64.60 46.65 66.20 54.20 61.40 47.55 54.25 49.60 51.65 48.55 59.90 60.25 50.60 53 .O0 54.25 50.30 50.25 63 25 45.30 61.75 72.05 68.25 63.45 51.65 57.65 51.40 54.75 55.15 45.70

22.50 26.80 16.60 27.80 16.50 13.50 17.80 19.70 20.50 22.60 22.10 15.00 18.00 18.30 1-9.20 18.10 24.10 22.80 19.70 19.10 21.70 27.10 24.70 22.30 15.00 21.50 20.30 25.20

(B/day ft*

OF)

60.214 58.889 69.552 70.181 . 65.108 62.667 86.741 61.292 57.005 55.268 64.646 62.127 66.667 59.278 63.880. 55.677 61.436 57.261 56.579 69.340 79.634 62.258 66.494 64.899 55.964 . 70.200 52.233 57.931 59.167


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

Locat ion

TA,MX

t

o

NorthShen

0732290 0533537 3b7

--```,``-`-`,,`,,`,`,,`---

API MPMS*3S-LD 93

south

-shell

Q qNI

/

QL

n //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

TN

D

Figure. C1

- Schematic o f Energy Flows and Temperatures


Not for Resale

A P I PlPPlSt19-1D 93

T

n

U

IA

m

0732290 0511518 O T 3

m

t

O

.

6 L

I

3

l

I

I

I

I

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

u

1

3 L

I

I 1 I I I

.

I I I I I I I

€

a

Time, t (hr)

Figure C2

- Sinusoidal

Daily Ambient Temperature Variation

--```,``-`-`,,`,,`,`,,`---

c34


Not for Resale

A P I MPMS*LS-LD 9 3

0732290 05LL5LS T 3 T

n

ul

cn

Q,

c

c

O

. r

ui

c

Q,

E

c

U Y

LL a

L O

c>

E

O

.c

c>

--```,``-`-`,,`,,`,`,,`---

U

LL

F

O u,

E

Y

L

-.

-r Thi8 document i 8 part of the API 8t8ndards äepelopmant proce86 and io intended for urne by API c O n r a i t t ~ 8 I t 8 h a l l not be reproduced Or circulated or quoted, i n whole or i n part, outaide of t h e cognizant API coamittee(s) except with the w r i t t e n approval of M I . This draft API standard w i l l be formatted and edited prior t o API publication. Copyright e1990. c35 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

v)

A P I M P M S t l i î . L D 93

m 0732290 0533520 753 m

c5

ur

v, QI c --```,``-`-`,,`,,`,`,,`---

E

O

Y

LL c

L

O C

O

,

.

E

O

c

0 Q

c

2S

œ

L

tu O

v,

a L


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

1

API MPMSlitLS-LD 73 9 0732270 05LL521 b78 9

n VI

VI

al

-

c

E O

VI

E

E

‘c

U Y

LL

L O c, V

o

LL

O

c,

o

c

O VI

E

u

L

tu

F

O

rn

--```,``-`-`,,`,,`,`,,`---


c37 Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

E v

A P I MPMS+1S=1D 93

m

m

0732290 0511522 524

O 4

e O

œ

n v) v)

aJ c E

CS œ

O

c

O

c aJ

O Y

-

LL

L O c>

U

IU

u.

E

O

.c &

ia

L

O v)

E

m

L

m

c O

v)

--```,``-`-`,,`,,`,`,,`---


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

E

.C

A P I PlPPlS*LS-LD 93

0732290 05LL523 4b0

(D

8

n v)

ur

aJ * E O

c v)

E

a

E

.c

O

-

Y

U

O

o

c

\ w

æ

O X

I

--```,``-`-`,,`,,`,`,,`---

2 '

-O

u ic ic

i O

1


c39 Not for Resale

õ O O

>

d

J

I

I

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Cu

A P I MPMS*LS=LD 93

I

= 0732290 0511.524 3T7 1

1

I

i

v)

-r

I

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\ --```,``-`-`,,`,,`,`,,`---

4

O

v)

c

VI

Il

oz

c3

I

Not for Resale

E

\ œ

c

4


O

.

n

Cu

c,

e

2

U \

J c, Eo

Y

I I .L

c

O

. r

c,

m

w

O UY

c

œ

L

m

c O Y,

C

e


o c

m

Not for Resale

O

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

API MPMS*’c’L9=1D 9 3 W 0732290 0511525 233

A P I MPMS*IJS-LD 93

0 7 3 2 2 9 0 0511526 L 7 T W

--```,``-`-`,,`,,`,`,,`---


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API MPMS*LS*LD 93 m 0732290 05LL527 006 m

API PUBLICATION 2518 005=llCllENTATIO)( FILE

--```,``-`-`,,`,,`,`,,`---

SECTIOIS O

DEVELOPMENT OF SOUR INSOLATION PARØWETERS

O1 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I PUBLICATION 2518 DOCUMENTATION F ILE SECTION D

CONTENTS PAGE .

DESCRIPTION

SECTION

03.10 03.11 03.12 03.13

............................................. 03 IN7RODUCTIOff............................................. 04 SOLAR INSOLATION EQUATIONS...............................04 Declination. 6 .........................................04 Zenith Angle a t Solar Noon. 8 s ........................ ~ 05 Sunset Hour Angle. o ...................................DS Atmospheric Transmittance f o r Bean Sol ar I n s o l a t i o n a t Solar Noon. TB. $N ................................... 05 Atmospheric Transmittance f o r Diffuse Sol a r Insolat i o n a t Solar Noon. 7 ~SN. .................................... 06 Ratio o f Hourly t o Daily Total Solar I n s o l a t i o n on a . Horizontal Surface a t Solar Noon. rH. SN ................ D7 Hourly Total Solar Insolation on a Horizontal Surface a t Solar Noon. IH. N ................................... 07 Diffuse Solar InsoT a t i o n a t Solar Noon. ID. SN .......... D7 Beam Solar I n s o l a t i o n a t Solar Noon. 16.94 ............. Dû SAMPLE . 3îCUìATIONS...................................... 08 Cal 1late 6 From Eq (D.1) .............................. D9 Cal cu1ate USN From Eq (0-2) ............................ D9 D9 Cal 1late o trom Cq (D.31 .............................. Cal 1late ao a l and k From Eqs (0-4) through (0.6) . D9 Deterniíne ro. r i and r k From Table 01 .................. D9 Cal 1ate ao. al and k From Eqs (0-7) through (D-9) .... D10 Cal CU1ate 7B. SN From Eq (D.10) ......................... D10 Cal cu1a t e ID.SN From Eq (D-11)......................... D 10 Cal CU1l a t e a and b From Eqs (D-12) and (0-13)........... D 10 D10 Cal 1ate w, SN From Eq (0-14)......................... ate IH. SN From Eq (0-15) ......................... D11 Cal CU1 Cal cu1ate ID,SN From Eq (0-16).........................D 11 Cal CU1ate 18. SN From Eq (0.17) ......................... D 11

04.0

CONCLUSION

NOMENCLATURE

02.5

D2.6 02.7 02.8 02.9 03.0

03.1 D3.4 03.5 D3.6 03.7 03.8 03.9

.

CU

.

CU CU

CU

CU

...............................................

D11

TABLES

01 02

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

02.0 02.1 02.2 02.3 D2.4

...................... ........................

Correction Factors for Climate Type Summary o f Sample Problem Results

D2 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

06 012

--```,``-`-`,,`,,`,`,,`---

01 .O

API MPMS*19.LD 93 m 0732290 0511529 9 8 9 m A P I WBLICATION 2518 DOCWENTATION FILE SECTION D WENCLATURE

DESCRI PTI ON

SYMBOL --```,``-`-`,,`,,`,`,,`---

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A l titude Defined by Eq (0-12) a Defined by Eq (0-7) a0 Defined by Eq (D-4) ao* Defined by Eq (0-8) a1 Defined by Eq (0-5) al* b Defined by Eq (0-13) Daily t o t a l s o l a r insolation on a horizontal surface " IB,SN Beam s o l a r insolation a t s o l a r noon Diffuse s o l a r insolation a t s o l a r noon ID,SN Hourly t o t a l solar insolation on a horizontal IH,SN surface a t solar noon k Defined by Eq (0-9) k* Defined by Eq (0-6) n Year day number Correction factor f o r climate type from Table D1 r0 Correction factor f o r climate type from Table D 1 '1 Correction factor f o r climate type from Table Di rK Ratio of IH,SN t o HH rH ,SN Decl ination angle d Zenith angle a t s o l a r noon 8SN Atmospheric transmittance f o r beam s o l a r insolation 76,SN a t s o l a r noon Atmospheric transmittance f o r diffuse solar insol ation 7D,SN --a t s o l a r nom deg Lati tude 9 Sunset hour angle deg o A

B 0

H SN

Subscripts : Beam

Diffuse Horizontal Sol a r Noon D3


Not for Resale

. .

A P I MPMS*19.LD

01.0

93

= 0732290 0511530 bTO

INTROWCTION

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

This section of the Documentation File to API Publication 2518, Second Edition, contains equations that may be used to determine the solar insolation paranieters required to calculate the vapor space temperature factor, K i . These equations have been selected from Duffie and Beckinan [24]* and are arranged in the order required to calculate IH,SN, ID,SN, and 1 8 , given ~ ~ n, 4, HH and A. Section 02 presents the equations to calculate each o f the required solar insolation parameters . Section 03 presents sample calculations illustrating the use o f the equations for .a sample problem. Table 02 sumarizes the results of the sample problem. These results are also used in Section C6 of this Documentation File to develop an equation for the vapor space temperature factor, Ki. W.0 SOLAR INSOUTION EQUATIONS

02.1 Declination, 6 lhe declination, 6, is the angular position o f the sun at solar noon with respect to the plane o f the equator, where a north declination i s considered positive. The declination varies between -23.450 and +23.450 and is only a function o f the day of the year, n, where 1 n 5 365.

6 = 23.45 Sin

[

360 (284 + n) 365

]

[see Ref. 24, pg. 11, Eq (1.6.1)]

Numbers i n brackets refer to the numbered references listed at the end of this Documentation File. 04 --```,``-`-`,,`,,`,`,,`---


Not for Resale

API

02.2

M P N S * L S - L D 93

0732290 0.511531 537

Zenith Angle at Solar Noon, BSN

The zenith angle at solar noon, b j N , is the angle at solar noon between the beam radiation and the nomiai to a horizontal surface. At solar noon, the zenith angle is a function o f only the declination, 6, and latitude, 4. Cos gSN = Cos 6 Cos

4 + Sin 6 Sin 6

(0-2)

[see Ref. 24, pg. 13, Eq (1.6.4)] 02.3

Sunset Hour Anqle, o

The sunset hour aqle, o, is the angular displacement of the sun, west of the local meridian, at sunset due to the rotation o f the earth on its axis at 1 5 O per hour. --```,``-`-`,,`,,`,`,,`---

COS w = -Tan 9 Tan 6

(0-3)

[see Ref. 24, pg. 13, Eq (1.6.7)] 02.4

Atmospheric Transmittance for Beam Solar insolation at Solar Noon,

7ß-3

The atmospheric transmittance for beam solar insolation at . solar noon, r g , ~ may ~ , be determined from Eq (0-10). The constants ao*, al*, and k* must first be determined from Eqs (0-4) through (0-6) for the'specified altitude, A. The constants '0, ri and rK may be selected from Table D1. 0.4237

-

0.00821 [6.0

-

(A/3281)I2

[see Ref. 24, pg. 62, Eq (2.8.2)J

al i

= 0.5055 t 0.00595 [6.5

-

(A/3281)l2

[see Ref. 24, pg. 62, Eq (2.8.3)]


Not for Resale

(0-4) //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

-

API MPMS*L9*3D 93

k* = 0.2711 t 0.01858 [2.5

-

0732290 O533532 473

(A/3281)J2

[see Ref. 24, pg. 62, Eq (2.8.4)J

Table O1

- Correction Factors for Cliute Type*

Climate Type Tropical Mid-Latitude Summer Subarctic Summer Mid-Lati tude Winter pg. 62, Table 2 . 8 . 1 .

ao-

=

ao*ro

[see Ref. 24, pg. 631

al

=

al*rl

[see Ref. 24, pg. 631

k

=

k*rK

[see Ref. 24, pg. 631

TB,SN = a0 + al exP

(-k/cOS

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

* See Ref. 24,

BSN)

--```,``-`-`,,`,,`,`,,`---

[see Ref. 24, pg. 62, Eq (2.8.l)J

02.5 Atmospheric Transmittance for Diffuse Solar Insolation at Solar Noon,

The atmospheric transmittance for diffuse solar insolation, a t solar noon, TD,SN, may be determined by Eq (0-11). íD,SN = 0.2710

-

(0-11)

0.2939rD,SN

[see Ref. 24, pg. 64, Eq (2.8.7)J


Not for Resale

API NPNS*LS*LD 93

0732290 0511533 30T

Ratio of Hourly t o Daily Total Solar Insolation on a Horizontal Surface a t Solar Noon, rH.3

D2.6

The r a t i o rH,SN is the r a t i o of the hourly t o t a l solar insolation on a horizontal surface a t solar noon, IH,SN, t o the d a i l y total solar insolation on a horizontal surface, HH. T h i s r a t i o may be calculated from Eq (O-14), where the coefficients a and b a r e first determined froin Eqs (0-12) and (0-13), respectively

.

a

= 0.4090

+ 0.5016

Sin (o

-

60)

(0-12)

--```,``-`-`,,`,,`,`,,`---

[see Ref. 24, pg. 79, Eq (2.13.2a)J = 0.6609

-

0.4767 Sin (o

-

60)

(0-13)

[see Ref. 24, pg. 79, Eq (2.13.2b)l

(0-14)

[see Ref. 24, pg. 79, Eq (2.13.1)J O ,7 Hourly Total Solar Insolation on a Horizontal Surface.at Solar Noon, 1 w . u

The hourly total solar insolation on a horizontal surface a t solar noon, IH,SN, may be determined from the r a t i o SN and the daily total solar insolation on a horizontal surface, HH, using Eq (D-15).

(D-15)

IH,SN = W,SN HH 02.8

Diffuse Solar Insolation a t Solar Noon, In lhe diffuse s o l a r insolation a t solar noon, ID,SN, may be determined from

IH,SN, 7 g , S ~and

7 0 , s ~using

Eq (0-16).


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

b

'0,SN = IH,SN

[

]

(D-16)

kSN

?B,SN

+

%,SN

Beam Solar Insolation at Solar Noon, IR-^

D2.9

The beam solar insolation at solar noon, 16,949 may be determined from IH,SN, ID,SN and #SN using Eq (D-17).

18,sN

03.0

[

-

IH,SN ID,SN cos bSN

]

(0-17)

SAMPLE CALCULATIONS

This section presents sample calculations illustrating how Eqs (D-1) through (0-17) may be used to determine the solar insoJation parameters f o r a sample problem. The Given Conditions chosen for this sample problem are the same as those that were used to develop the A P I Computer Data Base [39]. G i'ven Conditions :

n = 105 year day number 4 35 deg. north latitude J

ft. altitude HH = 1500 B/day ft2 = 2000

lhe Calculated Results o f this sample proulem are summarized in Table OZ. These results are also used in Section C6 to develop an equation for the vapor space temperature factor, KT, for the case of a "two color fixed-roof tank with typical. solar insolation parameters" (see Eqs (C-84)through (C-88)).


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

A

API MPMS*l9-LD 93

0732290 051b535 182 H

Calculate 6 from Eq (0-1)

D3.1

1360 (284 + ï05)]

6

(23.45) Sin

=

I

365

L

J

* 9.41490'

03.2 Calculate

8SN

from Eq (D-2)

Cos ûSN = Cos (9.41490) Cos (35) + Sin (9.41490) Sin (35) = 0.90195 8SN = 25.58480 Calculate w from Cos o

o

03.4

--

ai* =

*

k* = =

03.5

--

Tan (35) Tan (9.41490) -0.116106 = 96.66740

Calculate an , ai ao*

Es (0-3)

t

and k* from Eqs (0-4) through (0-61

0.4237 - 0.00821 [6.0 0.185144 0.5055 + 0.00595 E6.5 0.711948 0.2711 + 0.01858 [2.5 0.337499

-

(2000/328i)]2

-

(2000/3281)]2

-

(2000/3281)]2

Determine rn, ri and TK from Table O1

-

ro 0.97 ri = 0.99 rK = 1.02

D9 --```,``-`-`,,`,,`,`,,`---


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

D3.3

API MPMS*19mLD 93

03.6

0732290 0511536 017

Calculate an, ai and k from Eqs (D-7) through (0-9) a o - - (0.185144)(0.97) =' O. 179590 a l = (0.711948)(0.99) = 0.704829 k = (0.337499)(1.02) = 0.344249 Calculate ~ R - G Nfrom Ea (0-101

+ 0.704829

r g , s ~= 0.179590 = 0.6607?? 03.8

--```,``-`-`,,`,,`,`,,`---

03.7

exp (-0.344249/Cos (25.5848))

Cal cul ate rn-s~ from Eq (0-111

-

TD,SN = (0.2710) (0.2939) (0.660790) = 0,0767938 Calculate a and b froin Eqs (0-12) and (0-13) a = 0.4090 t 0.5016 Sin (96.6674 = 0.708540 b = 0.6609 0.4767 Sin (96.6674 = 0.376230

-

03.10

Calculate

fx ",SN

W.SN

I

[

-

60)

- 60)

from Ea (D-14)

[(0.708540)

t

[GJ ki"(96.6674) -

(0.376230)][1

- COS (96.6674)]

(2n)(96.6674/360) cos (96.6674)

= 0.133277

O10 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

03.9

Not for Resale

1

1

API MPMS+LS.LD

03.11

= (O. 133277) (1500) = 199.915

B/hr f t 2

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Calculate I n 3 from Es (0-16)

ID,SN

O. 0767938 = (199.915)

O. 660790 =

03.13

0732290 0511537 T55

Calculate I H - W from Eq (0-15)

IH,SN

03.12

93

t

I

O. 0767938

20.8142 B/hr ft2

Calculate IR w from Eq (0-171 (199.915

-

20.8142)

Cos (25.5848)

'6,SN

= 198.571

B/hr ft2

04. O CONCLUSION

--```,``-`-`,,`,,`,`,,`---

The typical solar insolation parameters developed in this Section D of the Documentation File were used in Section C6 to develop the equation for calculating the daily vapor temperature range, ATv.

o11 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

A P I MPMS*LS.IiD

Table 02

~

-

93

0732290 0511538 991

Sumnary o f Sample Problem Results

~~~~

Value

Description

Symbol

Units

~

n

4

"

A

Year Day Number Lati tude Daily Total Solar Insolation on a Horizontal Surface A l t i tude

1o5 35 1500 2000

--deg. nor11 %/day f t ft

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

G iven I n f ormat i on

Calculated Resul t s 9.41490 25. sa48 96.6674 O. 185i44 O. 711948 0.337499 0.97 0.99 1 .oz O. 179590 O. 704829 O. 344249

Decl inat ion Angle Zenith Angle a t Solar Noon Sunset Angle

r0

r1 T J

al

--I--

4tmspheric Transmittance f o r Beam Solar Insolation a t Solar Noon Itmospheric Transmittance for Diffuse Sol ar Insol ation a t Solar Noon

.-.--

IH,SN

IO, SN IB, SN

tatio o f IH SN t o HH iourly Total Solar Insolation on a Horizontal Surface a t Solar Noon )iffuse Solar Insolation a t Solar Noon Beam Solar Insolation a t Solar Noon

D12 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

O. 660790 O. 0767938 O. 708540 O. 376230 O. 133277 199.915 20.8142 198.571

--```,``-`-`,,`,,`,`,,`---

6 6SN

A P I MPMS*1So1D 93

m 0732290 0511539

828

m

--```,``-`-`,,`,,`,`,,`---

API WBLICATION 2518 DOCUMENTATION FIL€

SECTION E

DEVELOPMENT OF PAINT SOLAR ABSORPTANCE, a

El Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

API.MPMS*LS.LD 93 m 0732290 05LL5YO 5 Y T m

API PUSLICATION 2518 MCUMENTATION FI LE SECTION E

CONTENTS SECTION

DESCRIPTION

........................................... INTRODUCTION. ............................................. SOLAR ABSORPTANCE FUNDAMENTALS.. .........................

E4

DEVELOPMENT OF PAINT FACTORS FOR API PUBLICATION 2518, .FIRST EDITION

E5

NOMENCLATURE..

E l .o €2.0

€3.0 €4.0 €5.0 E6.0

PAGE -

............................................

E3 E4

RELATIONSHIP BETWEEN SOLAR ABSORPTANCE AND PAINT FACTORS. E8

..;i..... E8 CONCLUSION. ............................................... E9 EFFECT

OF PAINT CONDITION ON SOLAR ABSORPTANCE..

TABLES

El €2 E3

E4 E5

.................... €6 .............................................. E10 ............................................... E l l ......................... E12 .......................................... E13

P a i n t C l a s s i f i c a t i o n f o r Tanks Tested S o l a r R e f l e c t a n c e and S o l a r Absorptance o f Tank P a i n t s [A61 S o l a r R e f l e c t a n c e and Sol ar Absorptance o f Tank P a i n t s [3] P a i n t F a c t o r and Sol a r Absorptance o f S e l e c t e d Tank P a i n t C o l o r s and C o n d i t i o n s [A61 S o l a r Absorptance f o r S e l e c t e d Tank P a i n t C o l o r s and Conditions.

FIGURES EI E2

E f f e c t of S o l a r R e f l e c t a n c e on .Paint F a c t o r [From Fig. IV-3 o f Ref. A61 E f f e c t o f P a i n t C o n d i t i o n on S o l a r Absorptance

......................................... E14 ........... E15

E2 --```,``-`-`,,`,,`,`,,`---


Not for Resale

A P I M P M S U L S - L D 93

0732290 051L54L Y8b

API WBLICATION 2518 DOCUMENTATION FILE SECTION E

FP Q

7

UNITS

factor absorptance of paint absorptance of paint in good condition absorptance of paint in poor condition reflectance o f paint transmittance of paint

di mens i on1 ess dimensionless dimensi on1 ess dimensionless di mens i on1 ess dimensionless

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

. QG QP P

Paint Sol ar Solar Solar Sol ar Sol ar

DESCRIPTION

E3 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

El .O

m

O732270 0511542 312

m

INTROWCTION

This section of the Documentation File to API Publication 2518, Second Edition, contains a development of the solar absorptance, a, for selected paint colors, paint types and paint conditions. The values developed are based on information that was presented in Appendix IV of API Publication 2518, First Edition [A6]*. Section E2 presents fundamental definitions and a relationship between solar absorptance and solar reflectance. Section E3 describes the work that resulted in the paint factors, Fp, that appear in API Publication 2518, First Edition. Section E4 describes the relationship between solar absorptance and paint factor. Section E5 develops a relationship between the solar absorptance of paints in poor condition and good condition. Section E€ summarizes the set o f solar absorptance values that were selected for use in API Publication 2518, Second Edition. E2.0

SOLAR AûSûRPTANCE FUNDAMENTALS

Solar radiation that impinges on a surface is either: (1) absorbed by the surface; (2) reflected from the surface; or (3) transmitted through the surface. The fraction of the incident solar radiation (referred to as "insolation") that is absorbed is referred to as the absorptivity, a , of the surface; the fraction that is reflected is referred to as the reflectivity, p , of the surface; and the fraction that i s transmitted i s referred to as the transmittance, 7, of the surface, where:

*

Numbers in brackets refer to the numbered references listed at the end of this Documentation File. E4 --```,``-`-`,,`,,`,`,,`---


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS+19.1D 73

API

MPMS*LS-LD 93 m 0732290 05LL543 259 m

a + p + 7 = 1

F o r the m e t a l surfaces o f fixed-roof tanks, the transmittance i s zero, or: T I O

(E-1) then reduces t o : a + p = l '

(E-3)

The f o l lowing discussion focuses p r i m a r i l y on the values o f absorptance, a, o f a surface f o r use i n calculating the thermal breathing losses o f fixedr o o f tanks. I f the reflectance, p, o f a surface i s known, Eq (E-3) may be used t o determine the correspotiing absorptance, a, o f the surface. The e x t e r i o r surface of fixed-roof tanks i s normally coated w i t h a paint t o reduce corrosion. A wide range of paint colors have been used, sometimes with a d i f f e r e n t c o l o r on the tank r o o f than on the tank shell. The absorptance o f tank paint depends upon the paint color, paint type and p a i n t condition. Newly painted tank surfaces, o r painted surfaces i n a good condition w i l l have a lower absorptance than weathered painted surfaces o r painted surfaces i n poor condition. €3.0

DEVELOPMENT OF PAINT FACTORS FOR API PUBLICATICM 2518, FIRST

EDITION

A t the time t h a t the F i r s t Edition o f A P I Publication 2518 [A61 was

--```,``-`-`,,`,,`,`,,`---

published, the importance of the e f f e c t o f p a i n t absorptance on the thermal breathing loss was recognized. A paint with a low absorptivity, such as white paint, was known t o affect the thermal breathing l o s s i n two s i g n i f i c a n t ways: 1.

It reduces the transfer of heat t o and from the tank vapor space and

therefore reduces the volume o f thermal breathing loss. 2.

o f heat t o the bulk l i q u i d and therefore breathing l o s s by lowering the stock vapor

It reduces the transfer

reduces the thermal pressure.

ES Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Eq

A P I MPMS*19*1D 93

0732290 0511544 195 D

During the development o f the First Edition to API Publication 2518, a Paint Factor Task Group was formed and was given the assignment of developing a practical correlation o f the effect o f paint on the thennal breathing loss from fixed-roof tanks. Through discussions and correspondence, the task group worked with paint chemists and the staff o f one large paint manufacturer. In addition, pertinent 1 iterature was studied and analyzed. Evaporation loss tests, other than those used in developing the breathing loss correlation [see Eq (3) in Ref. A6], were studied and tabulated [see Table' IV-2 in Ref. A6]. Tests were performed to determine the difference in liquid body temperature in large tanks painted aluminum versus those painted white. Tests were performed with both artificial light and sunlight on various painted surfaces to determine their refl ectance.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

In this discussion, reflectance refers to measurements made with a. spectrophotometer which uti1 ires an integrating sphere. On this scale, 100 represents the reflectance of pure magnesium oxide (MO) sprayed on tile until no increase in the instrument reading can be observed. This instrument measures only the visible spectrum. Although heat for evaporation is partially supplied to a tank by the nonvisible (infared) portion of the sun's rays, it -was assumed that the effect o f this portion is proportional to the visible (measured) portion of the sun's rays.. It was not concluded, however, that this relationship will hold for all paint formulations and climatic conditions.

In developing the correlation for thermal breathing loss [Eq (3) in Ref. Ab], test data from 64 painted tanks were selected for detailed analysis. The paint classification for the 64 tanks tested is as follows: Table El

-

Paint Classification f o r Tanks Tested

Roof Col or

!

~

White A l umi num Uhi te Al uni num White Gray

Shell Color _

~

_

White White Al umi num Al uminum Gray Gray

Total

18 2 4 4

12 24

64

E6 --```,``-`-`,,`,,`,`,,`---


I o",uf;n;s

Not for Resale

API MPMS*17obD 93

0732290 0511545 O21

A t the time that the F i r s t Edition of A P I Publication 2518 was published, l i t t l e

Early i n the study of p a i n t reflectance, a d e f i n i t e relationship appeared t o e x i s t between r e l a t i v e loss and tank paint reflectance. It also became obvious t h a t the broad paint c l a s s i f i c a t i o n s o f white, aluminum, gray, etc. were not -sufficiently definitive. Paints have a wide range o f reflectance, varying from a f r e s h l y painted laboratory sample t o a surface i n a d i r t y and extremely weathered condition. Paints o f the same nominal c o l o r and i n the same condition have a wide range o f reflectance, depending upon formulation. One paint manufacturer reported t h a t the reflectance o f new white paint on a tank might range between 0.80 and 0.86, with a maximum of 0.88, and t h a t the reflectance o f new black p a i n t on a tank might range between 0.04 and 0.08. New aluminum paint also has a wide range of reflectance, depending upon the grade o f aluminum powder and the type of formulation. One type of aluminum paint, formulated with a specular. type o f pigment (polished scales), may have a reflectance t h a t might range between 0.60 t o 0.70, with an average of 0.68. Another type o f aluminum paint, u t i l i z i n g a d i f f u s e type of pigment, may have a reflectance as l o w as 0.35. Aluminum paints o f intermediate reflectance can be formulated from mixtures of these two paint types. Thus, aluminum color paints cover a wide range on the t o t a l reflectance scale. Approximate reflectance values f o r various paint colors and p a i n t conditions are presented i n Table €2. These values are based on: (1) the thermal breathing l o s s correlation t e s t data [see Tables 11-1, 11-2 and 11-3 i n Ref. A6]; (2) supplementary test data; (3) information supplied by p a i n t manufacturers; and, (4) the results o f f i e l d t e s t s conducted by the task group.

For reference purposes, Table E3 l i s t s the reflectance values o f various p a i n t colors and paint conditions reported by Nelson [ J I . Table E4 sumarizes the set o f paint factors, Fp, that were developed by the Paint Factor Task Group f o r use w i t h the thermal breathing loss correlation [Eq


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l o s s data on fixed-roof tanks with paint colors other than white, aluminum o r gray was available.

A P I MPMS+Lï.LD

93

m

O732290 0511546 TbB

These paint factors were compiled by the task group from a judicious review o f a l l available data. These p a i n t f a c t o r s do not represent a precise evaluation of the effect of tank paints on evaporation l o s s from tanks. They do, however, present useful and reasonable paint f a c t o r s t h a t are based on t h e alignment o f the r e l a t i v e test data and on the agreement of the test d a t a f o r al uminum painted tanks and gray-painted tanks. (3) i n Ref. A6].

RELATIONSHIP BETYEEN SOLAR ABSORPTANCE AND PAINT FACTORS

E4.0

Figure El [from Fig. IV-3 of Ref. A61 i l l u s t r a t e s the effect o f solar reflectance, p, on the paint factor, Fp. T h i s figure shows a l i n e a r 1.5. Eq (E-3) expresses relationship between p and Fp f o r values of Fp t h i s 1inear relationship: --```,``-`-`,,`,,`,`,,`---

Fp = 1.74

- 0.90 p

(E-3)

Substituting Eq (E-2) i n t o (E-3) and solving for the s o l a r absorptance, a, we obtain: ’

I

Q

-

1.11 F p - 0.94

1

(E-4)

Eq (E-4) was used t o convert the values of absorptance, u, i n Table E4.

paint factor,

Fp, t o solar

ES.0 EFFECT OF PAINT CONDITIW ûN SûiAR A8SûRPTUCE

The solar absorptance values listed i n Table E4 include values for paint i n good condition, ~ Y G , and values f o r paint i n poor condition, op.

Figure E2 is a plot of a;p versus a6 f o r each of the paints l i s t e d i n Table €4. lhe values plotted may be f i t w i t h a linear relationship that must go through the point where a~ 1 and ap = 1. Eq (E-5) expresses this l i n e a r re1 a t ionship:

-

(E-5)


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A P I MPMS+LS-1D 93

E6. O

m

0732290 051154?7 9 T 4

m

CONCLUSION

Table E5 summarizes the set of solar absorptance values t h a t were selected f o r use i n API Publication 2518, Second Edition. The values selected were based upon a careful evaluation o f the values presented i n Tables E2 and ?4. Use was made of the values i n Table E4 for only the cases where the t a n k roof and shell are painted the same color. Also, Eq (E-5) was used t o determine the poor condition values from the good condition values for gray and red color paints. The values of Nelson [3] listed i n Table E3 were not incorporated into Table ?5, but are listed i n this section o f the Documentation F i l e only for reference.

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E9 Not for Resale

A P I MPMS*Lî.LD

Table E2

-

73

m O732270

0511548 ô30

Solar Reflectance and Solar Absorptance o f Tank Paints [A61

-~ ~

Pai n t

Paint Col or

Shade

or Type

~-

Paint

Condi t i on

Sol a r Reflectance

Sol a r Absorptance

a (2) P (1) (di mensi on1ess) (dimension1 ess)

----

1.OO( 1)

0.00

----

Good

0.83

0.17

A l uni num

Specul ar

Good

0.65

0.35

A l umi num

Specular

Average

0.60

0.40

A l umi num

Diffuse

Good

0.45

0.55

A l umi num

Diffuse

Average

0.40

0.60

Aluminum

Diffuse

Extremely Weathered

0.30

0.70

Red

Primer

Good

0.11

0.89

----

----

0.06

0.94

Magnes i um

----

White

~~~

~

Oxide (3)

B1 ack

Notes: (1) Values of p are from Table IV-1 of Ref. A6. (2) Values o f Q are calculated from the relationship: u = 1-p

(3) Magnesium oxide i s the reflectance standard whose value i s

assumed t o be 1.00.

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Not for Resale

m

A P I MPMStLS-LD 93

Table E3

-

0732270 0511549 777

Solar Reflectance and Solar Absorptance o f Tanks Paints [3]

-~

Pai n t Col or

Sol a r Ref 1ect ance Q P (dimensionless] (dimensi on1 ess) Sol a r Absorptance

Paint Condition

Paint Shade or Type

A l umi num A l umi num A l umi num

-------

O. 330 0.408 O. 645

O. 355

Black

---

1.o00

o. O00

B1 ue

Light Pal e Dark

81ue

---

O. 150 O. 272 O. 505 O. 545

O. 850 0.728 0.495 0.455

Cream

Light

O. 115

O. 885

Gray Gray Gray

61ossy Light

o. 190

---

O. 430 O. 530

0.810 O. 570 O. 470

Green Green Green Green

Light Dark Dark

0.215 O. 592 O. 596 o. 787

O. 785 O. 408 0.404 0.213

Metal

Bare

o. 900

0.100

Pink

Light

O. 135

O. 865

Red Red Red Red

Iron Oxide ---

O. 305 O. 724 O. 787 o. a28

O. 695 O. 276 0.213 0.172

0.355

O. 645

o. 100

o. 900

O. 435

O. 565

81ue B1 ue

---

Dark Bright

White

-----

Y el 1ow

---

Tan

--```,``-`-`,,`,,`,`,,`---


O. 670

o. 592

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Not for Resale

-

Solar Absorptance f o r Selected Tank Paint Colors and Conditions

Pai n t Col or

Paint Shade

or

Type

Solar Absorptance, a (dimensionless) Paint Condition Good

Poor

A l uminum

Specul a r

0.39

0.49

Aluminum

Diffuse

0.60

0.68

Gray

Light

0.54

0.63

Gray

Medi um

0.68

0.74

Red

Primer

0.89

0.91

----

0.17

0.34

I White I


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Table E5

A P I MPMS*LSnLD 93 W 0732290 0511552 261 W

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0.80

0.40

0.60

Solar k f k h M 8 ,

Figure El

-

p

(dinensionless)

Effect of Solar Reflectance on Paint Factor [From Fig. IV-3 o f Ref. A61


0.20

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A P I flPflS*LS-LD 9 3

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O

0.4

1

.O. 6

I

0.8

Solar Absorptance o f Good Condition Paint, ('G (dimension1ess) Figure E2

- Effect of Paint Condition on Solar Absorptance

El 5 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

l

1.0

0732290 0511554 034

--```,``-`-`,,`,,`,`,,`---

API, MPMS*Lq=1D 93

API PUBLICATION 2518 DOCUMEMTATION FILE

SECTION F

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

DEVELOHENT OF LIQUID SURFACE TEMPERATURE EQUATIOHS

F1 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

A P I MPMS*17-1D

93

= 0732290 0511555 T 7 0

A P I PUBLICATION 2518 DOLUMENTATION FILE SECTION F CONTENTS DESCRIPTIOW NOMENCLATURE.. F1.O F2.0 F3.0 F4.0 F4.1 F4.2 F5.0 F5.1 F5.2 F5.3 F6.0

PAGE

....... .................................

INTROWCTION..............................................

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

SECTION

F3 F4

............. .................. F4 AVERAGE GAS SPACE TEMPERATURE.. .................... ... . F5 LIQUID SURFACE TEMPERATURE RANGE.. ........... ........ . F5 Liquid Surface Temperature Range Corre1ation.. ......... F5 Liquid Surface Temperature Range Equation.. ............ F6 AVERAGE LIQUID SURFACE TEMPERATURE.. . ................... F8 Heat Transfer Model .................................... F8 Comparison With Test Data. .... ........ ............. F10 Average Liquid Surface Temperature Equation.. .......... F10 CONCLUSION.. ................ ..... ...................... F11 LIQUID BULK TEMPERATURE..

*.

TABLES F1

Tehperature Difference Ratio ( T ~ - T ~ ) / ( T ~ - T B A ) Calculated From the A P I Test Data [ 3,381

................ F12

FI6üñES

F2 F3 F4 FS

Effect o f Paint Solar Absorptance on the Liquid Bulk Temperature Liquid Surface Temperature Range Versus Gas Space Temperature Range f o r A P I Computer Data Base Cases 1 through 200 Liquid Surfact Temperature Range Versus Gas Space Temperature Range f o r API Computer Data Base Cases 201 through 400 Liquid Surface Temperature Range Versus Gas Space Temperature Range f o r A P I Computer Data Base Cases 401 through 560 Schematic of Energy Flows and Temperatures Neat the Liquid Surface.. .. . . ..

.............................................. F13 ............................................F14 ..........................................

.......................................... F16 .... . .. ..... ............... ........ F17 F2


F15

Not for Resale

--```,``-`-`,,`,,`,`,,`---

F1

A P I MPMS*LS-LD 93

0732290 OSLLSSb 907

API PUBLICATION 2518 DOCUMENTATION FILE SECTION F

SYMBOL -

A a b C

G

" h KL k T hT Q

P

UNITS -

DESCRIPTION Area Defined by Eq (F-21) . Defined by Eq (F-22) Heat capacity Defined by Eq (F-9) Daily t o t a l solar i n s o l a t i o n on a horizontal surface Heat transfer c o e f f i c i e n t Defined by Eq (F-6) Thermal conduct iv i t y TemperatUre Temperature change Sol a r absorptance Density

SUBSCRIPTS A AA B BA BN BX

G GA 61J GX

L LA LN LX

Ambient Ambient, Daily Average Liquid Bulk Liquid Bulk, Daily Average l i q u i d Bulk, Daily Minimw Liquid Bulk, Daily Maximum Gas Gas, Daily Average Gas, Daily Minimum Gas, D a i l y Maximum Liquid Surface Liquid Surface, D a i l y Average Liquid Surface, D a i l y Minimum Liquid Surface, D a i l y Maximum

F3 --```,``-`-`,,`,,`,`,,`---


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ft2 d imension1ess dimensi on1ess

B/lh

OF

dimensi on1ess B/day ft2 B/hr f t 2 OF dimensionless B/hr f t OF OF OF

dimension1ess 1w f t 3

A P I MPMS*19.LD

93

0732290 0511557 8 4 3 H

F1. O INTRODUCTION

This section of the Documentation File to API' Publication 2518, Second Edition, presents the development o f the equations required to determine the daily maximum 1 iquid surface temperature, TLX, the daily average 1 iquid surface temperature, T u , and the daily minimum liquid surface temperature, TLN. Section f2 develops an equation for estimating the liquid bulk temperature, Ts, when this temperature is not available from tank operating records. This equation is based on data from in API Publication 2518, First Edition [A6]*. Section F3 presents an equation for determining the daily average gas space temperature, TM. Section F4 develops an equation for determining the daily liquid surface temperature range, ATL. This theoretical equation i s confirmed by a correlation developed from the API Computer Data Base 1391.

Section F6 presents a summary of the equations requi.red to calculate the daily maximum 1 iquid surface temperature, TLX, the daily average liquid surface temperature, T u , and the daily minimum liquid surface temperature, TLN. The equations are presented in the order required for calculation. F2.0

LIQUID BUM TMPERATURE

-The liquid bulk temperature, TB, is the average temperature of the liquid stock in the storage tank. This information is usually available from tank gaging records or other tank operating records.

*

Numbers in brackets refer to the numbered references listed at the end of this Documentation file. F4


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Section F5 develops an equation for determining the daily average 1 iquid surface temperature, Tu. This theoretical equations is confirmed -by the API lest Data [33,38].

A P I NPNS*Lq.LD

73

m

O732270 05LL558 7 8 T

If the liquid bulk temperature is not available, it may be estimated from the daily average ambient temperature, TM, and the tank shell paint solar absorptance, o, using Eq ( F - 1 ) .

Figure F1 i s a plot o f liquid bulk temperature, TB, above that in a white tank versus shell paint solar absorptance, a. This figure is from figure IV-2 o f API Publication 2518, First Edition [A6]. Eq (F-1) was developed from the straight line on Figure F1 and from the assumption that the liquid bulk temperature in a white tank is the same as the average ambient temperature, TM.

AVERAGE 6As SPACE TMPERATURE --```,``-`-`,,`,,`,`,,`---

F3.0

r

TM = 0.7751~+ 0 . 2 2 5 1 ~+ 0.0140

Q

HH.

(F-2) A

This section contains the development of two equations for the daily liquid surface temperature range, ATL: ( i ) a correlation from the API Computer Data Base [39]; and (2) a theoretical equation from a heat transfer analysis. F4.1

Liquid Surface Temperature Ranqe Corre1 ation

A correlation between the liquid surface temperature range, ATL, and the gas space temperature range, ATG, was developed from the 560 sets of calculated

results that are contained in the API Computer Data Base [39]. lhe daily liquid surface temperature range, ATL, and the daily gas space temperature range, ATG, are defined by Eqs (f-3) and (F-4).

f5 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

.API

MPNS+Lî=LD 93 m 0732290 0511557 bLb

The resulting correlation i s shown i n Eq (F-5):

Although the data i n Figures F2 through F4 e x h i b i t a s l i g h t curvature, the l i n e a r correlation results i n an excellent f i t o f the values, w i t h a c o r r e l a t i o n c o e f f i c i e n t o f 0.998344.

F4.2

Liquid Surface Temperature Range Equation

This section contains the development of a theoretical equation f o r the l i q u i d surface temperature range, ATL, from a heat transfer analysis. The API Test Data [33,38] indicates t h a t the top l a y e r o f l i q u i d stock behaves thermally as i f i t were - a layer of s o l i d material during the d a i l y thermal heating cycle. Heat i s transferred i n a v e r t i c a l d i r e c t i o n through t h i s top layer by steady periodic heat transfer. l h e case o f heat transfer between a f l u i d medium with a- steady p e r i o d i c temperature change i n contact with the plane surface o f a s e m i - i n f i n i t e s o l i d material i s treated by Jakob [Jakob, M., "Heat Transfer", Volume 1, John Wiley & Sons, Inc., 1949, pp. 296-2991. This analysis may be applied t o the top l a y e r o f l i q u i d stock i n a storage tank and r e s u l t s i n Eq (F-6), (F-7) and (F-8):


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--```,``-`-`,,`,,`,`,,`---

Figures F2, F3 and F4 are p l o t s o f l i q u i d surface temperature range, ATL , versus gas space temperature range, ATG, from the API Computer Data Base [39). Each of these figures contains about 1/3 o f the 560 calculated values i n the A P I Computer Data Base.

.

A P I MPMS*LS.LD

93

0732270 05LL5bO 338

or (F-7)

ATL = KL AT6

where: (F-8)

'.(

(F-9)

PL CL L

2 4 h i ] 1

lhe following values for p ~ CL , and kL from the A P I Base Case [39J were used calculated G and KL: (F-10)

--```,``-`-`,,`,,`,`,,`---

PL = 53 w f t 3 CL

kL

=

0.45 Btu/lbm

(F-il) OF

(F-12)

0.08 Btu/hr f t OF

hG = 0.65 Btu/hr ft2

(F- 13) OF

The resulting values calculated for G and KL respectively, are:

'irem

Eqs

(F-9)

nd

(F-a),

(F-14)

G = 0.5911

(F-15)

KL = 0.5185


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API MPMS*Lq.LD

93 W 0732290 0511561 274 W

This value f o r KL i s supported by the correlation result o f Eq (F-5).

(F- 16)

F5.0

AVERAGE LIQUID SURFACE TENPERANRE

F5.1

Heat Transfer Model

This section develops a simplified equation f o r estimating the daily average liquid surface temperature, Tu, from the liquid bulk temperature, TB, and the daily average gas space temperature, T u . Figure F5 is a schematic o f the energy flows and temperatures near the liquid surface. The heat transfer equations are Eqs (F-17) and (F-18).

The heat balance equation at the liquid surface is:

QG

=

(F-19)

QL

Substituting Eqs (f-17) and (f-18) i n t o Eq (F-19) and solving for TL we obtain: (F-20)

where:

aa(

h6

hG

+

] I

(F-21)

hL


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

The value for KL listed in Eq (F-15) may be rounded to 0.500 f o r ease of calculation. Finally, substituting this value for K i into Eq (F-7), we obtain:

A P I MPMS*L9-LD 93

]

"

b.(

hg

+

0732290 O S L L 5 b 2 100

(F-22)

'L

The r a t i o a/b may be determined from Eqs (F-21) and (F-22) as follows: a

h6

(F-23)

-I-

hl Substituting Eq (F-23) between b and a.

i n t o Eq (F-22) we obtain the following r e l a t i o n s h i p

b = 1 - a

(F-24)

During the d a i l y thermal breathing process, the l i q u i d bulk temperature, TB, can be assumed t o be constant. A t the maximum, average and minimum gas space temperature conditions, Eq '(F-20) becomes: (F-25) (F-26)

The d a i l y l i q u i d surface temperature range, ATL, and the d a i l y gas space temperature range, ATG, were defined by Eqs (F-3) and (F-4). Substituting Eqs (F-25) and (F-27) i n t o Eq (F-3), we obtain:

(F-28)


Not for Resale

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(F-27)

API MPMS*LS.LD

73 M 0732270 05LL563 047 H

From Eq (F-16) in Section F4.2, we know that a = 0.500. Substituting this value for a into Eq (F-28), we obtain b = 0.500. Substituting these values for a and b into Eqs (F-25), (F-26) and (F-27), we obtain: TLX = 0.5OOTu

TM TLN

F5.2

+ 0.50OT~

(F-29)

= 0.500T~+ 0.SOOTg

-

(F-30) (F-31)

0 . 5 0 O T ~t 0 . 5 0 0 T ~

Comparison With Test Data

To cczpare the pesults o f this analysis with the API Test Data [33,38], it is first convenient to form the ratio (Tw TB)/(TGA - TB) using Eq (F-30) from the above analysis as follows:

-

= 0.500

(F-32)

Table F1 presents the above ratio calculated from API Tests 1 through 6. A P I lests 7 through 10 could not be used fcr this comparison since the liquid surface themcouple appeared to be reading the gas temperature rather than the liquid surface temperature. The average value calculated for the ratio ( T u l ~ ) / ( T m Tg) from the API Test Data is 0.467. This value calculated from test data i s close t o the value of 0.500 in Eq (F-32), thus verifying the heat transfer analysis i n Section F5.1.

-

F5.3

Average Liquid Surface Temperature Equation

Substituting Eq (F-2) for TGA into Eq (F-30) and solving for TLA, we obtain finally the following expression for the daily average 1 iquid surface temperature, TM. (F-33)

F10 --```,``-`-`,,`,,`,`,,`---


. Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

'

Tg = value from tank operating data

or (F-34.)

T ~ - T m + k - l 2.

Determine TI A TM = 0.437Tw

3.

+ 0 . 5 6 3 T ~ + 0.00789~"

Determine ATy

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(F-36)

ATy * 0.723AT~ + 0.0279a)l~ 4.

Determine AT1 (F-37)

ATL = 0.SOOATv 5.

Determine T i 1 TLX =

6.

(F-35)

(F-38)

TM + 0.500AT~

Determine TIM TLN = TLA

- 0.500AT~

(F-39)

I t is possible to combine some o f the above equations to reduce the number of equations, but they are listed separately here for .clarity.


Not for Resale

--```,``-`-`,,`,,`,`,,`---

Determine TS

1.

m

Calculated From the API Test Data 133,381

Test No.

API-1

TBA

~-

(i::;:)

TGA

(OF) -

(d imensi on1ess ]

(OF) -

52.8

58.2

65.3

5.4

12.5

0.432

API-2

52.7

60.0

67.3

7.3

14.6

O. 500

API-3

53.2

61.O

70.5

7.0

17.3

O. 451

API-4

53.9

61.8

70.2

7.9

16.3

O. 485

API-5

53.7

60.5

67.3

6.8

13.6

O. 500

API-6

53.8

56.5

60.0

2.7

6.2

O. 435

Average

--

O. 467

Note: (1) The nean values TEA? TM, TVA l i s t e d in t h i s table were :alculated from the maximum and minimum values measured

API tests [33,38].

--```,``-`-`,,`,,`,`,,`---

in the

FI2 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*LS*LD 93

m 0732290

05LL5bb 8 5 6

m

5 '

4

3

I

a 4

I

2

4) = 6a

-1

1

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

O

o. 2

O. 6

0.4

0.8

Solar Absorptance, a (dimension1ess)

Figure FI

--```,``-`-`,,`,,`,`,,`---


-

Effect of Paint Solar Absorptance on the L i q u i d Bu1 k Temperature [A61

F13 Not for Resale

1.0

A P I MPMS*LS.LD

93

0732290 05LL5b7 792 U

3 I

I

x)

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al

.......

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//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

2

A P I NPNS*LS-LD 93

1

0732290 05LL5b9 5 6 5 W

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a

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t

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Qi

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0732290 0 5 3 3 5 7 0 2 8 7 W

--```,``-`-`,,`,,`,`,,`---

TB I

//

Figure F5

7

- Schematic Ò f Energy Flows and Temperatures Near the L i q u i d Surface


Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*39*LD 93

A P I MPMS*19*1D 93

0732290 0.511571 113 W

--```,``-`-`,,`,,`,`,,`---

API WBLICATION 2518 DOCUMENTATIW FILE

SECTION 6

GI Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

SENSITIVITY ANALYSIS OF STANDING STORAGE LOSS EQUATION

API MPMS*LS-LD 93

0732290 0533572 05T W

API WBLICATION 2518 WCUMENTATION FILE SECTION 6

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

CONTENTS

NOMENCLATURE..

........................................... 63

................................... ......... 65

G 1 .O

INTRODUCTION

62.0

VARIABLES USED I N TH€ SENSITIVITY ANALYSIS

63.0

63.1 63.2 64.0

64.1 64.2 64.3 G5.0

PAGE -

DESCRIPTION

SECTION

............... 65 SAMPLE CALCULATIONS FOR THE BASE CASE. ........... ........ 65

. . . . . .... .................................. 66 66 ....................... SENSITIVITY ANALYSIS RESULTS.. ........................... 611 Breather Vent Setting S e n s i t i v i t y ...................... 611 Vapor Pressure S e n s i t i v i t y............................. 611 Base Case Conditions.. Calculated Results..

Comparison Between the F i r s t and Second Editions o f A P I Publication 2518

CONCLUSION..

................................. 611 ............................................. 612

TABLES 61 62 63

Range o f Values and Base Case Value Used i n S e n s i t i v i t y Analysis Input and Output Variables f o r the S e n s i t i v i t y Analysis.. Effect o f Reid Vapor Pressure on Emissions Calculated From Both the f i r s t and Second E d i t i o n o f API Publication 2518.. .

...................................................613

614

................... ...... . .......... 616

FIGURES 61 62 G3 64 GS 66 67 68 G9 610

............... 617 .......... 618 P ....................... ......... G19

Effect o f Tank Diameter, D, on Emissions.. Effect o f Vapor Space Outage, Hy , on Emissions Effect o f Daily Total Solar Inso a t i o n on a Horizontal Surface, I , on Emissions Effect o f Tank Paint Solar Absorptance, u, on Emissions.. Effect o f Stock Vapor Molecular Weight, My, on Emissions. Effect o f D a i l y Average Ambient Temperature, TM, on Emissions Effect o f D a i l y Ambient Temperature Range, ATA, on Emissions Effect o f Breather Vent Pressure and Vacuum Settings, P p and PBV, on Emissions. E!fect of Stock Reid Vapor Pressure, RVP, on Emissions.. Effect of Stock Vapor Pressure, PYA, on Emissions

....... .... .................................. 622 ............................................. 623 ............................... 624 . 625

........ 626

62

--```,``-`-`,,`,,`,`,,`---


620 621

Not for Resale

A P I flPMS*:LS.ZD 93 M 0732290 0511573 T9b

API WBLICATION 2518 DOCUMENTATION F I LE

SECTION G NOMENCLATURE UNITS -

DESCRIPTION

63 --```,``-`-`,,`,,`,`,,`---


Not for Resale

d i mens i on1 ess OR

ft

1b/day 1b/day ft

Btu/ft* day dimensionless d imens ion1es s 1biday 1b/l bmol e psia

psi a psi a psi a psi psi psi OR

OR OR OR OR

or or or or or

OF

OF OF OF OF

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Constant i n the vapor pressure equation Constant i n the vapor pressure equation Tank diameter Daily standing storage loss calculated from API Publication 2518, First Edition [A61 Daily standing storage l o s s calculated from API Publication 2518, Second Edition [A71 Vapor space outage Daily total- solar insolation on a horizontal surface Vapor space volume expansion f a c t o r Vented vapor s a t u r a t ion factor Daily standing storage l o s s Stock vapor molecular weight Atmospheric pressure Breather vent pressure s e t t i n g (always a posit ive val ue) Breather vent vacuum s e t t i n g (always a negative val ue) Stock vapor pressure a t the d a i l y average 1iquid surface temperature Stock vapor pressure a t the d a i l y minimum 1iquid surface temperature Stock vapor pressure a t the daily maximum 1iquid surface temperature Stock daily vapor pressure range Breather vent pressure s e t t i n g range Reid vapor pressure Daily average ambient temperature Liquid bu1 k temperature Daily average 1iquid surface temperature Daily ambient temperature range Daily minimum 1iquid surface temperature

API MPMS*LSoLD 9 3

0732290 0533574 922

API PUBLICATION 2518 OOCUMENTATION FILE SECTION 6 NonENCiATüRE (Continued) --```,``-`-`,,`,,`,`,,`---

UNITS -

DESCRIPTION Daily maxiniuni 1 iquid surface temperature Daily vapor temperature range . Tank vapor space vol une Stock vapor density Tank paint solar absorptance

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\


Not for Resale

OR

or

OF

OR o r OF

ft3 1 b/ft3 dimension1ess

A P I MPMS+Lï-LD 93

m

0732290 O511575 8b9

si. o INTRODUCTION This section of the Documentation File to API Publication 2518, Second Edition [ A l ] * contains a sensitivity analysis of the standing storage loss equation. The objective of this analysis is to determine the affect of the variables in the standing storage loss equation on the calculated loss over a range of conditions for each variable. Section 62 summarizes the variables used in the sensitivity analysis. Section 63 presents sample calculations for the Base Case conditons. Section 64 presents the results o f the sensitivity analysis. --```,``-`-`,,`,,`,`,,`---

Section 65 presents conclusions from the sensitivity analysis. 62.0

VARIABLES USED

IN THE SENSITIVITY ANALYSIS

Table Gï lists the input variables that were studied as part of the sensitivity analysis. For each input variable, a "Base Case" value and a range were sel ected. In performing the sensitivity analysis, each o f the input variables was kept at the Base Case value while the value of the input variable being studied was varied over the desired range. In this way, the sensitivity of the A P I standing storage loss model was evaluated around the Base Case conditions. 63.0 SIMPLE CALCULATIONS FOR THE BASE CASE

This section summarizes sample calculations o f the standing storage loss for the Base Case conditions.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

!.

Numbers in brackets refer to the numbered references listed at the end of this Documentation F le.


Not for Resale

J

A P I MPMS*LS-LD 93

63.1

= O732290 051257b

7T5

Base Case Conditions

63.1.1

Tank Conditions

D = 100 ft Hyo = 30 ft Q = 0.50 PBP = 0.03 psig PBV -0.03 psig

-

63.1.2

Meteorological Conditions

TM = 519.690R (6O.OOOF) ATA = 20.00oR (20.00oF) I = 1500 Btu/ft* day PA = 14.696 psia 63.1.3

Stock Conditions

-

--```,``-`-`,,`,,`,`,,`---

Type Crude Oil RVP = 2.0 psi My = 80 lb/lbmole Cal cul ated Resul t s

63.2

63.2.1

Determine TB

TB=TMt6Q-1 TB = (519.69) t (6)(0.50) TB = 521.690R (62.000F)

-

(I)


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I NPNS*37=3D 73 H 0732290 0533577 6 3 3 H

Determine TLA

63.2.2

TM = 0 . 4 4 T ~+ 0.56Tg + 0 . 0 0 7 9 ~ 1 TM = (0.44)(519.69) i (0.56)(521.69) TM = 526.740R (67.05OF) 63.2.3

+

(0.0079)(0.50)(1500)

Detemine Aly

ATy = 0.72AT~+ O.O2&1 ATy = (0.72)(20.00) + (0.028)(0.50)(1500) ATv = 35.400R (35.400F) Determine TLX

63.2.4

--```,``-`-`,,`,,`,`,,`---

-

TLX TM + 0.25ATv TLX = (526.74) + (0.25)(35.40) TLX 535.590R (75.90OF)

63.2.5

Determine TLN

-

TLN = T u 0.25ATy TLN = (526.74) (0.25)(35.40) TLN = 517.89OR (58.20OF) 63.2.6

-

Determine A

--

-

12.82 0.9672 I n (RVP) A A (12.82) (0.9672) ln(2.0) A = 12.15

-


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A P I MPMS*.19.LD 9 3

63.2.7

Determine

B

-

-

m 0732290 0511578

578

m

B (6-7)

7261 1216 ln(RVP) B = (7261) (1216) ln(2.0) B = 64180R

-

Determine Pyx

1

c

-

Pyx = exp (12.15)

63.2.9

(535.59)

L

1.1817 psia

Determine PYA

PYA

'VA

(6418)

r'

I I

exp A

B

- TU

= exp (12.15)

(6418) (526.74)

psia //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

= 0.9662

-

--```,``-`-`,,`,,`,`,,`---

63.2.8


Not for Resale

API MPMS*LS.LD

63.2.10

93 W 0732290 0511579 404 W

Determi ne PVN

--```,``-`-`,,`,,`,`,,`---

1 (12.15)

-

-

1

-1 (641

(51 I . 89)

0.7846 psia

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

63.2.11 Deterni ne APv (G-11)

APV Pvx - PvN APv = (1.1817) - (0.7846) APy = 0.3971 p s i 63.2.12 Determine APB

(6-12)

APE! = PEP - PBV APB = (0.03) - (-0.03) APB = 0.06 psi 63.2.13 Determine V v

(G- 13) (3.1416) (100)*(30)

vV = 235,620 ft3

G9 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

A P I MPMS*l,S-l,D

93

0 7 3 2 2 9 0 0511580 126 I

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

'V 'VA -

UV =

(6- 14)

*LA (80.00) (0.9662) (10.731)(526.74)

-

wv - 0.01367 63.2.15

lb/ft3

Determine KE (6- 15)

(35.40) (526.74)

KE

+

(0.3971)

-

(0.0600)

(14.696)

-

(0.9662)

KE = 0.09176

63.2.16

Determine

KS

1

(6-16) 1

KS

KS

63.2.17

1

+

(0.053)(0.9662)(30)

= 0.3943

Determine

Ls

vv

WV KE KS Ls = (235,620) (0.01367) (039176) (0.3943) 1s 116.5 lb/day Ls

=

-

--```,``-`-`,,`,,`,`,,`---


Not for Resale

(6-17)

API MPMSsLS-LD 93 H 0732290 05LL58L O b 2

64.0

SENSITIVITY ANALYSIS RESULTS

Table 62 lists the input and output variables from the API standing storage loss equation for each of the 57 cases which were studied as part of the sensitivi ty analysis. Figures G1 through G10 illustrate the effect of the input variables on the emissions calculated by the API standing storage loss equation. The Base Case condition is also indicated on each figure.

Figure 68 indicates that the breather vent pressure and vacuum settings (up to tO.05 psig) have little effect on the standing storage loss. 64.2 Vapor Pressure Sensitivity

The sensitivity analysis also include an evaluation of the effect of vapor pressure on emissions. Vapor pressure is. affected by stock type, Reid Vapor Pressure and temperature. Table 62 and Figures 69 and 610 show the effect o f Reid Vapor Pressure and resulting true vapor pressure, respectively, on emissions for crude oil. Even though the RVP was kept constant in most of the sensitivity analysis, the TVP varied from 0.3547 psia in Case No. 29 to 2.2815 psia in Case No. 33. This variation in TVP occurred implicitly as the calculated liquid surface temperature vaired due to varying the ambient temperature. Currently, stocks with a TVP greater than 1.5 psia are not commonly stored in fixed-roof tanks. . C4.3

Comparison Between the First and Second Editions o f API Publication 2518

A comparison was made between standing storage loss calculated from the First Edition (A61 and the Second Edition [A71 of API Publication 2518. The RVP


Not for Resale //^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

--```,``-`-`,,`,,`,`,,`---

64.1 Breather Vent Settinq Sensitivity

A P I MPMS*lcLS-LD 93

_ ~ _ _

m

0732290 0 5 3 3 5 8 2 T T 9

m

was varied from 0.001 psi to 12.0 psi, while the other variables were kept at the Base Case conditions. Table 63 summarizes the calculated results. The last column .indicates the ratio of the standing storage loss calculated f r m the First Edition to that calculated from the Second Edition. It should be noted that the ratio equals about 1.0 when the RVP equals about 12 psi or the NP equals about 10 psia. Figures G9 and 610 graphically illustrate the effect of RVP and TVP on standing storage loss. It should be noted that the emissions predicted by the Second Edition are close to the enissions predicted by the First Edition whewthe vapor pressure i s over about 2 psia. For low vapor pressures, the emissions calculated from the Second Edition are significantly less than those calculated from the first Edition, indicating that the First Edition overpredicts emissions for low vapor pressure stocks (less than 2.0 psia). 65. O

CONCLUSIONS

The sensitivity analysis showed that the breather vent pressure and vacuum settings had little affect on the calculated loss.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

The sensitivity analysis showed that for high vapor pressure stocks (greater than 2.0 psia) the evaporation losses calculated from the. Second Edition are close t o those calculated from the First Edition, and that for low vapor pressure stocks (less than 2.0 psia) the First Edition overpredictes the evaporation loss.


Not for Resale

--```,``-`-`,,`,,`,`,,`---

The sensitivity analysis showed that the standing storage loss equation exhibits the same trends that were shown by a similar sensitivity analysis performed on the API Coniputer Model (391. This similarily in sensitivity helps val idate the standing storage loss equation.

API MPMS*LS-LD 73 W 0732270 05LLSB3

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A P I NPMS+LS.LD

Table 63

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O732290 05LL5Bb 644

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E f f e c t o f Reid Vapor Pressure on Emissions Calculated Fron

From Both the F i r s t and Second E d i t i o n o f A P I Publication 2518

A

8

PB

E1

(1)

(2)

(3)

(5)

(-1

(OR)

( P W

(1b/daY

0.001

19.50

15,660

O. 00002705

O. 00003607

O. 1217

O. 00759

16.03

O. 003

18.44

14,320

O. 0001223

o. O001591

O. 3396

O. 03312

10.25

0.01

17.27

12,860

O. 0006232

O. 0007893

1.0277

O. 1664

6.176

0.03

16.21

11,520

O. 002817

0.003481

2.867

O. 7249

3.955

0.1

15.05

lo', 060

0.01450

0.01745

8.740

3.599

2.428

O .3

13.98

8,725

O. 06428

O. 07546

24.12

14.89

1.620

1 .o

12.82

7,261

O. 3335

0.3811

74'. a2

59.67

1.254

2.0

12.15

6,418

O. 8587

O. 9662

146. O

116.5

1.253 . -

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11.76

5,925

1.496

1.668

219.9

168.9

1.302

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11.26

5,304

2.983

3.289

381.3

282.1

1.352

10.81

4,732

5.694

6.212

707.9

534.5

1.324

10.59

4,461

7.682

8.339

1028.

846.4

1.215

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9.919

10.723

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(1) Calculated from: A = 12.82 0.9672 In (RVP). (2) Calculated from: 8 7261 1216 I n (RVP). (3) Calculated from: PB = exp [A (8/T ), where Tg 521.69*R (62.00oF). (4) Calculated from: PYA = exp [A (û/!m)J, where TM = 526.74 (67.05OF). (5) Calculated from API Publication 2518, F i r s t Edition [A61 f o r the Base Case Conditions l i s t e d i n Table G 1 and f o r the RVP l i s t e d i n t h i s tab1e. (6) Calculated from A P I Publication 2518, Second Edition [A71 f o r the Base Case Conditions l i s t e d in Table G l and for the RVP l i s t e d i n t h i s table.

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A P I MPMS*19-LD 93

0732290 0511597 4 2 T

DOCWENTATION FILE

SECTION H

COMPARISON OF STANûIN6 STORAGE LOSS EQUATION W I T H TEST DATA

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

m:

This document is part of the API standards development procese and i s intended for use by ApI complittees I t ahall not be reproduced or circulated or quoted, i n whole or i n part0 outside o f the cognizant A P I c-ittee(s) except with t h e written approval of API. This draft API standard w i l l be formatted and edited prior t o APT publication. C o p y t i g h t e 1 9 9 0 .

m.

HI Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

--```,``-`-`,,`,,`,`,,`---

API WBLICATION 2518

API MPMS*LS-LD 93

0732290 0533598 366

API PUBLICATION 2518 ûûCUHENTATION FILE SECTION H

CONTENTS PAGE NOMENCLATURE.. ........................................... H3 INTROOUCTION.. ........................................... H4 COMPARISON WITH THE API TEST DATA [38]................... H4 COMPARISON WITH THE EPA TEST DATA [ZO].. ................. H5

SECTION

DESCRIPTION

H1.O H2.0

H3.0

H4.0 H5.0

.

................. H5 ........................................... i . H6

COMPARISON WITH THE WOGA TEST DATA [17]. CONCLUSION..

H1 H2 H3

Sumary o f Calculated and Measured Variables f o r the API Tests [38] Sunaiary o f calculated and Measured Variables f o r the €PA Tests [20].. Suanary o f Calculated and Measured Variables f o r the WGA Tests [17].

........................................... H7 ......................................... H8 ......................................... H9

FIGURES

H1 H2 H3

HI H5 H6 H7 H8

Calculated Versus Measured Vapor Space Temperature Range AT for the API Tests [38] Ca culated Versus Heasured Vented Gas Volume Outflow, Q, f o r the API Tests [38] Calculated Versus Measured Daily Standing Storage Loss, Ls, f o r the API Tests [38] Calculated Versus Measured Vapor Space Temperature Range, AT f o r the EPA Tests [20] Ca culated Versus Measured Vented Gas Volume Outflow, Q, for the €PA Tests [20] Calculated Versus Measured Daily Standing Storage Loss , Ls, for the €PA Tests [20] Calculated Versus Measured Vented Gas Volume Outflow, Q, for the UûGA Tests [ I t ] Calculated Versus Measured Daily Standing Storage Loss , Ls, for the WûGA Tests [17]

r

7

.............................. H10 ................................... Hll

............................... H12 .............................. H13 ................................... H14 ............................... .H15 .................................. HI6 ..............................

H2 --```,``-`-`,,`,,`,`,,`---


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H17

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

TABLES

A P I flPflS*LS-LD 9 3 M 0732290 0511599 2 T 2 M -

A P I PUBLICATION 2518 00CWENTATlON FILE

SECTION H NOMMCIATURE

B D

"vo I

KE LS MV PA

PEP PBV

Q TAX TAN TB ATV VV a

Constant i n the vapor pressure equation Constant i n the vapor pressure equation l a n k diameter Vapor space out age Daily t o t a l solar i n s o l a t i o n on a horizontal surface . Vapor space expansion f a c t o r D a i l y standing storage loss Stock vapor molecular weight Atmospheric pressure Breather vent pressure s e t t i n g (always a positive value) Breather vent vacuum s e t t i n g (always a negative val ue) Vented gas volume outflow Daily maximum ambient temperature Daily minimm ambient temperature Stock 1i q u i d bu1 k temperature Daily vapor temperature range l a n k vapor space volume l a n k point sol a r absorptance

H3 --```,``-`-`,,`,,`,`,,`---


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dimensi on1ess OR

ft ft 8 tu/ f t 2 day d imension 1ess 1b/day 1b/l bmole psia Psig

Psig ft 3/â ay OR

OR

OR OR

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//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

A

UNITS -

DESCRIPTION

SYMBOL

. A P I NPMS*Lî=LD 93

H1.0

m

0732290 052Lb00 844

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IHTROMICTION

This section of the Documentation File to APJ Publication 2518, Second Edition [A7]* contains a comparison o f the standing storage loss equation with the API test data [38], EPA test data [20] and UOGA test data [17]. H2.0 COMPARISON WITH THE API l'EST DATA 1383

Table H1 sumarizes the input information from Tests API-1 through API-10 which was used to calculate the standing storage loss. This table also compares the matured and calculated results. All o f the 10 API tests [38] continued sufficient information to make a comparison between the measured and calculated results for ATy, Q and Ls. . .

Table H1 sumarizes a comparison between the measured and calculated vapor space temperature range, ATv. The average difference is -17.5%. Figure H1 311 ustrates this comparison graphically. Table H1 sumarizes a comparison between the measured and calculated vented gas volume .outlfow, Q, which was calculated from Q = Vy KE* The average difference .is -11.3%. Figure H2 illustrates this comparison graphically. Table H1 sumarires a comparison between the measured and calculated daily standing storage loss, Ls. The average difference is -14.3%. Figure H3 il lustrates this comparison graphically.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

In general, the Comparison between the API test data and the predictions made by the standing storage loss equation are excellent.

--```,``-`-`,,`,,`,`,,`---


Not for Resale

API MPMS*LS*LD 93 m 0732290 0511bOl 780

H3.0

COWPARISON WITH THE EPA TEST DATA [20]

Table H2 sumarizes the i n p u t information from the EPA tests which was used t o calculate the standing storage loss. T h i s table also compares the measured and calcul ated results. Only 12 of the 15 €PA tests [20] were suitable for making a comparison between the measured and calculated results for ATy, Q and Ls.

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Table H1 summarizes a comparison between the measured and calculated vapor space temperature range, ATy. lhe average difference is 10.7%. Figure "4 illustrates this comparison graphicaily. Table H1 summarizes a comparison between the measured and calculated vented gas volume outflow, Q. The average difference i s 77.3%. Figure H5 illustrates this comparison graphically . Table H1 sumarizes a comparison between the measured and calculated daily standing storage loss, Ls. lhe average difference is 111.3%. Figure H6 illustrates this comparison graphical ly. I n general, the thermal response of the tank vapor space i s predicted quite well, thus indicating that the heat transfer aspects o f the standing storage loss wdel compare well nith actual measurements. M.O

COMPARISON W I T H THE WOW TEST DATA [17]

Table H3 summarizes the i n p u t information from the WOW tests which was used t o calculate the standing storage loss. T h i s table also compares the measured and cal cul ated results . During the UOGA tests, measurements were not made o f the vapor space temperature, Ty. Thus, i t is not possible t o compare the predicted values w i t h the measured values for this variable.

H5 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

--```,``-`-`,,`,,`,`,,`---

API

MPMS*Lq=LD 93 M 0732290 05LLb02 bL7

Only 8 o f the 44 WGA tests [I71 were suitable for making a comparison between the measured and calculated results for Q and Ls. Table H3 sumarites a comparison between the measured and calculated vented gas volume outflow, Q. The average difference is 79.3%. Figure H7 illustrates this comparison graphically.

In general, the comparison between the measured and calculated vented gas volume outflow, Q, for the WOGA tests is about as good as that for the EPA tests. Again, this illustrates that the standing-storage loss model incorporates a good charateriration o f the tank vapor space thermal response.

The comparison with the API test data [38], EPA test data [20] and WOGA test data [17] validated the suitability o f the standing storage loss equation. The API tests provided a more accurate and extensive set o f test data for comparison with the A P I standing storage loss equation. The average difference between the calculated and measured standing storage loss is 14.3%. .

--```,``-`-`,,`,,`,`,,`---

//^:^^#^~^^""~:@":^*^~$~"#:*~^"~"~":*@~~^^~:^":^@::~*\\

Table H3 sumarizes a comparison between the measured and calculated daily standing storage loss, Ls. The average difference is 28.1%. Figure H8 illustrates this comparison graphically.

The EPA and WOGA test data, although of lesser suitability for an accurate validation, also confiraped the suitability of the standing storage loss equation. The average difference between the calculated and measured standing storage loss is. 111.3% for the €PA tests and 28.1 for the WOGA tests.


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API WBLICATION 2518 DOCUHENTATIOII FILE

REFERENCES

R1 Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

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A P I MPMStLS-LD 93

API WBLICATION 2518 WCtEHENTATION FILE REFERENCES

CONTENTS

SECTION R1 R2 R3

0732290 0 5 L L b L 5 275 M

DESCRIPTIN

PAGE .

.............................................R3 American Petroleum Institute Publications................ R3 L i terature References ..................................... R4 Introduction

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H 0732290 0 5 L L b L b 101

R1 INTRODUCTION

This section of the Documentation File to API. Publication 2518, Second Edition, contains a list of the references that are cited in this Documentation File. In addition to those that are cited, the list also contains references that were reviewed as part o f preparing the Second Edition to API Publication

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A P I MPMS*LS=LD 93

2518.

Section R2 contains a list of API publications that relate to atmospheric storage tanks. These are arranged in numerical order according to their API publ ication number. Section R3 contains a list of literature references. These are arranged i n chronological order according to their publ ication date. R2 Al.

AHERICAN PETROLEW INSTIME PUBLICATIONS American Petroleurn Institute, " Inspection of Atmospheric and Low-Pressure Storage' Tanks", Recommended Practice RP-575, First Edition, Washington, D.C.,

A2.

1990.

-

American Petroleum Institute, "Welded Steel Tanks for Oil Storage", Standard 650, Seventh Edition, Washington, D.C., November 1980.

A3.

A4

AS.

American Petroleum Institute, "Evaporation Loss in the Petroleum IndustryCauses and Control", Bulletin 2513, First Edition, Washington, D.C., February 1959. American Petroleum Institute, "Evaporative Loss from External Floating-Roof Tanks" Publication 2517, Third Edition, Washington, 0.C; , February 1989.

7

A6.

'

American Petroleum Institute, "Evaporation Loss from Fixed-Roof Tanks", Bulletin 2518, First Edition, Washington, D.C., June 1962, Reaffirmed August 1987.

47. --```,``-`-`,,`,,`,`,,`---

A8.

A9.

American Petroleum Institute, "Evaporative Loss from Fixed-Roof Tanks", Pub1 ication 2518, Second Edition,

1

American Petroleum Institute, "Evaporation Loss from Internal Floatinq-Roof D.C., June 1983.

Tanks" ' Publication 2519, Third Edition, Washington,

American Petroleum Snstitute, "Use of Pressure-Vacuum Vent Valves for Atmospheric Pressure Tanks to R e d u Edition, Washington, D.C., September 1966.

AIO. American Petroleum Insti tute, "Petrochemical Evaporation Loss from Storage Tanks" ' Bulletin 2523, First Edition, Washington, D.C., November 1969.


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All. American Petroleum Institute, 'Guide for Inspection of Refinery Equipment", Chapter XIII, Atmospheric and low-Pressure Storage Tanks, Fourth Edition, Washington, D.C. , April 1981. --```,``-`-`,,`,,`,`,,`---

R3 LITEñATüM REFERENCES 1.

Boardman, H.C., 'Storage o f Volatile Petroleum Products", Petroleum Refiner, Vol. 25, No. 4, April 1946, pp. 109-116.

2.

American Petroleurn Institute, Symposium on Evaporation Loss of Petroleum f r m Storage Tanks, Papers Presented During the 32nd Annual Meeting of the AmerScan Petroleum Institute, Held in Chicago, IL, November 10, 1952, (Also Published in API Proceedings, Vol. 32, Part I, 1952, pp. 212-281).

3.

Nelson, Y.L. , 'How Paintinq Affects Storage Tank Losses", lhe Oil and .Gas Journal , Vol 52, November 2, 1953, pg. 130.

.

N.H., "How to Calculate Vapor Losses", Petroleum Processing, April 1954, pp. 537-540.

i. Prater,

Walker, E.H., Storage Tanks at a Meetinu U.K., May 11:

R.M. Eltringham, and A. Puttick, "Evaporation Loss From Petrol in the United Kingdom A Practical Survey", Paper Presented

-

of The institute of Petroleum at 26 Portland Place, London, 1955.

6.

Hoffman, E.L., "The Effect òf Paint Colors in Reducing Storaqe lank Losses", Paper Presented at the 35th Annua1 keting of the American Petroleum Institute, Marketing Division, Operations and Engineering Connnittee, San Francisco, Cal ifornia, November 14, 1955.

7.

Snyder, A.D., "Theoretical Analysis of Breathing Volatile Liquid Vapor Losses from Fixed-Roof Storaqe Tanks" , Report, Prepared by O1 in Mathison b m Institute, Committee on Evaporation Loss, July 7, ï965.

8.

Cinnamon, S.J., "Investiqation of a Method for Reducing Vapor Losses in Storaae M.S. Thesfs, Submitted to Purdue University, _ _ _ - - o_f. Volatile Liauids". - -~ Deparhent of Chemical Engineking, August -1965. . -

9.

-.

Cinnamon, S.3. and 3.E. Myers, "Reducinq Liquid Storage Losses", Chemical Engineering Progress, Vol. 61, No. 12, Deceinber 1965, pp. 69-74.

10. Air Pollution Control Association, "Control of Atmospheric Emissions from Petroleurn Storaqe Tanks", Informative Report No. 2, Prepared by the TI-3 Petroleum Comnittee, Presented in the Journal of the Air Pollution Control Association, Vol. 21, No. 5, May 1971, pp. 260-268. 11. NUKEM GtnbH, 'Development of a Method for the Recognition o f Environmental Damage üsinq t of Tank Installations", Prepared for the Ministry of the Interior, Federa Republic of Germany, 1972.


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API UPMS*LS=LD 93

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12. Matsumura, I . ,

"Evaporation Loss o f Hydrocarbons i n Hand1ing Petroleum", B u l l e t i n o f the Japan Petroleum I n s t i t u t e , Vol. 16, No. 2, November 1974, pp. 132-139.

13.

BMI-DGMK, "Measurement and Determination of Hydrocarbon Emissions i n the Course o f s t t

14. Ball, D.A.,

A.A. Putnian and R.6. Luce, "Evaluation of Methods f o r Measurin and Control1 inq Hydrocarbon Emissions from Petroleum Storage Tanks": Batte1l e Columbus Laboratories, Prepared f o r the U.S. Environmental Protection Agency, EPA, Report No. 450/3-76-036, November 1976.

, "Estimate Tank Breathins Loss", Hydrocarbon Processing, January 1977, pp. 117-120, (Errata contained i n Hydrocarbon Processing, July 1977, pp. 82-83).

15. Zanker, A.

16. Schwanecke, R.,

"Evaporation Losses from L i q u i d Tanks", Wasser, Betrieb, Vol. 15, No. 7, July 1977, pp. 254-258.

L u f t and

17. Engineering-Science, Inc. , "Hydrocarbon Emissions From Fixed-Roof Petroleum Tanks"

- 9

Prepared f o r the W

e

s

t

e

"Field Data Developed for Fixed-Roof Tank Emissions", l h e Oil and Gas Journal, January 2, 1978, pp. 90-97.

18. Harrer, R.D.,

19. Wilson, A.L.,

"Suqqested Emission Factors f o r Fixed-Roof Storage Tanks", Paoer Presented a t the Meeting o f the A i r P o l l u t i o n Control Association, Anaheim, Cal i f o r n i a , November f3, 1978.

20.

Engineering- Sci ence, Inc. , "Synthetic Organi c Chemical Manufactur in Industry, Emission Test Report, Breathing Loss Emissions from Fixed-Roo Petrochemical Storage Tanks", Prepared for the U.S. Environmental Protection Agency, EPA Report No. EMB-78-OCM-5, February 1979.

21.

Moryzkov, V.S., L.L. Tatarnikov, E.Y. Kardash and A.S. Yarmukhametov, "Losses o f Crude O i l and Products i n Operation of Refinery Storaqe Tanks",

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Chemi stry) , 1976.

1

22.

Cinquemani, V., J.R. Owenby, Jr., and R.G. Baldwin, "Input f o r Solar Systems', Prepared by the U.S. Dept. o f Commerce, National Oceanic and Atmospheric Administration, Envi ronmental and Information Service, Nat ional Climatic Center, Asheville, North Carolina, Prepared f o r the U.S. Dept. o f Energy, Div. of S o l a r Technology, under Interagency Agreement No. E (49-26)1041, November 1978 (Revised August 1979).

23.

Erbar, J.H., "Predicting Hydrocarbon Emissions from Fixed Roof F i e l d Storage Tanks", Prepared for the American Petroleum I n s t i tute, Environmental Affairs Department, Task Force on Hydrocarbon Emissions from Production Operations,

1980.

RS Copyright American Petroleum Institute Reproduced by IHS under license with API No reproduction or networking permitted without license from IHS

Not for Resale

API MPMS*L9-LD 9 3

25.

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Duffie, J.A. and W.A. Beckman, "Solar Engineerinq o f Thermal Processes", John Wiley and Sons, 1980.

7

Laverman, R.J., "Evaluation o f the Temperature Factor for Thermal Breathin Loss Estimation from fixed Roof Tanks", Chicago Bridge di Iron Co., CB? Research Report No. RC-3000-2, March 11, 1981.

26. Laverman, R.J., "Thermal Breathinq Loss Analysis for a Roof Vent Area Diffusion Rate Controlled Hodel", Chicago Bridge h Iron Co., CBI Research Report No. RC3000-1, March 11, 1981. 27.

Beckman, J.R.

and J.R.

Gilmer, "Model for Predictinq Emissions From Fixed-

4

Roof Storaqe Tanks", Industrial Development, Vol. 20, No. 4, April 1981, pp. 646-651.

28. U.S. Environmental Protection Agency, "Compilation of Air Pollutant Emission Factors Section 4.3 Storaqe of O r g a n i m

(

29. TRW Environmental, Inc., "Backqround Documentation for Storage o f Organic Liquids", Prepared for th\ Contract No. 68-02-3174, May 1981. 30.

Beckman, Duffie and Associates, "Evaporation Loss of Petroleum from Storaqe Final Report, Prepared for the American Petroleum Institute, Comi ttee on Evaporation Loss Measurement, August 1, 1982.

Tanks" '

31. Verein Deutscher Ingenieure, "Emission Control : Refineries", VDI 2440, June 1983. 32. Beckman, J.R., Transfer D -223,

"Breathing Losses from fixed-Roof Tanks by Heat and .Mass i f f u s i o s NO. 3, 1984, pp. 472-479.

33. Environmental Monitoring a Services, Inc. (subsidiary of Combustion Engineering Co.), "Breathinq Loss Emissions from Fixed Roof Tanks", Final Report, Prepared for the American Petroleum Institute, Committee on Evaporation Loss Measurement, June 1985. 34* U.S. Environniental Protection Agency, "Compilation of Air Pollutant Emission Factors, Section 4.3, Storage of Organic Liauids", USEPA Report No. AP-42, Third Edition, Septeaiber 1985. 35.

Dept. of Commerce, National Oceanic and Atmspheric Administration, "Comparative C1 imatic Data Through 1984", National -C1imatic Data Center, Asheville, North Carolina, 1986. U.S.

36. Beckman, J.R. and 3.A. Holcoinb, "Experimental and Theoretical Investigation o f Working Emissions from Fixed-Roof Tanks", Industrial and Engineering Chemistry, Process Design h Development, Voì. 25, No. 1, 1986, pp. 293-298. --```,``-`-`,,`,,`,`,,`---

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Beckman, J.R., Crude O i l S

37.

"Model Development t o Predict Hydrocarbon Emissions from t o r a g e t CaliforniaAgreement No. A4-045-32, July 20, 1986.

38.

Knodel, B.D. and R.J. Laverman, "Data Base Generation, Analysis and Revision o f API Publication 2518, Task 1: Validate Computer Model", Final Report f o r for the American . Petroleum I n s t i t u t e , Conmittee on Evaporation Loss Measurement, Task Group 2518, September 11, 1986.

39.

Rinehart, J.K. and R.J. Lavemn, "Data Base Generation, Analysis and Revision of API Publication 2518, Task 2: Generate Computer Data Base", Final Report f o r Task 2, Prepared by CBI Industries, Inc., Prepared f o r the Ameri can Petroleum I n s t itute, C o m i t t e e on Evaporation Loss Measurement, Task Group 2518, February 16, 1987.

40.

Rinehart, J.K. and R.3. Laverman, "Data Base Generation, Analysis and Revision o f API Publication 2518, Task 3: Correlate Data Base", Final Report for Task 3, Prepared by CBI Industries, Inc., Prepared f o r the American Petroleum I n s t i t u t e , Comit t e e on Evaporation Loss Measurement, Task Group 2518, August 26, 1988.

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A P I M P M S U L S - L D 93

0732290 0511621 579

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Order No. 852-30553

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1-01102-4/93-1(3


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American Petroleum Institute 1220 L Street, Northwest

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