Documentation for Proposed Changes to AP-42 Chapter 7 Section 7.1 - Organic Liquid Storage Tanks 2018
Proposed Revisions:
References to section and paragraph numbers pertain to the numbering in the draft proposal.
1) Editorial.
a. Performed wordsmithing throughout for clarity, consistency and correctness.
b. 7.1.1.1 Added a new section titled Scope, to provide an overview of the chapter.
c. 7.1.3.2 Separated the calculation of standing loss from the calculation of working loss for
floating-roof tanks, rather than having the two intertwined.
2) Nomenclature.
a. Edited variable labels for consistency and updated Table 7.1-1 accordingly.
3) Scope.
a. Added a Scope section up front, to explain the scenarios for which the document is and is not
intended.
4) TANKS 4.09
a. Added commentary that the software program TANKS 4.09, which has not been updated to
incorporate these revisions, has known errors and is no longer supported by EPA.
5) Equations.
a. See Appendix A for a summary of the disposition of each equation.
b. Temperature Equations, [see Appendix B] The temperature equations that have been in AP-
42 Chapter 7.1 were derived in API Publication Chapter 19.ID, "Documentation File for API
Manual of Petroleum Measurement Standards Chapter 19.1 - Evaporative Loss From Fixed
Roof Tanks," First Edition, March 1993. The original development of these equations took
place prior to the proliferation of desktop computers, and thus there was a tendency to make
approximations and substitutions that would simplify the calculations. Given the present
accessibility to computers, however, such simplifications are unnecessary, and the equations
have been revised to more accurately reflect the theoretical derivations. Development of the
revised temperature equations is summarized in Appendix B of this document and presented
in more detail in Annex I of API MPMS Chapter 19.4, "Evaporative Loss Reference Information
and Speciation Methodology," Third Edition, October 2012.
i. Specifically, edited the coefficients in the default expressions for Tla and AT^to be based
on a uniform assumption of 0.5 for the tank height-to-diameter ratio (H/D), expressed
these coefficients to one significant figure, and added a more general form of these
equations with H/D as a variable.
ii. Added text advising that the equation for calculating TB from an assumption of equilibrium
with ambient conditions should be used only for tanks that may be reasonably assumed to
be in equilibrium with the atmosphere and for which measured liquid bulk temperatures
are not available. That is, it is always preferable to use measured liquid bulk temperature
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
data rather than to calculate the liquid bulk temperature from an assumption of
equilibrium with ambient atmospheric conditions.
iii. Also, replaced the former equation for calculating TB from ambient conditions, which did
not account for the amount of solar radiation striking the tank, with an equation
developed from the same theoretical energy transfer model from which the other
temperature equations were developed.
iv. Added separate equations to calculate Tla for floating-roof tanks, with separate equations
for different types of floating roof decks.
v. Also added separate equations to calculate TB for floating-roof tanks that are in
equilibrium with the atmosphere and for which measured liquid bulk temperatures are
not available.
c. Alternative Equations. Added language to clarify, in the instances of alternative equations,
which equations are preferred as being more accurate. This pertains particularly to the
equations for KE, APv, and Lw for fixed-roof tanks.
i. Ke. Clarified that Equation 1-5 (formerly Equation 1-7) is the general and preferred form of
equation for calculating KE, and that the simpler expressions for KE in Equations 1-12 and
1-13 are approximations that are acceptable when certain criteria are met. Also added
text explaining that the value of KE cannot be greater than 1.
ii. hPv¦ Recommended that the range in vapor pressure, APy, should always be calculated
directly as (Pvx~ Pvn), the difference between the maximum and minimum vapor
pressures, and not by means of the old alternative. Moved the old alternative
approximation for APyto a new section for historical equations that are no longer
recommended. This approximation had simplified the calculation of /\PV by avoiding the
need to calculate PVx and Pvn¦ However, it sometimes introduced significant error and is
now unnecessary given computer tools for performing calculations.
iii. Lw¦ Recommended that the fixed-roof tank working loss, Lw, should always be calculated
from the general form of equation that retains temperature as a variable, and not by
means of the old alternative. Moved the old alternative approximation for Lw to a new
section for historical equations that are no longer recommended.
d. Vapor Space Temperature. Added an equation for calculating the temperature of the vapor
space, Tv. It is used in Equation 1-22 for calculation of the stock vapor density, Wv, which
previously used the average liquid surface temperature, Tla, as an approximation of the vapor
space temperature. See Appendix B for the derivation of this equation.
e. Vapor Density. Revised the calculation of vapor density to use the vapor space temperature
rather than use the liquid surface temperature as an approximation of the vapor space
temperature.
f. Net Throughput. Provided guidance explaining that net throughput is most accurately based
on changes in liquid level, rather than pumping volume, for tanks in which pump in and pump
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
out occur at the same time, and revised the equations to accommodate use of accumulated
changes in liquid level.
6) True Vapor Pressure.
a. Explained how this term is defined for purposes of this document, and updated guidance on
how true vapor pressure values may be determined.
b. Added a reference to ASTM D6377 for measuring the true vapor pressure of crude oil.
c. Added a reference to ASTM D5191 as an acceptable alternative to ASTM D323 for determining
Reid vapor pressure.
7) Pressurized Tanks.
a. Explained that the equations for standing and working losses from fixed-roof tanks account for
vent settings, and are thus applicable to pressurized tanks which may vent to the atmosphere
when filling.
b. Also explained that the equations are not applicable to cases where the vent settings are
sufficiently high that the tank is designed to not vent to atmosphere. In such cases, leakage
through the vents is estimated as equipment leaks rather than as storage tank emissions.
8) Insulated Tanks.
a. Added guidance for estimating emissions from fully insulated tanks (i.e., both shell and roof
are insulated). This guidance includes an assumption of the liquid surface temperature being
equal to the liquid bulk temperature, in that there is minimal heat loss through the roof or
shell of the tank.
b. It also assumes no generation of breathing loss from the ambient diurnal temperature cycle in
that there is minimal heat transfer through the roof and shell of the tank.
c. The guidance explains, however, that a fully insulated tank may have breathing losses driven
by temperature cycles in the heating of the liquid stock and provides equations to estimate
such heating-cycle losses.
9) Partially Insulated Tanks.
a. Added guidance that a partially insulated tank (i.e., shell is insulated but roof is not) may be
modeled as an uninsulated tank in that significant heat transfer will take place through the
tank roof.
b. Alternatively added temperature equations for more accurate modeling of partially insulated
tanks, rather than modeling as not insulated. See Appendix B.
10) Distillate Flushing.
a. Added a brief discussion of distillate flushing in the sections on Floating Roof Landings and
Tank Cleanings. This refers to flooding the bottom of a nearly empty tank with a light distillate
such as diesel to reduce the vapor pressure of a more volatile stock such as gasoline.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
b. This discussion is qualitative and does not include equations.
11) Floating Roof Landing Emissions.
a. Added text suggesting that emissions from a landing for which the duration is less than a day
may be estimated by prorating the estimated emissions for a one-day landing event to the
portion of the day involved.
b. Added an upper limit on the estimated refilling loss.
c. Ke- The procedure for estimating floating roof landing loss had calculated KE using the old
approximation for /\PV, which has been moved to the section for historical equations that are
no longer recommended. The revised text cites the equations now given for KE in the section
for fixed-roof tanks, in which /\PV is calculated directly as (Pvx~ Pvn)-
12) Tank Cleaning Emissions.
a. Added a section for estimating emissions resulting from the cleaning of storage tanks.
b. The methodology is specifically for estimation of emissions while forced ventilation is
operating in the tank, regardless of whether or not cleaning operations are taking place.
13) Flashing Emissions.
a. Added a section for estimating emissions resulting from flashing.
14) Short Time Periods.
a. Added explanation for why the equations for routine emissions should not be used for time
periods shorter than one month.
15) Special Cases.
a. Added references to API publications for selected special cases:
i. Internal floating-roof tanks with closed vent systems. This refers to internal floating-roof
tanks that vent to the atmosphere, but which have self-closing vents rather than the more
typical open vents. Reference is made to an API document, with a recommendation of
simply applying a 5% reduction from the estimated emissions for a freely vented internal
floating-roof tank.
ii. Case-specific liquid surface temperature. This refers to accounting for certain parameters
which have default values assigned in the development of the equations for this
document. These parameters include the height-to-diameter ratio of the tank and the
thermal resistance of the floating roof. However, equations with the height-to-diameter
ratio as a variable have been added to the proposed revision, and thus this section may
now be extraneous.
16) Figures.
a. Added figures for the slotted guidepole "flexible enclosure" and the guidepole/ladder
combination "ladder sleeve."
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
17) Tables.
a. Replaced old tables with updated tables from API MPMS 19.4, including:
i. Table 7.1-2. Properties of Selected Petroleum Stocks. Revised the default vapor pressure
constants for No. 6 Fuel Oil and added Vacuum Residual Oil as a new default stock, and
added Distillation Slope and Vapor Pressure Constants to this table (each of which had
been in separate tables).
ii. Table 7.1-4. This is a new table with equations for the height of the liquid heel and the
vapor space under a landed floating roof, which may be used in estimating emissions from
floating roof landings and tank cleanings.
iii. Table 7.1-5 This is a new table for LEL Values for Selected Compounds, which may be used
in estimating tank cleaning emissions.
iv. Table 7.1-6. This is the table for Paint Solar Absorptance, in which the previous categories
of "Good" and "Poor" have been relabeled "New" and "Aged." In addition, a new
category has been added labeled "Average," which is the average of the values from the
New and the Aged categories.
v. Table 7.1-7. Meteorological Data. Wind and atmospheric pressure have been added to
this table. Wind had been in a separate table, and atmospheric pressure had not
previously been included in the tabulation of meteorological data.
vi. Table 7.1-8. Rim Seals. Added emission factors for "tight fitting" rim seals.
vii. Table 7.1-12. Deck Fittings. Added emission factors for a flexible enclosure as a slotted
guidepole control and a ladder sleeve as a ladder-guidepole control. Also added text to
indicate which legs are for IFR-type decks and which are for EFR-type decks.
viii. Tables 7.1-20 and 7.1-21. New tables summarizing the equations needed for estimating
emissions from tank cleaning events.
18) Sample Calculations.
a. All Examples. Revised the temperature calculations in accordance with changes made to
these equations in the body of the document.
b. Example 4. Gasoline in an IFRT. Reworked to use Raoult's Law to obtain partial speciation
from liquid-phase concentrations, rather than a vapor profile from EPA's SPECIATE database.
Raoult's Law is the approach presented in Section 7.1-4, Speciation Methodology, and thus
seems the more appropriate approach to illustrate in the examples.
c. Example 5. Floating Roof Landing. Added this as a new example.
d. Example 6. Tank Cleaning. Added this as a new example.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Appendix A - Disposition of Each Equation
Documentation for equations.
New No. Old No. Change?
Reference
1-1 1-1 None
1-2 1-2 None
1-3 1-3 None
1-4 1-4 None
1-5 1-7 None. Moved the more general and accurate equation to
precede the more approximate and case-specific equations.
1-6 - A7V. New more general equation to calculate the vapor space Appendix B
temperature range, with H/D as a variable.
1-7 1-8 A7V. Revised the coefficients to be based on a uniform Appendix B
assumption of 0.5 for the tank height-to-diameter ratio, and
expressed these coefficients to one significant figure.
1-8 - A7V. New equation for the case of a partially insulated tank. Appendix B
1-9 1-9 None
1-10 hPv. This was an alternative approximation that simplified the
calculation of /\PV by avoiding the need to calculate PVx and PVn
in Equation 1-9. However, it sometimes introduced significant
error and is now unnecessary given computer tools for
performing calculations. As it is no longer recommended, this
equation has been moved to a new section for historical
equations.
1-10 1-11 None
1-11 1-12 None
1-12 1-5 Coefficients revised in expression for A7V. See new 1-7
1-13 1-6 None
1-14 1-13 None
1-15 1-14 None
1-16 1-15 None
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change?
Reference
1-17 1-16 None
1-18 1-17 None
1-19 1-18 None
1-20 1-19 None
1-21 1-20 None
1-22 1-21 Wv. Replaced Tla with Tv. In that Wv is the stock vapor density, See new
the temperature in question is that of the vapor space. Earlier 1-32 - 1-34
versions of the temperature equations had sometimes used
liquid surface temperature as a surrogate for the vapor space
temperature, but it would be more accurate to use the vapor
space temperature. Expressions for vapor space temperature
have been added as Equations 1-32 through 1-34.
1-23 1-22 None
1-24 1-23 None
1-25 1-24 None
1-26 1-25 None
1-27 - Tla- New more general equation to calculate the liquid surface Appendix B
temperature, with H/D as a variable.
1-28 1-26 Tla- Revised the coefficients to be based on a uniform Appendix B
assumption of 0.5 for the tank height-to-diameter ratio, and
expressed these coefficients to one significant figure.
1-29 - Tla- New equation for the case of a partially insulated tank. Appendix B
1-30 1-27 None
1-31 1-28 7b. Replaced the old equation, which did not account for Appendix B
insolation as a variable, with a new equation that does account
for insolation as a variable.
1-32 - Tv. New general equation to calculate the vapor space Appendix B
temperature, with H/D as a variable.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change? Reference
1-33
—
Tv. New simplified equation to calculate the vapor space
temperature, with H/D set to 0.5.
Appendix B
1-34
-
Tv. New equation to calculate the vapor space temperature for
the case of a partially insulated tank.
Appendix B
1-35
1-35
Lw¦ Replaced the expression for throughput as a function of full-
tank turnovers with a variable, VQ, which accounts for changes
in liquid level.
See new 1-38
1-36
1-30
N. Changed calculation of net turnovers to be based on
measured increases in liquid level, rather than on pump
throughput, to more accurately account for scenarios in which
pump-in and pump-out occur simultaneously. Calculation based
on pump throughput is now shown as a fallback in the event
that changes in liquid level are not known. Also, now accounts
for low liquid level as well as high liquid level in determining the
net working height of the tank. Old Equation 1-30 is now 60-3.
1-37
1-30
1-31
Determination of N using the old approach based on pump
throughput, but using net working height (Hlx - HLn) rather than
maximum liquid height (Hlx). That is, accounting for low liquid
level as well as high liquid level. Old Equation 1-31 is now 60-4.
1-38
-
VQ. New equation to calculate the net throughput as a function
of cumulative increases in liquid level.
Simple
geometry
1-39
-
VQ. Expression to determine throughput that accommodates
the old approach based on pump throughput.
1-40
1-36
None
1-41
1-37
1-29
1-32
1-33
1-34
None
Lw¦ This was an alternative approximation that simplified the
calculation of Lw by assigning a default temperature to the
vapor density term. This simplification is now unnecessary
given computer tools for performing calculations. As it is no
longer recommended, this equation has been moved to a new
section for historical equations.
These equations have been replaced by the text preceding 60-2.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change?
Reference
2-1 2-1 Broke the old equation into two equations to show that the sum
2-2 of the rim seal, deck fitting and deck seam losses constitutes the
standing loss.
2-3 2-2 None
2-4 2-3 None.
2-5 - Tla- New general equation to calculate the liquid surface Appendix B
temperature for an internal floating-roof tank, with H/D as a
variable.
2-6 - Tla- New simplified equation to calculate the liquid surface Appendix B
temperature for an internal floating-roof tank, with H/D set to
0.5.
2-7 - Tla- New equation to calculate the liquid surface temperature Appendix B
for a steel peripheral pontoon type external floating-roof tank.
2-8 - 7b. New general equation to calculate the liquid bulk Appendix B
temperature for a steel peripheral pontoon type external
floating-roof tank, with H/D as a variable.
2-9 - 7b. New simplified equation to calculate the liquid bulk Appendix B
temperature for a steel peripheral pontoon type external
floating-roof tank, with H/D set to 0.5.
2-10 - Tla- New equation to calculate the liquid surface temperature Appendix B
for a steel double-deck type external floating-roof tank.
2-11 - Tb. New general equation to calculate the liquid bulk Appendix B
temperature for a steel double-deck type external floating-roof
tank, with H/D as a variable.
2-12 - Tb. New simplified equation to calculate the liquid bulk Appendix B
temperature for a steel double-deck type external floating-roof
tank, with H/D set to 0.5.
2-13
2-5
None
2-14
2-6
None
2-15
2-7
None
2-16
2-8
None
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change? Reference
2-17 - None. This equation is in the old version, but not numbered.
2-18 2-9 None
2-19 2-4 None. This is for working loss from a floating-roof tank, but in
the previous version it was inserted among equations for
determining the components of standing loss. It has been
moved to follow the standing loss calculations in the proposed
revisions.
2-20 - Q. New equation to calculate the net throughput as a function
of cumulative decreases in liquid level.
3-1 2-10 None. Separated estimation of floating roof landing losses into
a different section.
3-2 2-11 None
3-3 2-12 None
3-4 2-13 None
3-5 2-14 None
3-6 2-15 Clarified that the temperature, T, is the temperature of the
vapor space, 7V.
3-7 2-16 None
3-8 2-17 None
3-9 2-18 None.
3-10 2-19 None
3-11 2-20 None
3-12 2-21 None
3-13 2-22 None
3-14 2-23 None
3-15 2-24 None
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change? Reference
3-16
New equation to calculate an upper limit on the filling loss
based on the total mass of volatile material remaining in the
bottom of the tank.
3-17
2-25
Corrected "density" to read "concentration."
3-18
2-26
2-27
Replaced old equation 2-26 with the more general expression in
old equation 2-27. New equation 3-18 is the same as old
equation 2-27. Thus effectively no change.
3-19
2-28
None
3-20
2-29
Edited text to reference revised equation numbers. No change
in result.
3-21
2-30
Substituted 1 for rid, in that the number of days, rid, is stated in
the text as being set to 1. Thus effectively no change.
—
2-31
Deleted the historic approximation for estimating Ke, and added
a reference in the text to the more accurate expression in new
equation 1-5.
See old 1-10
3-22
2-32
None
4-1
New equation included for estimating emissions from tank
cleaning events, which had not been addressed previously.
Development of
these equations is
presented in the
text
4-2
-
ditto
ditto
4-3
-
ditto
ditto
4-4
-
ditto
ditto
4-5
-
ditto
ditto
4-6
-
ditto
ditto
4-7
-
ditto
ditto
4-8
-
ditto
ditto
4-9
..
ditto
ditto
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No.
Old No.
Change?
Reference
4-10
-
ditto
ditto
4-11
-
ditto
ditto
4-12
-
ditto
ditto
4-13
-
ditto
ditto
5-1
New equation for estimating flashing losses based on the
laboratory gas-to-oil ratio (GOR). Flashing losses had not been
addressed previously.
measurement is in
scf; apply unit
conversion to
obtain lb-moles;
multiply by
molecular weight
to obtain pounds
6-1
3-1
None
8-1
New equation included for estimating emissions from fully
insulated fixed-roof tanks, which had not been addressed
previously.
These equations
express the
assumption that
all phases within a
completely
insulated tank are
at the same
temperature.
8-2
-
ditto
ditto
40-1
4-1
None
40-2
4-2
None
40-3
4-3
None
40-4
4-4
None
40-5
4-5
None
40-6
4-6
None
40-7
4-7
None
40-8
4-8
None
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Documentation for equations.
New No. Old No. Change?
40-9 4-9 None
60-1 1-10 APy. This was an alternative approximation that simplified the
calculation of /\PV by avoiding the need to calculate PVx and PVn
in Equation 1-9. However, it sometimes introduced significant
error and is now unnecessary given computer tools for
performing calculations. As it is no longer recommended, this
equation has been moved to a new section for historical
equations.
60-2 1-29 No longer recommended as Equation 1-35 is preferred; this
equation moved to new section for historical equations.
60-3 1-30 Replaced by 1-36 and 1-37.
60-4 1-31 Replaced by 1-36 and 1-37.
Reference
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Appendix B - Background on the Revised Temperature Equations
Discussion.
Prior Simplifications Now Unnecessary. The temperature equations that have been in AP-42 Chapter 7.1
were documented in API Publication Chapter 19.ID, "Documentation File for API Manual of Petroleum
Measurement Standards Chapter 19.1 - Evaporative Loss From Fixed Roof Tanks/' First Edition, March
1993. The original development of these equations took place prior to the proliferation of desktop
computers, and thus there was a tendency at that time to make approximations and substitutions that
would simplify the calculations. Given the present accessibility to computers, however, such
simplifications are now unnecessary, and the equations in the proposed revisions to AP-42 have been
revised to more accurately reflect the theoretical derivations.
For example, there was a development of a "gas space" (vapor space) temperature, alternatively labeled
Tg or Tv in the documentation file, but this temperature was not used in the final equations. Rather, the
final equations substituted the average liquid surface temperature, TLA, for the vapor space temperature
in equations such as the calculation of vapor density, Wv, in order to avoid the additional calculation for
the vapor space temperature. The proposed revisions include a calculation of the vapor space
temperature, Tv, and use of that temperature in the calculation of vapor density, Wv.
Significant Uncertainty in the Calculations. The storage tank temperature equations were derived from
a theoretical energy transfer model that includes numerous parameters, some of which were assigned
default values and some of which were retained as variables. For example, angle of the sun, reflectivity
of the surrounding ground surfaces, average liquid level, and insulation value of a given floating roof
design were all assigned default values, whereas ambient temperature, liquid bulk temperature, average
incident solar radiation (insolation), and reflectivity of the tank exterior surfaces were retained as
variables in the final equations.
The resulting equations have significant uncertainty when applied to a specific scenario, in part because
the default values assigned to certain parameters may not be representative for the given scenario, and
in part because the parameters retained as variables are assigned average values when the actual values
may vary greatly over time (e.g., ambient temperature). Given the uncertainty in this approach to
calculating storage tank temperatures, the prior practice of expressing the coefficients in the equations
to two significant figures was deemed inappropriate and potentially misleading, and thus the
coefficients in the revised equations are expressed to one significant figure.
Inconsistencies in the Prior Equations. Review of the earlier documentation also revealed multiple
inconsistencies, such as a default value of 0.45 being assigned to the tank height-to-diameter ratio in
one instance and a value of 2.0 in another instance. The revised equations include one set of equations
with the height-to-diameter ratio retained as a variable and another set of equations with a default
value of 0.5 assigned to the height-to-diameter ratio. While the dimensions of storage tanks in the
petroleum industry vary dramatically, many tanks are 40 or 48 feet tall and 90 to 120 feet in diameter.
Illustrations of the impact of the changes in the defaults equations for the average liquid surface
temperature, TLA, and the range in vapor space temperature, ATV, are shown in the table below.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Comparison of Estimated Emissions -- Prior Defaults versus Revised Defaults
Calculating the average liquid surface temperature, Tla, and the range in vapor space temperature, ATv, from default equations.
Cases illustrate low and high throughputs and low and high temperatures.
Assumptions for these examples:
Location: New Orleans, LA
Average Ambient Temperature: 68.0 deg F
Avg Ambient Temperature Range: 19.1 deg F
Average Insolation: 1444 Btu/(ftA2 day)
Tank Type: FRT(no floating roof)
Insulated? No
Paint: white
Diameter: 40 feet
Product: #2 Fuel Oil
Calculated Using Prior Defaults
Calculated Using Revised Defaults
Calculated Using Revised Defaults
(paint in good condition)
(paint in new condition)
(paint in average condition)
Liquid
Liquid
Liquid
Liquid
Bulk
Surface
Avg
Estimated Losses
Total
Surface
Avg
Estimated Losses
Total
Surface
Avg
Estimated Losses
Total
Throughout
Temp
Temp
TVP
This Period
Emissions
Temp
TVP
This Period
Emissions
Temp
TVP
This Period
Emissions
Case
(gallons)
(deg F)
(deg F)
(psia)
Standing Working
(lbs)
(deg F)
(psia)
Standing Working
(lbs)
(deg F)
(psia)
Standing Working
(lbs)
1
1,297,800
60.0
65.4
0.008
70 31
100
64.4
0.007
59 30
89
65.0
0.008
69 30
99
2
12,978,000
60.0
65.4
0.008
70 308
377
64.4
0.007
59 298
357
65.0
0.008
69 303
371
3
1,297,800
120.0
99.0
0.021
175 83
258
100.4
0.022
156 86
242
101.0
0.023
181 87
268
4
12,978,000
120.0
99.0
0.021
175 834
1,009
100.4
0.022
156 859
1,015
101.0
0.023
181 871
1,052
The table that follows illustrates the sensitivity of estimated emissions to the height-to-diameter ratio of the tank, using the same example as
described above but using varying values for the height-to-diameter ratio in the temperature equations. The relatively low sensitivity of
estimated emissions to the height-to-diameter ratio has historically been cited to justify use of a default value for this parameter. However,
both height and diameter of the tank are values that are generally known, and thus inclusion of the height-to-diameter ratio as a variable does
not add significant burden when the calculations are being performed by a computer program.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Accounting for Insolation in Liquid Bulk Temperature. The prior equation for calculating the liquid bulk
temperature, TB, from an assumption of equilibrium with ambient conditions was not derived from the
theoretical energy transfer model, but rather was derived from limited empirical data. The resulting
expression did not account for geographical differences in average insolation, and thus gave the same
increase above ambient temperature for Nome, AK as for Phoenix, AZ.
The table below shows a comparison of the increase in liquid bulk temperature, TB, above average
ambient temperature, TAa, estimated by both the prior and the revised equations for a tank in
equilibrium with ambient conditions, for different scenarios of paint color/condition and insolation. It's
evident that the difference between the two approaches is generally a fraction of a degree, but the
revised equation is more rational in that it accounts for insolation.
Comparison of the estimated increase in liquid bulk temperature, TB, above average ambient
temperature, TAa, for a tank in equilibrium with ambient conditions.
Tank
color/condition: White/New Temperature increase (F) above ambient, for the given equation:
revised
a
0.17
0.17
0.17
I
838
1370
1872
prior
+ 6a- 1
0.02
0.02
0.02
+ 0.003al
0.43
0.70
0.95
Tank
color/condition:
White/Average
a
0.25
0.25
0.25
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
prior revised
+ 6a-l +0.003al
0.50
0.50
0.50
0.63
1.03
1.40
Tank
color/condition:
Light
Gray/Average
a
0.58
0.58
0.58
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
prior revised
+ 6a- 1 + 0.003al
2.48
2.48
2.48
1.46
2.38
3.26
Tank
color/condition:
Dark
Green/Average
a
0.9
0.9
0.9
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
prior revised
+ 6a-l +0.003al
4.40
4.40
4.40
2.26
3.70
5.05
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Accounting for Tank Type in the Calculation of Tank Temperatures. AP-42 Chapter 7.1 has historically
used the equation developed for calculating the liquid temperatures of fixed-roof tanks to also calculate
the liquid temperatures for floating-roof tanks. There are differences, however, in the energy transfer
models for each tank type. The fixed-roof tank has a vapor space beneath the fixed-roof and an open
liquid surface within the tank. An internal floating-roof tank has a similar vapor space beneath the fixed-
roof, but has a floating roof covering the liquid surface. An external floating-roof tank does not have a
fixed roof and an enclosed vapor space, but rather has solar radiation directly incident upon the floating
roof. The proposed revisions to AP-42 introduce separate equations to calculate liquid temperatures for
each tank type, accounting for the heat conductance characteristics of floating roofs and for the absence
of an enclosed vapor space for external floating-roof tanks.
The table below shows a comparison of the increase in liquid bulk temperature, TB, above average
ambient temperature, TAa, estimated by both the prior and the revised equations for both fixed-roof
tanks (FRTs) and external floating-roof tanks (EFRTs), assuming equilibrium with ambient conditions, for
different scenarios of paint color/condition and insolation.
Comparison of the estimated increase in liquid bulk temperature, TB, above average ambient
temperature, TAa, for an EFRT vs an FRT in equilibrium with ambient conditions.
Tank
color/condition: White/New Temperature increase (F) above ambient, for the given equation:
FRT EFRT
a I + 0.003al + 0.007al
0.17
0.17
0.17
838
1370
1872
0.43
0.70
0.95
1.00
1.63
2.23
Tank
color/condition:
White/ Average
a
0.25
0.25
0.25
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
FRT EFRT
+ 0.003ctl + 0.007ctl
0.63
1.03
1.40
1.47
2.40
3.28
Tank
color/condition:
Light
Gray/Average
a
0.58
0.58
0.58
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
FRT EFRT
+ 0.003al + 0.007al
1.46
2.38
3.26
3.40
5.56
7.60
Tank
color/condition:
Dark
Green/Average
a
0.9
0.9
0.9
I
838
1370
1872
Temperature increase (F) above ambient, for the given equation:
FRT EFRT
+ 0.003al + 0.007al
2.26
3.70
5.05
5.28
8.63
11.79
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Partially and Fully Insulated Storage Tanks. AP-42 Chapter 7.1 has historically excluded insulated tanks
from the scope of the document, but the proposed revisions add guidance for insulated tanks. This
guidance distinguishes between a fully insulated tank (being a tank with effective insulation covering
both the roof and the shell), and a partially insulated tank (being a tank having an insulated shell but an
uninsulated roof).
The proposed revisions indicate that for a fully insulated tank an assumption may be made of the liquid
surface temperature being equal to the liquid bulk temperature, in that there is minimal heat loss
through the roof or shell of the tank. It may further assumed that there is no generation of breathing
loss from the ambient diurnal temperature cycle in that there is minimal heat transfer through the roof
and shell of the tank. However, equations are provided to estimate breathing losses driven by
temperature cycles in the heating of the liquid stock in a fully insulated tank.
The proposed revisions indicate that a partially insulated tank may be modeled as an uninsulated tank in
that significant heat transfer will take place through the tank roof. Alternatively, equations derived from
the theoretical energy transfer model are provided for more accurate modeling of partially insulated
tanks.
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Derivation of Equations.
Symbol
Description
Units
CB
conductance of bottom
Btu/(ft2 hr °F)
Ce
conductance of EFR and liquid surface
Btu/(ft2 hr °F)
Cf
conductance of floating roof
Btu/(ft2 hr °F)
Ci
conductance of IFR and liquid surface
Btu/(ft2 hr °F)
CL
conductance of free liquid surface
Btu/(ft2 hr °F)
Crv
conductance of roof in vapor space
Btu/(ft2 hr °F)
CSL
conductance of shell in liquid space
Btu/(ft2 hr °F)
CSV
conductance of shell in vapor space
Btu/(ft2 hr °F)
D
tank diameter
ft
f
portion of insolation transferred to EFRT stock
dimensionless
Hs
tank shell height
ft
1
insolation
Btu/(ft2 day)
Ih
hourly insolation factor
Btu/(ft2 hr)
Taa
average daily ambient temperature
°R
Tb
average liquid bulk temperature
°R
Tb
equilibrium liquid bulk temperature
°R
Tla
average daily liquid surface temperature
°R
Tln
average daily minimum liquid surface temperature
°R
Tlx
average daily maximum liquid surface temperature
°R
Tv
average vapor temperature
°R
Tv
equilibrium vapor temperature
°R
A
solar absorptance
dimensionless
Or
solar absorptance (roof)
dimensionless
as
solar absorptance (shell)
dimensionless
ATv
average daily vapor temperature range
°R
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Temperature of the Fixed-Roof Tank Vapor Space at Equilibrium. TV
An equation for calculating the temperature of the vapor space, 7V, is new to AP-42. It is used in Equation 1 -22 for
calculation of the stock vapor density, Wv, which previously used the average liquid surface temperature, Tla, as an
approximation of the vapor space temperature.
General equation:
Tv = [2Taa Csv Hs/D + Taa Crv + Tb Cl + (0.5aRl + 0.309 asl Hs/D)/24]/[2 Csv Hs/D + Cl + Crv]
Rearranging:
Tv = [(2 csv Hs/D + cRV) TAA + cL TB + (0.5/24) aRl + (0.309/24) (Hs/D) asl] / [2 csv Hs/D + cL + cRV]
Default values:
Csv = 1.1 tank shell enclosing the vapor space (single layer of steel, uninsulated)
Crv = 1.1 tank (fixed) roof enclosing the vapor space (single layer of steel, uninsulated)
cL = 0.8 FRT (free liquid surface, no floating roof)
Fixed-Roof Tank - uninsulated:
The average vapor temperature, Tv, may be calculated using the following equation:
Tv = [(2.2 Hs/D + 1.1) Taa + 0.8 T„ + 0.021 aRl + 0.013 (Hs/D) asl] / [2.2 Hs/D + 1.9] (1-32)
API assigns a default value of Hs/D = 0.5 and an assumption of aR = as, resulting in the simplified equation shown below:
Tv = 0.7 Taa + 0.3 TB + 0.009 a I (1-33)
Fixed-Roof Tank - partially insulated (insulated shell, uninsulated roof):
When the shell is insulated, the temperature equations are independent of Hs/D.
Tv= 0.6 Taa + 0.4 TB + 0.01 aR I (1-34)
Fixed-Roof Tank-fully insulated (insulated shell, insulated roof):
When the tank shell and roof are fully insulated, the temperatures of the vapor space and the liquid surface are taken as
equal to the temperature of the bulk liquid.
Tv = Tb
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Temperature Range of the Fixed-Roof Tank Vapor Space at Equilibrium. ATV
General equation:
ATV = (Tax - TAN)(1 - Cl/M) + 2IH /M
where:
lH = (0.5aRl + 0.309 asl Hs/D)/24
M = 2 Csv Hs/D + Crv + Cl
and thus:
ATV = [1 - cL / (2 csv Hs/D + cL + cRV)] (Tax - TAN) + 2 [(0.5/24) aRl + (0.309/24) (Hs/D) asl] / (2 csv Hs/D + cL + cRV)
Default values given at Tv above.
Fixed-Roof Tank - uninsulated:
ATV = [1 - 0.8 / (2.2 Hs/D + 1.9)] (Tax - Tan) + [0.042 aRl + 0.026 (Hs/D) asl] / (2.2 Hs/D + 1.9)
For default Hs/D = 0.5, when aR = as:
ATv = 0.7 (Tax — Tan) + 0.02 (X I
Fixed-Roof Tank - partially insulated (insulated shell, uninsulated roof):
When the shell is insulated, the temperature equations are independent of Hs/D.
ATv = 0.6 (Tax — Tan) + 0.02 CXr I (1"8)
Fixed-Roof Tank-fully insulated (insulated shell, insulated roof):
When the tank shell and roof are fully insulated, the temperatures of the vapor space and the liquid surface are taken as
equal to the temperature of the bulk liquid. When the bulk liquid is maintained at a constant temperature:
ATV = 0
Note, however, that when there are cycles to the temperature of the bulk liquid, these heating cycles will result in
corresponding cycles in the temperature of the vapor space.
(1-6)
(1-7)
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Temperature of the Bulk Liquid at Equilibrium. TB
Fixed-Roof Tanks and Internal Floating-Roof Tanks
TB = Taa + (cL D lH + KM)/(JM - cL 2D)
where:
lH = (0.5aRl + 0.309 asl Hs/D)/24
K = 0.0257asIHs
M = 2 Csv Hs/D + Crv + Cl
J — 2csl Hs + Cb D + Cl D
and thus:
Tb = Taa + {cL D [(0.5/24) aRl + (0.309/24) (Hs/D) asl] + [(0.0257 asIHs)(2 csv Hs/D + cL + cRV)]} /
Note: For IFRTs, use Ci rather than cL. where (1/cJ = (l/2cL + l/cF) and l/cF is the thermal resistance of the floating roof
Fixed-Roof Tank and Internal Floating-Roof Tank - uninsulated:
For tanks with a fixed roof, the heat gain to the bulk liquid from insolation is almost entirely through the tank shell, and
thus the relationship of liquid bulk temperature to ambient temperature is not sensitive to Hs/D.
Insulated Tanks:
When the tank is insulated, the liquid bulk temperature is likely not in equilibrium with ambient conditions.
In such cases, the actual temperature of the bulk liquid should be used.
External Floating-Roof Tanks
Tb = Taa + [0.785 f aRl + 0.485 (Hs/D) asl]/(12n cSL Hs/D + 6n cB + 6n cE)
Default values given at TB except for:
f = 0.9 EFRT (steel pontoon deck with single-deck center area)
f = 0.5 EFRT (steel double-deck)
cE = 1 EFRT (steel pontoon deck with single-deck center area, exposed to wind)
cE = 0.4 EFRT (steel double-deck, exposed to wind)
External Floating-Roof Tank - steel peripheral pontoon deck (single deck center area):
Tb - Taa + 0.003 CXs I
(1-31)
TB = Taa + [0.71 aRl + 0.485 (Hs/D) asl] / (170 Hs/D + 57)
For default Hs/D = 0.5, when aR = as:
(2-8)
Tb — Taa + 0.007 (X I
(2-9)
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
External Floating-Roof Tank - steel double deck:
Tb = Taa + [0.39 CXrI + 0.485 (Hs/D) asl] / (170 Hs/D + 45) (2-11)
For default Hs/D = 0.5, when aR = as:
Tb = Taa + 0.005 a I (2-12)
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Temperature of Fixed-Roof Tank Liquid Surface at Equilibrium. TL
Average Liquid Surface Temperature, Tla
Tla = (0.5 - cL /2M) Taa + (0.5 + cL /2M) Tb + lH /(2M)
where:
M = (2 Csv Hs/D + Crv + Cl)
lH = [(0.5otRl + 0.309 asl Hs/D)/24]
and thus:
Tla = {0.5-cl/[2(2 Csv Hs/D + Crv + Cl)]} Taa + {0.5 + cL/[2(2 Csv Hs/D + Crv + Cl)]}Tb +
[(0.5/24)
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Average Temperature of External Floating-Roof Tank Liquid Surface at Equilibrium. TLA
External Floating-Roof Tanks
Tla = [cf Taa + 2cl Tb + (f /24)cxrI] / (2cl + Cf)
Default values given at Tv and TBefr except for:
cF = 3 EFRT (steel pontoon deck with single-deck center area, exposed to wind)
cF = 0.6 EFRT (steel double-deck, exposed to wind)
Note: For floating roofs, the effective liquid surface conductance (i.e., between the bulk liquid and the vapor
space) is a function of the free liquid surface conductance cL and the floating roof deck conductance cF.
The effective liquid surface conductance cjor an IFRT or cEfor an EFRT relates to the free liquid surface
conductance cL and the floating roof deck conductance cF as follows:
1/c, = 1/(2cl) + 1/cf
1/ce = 1/(2cl) + 1/cf
The EFRT model forTLA is independent of Hs/D for a given value of TB, in that it is a function of Taa rather than Tv.
External Floating-Roof Tank - steel peripheral pontoon deck (single deck center area):
Tla = 0.7 Taa + 0.3 Tb + 0.008 aRl (2-7)
External Floating-Roof Tank - steel double deck:
Tla = 0.3 Taa + 0.7 Tb + 0.009 aRl (2-10)
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Documentation for Proposed Changes to AP-42 Chapter 7.1 - Organic Liquid Storage Tanks 2018
Average Temperature of Internal Floating-Roof Tank Liquid Surface at Equilibrium. TLA
Internal Floating-Roof Tanks
Tla = [cf Tv + 2cl Tb] / (2cl + Cf)
where:
Tv = [(2 Csv Hs/D + cRV) Taa + c, Tb + (0.5/24) aRl + (0.309/24) (Hs/D) asl] / [2 csv Hs/D + c, + cRV]
and thus:
Tla = ({cF [(2 csv Hs/D + cRV) TAA + c, TB + (0.5/24) aRl + (0.309/24) (Hs/D) as I] /
[2 Csv Hs/D + Ci + cRv]} + 2cl Tb) / (2cl + Cf)
Rearranging:
Tla = {cF (2 csv Hs/D + cRV) TAA + [(cF c,) + 2cL (2 csv Hs/D + c, + cRV)] TB + cF (0.5/24) aRl + cF (0.309/24) (Hs/D) asl}/
[2 Csv Hs/D + Ci + cRv) (2cl + Cf)]
Default values given at Tv and TBefr except for:
cF = 0.5 IFRT (aluminum skin-and-pontoon deck)
cF = 1.5 IFRT (steel pan deck)
cF = 1.3 Domed EFRT (steel pontoon deck with single-deck center area)
cF = 0.5 Domed EFRT (steel double-deck)
The actual conductance of a floating roof is generally not known. The default values given above for aluminum skin-and-
pontoon decks and steel double decks assume an uninterrupted vapor space between the top and bottom layers of
metal, but in reality there are bulkheads and other attachment points that act as thermal bridges between these metal
layers. The case of a steel pan is based on the entire deck being a single layer of steel, with no enclosed flotation
compartments. The case of a steel pontoon deck with a single-deck center area accounts for some of the deck having a
vapor space within enclosed compartments and some not, and thus represents an intermediate case. Therefore the steel
pontoon deck has been selected to represent IFRs in general.
Internal Floating-Roof Tank:
Tla = {[2.86 (Hs/D) + 1.43] Taa + [0.91 + 3.52 (Hs/D) + 2.88] TB + 0.027 aRl + 0.017 (Hs/D) asl} / [6.38 (Hs/D) + 5.22]
Tla = {[2.86 (Hs/D) + 1.43] Taa + [3.52 (Hs/D) + 3.79] T„ + 0.027 aRl + 0.017 (Hs/D) asl} / [6.38 (Hs/D) + 5.22]
(2-5)
For default Hs/D = 0.5, when aR = as:
Tla = 0.3 Taa + 0.7 Tb + 0.004 a I (2-6)
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