EN ISO 13704:2007

SLOVENSKI STANDARD
01-april-2009
3HWURNHPLþQDLQGXVWULMDWHULQGXVWULMD]DSUHGHODYRQDIWHLQ]HPHOMVNHJDSOLQD
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Petroleum, petrochemical and natural gas industries - Calculation of heater-tube
thickness in petroleum refineries (ISO 13704:2007)
Erdöl- und Erdgasindustrie - Berechnung der Wanddicke von Heizrohren in
Erdölraffinerien (ISO 13704:2007)
Industries du pétrole, de la pétrochimie et du gaz naturel - Calcul de l'épaisseur des
tubes de fours de raffineries de pétrole (ISO 13704:2007)
Ta slovenski standard je istoveten z: EN ISO 13704:2007
ICS:
75.180.20 Predelovalna oprema Processing equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 13704
NORME EUROPÉENNE
EUROPÄISCHE NORM
November 2007
ICS 75.180.20
English Version
Petroleum, petrochemical and natural gas industries -
Calculation of heater-tube thickness in petroleum refineries (ISO
13704:2007)
Industries du pétrole, de la pétrochimie et du gaz naturel - Erdöl- und Erdgasindustrie - Berechnung der Wanddicke
Calcul de l'épaisseur des tubes de fours de raffineries de von Heizrohren in Erdölraffinerien (ISO 13704:2007)
pétrole (ISO 13704:2007)
This European Standard was approved by CEN on 3 November 2007.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13704:2007: E
worldwide for CEN national Members.

Contents Page
Foreword.3

Foreword
This document (EN ISO 13704:2007) has been prepared by Technical Committee ISO/TC 67 "Materials,
equipment and offshore structures for petroleum and natural gas industries" in collaboration with Technical
Committee CEN/TC 12 “Materials, equipment and offshore structures for petroleum, petrochemical and
natural gas industries” the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by May 2008, and conflicting national standards shall be withdrawn at the
latest by May 2008.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 13704:2007 has been approved by CEN as a EN ISO 13704:2007 without any modification.

INTERNATIONAL ISO
STANDARD 13704
Second edition
2007-11-15
Petroleum, petrochemical and natural gas
industries — Calculation of heater-tube
thickness in petroleum refineries
Industries du pétrole, de la pétrochimie et du gaz naturel — Calcul de
l'épaisseur des tubes de fours de raffineries de pétrole

Reference number
ISO 13704:2007(E)
©
ISO 2007
ISO 13704:2007(E)
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©  ISO 2007
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ii © ISO 2007 – All rights reserved

ISO 13704:2007(E)
Contents Page
Foreword .iv
1 Scope.1
2 Terms and definitions .1
3 General design information.3
3.1 Information required .3
3.2 Limitations for design procedures .4
4 Design.4
4.1 General .4
4.2 Equation for stress.7
4.3 Elastic design (lower temperatures).7
4.4 Rupture design (higher temperatures) .8
4.5 Intermediate temperature range .8
4.6 Minimum allowable thickness.8
4.7 Minimum and average thicknesses.8
4.8 Equivalent tube metal temperature .9
4.9 Component fittings.13
5 Allowable stresses .15
5.1 General .15
5.2 Elastic allowable stress .16
5.3 Rupture allowable stress.16
5.4 Rupture exponent.16
5.5 Yield and tensile strengths.16
5.6 Larson-Miller parameter curves.16
5.7 Limiting design metal temperature.17
5.8 Allowable stress curves.17
6 Sample calculations.18
6.1 Elastic design .18
6.2 Thermal-stress check (for elastic range only).19
6.3 Rupture design with constant temperature.23
6.4 Rupture design with linearly changing temperature .25
Annex A (informative) Estimation of remaining tube life.28
Annex B (informative) Calculation of maximum radiant section tube skin temperature .33
Annex C (normative) Thermal-stress limitations (elastic range) .44
Annex D (informative) Calculation sheets.48
Annex E (normative) Stress curves (SI units).50
Annex F (normative) Stress curves (USC units).70
Annex G (normative) Derivation of corrosion fraction and temperature fraction.90
Annex H (informative) Data sources .98
Bibliography.103

ISO 13704:2007(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 13704 was prepared by Technical Committee ISO/TC 67, Materials, equipment and offshore structures
for petroleum, petrochemical and natural gas industries, Subcommittee SC 6, Processing equipment and
systems.
This second edition cancels and replaces the first edition (ISO 13704:2001), which has been technically
revised.
iv © ISO 2007 – All rights reserved

INTERNATIONAL STANDARD ISO 13704:2007(E)

Petroleum, petrochemical and natural gas industries —
Calculation of heater-tube thickness in petroleum refineries
1 Scope
This International Standard specifies the requirements and gives recommendations for the procedures and
design criteria used for calculating the required wall thickness of new tubes and associated component fittings
for petroleum-refinery heaters. These procedures are appropriate for designing tubes for service in both
corrosive and non-corrosive applications. These procedures have been developed specifically for the design
of refinery and related process-fired heater tubes (direct-fired, heat-absorbing tubes within enclosures). These
procedures are not intended to be used for the design of external piping.
This International Standard does not give recommendations for tube retirement thickness; Annex A describes
a technique for estimating the life remaining for a heater tube.
2 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2.1
actual inside diameter
D
i
inside diameter of a new tube
NOTE The actual inside diameter is used to calculate the tube skin temperature in Annex B and the thermal stress in
Annex C.
2.2
component fitting
fitting connected to the fired heater tubes
EXAMPLES Return bends, elbows, reducers.
NOTE 1 There is a distinction between standard component fittings and specially designed component fittings; see 4.9.
NOTE 2 Typical material specifications for standard component fittings are ASTM A 234, ASTM A 403 and
ASTM B 366.
2.3
corrosion allowance
δ
CA
additional material thickness added to allow for material loss during the design life of the component
2.4
design life
t
DL
operating time used as a basis for tube design
NOTE The design life is not necessarily the same as the retirement or replacement life.
ISO 13704:2007(E)
2.5
design metal temperature
T
d
tube-metal or skin temperature used for design
NOTE This is determined by calculating the maximum tube metal temperature (T in Annex B) or the equivalent
max
tube metal temperature (T in 2.8) and adding an appropriate temperature allowance (see 2.16). A procedure for
eq
calculating the maximum tube metal temperature from the heat-flux density is included in Annex B. When the equivalent
tube metal temperature is used, the maximum operating temperature can be greater than the design metal temperature.
When the equivalent tube metal temperature is used to determine the design metal temperature, this design metal
temperature is only applicable to the rupture design. It is necessary to develop a separate design metal temperature
applicable to the elastic design. The design metal temperature applicable to the elastic design is the maximum calculated
tube metal temperature among all operating cases plus the appropriate temperature allowance.
2.6
elastic allowable stress
σ
el
allowable stress for the elastic range
See 5.2.
2.7
elastic design pressure
p
el
maximum pressure that the heater coil can sustain for short periods of time
NOTE This pressure is usually related to relief-valve settings, pump shut-in pressures, etc.
2.8
equivalent tube metal temperature
T
eq
calculated constant metal temperature that in a specified period of time produces the same creep damage as
does a changing metal temperature
NOTE In 4.8 the equivalent tube metal temperature concept is described in more detail. It provides a procedure to
calculate the equivalent tube metal temperature based on a linear change of tube metal temperature from start-of-run to
end-of-run.
2.9
inside diameter
∗
D
i
inside diameter of a tube with the corrosion allowance removed; used in the design calculations
NOTE The inside diameter of an as-cast tube is the inside diameter of the tube with the porosity and corrosion
allowances removed.
2.10
minimum thickness
δ
min
minimum required thickness of a new tube, taking into account all appropriate allowances
NOTE See Equation (5).
2.11
outside diameter
D
o
outside diameter of a new tube
2 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
2.12
rupture allowable stress
σ
r
allowable stress for the creep-rupture range
See 4.4.
2.13
rupture design pressure
p
r
maximum operating pressure that the coil section can sustain during normal operation
2.14
rupture exponent
n
parameter used for design in the creep-rupture range
NOTE See figures in Annexes E and F.
2.15
stress thickness
δ
σ
thickness, excluding all thickness allowances, calculated from an equation that uses an allowable stress
2.16
temperature allowance
T
A
part of the design metal temperature that is included for process- or flue-gas mal-distribution, operating
unknowns, and design inaccuracies
NOTE The temperature allowance is added to the calculated maximum tube metal temperature or to the equivalent
tube metal temperature to obtain the design metal temperature (see 2.5).
3 General design information
3.1 Information required
The design parameters (design pressures, design fluid temperature, corrosion allowance and tube material)
shall be defined. In addition, the following information shall be furnished:
a) design life of the heater tube;
b) whether the equivalent-temperature concept is to be applied and, if so, the operating conditions at the
start and at the end of the run;
c) temperature allowance (see ISO 13705), if any;
d) corrosion fraction (if different from that shown in Figure 1);
e) whether elastic-range thermal-stress limits are to be applied.
If any of items a) to e) are not furnished, use the following applicable parameters:
⎯ design life equal to 100 000 h;
⎯ design metal temperature based on the maximum metal temperature (the equivalent-temperature concept
shall not apply);
ISO 13704:2007(E)
⎯ temperature allowance equal to 15 °C (25 °F);
⎯ corrosion fraction given in Figure 1;
⎯ elastic-range thermal-stress limits.
3.2 Limitations for design procedures
3.2.1 The allowable stresses are based on a consideration of yield strength and rupture strength only;
plastic or creep strain has not been considered. Using these allowable stresses can result in small permanent
strains in some applications; however, these small strains do not affect the safety or operability of heater
tubes.
3.2.2 No considerations are included for adverse environmental effects, such as graphitization,
carburization or hydrogen attack. Limitations imposed by hydrogen attack can be developed from the Nelson
[1]
curves in API 941 .
3.2.3 These design procedures have been developed for seamless tubes. They are not applicable to tubes
that have a longitudinal weld. ISO 13705 allows only seamless tubes.
3.2.4 These design procedures have been developed for thin tubes (tubes with a thickness-to-outside-
diameter ratio, δ /D , of less than 0,15). Additional considerations can apply to the design of thicker tubes.
min o
3.2.5 No considerations are included for the effects of cyclic pressure or cyclic thermal loading.
3.2.6 Limits for thermal stresses are provided in Annex C. Limits for stresses developed by mass, supports,
end connections and so forth are not discussed in this International Standard.
3.2.7 Most of the Larson-Miller parameter referenced curves in 5.6 are not Larson-Miller curves in the
traditional sense but are derived from the 100 000 h rupture strength as explained in Clause H.3.
Consequently, the curves might not provide a reliable estimate of the rupture strength for a design life that is
less than 20 000 h or more than 200 000 h.
3.2.8 The procedures in this International Standard have been developed for systems in which the heater
tubes are subject to an internal pressure that exceeds the external pressure. There are some cases in which a
heater tube can be subject to a greater external pressure than the internal pressure. This can occur, for
example, in vacuum heaters or on other types of heaters during shutdown or trip conditions, especially when a
unit is cooling or draining, forming a vacuum inside the heater tubes. Conditions where external pressures
exceed the internal pressures can govern heater-tube wall thickness. Determination of this (i.e. vacuum
design) is not covered in this International Standard. In the absence of any local or national codes that can
apply, it is recommended that a pressure vessel code, such as ASME VIII (Division 1, UG-28) or EN 13445,
be used, as such codes also address external pressure designs.
4 Design
4.1 General
There is a fundamental difference between the behaviour of carbon steel in a hot-oil heater tube operating at
300 °C (575 °F) and that of chromium-molybdenum steel in a catalytic-reformer heater tube operating at
600 °C (1 110 °F). The steel operating at the higher temperature creeps, or deforms permanently, even at
stress levels well below the yield strength. If the tube metal temperature is high enough for the effects of creep
to be significant, the tube eventually fails due to creep rupture, although no corrosion or oxidation mechanism
is active. For the steel operating at the lower temperature, the effects of creep are non-existent or negligible.
Experience indicates that, in this case, the tube lasts indefinitely, unless a corrosion or an oxidation
mechanism is active.
4 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
Since there is a fundamental difference between the behaviour of the materials at these two temperatures,
there are two different design considerations for heater tubes: elastic design and creep-rupture design. Elastic
design is design in the elastic range, at lower temperatures, in which allowable stresses are based on the
yield strength (see 4.3). Creep-rupture design (which is referred to below as rupture design) is the design for
the creep-rupture range, at higher temperatures, in which allowable stresses are based on the rupture
strength (see 4.4).
The temperature that separates the elastic and creep-rupture ranges of a heater tube is not a single value; it is
a range of temperatures that depends on the alloy. For carbon steel, the lower end of this temperature range
is about 425 °C (800 °F); for type 347 stainless steel, the lower end of this temperature range is about 590 °C
(1 100 °F). The considerations that govern the design range also include the elastic design pressure, the
rupture design pressure, the design life and the corrosion allowance.
The rupture design pressure is never more than the elastic design pressure. The characteristic that
differentiates these two pressures is the relative length of time over which they are sustained. The rupture
design pressure is a long-term loading condition that remains relatively uniform over a period of years. The
elastic design pressure is usually a short-term loading condition that typically lasts only hours or days. The
rupture design pressure is used in the rupture design equation, since creep damage accumulates as a result
of the action of the operating, or long-term, stress. The elastic design pressure is used in the elastic design
equation to prevent excessive stresses in the tube during periods of operation at the maximum pressure.
The tube shall be designed to withstand the rupture design pressure for long periods of operation. If the
normal operating pressure increases during an operating run, the highest pressure shall be taken as the
rupture design pressure.
In the temperature range near or above the point where the elastic and rupture allowable stress curves cross,
both elastic and rupture design equations are to be used. The larger value of δ should govern the design
min
(see 4.5). A sample calculation that uses these methods is included in Clause 6. Calculation sheets (see
Annex D) are available for summarizing the calculations of minimum thickness and equivalent tube metal
temperature.
The allowable minimum thickness of a new tube is given in Table 1.
All of the design equations described in Clause 4 are summarized in Table 2.
ISO 13704:2007(E)
Key
pD
ro
δ =
σ
2σ + p
rr
δ is the corrosion allowance
CA
D is the outside diameter
o
σ is the rupture allowable stress
r
p is the rupture design pressure
r
B = δ /δ
CA σ
a
Note change of scale at X = 1.
Figure 1 — Corrosion fraction
6 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
4.2 Equation for stress
In both the elastic range and the creep-rupture range, the design equation is based on the mean-diameter
equation for stress in a tube. In the elastic range, the elastic design pressure, p , and the elastic allowable
el
stress, σ , are used. In the creep-rupture range, the rupture design pressure, p , and the rupture allowable
el r
stress ,σ , are used.
r
The mean-diameter equation gives a good estimate of the pressure that produces yielding through the entire
tube wall in thin tubes (see 3.2.4 for a definition of thin tubes). The mean-diameter equation also provides a
good correlation between the creep rupture of a pressurized tube and a uniaxial test specimen. It is, therefore,
[16], [17], [18], [19]
a good equation to use in both the elastic range and the creep-rupture range . The mean-
diameter equation for stress is as given in Equation (1):
ppʈD ʈD
o i
s = -=11+ (1)
Á˜ Á˜
˯ ˯
22dd
where
1)
σ is the stress, expressed in megapascals [pounds per square inch ];
p is the pressure, expressed in megapascals (pounds per square inch);
D is the outside diameter, expressed in millimetres (inches);
o
D is the inside diameter, expressed in millimetres (inches), including the corrosion allowance;
i
δ is the thickness, expressed in millimetres (inches).
The equations for the stress thickness, δ , in 4.3 and 4.4 are derived from Equation (1).
σ
4.3 Elastic design (lower temperatures)
The elastic design is based on preventing failure by bursting when the pressure is at its maximum (that is,
when a pressure excursion has reached p near the end of the design life after the corrosion allowance has
el
been used up. With the elastic design, δ and δ (see 4.6) are calculated as given in Equations (2) and (3):
σ min
∗
pD p D
el o el i
δ= orδ= (2)
σ σ
22σσ+−pp
el el el el
δ = δ + δ (3)
min σ CA
where
*
D is the inside diameter, expressed in millimetres (inches), with corrosion allowance removed;
i
σ is the elastic allowable stress, expressed in megapascals (pounds per square inch), at the design
el
metal temperature.
1) The unit “pounds per square inch (psi)” is referred to as “pound-force per square inch (lbf/in )” in ISO/IEC 80000.
ISO 13704:2007(E)
4.4 Rupture design (higher temperatures)
The rupture design is based on preventing failure by creep rupture during the design life. With the rupture
design, δ and δ (see 4.6) are calculated from Equations (4) and (5):
σ min
∗
pD pD
ro ri
δ= orδ= (4)
σ σ
22σσ+−pp
rr r r
δ = δ + f δ (5)
min σ corr CA
where
σ is the rupture allowable stress, expressed in megapascals (pounds per square inch), at the design
r
metal temperature and the design life;
f is the corrosion fraction, given as a function of B and n in Figure 1;
corr
B = δ /δ
CA σ
n is the rupture exponent at the design metal temperature (shown in the figures given in Annexes E
and F).
The derivation of the corrosion fraction is described in Annex G. It is recognized in this derivation that stress is
reduced by the corrosion allowance; correspondingly, the rupture life is increased.
Equations (4) and (5) are suitable for heater tubes; however, if special circumstances require that the user
choose a more conservative design, a corrosion fraction of unity (f = 1) may be specified.
corr
4.5 Intermediate temperature range
At temperatures near or above the point where the curves of σ and σ intersect in the figures given in
el r
Annexes E and F, either elastic or rupture considerations govern the design. In this temperature range, it is
necessary to apply both the elastic and the rupture designs. The larger value of δ shall govern the design.
min
4.6 Minimum allowable thickness
The minimum thickness, δ , of a new tube (including the corrosion allowance) shall not be less than that
min
shown in Table 1. For ferritic steels, the values shown are the minimum allowable thicknesses of schedule 40
average wall pipe. For austenitic steels, the values are the minimum allowable thicknesses of schedule 10S
average wall pipe. (Table 5 shows which alloys are ferritic and which are austenitic.) The minimum allowable
thicknesses are 0,875 times the average thicknesses. These minima are based on industry practice. The
minimum allowable thickness is not the retirement or replacement thickness of a used tube.
4.7 Minimum and average thicknesses
The minimum thickness, δ , is calculated as described in 4.3 and 4.4. Tubes that are purchased to this
min
minimum thickness have a greater average thickness. A thickness tolerance is specified in each ASTM
specification. For most of the ASTM specifications shown in the figures given in Annexes E and F, the
0 0
tolerance on the minimum thickness is % for hot-finished tubes and % for cold-drawn tubes. This
( ) ( )
+28 +22
is equivalent to tolerances on the average thickness of ± 12,3 % and ± 9,9 %, respectively. The remaining
ASTM specifications require that the minimum thickness be greater than 0,875 times the average thickness,
which is equivalent to a tolerance on the average thickness of + 12,5 %.
8 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
With a % tolerance, a tube that is purchased to a 12,7 mm (0,500 in) minimum-thickness specification
(+28)
has the following average thickness:
(12,7)(1 + 0,28/2) = 14,5 mm (0,570 in)
To obtain a minimum thickness of 12,7 mm (0,500 in) in a tube purchased to a ± 12,5 % tolerance on the
average thickness, the average thickness shall be specified as follows:
(12,7)/(0,875) = 14,5 mm (0,571 in)
All thickness specifications shall indicate whether the specified value is a minimum or an average thickness.
The tolerance used to relate the minimum and average wall thicknesses shall be the tolerance given in the
ASTM specification to which the tubes are purchased.
Table 1 — Minimum allowable thickness of new tubes
Minimum thickness
Tube outside diameter
Ferritic steel tubes Austenitic steel tubes
mm (in) mm (in) mm (in)
60,3 (2,375) 3,4 (0,135) 2,4 (0,095)
73,0 (2,875) 4,5 (0,178) 2,7 (0,105)
88,9 (3,50) 4,8 (0,189) 2,7 (0,105)
101,6 (4,00) 5,0 (0,198) 2,7 (0,105)
114,3 (4,50) 5,3 (0,207) 2,7 (0,105)
141,3 (5,563) 5,7 (0,226) 3,0 (0,117)
168,3 (6,625) 6,2 (0,245) 3,0 (0,117)
219,1 (8,625) 7,2 (0,282) 3,3 (0,130)
273,1 (10,75) 8,1 (0,319) 3,7 (0,144)

4.8 Equivalent tube metal temperature
In the creep-rupture range, the accumulation of damage is a function of the actual operating tube metal
temperatures (TMTs). For applications in which there are significant differences between start-of-run and
end-of-run TMTs, a design based on the maximum temperature can be excessive, since the actual operating
TMT is usually less than the maximum.
For a linear change in metal temperature from start of run, T , to end of run, T , an equivalent tube metal
sor eor
temperature, T , can be calculated as shown in Equation (6). A tube operating at the equivalent tube metal
eq
temperature sustains the same creep damage as one that operates from the start-of-run to end-of-run
temperatures.
T = T + f (T − T ) (6)
T
eq sor eor sor
where
T is the equivalent tube metal temperature, expressed in degrees Celsius (Fahrenheit);
eq
T is the tube metal temperature, expressed in degrees Celsius (Fahrenheit), at start of run;
sor
ISO 13704:2007(E)
T is the tube metal temperature, expressed in degrees Celsius (Fahrenheit), at end of run;
eor
f is the temperature fraction given in Figure 2.
T
The derivation of the temperature fraction is described in Annex G. The temperature fraction is a function of
two parameters, V and N, as given in Equations (7) and (8):
*
ʈ
DTAʈ
Vn= ln
0Á˜
Á˜
*
˯s
˯T 0
sor
(7)
ʈ
Dd
Nn=
Á˜
d
˯
(8)
where
n is the rupture exponent at T ;
0 sor
∗
2)
∆T is the temperature change, equal to T − T , expressed in kelvin [degrees Rankine ], during
eor sor
the operating period;
∗
T = T + 273 K (T + 460 °R);
sor
sor sor
ln is the natural logarithm;
∆δ is the change in thickness, equal to φ t , expressed in millimetres (inches), during the
corr op
operating period;
φ is the corrosion rate, expressed in millimetres per year (in inches per year);
corr
t is the duration of operating period, expressed in years;
op
δ is the initial thickness, expressed in millimetres (inches), at the start of the run;
σ is the initial stress, expressed in megapascals (pounds per square inch), at the start of the run,
using Equation (1);
A is the material constant, expressed in megapascals (pounds per square inch).
The constant A is given in Table 3. The significance of the material constant is explained in Clause G.5.

2) Rankine is a deprecated unit.
10 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
Figure 2 — Temperature fraction
ISO 13704:2007(E)
Table 2 — Summary of working equations
Elastic design (lower temperatures):
∗
pD pD
el o el i
δ= orδ= (2)
σ σ
22σσ+−pp
el el el el
δ = δ + δ (3)
min σ CA
Rupture design (higher temperatures):
∗
pD pD
r o ri
δ= orδ= (4)
σ σ
22σ+ppσ−
rr r r
δ = δ + f δ (5)
min σ corr CA
where
δ is the stress thickness, expressed in millimetres (inches);
σ
p is the elastic design gauge pressure, expressed in megapascals (pounds per square inch);
el
p is the rupture design gauge pressure, expressed in megapascals (pounds per square inch);
r
D is the outside diameter, expressed in millimetres (inches);
o
*
D is the inside diameter, expressed in millimetres (inches), with the corrosion allowance removed;
i
σ is the elastic allowable stress, expressed in megapascals (pounds per square inch), at the design
el
metal temperature;
σ is the rupture allowable stress, expressed in megapascals (pounds per square inch), at the design
r
metal temperature and design life;
δ is the minimum thickness, expressed in millimetres (inches), including corrosion allowance;
min
δ is the corrosion allowance, expressed in millimetres (inches);
CA
f is the corrosion fraction, given in Figure 1 as a function of B and n, where B = δ δ ;
CA σ
corr
n is the rupture exponent at the design metal temperature.
Equivalent tube metal temperature:
TT=+f(T −T) (6)
eq sor T eor sor
where
∗
∆ T (= T − T ) is the temperature change, expressed in kelvin (degrees Rankine), during the
eor sor
operating period;
T is the tube metal temperature, expressed in degrees Celsius (Fahrenheit), at the start of the run;
sor
T is the tube metal temperature, expressed in degrees Celsius (Fahrenheit), at the end of the run;
eor
∗
T = T + 273 K (T + 460 °R);
sor
sor sor
A is the material constant, expressed in megapascals (pounds per square inch) from Table 3;
σ is the initial stress, expressed in megapascals (pounds per square inch), at the start of the run
using Equation (1);
∆δ (= φ t ) is the change in thickness, expressed in millimetres (inches), during the operating
corr op
period;
δ is the initial thickness, expressed in millimetres (inches), at the start of the run;
φ is the corrosion rate, expressed in millimetres per year (inches per year);
corr
t is the duration, expressed in years, of the operating period.
op
12 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
Table 3 — Material constant for temperature fraction
Constant
A
Material Type or grade
MPa (psi)
5 8
Low-carbon steel —
7,46 × 10 (1,08 × 10 )
5 7
Medium-carbon steel B
2,88 × 10 (4,17 × 10 )
7 9
C-½Mo steel T1 or P1
2,01 × 10 (2,91 × 10 )
7 9
1-¼Cr-½Mo steel T11 or P11
5,17 × 10 (7,49 × 10 )
5 8
2-¼Cr-1Mo steel T22 or P22
8,64 × 10 (1,25 × 10 )
6 8
3Cr-1Mo steel T21 or P21
2,12 × 10 (3,07 × 10 )
5 7
5Cr-½Mo steel T5 or P5
5,49 × 10 (7,97 × 10 )
5 7
5Cr-½Mo-Si steel T5b or P5b
2,88 × 10 (4,18 × 10 )
5 7
7Cr-½Mo steel T7 or P7
1,64 × 10 (2,37 × 10 )
6 9
9Cr-1Mo steel T9 or P9
7,54 × 10 (1,09 × 10 )
6 8
9Cr-1Mo V steel T91 or P91
2,23 × 10 (3,24 × 10 )
6 8
18Cr-8Ni steel 304 or 304H
1,55 × 10 (2,25 × 10 )
6 8
16Cr-12Ni-2Mo steel 316 or 316H
1,24 × 10 (1,79 × 10 )
6 8
16Cr-12Ni-2Mo steel 316L
1,37 × 10 (1,99 × 10 )
6 8
18Cr-10Ni-Ti steel 321
1,32 × 10 (1,92 × 10 )
5 7
18Cr-10Ni-Ti steel 321H
2,76 × 10 (4,00 × 10 )
a 6 8
347 or 347H
18Cr-10Ni-Nb steel 1,23 × 10 (1,79 × 10 )
5 7
Ni-Fe-Cr Alloy 800H / 800HT
1,03 × 10 (1,50 × 10 )
5 7
25Cr-20Ni HK40
2,50 × 10 (3,63 × 10 )
a
Formerly called columbium, Cb.

The temperature fraction and the equivalent temperature shall be calculated for the first operating cycle. In
applications that involve very high corrosion rates, the temperature fraction for the last cycle is greater than
that for the first. In such cases, the calculation of the temperature fraction and the equivalent temperature
should be based on the last cycle.
If the temperature change from start-of-run to end-of-run is other than linear, a judgment shall be made
regarding the use of the value of f given in Figure 2.
T
Note that the calculated thickness of a tube is a function of the equivalent temperature, which, in turn, is a
function of the thickness (through the initial stress). A few iterations can be necessary to arrive at the design.
(See the sample calculation in 6.4.)
4.9 Component fittings
Component fittings manufactured in accordance with ASME B16.9 are considered suitable for use at the
pressure-temperature ratings specified therein. Other component fittings shall be specially designed in
accordance with this subclause.
ISO 13704:2007(E)
r = outer radius
o
r = inner radius
i
For other symbols, see text below Equation (9).
Figure 3 — Return bend and elbow geometry
The stress variations in a return bend or elbow (see Figure 3) are far more complex than in a straight tube.
The hoop stresses at the inner radius of a return bend are higher than in a straight tube of the same thickness.
It might be necessary for the minimum thickness at the inner radius to be greater than the minimum thickness
of the attached tube.
Because fabrication processes for forged return bends generally result in greater thickness at the inner radius,
the higher stresses at the inner radius can be sustained without failure in most situations.
The hoop stress σ , expressed in megapascals (pounds per square inch), along the inner radius of the bend is
i
given by Equation (9):
2rr−
cl m
σ = σ (9)
i
2rr−
()
cl m
where
r is the centre line radius of the bend, expressed in millimetres (inches);
cl
r is the mean radius of the tube, expressed in millimetres (inches);
m
σ is the stress, expressed in megapascals (pounds per square inch), given by Equation (1).
The hoop stress σ , expressed in megapascals (pounds per square inch), along the outer radius is given by
o
Equation (10):
2rr+
cl m
ss= (10)
o
2(rr+ )
cl m
Using the approximation that r is almost equal to D /2, Equation (9) can be solved for the stress thickness at
m o
the inner radius. For design, the stress thickness is given by Equation (11).
14 © ISO 2007 – All rights reserved

ISO 13704:2007(E)
Dp
o
δ = (11)
σi
2Npσ +
i
where
δ is the stress thickness, expressed in millimetres (inches), at the inner radius;
σi
r
cl
42−
D
o
N = (12)
i
r
cl
41−
D
o
σ is the allowable stress, expressed in megapascals (pounds per square inch) at the design metal
temperature.
NOTE 1 p represents both elastic design pressure and rupture design pressure.
The return bend thickness evaluations shall be made using both elastic design pressure and rupture design
pressure, and the governing thicknesses shall be the larger values at the inner and outer radii.
Using the approximation given above, Equation (10) can be solved for the stress thickness at the outer radius.
For elastic design, the stress thickness is as given in Equation (13):
Dp
o
δ = (13)
σo
2Npσ +
o
where
δ is the stress thickness, expressed in millimetres (inches), at the outer radius;
σo
r
cl
42+
D
o
N = (14)
o
r
cl
41+
D
o
σ is the allowable stress, expressed in megapascals (pounds per square inch), at the design metal
temperature.
NOTE 2 p represents both elastic design pressure and rupture design pressure.
The return bend thickness evaluations shall be made using both elastic design pressure and rupture design
pressure, and the governing thicknesses shall be the larger values at the inner and outer radii.
The minimum thickness, δ , at the inside radius and the minimum thickness, δ , at the outside radius shall
σi σo
be calculated using Equations (11) and (13). The corrosion allowance, δ , shall be added to the minimum
CA
calculated thickness.
The minimum thickness along the neutral axis of the bend shall be the same as for a straight tube.
5 Allowable stresses
5.1 General
The allowable stresses for various heater-tube alloys are plotted against design metal temperature in
Figures E.1 to E.19 (
...