Cryogenic Air Separation:

Material Selection, Pressure Relief Device Design, and Safety Considerations

For the Linde Double Distillation Column

Aaron Farnsworth

ECH 4615 - Product and Process Design

Spring 2016

Final Design Report

Table of Contents

Introduction………………………………………..………………………………………………1

Linde Double Column……………………………………………………………………………..2

Operating Conditions and Equipment Size………………………………………………………..3

Operating Risks……………………………………………………………………………………3

Minimum Design Metal Temperature…………………………………………………………….5

Material Selection…………………………………………………………………………………8

Configuration of Relief Devices…………………………………………………………………12

Calculactions……………………………………………………………………………………..13

Conclusions………………………………………………………………………………………21

References………………………………………………………………..………………………22

List of Tables

Table #1……………………………………………………………..…………………………….3

Table #2……………………………………………………………..…………………………….4

Table #3……………………………………………………………..……………………….……8

Table #4……………………………………………………………..………………...…………12

Table #5……………………………………………………………..……………………...……21

Table #6……………………………………………………………..………………………...…21

List of Figures

Figure #1…………………………………………………………………………..………………2

Figure #2…………………………………………………………………………..………………6

Figure #3……………………………………………………………..……………………………7

Figure #4……………………………………………………………..……………………………9

Figure #5……………………………………………………………..………………..…………10

Aaron Farnsworth

ECH 4615

1

Introduction

The design of a pressure relief device (PRD) depends on many details of the process,

including operating pressure and temperature, material properties, and design specifications such

as the design pressure, the required relieving flowrate, and a safety factor. The objective of this

study is to analyze the safety of the Linde double column in an air separation process by making

engineering assumptions, design decisions, and calculations that lead to the material selection

and the configuration and size of the PRD’s necessary to ensure safe working conditions for air

separation.

The hazards of this process pertain to pressurized vessels and the extremely low

temperatures required for cryogenic air. Pressure relief is particularly important for cryogenic

conditions because of the volatility of liquid air components. If control of the temperature in the

process fails, the PRD must be able to handle the overpressure induced by rapid expansion of

cryogenic nitrogen and oxygen into gaseous phase under ambient conditions. The PRD should

also be able to manage small overpressures of the system in order to keep the process at design

conditions, helping to maintain good distillation and prevent equipment damage. The focus for

mitigating overpressure hazards is on proper design of a safety pressure relief valve and a rupture

disc in parallel for each unit of the Linde double column.

Many aspects of a safe design are governed by the cold temperature, which reaches as

low as 78 Kelvin at the entrance of the upper column. It is important to consider the minimum

design metal temperature (MDMT) in material selection and sizing, which in turn affects the

maximum allowable working pressure (MAWP) of the vessel, which is an important

specification for sizing relief devices. Most of the relevant material properties are strong

functions of temperature, as are the pressures exerted by the volatile liquids and gases that

comprise the process air components. Other safety concerns are equipment failure due to

embrittlement, corrosion, or fatigue, asphyxiation due to nitrogen exposure, and combustion due

to oxygen exposure.

These design choices and calculations must also conform to the American Society of

Mechanical Engineers (ASME) pressure vessel codes, or those of the local equivalent institution.

The ASME guidelines, however, often leave room for interpretation and application, so safety is

a critical facet of design at every stage for the chemical engineer, and is ultimately the

responsibility of the engineer.

Aaron Farnsworth

ECH 4615

2

This study is an overview of the safety considerations for a pressurized vessel at

extremely cold temperatures, specifically for the Linde double column, and the analysis below of

safety issues and pressure relief design can be applied to the upstream and downstream

components of the air separation plant, namely other distillation columns, compressors, piping,

and storage facilities.

Linde Double Column

The system in question constitutes two distillation columns, an upper column stacked on

a lower column, where the condenser of the lower column is the reboiler of the upper column, so

that a heat exchanger connects the two systems. The nitrogen distillate from the lower column

enters the heat exchanger contained in the upper column and is condensed by the liquid oxygen

bottoms of the upper column. Although heat is exchanged between the columns, they are

separate units that operate under different pressures, so pressure relief must be handled

individually for the two columns. Figure #1 depicts a simplified single column process (left), the

Linde double column schematic (middle), and the separation of the two columns at different

pressures, connected by a condenser-reboiler heat exchanger (right).

Figure #1 – Representative Schematics of Air Separation Columns [1]

Aaron Farnsworth

ECH 4615

3

Operating Conditions and Equipment Size

This study is based on a design by CryoColumn, a fictitious engineering company that

sized the equipment for an air separation plant. The Linde double column equipment sizes from

that project are listed below, along with the operating conditions at steady-state. T-101 represents

the lower column and T-102 represents the upper column.

Table #1 – Operating Conditions and Column Sizes

T-101 T-102

Temperature, K 99 78

Pressure, atm 5 1

Diameter, m 3.50 10.82

Height, m 9.75 17.07

Operating Risks

As Table #1 indicates, the lower column is pressurized to 5 atmospheres and the

operating temperatures are low enough to liquefy various components of air. Any pressurized

vessel is required by the ASME to maintain a PRD of some kind to prevent overpressure and

explosion, but the presence of liquid nitrogen and oxygen make this issue particularly significant.

Any loss of temperature control, such as a crack in the vessel due to embrittlement or a failure in

the automatic control system, could create rapid vaporization. Another possible cause of rapid

overpressure which demands preparation in any system is the risk of external fire [2]. Because of

these risks, a multiple device pressure relief system should be employed.

In assessing operational hazards and inefficiencies, an important engineering tool is the

Hazard and Operability (HAZOP) study, wherein weaknesses are systematically identified and

addressed in order target problems before they occur. Using the Linde upper column as an

example node of a HAZOP study in Table #2, the cause and effects of overpressure can be

identified and safe design can be modeled based on the results:

Aaron Farnsworth

ECH 4615

4

Table #2 – HAZOP Selection

DEVIATION CAUSES CONSEQUENCES EXISTING

PROVISIONS

RECOMMENDATIONS

High + Pressure Loss of

temperature

control

1.Increased air pressure

causes flooding, affecting

distillation

2. Total vaporization causes

overpressure in lower column

because of loss of shell-side

liquid in heat exchanger

1. Automatic

control scheme on

Joule-Thomson

valve between

columns for

temperature control

Design pressure relief

devices on upper and lower

Linde columns to control

overpressure events

It is important to manage overpressurization because of its deleterious effect in the

distillation process, but the more serious risks are explosion, asphyxiation, and combustion. In

any kind of enclosed or immediate environment, the vaporization of purified components of

liquid air is dangerous. Nitrogen, for example, although comprising about 79% of breathable air

and perfectly safe in that context, is a serious asphyxiation hazard when it displaces oxygen. This

must be considered for any pressure relief event and for routine maintenance safety.

Vaporization of nitrogen can be an insidious risk because of its inert nature and its

colorless and odorless properties. One liter of liquid nitrogen can displace 695 liters of air when

warmed to room temperature [3]. The Occupation Safety and Health Administration (OSHA)

defines oxygen deficiency as an O2 content below 19.5% by volume, and although a person can

survive a few minutes without breathing, only two breaths of oxygen deficient air could be fatal

[4]. This hazard presents itself if there is a gaseous leak from the distillate, if vaporization of

liquid N2 leads to overpressurization, if a relief outlet is placed near a working area, or simply

during routine maintenance.

Vaporization of oxygen is also a risk due to increased combustibility in an oxygen rich

environment. Even substances that are not normally combustible can become hazardous in the

presence of purified O2 as is attained during distillation in the Linde column [5]. Special

attention must be paid to the material selection of the column, the piping, the PRD’s, and any

other equipment in contact with an O2 rich process fluid. Aluminum, for example, although

affordable and suitable for cryogenic temperatures, reacts easily with oxygen and releases a

Aaron Farnsworth

ECH 4615

5

dangerous amount of energy during combustion. The lubricants used in manufacturing the

process equipment also must be carefully removed because of this risk [5].

The cryogenic temperature is significant regarding design materials and equipment

construction. The salient safety factor here is embrittlement. Although metals tend to gain tensile

strength as temperature decreases, they also lose ductility and toughness, and at low enough

temperatures embrittlement becomes a possibility, where brittle fracture can cause catastrophic

failure [6]. For this reason, the MDMT is critical in selecting and sizing the equipment.

Corrosion and fatigue are safety concerns over time, which demand regular inspections of

the equipment and reevaluating ratings, such as the MAWP, as the material degrades. No vessel

will maintain a constant pressure rating because of these issues, so maintenance, cleaning, and

replacement should be a part of regular upkeep throughout the lifespan of the vessel itself and its

PRD’s.

Cleaning the system is also important in preventing combustion. Although the process is

air is treated before entering the Linde column, some contaminants can cause a combustion risk

in the O2 rich environment even in the parts-per-million range as they build up over time. This

danger has to be continually addressed in order to prevent a potential disaster. The necessity of

maintenance also underscores the subtle risk of asphyxiation due to N2 inhalation in working

areas as various sections may be exposed.

HAZOP studies, material selection, PRD’s, and good maintenance are key in protecting

from overpressurization of the Linde double column and for mitigating asphyxiation and fire

hazards. The material used should conform to the peculiar risks of air separation, even at extra

cost, and the relief system should by designed to account for vaporization possibilities and

should not vent into the immediate environment but higher into the atmosphere, where the

individual components of vaporized air pose no human or environmental risk.

Minimum Design Metal Temperature (MDMT)

MDMT is a property of metals, mostly dependent on crystalline structure, and is affected

by annealing and wall thickness for a given material. This design temperature exists to prevent

metals that are prone to brittle failure at low temperatures from being misused. In a cryogenic air

process, the temperature can reach as low as 78 K, or about -195° C (-319° F). This means that

the material selection and wall thickness of the column must have an MDMT equal to this value.

Aaron Farnsworth

ECH 4615

6

Brittle fracture occurs by rapid crack propagation in the crystalline structure, as opposed

to ductile fracture which occurs by dislocation motion [7]. If the stress necessary to cause

dislocation motion is increased, as generally occurs by lowering temperature, then failure will

involve crack propagation instead. Most metals have a ductile to brittle transition temperature

range below which crack propagation is a serious risk [6]. Brittle failure is sudden and

catastrophic, which makes it less predictable and more dangerous than ductile fracture, so the

MDMT accounts for this property in order to avoid catastrophic failure.

MDMT has the opposite relation to wall thickness as MAWP. Generally, increased wall

thickness is associated with strength and stability, as is the case with the maximum allowable

pressure, but increased wall thickness also raises the MDMT. Smaller thickness allows for more

plastic deformation before fracture, and with increased thickness comes rigidity, which prevents

plastic deformation and can lead to brittle instead of ductile fracture [8]. Also, a thick shell will

have a greater temperature difference between the outer and inner walls, which makes crack

propagation more likely. Therefore, if process temperatures are below the ductile to brittle

transition range, the equipment walls need to be thick enough to withstand pressure and thin

enough to lower the MDMT.

The crystalline structure of a metal is a crucial factor in predicting whether dislocation

motion or crack propagation will occur. Iron, for example, normally exhibits a body-centered

cubic structure (BCC) known as α-ferrite, but at 912° C it transitions to a face-centered cubic

structure (FCC) known as γ-austenite [9]. Because the FCC structure has more closely packed

atomic planes than BCC, it more readily allows dislocation motion and so becomes more ductile.

Figure #2 depicts the more closely packed planes of the γ-austenite FCC crystalline structure.

Figure #2 – BCC versus FCC Crystal Structures

Aaron Farnsworth

ECH 4615

7

Annealing can also increase ductility and lower the MDMT by redistributing dislocations

and lowering the required stress for deformation. The ASME has guidelines regarding the use of

various metals at low temperatures based on their properties and heat treatment, and impact

testing by the Charpy method at the operating temperature is usually required.

Material Selection

The proper material for processing cryogenic air must remain ductile at extremely low

temperatures to prevent embrittlement, which implies an MDMT at the lowest process

temperature of 78 K, and must have the strength and toughness to withstand the highest system

pressure of 5 atm at these conditions.

Because brittle fracture is the primary risk associated with extremely low temperatures,

the metal selection centers around the MDMT. As discussed above, FCC crystalline structures

have more closely packed planes than BCC structures, and closely packed planes in a cubic

structure allow for easier dislocation motion due to stress. Since dislocation motion is the

mechanism that allows ductility, FCC metals have a much lower MDMT and sometimes do not

even exhibit the ductile to brittle transition phase.

Figure #3 – Ductile to Brittle Transition Trends [10]

Aaron Farnsworth

ECH 4615

8

The graphs from Dutta’s report (Figure #3) provide context for choosing a material by its

crystalline structure and choosing a steel by its nickel content. The right hand graph shows that

FCC structured alloys have increased fracture toughness with decreasing temperature, while

BCC and HCP (hexagonal close-packed) structures lose toughness. In particular, BCC clearly

exhibits the ductile to brittle transition phase marked by a sharp drop in toughness close to the

operating temperature of the Linde column. The left hand graph shows that the ductile to brittle

transition effect becomes less accentuated with increased nickel content in nickel-steels, until at

18% nickel the trend is broken and good toughness is maintained across the entire temperature

range.

In keeping with iron’s ability to change from a ferritic BCC to an austenitic FCC

structure, various steels (iron-carbon alloys) can attain and keep an austenitic structure

depending mainly on temperature and nickel content. The Nickel Institute reports that “In both

wrought and cast steels sufficient nickel should always be present to ensure adequate stability of

the austenitic matrix at low temperatures” [11].

Because of its FCC structure, mechanical properties at low temperature, and resistance to

corrosion, a 300 grade austenitic stainless steel is the material of choice for the Linde double

column and its associated piping and relief devices. In the information below, the various

relevant properties of grade 300 stainless steels are explored in order to highlight their usefulness

in an air separation capacity and to choose the most suitable type.

Table #3 – Stainless Steel 304 & 316 Compositions [12]

UNS# ALLOY C Mn Cr Mo Ni Fe Si P S Al Cu Zn

S30400 SST-304 .08 2 18-20 -- 8-10.5 BAL 1 .045 .03 -- -- --

S31600 SST-316 .08 2 16-18 2-3 10-14 BAL 1 .045 .03 -- -- --

The compositions of the low carbon stainless steels give them the necessary properties

for handling intense industrial conditions. While the alloying of nickel in steel provides the

austenitic crystalline structure desired, the high chromium content and the addition of

molybdenum provide strong corrosion resistance. Types 304 and 316 are displayed in Table #2

because they are the most commonly used austenitic stainless steels in cryogenic processes [11]

and are to be compared in the following figures provided by DeSisto and Carr [13].

Aaron Farnsworth

ECH 4615

9

Figure #4 – Stainless Steel Mechanical Properties [13]

Aaron Farnsworth

ECH 4615

10

Figure #5 – Stainless Steel 316 Stress-Strain Curves [13]

Aaron Farnsworth

ECH 4615

11

Based on these data, the best material selection is stainless steel type 316 (UNS

#S31600). The critical advantage of type 316 over the other stainless steels is its ability to remain

ductile at lower temperatures. The report by DeSisto and Carr correctly concludes from the data

that “The ductility of the stainless steels tested generally decrease with decreasing temperature.

An exception is Type 316 which increases from room temperature to -105 F, remains constant to

-320 F and drops at -452 F” [13].

In the comparative graphs of the stainless steels (Figure #4), the top graph shows tensile

strength generally increasing with decreased temperature, where type 304 has a clear advantage

over type 316. However, since the Linde column is not operated at any extremely high pressure,

ductility is the more important attribute. The bottom graph shows a comparison of % elongation,

the quantitative measure of ductility [9]. Type 316 is clearly unique in its ability to maintain

ductility at cryogenic temperatures. At -320° F, which is approximately 78 K, type 316 nearly

retains its maximum value of % elongation, so it meets the requirement for the MDMT.

The evidence for this ductility is also found in the stress-strain curves for type 316

(Figure #5). While its tensile strength increases as the temperature decreases, the curves continue

to extend about the same distance along the strain axis down to about 78 K, below which it starts

to embrittle.

Another advantage of type 316 over type 304 is its resistance to hydrogen embrittlement

[14], wherein hydrogen atoms (H2 being a minor component of the process air) can diffuse

through a metal and form voids that can eventually lead to brittle failure. Although air separation

does not involve a highly corrosive environment as with chlorides, acids, brine, etc., the

longevity desired in an air separation plant makes noncorrosive properties beneficial over time.

Although costlier than many other industrial materials, type 316 stainless steel clearly

exhibits the properties required for safe working conditions in cryogenic air separation. In

summary, Table #4 constructed by Schmidt, et al. shows the logic behind metal selection for

cryogenic operation.

Aaron Farnsworth

ECH 4615

12

Table #4 – Material Selection for Cryogenic Service [5]

Higher carbon steels are omitted due to low temperature operation, copper is untenable

because of its very high cost for industrial sized equipment, and stainless steel is superior to

aluminum in both strength and combustion risk. Among the stainless steels, type 316 has a

unique advantage in ductility at 78 K and also has improved resistance to corrosion and

hydrogen embrittlement.

Configuration of Relief Devices

A multi-device safety pressure relief system is used for air separation because of the

volatility inherent in cryogenic air components. Although a simple relief valve is normally

sufficient for vessels under relatively low pressure, the risk of rapid vaporization demands a

relief system capable of preventing equipment fracture and explosion. Therefore, a rupture disc

in parallel with a direct acting pressure relief valve is used for each unit in the Linde double

column.

The safety relief valve to be employed is a conventional direct-acting relief valve. This

type of valve is a simple, reliable spring loaded device that is appropriate for applications with

less than 10% back pressure [15]. Since the relieving load from the Linde column is released to

the atmosphere, the backpressure is negligible. Similarly, a conventional prebulged rupture disc

is to be employed in order to provide rapid pressure relief. This is a non-reclosing relief device

that bursts under a set pressure value, releasing the vapor buildup to the atmosphere. This device

also happens to be commonly constructed of 316 stainless steel, the material of choice for this

system [15].

Aaron Farnsworth

ECH 4615

13

The proper location for these devices is near the top of each column, upstream of the

condenser. In T-101, the lower column, this would be upstream of the reboiler for T-102, which

acts as the lower column’s condenser. This location is useful for preventing downward vapor

flow and, in case of flooding, prevents a cryogenic liquid discharge which would be dangerous to

contact because of its extremely low temperature [16].

Calculations

In sizing relief devices for the two distillation columns, the calculation involves

determining a design pressure, the pressure vessel’s wall thickness, the MAWP of the vessel, the

required relieving flowrates (based on the most likely severe overpressure scenario), the

maximum relieving pressures, the relief devices’ set pressures, and finally the area and diameter

of each relief device based on an equation describing choked flow. For clarity, listed below are

the various terms involved and their definitions.

Operating Pressure, P – The calculated, targeted pressure for optimal distillation.

Design Pressure, PD – Determined at the discretion of the engineer, the likely maximum

pressure involved accounting for dynamic pressure variations and spikes, 10 to 25%

above the operating pressure.

MAWP, PMAWP – Maximum Allowable Working Pressure, the maximum pressure the

equipment is allowed to endure at its operating temperature at which the relief devices are

set to open.

Set Pressure, Pset – Typically the MAWP, the upstream pressure at which the relief

devices are designed to open. Valves begin leakage at about 92 to 95% of Pset.

Overpressure – Pressure increase over Pset; relief valves are required to reach relieving

capacity at 10% or less overpressure.

Accumulation – Pressure increase over the MAWP.

Maximum Allowable Accumulation, Pmax – The required maximum accumulation based

on the relief system configuration and pressure vessel type.

Backpressure – The pressure downstream of the PRD.

Aaron Farnsworth

ECH 4615

14

Required Relieving Flowrate, W – Based on the most likely and severe overpressure

scenario as determined by a Hazard and Operability (HAZOP) study, the mass flowrate

capacity required of a PRD.

Wall Thickness, δ – The pressure vessel shell thickness, the nearest gauge thickness

rounded up from the thickness calculated by the design pressure.

Ultimate Tensile Strength, TS – The highest pressure a material can withstand before

failure, a strong function of temperature.

Longitudinal Seam Efficiency, E – Also Efficiency of Weld, a pressure vessel property

based on manufacture that is determined by a radiographic test for flaws in the material.

Inner Radius, RI – The inner radius of the pressure vessel.

Safety Factor, SF – An engineering tool for creating a mathematical buffer that accounts

for unpredictable errors and weaknesses, required for pressure vessels by the ASME.

Area, A and Diameter, D – The determining characteristics in sizing a relief device.

Heat Capacity Ratio, γ – The ratio of constant pressure heat capacity to constant volume

heat capacity.

Molecular Weight, MW – Mass per mole of the relieving vapor flow.

Operating Temperature, T – The absolute temperature of the system.

Universal Gas Constant, R – Value depends on units used.

Compressibility Factor, Z – Used to account for nonideal behavior of gases, particularly

at high pressures and low temperatures.

Critical and Reduced Temperature and Pressure, Tc, Pc, Tr, & Pr – Parameters for

approximating Z. Critical values are particular to each chemical species, and reduced

values are the ratio of the system’s value to the critical value.

Pitzer Acentric Factor, ω – Used in the corresponding states theorem to estimate the

compressibility factor.

Discharge Coefficient, KD – A coefficient accounting for choked flow through a PRD.

Backpressure Correction Factor, KB – A coefficient accounting for downstream pressure.

Subscripts 1 & 2 – T-101 (lower column) and T-102 (upper column), respectively.

Subscripts V and RD – Valve and rupture disc, respectively.

Aaron Farnsworth

ECH 4615

15

The ASME design codes for an unfired pressure vessel with multiple PRD’s specify that

the set pressure Pset may be up to 105% of the MAWP as long as at least one PRD is set at the

MAWP. In this case, the valve should be set at the lower pressure because the rupture disc is a

non-reclosing emergency measure. Likewise, the maximum allowable accumulation Pmax is

116% of the MAWP for multiple devices [2].

The calculations for sizing the relief devices are detailed below first for T-101, valve and

rupture disc, and second for T-102, valve and rupture disc.

The design pressure is based on the operating pressure and, depending on the application

and likelihood and severity of pressure spikes due to dynamic effects, could be 10 to 25% above

the operating pressure. In this case, the design pressure is taken at 20% above operating pressure

due to extreme volatility of liquid N2 and O2.

𝑃𝐷,1 = 1.2𝑃1 = 88.2 𝑝𝑠𝑖𝑎

The design pressure is the first approximation of PMAWP in the equation

𝑃𝑀𝐴𝑊𝑃 = (𝑇𝑆)(𝛿)(𝐸)

(𝑅𝐼)(𝑆𝐹)

Here, the tensile strength of 316 stainless steel at 99 K is determined from the data

provided by DeSisto and Carr by quadratic interpolation to be 172,370 psi [13]. In absence of a

weld efficiency value from the manufacturer, an intermediate figure of 0.80 is assumed. The

inner radius of T-101 is about 69 in and for pressure vessels the ASME requires a safety factor of

5 [17]. Solving for thickness δ1,

𝛿1 = (88.2 𝑝𝑠𝑖)(69 𝑖𝑛)(5)

(172,370 𝑝𝑠𝑖)(0.80)= 0.22 𝑖𝑛

Aaron Farnsworth

ECH 4615

16

Since commercial steels are typically available in standard gauge thicknesses [18], the

nearest gauge rounded up is used for convenience and as an extra safety measure. For 0.221 in,

the nearest standard size is gauge 4, which is approximately 15/64 of an inch or 0.234 in. This

value is then used to back-calculate the true MAWP using the available steel size.

𝑃𝑀𝐴𝑊𝑃,1 = (172,370 𝑝𝑠𝑖)(0.234 𝑖𝑛)(0.80)

(69 𝑖𝑛)(5)= 𝟗𝟑. 𝟓 𝒑𝒔𝒊𝒂

This is the defining characteristic of a pressure vessel, and its final value is normally

presented on the manufactured equipment. In the design-phase, MAWP values are calculated as

above, but there may be a minimum thickness required by regulation or policy in order to

maintain structural integrity or weldability. A corrosion allowance is also usually added onto the

final calculation, but type 316 stainless steel has such excellent corrosion resistance properties

that the effects would be negligible here [19]. It should also be noted that an increased minimum

thickness could raise the MDMT, and the final thickness should be impact tested at the process

temperature. If these issues arise, the minimum required value can be re-inserted into the

equation to calculate the actual MAWP, from which PRD sizing proceeds to the equation for

choked flow.

Although choked flow is a dynamic fluid effect describing compressible flow, it can be

adequately approximated by the equation [2]

𝑊 = 𝐾𝐷𝐾𝐵𝑃𝑚𝑎𝑥(𝐴)√𝛾(𝑀𝑊)

𝑅𝑇𝑍[

2

(𝛾 + 1)]

(𝛾2−1)

The variable of interest for sizing a PRD is the diameter D, which depends on the area A.

The expression can be simplified by defining a constant fluid property C:

𝐶 = √𝛾

𝑅[

2

(𝛾 + 1)]

(𝛾2−1)

Aaron Farnsworth

ECH 4615

17

Solving for relief area on the valve for T-101, we have

𝐴𝑉,1 = 𝑊1

𝐾𝐷𝐾𝐵𝑃𝑚𝑎𝑥,1(𝐶)√

𝑇1𝑍1

(𝑀𝑊)

The mass flow W through the PRD is the maximum required relieving flowrate based on

possible overpressure events [20]. In case of a temperature increase, the vaporization of the

liquid air components would likely begin in the upper column since its cryogenic liquid provides

the heat exchange necessary for liquefaction in the lower column. If the liquid components of T-

102 vaporized, it would certainly cause vaporization in T-101 due to the lack of a heat sink.

Since the two columns are thermodynamically connected in this way, the relieving flowrate has

to account for total vaporization of the mass flow through both columns.

For this system, even though the distillate is mostly nitrogen, the overpressure event

described above would require the relief of vaporized nitrogen, oxygen, argon, and other minor

components. The required area for a PRD depends on this event, so the required mass flow rate

W of air through the PRD is based on the vaporization of all the liquid flow normally passing

through the column. For T-101, this amounts to W1 = 34.2 kg/sec.

For design-phase calculations, the discharge coefficient KD for a valve has a typical value

of 0.975 [2]. In each case for this system, the backpressure is simply atmospheric, so its

correction factor KB can be approximated as 1. The maximum allowable accumulation Pmax is

determined by the ASME for a pressure vessel with multiple relief devices as 116% of the

MAWP. In this case,

𝑃𝑚𝑎𝑥,1 = 1.16𝑃𝑀𝐴𝑊𝑃,1 = 108.7 𝑝𝑠𝑖𝑎 = 749.24 𝑘𝑃𝑎

The compressibility factor must be determined for a gas that deviates from ideal behavior

due to high pressure or low temperature. As a reasonable approximation, the theorem of

corresponding states is applied using Table E.1 from Smith, Ness, and Abbott [21].

Corresponding states asserts that fluids tend to have similar compressibility factors based on

similar reduced temperature and pressure values, these reduced values describing the proximity

Aaron Farnsworth

ECH 4615

18

to their critical values such that Tr = T / Tc and Pr = P / Pc. Using property tables for values of Z0

and Z1 corresponding to reduced temperature and pressure, the correlation [21] is

𝑍 = 𝑍0 + 𝜔𝑍1

This method of determining real gas behavior is appropriate for the Linde column

because the Pitzer acentric factor ω is zero or nearly zero for all the main components of air.

Neglecting the second term, then, the value of Z0 provides a good approximation of the

compressibility factor.

Since critical properties, and molecular weight values are available for air, it can

be treated as a pure substance being relieved in the choked flow equation. For air throughout the

Linde column, the heat capacity ratio γ is taken as 1.47 [22], the molecular weight is 29 kg/kmol,

and the universal as constant R is 8,134 J / kmol-K.

The critical properties of air are given as Tc = 132.2 K and Pc = 37.45 bar [21]. In T-101,

with temperature at 99 K and pressure at 5 atm (or 5.07 bar), the reduced properties are Tr,1 =

0.75 and Pr,1 = 0.14. Based on a bilinear interpolation of Table E.1, Z0 is approximately 0.90,

therefore this is the value of the compressibility factor Z.

With all parameters now defined for an overpressure relief scenario via the valve in T-

101, required relieving area AV,1 and valve diameter DV,1 are calculated as follows:

𝐴𝑉,1 = 34.2 𝑘𝑔/𝑠𝑒𝑐

(0.975)(1) (749,240 𝑘𝑔

𝑚 𝑠𝑒𝑐2) (0.0118 √𝐾 𝑘𝑚𝑜𝑙𝑘𝑔 𝑚2

𝑠𝑒𝑐2

)

√(99 𝐾)(0.90)

29 𝑘𝑔/𝑘𝑚𝑜𝑙

𝐴𝑉,1 = 0.0070 𝑚2 = 𝟏𝟎. 𝟖 𝒊𝒏𝟐

𝐷𝑉,1 = √4𝐴

𝜋= 𝟑. 𝟕 𝒊𝒏

Aaron Farnsworth

ECH 4615

19

The sequence of calculations and the units involved shown here are applied in the same

manner to the rupture disc in T-101 and to both PRD’s in T-102. The only difference in

calculating the rupture disc size for T-101 is the value for KD, which is now taken as 0.62 [23].

All other values remaining the same,

𝐴𝑅𝐷,1 = 𝟏𝟕. 𝟎 𝒊𝒏𝟐

𝐷𝑅𝐷,1 = 𝟒. 𝟕 𝒊𝒏

The conditions in the upper column, T-102, involve lower temperature and approximately

atmospheric pressure. The MAWP for this column is calculated as follows, using the tensile

strength of 316 stainless steel at 78 K, the larger inner radius of 213 in, and a design pressure of

20% above operating pressure:

𝑃𝐷,2 = 1.2𝑃2 = 17.6 𝑝𝑠𝑖 = (184,300 𝑝𝑠𝑖)(𝛿2)(0.80)

(213 𝑖𝑛)(5)

𝛿2 = 0.127 𝑖𝑛

The next highest standard gauge thickness is gauge 10 which is approximately 9/64 of an

inch or 0.140 in. The MAWP is back-calculated as:

𝑃𝑀𝐴𝑊𝑃,2 = (184,300 𝑝𝑠𝑖)(0.140 𝑖𝑛)(0.80)

(213 𝑖𝑛)(5)= 𝟏𝟗. 𝟒 𝒑𝒔𝒊𝒂

For choked flow, the heat capacity ratio, gas constant, molecular weight, discharge

coefficients for valve and rupture disc, and backpressure correction factor remain the same. The

new required relieving flowrate is again the hypothetical vaporized liquid flow through the

column, in this case 24.4 kg/sec. The maximum allowable accumulation is again 116% of the

MAWP, or 22.5 psia (155.1 kPa). Finally, the compressibility factor is determined to be 0.97

using the theorem of corresponding states.

Aaron Farnsworth

ECH 4615

20

For these new values,

𝐴𝑉,2 = 24.4 𝑘𝑔/𝑠𝑒𝑐

(0.975)(1) (155,100 𝑘𝑔

𝑚 𝑠𝑒𝑐2) (0.0118 √𝐾 𝑘𝑚𝑜𝑙𝑘𝑔 𝑚2

𝑠𝑒𝑐2

)

√(78 𝐾)(0.97)

29 𝑘𝑔/𝑘𝑚𝑜𝑙

𝐴𝑉,2 = 0.022 𝑚2 = 𝟑𝟒. 𝟏 𝒊𝒏𝟐

𝐷𝑉,2 = √4𝐴

𝜋= 𝟔. 𝟔 𝒊𝒏

Likewise, the rupture disc size is calculated using a discharge coefficient of 0.62:

𝐴𝑅𝐷,2 = 0.035 𝑖𝑛2 = 𝟓𝟑. 𝟖 𝒊𝒏𝟐

𝐷𝑅𝐷,2 = 𝟖. 𝟑 𝒊𝒏

Finally, the set pressure at which each PRD i s designed to activate must be determined.

For pressure vessels with multiple relief devices, the ASME requires that one PRD be set at the

MAWP while others may be designed to open at up to 105% of the MAWP. Since the rupture

disc is a non-reclosing device and a measure of last resort, it is the device set at 105% MAWP

value for each column. Tables #5 & 6 below contain the results including the calculated set

pressure values.

Aaron Farnsworth

ECH 4615

21

Table #5

T-101

Table #6

T-102

PMAWP 93.5 psia PMAWP 19.4 psia

AV 10.8 in2 AV 34.1 in2

DV 3.7 in DV 6.6 in

Pset,V 93.5 psia Pset,V 19.4 psia

ARD 17 in2 ARD 53.8 in2

DRD 4.7 in DRD 8.3 in

Pset,RD 98.2 psia Pset,RD 20.4 psia

Conclusions

The design phase of any chemical engineering project is the most important time to

consider safety issues and take preventative measures. A design specification such as material

selection cannot be reconsidered after the fact, and the result of an error would either be an

enormous monetary expense or eventual failure of the system, which could mean injury and loss

of life. This study is an overview of the main safety issues confronting the cryogenic air

separation process at the Linde double column. It is not exhaustive of all hazards and

preventions, but it can be used as a guide for detailing and designing safety measures for other

parts of the plant.

A HAZOP study should be the starting place for identifying dangers inherent in the

system, from which design decisions can be intelligently made such as material selection, PRD

configuration and sizing, automatic control schemes, maintenance schedules, etc. It is also

imperative that local regulations be accounted for and requirements met. Examples in this study

include the ASME requirements for pressure vessels in various applications and information

regarding N2 safety from the U.S. Chemical Safety and Hazard Investigation Board.

The main hazard that cannot be perfectly prevented or ruled out is human error, so safety

systems are often multi-layered and redundant, such as the multi-device pressure relief

configurations for the distillation columns and several effective safety factors worked into

calculations. Safety is a constant priority for engineers, who work to control complex physical

systems at extreme conditions, and the most important tools in preventing disasters are design-

phase decisions and vigilance.

Aaron Farnsworth

ECH 4615

22

References

[1] The Linde Group, “Cryogenic Air Separation: History and Technological Progress,” Pullach,

Germany.

[2] D. A. Crowl and S. A. Tipler, Back to Basics, “Sizing Pressure-Relief Devices,” AIChE,

2013, https://www.aiche.org/sites/default/files/cep/20131068_r.pdf

[3] Canadian Centre for Occupational Health and Safety, “Cryogenic Liquids – Hazards,” May

2016, https://www.ccohs.ca/oshanswers/chemicals/cryogenic/cryogen1.html

[4] U.S. Chemical Safety and Hazard Investigation Board, “Safety Bulletin: Hazards of Nitrogen

Asphyxiation,” No. 2003-10-B, June 2003.

[5] W. P. Schmidt, K. S. Winegardner, M. Dennehy, and H. Castle-Smith, Safe Design and

Operation of a Cryogenic Air Separation Unit, Houston TX, Apr 2001,

http://www.airproducts.com/~/media/downloads/white-papers/S/en-safe-design-and-

operation-of-an-air-separation-unit-whitepaper.pdf

[6] F. Khazrai, H. B. Haghighi, and H. Kordabadi, Hydrocarbon Processing, “Avoid Brittle

Fracture in Pressure Vessels,” Gulf Publishing Company, 2016,

http://www.hydrocarbonprocessing.com/Article/2780107/Avoid-brittle-fracture-in-

pressure-vessels.html

[7] University of Cambridge, “Ductile to Brittle Transition,” 2015,

http://www.doitpoms.ac.uk/tlplib/BD6/ductile-to-brittle.php

[8] S. Sutar, G. Kale, and S. Merad, International Journal of Innovations in Engineering

Research and Technology, “Analysis of Ductile-to-Brittle Transition Temperature of

Mild Steel,” Vol. 1, Iss. 1, Novateur Publications, Nov 2014,

http://oaji.net/articles/2014/1511-1419830589.pdf

[9] W. D. Callister, Jr. and D. G. Rethwisch, Materials Science and Engineering, 9th ed., Wiley,

2014.

[10] Piyush K. Dutta, US Army Corps of Engineers: Cold Regions Research & Engineering

Laboratory, “Behavior of Materials at Cold Regions Temperatures [sic],” Special Report

No. 88-9, July 1988.

Aaron Farnsworth

ECH 4615

23

[11] A Designers’ Handbook Series, “Design Guidelines for the Selection and Use of Stainless

Steel,” Nickel Development Institute, No. 9014, 1974,

https://www.nickelinstitute.org/~/Media/Files/TechnicalLiterature/DesignGuidelinesforth

eSelectionandUseofStainlessSteels_9014_.pdf

[12] Engineers Edge, “Stainless Steel Specification and Composition Table Chart,” 2016,

http://www.engineersedge.com/stainless_steel.htm

[13] T. S. DeSisto and F. L. Carr, Watertown Arsenal Laboratories, “Low Temperature

Mechanical Properties of 300 Series Stainless Steels and Titanium,” Report No. WAL-

TR-323.4/1, Watertown, MA, Dec 1961.

[14] C. San Marchi, Technical Reference on Hydrogen Compatibility of Materials, “Austenitic

Stainless Steels: Type 304 & 304L (code 2101),” Sandia National Laboratories, May

2005, http://www.sandia.gov/matlsTechRef/chapters/2101TechRef_304SS.pdf

[15] K. S. N. Raju, Chemical Process Industry Safety, 1st ed., McGraw Hill.

[16] Separation Processes, “Over-Pressure and Relief Location,” Ch. 6,

http://www.separationprocesses.com/Operations/POT_Chp06.htm

[17] The Pennsylvania Code, “Maximum Allowable Working Pressure,” Pa. Code 3a.151,

http://www.pacode.com/secure/data/034/chapter3a/s3a.151.html

[18] Microscopy Products for Science and Industry, “Standard Gauge for Sheet and Plate Iron

and Steel,” Ted Pella, Inc., https://www.tedpella.com/company_html/gauge.htm

[19] North American Stainless, “Long Products Stainless Steel Grade Sheet,”

http://www.northamericanstainless.com/wp-content/uploads/2010/10/Grade-316-

316L1.pdf

[20] Crosby Pressure Relief Valve Engineering Handbook, No. TP-V300, Crosby Valve Inc.,

May 1997, https://swan-associates.com/documents/Eng_Handbook.pdf

[21] J. M. Smith, H. C. Van Ness, and M. M. Abbott, Introduction to Chemical Engineering

Thermodynamics, 7th ed., McGraw Hill, New York, 2005.

[22] Frank M. White, Fluid Mechanics, 4th ed., McGraw Hill.

[23] Rupture Disc Sizing, Technical Bulletin 8102, Fike Corporation, Blue Springs MO, Feb

2000, http://www-

eng.lbl.gov/~shuman/XENON/REFERENCES&OTHER_MISC/tb8102.pdf