1

A Method to Mitigate Corrosion in Ballast Tanks of a Double Hull Tanker

Mo Husain (M) and Gary D. Shilling (V)

ABSTRACT

Ocean-going ships are especially vulnerable to corrosion, particularly their ballast tanks, which are essentially empty and filled with

air during ‘cargo leg’ portions of a voyage. Because of varying air and seawater contents ballast tanks have become especially

vulnerable, requiring , expensive periodic cleaning, resurfacing and structural repairs. It has been found that an atmosphere of inert

gas has a significant anti-corrosion effect on steel surfaces subject to salt water. This protective effect is increasingly being exploited

to protect the interior of the ballast tanks. The proposed method, described herein, uses the gas mixture from currently-available inert

gas generators, to provide a distribution system that guarantees access of the protective mixture to all points in a tank and to also

provide means to “gas free” the space for human access.

KEY WORDS: Ballast Tanks, Corrosion, Inert Gas, Gas

Freeing, Diffuser, Ship Structure

INTRODUCTION

The objective of this paper is to describe a distribution system

method that provides access of the inert gas protective mixture

to all points in the tank and also provides means of “gas

freeing” the space for human access.

Oceangoing tanker ships provide spaces for loading cargo and,

separately, spaces for holding seawater ballast when not loaded.

Tankers over 20,000 dwt. carrying crude oil, the ullage space

above the cargo in each tank must be filled with an inert gas to

prevent explosion hazards. Ballast tanks nominally contain

only seawater or are empty, and inert gas is not traditionally

required. Ballast tanks corrode badly because of varying air and

seawater contents, and this type of damage is becoming a

serious economic problem in some ships, especially tankers.

An atmosphere of inert gas has been found to have a significant

anti-corrosion effect on steel surfaces subject to salt water. This

protective effect is increasingly being exploited to protect the

interior of ballast tanks. Conveniently, tanker vessels are

already required to use an onboard inert gas generator, and this

gas mixture has been found to work well against corrosion. In

its use in cargo tanks, this use of gas to replace air is called

inerting. Furthermore, additional inert gas may have to be

introduced to an already inerted tank, to reduce the oxygen

content further – occasionally needed to offset the oxygen

ingress through structural leaks – a process called purging

Before taking on cargo, a tanker normally discharges the ballast

used on the previous voyage and allows the empty ballast tanks

to fill with air; the new anti-corrosion approach requires that the

tank be filled with inert gas instead, and this gas is displaced by

water when the ship again off loads cargo.

As tanks must be entered from time to time for inspection and

repair, it must be entered by crew or workers. However, the

inert gas, having low oxygen and elevated carbon dioxide, is

dangerous to personnel and must be gas-free before the tank can

be entered.

Corrosion of metal structures is practically unavoidable in the

marine environment, especially in enclosed spaces having

access to seawater. The extent of corrosion damage in ballast

tank interior structures has increased significantly in recent

times. OPA 90, which mandated double hulls for ocean-going

tankers, required the addition of large enclosed volumes, most

of which are adapted for ballast and therefore often nearly filled

with seawater and at other times with dead, humid air and

petroleum-derived gases and vapors.

These spaces are difficult to access, and yet must be inspected

and repaired, perhaps cleaned or coated by workers from time to

time, thus requiring occasional safe human access. In addition,

the desire to minimize structure in cargo spaces has required

increased load-bearing structure in ballast spaces, voids, and

difficult to reach nooks and crannies throughout the tank space.

Even under moderate conditions, the ballast spaces provide a

most hospitable environment for accelerated corrosion.

Sometimes the deck can absorb solar heat, creating temperatures

up to 140 degrees F in interior spaces. For a new vessel,

deterioration starts on the first day of operation and accelerates

throughout its lifetime.

The economic consequences for ship operators are staggering.

Corrosion-related hull repair and out-of-service costs are

increasing. A related issue, which is yet to be fully explored, is

the porous nature of the surface corrosion product, which may

retain flammable or toxic gases to some degree even after

cleaning.

Ballast tank corrosion has now become the principal reason for

reduced service life of double hull tankers.

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COATING AND CATHODIC PROTECTION

Coatings have always been the primary defense against

corrosion, although they have not always been required for

ballast tanks in the past Additionally coatings have proven to not

be effective because of cracks caused by structural deformations

and bacterial actions There is nothing new in the use of coatings,

so these problems continue to plague the effectiveness of

coatings

Ballast spaces represent about half of the ship’s vulnerable area.

In many cases they have small spaces that are hidden by

structure and are essentially inaccessible, so complete coverage

by applied coatings cannot be assured. Fluids, gases and

microorganisms can reach anywhere. Despite these factors, ship

operators are adopting a different approach: apply coatings, use

anodic protection for the ballast leg of the voyage, and finally

inert the empty tank during the cargo leg. These measures, as

they are being applied in these new circumstances, are not

effective. An apt view of the situation is provided by the Center

for Tankship Excellence:

”There is no magic coating that will solve this problem. Using

waterborne zinc silicate or a really well designed solvent free

epoxy might be a substantial help, but unless the yards are

forced to completely change their coating procedures, - a very

good idea, by the way – will be forced to continue to use

“application friendly” coatings which in longevity are little

better than the coal tar epoxies of 25 years ago – and in some

cases worse. No paint vendor will guarantee these coatings fore

more than 10 years and these are bit of a joke……… There have

been numerous reports of double hull tankers less than five

years old requiring massive coating repair. The best that an

owner of a double hull VLCC relying on coating can hope for is

to put off a 15 million dollar reblast and recoat for ten or so

years. The problem for the regulator is that most owners will

put off this kind of expenditures for too long, which will

generate a series of casualties, some of which may only involve

spillage, but some of which will involve the loss of a crew.”

Cathodic protection uses attached zinc anodes to absorb

electrolytic current flow that would otherwise cause oxidation.

To quote again from the Center for Tankship Excellence,

“….But this has to be done properly and currently most tanker

owner do a putrid job of maintaining cathodic protection in

ballast tanks. The method of choice is a superintendent

periodically inspects a tank, kicks the anode, and pontificates

that the anode is or is it not still effective ….. somebody kick an

anode and write down 30% wasted….”

International regulations require the use of inert gas in cargo

tanks to prevent fire and explosion, but not in ballast tanks.

However, empty ballast tanks are still vulnerable to the leakage

of oil or gas from outside and the use of inert gas would have

some fire protective value. As discussed below, however, the

distribution of inert gas to all interior surface is not assured and

thus the use of inert gas in the ballast tanks must provide for

total distribution along the tank inner surface. This is the

novelty of the invention, the combination of inert gas creation

combined with its total distribution over all surfaces of the

ballast tank interior.

CORROSION PROCESS

Electrochemical Corrosion

Corrosion is primarily an electrochemical process; it is the

deterioration of a metallic surface as a consequence of two

chemical processes such as:

Anode reaction: 2Fe => 2Fe2+

+ 4e-

Cathode reaction: O2 + 2H2 + 4e- => 4OH

-

These two reactions remove iron from one site and create iron

oxide at a closely adjacent site. The resulting erosion creates

pitting, providing additional area for further corrosion. The ionic

forms constitute an electrical current. Zinc anodes provide

protection by absorbing this current, which is an essential part of

the corrosion process.

Galvanic Corrosion

Galvanic corrosion occurs when two or more dissimilar metals

are connected through a conductive environment such as salt

water. Processes similar to those above deplete material from

the anodic material and deposit it in some form on or around the

cathodic material.

Microbiologically Induced Corrosion (MIC)

Certain biological organisms can cause a high rate of corrosion,

affecting most alloys such as ductile iron, steel (including

stainless) and copper. The numerous microorganisms that

participate in these reactions are often characterized by their

visible effects. Sludge-producing or sulfur-oxidizing life forms

are involved in corrosion processes. Note in this connection that

lack of oxygen does not prevent damage from these organisms.

Typically, those of importance to us are either aerobic, requiring

oxygen, or anaerobic, requiring no oxygen. Some sulfate-

reducing bacteria, often well represented in harbor water, can

create corrosion nodules and pits in a typical ballast tank

environment.

BALLAST TANK PROTECTION METHODS

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Protective coatings are used and are partially effective, but

periodic detail tank cleaning and recoating is required in order to

remove deposits and residues of marine organisms, scale and

mud and to refresh the surface. An inerting method developed

and used successfully on a trial basis was on the tanker Empress

des Mer. Since then, Hellespont Shipping has installed inerting

system for the ballast tanks on many of their tankers. This

method uses a single feed pipe from the inert gas generator that

extends from the deck downward to the tank bottom and then

horizontally to the inner bulkhead, that is, an L-shaped pipe. In

2004 the American Bureau of Shipping (ABS) issued

guidelines for inerting ballast tanks of double hull tankers,

which also used a single feed pipe method. The central problem

with tank single feed pipe inerting systems is that the tank

interiors to be protected are not simple rectangular spaces; they

have complex structural features and voids. Additionally, they

are usually contaminated by corrosion causing marine growth

carried in by ballast water.

SYSTEM OBJECTIVE

The inert gas to be used is air from which nearly all of the

oxygen has been removed by a controlled combustion process.

This hardware is off-the-shelf marine hardware that uses diesel

fuel as the reactant. The objective is to direct the resulting inert

gas all the way to the vulnerable surfaces and thus to deprive

this critical region of oxygen. A corollary objective is to

suppress the growth of marine organisms in the vulnerable

surface region. Overall, this action will limit corrosion and also

reduce the need for periodic tank cleaning, an expensive and

somewhat hazardous, labor-intensive activity. Ultimately, the

cost of the corrosion prevention system must appear as a

component of the bottom line to offset cleaning and

maintenance costs.

SYSTEM COMPONENTS AND DESIGN

OBJECTIVE

The inert gas generator and its fuel supply, instrumentation and

auxiliaries can be obtained as a single, standardized

procurement package. The remainder of the system consists of

piping, metallic or plastic, together with valving,

instrumentation and an automatic control. The system objective

is to maintain a relatively uniform and consistent contact

between the inert gas and the interior structural surfaces of the

tank. Piping and valves deliver the inert gas from the inert gas

generator through a pressure boosting pump to specialized

diffuser nozzles. The key requirement for the number and

placement of the nozzles is to secure rapid and complete mixing

of the inlet gas with the mixture prevailing in the tank.

Complete mixing is the critical element in achieving inert gas

access to the entire inner surface of the tank, including, for

example, structural elements and recesses. The nozzles must be

planned to create an even and effective dispersion of the inert

gas to all quarters.

A methodology has been developed by means of which an

effective and economical system can be designed in detail for a

ballast space of almost arbitrary geometry. The ship is an

economic entity. The corrosion control system is, after all, not

a primary component of the ship; it is a convenience and an

economy measure and an economic element, and its installation

in a working ship cannot remove the vessel from its working

environment, while engineers ponder the design and validate its

operation. For retrofit, the installation must be planned in

advance and installed during routine maintenance. In this

connection, some level of flexibility is designed into the

installation, in the sense that a careful survey would be made

after a period of service in order to detect deficiencies, and

therefore to adapt the distribution system to observed patterns of

corrosion.

The control system, coupled with gas measuring instruments

located through out the ballast tanks, are crucial to the safe and

economic operation of the system. When gas freeing in a ballast

tank, the control system must monitor the level of oxygen

throughout the ballast tank. Additionally, while the tank is

occupied by personnel, the oxygen level throughout must be

monitored and the air flow regulated to ensure proper conditions

are sustained. For this reason the automatic control system must

be a fail-safe system, typically constructed with duplicate

synchronous components.

When inerting a tank, the gas measuring instruments connected

to the control system must provide for monitoring the

concentration of inert gas throughout the tank such that controls

can be activated to reduce, increase or distribute differently the

flow of inert gas to achieve the desired concentrations

throughout. Although this is important to the economic

operation of the system, a more important factor is management

of the time that inert gas is flowed to the different tanks.

DESIGN TOOL

Gas (Mixing) Dynamics & Computational Fluid

Dynamics

Finite-element modeling for defining the mixing and

distribution of a gas mixture in a complex three dimensional

space has been reviewed. It is unlikely that a complete

computational fluid dynamics model can be developed for each

tank in each vessel, but such a region-specific approach will at

least be needed to study typical structural anomalies. An

analytical approach of this kind has provided a library of

processes for designing the system.

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A relatively simple mathematical model has been developed to

simulate performance of inert gas introduction into the tanks

through multitude of nozzles on a matrix like grids. The nozzles

numbers and arrangement could be varied, as well as through-

put of inert gas through the nozzles. The mathematical model

developed is a ‘linear first order differential equation’ analysis.

(Appendix A).

SYSTEM DESCRIPTION FOR SHIPBOARD

APPLICATION

The inerting of ballasting tanks as described herein comprises of

piping grid, nozzles (diffusers) placed on the piping at a certain

interval, header pipes connecting the piping grid to the inert gas

generator via a compressor. This application uses a system

similar to a previously developed ballast water treatment

product to dispense inert gas into ballast water. This corrosion

prevention system is focused on distributing inert gas into the

void of a ballast tank rather than into the ballast water.

The method uses a matrix or grid of nozzles (diffusers)

connected to the ship’s inert gas supply.

Fig. 1 Perspective View of Ballast Tank

The pressure required to drive these nozzles is of the same order

of magnitude as that required to dispense inert gas into the cargo

tanks in the fire protection system, and can be similarly

controlled. An analytical mathematical modeling system for

designing nozzle placement is discussed in the appendix.

A typical installation would use nozzles spaced perhaps ten feet

apart, disposed in a pattern favoring access to hidden locations.

These nozzles (diffusers) would be similar to those used in a

waste water treatment plant, where aeration is needed and where

there can be an accumulation of sludge just as there often is in

ballast tanks. The nozzles would be directed downward to

extend protection into a sludge layer. The diffusers are

Fig. 2 Gas Diffuser

commercially available in the US and have a history of higher

than normal reliability.

Continuous and complete circulation of inert gas could be

achieved in a few hours. The same process is used to dispel the

inert gas and replace it with air.

Figure 3 is (next page) a detailed illustration of ballast tank with

diffusers and piping.

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Fig. 3 – Detailed Illustration of ballast tank with diffusers and piping

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DISCUSSION OF PERFORMANCE

System performance and design algorithms are derived from the

analytical model presented in Appendix A. The specific

candidate tank selected for inerting in this paper is similar to the

tank analyzed in ABS Guide for: INERT GAS SYSTEM FOR

BALLAST TANKS – 2004 with the following assumptions:

Assumptions:

Tanker Class - ULCC

Volume of the Tank – 15,000 m3

Constituents of the gas: N2 – 87%, CO2-14% & O2-3%

Oxygen Reduction Desired – up to 5%

Number of Nozzles – 150 - 660

Gas-Flow thru Nozzles – 10 CFM or 0.283 m3 per minute

Based on the following figure 4 &5 and Table 5 of the Appendix

A, 440 nozzles are selected as an ‘economically pragmatic’

number of nozzles for a tank of approximately 15,000 m3 of an

ULCC tanker vessel.

Fig. 4 Oxygen Content Reduction By Time for 440 Nozzle

Installation

Fig. 5 Oxygen Content By Time When Gas Freeing Inert Gas

Filled tank

With 440 nozzles, time required to inert the tank, down to 5%

oxygen is approximately 4.5 hours.

Inert Gas Consumed during inerting is approximately 34,263

cubic meters.

With 440 nozzles, time required to “gas-free” the tank is 4.17

hours.

Volume of air required to “gas-free” the tank is approximately

24, 919 cubic meters.

CONCLUSIONS

This paper described an effective “inerting” system for

protecting ballast water tanks and other voids and closed spaces

from corrosion, resulting from contact with fresh or salt water,

or other fluids that support electrolytic corrosion. The

distribution system guarantees access of the inert gas to all

points in the tank, thus preventing corrosion in many ‘hidden’

spots due to complex structural design in the ballast tanks of a

double hull tanker. The system is also designed to be used to

“gas free” tanks for human access and to sustain safe personnel

conditions during periods of occupation . This system is

economical to install and maintain, because it uses highly

reliable ‘off-the-shelf’ components, making use of currently

available inert gas generators, typically already on-board large

oil carrying tankers. Finally, a methodology for designing

optimum installation elements for the system is included for all

tanks in general and specifically for a 15,000 cubic meter tank.

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ACKNOWLEDGEMENTS

We would wish to express our appreciation and gratitude to our

Chief Scientist Charles F. Quirmbach for his immense

contribution in the production of this paper. We also thank our

Sr. Vice President Robert E. Apple and Henry M. Hunter for

their review of this paper and thoughtful analytical comments.

REFERENCES

[1] ABS – Guide for: Inert Gas System For Ballast Tanks –

2004

[2] DRAGOS RAUTA – Corrosion in Double Hull Tankers –

TANKER Operator, May 2004

[3] JACK DEVANNEY - Ballast Tank Protection - Center for

Tankship Excellence.

[4] MICHAEL B. KENNEDY - Abstract of Presentation at 28th

T.S.C.F.

[5] JAMES B BUSHMAN, P.E - Corrosion and Cathodic

Protection Theory

[6] JOHN PARENTE, JOHN C. DAIDOLA ET AL - Final

Report -Commercial Ship Design and Fabrication for

Corrosion Control – SR- 1377 - M Rosenblatt & Son -1996

[7] RICHARD MARTIN - The New Supertanker Plague –

WIRED Magazine 2002

[8] RONALD J. HUGGINS P.E - Microbiological Influenced

Corrosion

[9] ERIC ASKHEIM ET AL – Det Norske Veritas, Hovik,

Norway – How and Why Corrosion Protection of Ballast Tanks

Has Become the Business of Classification Societies

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APPENDIX A

Derivation of Equations of Gas Flow

This paper analytically models two complimentary processes:

• Flowing inert gas into a ballast tank to impede

corrosion; and

• Flowing free air into a ballast tank filled with inert

gases to render the space humanly accessible.

The analytic models developed herein can be used to optimize

both processes by proper selection of the crucial parameters.

In the first case, gases from an inert gas generator are flowed

into a tank through pipes with nozzles uniformly placed

throughout the tank. The number and placement of the nozzles

are crucial in order to ensure uniform and timely mixing of the

inert gases with the current gas content of the tank. For example,

at the extreme, use of a single pipe for flowing inert gases into

the tank cannot ensure there are no pockets of the original

corrosive gas mixture. Furthermore, since the tank must be

continually vented to avoid increased pressure, only one inert

gas outlet cannot ensure the gas being vented is not the newly

inserted inert gas rather than the original corrosive mixture.

In the second case, the problem is how to timely and effectively

raise the oxygen density in a tank to 23% throughout the tank

from a typically low value of 5% when filled by inert, non-

corrosive gas.

The key parameters in the modeling process are the volume of

the tank and the number of nozzles used to flow inert gas or free

gas into the tank. The approach to this modeling process is to

develop a quantitative description of the amount of gas in the

tank as the gas content is transformed from a set of initial

conditions to a set of final conditions. In the first case, the

objective is to transform the content of a ballast tank from a

corrosive gas to a non-corrosive gas. In the second case, the

objective is to transform the content of a ballast tank from one

filled with inert gas to one filled with free air. For both cases a

differential equation is formulated and solved that specifies the

total quantity of oxygen in the tank at any time as the ballast

tank content is transformed.

Let V represent the fixed volume of a tank, and identify Q(t) as

the amount of oxygen present in the tanks at time t.

Assume a gas of concentration, ci, flows into the volume at a

fixed rate Fi . Units of ci are in terms of grams / unit volume;

units Fi are in terms of volume per unit time. Assume Fo

represents the fixed rate that the gas leaves the volume.

Assume also that the new gas is mixed instantly, a reasonable

assumption as long as many nozzles are uniformly distributed

throughout the tank.

If Q(t) is known, the concentration of the gas can be determined

as a function of time by:

(A1)

Applying the conservation principle:

Rate of Q in = ci Fi (A2)

Rate of Q out = c(t) Fo (A3)

Note that Fi is the total flow of all gases into the container and

Fo is the total flow of all gases out of the container. ci is the

concentration of oxygen in the total flow into the container, and

c(t) is the concentration of oxygen exhausted out of the

container. Clearly ci Fi is different from c(t)Fo , but Fi does equal

Fo.

With the above the equation can be written:

where

In this case

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yielding

Qf is the final gas concentration.

The integral equation enabling the solution for y(t) is:

Evaluating the indefinite integral on each side of the above

equation yields:

for arbitrary constant c1.

Applying the exponential to both sides of the above equations

yields:

where

Solving for c2,

As a consequence of the continuity of the exponential function

and of Q, (18) can be written as

From this Q(t) can be solved for as:

Applying the initial conditions of

to solve for c:

Substituting for c in Eq. A20:

where Qf

Recognizing that V/F is the time, Tf, required to fill the volume

V with gas flowing in at a rate of F, the interpretation of this

quantity can be redefined as:

The final form of the equation is:

Where

APPLICATION OF EQ. A27 TO A 15,000 CUBIC

METER TANK

Equation A27 is applied to determine the quantity of Oxygen

over time for a 15,000 cubic meter tank as follows. Before

applying A27 the characteristics of the output of an inert gas

generator are needed. These details and calculations are

presented in the following table. This table is based on the ideal

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gas equation, PV = nRT. In particular, column F is calculated

from the density form of the ideal gas equation, n/V = P/RT.

The following parameters are used in this table.

Characterization of output of inert gas generator, where:

• P = pressure, in Pascals.

• R = Universal gas constant

• M3 = Meters cubed

• Pp = Partial pressure in Pascals

• V = Volume

• T = Temperature

• n = Number of moles

Table 1. Parameters for determining mass gas flow

Inert

Volume

Percent P Temp R Grams/MinOxygen 0.03 101,325 288 8.3144621 13,540.2

CO2 0.14 101,325 288 8.3144621 80,981.6

Nitrogen 0.83 101,325 288 8.3144621 327,953.8

Total 1 303,975 422,475.6

The initial conditions for applying Eq. A27 to a 15,000 cubic

meter tank are detailed in the following table.

Table 2. Conditions for modeling inerting and gas freeing

Volume of container 15,000 cubic meters

Number of diffusers 150 - 660 count

Gas pressure on each diffusers 30 psi

Volume discharge from each diffuser 10 cubic meters / minute

Oxygen mass percent of inert gas 3.00%

Oxygen mass percent of fresh air 23.00%

Oxygen Mass density in fresh air 1,429 grams /cubic meter

Oxygen Mass density in inert gas 40.62 grams / cubic meter

Oxygen mass in free air filled tank 21,435,000 grams

Oxygen mass in inert gas filled tank at 5% mass density 2,644,168 grams

Oxygen mass in inert gas filled tank at 3% mass density 609,300 grams

Input Conditions

Using the above, the quantity Tf is detailed in the following

table for various numbers of nozzles.

Table 3. Determining time of gas flow for 15,000 cubic foot

tank

Number of diffusers 150 220 330 440 550 660

Discharge volume per diffuser

(cubic feet per minute) 10 10 10 10 10 10

Discharge volume per diffuser

(cubic meters per minute) 0.28 0.28 0.28 0.28 0.28 0.28

Total volume discharged (cubic

meters per minute) 425 623 934 1,246 1,557 1,869

Tf (minutes) 35.31 24.08 16.05 12.04 9.63 8.03

Calculation of Tf for Various Number of Nozzles

The following graphs, Fig. 5 & 6, present the results of

application of Eq. A27 to the two processes:

• Replacing a corrosive gas mixture with a non-corrosive

mixture; and

• Detoxifying a tank filled with inert gases.

These curves are plotted from Tables 4 and 5.

Fig. 5 Oxygen content by time for range of nozzles from 150 to

660 while inerting 15,000 cubic foot ballast tank

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Fig. 6 Oxygen content by time for range of nozzles from 150 to

660 while gas freeing 15,000 cubic foot ballast tank

Table 4. Oxygen mass reduction by time for range of nozzles

from 150 to 660 while inerting a 15,000 cubic meter tank

150 220 330 440 550 660

0 23.0% 23.0% 23.0% 23.0% 23.0% 23.0%

15 22.2% 21.8% 21.2% 20.7% 20.1% 19.6%

30 21.4% 20.7% 19.6% 18.6% 17.6% 16.8%

45 20.6% 19.6% 18.1% 16.8% 15.5% 14.4%

60 19.9% 18.6% 16.8% 15.2% 13.7% 12.5%

75 19.2% 17.6% 15.5% 13.7% 12.2% 10.9%

90 18.5% 16.8% 14.4% 12.5% 10.9% 9.5%

105 17.9% 15.9% 13.4% 11.4% 9.7% 8.4%

120 17.2% 15.2% 12.5% 10.4% 8.8% 7.5%

135 16.6% 14.4% 11.6% 9.5% 7.9% 6.7%

150 16.1% 13.7% 10.9% 8.8% 7.2% 6.1%

165 15.5% 13.1% 10.2% 8.1% 6.6% 5.6%

180 15.0% 12.5% 9.5% 7.5% 6.1% 5.1%

195 14.5% 11.9% 8.9% 7.0% 5.6% 4.8%

210 14.0% 11.4% 8.4% 6.5% 5.3% 4.5%

225 13.6% 10.9% 7.9% 6.1% 4.9% 4.2%

240 13.1% 10.4% 7.5% 5.7% 4.7% 4.0%

255 12.7% 9.9% 7.1% 5.4% 4.4% 3.8%

270 12.3% 9.5% 6.7% 5.1% 4.2% 3.7%

285 11.9% 9.1% 6.4% 4.9% 4.0% 3.6%

300 11.6% 8.8% 6.1% 4.7% 3.9% 3.5%

315 11.2% 8.4% 5.8% 4.5% 3.8% 3.4%

330 10.9% 8.1% 5.6% 4.3% 3.7% 3.3%

345 10.5% 7.8% 5.3% 4.1% 3.6% 3.3%

360 10.2% 7.5% 5.1% 4.0% 3.5% 3.2%

375 9.9% 7.2% 4.9% 3.9% 3.4% 3.2%

390 9.6% 7.0% 4.8% 3.8% 3.3% 3.2%

405 9.4% 6.7% 4.6% 3.7% 3.3% 3.1%

420 9.1% 6.5% 4.5% 3.6% 3.3% 3.1%

435 8.8% 6.3% 4.3% 3.5% 3.2% 3.1%

435 8.8% 6.3% 4.3% 3.5% 3.2% 3.1%

Reduction of Oxygen Mass By Inert Gas Flow

Number of NozzlesTime

Minutes

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Table 5. Oxygen mass reduction by time for range of nozzles

from 150 to 660 while gas freeing a 15,000 cubic meter tank

150 220 330 440 550 660

0 5.0% 5.0% 5.0% 5.0% 5.0% 5.0%

15 5.7% 6.1% 6.6% 7.1% 7.6% 8.1%

30 6.5% 7.1% 8.1% 9.0% 9.8% 10.6%

45 7.2% 8.1% 9.4% 10.6% 11.7% 12.7%

60 7.8% 9.0% 10.6% 12.1% 13.3% 14.5%

75 8.4% 9.8% 11.7% 13.3% 14.7% 15.9%

90 9.0% 10.6% 12.7% 14.5% 15.9% 17.1%

105 9.6% 11.4% 13.6% 15.5% 16.9% 18.1%

120 10.2% 12.1% 14.5% 16.4% 17.8% 19.0%

135 10.7% 12.7% 15.2% 17.1% 18.6% 19.7%

150 11.2% 13.3% 15.9% 17.8% 19.2% 20.2%

165 11.7% 13.9% 16.6% 18.4% 19.8% 20.7%

180 12.2% 14.5% 17.1% 19.0% 20.2% 21.1%

195 12.6% 15.0% 17.7% 19.4% 20.6% 21.4%

210 13.1% 15.5% 18.1% 19.9% 21.0% 21.7%

225 13.5% 15.9% 18.6% 20.2% 21.3% 21.9%

240 13.9% 16.4% 19.0% 20.5% 21.5% 22.1%

255 14.3% 16.8% 19.3% 20.8% 21.7% 22.2%

270 14.6% 17.1% 19.7% 21.1% 21.9% 22.4%

285 15.0% 17.5% 20.0% 21.3% 22.1% 22.5%

300 15.3% 17.8% 20.2% 21.5% 22.2% 22.6%

315 15.6% 18.1% 20.5% 21.7% 22.3% 22.6%

330 15.9% 18.4% 20.7% 21.8% 22.4% 22.7%

345 16.2% 18.7% 20.9% 22.0% 22.5% 22.8%

360 16.5% 19.0% 21.1% 22.1% 22.6% 22.8%

375 16.8% 19.2% 21.3% 22.2% 22.6% 22.8%

390 17.0% 19.4% 21.4% 22.3% 22.7% 22.9%

405 17.3% 19.7% 21.6% 22.4% 22.7% 22.9%

420 17.5% 19.9% 21.7% 22.5% 22.8% 22.9%

435 17.7% 20.0% 21.8% 22.5% 22.8% 22.9%

435 18.0% 20.2% 21.9% 22.6% 22.8% 22.9%

Gas Freeing Inert Gas Filled Tank With Fresh Air

Time

Minutes

Number of Nozzles

13

DEVEVELOPMENT OF NOZZLE DENSITY FORM OF

DESIGN EQUATIONS

Equation 27 is converted into a density form by dividing both

sides of the equation by the volume V and substituting the

following definitions;

Since the total flow F is determined by the number of nozzles

and the flow through each nozzle, F can be expressed as:

where N is the number of nozzles and r is the flow rate through

each nozzle. Eq. A29 can then be expressed as:

Defining the nozzle density as

Eq. 34 becomes

Making the substitutions identified in Eqs. A30 through A34

yields the density form of Eq. A27.

In this form the volume of the tank no longer explicitly appears.

It is incorporated implicitly in the quantity Nd .

Finally, Eq. A37 can be simplified to facilitate its application

directly to designing the number of nozzles required for a tank

by setting c(t) to the objective oxygen percentage, cx , and

solving for Nd .

Taking the natural log of both sides and simplifying yields:

Equation 39 enables the nozzle density to be direction calculated

by specifying the objective oxygen density and the objective

time to reach the objective oxygen density.

The results of applying Eq. A39 are presented in Fig. 7 for the

objective of reducing the Oxygen content from 1,429 grams per

cubic meter of fresh air to 182 grams per cubic meter (5%) by

flowing inert gases into a tank with 3% Oxygen mass. Fig. 7

shows that if Oxygen reduction down to 182 grams per cubic

meter is desired to be achieved within 200 minutes, a nozzle

density of 40 nozzles per 1,000 cubic meters is required or one

nozzle per 25 cubic meters of tank volume. If the tank volume is

15,000 cubic meters, at least 600 nozzles are required.

Application of Eq. A39 to determine the number of nozzles

required in a tank to replace inert gases with free air within a

specified time period can be approached similarly to the process

described above.

Fig. 7. Time required to fully inert a tank as a function of the

nozzle density placement