653
1 INTRODUCTION
Inrecentyearswehaveseenthegrowinginterestin
theexploitationofseabeddeposits.Thisisduetothe
increaseindemandforminerals.Theuseofareasof
shelves in sea mining (Karlic 1984, Depowski et al.
1998)providesanumberofrawmaterials,notonlyoil
andgasbutalsomet
allicmaterialssuchastitanium,
zirconium,tin,gold,platinumandferruginoussands,
diamonds, phosphate rock, gravel and sand. The
increasing interest has been stirred in huge areas of
polymetallic nodules and polymetallic massive
sulphide (SMS)(Abramowski& Kotliński 2011, SPC
2013). However, their operation is associated with
ma
ny problems in science and technology (Sobota
2005).NautilusMineralscanboastaboutthebiggest
success to date leading exploitation at the depth of
approx. 1600 meters on Solwara
(www.nautilusminerals.com). Transport from the
seabedatsignificantdepthstothesurfacehasposed
thebiggestproblemsforresearchersanddesignersso
far. The proposed solutions to date have their
adv
antages and disadvantages (Sobota 2005, SPC
2013), the largest of which is their high energy
intensityaffectingthehighcost.Thereforethesearch
forlesscost‐intensivemethodshasbeendeveloping.
The Theoretical Basis of the Concept of Using the
Controlled Pyrotechnical Reaction Method as an Energy
Source in Transportation from the Sea Bed
W.Filipek&K.Broda
A
GHUniversityofScienceandTechnology,Krakow,Poland
ABSTRACT:Inrecentyearswehaveobservedtheglobalgrowinginterestinundersea exploitationofmineral
deposits.Researchonvariousconceptsofoperatingsystemsontheseabedhasbeenconducted,wheredifferent
methodsoftransportingexcavatedmaterialfromthebottomtothesurfaceareused.Greatdepths,wherethere
arethemostint
erestingresources(eg.IOMlotfortheClarion‐Clipperton4500m)setveryhightechnicaland
technological demandswhich results in intensive search for solutions. The authors of the paper want to
explain the concept of the use of pyrotechnic materials for tra
nsportation in the aquatic environment. The
presentedmethodisdesignedforthecyclictransportfromgreatdepths(lessthan200mfromtheseabed).The
principleofoperationoftherelayunitisbasedonthechangeintheaveragedensityoftheentiremodulewhich
isinseparablyconnectedwiththeforceofbuoya
ncyactingonthesubmergedbody.Changingthedensityofthe
wholemoduletothegivendepthofimmersionisstrictlydependentontheamountofenergysuppliedtothe
systembyapowersourceintheformofacontrolledpyrotechnicreaction.However,duringtheascentenergy
demanddecreases.Theproblemoftra
nsportofspoilfromdepthnotonlyboilsdowntosuchconsiderationsas
initiationoftheprocess ofascent.Oneshouldalsoconsiderhowtousetheexcessenergyoccurringduringthe
movement of the object toward the surface. The authors of the paper present the concept of ma
king the
transportofcyclicdepths(lessthan200mfromtheseabed)takingintoaccounttheoptimaluseofenergyfrom
controlledpyrotechnicreaction.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 4
December 2017
DOI:10.12716/1001.11.04.12
654
The authors proposed the implementation of a
newmethodwhich involvesthe use ofpyrotechnics
asasourceofenergyintransportfromtheseabedat
significant depths and presented its theoretical
aspects and also carried out experiments (Filipek &
Broda,2016,2017).Boththedepthwhichcanbeused
in this method and determination of the energy
requiredfortransportwereshown,dependingonthe
densityof thetransportedmaterial(output). Control
methodsforpyrotechnicreactionwerealsoproposed.
The results confirmed the possibility of the use of
pyrotechnic materials for the transportation from
significantdepths.
In the article
the authorscomparethree concepts
for the transport of excavated material from the
seabedintermsofenergydemand.
Considering the first concept, we are estimating
what amount of energy is needed to pull the load
from a certain depth to the surface. In the next
concept, based on hydraulic transport,
we define
minimum energy guaranteeing the output mining
from the seabed. In discussing the third concept,
basedontheuseofcontrolledpyrotechnicreactionas
asourceofenergyfortransportfromtheseabed,we
focus on the comparison of the method of
transportationwiththepreviousenergyconditionsin
ordertodetermineitssuitability.
Inourdeliberations,thebenchmarkisE
ppotential
energy. For greater transparency of considerations
relating to the first and second concept, we assume
thateverytransportedloadofmmassandVvolume,
can bereplaced with the theoretical sphere of r
radiusofthesameweightandvolumeand
density.
2 DETERMINATIONOFTHEMINIMUMENERGY
REQUIREDTOPULLTHELOADFROMH
DEPTH.
In our deliberations we skip rope impact on
movement issues. We assume that the load (output
and the container) has the shape of a sphere of r
radius.Theaveragedensityofthetransportedcargo
is
,andthedensityofthesurroundingfluidloadis
p. We are considering mining (transport) of cargo
fromHdepth.Theextractedload(emerging)outof
this depth of v velocity is affected by F
v resistance
forceof movementinliquid andthe Qpower being
thedifferenceintheweightofQ
cloadandbuoyancy
Q
w(1).
()
cw p p
QQ Q mgV g gV
(1)
Sincewehaveassumedthesphericalshapeofthe
load–V=¾
r
3
.Therefore:
3
4
()
3
p
Qgr
(2)
As the load moves towards the surface in the
liquid of significant density, we should take into
accounttheresistancetomotionwhich,foranobject
moving ina liquid vvelocity, canbe represented in
generalform(Roberson&Crowe1995,Tuliszka1980,
Duckworth1977)(3)
22
2
22
pp
vx x
vv
FC SC r
(3)
Where C
x means drag coefficient. The situation
aboveisshownschematicallyinFigure1.
Figure1.Distributionofforcesactingontheextractedload
fromHdepth
The amount of energy required for the ascent of
the object at the given depth to the surface without
theimpactoftheropeismarkedforthefirstmethod
with E
1. This energy is equal to the sum of the Ep
potential energy and the energy associated with E
v
movement:
1
p
v
EE E
(4)
E
p potential energy in accordance with generally
knownequationis equal tothe productof the force
andthedistance.Accordingtothis:
3
4
()
3
pp
EQH gHr
(5)
AndE
v–relatedenergyamountsto
2
2
2
p
vv x
v
EFHC Hr
(6)
InsumforE
1(7)
2
32
1
2
2
4
()
32
4
()
32
p
pv p x
p
px
v
EE E gHrC Hr
v
Hr gr C
(7)
Aninterestingfinding,accordingtotheauthors,is
what constitutes the ratio of the energy associated
withE
vmovementtoEppotentialenergy.Itshouldbe
notedthatthepotentialenergyisalwaysthesamefor
the depth and density of the fluid, and the energy
associated with the movement depends on the
velocity and this is the only type of energy that we
cancontrol(velocitychange),andithas
animpacton
transportcosts.Thisratiotakesthefollowingform:
655
2
2
2
2
3
3
2
4
8
()
3
p
x
p
vx
pp
p
v
CHr
EC
v
Cv
Egr
gHr
(8)
where:
31
8
p
x
p
C
C
g
r
Aftertransformationof(8)weobtain:
2
vp
ECEv
(9)
Substitutingtheaboveequationin(4)formula,we
obtain:
22
1
(1 )
pp p
E E CE v E Cv
(10)
Fromtheaboveequationitcanbeconcludedthat
thetotalenergyE
1isthesquarefunctionofvvelocity
ofthetransportedload.
3 DETERMINATIONOFMINIMUMENERGY
GUARANTEEINGTHATTHELOADWILLBE
TRANSPORTEDINTHEMOVINGFLUID
The starting point for our consideration is to
determinetheminimumfluidv
pvelocityatwhichyou
wecanbalancethetransportedweightadoptedinline
withtheshapeofasphere.
Inourdiscussion,weassumealsothatthesphere
does not move or v = 0 (equilibrium). Under this
assumption,F
vresistancemovementinthefluidwill
bedirectedagainstQforce.Thissituationispresented
inFigure2.
Figure2.Thedistributionofforcesactingonthestationary
loadinamovingfluid.
Inthecaseinquestionwhenv=0forcesQandFv
mustbeequal.Thus:
v
QF
(11)
Aftersubstituting(2)and(3)valuesforv
pvelocity
weobtain:
2
32
4
()
32
pp
px
v
g
rC r
(12)
From this equations we determine the desired v
p
velocityoftheliquid:
2
8
3
p
p
xp
g
vr
C
(13)
In order to check the accuracy of our
considerations, we calculate E
v equations (for vp
velocity), which is marked as E
vp to Ep. For the case
when v = 0 this equations should constitute 1.
Therefore:
2
2
2
3
3
2
4
8
()
3
p
pp
x
v
p
p
x
pp
p
v
CHr
E
v
C
Egr
gHr
(14)
Substituting the following equation (13) into the
formulabelowweobtain:
318 1
1
83 1
p
v
pp
x
ppxp
E
C
g
r
Eg rC
(15)
In this way we may conclude the correctness of
ourreasoning.
Inthenextstepwewillmovetheloadinsidethe
pipe ofR radiusandH length(height),wherein the
loadistransportedtothesurface.Velocityofthefluid
inthepipelineisv
pandthedensity
p.Figure3shows
thiscase.
Figure3. Spherical load within the pipeline, wherein the
fluidismovingataspeedv
pinastateofequilibrium.
LetusconsidertheabovecasewheretheforcesQ
andF
vareequal,i.e.,loadisatrest(rateofloadascent
v = 0). In our deliberations we have to take into
account the energy needed to impart v
p velocity for
thefluidinthepipelineandtheenergylossline.We
donottakeintoaccountthelocalloss,whichactually
occurs because we consider the simplest case of a
simplepipeline.Infact,duetotheomittedloss,local
energy demand will be far greater. Starting from
Hagen‐Poisseuilleequation(Roberson&Crowe1995,
Tuliszka 1980, Duckworth 1977), we determine the
linearlosses(intheformofpressureloss):
2
22
pp
L
v
H
p
R
(16)
656
ThusE
slossenergyequals:
s
L
E
pV
(17)
whereVisthevolumeofliquidflowingatv
pthrough
theperpendicularsectionofthepipelineofRradius
andinttime.Thus
2
p
VRvt
(18)
whereas flow time can be determined in a simple
equationt=H/v
p.Aftersubstitutionweobtain:
22
p
p
H
VRv RH
v
(19)
Finally,lossenergywillamountto
2
2
22
22 4
pp
s
pp
v
HH
ERHv
R
(20)
Total energy E
2 required that the load is in a
steadystate(v=0)isthesumoftheenergiesE
sand
lossofkineticenergyE
kliquid
2
s
k
EEE
(21)
After substituting (20) equation to the formula
aboveandtheknownequationforkineticenergywe
obtain
22
2
2
1
222
pp pp
L
vv
H
EpV VRH
R
(22)
Substitutingequation(13)totheformulaabovewe
obtain:
2
2
2
8
1
22 3
4
() 1
32
pp
xp
p
x
Hg
ERH r
RC
RHg H
r
CR
(23)
Comparingtheresultantenergydependenceofthe
potentialenergyrequiredtotransporttheload(5),we
obtaintheequation:
2
2
2
2
3
4
() 1
32
1
1
4
2
()
3
p
x
px
p
RHg H
r
CR
ERH
ECR
r
gHr
(24)
Comparing the parameters appearing in the
formulaabove,weconcludethatthisratiowillalways
assume the value greater than 1 and thus the total
energyneededtomaintaintheloadatsteadystateis
alwaysgreaterthanthepotentialenergy.
4 THECONCEPTOFOPTIMIZINGTHEUSEOF
ENERGYFROMTHECONTROLLED
PYROTECHNICREACTIONINTRANSPORT
FROMTHESEABED.
Inourpaper(Filipek&Broda2016)wedemonstrated
thatthedescription ofthe pressure distributionas a
functionofdepthisvirtuallyimpossiblewithoutthe
knowledge of the local change of the density of
liquidswiththealtitudeand
thelocalchangesinthe
gravitational acceleration of depth. Therefore, we
assumedthatthepressureof1barcorrespondstothe
pressureof10mofwatercolumn(0.1MPa).Or
5
2
7
2
1[ ] 10 10 [Pa] 0,1[MPa]
100 [ ] 1 10 [Pa] 10[MPa]
bar mH O
bar kmH O
(25)
From the considerations set out in the papers
(Filipek& Broda,2016,2017) itturnsoutthatinthe
case of using a controlled pyrotechnic reaction as a
source of energyfortransport from the seabed, two
main reaction products emerge, namely carbon
dioxide and nitrogen. Due to the
low pressure of
condensation (e.g. at as low pressure as 4 MPa at
temperatureof4°C(277 K),whichcorrespondstothe
pressure at depth of 400 m, carbon dioxide is
transformed from a gas to liquid) we can therefore
regarditasanadversereactionproductwhichshould
be
eliminated. At pressures above 22 MPa (which
corresponds to the depth of 2200 m), the density of
the liquid CO
2 is greater than the density of water.
Accordingly,theCO
2asthereactionproductbecame
anegativeballast.
Let us assume that in further consideration the
working medium will be pure nitrogen at a
temperature equal to the temperature of the
surrounding fluid. This does not mean that our
conceptofcyclictransportofCO
2willnotbeincluded
asaworkingmedium.Worksonthesolutiontothis
problem are underway and the results will be the
subject of subsequent publications. In further
discussion, in order to determine the hydrostatic
pressureandmediumdensityρp,wherethetransport
takes placewe adoptedclean water.
Justificationfor
the choice were presented in the paper (Filipek &
Broda 2016).Graphsofthe density of water, carbon
dioxideandnitrogenpressure(hydrostaticpressure),
temperatureof4°C(277K)areshowninFigure4.
Figure4. The dependence of H 2O, CO2 and N2 densityon
pressure (based on data from the
http://www.peacesoftware.de/
einigewerte/einigewerte_e.html).
657
Thearticle(Filipek&Broda,2016)introducedthe
equation(26)determiningtheratioofthetotalenergy
topotentialenergyinrelationtotheconceptofusing
a controlled pyrotechnic reaction as a source of
energyfortransportfromtheseabed:
3
p
pp
E
E
(26)
wherein in our discussion ρ
α is the density of the
controlled pyrotechnic reaction cooled to ambient
fluid.Inviewoftheabovedescribedassumptions,ρ
α
is therefore density of nitrogen at a given pressure
(hydrostatic pressure) and at a given temperature.
The above relationship as function of pressure is
showninFigure5.
Figure5. Relationship of total energy E3 to the potential
energyE
ptoppressurefornitrogenastheworkingmedium.
Inourconcept, inorder to retrieve theload of V
volume and ρ density, we should generate Q
w
buoyancybycreatingV
αvolumeandραdensityasthe
result of the controlled pyrotechnic reaction. The
desiredVαvolumecanbederivedfromtheequation
(Filipek&Broda,2016):
p
p
VV
(27)
In fact, V
α value is closely related to depth, and
hence to the hydrostatic pressure. Due to this fact,
morecorrectformof(27)equationis(28)
()
()
() ()
p
p
p
Vp V
pp
(28)
During the ascent the difference between inner
andouterpressureincreases.Inordertoachievethese
pressurestocompensate,theexcessnitrogenmustbe
dissipated or we have to increase the volume
occupiedby nitrogenproportionatelyto theincrease
ofhydrostaticpressure.Consequently,thedensityof
nitrogen will change
(decrease) resulting in an
increase in Q
w buoyancy. Due to the increasing
buoyancy, theload amountcan beincreased. Let us
consider a case in which V
generated at a given
depthisnotchangedduringtheascent.Assumethat
atagivendepthfromwhichwebegintoconsiderthe
processofloadtransportthevolumeamountstoV=
Vo. In addition, we assume that the volume V
(p)
generatedatagivendepthamountstoV
and
p(p)=
po and
(p) =
o. Rearranging (28) equation, we
obtainthefollowing:
() ()
()
()
p
p
pp
Vp V
p
(29)
Therefore,theincreaseinbuoyancygeneratesthe
possibility of increasing the amount of the
transported load of
density by additional
V
volume. Having included the above variables we
obtainthefollowing
() ()
()
()
ppoo
o
ppo
pp
VVp V V V
p
(30)
Calculating
V/Vo relationship, we obtain the
followingequation:
() ()
1
()
ppo
oppoo
pp
V
Vp
(31)
Nowimaginethatthetransportsystemconsistsof
sequentiallyconnectedserial(vertical)equaltransport
elements. Let us consider what additional load our
systemcantransportinrelationtotheadoptedinitial
loadofV
ovolume.Todothis,increasesthevolumeof
the individual elements of the transport system
should be added, which we can express in the
followingequation:
() ()
1
()
() ()
1
()
ppo
oppoo
i
ppo
ppoo
ii
V
Vi
ii
di
i
(32)
The analytical solution of the above equation
exists. The authors worked it out but because of a
complicated form authors used in this case, the
iterative method is applied, assuming that the
lowermost part of the system is at a depth
correspondingtothepressureof100MPaat
adepth
corresponding to the final pressure of 1 MPa. The
individual elements of the transport system are
spaced (vertically) with a distance corresponding to
thepressureof1MPa.
The results are shown in the graph (Figure 6),
assumingthat
o=
/
ppwhere
ppisthedensityofthe
fluidatthesurface.Fromthegraphitisclearthatthe
system has a large reserve of energy as such for
examplefor
o=2systemitcanalsotransportthe36‐
times the volume of transported load in one V
o
segment, of course, with the established intervals
betweenthesegments.
In the next step we will try to determine how
much energy we are able to recover with the
previouslymadeassumptions.
658
Figure6. The relationship of the growth times of the
transported V
o volume todensity oftransported
load in
relationto
ppfluiddensityatthesurface.
Letusconvert(26)intothefollowingform:
3
p
p
p
EE
(33)
WhereE
ppotentialEnergycanbeexpressed with
thefollowingequation
p
p
p
EpV
(34)
which was derived in Filipek & Broda (2016).
Substituting(34)into(33)weobtain
3
p
p
EpV
(35)
E energy increase resulting from V volume
increaseamountsto:
E
pV
(36)
Consideringrelation
E/E3weobtain
3
1
ppop
p
po o p
E
E
(37)
Forthewholetransportsystemwiththeprevious
assumptions(37)equationtakesthefollowingform:
3
()
()
() () () ()
1
() ()
E
i
ppop
ppoo p
Ei
Ei
ii ii
ii
(38)
On the basis of the equation we can compile a
graph(Fig.7)
Figure7. Relation of multiplicity factor to the related
densityofthe
transportedloadto
ppfluiddensityatthe
surface.
Inthegraphwecanclearlyobservetheextremum.
The optimal energetic status of the system
correspondstothisextremum.
5 CONCLUSION
Inthispaper,consideringenergydemandinthethree
concepts of output transport from the seabed, the
authorsadoptedinfactNewtonʹsfirstlawasapoint
of
reference:ʺif the body does not act affected by
external forces, or the forces are balanced, the body
remains at rest or moves with rectilinear uniform
motionʺwhich is the development of the Galileo’s
ideas (Halliday &Resnick 1978, Feynman 1963). He
noted that if we remove the obstacles to the
movement,itwillnolongerbenecessary tosupport
the movement by any force. Rectilinear uniform
motion will be performed by itself, without any
externalhelp. Suchmovement issometimes referred
toasfree movement.Suchadoption ofthereference
pointallowsto determineenergy demand, butfrom
the physical point
of view wehave to take into
considerationthreedifferentcasesinfactalthoughin
each case operating forces are balanced. In the first
case, considered transported load to be taken to the
surface is held at a constant v velocity, therefore,
accordingtoNewtonʹsfirstlawofmotion
themotion
is rectilinear and uniform. In the second and third
case the v velocity of the objects equals zero. As a
result,theoreticallyconsideredobjectwillneverreach
the surface. However, both these cases also
substantiallydifferfromeachotherphysically.Inthe
secondcasewehavefromthephysical
pointofview
the so called system of stable equilibrium (Halliday
&Resnick 1978, Feynman 1963) and unless
deliberatelyintendedotherwise,thebodyisatrest.
In order to retrieve the transported object to the
surfacewemustprovideadditionalenergywhichwill
be greater than the value determined from the
equation (23). While in the third case under
consideration we have, from the physical point of
view, the system of the so called unstable balance
(Halliday &Resnick 1978, Feynman 1963). Slight
deflectionoftheobjectinquestionfromthepointof
equilibrium results in the freedom of movement
without the need
to provide additional energy. In
ordertocomparethesethreeconceptsunambiguously
659
for the transport of load from the seabed to the
surface, we must clearly align the method based on
which will base the comparison. Assume that the
reference is the minimum energy E
o necessary for a
considered object to remain at rest v = 0, that is, a
steadystateandprovidingahigherenergyE
o=E+dE
allowedto startthe processof itsascent. Inthe first
considered case for v = 0, we obtain, in accordance
withequation(10),E
1=Ep=Eo.
Inthe lattercase ofconverting theequations (24)
weobtain:
22
2
22
11
11
22
po
xx
RH RH
EE E
CR CR
rr
(39)
InthisequationC
xisunknown,theva lueofwhich
in a general way, we are not able to determine
without knowing the geometry of the load being
transported by pipeline of R radius. Assumption
adoptedearliertoreplacethisloadwithasphereisof
coursecorrectwhenitcomestosucha
sizeasV,rand
.ItdoesnotconcernCxparameter.
Aroughvalueofthisparametercanbeestimated
asC
x<1.TheratioR/rcanbereplacedbythevalueof
volume concentration C
v (Sobota 2005) which has a
valuewithinarangeoffrom0.1to0.16.LinearDrag
coefficient falls between 0.0076 to 0.0101 (Sobota
2005).Rvalue,however,isgenerallylessthan1[m].
Fromtheseconsiderationsemergesapictureofavery
energy‐intensive methods of transporting excavated
material
fromtheseabedtothesurface.
Morepreferred approachis tousethemethodof
controlledpyrotechnicreactionasasourceofenergy
in transport from the seabed. In the case, when the
workingfluidisnitrogenratioofE
3toEoisshownin
Figure5,whichshowsthatthisratiodoesnotexceed
2.4.Thismethod, however,is moreenergy‐intensive
thanthemethodanalyzedasfirst.However,thereis
one very positive aspect of this method. In the first
method, there is an additional demand for energy,
which is
directly proportional to the square of the
speedofascentobjectonthesurface.Inthecaseofthe
thirdmethod,onceinitiated,the processof ascentis
theoreticallyself‐supported.Additionally,itgenerates
excessenergythatcanbeexploited.
InFigure6andtheequation(31,32)itisevident
thattheapplicationofcontrolledpyrotechnicreaction
asasourceofenergyfortransportfromtheseabedis
muchmoreadvantageousinthecaseofusingaserial
connection than the conveying elements for the
transportofasingleload.
ACKNOWLEDGMENTS
This article was written within Statutes Research
AGH,No.
11.11.100.005
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