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Water Resour Manage (2010) 24:1645–1675DOI 10.1007/s11269-009-9518-y

Transatlantic Freshwater Aqueduct

Viorel Badescu · Dragos Isvoranu ·Richard B. Cathcart

Received: 5 August 2008 / Accepted: 6 October 2009 /Published online: 22 October 2009© Springer Science+Business Media B.V. 2009

Abstract This paper offers a technical and geopolitical reappraisal of a macro-engineering proposal to plumb Earth’s freshwater, siphoning some of it from a regionof surplus (Amazon River Basin) to a region of shortage (arid northern Africa) viahis positively buoyant (subsurface floating) seabed-anchored Transatlantic Freshwa-ter Aqueduct. Two different routes for the pipeline, of length 4,317 and 3,745 km,respectively, have been considered. Pipe diameters larger than 60 m are necessaryfor “reasonable” low pumping power (i.e., less than 20 GW). Using a bundle ofsmaller size pipes instead of a larger single pipe might overcome technical difficultiesbut the advantage of simplifying the construction technology might be exceeded bythe disadvantage of consuming more power in operation. To keep the number ofpumping stations reasonably small (i.e. fewer than 20) a single pipe of diameterhigher than 30 m (or bundles of smaller diameter pipes) is required. The AtlanticOcean currents may be used to provide the necessary power for pumps. The availablepower possibly provided by the North Brazil Current ranges between 2 and 9 GW.The North Equatorial Current may provide less than 0.3 GW power while the NorthEquatorial Counter Current provides the largest power availability, ranging between

V. Badescu (B) · D. IsvoranuCandida Oancea Institute, Polytechnic University of Bucharest,Spl. Independentei 313, Bucharest 060042, Romaniae-mail: [email protected]

D. Isvoranue-mail: [email protected]

R. B. CathcartGeographos, 1300 West Olive Avenue, Suite M, Burbank, CA 91506, USAe-mail: [email protected]

1646 V. Badescu et al.

2 and about 100 GW. A rough cost estimate of the project is about 20,600 GUSD and18,400 GUSD, respectively, for two pipeline routes.

Keywords South America · Amazon River · Northern Africa ·Bulk freshwater transfer · Undersea floating pipeline · Macro-engineering

1 Introduction

Freshwater garnishment macro-projects involve artificial large-scale bulk transfersof that vital fluid over great geographical distances under applied forecasting andmanagement conditions, from regions of surplus to regions of deficit, for the eco-nomic purpose of social advancement of the drier region by subsequent agriculturaland industrial development (Tvedt et al. 2006). In some significant cases, however,the reverse situation exists. For example, the possibility of an Alaska-CaliforniaUndersea Aqueduct furnishing a reliable long-term freshwater supply solution forCalifornia’s chronic urban freshwater shortages was considered from 1965 until 1991(California Undersea Aqueduct 1975). Also, unsettling early twenty-first centuryhydrological news that the Colorado River’s runoff is decreasing due to measured re-gional climate change has positively stimulated the political prospects in California ofthat old macro-project proposal as a possible urban water supply semi-replacementinfrastructure (Barnett and Pierce 2008).

The Amazon River accounts for ∼15% of global runoff but this potentially usefulfreshwater runoff (2 × 105 m3/s, with fluctuations within its predictable climateregime variability pattern (Milly et al. 2008; Garreaud et al. 2009) loses its socialand commercial value as it mixes with the saltwater of the Atlantic Ocean. Thesebasic facts of modern human life inspired Heinrich Hemmer to propose an audaciousanchored submarine floating oceanic freshwater pipeline macro-project connectingSouth America’s water-surplus Amazon River Basin with the arid landscape ofnorthern Africa. “A pipeline stretching from the mouths of the river Amazon [nearMacapá, Brazil, at 0◦ 15′ 0′′ North Latitude by 51◦ 10′ 0′′ West Longitude] toNorth Africa would be about 4,300 km-long. At a speed of 2 m/s and a capacity of10,000 m3/s, it would have a diameter of 80 m. . . . Calculating a demand of 10,000 m3

fresh water [per] hectare per year, 315,000 km2 could be fully irrigated” (Hemmer1993).

Published by the UNO in 1997, the FAO Land and Water Bulletin 4, “Irrigationpotential in Africa: a basin approach”, substantiated the imported freshwater Saharairrigation demand assumption made by Hemmer. Currently, part of the Sahara isirrigated using vertically pumped groundwater but that supply is slow to rechargenaturally and hydrological experts in Libya predict that the practice will be forcedto cease circa 2060. Therefore, freshwater imports to the Sahara will be requiredsometime after the mid-twenty-first century. In the geographical context of northernAfrica, desalination—currently costing ∼USD 1–3/m3—is deemed to be the compe-tition for Hemmer’s macro-project and, in this sense, will set the price ceiling whenall other factors such as security and environmental impacts have been taken intoaccount (Dore 2005). In most cases, vertical distance is the primary driver of potablewater conveyance costs, not the horizontal distance (Zhou and Tol 2005).

Transatlantic Freshwater Aqueduct 1647

However, some irrigation and drainage macro-engineering experts have assertedthat the twenty-first century world has exited an “Age of Water Development” andentered an “Age of Water Management”. “Though there is still much undevelopedwater in the Amazon and Congo rivers, the total development, pumping, andtransportation costs are likely to exceed the value of this water before it gets to theplaces where it is most needed” (Allison 2003). In this context, a closer look at theTransatlantic Freshwater Aqueduct (TFA) macro-project is useful. In the following,the TFA macro-project is analyzed in some detail from technical, economical andenvironmental points of view.

2 Macro-Engineering Relevancy

Until circa 1965, the conception and management tasks associated with geograph-ically and economically large-scale infrastructure construction macro-projects (alsosometimes called “mega-projects”) were typically overseen by civil engineers. Asmacro-projects become more and more complex to complete, and globalization ofthe world’s ecosystem-nation economies proceeds further during the twenty-firstcentury, the challenges associated with the management of these macro-projectsbecome more complicated. The importance of global and regional coordination inconservation is increasing and between-country collaboration seems to be a socialand economic necessity. Macro-engineers deal mostly with the conception of na-tional, international and extra-terrestrial infrastructures (Badescu et al. 2006; Beech2008). Modern macro-engineers utilize new and versatile materials, wield honedskills in the prediction of behaviors of built structures under varying loads, employnew technical capacities for moving earth, air and water and, as well, up-to-dateorganizational techniques for managing the material and power logistics and human(even, sometimes, robotic), labor required of geographically large-scale macro-projects (Singh 2007). Circa 2009, construction is big business with yearly worldwideexpenditures totaling ∼4,000 GUSD, with about one eighth of that devoted mainlyto water supplies building activity (maintenance, up-grading of obsolete installations,new infrastructure).

One of the most remarkable results possible with the TFA macro-project isthat an entirely novel kind of intercontinental (South America-northern Africa)and international “watercourse ecosystem” integration will be the ultimate macro-engineering product achievement goal. The TFA infrastructure is an oceanic macro-engineering project proposal of greater complexity than any tackled previously(Schuiling et al. 2005, 2007; Badescu and Cathcart 2008) and, therefore, required toconsider political risks, innovational risks, and organizational risks, weather extremes(in desert, jungle and oceanic), transient workforces, likely human labor constructionerrors, to name a few.

While the climate regime of the Sahara will remain much as it is nowadays fora very long period to come, the Amazon River Basin’s climate regime is projectedto change markedly and severely by 2100 if global changes that include atmospherewarming continues at the supercomputer-modeled pace (Williams et al. 2007; Cookand Vizy 2008). Specifically, for the Amazon River Basin, a dramatic ecological shiftis forecast, but no reliable useful forecasting details are given. It is a fact that, untilrecently, water policy makers in Brazil and elsewhere underestimated past human


exploitation of the Basin’s resources (Heckenberger 2009). Some geoscientist nowsuggest that reforestation of the Amazon River Basin, abandoned after pandemicsinstigated by early European explorers and settlers, drastically reduced the numbersof native Amazonians by tens of millions approximately 500 years ago, and maythus have caused the so-called “Little Ice Age” in Europe (Nevle and Bird 2008).Nowadays, deforestation seems to be the main effect of human inhabitation of theBasin.

Currently, the Amazon River discharges ∼6,300 km3 annually, politically gov-erned by, in part, the “Treaty for Amazonian Cooperation” signed by appropriateecosystem-country representatives on 3 July 1978 (Landau 1980). On 23 May 2008,12 South American ecosystem-nations signed the Union of South American NationsTreaty, UNASUL (Uniao de Nacoes Sul-Americanas, in Portuguese). Just how, orif, this historically recent agreement will affect the in-force 1978 Treaty is unknown.Indeed, one hopes that legal imposition of the TFA macro-project will assist in theongoing political and scientific effort to preserve the enormous catchment’s forestedterrain by imposing a consumer demand limitation factor on the Amazon RiverBasin’s owners (Kindermann et al. 2008).

During June 2008 Brazil and Venezuela signed an agreement to cooperate intheir shared part of the Amazon River Basin to help preserve the rainforest, ofwhich Brazil legally controls ∼63%. Note, however, that most of the AmazonRiver’s freshwater derives from the glaciers and rivers draining the eastern slopeof the Andes, especially Peru and Ecuador (Goulding et al. 2003). With lowlanddeforestation there will, of course, be more fluvial erosion of the land, muddying thewaters to some unpredictable future state. There are, however, numerous conflictingreports of Amazon River Basin deforestation rates and some science journal reportsstate that deforestation has diminished or even stopped. The unlikely possibility ofcomplete Amazon River Basin deforestation is not considered herein.

Brazil has become a food-producing and food-exporting Superpower and yet“Brazil could, in principle, triple its area under cultivation over time—without fellingany more rain forest” (Omestad 2008). Inter-basin freshwater transfer is sometimesconsidered in this context, despite Brazilian legislation that does not cover thissituation, and future geopolitical conflicts may arise (De Carvalho and Magrini 2006).Whilst some freshwater supply experts would likely suggest the intra-Brazil waterdiversion from the Amazon River to the semi-arid northeast regions of Brazil, thismacro-engineering option remains open even with construction of the TFA. (Similarshorter diversions of freshwater have already been proposed for the Congo River inCentral Africa).

3 Transatlantic Freshwater Transport—Bag Trains or a Pipeline?

It was after 1850, when the first undersea telegraph cables had been successfully laid,that the Earth’s ocean, and its seafloor, became a human destination rather thanmerely a barrier or byway to commercial transport and telecommunication (Bouma1990). During the final decade of the twentieth century, Aquarius Water Trans-portation became the first private-sector company to tugboat-tow very capaciouspolyurethane bags—sometimes dubbed “Medusa bags” or “Dracones”—containingdrinkable freshwater to various isolated, water-deficit Cyclades Islands offshore of


mainland Greece. Dracone technology of 1956, then consisting of sausage-shaperubberized cotton dinghy fabric bags invented by the UK engineer Sir WilliamRede Hawthorne, was first commercially deployed to service the Greek islandscirca 1962. Freshwater shortages still plague the Greek islands and supplementalmeans, such as dedicated tanker ships and land-based desalination plants on theislands are being considered by authorities (Kaldellis and Kondili 2007). From 2000,another commercial entity, Nordic Water Supply, commenced deploying similar20,000 m3 floating bags that transport bulk freshwater from Turkey to northernCypress. Dracones with capacities of ∼35,000 m3 were proposed as supplementsto the inadequate, sometimes catastrophically dwindling, freshwater supplies ofcoastal cities in India (Cathcart 2005). To make freshwater delivery economicallyeffective by this means, the vital-to-life and industry fluid must be transported in largediscrete volumes, ideally in quantities >250,000 m3. A towable plastic or waterprooftensioned textile floatable bag of ∼250,000 m3 would likely be about 350 m longby 72 m wide with a depth thickness of approximately 14 m. Since the density ofseawater is nearly 3% more than freshwater, a Dracone or Medusa bag will floatanywhere on the ocean’s surface with a freeboard of ∼2.5–3% of the total fabric/filmbag’s thickness. In other words, for a flexible fabric/film freshwater-carrying bag atleast 14 m thick the maximal freeboard will be ∼420 mm, resulting in a pressure of∼4.2 kN/m3 exerted on the container’s membrane at the waterline, reducing to nil atits greatest floatation draft below the seawater’s sub-aerial surface interface with air.

An investigation of the prospects of a turn-key macro-project for the bulk transferof freshwater from Turkey to northern Cypress via a ∼750 km-long submergedbuoyant pipeline fabricated of high-density polyethylene, to be anchored to theMediterranean Sea’s bed by vertical anchor wires, was approved by the TurkishGovernment Decree No. 98/11202 of 27 May 1998. The emplaced seabed anchors(the design characteristics of which were unspecified or undisclosed) were intendedto be spaced about 500 m apart. Turkey assigned leadership for the proposed macro-project to Alsim-Alarko A.S., a holding company of a Turkish group of companieswhich has been trading as “Alarko” since 1972, and the company offered a finishedFeasibility Report to the Government by 1999. The Government required the posi-tively buoyant submarine freshwater pipeline, with an inside diameter of 1.48 m, tohave the capability and volume capacity to convey gravitationally 75 × 106 m3/year—that is, a volumetric flow of 2.38 m3/s. Investigating engineers found that wall-frictionis the dominant cause of hydraulic losses and that temporary under-pressurizationsand water hammer caused by valve openings/closures do pose major problems tothe sustained, successful installed operation of the post-Dracone era pipeline macro-project facility. As of 2009, the planned bulk freshwater transfer facility in the easternMediterranean Sea Basin linking mainland Turkey with Cypress remains unbuilt.

The macro-engineering project concept of an extended tubular-shaped submergedfloating pipeline carrying only bulk freshwater seems to have been invented byMcCammon and Lee (1966). The idea was then adopted by Ellis L. Armstrong(1972), briefly surveyed in 1974 by Yuri M. Savvin, popularly revived by Joseph G.Debanne (1975) and the US Department of the Interior’s Bureau of Reclamation,also in 1975, and finally in an ahistorical context by Ernst G. Frankel (1998).Rather surprisingly, none of these individuals, or teams of macro-engineers, evermentioned the possibility of additional supplemental carrier uses for very long-distance submerged positively buoyant freshwater oceanic pipelines—uses such as,


for example, undersea telephonic cables or, later, low-mass and high-capacity fiber-optic telecommunications cables. In terms of twenty-first century telecommuni-cations, optical fiber reduces every other transmission medium to insignificance(Huurdeman 2003). There is only one submarine telecommunications cable connect-ing Argentina in South America with Senegal in Africa via the Cape Verde Islands—the 8,500 km-long Atlantis-2, operational since 1999.

4 TFA Model

The TFA might be constructed with assembled lengths of steel pipe. Alternatively,the TFA may consist of an inflatable large-diameter plastic or modern tensionedtextile material (Davenport 2004). Such a barely-submerged hose-like pipe would bea double-walled, honeycombed structure of flexible or textile material manufacturedas needed in a dedicated land-based factory and/or aboard an efficient fabricationship at sea. Freshwater should be injected into the cavity between the twin-walledbendable hose-like freshwater conveyances before, finally, the tubular TFA is fullycharged with deliverable freshwater. Pressurizing the freshwater will, thus, engorgethe pipeline, producing a stiff structure. The steel-made or hose-like TFA will bepositively buoyant, and anchored at a floating depth of ∼100 m beneath the AtlanticOcean surface (Fig. 1).

4.1 Possible TFA Routes

The distance between the starting point of the positively buoyant (subsurface float-ing) seabed-anchored TFA pipe and a given location on the seashore was evaluatedby two analytical procedures, i.e. by considering the orthodrome and loxodromepath, respectively. These procedures (which are described in “Appendix”) are usefulwhen the geographical co-ordinates of both geographical locations are known. Athird, combined analytical-numerical procedure, was also used to find the distancebetween the Amazon River freshwater intake location (described by its latitudeand longitude) and the closest unloading location on the African land for a given(loxodrome) direction. This procedure uses the accurate Atlantic Ocean bathymetry

Fig. 1 Part of a submergedfloating pipeline with anchorlines arranged at intervalsand in a V shape and withbuoyancy elements arrangedfor each anchor point. 1 pipe;2 anchor line; 3 buoyancyelement; 4 anchor point


data given by Smith and Sandwell (1997). The estimates by the three procedures,though close to each other, actually do not coincide.

Two different routings for the pipeline have been considered (Fig. 2). Nouakchott,Mauritania (18◦ North Lat. by 15◦ West Long.) might be one appropriate unloadingterminal for TFA since its contents could fill an overland pipeline planned to belaid across the Sahara (Charlier 1991). If it is created, Charlier’s trans-Sahara canal-pipeline, could water farms, gardens and cities shaded from the sun beneath a SaharaTent Greenbelt (Cathcart and Badescu 2004). Mauritania’s socio-economics, duringthe twentieth century, was based mainly on extractive industry (Bennoune 1978);installation of the TFA would introduce a major import component to the nationaleconomy. If the TFA pipeline starts in the mouth region of the Amazon River at theEquator in South America (0◦ North Lat. by 50◦ West Long.) and its terminus is atNouakchott (Route 1) that amounts to a distance (on a great circle) of 4,317.18 km.In case the TFA pipeline terminates at Conakry, Guinea (10.57◦ North Lat. by17.83◦ West Long.; Route 2), the distance (on a great circle) is 3,745.49 km. Publicfreshwater supplies in Conakry, Guinea were reformed by the early-twenty-first

Fig. 2 Two possible routes for the Transatlantic Freshwater Aqueduct


century, yet remain rather inadequate and can be enlarged and improved markedly(Clarke et al. 2002). The difference in length between Route 1 and Route 2 is 621 km,which is about 14% of the length of Route 1.

Figure 3 shows the bathymetry of the Atlantic Ocean for the two routes (i.e.Route 1: Amazon River mouth–Nouakchott and route 2: Amazon River mouth–Conakry). One can see that Route 2 is more advantageous from the point of viewof the free-falling torpedo anchors necessary to stabilize the TFA pipeline. Indeed,the length of the cables for Route 2 is between 3,500 and 4,500 m while for Route 1the cable length ranges between about 3,000 m and nearly 6,000 m.

4.2 TFA Using a Single Pipe

4.2.1 Pumping Power

As a first scenario a TFA consisting of a single pipe will be considered. The pumpingpower Ppump [W] required to force the movement of the freshwater in the pipe isgiven by:

Ppump = Q�ppipe (1)

where Q [m3/s] is the volumetric flow rate, �ppipe [Pa] is the linear pressure dropalong the pipe (i.e. �ppipe ≡ pinlet − poutlet, where pinlet and poutlet are the freshwaterpressure at the inlet and outlet of the pipe). Local pressure drops were neglected inEq. 1. Given the expected unusually large size of the pipe and the large volumetricflow rate, the common Nikuradse and Moody diagrams are of little help in orderto assess a realistic friction coefficient for evaluating the specific pressure drop�ppipe. Hence, we preferred to simulate the freshwater flow in the duct based on theincompressible isothermal Reynolds averaged Navier–Stokes equations. Steady-stateis accepted here. The scalable k-epsilon scheme has been used as closure turbulencemodel. A few details about the model are given next. The continuity equation is:

∂

∂x j

(v j

) = 0 (2)

Fig. 3 Atlantic Oceanbathymetry for the twoselected routes chartedin Fig. 1


where the bar above a quantity means a Reynolds average, x j( j = 1, 2, 3) [m] arespatial coordinates and v j( j = 1, 2, 3) [m/s] are freshwater velocity components. TheEinstein summation rule is accepted here and in the following. The conservation ofmomentum reads:

ρ∂

∂x j

(v jvi

) = − ∂ p∂xi

+ ∂

∂x j

(tij − ρv′

iv′j

)(3)

where ρ [kg/m3] and p [Pa] are freshwater density and pressure, respectively, theprimes denotes fluctuating quantities. The viscous and turbulent stresses, tij [Pa] andτ ij [Pa], respectively, are defined as:

tij ≡ μL

(∂vi

∂x j+ ∂v j

∂xi

)(4)

τ ij ≡ −ρv′iv

′j = μt

(∂vi

∂x j+ ∂v j

∂xi

)− 2

3ρkδij (5)

μt ≡ Cμρk

2

ε(6)

where μL [Ns/m2] is laminar dynamic viscosity, μt[Ns/m2] is the turbulent dynamicviscosity, Cμ is the dimensionless turbulent viscosity coefficient and δij is Kronecker’ssymbol. The transport equations for the turbulent kinetic energy, k [m2/s2], andturbulent dissipation, ε [m2/s3], are, respectively:

ρ∂

∂x j

(v jk

)= Pk − ρ ε + ∂

∂x j

[(μL + μt

σk

)∂k∂x j

]

(7)

ρ∂

∂x j

(v jε

) = Cε1ε

kPk − Cε2

ρ ε2

k+ ∂

∂x j

[(μL + μt

σε

)∂ε

∂x j

](8)

where σ k and σε are dimensionless fitting coefficients which are determined byadjusting the results to experimental data and Pk [kg/(m s3)] is the turbulent kineticenergy production term, defined by:

Pk ≡ −ρv′iv

′j∂vi

∂x j(9)

Note that a more rigorous compressible approach may also be used (which meanstaking account of the dependence of freshwater density on pressure and temper-ature). Some preliminary tests show that the assumption adopted here gives areasonably accurate useful result.

A linear segment of pipe of length Lsample = 500 m has been discretized in orderto model the pressure drop and freshwater averaged velocity. The pressure drop forthe whole pipe was simply obtained by multiplication of the pressure drop for thatsegment by the number of such segments the pipe of length L [m] would contain.


Boundary conditions comprise inlet turbulent intensity and inlet mass flow rate(i.e. minlet = (

ρfw Q)

inlet [kg/s], where ρ fw [kg/m3] is freshwater density) and null areaaveraged relative pressure at outlet (i.e. poutlet = 0 Pa).

The standard model dimensionless coefficients (Wilcox 1993) have been adoptedin calculations

σk = 1, σε = 1.3, Cμ = 0.09, Cε1 = 1.44, Cε2 = 1.92 (10)

These values are appropriate for a large number of fully developed turbulent flowsincluding this one, where Reynolds number is well over 106. Simulation has beenperformed with a custom designed 3D finite volume Navier–Stokes code (Ferzigerand Peric 1995).

The volumetric freshwater flow rate Q = 10,000 m3/s has been considered duringall calculations. The linear pressure drop �ppipe decreases significantly by increasingthe pipe’s inner diameter Dint [m], as expected (Fig. 4a). There are rather slightdifferences between the two routes of Fig. 1. The corresponding averaged velocity ofthe fresh water is illustrated in Fig. 4b. It ranges between 1 and 32 m/s. The requiredpumping power Ppump [W] is depicted in Fig. 4c. Pipe diameters larger than 60 m arenecessary for “reasonable” low pumping power (i.e., less than 20 GW).

4.2.2 Maximum Pipe Wall Thickness

We shall consider a cylindrical pipe element of length �L [m] at depth h [m] belowsea level. The element is short enough to allow neglecting the axial variation ofvarious physical parameters (Fig. 5a). The pipe wall’s thickness is δ [m]. The force

Fig. 4 a Linear pressure drop �ppipe, b freshwater speed and c pumping power Ppump as a functionof the pipeline inner diameter Dint, for the two routes of Fig. 1


Fig. 5 a Geometry of the pipe and the forces acting on it; b external and internal pressure,respectively

balance on this single pipe element is (the positive sense is oriented towards theocean surface, local sea level, in Fig. 5a):

FA − Fp,ext + Fp,int − Fw, fw − Fw,pipe − R = 0 (11)

where R [N] is the resultant force, FA [N] is the Archimedean force, Fp,ext [N] andFp,int [N] are the forces due to the external and internal pressure, respectively, whileFw, fw [N] and Fw,pipe [N] are the weights of Amazon River freshwater inside thepipe and pipe’s walls, respectively. We denote by ρsw [kg/m3] and ρ pipe [kg/m3] massdensity of seawater and the pipe wall’s material, respectively. Two hypotheses areaccepted now: (1) the pipe wall thickness is much smaller than pipe inner diameter(δ << Dint) and (2) the pipe element keeps its generally cylindrical shape whateverthe values of various forces are. Elementary physics gives:

FA = π (Dint + 2δ)2

4gρsw�L ∼= π D2

int

4gρsw�L,

Fw, fw = π D2int

4gρ fw�L,

Fw,pipe = π[(Dint + 2δ)2 − D2

int

]

4gρpipe�L ∼= π Dintδgρpipe�L

(12–14)

Computation of Fp,ext and Fp,int is slightly more involved and requires the use ofFig. 5b. The hydrostatic seawater pressure pext(φ) [Pa] at the level of point M isgiven by:

pext (φ) = ρswg[h + (Dint + δ) (1 − cos φ)

](15)


Fp,ext is obtained by integrating for 0≤φ≤π the product between �L and theprojection of pext(φ) on Oy axis in Fig. 5b:

Fp,ext =π∫

0

�L cos φpext (φ) dφ ∼= −ρswg�Lπ D2

int

8(16)

Here Eq. 15 and the approximation (1) above were also used. The internal pressureat the level of point N in Fig. 5b, pint(φ), is given by the sum between the pressure pcreated by the pump and the hydrostatic pressure:

pint (φ) = p + ρ fwgDint (1 − cos φ) (17)

After integration, we found:

Fp,int =π∫

0

�L cos φpint (φ) dφ ∼= −ρ fwg�Lπ D2

int

8(18)

Use of Eqs. 11–16 gives the resultant force per unit pipe length:

R�L

= π D2intgρpipe

[(δ

Dint

)

max

− δ

Dint

](19)

where(

δ

Dint

)

max

≡ 3

8

ρsw − ρ fw

ρpipe(20)

Most existing submarine hydrocarbon pipelines have been constructed with steel.The American Petroleum Institute has published “API 5L: Specification for LinePipe” which is the most commonly used standard for carbon steel pipe and lowalloy steel pipe. The American Society for Testing and Materials (ASTM) has alsopublished some standards (such as “ASTM A312” and “ASTM A790”) that are usedfor stainless steel and duplex stainless steel pipe. Only steel pipes are considered inthe remaining part of the present work.

The resultant force per unit pipe length decreases by increasing the ratio δ/Dint,from a maximum value (when δ/Dint →0) to zero (when δ

/Dint = (

δ/

Dint)

max. Theratio R/�L reaches an extreme value when ∂

(R

/�L

)/∂ Dint = 0. Using Eqs. 19 and

20 we found, after simple algebra, that R/�L is a (negative) minimum for:(

δ

Dint

)

opt≡ 2

(δ

Dint

)

max

(21)

However, only positive values of R/�L are of real technical interest, which meansthe resultant force is oriented towards the ocean surface (i.e., a TFA is considered).

4.3 TFA Using Bundle of Pipes

4.3.1 Pumping Power

The large freshwater volumetric flow Q resulted in a large diameter pipe, raisingtechnological difficulties. Using a bundle of smaller size pipes, instead of a largersingle pipe, might be an efficacious solution in this instance. This case will be


examined next, from the viewpoint of the amount of material needed to constructthe TFA and the required pumping power.

We supposed a bundle of n pipes of equal diameter Dint,n [m] and wall thicknessδn [m] is used instead of a single pipe, under the assumption that both the volumetricfreshwater flow and the freshwater speed remain the same. This means that the crosssection area of the pipe bundle equals the cross section area of the single pipe andsimple algebra gives the inner diameter Dint,n of a pipe in the bundle:

Dint,n = Dint√n

(22)

The volume of material Vmat,1 [m3] required by a single pipe with δ << Dint isgiven by:

Vmat,1∼= π Dintδ (23)

The freshwater speed w1 [m/s] inside this pipe is given by:

w1 = 4Q

π D2int

(24)

The volume Vmat,n [m3] of the bundle pipe material is:

Vmat,n∼= nπ Dint,nδn = π Dintδn

√n (25)

Here Eqs. 22, 23 and the assumption δn << Dint,n were also used. The followingtrivial relationship applies:

δn

Dint,n≤

(δn

Dint,n

)

max

(26)

The equality sign in Eq. 26 overestimates the amount of material in the pipe bundleand this is the assumption adopted now for both the pipe bundle as well as the singlepipe:

δn =(

δn

Dint,n

)

max

Dint,n =(

δn

Dint,n

)

max

Dint√n

, δ =(

δ

Dint

)

max

Dint (27a, b)

Using Eqs. 23, 25 and 27a, b give:

Vmat,n∼= π D2

int

(δn

Dint,n

)

max

, Vmat,1∼= π D2

int

(δ

Dint

)

max

(28a, b)

But Eq. 20 does not depend on pipe size and, as a consequence:(

δn

Dint,n

)

max

=(

δ

Dint

)

max

(29)

Then, from Eqs. 28a, b and 29 we found:

Vmat,n∼= Vmat,1 (30)

We came to the important reported result that the amount of material is approxi-mately the same, whatever the total number of aggregated pipes in the bundle.


The volumetric flow Qn [m3/s] and the water speed wn[m/s] in a single pipe in thebundle are, respectively:

Qn = Qn

, wn = w1 (31, 32)

The pumping power in a single pipe and in the bundle of pipes, Ppump,1 [W] andPpump,n [W], respectively, are:

Ppump,1 = ρ fw Q�p1, Ppump,n = nρ fw Qn�pn = ρ fw Q�pn (33, 34)

where �p1 [Pa] and �pn [Pa] are the pressure drop in a single pipe and in one pipe inthe bundle, respectively, given by the usual Darcy–Weisbach relationships (Ionescu1977; Valiantzas 2008):

�p1 = λ1L

Dint

w21

2g, �pn = λn

LDint,n

w2n

2g= λn

LDint

w21

2g

√n (35, 36)

Here λ1 and λn are the dimensionless friction coefficients in a single pipe and in onepipe in the bundle, respectively. Also, in Eq. 36 one used Eqs. 22 and 32. Usage ofEqs. 33–36 gives:

Ppump,n

Ppump,1= λn

λ1

√n (37)

The friction coefficients λ1 and λn depend on the appropriate Reynolds numbers Re1

and Ren, respectively, defined by:

Re1 ≡ w1 Dint

ν fw, Ren ≡ wn Dint,n

ν fw= Re1√

n(38, 39)

where ν fw [m2/s] is the kinematic viscosity of freshwater and Eq. 22 was used inEq. 39. Also, λ1 and λn depend on appropriate dimensionless roughness factors ε1

and εn, respectively, defined by:

ε1 ≡ kDint

, εn ≡ kDint,n

= ε1√

n (40, 41)

where k [m] is the pipe wall roughness (assumed to be the same whatever the pipediameter is). In Eq. 41 we used Eqs. 22 and 40. The following procedure may be usedto compute the coefficients λ1 and λn (in the following, Re and ε stand for any of Re1

or Ren and ε1 or εn, respectively). The threshold dimensionless coefficient λtr and thethreshold Reynolds number Retr are first computed from (Ionescu 1977):

λtr ≡ (1.14 − 2 log ε)−2 , Retr ≡ 200

ε√

λtr(42, 43)


Fig. 6 Ratio between thepumping power required by abundle of n pipes and a singlepipe of similar cross sectionare, Ppump,n and Ppump,1,respectively, as a function of n.Calculations performed forroute 2 in Fig. 1

Then, λ is given by:

λ =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

0.0032 + 0.221

Re0.237 Re ≤ Retr

0.11

(ε + 68

Re

)0.25

Re > Retr

(44)

The upper and lower lines in Eq. 44 are Nicuradse and Altshul relationships used forsmooth and rough pipes, respectively (Ionescu 1977).

In computation we used ν fw = 1.005 · 10−6 m2/s, which corresponds to freshwaterat 20◦C. Also, k = 3 mm, which applies to steel water pipes after long term operation(Ionescu 1977). Computations were made for different values of the inner diameterDint of the single pipe and number n of pipes in a bundle. Results are shown in Fig. 6.The ratio Ppump,n/Ppump,1 does not depend on Dint but increases by increasing n.Thus, the advantage of simplifying the construction technology might be exceededby the disadvantage of consuming more power in operation. The optimum numbern of pipes should be determined from an economic compromise, which must includethe cost of pumping stations, whose number depends on n, too (see Section 4.3.2).

Figure 7a shows the pumping power Ppump,n in the case of a bundle of n pipesused to transport the freshwater from South America to Africa. The abscissa showsthe pipe diameter of an example pipe in the bundle. Thus, the freshwater speed inthe pipes is different for the six curves in Fig. 7a, because the total volumetric flowrate is the same for all six bundles (i.e. Q = 10,000 m3/s). Under these circumstances,the pumping power Ppump,n for a bundle of n > 1 pipes of a given diameter is lowerthan the pumping power for a single pipe of the same diameter, as expected. This is aconsequence of the higher linear pressure drop in the second case, shown in Fig. 7b.

4.3.2 Maximum Distance Between Pumping Stations

The next reasoning applies for a single pipe, operating alone or in a bundle of pipes.The meridian tension σ 1 [N/m2] and the circumferential tension σ 2 [N/m2] in a


Fig. 7 a Pumping power and b linear pressure drop for bundles on n pipes, as a function of thediameter of a single pipe in the bundle. Route 2 in Fig. 1 is considered

thin-wall revolution shell are related to the pressure pint [Pa] inside by (Buzduganet al. 1972, p. 494):

σ1

R1+ σ2

R2= pint

δ(45)

where R1 [m], R2 [m] and δ [m] are the main curvature radii and pipe wall materialthickness, respectively. For a cylindrical pipe of inner diameter Dint [m] one hasR1 → ∞ and use of Eq. 45 yields:

pint = 2σ2δ

Dint(46)

Freshwater motion in the Atlantic Ocean pipeline is ensured by a number of pumpingstations placed at equal distance Lst [m]. The value of the pumping pressure at theexit of a pumping station is denoted pin [Pa]. This value must be large enough tocover the pressure losses due to friction during the freshwater movement towardsthe next pumping station. Thus, along the pipe segment between two stations thepumping pressure p [Pa] decreases due to friction from pin to zero. pin is much higherthat the hydrostatic pressure, which may be neglected in Eq. 17 (i.e. pint ∼= pin at theexit of a pumping station). From Eq. 46 we derived:

pin = 2σ2δ

Dint(47)


The following linear static pressure loss is adopted in the following:

pin = �pLst

L(48)

where �p [Pa] and L [m] are the pressure loss and length for the whole Atlanticpipeline, respectively. In case a single pumping station would exist, then Lst = L andfrom Eq. 48 one finds pin = �p, as expected. Usage of Eqs. 47 and 48 yields:

Lst

L= 2

σ2

�pδ

Dint(49)

The total pipe length L is a given. Once a pipe material is selected, the strengthvalue for σ 2 may be estimated. Also, δ and Dint are design parameter, which allowevaluating the total pressure loss �p (see Fig. 7). Then, Eq. 49 may be used tocalculate the distance Lst between two pumping stations.

Figure 8 shows the maximum distance between pumping stations Lst in case abundle of n pipes is used to transport the freshwater. The abscissa shows the pipediameter of a pipe in the bundle. Comments associated to Fig. 7 apply here, too. Fora given pipe diameter, the distance Lst increases by increasing the number of pipesin the bundle. To keep the number of stations reasonably low (i.e., fewer than 20) asingle pipe of diameter greater than 30 m is required. Alternatively, a bundle of tenpipes of 11 m diameter may be used, for example.

4.3.3 Resultant Buoyant Force and Seabed Anchoring System

Use of Eqs. 19 and 49 allowed us to evaluate the lifting force Rst [N] acting on thepipe connecting two geographically separated pumping stations:

Rst = Rstδ

Dint

[(δ

Dint

)

max

− δ

Dint

] (Rst ≡ 2ρpipegL

σ2

�pπ D2

int

)(50, 51)

The lifting force Rst vanished for δ/Dint = 0 and for δ/Dint = (δ/Dint)max. Thus, Rst

reaches a maximum for an optimum value (δ/Dint)opt somewhere between these

Fig. 8 Maximum distancebetween freshwater pumpingstations for bundles on n pipes,as a function of the diameterof a pipe in the bundle. Route2 in Fig. 1 is considered


extreme values. This optimum value is obtained from ∂ Rst/∂

(δ/

Dint) = 0. From

Eq. 50 we easily found:(

δ

Dint

)

opt= 1

2

(δ

Dint

)

max

(52)

and

Rst,max = Rst

4

(δ

Dint

)2

max

(53)

The anchor lines number and strength should be evaluated in order to cover theselifting forces.

Deep-sea anchors must resist the movement force of the TFA to which they areattached by cables with either (1) great mass such as inexpensive, pre-fabricated off-worksite concrete blocks or (2) by hooking into the seabed as a form of embedment.Wind and ocean currents are not the largest forces these anchors must resist; thevertical movement of passing waves, even including rare extreme waves (Smith2006), develop the largest loads that must successfully and always be resisted. TheTFA will be situated below the strongest surface waves so steady ocean currents arelikely to be the major load to be resisted by the affixed anchors. The TFA shouldnot pose a navigation hazard to deep-draft shipping nor should it be so deep as tomake maintenance exceptionally difficult or costly for its owner-operators. One mayopt for a top-of-TFA final emplacement depth of ∼100 m even though attenuated,geomagnetic disturbances can affect seafloor cables and metallic pipelines immersedeven 100 m or more (Boteler and Pirjola 2003). The TFA route must be markedon all paper charts and electronic navigational databases and, perhaps, even visiblytraced at regular intervals on the Atlantic Ocean’s equatorial zone surface by solar-powered/battery backup light-and-acoustic signal buoys.

The Atlantic Ocean’s seafloor is a complex and still rather poorly understoodplace that differs fundamentally from terrestrial places such as the Amazon RiverBasin and arid northern Africa, where a lengthier history of macro-engineeringpractice and experience exists. The oceanographic data in the seabed region directlyrelevant to the TFA is almost unknown. Accurate sea-bottom mapping and assess-ment is vital for the anchors and more oceanographic research must be financed andorganized before the TFA is undertaken.

The world’s ocean has not yet become a completely monitored outdoor oceano-graphic “laboratory” because there remain significant mooring design challenges(Frye 2004). Taking into account realistic present-day and near-term future materialstrengths, 10–30 m is the rough accepted maximum depth in dry rock on land thata streamlined rod-shaped anchor can penetrate and still retain its full structuralintegrity as a manufactured object. In seawater, the attainable free-fall velocity orterminal velocity of deliberately-dropped-overboard torpedo-shaped anchors willbe almost entirely determined by the equilibrium of buoyant and hydrodynamicdrag (Xiao 2006). Field tests undertaken to prove the feasibility of sub-seabedgeosequestration of nuclear waste encapsulated in a 2,000 kg free-falling penetratorproved that a streamlined steel-casing torpedo can easily burrow ∼40 m into abyssalAtlantic Ocean sediment. When deployed, after it reaches a state of dynamicequilibrium, it then travels downwards at a constant velocity of nearly 45 m/s until itimpacts the seafloor suddenly, when, by virtue of its own momentum, it penetrates


and buries itself (Colliat 2002; Freeman et al. 1984). The anchor acts like a frictionpile when it functions as an ultra-deepwater mooring. If a strong single mooringwire were attached to such objects, it is very probable that friction between thefalling object and the surrounding saturated sediment would, alone, prevent suchsettled anchoring penetrators from dislodging, allowing the TFA to dangerouslydrift out of its mapped proper underwater placement. Penetrative anchors wouldbe isolated from all physically adverse event-processes at the seawater–sedimentinterface such as normal ocean bottom seawater currents and infrequent turbiditycurrents. Offshore Mauritania, the continental margin is infrequently affected byturbidity currents in the Cap Timiris Canyon (Zuhlsdorff et al. 2008). However, CapTimiris Canyon’s head is located many kilometers north of the intended TFA landfallin Mauritania near Nouakchott.

4.4 Energy to Pump Freshwater through the TFA

There are various possible sources to provide the energy necessary to pump thefreshwater. Sustainable development requires, however, usage of renewable energysources. Solar energy can be used for water pumping systems (Glasnovic andMargeta 2007) and is an obvious solution in case of the sunny region wherein theTFA is to be emplaced. However, the most elegant way is to harness the naturalocean currents in the region where the TFA is planned for operational emplacement.Apart from providing the pumping energy this will ensure, in part, the pipe’sprotection against mechanical damage, diminishing the external forces acting on it.The availability and the limitations of the relevant ocean current energy is presentednext.

The Atlantic Ocean’s near-surface seawater layer, which interfaces with the air, isa turbulent fluid, spatially varying in important seawater characteristics and naturallysubject to strong winds (Soloviev and Lukas 2006). The chosen TFA routes stayalmost entirely within the atmosphere’s Inter-tropical Convergence Zone (ITZ).The ITZ is a latitudinal migrating belt of low-pressure air encircling the Earthat the Equator; it is farthest north of the Equator during July and is slightly south ofthe Equator during January. Within this permanent belt of moving air, surface windspeeds are usually slight and rainfall caused by powerful passing thunderstorms canbe marked. In the region to be traversed by the TFA there are three main AtlanticOcean currents: the North Brazil Current, the North Equatorial Current and theNorth Equatorial Counter Current.

The warm North Brazil Current (NBC) is a well-established western boundarycurrent that carries warm water of South Atlantic origin northwest along the coastof Brazil, across the Equator and into the northern hemisphere (Fig. 9a). Averagetemperatures of the NBC range from 22◦C to 29◦C. Maximum speeds are typicallyfound in its southern portion. Peak speeds of 110 cm/s have been recorded, althoughgenerally the current flows between 60 and 100 cm/s. At about 44◦W, the NBC is a300 km wide swath (Bischof et al. 2003).

The equatorial Atlantic Ocean is a complex region dominated by the presence oflarge-scale westward currents and eastward countercurrents. The North EquatorialCurrent (NEC) is found in the North Atlantic Ocean from about 7◦ N Lat. to about20◦ N Lat. (Fig. 9b). In the late summer and early fall, temperatures range between30◦C and 32◦C and in the wintertime range between 24◦C and 28◦C. In the open


Fig. 9 Current streamlines inthe Atlantic Ocean. a NorthBrazil Current; b NorthEquatorial Current; c NorthEquatorial Counter Current

ocean NEC has a westward mean velocity between 10 and 15 cm/s. Its peak velocityvalues of 15 cm/s are prevalent in boreal summer (July/August), with a weakening to10–12 cm/s during spring and fall (Bischof et al. 2004a).

The North Equatorial Counter Current (NECC) lies between 3◦ and 10◦ N(Fig. 9c). The northern boundary of the NECC, when the NECC is present, is theNorth Equatorial Current (NEC). The mean eastward velocity for the NECC is42 cm/s and maximum velocities of up 50 cm/s have been measured in the wintertime.Eastward flowing surface speeds in the western section of the current have beenestimated to be up to 147 cm s−1 extending down to 350 m at 28◦ W. Long. (Bischofet al. 2004b).

Energy can be extracted from the ocean currents using submerged turbinescapturing energy through the processes of hydrodynamic lift or drag (Fig. 10a).These turbines have rotor blades, a generator for converting the rotational energyinto electricity, and a means for transporting the electrical current to the freshwaterpumping station (Fig. 10c). There, the electricity drives axial pumps to move thefreshwater inside the proposed bundle of pipes (Fig. 10b). Turbines can have eitherhorizontal or vertical axes of rotation. Prototype horizontal and vertical axis turbineshave been built and tested (Technology White Paper 2006). Turbines shown inFig. 10a may be anchored to the ocean floor in a variety of ways. They maybe tethered with cables, with the relatively constant current interacting with theturbine used to maintain location and stability. Various alternative designs have beenproposed, including the use of a barge moored in the current stream with a largecable loop to which water-filled parachutes are fastened. The parachutes would bepushed by the current, and then closed on their way back, forming a loop similar toa large horizontal waterwheel. For marine current energy to be utilized, a number of


Fig. 10 a Turbines convertingthe kinetic energy of oceancurrents into mechanicalenergy; later on, alternatorsconvert the mechanical energyinto electricity; b axial pumpused to move the freshwater inthe TFA bundle of pipes; thepumps are driven by electricalmotors receiving energy fromthe turbines shown in a;c Pumping station; axial pumpsshown in b are used to movethe freshwater inside thebundle of pipes

potential problems would need to be addressed, including avoidance of drag fromcavitations, prevention of marine growth buildup, corrosion control, and overallsystem reliability (Technology White Paper 2006).

Initial facility economic and physics studies suggest that for economic exploitation,velocities of at least 2 m/s would be required, although it is possible to generateuseful energy from velocities as low as 1 m/s. Previous studies (Technology WhitePaper 2006) show that major costs of these systems would be the cables to transportthe electricity to the onshore grid. The present TFA macro-project does not involveconnection to the onshore grid. (In a sense, each generation plant may be considereda “stranded power plant”, without connection to a power grid on land or in theocean.)

A rough estimate of the power Pcur [W] that could be extracted from the oceancurrents of the relevant region of the TFA follows. It is based on the formula:

Pcur = cp1

2Sρsww3

cur (54)

where cp is the dimensionless coefficient of performance of the turbine, S [m2] isthe collecting surface area, ρsw [kg/m3] is seawater mass density while wcur [m/s] isthe ocean current speed. The maximum power is obtained in the ideal case, when


cp,ideal = 16/27 = 0.593 and Eq. 54 becomes the well-known Betz formula (Betz 1966).Modern rotors achieve values for cp in the range of 0.4 to 0.5.

Using the power provided by the North Brazil Current is easier to undertake.Indeed, the large, nearly 500 km-wide continental platform near Brazil’s coastline(Fig. 3) offers an easier installation for the turbines We assumed the NBC is 300 kmbroad and the energy collection vertical surface layer is of 100 m thickness. Then,the collection surface area for the NBC is about SNBC = 3 · 107 m2. One may assumeboth the NEC and NECC have widths of 1,500 km (they are located in the Westernand Eastern Equatorial Atlantic, respectively). Again, the energy collection surfacelayer is 100 m in depth. Then, the energy collection surface for those currents isSNEC = SNECC = 15 · 107 m2. The following values are adopted: cp = 0.5 and ρsw =1,030 kg/m3. Figure 11 shows the dependence of Pcur as a function of speed currentof wcur for all the three currents. NEC may provide less than 0.3 GW power. NBCprovides between 2 and 9 GW, with an average power of about 3 GW, for a speed of0.8 m/s. NBCC provides the largest power availability, ranging between 2 and about100 GW.

5 Estimated TFA Cost

A rough estimate of the macro-project cost is proposed now. It is entirely basedon information taken from existing literature. The main obstacle is, however, thatcompanies/governments want to keep confidential, even totally secret, the true actualcosts of various infrastructures.

Most of the recently undertaken works for submarine pipelines (oil, gas, water)entail aspects that this macro-project won’t need: namely seabed trenching, heavy-duty crewed support ships for heavy and awkward to handle steel pipes that do notbuoy themselves, relatively short distances, built in heavily populated regions withhigh-wage labor and crowded seafloor situations (pipes, and wreckage already exist).There are only three macro-projects of comparable size, which will be outlined next.

Fig. 11 Power provided by theNorth Brazil Current, theNorth Equatorial Current andthe North Equatorial CounterCurrent, respectively, as afunction of the current speed.Usual range of variation forthe speed of these oceancurrents has been considered


First, one shall refer to the high-speed train-carrying “Transatlantic Tunnel”(Transatlantic Tunnel 2008). The tunnel would be 4,989 km-long and cost anestimated 12,000 GUSD. This project involves building an air evacuated “duct”,whose principles are different from those related to the TFA. Essentially, thesubmarine “Transatlantic Tunnel” is an airless pipe holding moving passenger andcargo capsules to and from Europe and North America.

Second, there is the Nord Stream underwater gas pipeline (from Russia to westernEurope) (Nord Stream 2008). When completed, it will be 1,200 km long and beinstalled in the Baltic Sea at a total cost of 7.3 GUSD (some predict an inflationarydoubling of this estimated building cost). This involves at-sea construction of an ordi-nary, non-floating, natural gas-conveying undersea pipeline, which will be emplacedin a costly dredged trench on the Baltic Sea’s floor.

Third, we shall now pay a bit more attention to the only large freshwaterpipeline ever proposed, the Alaska–California Pipeline of 1991 (California UnderseaAqueduct 1975). The positively buoyant submerged floating pipe, anchored to theseabed close to the USA’s western shoreline, was to have a finished diameter of 4.26m. It was to convey 4,000,000 acre-feet of freshwater annually (or, in other words,156.26 m3/s). That is similar to the present macro-project from many points of view.The Alaska–California Pipeline has many similarities with the TFA macro-project. Itincludes: (1) a fleet of semi-submersible work platforms with supporting equipmentand vessels; (2) ten pumping stations to move the freshwater; (3) intake and terminaldistribution structures on land. It is expected to take 15 years to complete this macro-project. In 1991, the 2,253 km-long submerged floating pipeline would likely havecost 110 GUSD (adjusted for inflation, the cost would be 173 GUSD in 2009).

We shall use information referring to the Alaska–California Pipeline to infer arough estimate for our TFA macro-project. The calculation is based on the idea thatcost increases linearly with pipeline length and water volumetric flow, respectively.Then, simple algebra shows that if a pipeline 2,253 km-long transporting 156.26 m3/scosts 173 GUSD, then the pipeline 3,750 km-long (Route 2) transporting 10,000 m3/sshould cost 18,425 GUSD in 2009. When Route 1 (4,200 km long) is considered, thecost is 20,636 GUSD. These strictly monetary costs are comparable with the estimatesfor the Transatlantic Tunnel. These values should be taken with much caution,of course. Conclusions referring to the Alaska–California Pipeline mega-projectapply here, too: “Using nontraditional materials, the cost of the pipeline could bedramatically reduced. In the absence of a sound, well-documented feasibility study,a reasonably accurate pipeline cost cannot be determined” (California UnderseaAqueduct 1975, p. 4).

Though the exact cost of the macro-project is difficult to estimate, savings associ-ated to using Route 2 instead of Route 1 are easier to compute. Here one refers to(1) costs related to pipe and pumping stations and (2) costs related to the anchoringsystem.

It looks reasonable to assume that the cost related to pipe and pumping stationsis proportional to pipe length. Then, using Route 2 instead of Route 1 means a costreduction of 3,750 km/4,200 km = 0.893.

To compute the cost associated to anchoring the pipe on it final position, one needsto know the approximate line length of anchors for the two proposed routes (Fig. 2).This depends, of course, on the intervening distance between two consecutiveanchors. This is normally shorter than the distance between two consecutive pumping


stations, which, in turn, depends on pipe diameter and number of pipes. Considering,for example, a 100 km gap between two consecutive anchors, simple addition ofthe mooring sea depths on the Route 1 yields 160.78 and 133.97 km for Route 2.Similarly, taking a 10 km gap and a suitable cubic spline interpolation of the mooringseabed depths on both routes, leads to a 1,643.5 km total length of the anchors onRoute 1 and to 1,370.4 km on Route 2. As one can easily see, the ratio betweenlength on Route 2 and Route 1 stays at an approximate value of 0.83 which is exactlythe ratio between the areas of the two routes mooring sea depth profiles in Fig. 3.

6 Environmental Considerations

Potential environmental impacts must be considered during the development of theTFA, some of which are briefly mentioned below.

There are some large-scale negative consequences of macro-project implemen-tation that should not be disregarded. Amazon River discharged water has beencorrelated as far as the Yucatan Peninsula: “. . . at least 60% of the freshwater inthe eastern Caribbean Sea is from the Amazon” (Hellweger and Gordon 2002).Also, the Amazon River discharge influences the Intertropical Convergence Zonesalinity and ocean currents during the year (Muller-Karger et al. 1998). There are,however, other beneficial aspects of the macro-project, both in the sea and on land.For example, the Amazon River freshwater plume, along with the Orinoco Riverfreshwater plume and the North Brazil Current, causes current rings to form in thetopmost seawater layer (10–30 m thick) that play some strengthening role in naturalhurricane maintenance and intensification (Ffield 2007). Such destructive hurricanesaffect the Caribbean Sea and the Gulf Coast of the USA. And, hurricanes reachingthe Gulf Coast often spawn tornadoes, another windy threat to life and property andNature (Belanger et al. 2009). The project will counteract these last aspects and thefinal decision about TFA feasibility will take into account both positive and negativeconsequences, of course.

The freshwater removed from the Amazon River’s basin after it has alreadyreached the ocean would be immediately treated to prevent bio-invasion macro-problems that might occur at the terminus in Mauritania; bubbling nitrogen gasthrough in-transit flowing freshwater to remove oxygen, transforms the freshwaterinto a fluid toxic to most unwanted small aquatic organisms and, at the same time,deoxygenating the conveyed liquid would help to prevent the corrosion and organiccoating of steel fittings, pumps (Tamburri 2002).

Note that freshwater can be garnered directly from the ocean’s surface at 1–2 km offshore from Brazil’s coastline where the Amazon River mouths are lo-cated (Nikiema et al. 2007; Cherubin and Richardson 2007). Hydrographic surveysrevealed that the Amazon River’s freshwater plume over the continental shelf istypically 3–10 m thick and about 80 km wide. This “lens” of 28◦C freshwater situatedabove ordinary seawater is a low-salinity, low-inorganic carbon plume of freshwatersitting atop the denser western tropical Atlantic Ocean saltwater, separated fromthe underlying ocean seawater by a distinct halocline (Ffield 2007). With the TFAfreshwater intake located 1 km offshore, one cannot complain legitimately aboutdestructive degradation of the Amazon River Basin (Malhi et al. 2008) and nocomplication of inland waterway navigation, which is already impacted by shifting


sand banks, need be an influential factor in the TFA operation (Fernandes et al.2007; Syvitski and Milliman 2007; Koppes and Montgomery 2009).

Other impacts that must be considered during TFA development and oceaniccurrent energy utilization include potential marine ecology impacts and multiplemaritime user conflicts. Resources harnessed for the construction and operationof these tandem technologies would also need to be addressed. Irregardless ofthe size and nature of the anticipated direct and indirect environmental impacts,macro-project planning would need to consider the protection of river and oceanspecies, particularly fish and large marine mammals. The slow-spinning turbine bladevelocities should allow water to flow freely and fish to safely evade the machine’svisibly or otherwise easily sensed whirling rotor blade structures. Protective fluidpermeable barriers, operating in conjunction with sonar-activated propeller bladeunit braking systems, could forestall any major physical harm to large migratoryor curious marine mammals. The exact quantity of the resident and migratory fishover the full length of the TFA is barely known. More survey work by fisheriesand oceanographic specialists is obviously required for proper TFA installation andoperation.

In locating the turbine units, consideration of site impacts on oceanic shippingroutes, and present-day as well as anticipated uses (such as commercial and recre-ational fishing and sport free and SCUBA diving) would, of course, be mandatory inthe establishing macro-project construction contract. Additional required concernsinclude the genuine need to introduce all possible damage mitigating factors, such asthe establishment of international fishery Exclusion Zones.

Concerns about risks from slowing the current flow through the operating pro-peller blade units because of energy extraction are justified. A rough estimate of theocean current attenuation effect follows. Figure 7a shows that a properly designedTFA macro-project consumes between 2.5 and 8 GW for freshwater movement.We assume here the average value 5 GW. Figure 11 allows to us to estimate thepower available from those regions of the ocean currents provided with energyconversion devices. Here only the North Equatorial Counter Current (NECC) willbe considered. It provides between 30 and 100 GW for current speeds between 1and 1.6 m/s. A reasonable approximate measure for the attenuation effect that theTFA macro-project has on the ocean currents movement is as the ratio between thepower extracted from the current and the whole available current power. This givesan attenuation effect between 16% and 5%, for the two current speeds above. Onemight expect even lower values of the attenuation effect, if we take into accountthat: (1) improved design TFA solutions may use less power than 5 GW, (2) onlythe NECC available power has been considered here and (3) not all the transversalsurface of the ocean currents is provided with energy conversion devices.

Another possible influence of the TFA macro-project on the oceanic currentsmight be due to the disappearance of the Amazon River’s plume from the AtlanticOcean. However, presently there is little influence by the Amazon River dischargeon the ocean currents. The Amazon River’s plume is 3–10 m thick and consists inlighter freshwater flowing over the heavier seawater while the ocean currents aremuch deeper water movements, extending down to 350 m, as described in Section 4.4.

Local estuary and marine effects, such as raised average local water temperatureand fluctuating salinity changes, particularly in the Amazon River’s estuary, causedby changes in the ratio of saltwater/freshwater mixing both seasonally and over the


long-term, would need to be considered for their specific potential impact on estuaryecosystems (Charlier and Justus 1993).

7 Conclusions

This paper offers a technical and geopolitical reappraisal of a macro-engineeringproposal to plumb Earth’s freshwater, siphoning some of it from a region of surplus(Amazon River Basin) to a region of shortage (arid northern Africa) via positivelybuoyant (subsurface floating) seabed-anchored Transatlantic Freshwater Aqueduct(TFA). The Authority responsible for the management and construction of the TFAshould be initiated by Brazil and would involve South American and African coun-tries. It is likely the South American economic unity organization set up by treaty willplay an important role. However, the TFA macro-project could harness the AmazonRiver’s plume. Therefore, the TFA macro-project would require UNO involvementand considerable international cooperation. Of course, this trans-national, UNO-sanctioned, constructing Authority should be established by experts in infrastructuremanagement and international law. Here, we have generally outlined some prudentorganizational practices proved to be useful over a long period of time by bothcommon practice and study.

Two different routes for the pipeline have been considered. Both start in themouth region of the Amazon River. The first route (length 4,317 km) ends in Africaat Nouakchott, Mauritania while the second route’s terminus point is at Conakry,Guinea (length, 3,745 km). In both cases, an exported freshwater volumetric flowrate V = 10, 000 m3

/s has been considered in calculations.

The linear pressure drop decreases significantly by increasing the pipe innerdiameter, with slight differences between the two routes. Pipe diameters larger than60 m are necessary for “reasonable” low pumping power (i.e., lower than 20 GW).The large-diameter pipe raises extreme technological difficulties. Using a bundleof smaller size pipes, instead of a larger single pipe, might be a solution in thiscase. However, the advantage of simplifying the construction technology might beexceeded by the disadvantage of consuming more electrical/mechanical power inoperation. An optimum number of pipes in the bundle should be determined froman economic compromise.

Freshwater motion in the Atlantic Ocean pipeline is ensured by a number ofpumping stations placed at equal distance Lst. For a given pipe diameter, the distanceLst increases by increasing the number of pipes in the bundle. To keep the numberof stations reasonably low (i.e., fewer than 20) a single pipe of diameter greater than30 m is required. Alternatively, a bundle of ten pipes of 11 m diameter may be used,for example.

Among the various possible sources to provide the energy necessary to pump thefreshwater, the ocean currents energy should be normally preferred. The availablepower, possibly provided by the North Brazil Current, ranges between 2 and 9 GW.The North Equatorial Current may provide less than 0.3 GW power, while the NorthEquatorial Counter Current provides the largest power availability, ranging between2 and about 100 GW.


A rough 2009 TFA cost estimate is 20,636 GUSD for Route 1 and 18,425 GUSDfor Route 2. These financial values should be taken with an abundance of intellectualcaution, of course.

Potential environmental impacts of the TFA macro-project are briefly mentionedat the end of this paper.

Acknowledgements The authors thank the referees for useful comments and suggestions.

Appendix

One denotes by ϕ and λ the geographical latitude and longitude, respectively, and byREarth(≈6,371 km)—Earth average radius. Two points M(ϕ1, λ1) and N(ϕ2, λ2) onEarth’s surface are considered.

A.1 Distance on orthodrome

The distance D [m] on the orthodrome between M and N is given by Gellert et al.(1980, p. 336)

D = π REarthg360◦ (55)

where g (in radians) is evaluated from:

cos g = sin ϕ1 sin ϕ2 + cos ϕ1 cos ϕ2 cos (ϕ2 − ϕ1) (56)

A.2 Distance on loxodrome

The distance s [m] on the loxodrome between M and N is given by Gellert et al.(1980, p 338):

s = REarth

cos α(ϕ2 − ϕ1) (57)

where the angle α between North and loxodrome direction (East positive) is evalu-ated from:

λ2 − λ1 = tan α[ln tan

(π

4+ ϕ2

2

)− ln tan

(π

4+ ϕ1

2

)](58)

A.3 Distance to land on a given course direction

The distance between the starting point location P1 (latitude ϕ1, longitude λ1 and seadepth h1) and the coast, on a loxodrome of given direction α is evaluated by using thefollowing combined analytical-numerical procedure. The point P1 is characterized bythe distance s1 = 0 from the starting point position. A distance step �s [m] to advanceon the loxodrome is chosen.


1. After one distance step on the loxodrome, a point P2(ϕ2,λ2,h2) is obtained. Noneof the three parameters of P2 are known at this stage. However, the distance fromP2 to the starting point position is given by Eq. 58, i.e.:

s2 = s1 + �s = REarth

cos α(ϕ2 − ϕ1) (59)

Use of Eq. 59 allows to compute the longitude ϕ2 of the point P2. Subsequently,the longitude λ2 is computed by using Eq. 58. The evaluation of sea depth h [m] atP2 requires a more involved procedure as follows. The bathymetry file is scannedand four points denoted M1(ϕ1, λ1, h1), M2(ϕ2, λ1, h2), M3(ϕ2, λ2, h3) and M4(ϕ1,λ2, h4) are found, such that (1) P2 is placed inside the rectangle M1 M2 M3 M4 and(2) M1 M2 M3 M4 is the smallest rectangle with property (1). Then, the followingchange P2 (ϕ2, λ2, h2) → P2 (ξ, η, h2) to the normal dimensionless coordinates(ξ ,η) is performed

ξ = −ϕ1 + ϕ2

ϕ2 − ϕ1+ 2

ϕ2 − ϕ1ϕ2

η = −λ1 + λ2

λ2 − λ1+ 2

λ2 − λ1λ2

(60, 61)

Finally, the sea depth h2 at P2 is computed by linear interpolation of the seadepths h1, h2, h3 and h4 in the points M1, M2, M3 and M4, respectively, by Olariuand Bratianu (1986, p. 143):

h2 = μ1h1 + μ2h2 + μ3h3 + μ4h4 (62)

where:

μ1 ≡ (1 − ξ) (1 − η)

4

μ2 ≡ (1 + ξ) (1 − η)

4

μ3 ≡ (1 + ξ) (1 + η)

4

μ4 ≡ (1 − ξ) (1 + η)

4

(63a–d)

2. After a second distance step on the loxodrome, a point P3(ϕ3, λ3, h3), locatedat distance s2 = 2�s from the starting point position, is obtained. Its threecoordinates are computed by the same procedure described at 1.

3. The procedure continues i steps, until the point Pi(ϕi, λi, hi) is characterized bya positive value hi. Thus, Pi is on land and the distance from the starting pointposition to the coast on direction α is (roughly) i�s.

The accuracy of this procedure depends of course on the size of �s.


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