The Technology

Salt water is about 2.5% denser than fresh water. A column of fresh water will have a freeboard of about 2.5% of its height (d). This freeboard pressurizes the column with a maximum differential pressure at the waterline. This pressure causes the bags to adopt their design shape in 3-dimensions and it is sufficient to maintain bag shape under tow. Technically a bag is a water-supported structure.

Stresses:

To contain the freeboard, the fabric of the bag goes into tension at most points according to the following equation where ρ is the density of freshwater and ρs is the density of salt water in lbs/cf and d is the vertical distance from the top, central part of the bag to the central bottom.

The fact that this static stress varies as d2 encourages the use of shallow bags. Determining the bag fill is an important part of project optimization. This optimization will also consider the cost of terminals, affected by water depth.

When an ocean wave meets the bag it simply pushes in the fabric wall creating a fresh-water wave, which passes through the bag and exits the opposite side. Although the bags are essentially transparent to waves, temporary stresses are induced in the fabric (wave-induced stress). The fabric must be appropriately strengthened to accept them.
Prototype fitted with strain gauges subjected to random waves and parallel wave trains.Stresses cannot be determined by calculation therefore small prototypes of scaled elastic modulus are tested in one of North America’s largest wave basins.
The bollard pull of the tug is taken by heavy straps at the bow of the bag and conveyed into the bag fabric and thence into the freshwater contents. The fabric (broadcloth and straps) of the bag is designed to accept these towing stresses with an appropriate safety factor. Fabric needs a much higher safety factor than, for example, steel. It is also much more elastic.

Designs:

There are two different plan shapes pending development.

The streamlined design with yaw-resisting tail below. The lines represent a possible strapping array:

The parallel-sided design below is less hydrodynamic and more subject to internal harmonic waves but cheaper to construct:

After years of design and cost assessment, industrial polyester woven cloth strengthened with woven polyester webbing provides a cost effective bag. Main straps distribute tow/mooring forces.

Commercial coated fabrics come with a long life warranty e.g. 15-yr. Properties of anti-biofouling and buoyancy for floatation when the bag is empty can be incorporated.

Drag:

The drag equation has three terms:

  • Wave drag, negligible for our velocity and length.
  • Form drag, which varies as maximum cross-section area, v2 and the form-drag coefficient.
  • Skin friction, which varies with wetted area and v2, calculated via the Reynold’s Number.

So drag varies as v2 encouraging low velocities. Bag plan shape is chosen to minimize drag and also result in no yawing at cruising speed. Skin friction per unit contents is minimized by low area-to-volume ratios.

Tow-tank test to determine form-drag coefficient and stability to yaw.

Construction of bags:

Working with thousands of meters of fabric is not novel. Air-supported structures are built by a well-established industry. Sector members have been consulted and are ready to construct super bags. Their projects, hundreds of meters in dimension, are well engineered and have withstood the test of time

Environment:

Concerns are non-existent. Should a bag develop a large tear, the freshwater will simply float out over the surface of the sea with all the effect of a good thunder shower.

Delivery:

The megabags are pulled by ocean-going tugs designed or sized for the appropriate voyage length, eg, 10-days.

Depending on the loaded capacity of the bag, there is an optimum tug boat size. This optimization is important and velocity is the major variable. If speeds are low, operating costs are similarly low but more capital equipment is needed to maintain a desired delivery volume of fresh water. So optimization is a play between the cost of capital, including equipment life, and operating costs, primarily fuel.

Coastal tug (3500 Hp):
Ocean-going tug (21,000 Hp):

Loading and unloading terminals:

When taking fresh water from a river before it enters the sea, salt-water contamination is avoided by extracting the water significantly upstream, which is then channeled in canals or conduits to the seashore. At the seashore a second pumping station sends the water through sea-floor conduits out to a buoy terminal located in appropriately in deep water.

The unloading terminal could employ a similar buoy and sea-floor conduit system in reverse or the cargo may be downloaded into small bags with an appropriate draft to navigate to various delivery points.