The Thin Pipe Model
The idea of using the energy of hydrothermal vents to mix nutrient into the near surface ocean has been through a number of iterations since a provisional patent application was first filed in March 2007. These are outlined below.
The Fat Pipe Embodiment
The first of these was the original "Fat Pipe" idea whereby the vent plume is confined in a large pipe (say 100m in diameter) made from a light, non-heat-resistant material such as polystyrene. The pipe allows mixing with seawater surrounding the vent in a ratio of 30:1 to cool the plume down to say 10 deg C. The warm water mixture is then carried up the pipe by convection bringing nutrients with it. The purpose of the pipe is to inhibit entrainment of further cold water thus preventing the plume from cooling down to the point where it would spread horizontally at depth in the manner of natural plumes.
This idea is flawed in two ways. On the one hand bottom waters are not a rich source of nutrients and convection is an inefficient method of pumping fluids.
The Thin Pipe Embodiment
The next idea was to bring about a phase change by raising the vent water in a heat-resistant thermally insulated pipe to a depth at which the hydrostatic pressure is sufficiently low to bring about boiling . Boiling greatly amplifies the volume flux for a given mass flux and high velocities can be generated. The top end of the pipe is fitted with an appropriately shaped nozzle, similar to a jet engine nozzle, which maximizes the momentum delivered to the water column. The resulting jet adds turbulent kinetic energy to the surrounding water which deepens the mixed layer by creating a toroidal eddy.
However, Newton's Third Law gives rise to a reaction which will cause the pipe to buck like an unrestrained fire-hose unless vanes and/or a floatation collar are used to inhibit this motion.
This idea too is flawed. The exit velocity from the nozzle cannot exceed the speed of sound in the medium being expelled. The medium in question is a hot sea-foam comprising 30 percent steam by mass. The velocity of sound in such a water-steam mixture will be lower than in either water or steam alone. According to some writers it could be as low 20 m/s.
A further difficulty is that the sea-foam generated in this way will mix rapidly with surrounding cold water and will condense back to water as soon as it emerges from the nozzle so that any buoyancy effects are immediately lost.
The Hybrid Embodiment
This last consideration lead to the realization that it is not desirable to mix the sea foam with the surrounding water. Generating a high velocity sea foam jet is not desirable, even if it were possible because a high degree of entrainment of surrounding cold water would result in the rapid annihilation of the bubble stream.
One way of minimizing contact between the sea foam and the surrounding water is to release the sea-foam at low velocities and high volume flux rates. This idea lead directly to the third embodiment, which is a hybrid embodiment involving both a fat pipe and a thin pipe.
An insulated thin pipe brings vent effluent from the ocean floor to well above the level at which it boils, so generating foam within the pipe. The foam is injected into the fat pipe. The foam bubbles reduce the mean density and total mass of fluid within the fat pipe which is open at both ends. As a result there will be a net body force on the fluid within the fat pipe causing it to move upwards. This continued vertical movement of water results in cold water entering the bottom of the fat pipe to be delivered to the region surrounding the top of the fat pipe. In practice the bottom of the fat pipe will be placed at a level where nutrient concentration is high and the top of the fat pipe will be in the mixed layer or euphotic zone where nutrient levels are low but where photosynthesis can occur.
This embodiment does not suffer from the flaws inherent in the first two embodiments described above. It utilizes buoyancy alone rather than momentum or turbulent kinetic energy to bring about ocean mixing. Velocities are lower so that turbulence and the mixing of hot foam and cold sea water are minimized as are Newton's Third Law effects.
Now that a mechanism has been clearly defined it is possible to model it. Various levels of detail and sophistication are possible depending on the simplifying assumptions that are made. At this stage of development a simple energy budget model constitutes an essential first step and that is all that will be dealt with here. This energy budget model will provide a useful basis for a more thorough hydraulic model which is developed below.
HydroThermal Vent Assumptions
The starting point for the model is the mass flux and temperature of the HydroThermal Vent (HTV) effluent which is the energy source. Much of the literature on HTVs deals with their biology and good physical data is hard to find. Typically vents are quoted as producing 5 to 10 MW of power. Some are much more powerful, fortuneately. The TAG HTV in the mid-North Atlantic is 1.7 GW.
Effluent temperatures are better known and a figure of 360° C is widely quoted. The significance of this temperature is that it is the reaction temperature at which silicates are formed and dissolved when sea water contacts hot subterranean magma. Assuming the temperature of benthic sea water is 4 deg C and that this has been warmed through ?T = 356° C the specific heat of water can be used to derive a mass flux from the quoted power. Thus the mass flux is equal to the vent power divided by the product of the temperature difference and the specific heat.
It is assumed that the entire output from the vent is captured by the thin pipe at the effluent temperature of 360°C.
Thin Pipe Assumptions
Flow in the thin pipe will be high Reynolds number (turbulent) flow. For a given diameter, length and roughness of the pipe and the pressure head difference, the upward velocity can be determined by the usual methods of hydraulics. This velocity is a strong function of pipe diameter. Here this calculation is skipped and it is assumed that the pipe diameter has been fixed at a value which yields a mass flux up the pipe that is numerically equal to the HTV mass flux derived above.
One aspect of thin pipe performance which cannot be ignored however is the loss of heat through the walls of the thin pipe. A temperature difference of hundreds of degrees is involved so that the pipe must be well insulated. The coefficient of thermal conductivity, k, of the pipe walls is the most crucial design parameter for reasons which will shortly become apparent.
Because ocean stratification is a vital aspect of the operating environment a realistic profile of salinity and temperature taken from WOCE Section P18 at latitude 45° S and longitude 155° E. Pressure and density values in were computed using an algorithm published by McDougall et al (2002). This profile was used to determine values of ambient quantities in all subsequent calculations.
The temperatures at which water boils at a given pressure, the saturation temperature, Tsat, was derived using algorithms published by the International Association for the Properties of Water and Steam (IAPWS). They are valid for temperatures between 273.15 K and 863.15 K. Although these algorithms only apply to fresh water they were deemed good enough for present purposes because corresponding algorithms for seawater could not be found.
Conductive Cooling of the Thin Pipe Fluid
The cooling of the vent effluent as it journeyed up the thin pipe was modelled numerically. A test volume was considered which traveled up the pipe with velocity, w, determine by dividing the volume flux by the pipe area. The heat lost in time dt from the test volume was calculated after assumming a realistic value for the coefficient of thermal conductuivity of the pipe wall insulation. Detailed calculations and results are shown in the PDF version of these pages.
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