Core Concepts of the Invention
The Ocean has a Temperature Profile
As Mark Denny puts it in How the Ocean Works "the thermocline separates the ocean into two parts: a well-lit, warm, and nutrient-poor surface layer and a dark, cold, and nutrient-rich deep layer. ...the two layered ocean is a lousy life-support system." The graph on the right depicts a typical temperature profile to a depth of 4000 meters, which is the average depth of the oceans.
Gravity separates the ocean into these two layers such that the less dense fluid is on top. The cool more dense fluid has a tendency to sink, and the warm less dense fluid has a tendency to rise. If we were to take a quantity of sea water from the surface of the ocean and cool it, dye it black and return it to the ocean we would observe that it would assume a depth identical to the corresponding temperature of the water at that depth. This is because the temperature determines the density, provided the salt content is approximately the same. So to create an upwelling in the deep ocean, it is required to raise the temperature of the deep ocean water, and it will assume a new depth, corresponding to the temperature of the water at that depth. If we know the temperature we are forcing on the deep water, we know the depth it will assume. This method of artificial upwelling of targeting the depth by forcing a temperature on the deep water has never been attempted. This is why previous attempts at artificial upwelling were not successful: The deep cold water is difficult to raise in large quantities because of the extra weight. And once raised, it has a tendency to sink.
The heat exchange method of artificial upwelling will effectively poke a hole through the thermocline, and bring nutrients into the realm of photosynthesizing organisms, and create an oasis in the ocean desert.
The Surface of the Ocean Provides Heat
The energy required to raise the temperature of ocean water is substantially greater than for most other substances. The amount of energy per unit mass required to raise the temperature of a substance by one degree Celsius is called the "specific heat". The specific heat of water is 3850 joules per kilogram degree Kelvin, which is more than iron at 460 or lead at 130 or aluminum at 910 or gold at 130. The process of upwelling by forcing a temperature on deep water will require a considerable amount of energy. The energy required to raise a cubic kilometer of seawater by 4 degrees Celsius is 15.4 petajoules. (petajoule = a million gigajoules). The entire power output of the U.S. at 500 gigawatts would take 8.5 hours to provide that much energy.
Fortunately it is not necessary to supply the energy for the upwelling as a supply of heat energy is readily available out in the deep ocean, namely the warmth of the surface of the ocean. The first thing we need to do is to find a way to move warm surface water down to the depths.
Waves Provide the Power for the Down-flow
Place a pipe into position
Consider a vertical pipe is positioned in the ocean such that the top end extends half a meter above sea level and the bottom is in the deep water. (See the figure on the right). There are no waves and the water level inside the pipe is naturally at sea level. If we were to pour water into the pipe we would not be able to fill it, because whatever we pour into the pipe falls out the bottom of the pipe into the deep water. You can stand there all day with a garden hose, and you will not be able to fill the pipe. You can try this in your swimming pool or in your bathtub, or in a glass of iced tea. Hold the pipe or straw in position and add some water. In each case the "sea-level" is quickly restored. Now see the figure below. When a pipe is maintained in a similar position in the ocean when there is wave action, the waves will pour water into the top of the pipe, resulting in a down-flow.
It turns out that the maximum down-flow for any given wave-height will result when the position of the top of the pipe is precisely at sea-level, as this is the elevation where the waves provide the most effective pressure on the pipe. In practice, the flow response is not so rapid as in the bathtub example, because of a significant pipe friction in a very long pipe. Also the huge mass of water contained in the down-flow pipe resists rapid changes in velocity due to momentum.
The Down-flow pipe is a submersed heater
Because the water at the surface of the ocean is warmer than the deep water, the water in the down-flow pipe is warm compared to the surrounding deep water, and the pipe and the warm water within it give up heat energy to the surrounding deep cool water. Once warmed, the deep water will rise because the warm water is less dense. We can observe this rising of warm water in a pot that is gently heated on the stove. The warm water does not stay on the bottom. It rises because warm water is less dense than cool water. It is for the same reason that smoke from a fire in a fireplace rises in a chimney.
Waves provide "wave pressure"
Waves out in the open deep sea are often greater than one meter, crest to trough. The absolute pressure at sea level when a sea is at rest is one atmosphere. If we could place a barometer at exactly sea level during wave action, the barometer would show us that during the trough of the wave the absolute pressure is one atmosphere (due to the weight of the atmosphere), and during the crest of the wave the absolute pressure would be more than one atmosphere due to the extra weight of the water above it. (If the barometer could read that quickly!) If we then average over time the absolute pressure at sea level during wave action we would see that this value is higher than one atmosphere. It is known that in deep water (where the depth is greater than one wavelength of surface waves) the waves do not significantly effect the pressure and a barometric reading is unchanging. A single pipe oriented with the top end at sea level and the bottom end well beneath the waves will have an average net pressure on it and a down-flow within it. The pressure is discontinuous, but the flow is not, since the mass of the water in the pipe has momentum. The analogous electrical circuit has a half-wave rectified voltage driving a resistor and an inductor in series. This flow of warm water to the depths provides the heat that powers the upwelling. No moving parts required.
How Much Pressure Do Waves Provide?
If we could place little equi-density spheres in the water equi-distant apart as in the figure, waves would cause the spheres to rotate in a circle, the largest circle being at the surface. According to Milne-Thompson, who wrote the textbook on Theoretical Hydrodynamics, the pressure moves with the water. That is to say, each black dot representing a small particle of water also represents a specific amount of pressure, the same as the static pressure when there are no waves, due to the weight of the atmosphere and the water above it. This pressure does not change for that particle of fluid when it is moved in a circle due to wave action. Therefore the pressure for a specific elevation changes over time due to the wave, and we do know the variation of pressure as a function of the depth and the wave height. At sea level, where the pressure from waves is at a maximum, the average pressure increase (expressed as head) is about 1/4 that of the wave height as measured from crest to trough.
Turbulent Flow has High Heat Conductance
Water is not a very good heat conductor, as is evident by the temperature change with depth in large bodies of water. However, water conducts heat very well if it moves in a turbulent fashion. Flow of a fluid is either laminar or turbulent. You can observe both laminar flow and turbulent flow from your garden hose. Turn the water on low, and the flow is laminar. Laminar flow is when the direction of the flow at every point remains constant. If you can imagine particles embedded in the fluid, each particle always follows another particle in laminar flow, and the pattern of flow is constant. Turbulent flow, on the other hand, mixes as it flows. A particle of fluid that is at one moment toward the periphery of a pipe containing turbulent flow will at another moment be more central. This mixing of the fluid makes the temperature more uniform throughout the flow, and more heat will leave the flow by way of the enclosing conduit. The flow in a pipe becomes more turbulent as the flow velocity increases, or the pipe diameter decreases.
Both the down-flow pipes, and the up-flow pipes (which enclose the down-flow pipes) will be designed to take advantage of the relatively high heat conductance of turbulent flow. By careful design, the down-flow and the up-flow in the heat exchange method of artificial upwelling can be turbulent in response to a wide range of ocean surface wave-heights.
Convective Heat Transfer
If the temperature of a conduit wall differs from that of the fluid, there is a heat transfer. The effectiveness of heat transfer depends on the temperature difference, the surface area, the heat conductivity of the fluid and the diameter of the conduit, and if the flow is turbulent it also depends on the density, the viscosity and the specific heat of the fluid and the velocity of the flow. In order to determine the amount of heat transfer from these parameters, we first obtain the convective heat transfer coefficient (h) which has the units of watts per square meter degree Kelvin. You can think of the convective heat transfer coefficient as the ability to conduct heat, analogous to a resistance that conducts electricity. And the temperature difference across a heat exchanger is analogous to a voltage that drives an electric current.
Two Physical Laws
In order to calculate the heat transfer in a heat exchanger, you need to know the temperature difference between the two sides. We know the entrance temperatures for the heat exchanger in the ocean, namely the ocean surface temperature and the deep water temperature, but not the exit temperatures. We can find out the temperatures, and the wave height required to power the down-flow if we satisfy two physical laws: The principle of the conservation of energy, and Newton's third law of motion. The physical principle of the conservation of energy requires that the rate at which the down-flow loses heat energy is equal to the rate of heat energy that crosses the heat exchanger. And the rate that the up-flow gains heat energy is equal to the rate of heat energy that crosses the heat exchanger. Newton's 3rd law of motion requires that the friction from the up-flow is equal to the buoyancy of the up-flow from the heating of the fluid. And it also requires that the force from wave pressure on the down-flow is equal to the friction of the down-flow plus the buoyancy of the down-flow.
The Right Kind of Pipe in the Right Place
The invention employs two kinds of pipe. One, which will be made of polyethylene, does not conduct heat well. This is the insulating pipe. It be used to deliver the warm surface water down to the heat exchanger at a predetermined depth, and it will also be the large enveloping container for the up-flow. The other pipe material, made of aluminum with a coating of marine paint, conducts heat very well. It will be used in the interior of the heat exchanger. The combination of these two kinds of pipe with an arrangement designed specifically for a particular location in the ocean, makes it possible to upwell deep ocean water without any moving parts whatsoever.
The Upwelling Performance is Predictable
By utilizing the physical laws of conservation of energy and Newtons 3rd law of motion and the engineering principles behind the fluid mechanics of heat exchangers we can predict the upwelling performance. With a given wave-height at the ocean surface, a given temperature profile of the ocean, and with the dimensions and positions of the two kinds of piping material, the rate of artificial upwelling can be estimated. It is important to design the device for a particular location in the ocean. The ocean is variable in temperature profile and wave heights with respect to location and season. One design may be effective in one part of the ocean and not function in another location or in another season.
The heat exchange method of artificial upwelling requires that the tops of the down-flow pipes be maintained nearly at sea-level. Sea-level, defined here as a midpoint between wave crest and wave trough, is affected by the tides. How the positioning of the upwelling device is achieved is not yet described on these pages.
A Vast Resource
The surface of the earth is 70 percent water. Ninety percent of this area is deep ocean. The average depth of the ocean is 3790 meters (that's 2.4 miles!). The amount of nutrient in the deep ocean is so vast that it could be used to grow food to feed everyone on earth. This resource cannot be depleted in our lifetimes, or anytime in the foreseeable future. It is now accessible.
Artificial Upwelling is Eco-Friendly
1- There will be less need for land agriculture. Farming is a major cause of soil erosion, degradation of wildlife habitats and exploitation of scarce water resources, and fertilizer runoff pollutes streams and rivers creating dead zones from hypoxia. Any increase of food gathered from the ocean means there will be less land needed for agriculture.
2- Marine species may be restored. Artificial upwelling will produce an abundance of forage fish, upon which many marine fish, mammals and birds depend. Feeding the beginning of the food chain benefits all species.
3. There is also the potential for the production of biofuels.
An important key to a sustainable future is learning to utilize this vast resource, which is: the deep ocean.