Oceanic Reverse Osmosis
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One of the great challenges of the Twenty-First Century demands of us that we find ways to provide clean, fresh water to all Humanity and do it at a reasonable cost. Given that the areas with the greatest need tend to lie far from adequate natural sources of fresh water but lie close to oceans, we can infer easily that the best plan for helping such areas will involve large-scale desalination of seawater. One commonly used method of desalination uses reverse osmosis to produce fresh water by pressing seawater against semi-permeable membranes. Reverse osmosis is a mature technology, but we can make a modest improvement in it by exploiting a property characteristic of the oceans Ė their depth.
Osmosis gives us an elegant example of chemical thermodynamics. In an osmotic system a semi-permeable membrane serves as the only active element and itís a remarkably passive one at that. In essence the membrane is a screen with holes so small that only small molecules, like water, can pass through it freely while large molecules, such as the hydrated ions of sodium and chlorine, cannot pass through at all. If we have seawater on one side of such a membrane and fresh water on the other, we will observe a net flow of water from the fresh side of the membrane to the saline side. If we apply enough pressure to the seawater (and if the membrane doesnít burst), the flow of water will reverse: in essence, we will squeeze fresh water out of salt water. That latter process is reverse osmosis.
Reverse osmosis desalination uses semi-permeable membranes wrapped into cylinders. It requires high-pressure pumps (with pressures exceeding 390 pounds per square inch (267.69 newtons per square centimeter)) to force seawater against the membranes and high-pressure turbines to recover as much of the pumping energy as possible. Such systems typically use pressures between 600 and 1200 psi (415 and 829 nt/cm2) and, as a consequence, they expend about three kilowatt-hours of energy on every cubic meter of fresh water that they produce. For small systems that may be a tolerable expense, but consider a major city (such as San Francisco or Los Angeles) whose water needs run to one million or more cubic meters per day.
For those cities and others like them thereís a way to make fresh water cheaper. We need only put the desalinators on the bottom of the ocean. If we put the cylinders containing the semi-permeable membranes a little less than one third of a mile to one half of a mile below the surface, they will encounter the pressures typically used in reverse-osmosis plants. All we would need to provide as the active part of the desalination plant is the means to pump the fresh water out of the cylinders and drive it up onto the land. The pumping will have to provide a bare minimum of 0.744 kilowatt-hour to every cubic meter of fresh water that the system produces in order to keep the reverse osmosis going.
Less than fifty kilometers off the coast of San Francisco, less for Los Angeles, water farms can sit on the bottom of the ocean. The technology to build such farms already exists: it was developed to establish oil wells under the Gulf of Mexico.
To start the project the builders will lay a pipeline (or pipelines) from a base on land across the seabed to the site of the farm, installing low-pressure pumps along the way. Coaxial cables attached to the pumps will provide electricity to run the pumps, which will move the fresh water to the distribution point.
Remotely-operated vehicles, attached to a generator ship through kilometer-long cables, will carry out the actual work of laying pipe and assembling the farm. By making the farm out of components that snap together like Legosģ the builders will reduce the construction of the water farm to a series of simple acts of assembly. Frames laid upon the seabed will hold the production pipes up out of the mud in order to ease the task of working with them. Those pipes and the desalinators that connect to them will snap together through couplings similar to the docking devices used on manned spacecraft. Once two components have been coupled together and the couplings locked, plugs that seal the componentsí ends will be unlocked and pulled back into widenings in the pipe that allow water to flow past them. Every few meters, on top of the production pipes, couplings will hold the reverse-osmosis desalinators, which will be coupled to their pipes and held upright by struts connected to the foundation frame.
An observer seeing the farm in operation will likely see a shimmer enveloping the desalinators and rippling its way down to the seabed. As fresh water gets squeezed into the desalinators, the salt left behind will raise the salinity of the water surrounding the devices, making it denser so that it flows downward off the desalinators thereby enabling more unprocessed seawater to reach the semi-permeable membranes. The higher salinity that will occur around the farm may offer an additional benefit in discouraging sea life from taking up residence and possibly clogging the desalinators.
Once the system begins producing fresh water, several days must elapse before all of the salt water in the pipes comes out and only fresh water emerges at the distribution point. The fresh water that emerges from the pipes will be cleaner than the water that San Francisco currently gets from the Hetch Hetchy Reservoir, some of the cleanest natural water in the United States. Indeed, if a water farm can produce something over 900,000 cubic meters of fresh water per day, the City of San Francisco can stop drawing water from Hetch Hetchy, drain the reservoir, and begin the centuries-long process of restoring the Hetch Hetchy Valley to its natural state and returning the Tuolumne River to its natural flow.
Several decades from now (now being July 2014) the reverse-osmosis process may be rendered obsolete by the arrival of the Omnifex technology. Reprogramming an Omniphage to treat water molecules as individual atoms and to absorb only water, leaving all other substances to be washed off its surface by the local current, seems a fairly straightforward proposition. With an Omniphage the process of extracting fresh water from seawater doesnít require a pressure difference, so an Omniphage-based desalinator can be put anywhere as long as it lies deep enough that it does not interfere with boating or shipping. If an Omniphage can process whatever material presses against its active surface at a rate of twelve millimeters per minute (as described in the essay on the Omnifex), then one square meter of Omniphage will produce 17.28 cubic meters of fresh water per day.
If we want to put an Omniphage desalinator on the bottom of San Francisco Bay, it would require an active area of 52,083 square meters in order to produce as much fresh water as the City of San Francisco gets from Hetch Hetchy. Letís take as our basic unit a panel one meter wide by one hundred meters long and note that we want to tilt it at least forty-five degrees away from the vertical on its short side to facilitate the flow of currents that will take away the increased salinity that accumulates on its active surface. We make an array of these panels by spacing them ten centimeters apart, so an array ten meters wide will contain ten thousand square meters of Omniphage. Five such arrays plus an additional twenty panels will provide what we need. That installation will cover an area of seabed a bit larger than a football field, so the builders could actually put it under, and anchor it to, the Golden Gate Bridge in order to take advantage of the current that runs there.
Because the desalination process reduces the entropy of the seawater it processes, it necessarily absorbs energy. The minimum energy that we calculated for reverse osmosis tells us how much energy, at minimum, any desalination process must expend (0.744 kilowatt-hour per cubic meter of fresh water produced) in order to satisfy that requirement. Our San Francisco desalinator plant would thus require electricity flowing continuously at 27,900 kilowatts to keep the fresh water flowing at a rate of 900,000 cubic meters daily.
Los Angeles gives us another good example of what we may be able to do. In 2003 the Los Angeles Department of Water and Power provided fresh water at a rate of a little over two million cubic meters per day. To match that yield builders would have to put an Omniphage-based installation with a footprint as big as the Rose Bowl on the bottom of Santa Monica Bay. The output can then be pumped through a pipe that runs alongside or under Ballona Creek, which was once the outlet of the Los Angeles River. The water can be pumped up to a point whence it can be distributed throughout the city. The water will require no treatment beyond the addition of a few minerals, because the water that comes out of an Omniphage differs not at all from distilled water.
Our builders might also put a water farm off the coast of Long Beach, anchoring it to the seabed among the artificial islands that hold the oil wells of Long Beach. The pipe carrying the output water from that farm would then run alongside the Los Angeles River as far north as downtown Los Angeles.
Our builders might also establish a water farm on the seabed off the coast at Malibu. The output would flow into a small tunnel running under Malibu Creek, get pumped up into and through the Santa Monica Mountains, and emerge near Calabasas. From there the water would be distributed eastward, throughout the San Fernando Valley.
That triple project may look daunting, but, given the existence of the Omniphage, it is actually less ambitious than whatís in place and functioning now. Currently Los Angeles gets most of its water from three major sources, which could all be shut down when the water farms come online:
1. The Los Angeles Aqueduct, which was built in 1913, brings water from the Owens Valley. In consequence Owens Valley, an agricultural community, has been decimated and Owens Lake has shrunk so much that one of the valleyís major (and unintended) exports is toxic dust from the lake bottom. Shutting off the aqueduct will enable the valley to heal and to regain its original health. Indeed, our builders can go further: if they establish a water farm between Santa Monica and Malibu, pump water over and through the Santa Monica Mountains and across the San Fernando Valley to the southern end of the old aqueduct above Sylmar, then they could reverse the flow, pumping fresh water up to the Owens Valley to augment its natural sources.
2. The California Aqueduct, which exists as an open canal down the full length of the San Joaquin Valley, brings water from Northern California. Instead of shutting it down completely, our builders keep the water flowing, but stop it at the siphons that carry it into the Tehachapi Mountains. At points along the canal local agencies remove specified amounts of water for use in irrigating farms on the west side (the dry side) of the Valley, one of the most productive agricultural regions on Earth.
3. The Colorado River Aqueduct gives our builders a wide range of options. Certainly they could stop the flow altogether and divide Californiaís share of the Colorado Riverís water among Nevada, Arizona, and Mexico. Or they might stop the flow near Palm Springs and distribute the water throughout the Coachella Valley. Or they might even stop the flow further east and use the water to irrigate part of the Mojave Desert, enabling the establishment of plantations of date palms, orange trees, lemons, limes, and anything else that can tolerate the desertís temperature extremes.
Of course all of the above depends upon our builders being able to get a working Omniphage and the power to run it. If those two things can be had, then one of the great problems of the Twenty-First Century will dissolve quite easily.
Derived from the Greek word for push or impulsion, osmosis denotes the phenomenon in which a solvent separated from a solution by a semi-permeable barrier flows across the barrier to dilute the solution. It seems almost magical, but in fact it gives us an excellent example of the workings of chemical thermodynamics.
As an example consider seawater separated from fresh water by a semi-permeable membrane. On average every kilogram of seawater contains 35 grams of sodium chloride and smaller amounts of other salts. If our osmotic system contains seawater at that level of salinity, then fresh water will flow across the membrane with a measured osmotic pressure of 390 pounds per square inch (267.69 newtons per square centimeter), the overpressure that must be imposed upon the solution to stop osmosis from happening. To explain osmosis we need to account for that pressure.
We can make an analogy between the sodium and chlorine ions suspended in water and the particles in an ideal gas. In this analogy the water plays the role of the container holding the gas. To see whether thatís a good analogy we calculate the pressure that the sodium/chlorine pseudo-gas exerts upon the walls of its container.
We use the ideal gas equation (p=nRT), in which we multiply the density of the gas particles by the ideal gas constant and the absolute temperature of the gas. This particular use of the ideal gas equation to describe a liquid solution was first described by J. H. vanít Hoff in 1885. In this case we have seawater consisting of 469 moles of sodium ions and 546 moles of chloride ions dissolved in 53,600 moles of water (one tonne of seawater). We take the absolute temperature of the system to be standard room temperature, T=293 degrees Kelvin (20 degrees Celsius). With those units set, we have R=8.314 joules per mole per degree Kelvin. We thus multiply 1015 moles of sodium and chloride ions per cubic meter of water by 2436.002 joules per mole and thereby calculate an osmotic pressure of 247.25 newtons per square centimeter, which compares favorably with the measured osmotic pressure of the seawater/fresh water system. If we add in the partial pressures due to sulfate, magnesium, calcium, potassium, and bicarbonate ions in the seawater, we calculate the osmotic pressure as 272.6 nt/cm2.
Our calculation gives us a correct value for the osmotic pressure, so we can feel confident that our analogy with an ideal gas comes close to the truth of the matter. Itís good enough for engineering, certainly: the vanít Hoff equation gives us a correct calculation of the osmotic pressure. As physicists, though, we want to know more; we want to understand whatís causing the solvent to flow across the membrane. So given that a solution behaves like a gas in a container, we ask How does it work? How does this model produce the phenomenon of osmosis?
Having analogized the solute ions to the particles in an ideal gas, letís look at an actual ideal gas (or a reasonable facsimile of one). Imagine a chamber filled with pure hydrogen gas at room temperature and a pressure of P(H2). Take a rubber balloon and fill it with pure nitrogen at a pressure of P(N2) and put it into the chamber. In a short time the balloon will expand due to hydrogen passing through the rubber skin and into the balloon. The expansion will stop when the partial pressure of the hydrogen inside the balloon equals the pressure of the hydrogen outside the balloon. The total pressure inside the balloon thus equals P(H2) plus the pressure caused by the stretched rubber, that latter pressure being equal to the partial pressure of the nitrogen P(N2).
We are accustomed to the concept of different pressures equalizing when their containers are connected. If we have compressed air in a cylindrical tank (of the kind used by scuba divers perhaps) and we open the valve, we know that some air in the tank will come out and that the air will continue to come out of the tank until the pressure inside the tank equals the pressure of the surrounding atmosphere. But the idea that partial pressures equalize separately involves a bit more subtlety. We need to look at our theory of gases on the molecular level.
Of course we understand in our present example that hydrogen molecules pass through submicroscopic pores in the rubber skin and that the nitrogen molecules are too big to pass through those pores. We also know that not all of the hydrogen molecules that approach the rubber pass through it; most hit the rubber and bounce off it, contributing to the pressure that the gas exerts upon the rubber. Now we remember that the rate at which the hydrogen molecules pass through the pores stands, in part, proportional to the density of the hydrogen. In the case of our balloon hydrogen will seep into the balloon faster than it seeps out, so there will be a net flow of hydrogen into the balloon until the hydrogen density on both sides of the rubber skin equalizes or until some applied pressure (as, for example, caused by the stretching of the rubber) stops the process.
If the gas both inside and outside the balloon has the same temperature, then equalization of the hydrogen density corresponds to an equalization of the pressure. If the balloon had started out empty, then the seepage of hydrogen into it would stop as soon as the rubber went taut. Any stretching of the rubber would produce a pressure that would increase the density of the hydrogen and cause a net outward seepage of the gas until the additional pressure went away.
Another assumption that we incorporate into the theory of ideal gases, which assumption conforms very closely to the nature of real gases, tells us that the molecules interact with each other only rarely. So, to a good approximation, the hydrogen molecules and the nitrogen molecules inside the balloon donít have any direct effect on one another. The nitrogen only has an indirect effect on the hydrogen by diluting it and that dilution causes the osmosis.
As long as the balloon is limp, the pressure on the inside, the sum of the partial pressures of the nitrogen and the hydrogen, must equal the pressure of the hydrogen atmosphere outside the balloon. That fact necessitates that the partial pressure of the hydrogen and, therefore, the density of the hydrogen, be less than the pressure and density of the hydrogen outside the balloon. Thus hydrogen will seep into the balloon faster than it seeps out. The balloon will fill with hydrogen until the rubber goes taut and then fill further until the rubber stretches enough to create a pressure equal to the partial pressure of the nitrogen. When the system has come to equilibrium, the stretched rubber produces a pressure that balances the partial pressure of the nitrogen and the pressure of the outside atmosphere balances the partial pressure of the hydrogen.
In a liquid solution one of our ideal-gas assumptions no longer operates. In a liquid the molecules interact with each other frequently and strongly. To gain an impression of how strongly we need only return to the pressure calculation that we carried out for sodium chloride in water. We had 1015 moles of sodium and chloride ions in one cubic meter of water producing 247.25 newtons per square centimeter (24.4 atmospheres) of osmotic pressure. That cubic meter contains 53,600 moles of water and if we apply the vanít Hoff equation to that fluid, we calculate a pressure of 13,057 newtons per square centimeter (1289 atmospheres). Of course, the only pressure that a cubic meter of water exerts comes from its weight: the mutual attraction of the water molecules cancels the 1289 atmospheres of gas pressure, thereby making water a liquid.
Imagine two open containers connected to each other through a semipermeable membrane, one through which water molecules will pass but salt ions wonít. Fill both containers to the same level, one with fresh water and the other with salt water (35 grams of sodium chloride per kilogram of water). The mechanical pressure on the membrane will be almost zero, the pressure on the salt side being slightly higher than the pressure on the fresh side due to the extra weight of the dissolved salt. But we also expect to measure 24.4 atmospheres of osmotic pressure difference across the membrane.
One cubic meter of seawater ponders 1025 kilograms and contains 35 kilograms of salt, so the water alone ponders 990 kilograms, ten kilograms less than we find in one cubic meter of fresh water. Even though seawater is heavier than an equal volume of fresh water, its water content is less dense than that of fresh water and therein lies our explanation of osmosis. In spite of the force drawing water molecules toward each other, the molecules are only loosely connected (so that they slide freely past one another, instead of being rigidly connected as in a solid), so we can describe their motions much as we describe the motions of particles in a gas. But unlike the case of a gas, whose particles move in more-or-less empty space (in accordance with our assumption of rare interactions), the molecules in a liquid rub up against each other: that fact makes the liquid effectively incompressible. Held together by electrostatic force, the molecules also repel each other if they come too close. If something, such as a piston, presses on the liquid, the force exerted on the molecules touching the piston will be exerted through those molecules onto their neighbors, which pass the force on to their neighbors, and so on. Because the molecules slide freely over one another, like greased ball bearings, the pressure exerted at any point in the fluid gets transmitted uniformly in all directions.
At the membrane the rate at which water molecules pass through the pores stands in direct proportion to the particle density of the water, so water seeps more rapidly from fresh to salt than it does from salt to fresh, thereby producing a net flow of fresh water into the salt water. That net flow will make the free surface on the salt side rise and the free surface of the water on the fresh side fall. In consequence a mechanical pressure will grow on the membrane until the difference in the water levels produces a mechanical pressure that exactly counters the osmotic pressure and brings the osmosis to an end. Raising the level of the salt water necessitates that something do work upon the water in order to satisfy the conservation of energy law. Most of that work comes from the fall of the fresh water and the remainder comes from the kinetic energies of the water molecules, the heat of the water.
By analogy with what happens with our balloon, we can attribute partial osmotic pressures to the components of the salt water. Those partial pressures must add up to a pressure equal to the osmotic pressure on the fresh water side of the membrane; otherwise, the difference in the total pressures would come manifest as a mechanical pressure. So on the salt side we have the partial pressure of the salt as 24.4 atmospheres and the partial pressure of the water as 1289-24.4 = 1264.6 atmospheres. As the hydrogen does in the balloon case, the water moves to equalize the two water partial pressures. Only two factors will stop the net flow of water from fresh to salt.
The first factor is dilution. If enough fresh water flows into the salt water, it will dilute the salt and thereby lower its osmotic pressure. If the salt concentration is diluted effectively to zero, then osmosis will stop: the osmotic pressure of the water on both sides of the membrane has equalized.
Application of a mechanical pressure to the salt side, as by pressing a piston down on the free surface, will also bring osmosis to a halt. The applied pressure increases the rate at which water seeps from the salt side of the membrane to the fresh side: it thus augments the seepage due to the osmotic pressure in the salt water. The amount of applied pressure that will bring the seepage from salt to fresh to equality with the seepage from fresh to salt equals the amount by which the osmotic pressure in the water on the salt side differs from the osmotic pressure in the fresh water, which difference equals the osmotic pressure that we attribute to the salt.
If we increase the applied pressure, we will further enhance the rate of seepage from salt to fresh and thereby generate reverse osmosis. We will cause the water molecules on the salt side to push into the pores harder than the molecules on the fresh side do, so there will be net seepage from salt to fresh as the more forceful molecules push through.
Thus we have a simple, straightforward description and explanation of osmosis.
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