The most radical difference between conventional pumped storage and EPS is the latter’s use of hundreds or thousands of mini-reservoirs—bags—which rest on top of the landscape, instead of two monolithic, sunk-in reservoirs made of materials like concrete and steel1. We need to know if these bags can meet the complex demands that EPS will place on them, and still be inexpensive enough.
The key requirement of a bag in an EPS system is tensile strength. It must withstand the forces exerted by water when the bag is full, and must do so for thousands of fill/drain cycles. It must last for several decades, possibly with minor repairs along the way—while individual bags will sometimes fail and have to be replaced, the average lifespan of a bag should be on the order of 30 years.
How much tensile strength is required? This is a function of the height of the water column in the bag, when it’s full (the hydraulic head). As discussed earlier, the pressure at the bottom of a column of water is 0.43 psi per foot of head, or 0.097 atm per meter. The Capitan-spec bags are 5 meters (16.4 feet) tall when full, which is roughly twice the typical height for pillow tanks that are considered large (they’re small from our perspective), so the water pressure at the bottom will be 0.48 atmospheres (7.1 psi).
The way a membrane, which has only tensile strength, resists pressure is by curving. Without detouring too far into the physics, this is governed by Laplace’s Law2. For a cylindrical bag (of which a slice out of our bag, not near the corners, is an approximation), the tension in the membrane equals the pressure difference across it, times the radius. So if you double the radius—make the bag less curved—the membrane has to withstand twice as much tension.
So, if we scale up a bag and make each of its dimensions twice as big (and then pump water into it with twice as much pressure, which is the only way to make it stand twice as tall), the radius at various points in the cross section will also double, and Laplace’s Law tells us that the tensile stress in the bag will double as well. (The volume of water in the bag went up by a factor of 8, which is good.) We will have to use somewhat stronger material than is used in a commercial pillow tank, but not drastically stronger. But in general, if we want the bag to be taller, we have to use stronger material.
In terms of water-flow properties, a EPS storage field must simulate the behavior of a conventional reservoir. It must accept and release water as the powerhouse demands, with predictable and low friction losses. As its behavior is a composite result of many bags filling or draining at once, each of those bags must have those properties too. Unpredictability in filling/draining behavior would be unacceptable. For example, a naive design might allow the bag to collapse unevenly and block off its own exit pipe, leaving water trapped in the bag. Or less drastically, as a bag is draining, its resistance to flow might suddenly increase because the bag height has become too small to allow free flow. To avoid these problems, attention must be paid to how the water enters and exits the bag, and to having the right degree of flexibility (neither too much nor too little) in the bag itself.
Albedo is a measure of how much incoming solar energy gets reflected away, versus being absorbed. Simply put, black bags of water in a sunny desert, in the summer, will get extremely hot—the water will start to boil before long. Reflective, white bags will stay much cooler, which is what we need for EPS, which runs on liquid water, not steam.
Excessive solar input will be an issue for EPS, especially at the lower storage fields, where temperatures are higher and cooling breezes are often absent. Some sites—think of Death Valley—may simply not be usable for EPS for this reason. Solar input, and bag temperatures, could be greatly reduced by having a shade (made of fabric-reinforced plastic, like the bags themselves) installed a few feet above the bags, but at a considerable cost; better to just look for a more amenable site. In any case, it’s crucial that the bags reflect away, rather than absorb, as much solar energy as possible.
Given the conditions where these bags live, they need to withstand a very wide range of temperatures. They might be well below freezing and covered in ice and snow in the winter, and approach the boiling temperature of water in the summer. For long and trouble-free life, we would like to have a wide margin of safety between the temperatures expected to occur, and those that the bags are designed to handle.
-40°C should be fine as a lower working temperature limit for the materials. (I’m not currently considering EPS sites in genuinely cold, snowy climates, like the Canadian Rockies, where there would be other problems to contend with, like keeping snow and ice off the bags.)3
As for the upper limit, something like 120°C (248°F) would be very safe, and well above the boiling temperature of water (100°C or 212°F). That may not be realistic for a low-cost material, but we’d like to have a working temperature of at least 80°C (176°F).
Requirements In Different Bag Areas
Inexpensive pillow tanks are meant for temporary use and are, in EPS terms, small. For cost reasons, they’re made as simply as possible, with a single kind of flexible membrane material comprising the whole bag. (The material chosen for a specific product depends on whether it’s made to hold fuel, oil, potable water, non-potable water, etc.) EPS bags are much longer-lived and designed for one purpose, and it makes sense to pay more attention to their specific properties. Since they are assembled out of narrower strips of material, we can tailor each part of the bag for the job it does.
The bottom of the bag hardly moves—it will expand and contract a little, but sandwiched between a heavy column of water and the ground, it doesn’t need to be particularly strong. All it needs to do is bridge small gaps between rocks underneath it, and resist abrasion caused by its very small degree of movement. So that’s one kind of material.
The top of the bag mostly goes up and down as the bag fills and drains. It will have to flex somewhat, but it doesn’t have to bend and fold freely. It’s better, in fact, if it doesn’t (as discussed below). It does have to endure intense desert sun, so it’s exposed to ultraviolet light and high temperatures, both of which are harmful to most polymer (plastic) materials, so it has to be able to withstand those. Another reason we need to reflect away sunlight is to keep the water from heating up too much.
The sides of the bag are where most of the flexure takes place as the bag fills and drains, and where the water pressure places the greatest demands on its tensile strength. This is the material that has to be very strong and flexible, able to withstand thousands of fill/drain cycles in which its shape is radically changed. At the same time, it will still have significant exposure to sunlight, and so, like the top of the bag, it must not break down when exposed to UV (ultraviolet) radiation or high temperatures. Given all these demands, it may be the most expensive part of the bag. Like the top, it doesn’t need abrasion resistance, though.
Flexibility is not an absolute quality, but is related to size. A sandwich bag is capable of folding over on itself within hundredths of an inch. That’s extremely flexible. There’s no reason for a water reservoir that’s 27 by 27 meters in area to have anything like that level of flexibility. If that reservoir is made so that it can be folded in two over a one-meter diameter, that’s probably as much flexibility as it would ever need. I’ll discuss below why too much flexibility can do more harm than good.
Shape & Construction
Manufacturers of these containers make them in many shapes and designs; the simplest is a plain pillow. Conceptually, this can be made by laying two squares of material in a stack, and then welding the edges together. When water is pumped into this structure, it will assume a pillow shape. In practice, given that the raw material comes in narrower strips and that we want to use different materials for different parts of the bag, we’ll weld together sub-assemblies out of strips and then make the final seam, but the process is about the same. The bag will have a square footprint, to maximize water capacity per dollar.
The Capitan bag spec called for a rectangular prism shape (which is not the shape a water-filled bag will assume in practice, but it’s easier to think about) that is 27 x 27 x 5 meters in size. That’s probably about the right amount of material, and works out to 1,998 square meters (2 x 27 x 27 + 4 x 27 x 5). Round that to 2,000. In the simple pillow configuration, that means two squares of 1,000 square meters each (31.6 m on a side).
To facilitate free flow of water into and out of the bag, a manifold is attached to the bottom of the bag during manufacturing. This rigid structure, made of glass-reinforced polymer or a similar material, affords a large area for water flow, while supporting the weight of the water column against the terrain below it. Smooth channels of large cross-sectional area convey water from the bag into a horizontal pipe which will enter the prefabricated chamber (which lies outside the footprint of the bag for ease of access), where the transient valve and attachment fitting are located. This allows the bag to be connected to the distribution piping system in the field. The area of the bag where it attaches to the manifold will be heavily reinforced, or made of stronger material, because that’s a natural stress point.
This is a possible high-level design for the manifold. A bathtub-shaped opening lets water flow in or out of the bag. Note that when the bag is full, 0.48 atmospheres (7.1 psi) of weight will bear on this whole structure, which must be designed to transfer that weight to the terrain beneath it. We want to minimize the cost of the manifold, so the opening should only be as large as required by hydrodynamics (i.e. the need to keep friction losses small). Computer simulation will be needed to validate the manifold design.
The weight of the bag itself (when empty) isn’t critical, but it will have an effect on handling—what size crane is needed to move it, for example. An overestimate is fine for now. Assume the membrane weighs a relatively heavy 40 ounces per square yard. That’s 1.35 kg per square meter. The Capitan bag design needs about 2,000 square meters of material as noted, for a mass of 2,700 kg (2.7 tons). The manifold will add to this; conservatively, estimate the whole assembly at 3.25 tons. A standard 5-ton truck crane will handle the load (but we’ll have to make sure we have enough road access to reach each pad). Or maybe we’ll want a stationary crane with longer reach, to cut down on the storage area lost to roads.
For truck transport and to be lifted onto its pad by crane, the bag will need to fold. Commercial pillow tanks are designed to fold very tightly for transport. Ours will only need to be transported a few times during their life, so all we need to do is loosely wrap the sides of the bag into a cylindrical shape, aligned with the manifold. The bag will have integral fasteners to tie it into this shape for transport.
By “pad,” I mean a surface location prepared for an individual bag, regardless of the exact shape of the surface, surface roughness, slope, presence or absence of additional material to improve the surface, and so on.
In cycling between its most empty and its most full state, the bag will “breathe”—that is, it will change from a flatter, more spread-out shape when drained, to a taller and more drawn-in shape with a smaller footprint when full. So there will be some movement between the bottom of the bag and the ground it’s resting on. It won’t be very much, but over time, a sharp rock in the wrong place could damage the bag. The material used for the bottom of the bag will need to have good abrasion resistance (like the Grand Canyon rafts I mentioned that were dragged over rocks for decades), but the pad should also be gone over by a road roller or similar machine to make sure the risk is minimized. Still, the tougher the bag is, the less we have to spend on the pads, which is critical for meeting overall budget.
After the pad surface is prepared as needed by excavation, filling, and rolling, a trench is cut from where the center of the bag will be, to the nearest distribution pipe. A small chamber is prepared (perhaps lined with a prefabricated plastic box), into which the feed pipe (which leads to the distribution pipe), the transient valve, and the capped fitting where the bag will attach are all installed. The feed pipe is covered with earth and the chamber is closed with a lid. At the center of the pad, a receiver is prepared into which the manifold, attached to the bottom of the bag, will be lowered. This will provide positive location for the bag and allow the connection between the bag and the distribution system to be made in the enclosed chamber, where dirt and debris can’t enter the system.
The pre-manufactured bag and manifold assembly is partially rolled up at the factory, and secured so it can be moved by crane and transported by truck to the site. There, the crane, with the help of workers on the ground, will precisely place the bag assembly on its pad, with the manifold dropping into its receiver, ensuring precise location as well as full support of the water column the bag will hold when filled. Workers in the valve chamber will attach a short length of pipe to span the final gap between the manifold and the piping system (these design details are provisional, and could change).
Finally, the bag can be unbundled and laid out flat on the pad, and the corners weighted down. At this point, the bag is vulnerable to wind, so as soon as possible, the transient valve should be opened, and a pump activated in the powerhouse to start pumping water into the new bag. Once enough water has entered the bag, its mass will protect it from wind.
Removal of a bag is just the installation process in reverse. First, the control system must empty the bag as completely as possible through its transient valve, after which the transient valve is closed. Then, the valve chamber can be opened, and a crew can disconnect the fitting connecting the manifold to the piping system. A cap is placed on the piping system end to keep dirt and debris out, and another cap is placed on the manifold end for the same reason.
Next, the bag is rolled up and secured into its transit position. A crane lifts the bag and transfers it onto a waiting truck, where it’s secured and transported to the repair shop or other destination.
Some threats to the bags have been discussed: UV exposure, temperature, and abrasion. Additional hazards include:
As mentioned above, the bag changes shape during operation. On too great of a slope, over many cycles, it might tend to walk downslope. It wouldn’t be able to move far without starting to damage the connection of the bag to its manifold, or the manifold to the fitting that connects it to the piping system. To prevent this, overall slope must be minimal; a slightly concave pad shape will help; and finally, the bag should never be drained below a certain level, ensuring a large mass of water in the bag at all times, which will keep it in place. (This should be simpler and more cost-effective than the alternative, which is to embed anchors in the site and fasten the bags to them.)
Runoff from rain or snow must be kept away from the pads or drained away, so that pad material is not eroded away from under the bags.
The tops of mountains are often very windy places (though high winds will sometimes occur at the bottom, too). The bags must handle windstorms. The worst case, of wind causing a whole bag to sail away, can be prevented by always leaving plenty of water in the bag, as just mentioned. Another concern is that wind could cause rippling of the top of the bag, like a loose sail, which could damage the material. This is one reason to use a less flexible material for the top of the bag, as discussed above, since such a material will have less tendency to ripple. It’s also a reason to keep air out of the bag—it will be harder for wind to move the bag material with a large mass of water in contact with it from below.
Snow, Ice, and Hail
The bags must, and should, be intrinsically tough enough to withstand these in moderation. As mentioned, EPS is most suited for hot, dry climates where snowfall is seldom heavy.
Large animals, such as elk or bears, should be kept out by a perimeter fence. The bag materials should withstand attacks by smaller animals and birds, and materials should be chosen that aren’t appealing to wildlife. Pillow tanks are deployed outdoors all over the world, so manufacturers should be a good source of information about this concern.
The region where EPS makes the most sense, the Southwestern U.S., is prone to wildfires. Some potential EPS sites are forested (usually at the upper storage area only), and vegetation at potential sites ranges from full-on Ponderosa forests, to scattered brush and grasses, to bare rock. Politically speaking, it will be much harder to get approval for sites where large stands of trees must be cleared, particularly if there’s an urban center nearby. (Unfortunately, proximity to urban centers is very desirable in terms of locating the stored electricity close to where it’s needed, rather than shipping it great distances in transmission lines.)
So in the near term, EPS may only be politically feasible at sites where there is almost no vegetation—the kinds of places that some city-dwellers would consider “useless,” or “wasteland.” In those places, wildfire is not a concern.
As for forested locations, given fire trends in recent years, a high-intensity forest fire is possible almost anywhere there are trees. (Some potential EPS sites I’ve looked at in California have already burned since I first noticed them.) So the EPS site itself will need to be cleared of vegetation, and kept cleared, including a significant firebreak on all sides. Damage to bags from wind-borne embers is likely, though spot fires will self-extinguish as soon as they burn through, if there’s water in the bag.
The site needs protection like any other grid component, such as a solar farm or power substation. There should be onsite security, motion detectors monitored by the central control system, camera drones that can be dispatched when needed, and so on.
A vandal could do far more damage to a solar farm than to an EPS site, with less effort. A rifle or handgun could destroy solar panels at a high rate. A rifle fired at an EPS bag would cause a small leak, which would be found by visual inspection before too long, and could be patched (after draining that individual bag if necessary). An EPS site should be a fairly disappointing vandalism target.
Because we need so much material, we’ll select the least expensive ones we can find that will meet all of our requirements.
The woven core material provides most of the tensile strength of the finished product. Polyester and nylon are common choices. Nylon is somewhat stronger, but stretches more, which is probably a negative rather than a positive for our application. Polyester has a working temperature range of -60 to 150°C, but reduction of tensile strength above 80°C (176°F) may be a concern (only direct sun exposure, of material not in contact with water, could cause such high temperatures). Nylon seems to have a similar temperature range.
Glass, as a core material, is most often used for rigid, rather than flexible, applications (such as fiberglass boats). It’s hard to find a tarp whose core material is glass. Glass might have a place in EPS, though, where the top of the bag should not be too flexible (as discussed above) and where the highest temperatures will be encountered.
The coating material has to provide many of the needed properties: UV resistance, abrasion resistance, compatibility with water, and resistance to cracking at cold temperatures and softening at high temperatures. PVC, the cheapest and most widely used coating (for things like tarps), doesn’t have the temperature range we need. Polyurethane-based materials might meet our needs. Another candidate is EPDM (which seems to have an excellent service temperature range of -50°C to 150°C).
High albedo is critical for the top and sides of the bag. Not all coating materials can be made with an intrinsically high albedo, so some materials would require an additional reflective coating on top of the base material. This is an extra manufacturing step, and must adhere well and have a long service life, so it’s another factor in the overall cost computation.
Assembly and Repair
Bag materials will come from the manufacturer in fixed-width rolls (the wider, the better, for our application) and will need to be joined to make bags. Welding (whether heat, ultrasonic, or RF) is the preferred way of fastening. It’s the quickest and simplest method because it involves only the material sheets themselves, and has no significant curing or setting time. Properly done, welding doesn’t negatively affect the strength or longevity of the material. Gluing is more complex and reduces longevity (due to a phenomenon called plasticizer migration) and will be avoided. This disqualifies some materials like Neoprene or Hypalon (a retired DuPont brand name for chlorosulfonated polyethylene or CSPE) that can’t be welded effectively. Neoprene and some other materials can be fused very well by vulcanizing them after assembly, but this requires putting the whole assembled item into an autoclave and heating it, which would be impractical at this scale.
Assuming we’re using different materials for different parts of the bag, these need to be compatible in terms of assembly (i.e. mutually weldable).
The ability to do small repairs with the bag left in place would be very advantageous. Some coating materials are too slippery to be patched, so this is another factor to take into account.
The firms that manufacture these materials are the experts, and the best materials and prices will be found by consulting with them.
As mentioned, the pillow tank is the simplest, but not the only design possible. Another widely sold design is called an onion tank, due to its shape:
It’s circular, and open at the top. What makes this possible is the tension ring, where the black and yellow materials meet in this picture.
Inspired by this, here’s a different EPS bag design:
The two tension rings are extremely strong (candidate materials would be aramid fiber [e.g. Kevlar], or steel). They don’t need to flex at all. The sidewall material is also very strong, but flexible. (It could be strengthened by a reinforcing mesh if that’s the cheapest way to get the required strength.) The hoops and the sidewall do most of the work of resisting the water pressure. That means that the top and bottom can be made of less costly, low-strength materials. (The top and side materials still need high albedo.)
When filled with water, it will assume a minimum-energy shape something like this:
This design is obviously more complex to build than the simple pillow tank. What’s good about it is that it gets more cost-effective (fewer dollars per cubic meter of water) as it gets wider: the tension rings and the material for the sidewall scale up only linearly with the diameter; the top and bottom scale up as the square of the diameter, but are cheaper.
This might be particularly good for a lower storage area, which is typically flat or gently sloped, and may be easy to excavate due to its alluvial nature. In that case, the lower storage tanks could be much larger than the upper ones, and combined with this tank design, the result would be lower cost.
Each bag will be equipped with an internal pressure sensor, near the bottom of the bag or in the manifold, so the control system can measure how much water it contains. This will have external connectors to hook up to the control system wiring which runs alongside the distribution piping network.
If air and/or water vapor have a tendency to accumulate at the top of the bag, an air bleed valve can be fitted to automatically vent these gases out. (Air might be entrained in the water as it passes through the turbine, and small bubbles might not have time to escape before the water reaches the bags in the lower storage field.)
Access to the inside of the tank for inspection is a useful capability. This can be done without draining the tank if a small porthole near the top of the bag can be opened, allowing a small remote-controlled submarine with cameras to be placed inside. A bag that’s been drained and removed from the site can be inflated with air, allowing workers to enter through the manifold.
I’ve mentioned that as far as I know, Capitan-sized bags are larger than anything sold commercially, just because no one has had a need for such large bags before. (And we don’t need just a few of them—our first production order will be for 2,000, plus spares.) Generally, commercial products get cheaper if you buy them in greater quantity, but I don’t think there’s a reliable formula for the size of the discount. A bag is relatively simple to make as manufactured goods go, so as it gets bigger, the price will tend to be dominated more and more by the cost of raw materials. This all means that we can expect some cost improvement from the large scale, but it’s hard to say how much.
Overall Price Estimate
At this point, a back-of-the-envelope calculation is the best we can do. The largest pillow tank for which I can find a price online is this one from Interstate Products, Inc. It’s for non-potable water use, the price is $10,301 (including a protective ground mat) and the capacity is 25,000 gallons. The dimensions aren’t given, but from the photos I estimate that this bag, empty, would cover about 8 x 25 meters. Times two for top and bottom, this amounts to 500 square meters of bag material. The price works out to $25.75 per square meter. Assuming a 50% markup over the cost of the bag material alone, we’re at $12.88 per square meter, which is in line with prices of similar materials sold in bulk.
I computed above that the Capitan bag design needs about 2,000 square meters of material. At $12.88 per square meter, a bag would cost $25,760. We need 2,000 bags (a thousand each at top and bottom); that comes to $51.5 million.
In the previous post I calculated “excellent” and “very good” overall project budgets of $750 million and $1 billion respectively for the Capitan system. Using the better $750 million figure, $51.5 million for bag material would be just under 7% of the total project budget. That seems reasonable and encouraging, which is all we should hope for from an estimate that was arrived at this way.
- Less expensive options like embankment dams are not feasible on mountaintops.
- Several laws are named after the prolific Pierre-Simon Laplace, and this is one of the simpler ones.
- By the way, -40 is the magic temperature that’s the same in Celsius and Fahrenheit.