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| Fig. 1: Aerial view of Hoover Dam and Lake Mead. (Source: Wikimedia Commons) |
A surprising 50% of the energy from the sun absorbed at the earth's surface is used to fuel the process of evaporation. [1] This has led scientists to consider how the energy in this process could be used as a renewable energy source. In 2015, research published in Nature described several types of devices that could be placed on large bodies of water to harness this energy. [2] These devices use a strain of soil bacterium B. subtilis that expands and contracts in response to changes in humidity. The bacteria is placed on a plastic strip, and the force from the change in size stretches and contracts the strip as a whole, motion which can be turned into electrical energy. [3] Of course, in general humidity varies on a daily timescale, but the device is designed in such a way that shutters surrounding the strips of spores open and close to block moisture. A second design utilizes the same bacterial spores but places them on a wheel with one half enclosed in plastic. The humidity is higher in the enclosed half due to wet paper that lines the plastic while the outside air is dry; the resulting elongation and contraction of the spores offsets the center of gravity from the axis causing the wheel to rotate. [3] More details on how these devices work can be found in Chen et al. and Humphrey. [2,4]
Evaporation as a renewable has come back into the news again due to further research also published in Nature analyzing the potential of these devices in the United States. The headline number is that these devices could generate 325 GW (which in perspective is 70% of the nation's total electricity generation) and has excited many journalists. [5,6] But it is worth understanding how the authors arrived at such a large figure to better understand the feasibility of this proposal.
At first glance, calculating the power generated by an evaporation-driven engine seems straightforward. Water is absorbed at a high chemical potential μs and released at a lower chemical potential μe. Under the simple modeling of the device as a reversible and isothermal engine, the power output depends on two factors: the evaporation rate E and the difference between these two chemical potentials w = μs - μe (the work done for every mole of water that evaporates). The complication in calculating the power comes from the fact that we cannot simply use the current evaporation rate in this calculation; the process of converting evaporation into energy affects how fast evaporation occurs. [1]
di Cavusoglu et al. identify two factors that describe how w affects E. [1] The first is the change in water vapor pressure across the engine. The air below the engine and just above the water is saturated, while the difference in chemical pressure w causes the water vapor pressure to drop. The ratio between these two vapor pressures is given by α(w) and can be interpreted as the relative humidity above the engine:
| α(w) = exp (-w/RTs) | (1) |
where R is the molar gas constant and Ts is the surface temperature. The evaporation rate then depends on this change in vapor pressure; in essence, increasing w causes E to decrease. [1] The second factor is the extra energy cost to evaporate the water through the evaporation engine as compared to normal circumstances. The authors define the ratio β(w) between these two energy costs, where L is the latent heat of the vaporization of water:
| β(w) = 1 + w/L | (2) |
We can thus interpret β(w) as the energy penalty for using the evaporation energy, accounting for solar energy removed from the environment as work. [1] Together these two parameters α and β can be used to model the evaporation rate and generated power.
As defined above, α and β are both dimensionless ratios. α can vary between 0 and 1, while β is greater than or equal to 1. Furthermore, because both parameters depend on w, they can be controlled dynamically in the evaporation engine by adjusting the resistance of the plastic sheets containing the spores, forcing the engine to exert more force. [1] Thus, no one specific value of α and β were used in the model; rather the evaporation rate was determined as a function of α and β and a variety of weather conditions. Then the model for the engine was designed with feedback to adjust w to achieve the optimal power density based on their model. To give an example from the paper of how the evaporation rate varies with these parameters, consider sample weather conditions of areal power from the sun of 200 W/m2, air temperature of 16°C, air pressure of 1 atmosphere (101.3 kPa), wind speeds of 2.7 m/s, and relative humidity of 0.3. For α = 0.2, the evaporation rate E would be approximately 2 mm H2O/day while for α = 1, E would be around 8 mm H2O/day. Under the same weather conditions, the evaporation rate E would be approximately 8 mm H2O/day for β = 1.0 and around 5 mm H2O/day for β = 1.05. Again, note that these numbers come from a theoretical model for the engines and not actual measurements.
The paper also briefly consider the effects of feedback loops induced by installing the evaporation engines. The atmosphere is a complex system, and the absorption of energy by evaporation engines is likely to causes small but non-negligible changes. In general, installation of evaporation engines would reduce the evaporation rate while increasing the surface temperature of a body of water. This would lead to higher convective heat loss and an overall shift to higher temperatures and lower relative humidities. Such small changes would actually be beneficial for extracting power from evaporation in isolation, however. [1]
Having established α and β as the key parameters for determining the power output of the evaporation engine, the paper then considers how these two factors vary under a variety of weather conditions. The most relevant factor turned out to be relative humidity, where the power output was found to increase with falling atmospheric relative humidity. Wind, however, was found to be weakly correlated with evaporation rates. [1]
Another advantage of the evaporation engine in general is that it decreases water loss on large bodies of water in arid climates. Fig. 1 shows one such example: Lake Mead created by the Hoover Dam on the border between Arizona and Nevada. In fact, all along the Colorado river, dams have been installed for energy generation and water storage for cities. The large surface area of the resulting reservoirs greatly increases the amount of water lost to evaporation, a problem that could be mitigated by a covering of evaporation engines. These water savings are also affected by the varying weather conditions, and the paper found that water savings were correlated with higher wind speeds and lower relative humidity. [1]
The values of α and β across a variety of weather conditions was then combined with metrological data across the United States. The 325 GW number comes from the assumption that all available lakes and reservoirs larger than 0.1 km2 (excluding the Great Lakes) are covered with ideal evaporation engine devices. [1]
The proposed solution (covering all reservoirs with evaporation engines) of course has a number of advantages and disadvantages. As mentioned before, the evaporation engine could be used to retain water and the paper even estimates that this number could be as high as half of the current water loss to evaporation. [1] Other advantages include the fact that evaporation engine is less sensitive to intermittent changes in weather conditions than solar and wind energy; this largely comes from the fact that the water itself stores energy and this heat can continue to fuel evaporation during the evening, especially in the arid southwest.
The disadvantages come from how such a covering of evaporation engines would affect the current usage of these reservoirs: the engines themselves would be an eyesore and basically eliminate the use of lakes and reservoirs for recreational purposes. It is likely this political aspect of evaporation engines that is the most damning for the 325 GW headline number; it seems highly improbable that states could be convinced to cover even a few of their bodies of water with evaporation engines.
Lastly, we need to consider the cost, which unfortunately is difficult to determine given the limited information provided by Chen ete al. [2] Sahin is quoted in Herkewitz as saying the "engine costs less than $5 to build." [7] Assuming this is the device described in Chen et al., we can estimate the evaporation engine is $5/(100 cm2) or $500 /m2. [2] In di Cavusoglu et al., 325 GW is estimated to be produced by 95,486.7 km2 of open water, an average energy density of 3.40 W/m2. [1] This gives an estimated cost of $147.06 per Watt - much higher than the current cost of solar cells. Furthermore, this estimate ignores the cost of installation and maintenance of such large arrays of evaporation engines. Although this is based on incomplete information on the costs of the engine, my analysis indicates that price would be yet another downside of this approach.
While evaporation may provide an additional avenue for renewable energy, it is important to understand that 325 GW is likely a gross overestimate of how much power any real implementation would practically provide. This is also suggested by the authors when they referring to this number as the "potential" amount of energy available. But, even ignoring the political aspects of covering all of the U.S.'s large bodies of water, idealistic assumptions are made concerning the thermodynamic process that lead to the conversion of evaporation into power. This does not mean the idea does not have applications, especially if used to cover only fractions of bodies of water, but it is important to correctly undestand the context under which the researchers have calculated the energy "potential" of evaporation.
© Brett Larsen. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] A.-H. di Cavusoglu et al., "Potential For Natural Evaporation as a Reliable Renewable Energy Resource," Nat. Commun. 8, 617 (2017).
[2] Xi Chen et al., "Scaling Up Nanoscale Water-Driven Energy Conversion into Evaporation-Driven Engines and Eenerators," Nat. Commun. 6, 7346 (2015).
[3] D. Toomey, "Could Evaporation Be a Significant Source of Renewable Energy?," Yale Environment 360. 28 Sep 17.
[4] M. Humphrey, "Harvesting Energy from Evaporation to Power the US," PH240, Stanford University. Fall 2017.
[5] I. Johnston, "Water Evaporation Could Provide Vast Amounts of Renewable Energy, Find Scientists," Independent. 26 Sep 17.
[6] A. Chen, "Water Evaporation Could Be a Promising Source of Renewable Energy," The Verge. 26 Sep 17.
[7] W. Herkewitz, "Here Is the World's First Engine Driven by Nothing But Evaporation," Popular Mechanics. 16 June 15.
