I discuss an alternative means to distill water efficiently using heat that is cascaded in multiple stages. I am making this thread to clarify the configuration as I believe it has potential for some applications... and it's interesting.
The simplest way to introduce the idea is to provide a straightforward example. Consider a pressure cooker. Fill the pressure cooker with water that you wish to distill. Now, place a nonpressurized vessel next to the pressure cooker, and fill this vessel with water from the same source. Place a large copper tubing coil at the bottom of this vessel. The top of this tubing coil is connected to the top of the pressure cooker. The bottom of the coil is connected to the bottom of the vessel via a needle valve. This needle valve is throttled to keep sufficient pressure in the pressure cooker (high enough for high temperature, but not so high that the relief valve lifts).
Now apply heat to the pressure cooker. The water in the pressure cooker will increase in temperature and steam will finally form and pressurize the vessel. The steam will fill the copper tubing. Since the steam temperature is well above 212F, then the water surrounding the copper tubing coil will boil. The steam in the copper tubing will condense to water in the process, and this water will drain from the needle valve provided. The steam released from the nonpressurized vessel can be directed through a condenser, and this water can also be collected. Therefore, a source of heat that would have normally produced x amount of distilled water can be made to produce nearly 2x amount of distilled water through "staging". Note that a means to increase efficiency can be had where water used to replenish each stage is preheated by the hot condensate that leaves that stage, and the water replenished to the final stage can be preheated to 212F by the steam leaving that stage. It's possible to provide so many stages that literally all the steam released from the final stage may be condensed by the water used to replenish all the stages. In this configuration the system is very highly efficient, and takes raw pathogen-laden water and generates hot distilled water at a high rate. Furthermore, it's possible to use the remaining heat to power the pressure pump required to replenish water to all the stages. Therefore, it's possible with nothing more than a biomass furnace or solar concentrator to generate distilled water at a high rate. Just apply heat, put the pump suction into the water source, and the thing makes distilled water at a high rate.
It's possible in principle to use a very large number of stages. For example, let's consider that the copper heat exchanger used will allow for boiling the water at the required rate when the steam temperature inside is only 20F higher than the surrounding water (numbers for illustrative purposes only). This implies that a first stage set at 312F could support a total of 5 stages. 312F corresponds to 80 psi. Ten stages could be had with 412F which corresponds to 283 psi. However, while a super efficient system such as this is interesting, anything beyond about 2 or 3 stages would probably be impractical for most settings.
Consider that a system can be designed for space heating purposes that also generates distilled water at a high rate. Using 2 or 3 stages, a furnace could be used to heat the first stage, then generate steam at the final stage that can be used for heating applications. This can not only purify a local water source, but also allow for reprocessing water that is otherwise discarded as waste (recycling water through distillation). This steam can also be used for air conditioning applications using the adsorption systems I have discussed elsewhere. Finally, consider for interest a system that starts with an efficient slow moving and durable piston steam engine to generate electricity and shaft power at a low rate that also provides steam engine exhaust at a sufficient pressure to the first stage of a 2 or 3 stage water distillation system. This would provide electricity, a large slow moving flywheel for mechanical power, hot purified water (that may be continually reprocessed), and space heating OR air conditioning... and all from a single heat source. It's hard to imagine anything more efficient in this setting. In truth, this is precisely the system I have considered as an ideal (my 'holy grail' kind of set up). While a daunting prospect, I do believe it can be had if designed for a low and continual output as this simplifies things.
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