I am happy to take Jed's calculation here. We can refer to the original should there be questions.
I prefer the inverse: the "Simplicity Paper" (1) is the reference. JR paper (2) is just useful to clarify some aspects of the original F&P paper.
Page 16 is the core of the paper, because it contains the formulas and calculations by which F&P justify the claims anticipated in the summary ("high rates of specific excess enthalpy generation (> 1kWcm-3) at temperatures close to (or at) the boiling point of the electrolyte solution") and in the conclusion ("We note that excess rate of energy production is about four times that of the enthalpy input even").
Therefore, page 16 is the essence of the "simplicity paper", but it is also the sloppiest part as you have seen by looking more carefully at it. Their calculation are inaccurate, not well explained (even JR made a better job in his 2020 paper) and contains incredible errors as the J unit in the first formula (it remained unchanged also in the peer reviewed article on PLA (3))!
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The big assumption here is that 50% of the liquid boils off in 10 minutes. The issues about "when the cell was dry" affect that similarly. So, if the cell dry endpoint is in fact later - even by 30 minutes let alone 3 hours - this energy balance fails.
Exactly, this is the biggest assumption because it affects the biggest term in the excess heat balance, that is the 171 W lost in vapor. In this case there are big issues both for the mass of liquid boiled off and for the duration of boiling.
Let's start from the latter. F&P assumed a duration of 600 seconds, they don't specified to which of the 4 cells they are referring to, or if 600 seconds is an average value. At page 13 they wrote: " For the second value of the pressure, 0.97 bars, the cell would have become half empty 11 minutes before dryness, as observed from the video recordings (see the next section) and this in turn requires a period of intense boiling during the last 11 minutes." In this case, the 11 minutes comes from a numerical simulation, but they say this period coincides with the boil-off duration observed in the video. A 10% error, not a big one, it's negligible with respect to the others we will see.
Anyway, this phrase confirms that F&P derived the boil-off period from the video recording, and the video published by Krivit in 2009 contains the blue arrows which mark the beginning and the end points of the boil-off period for each cell. The vertical position of these arrows and the time span between then determine the rate of lowering of the level inside the cell. From that video it comes out that the lowering time is comprised between 20 and 35 minutes, as explained in this old comment (4a) and the related jpeg (4b), a period two to three times and half longer than the 600 seconds considered in the calculation.
But this is not yet the biggest problem for the evaporative term of the heat balance. The biggest problem is about the evaporated mass not the time. If you look carefully at the video you will see that the lowering white column inside the cell is not made by liquid water, but instead by mostly foam. This description (5) in native English describes much better than my words the foaming nature of the content inside the cells during the so called boil-off period. Therefore the liquid mass which actually evaporates during the boil-off period is much smaller that the quantity calculated by F&P, who assumed that 2.5 Moles of water evaporated in a 600 seconds. This molar quantity corresponds to half of the volume filled with full liquid, not by mostly foam! So the calculation of the Enthalpy Output in Vapor at page 16 of the Simplicity Paper is totally inconsistent.
Your remarks about the Enthalpy Input in the cells are also correct. The voltage has not been made explicit, we don't know to which cell it refers, or if it is just an average of the four. Consider also that they recorded a voltage value every 300 seconds, so at best the 75 V comes from the average of three values.
Anyway the big, big problem is the foam. Notwithstanding they had the possibility "to repeatedly reverse and run forward the video recordings at any stage of operation, [so that] it also becomes possible to make reasonably accurate estimates of the cell contents" they omitted to consider that the lowering column inside the cell during the boil-off period was mostly foam.
So, due to large number of issues contained on page 16, I suggest to first concentrate ourselves on the calculation of the Enthalpy Output in Vapor, and then examine the issues about the Enthalpy Input.
(1) http://www.lenr-canr.org/acrobat/Fleischmancalorimetra.pdf
(2) https://www.lenr-canr.org/acrobat/RothwellJreviewofth.pdf
(3) http://coldfusioncommunity.net…n-Pons-PLA-Simplicity.pdf
(4a) RE: FP's experiments discussion
(4b) https://imgur.com/TLfr1jg
(5) RE: FP's experiments discussion
