Okay, I worked up some numbers and posted this over at Vortex. Peter Gluck ran some numbers. I believe he used the 1-year production of Pd only, which is ~180 million g. I think he forgot that we can continue using Pd for more than 1 year. In other words, after 20 years the total amount in use could be 20 * 180 million g = 3.6 billion g.
Here is my estimate --
Palladium is expensive and rare. If it turns out we can only generate cold fusion energy from palladium, and not some other metal such as nickel or titanium, this will probably limit the use of cold fusion to things like central generators which have a high duty cycle, making maximum use of the metal. However, palladium is not so rare that a Pd-D energy source would make only minimal contributions to overall energy production. It could generate more than coal, or natural gas, or any other single source today. Martin Fleischmann once estimated that it could produce about one-third to half of all electricity. I believe that is reasonable.
In other words, Ni or Ti would make cold fusion cheap and ubiquitous, but even with Pd we could supply a large fraction of today's energy, and it would be cheaper than any other energy source.
Here are three very rough estimates, with different assumptions.
The palladium supply in 2015 was 6.7 million ounces mined, 2.6 million from "secondary recovery" (recycling). That is 190 million grams mined, 74 million recycled.
No increase in production despite increased demand. Production from mines continues to be ~190 million grams per year, indefinitely. I think this is unrealistic. When demand increases, more mines are opened and extraction techniques improve.
The main use of Pd today is in catalytic converters. Assume that eventually, all cars are electric and no more use of Pd is needed for catalytic converters; nearly all Pd used for cold fusion.
No transmutation of Pd. The Pd is in sealed cells, so little is lost. 95% is recycled; 5% lost.
This means that after 20 years, annual losses would equal production and the supply would not increase. The total supply would then be 3.8 billion grams. (I ignore today's existing stocks.)
Additional assumptions regarding energy production
With Pd-D 200 W/g can be achieved, at any desired temperature up to the melting point of Pd. I believe the current record is 25 W/g, which is approximately the same power density as a uranium oxide fuel pellet in a conventional reactor. See "Power density is compared by volume or by surface area:"
(Note that Pd weights 14 g/cm^3.)
I think higher power density might be possible with nanoparticle Pd.
The Pd would mainly be used for applications with a high duty cycle, such as centralized electric power generation, railroad locomotives, and pacemakers. (Pacemakers have very low power but they must maintain a 100% duty cycle or the patient may die.) Assume the Pd is active 60% of the time.
With 3.8 billion g, that comes to 0.456 TW thermal output. Electricity requires 5 TW thermal to produce 2.3 TW electricity. Assume thermal conversion efficiency does not improve. In this case, 0.456 TW would produce 9% of electricity.
Cold fusion would make Pd quite valuable, so let us assume production doubles to 380 million grams.
Lead-acid batteries resemble cold fusion cells in that they are sealed and none of the metal is used up or lost. Nearly 100% of the lead is recycled. Assume that only 1% of Pd is lost every year, because most Pd generators are large, central units that are carefully recycled. After 100 years we would have 37.6 billion grams.
Assume no increase in the thermal efficiency of conversion, and the same 200 W/g and 60% duty cycle.
Total thermal output is then 4.5 TW which produces 90% of today’s electricity. However, there is no doubt demand will grow, so perhaps it would be about half of total electricity.
HIGHLY OPTIMISTIC ESTIMATE
Assume Pd can be extracted from seawater, or from mining asteroids. Asteroids are 80% iron and “20% a mixture of nickel, iridium, palladium, platinum, gold, magnesium and other precious metals such as osmium, ruthenium and rhodium.”
"The platinum group metals are some of the most rare and useful elements on Earth. According to Planetary Resources, a company that hopes to mine asteroids in space, those metals exist in such high concentrations on asteroids that a single 500-meter platinum-rich asteroid can contain more platinum group metals than have ever been mined on Earth throughout human history."
This would give us enough Pd to produce all of the energy on earth and in the solar system.