Advanced Kovarex enrichment process

TL;DR: We take the happy rocks out of the centrifuge and route them back in as long as they are in a quantity divisible by 10. When they are not, we take them out one by one until they are again.

The Kovarex enrichment process is a very interesting recipe in Factorio. Most recipes in the game take a certain amount of one or more ingredients and output a single product.

The Kovarex enrichment process, however, turns 40 uranium-235 (from here on ‘happy rocks’) and 5 uranium-238 (from here on ‘sad rocks’) into 41 happy rocks and 2 sad rocks. It effectively converts 3 sad rocks into 1 happy rock. It is precisely because you have to take these ‘extra’ happy rocks out of the process while putting the rest back in that makes it interesting.

The process is primed with 40 happy rocks. Since we get one or two happy rocks more out of the process than we put in, we want to have a system that ensures only excess rocks are taken out.

Obviously, we could just take all the rocks—both happy and sad—through a belt and route them back to an input. But that would be boring, so let’s use circuits instead.

1. This chest contains everything needed for the process; 40 happy rocks and a few sad rocks. Because inserters will fill the centrifuge to 80 happy rocks, this means there are a total of 120 happy rocks in this system.
2. This inserter inserts a limited amount of sad rocks into chest ① so that there’s always enough to convert into happy rocks.
3. This chest is where the centrifuge will output its products. Its contents are sent to modulo % arithmetic combinator ⑤.
4. Inserters only ever take out one type of item at a time, so by limiting the hand size to 10, we know for sure that happy rocks will be taken out 10 at a time. This is important.
5. This modulo % arithmetic combinator divides the signal by 10 and outputs the remainder. The output is 0 when the signal is divisible by 10.
6. This filter inserter only takes out happy rocks when the output of combinator ⑤ is greater than 0.
7. This stack inserter takes out both happy rocks and sad rocks if happy rocks mod 10 = 0, according to combinator ⑤. When combinator ⑤ outputs 1 or more, this inserter is disabled, and filter inserter ⑥ takes over.

So, chronologically:

The centrifuge finishes, stack inserter ④ takes out the sad rocks, 4 stacks of 10 happy rocks and one stack of 1 happy rock. The sad rocks are immediately passed along as 0 mod 10 is 0. The stacks of 10 are also passed along, since 10 mod 10 is also 0.

After the last stack of happy rocks is put into the chest, there is a non-divisible-by-ten amount of happy rocks, so filter inserter ⑦ stops and filter inserter ⑥ starts taking out happy rocks until the amount of happy rocks in chest ③ mod 10 is 0 again.

There is one little snag. When there is one happy rock in chest ③, it will send a signal of 1 to combinator ⑤, which will then send a signal of 1 to filter inserter ⑦ the next frame. But by then, the happy rock has already been taken out by filter inserter ⑦. This is easily solved by reading the hand contents of stack inserter ④ and sending that signal with hold (not pulse) to combinator ⑤ as well, effectively making its contents an extension of chest ③.

We now have a closed system that only takes new sad rocks as they are needed and only ever outputs the excess happy rocks.