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The most basic way to think of a pump is like a diode or a one-way/check valve. It allows fluid to move into one direction but not the other.
Additionally, pump can also pressurize fluids to keep the throughput high, but if you're not very familiar with Factorio's fluid dynamics, this rarely makes much of a difference in throughput; you'll likely get much more significant difference by increasing production, increasing consumption, and by keeping the pipelines short rather than by adding pumps.
Pump can also be connected to the circuit network, by using the red/green wires, this allows you to conditionally disable the pump, to stop all fluid flows under certain conditions. This allows you to, for example, only pump into your cracking plants when you have over/undersupply of certain.
I'd suggest keeping your green/red circuit production close to the raw materials. Green circuits and red circuits takes a massive amount of input material for a small number of output, and you will need a massive amount of both; by keeping production close to the raw materials, you effectively compresses those materials and you minimize the amount of traffic on the main bus.
If you messed up and now have full tanks, convert any excess light oil to solid fuel and store it in a chest for now, either do the same for heavy oil or add another tank (it's more efficient to convert heavy oil to light oil then light oil to solid fuel than to make solid fuel directly from heavy oil).
Once you have advanced oil processing, use the circuit network to regulate cracking via pumps (or power switches on the chemical plants; this takes more effort but gives you clear visual feedback about the process; you get "no power" icons when they're off). Convert heavy oil to light oil if you have more heavy oil than light oil. Likewise for light oil to petroleum. That way, the levels will be the same for all three fluids; you never run out of one while having excess of another, production never stalls unless you fill up all three. If either cracking operation is running constantly, it should be expanded until it runs intermittently.
You might get occasional spikes of demand for heavy oil for lubricant when you upgrade to blue belts. For that, have a tank of lubricant (you can use the circuit network and a pump if you don't want to keep 25k lubricant in stock).
In this context, pumps are being used as controlled valves. When connected to the circuit network, they'll only let fluid through when the enable condition is met. So if you e.g. have a pump feeding lubricant into a tank, wire the pump to the tank, and set its condition to lubricant<5000, it will stop pumping when there's 5000 lubricant in the tank. The chemical plant making the lubricant won't be able to empty its output slot and will stop making lubricant until the level drops and the pump activates.
I'm currently prepping a massive area and wiring it up to have ridiculous amount of solar panels and accumulators, 1000-2000 of each or something insane, just for infinite energy.
This seems like a sound idea, but a few of my ideas have seemed good at the time :P
Is there anything that could go wrong with just 100% solar power and overkill electrical storage for the night? i'm currently sandboxing in peaceful mode.
Once built solar power will reliably keep working forever without any need for complex designs or logistics or anything.
2000 isn't close to insane nor infinite energy, but youll figure that out.
I would say you probably have far too much petgas storage. If you are using the petgas as fast as you are manufacturing it, those tanks would never fill up anyway.
Also: large tank arrays such as in your picture do not have a very good fluid throughput ~ this is not a problem at small scale, but it can bite you hard later on if you get into the habit of building huge redundant storage arrays. Large storage buffers can also hide production problems & actually make it harder to debug or improve the refinery design.
I prefer to have a smallish stockpile of crude oil instead, as that can be converted into whichever oil fractions as & when needed (assuming there is enough refineries & cracking plants to meet the average demands of the factory).
1 storage tank per fluid type is enough for small-scale &/or measuring purposes (even in a large-scale refinery[i.imgur.com] suitable for a megafactory).
However, a small reserve storage buffer for the output products is often a good idea, especially if you are shipping the fluids to the rest of the factory areas by train.
The heavy & light pipes are remaining empty, because you have no control system for the cracking set up yet ~ so they are currently in "always-on" mode, sucking up all of the HO & LO to convert down to PG.
As you noted, you are going to need those other types later on. Heavy oil for lube, & light oil for solid fuel (most efficient conversion from crude).
Next step is to setup the automated system as I detailed in the rest of that previous post:
"Place a pump at the output of the heavy-to-light cracking plant, wire it to the heavy oil storage tank. Set pump to activate if heavy oil > 10,000. This will keep a reserve of 10k heavy (for lube etc), and automatically crack the excess to light oil.
Ditto for the light-petgas cracking, so it keeps a 10k reserve & cracks the rest to petgas."
Here is a rough suggestion, based on your pictured design but modified to include less storage & including some pumps for the automated cracking control circuits ~ https://i.imgur.com/37jg1U8.png edit - just noticed I missed one water connection in the middle of that pic, between the HO-LO & the LO-PG cracking blocks. Derp.
You described the problem quite well. Because you will always end up with excess light and heavy oils. The reason why is, that your light oil is meant to go into SolidFuel and your heavy oil is meant to go into Lubricant. Yet you will need far less of the SolidFuel and Lube than you need of petrolium gas.
This is where the "Advanced Oil Processing" Research comes in. It allows you to use a process called Cracking, a real life thing in where larger and thus havier chains of Hydrocarbons(oil things) are broken down into smaller pieces using superheated steam and metal Catalysts.
In factorio, you will simply have to set up a few chemical plants. These will be able to reduce heavy oil into light oil and light oil into petroleum.
Basicly what you want to do, is connect a pump to your storage for heavy oil and then use a red or green wire to connect the pump to the tank directly. On the tank make sure the Circuit Condition is reading contents. On the pump, configure it to activate when condition Heavy Oil greater than <your desired amount in storage>.
That way the pump is gonna syphon off any excess Heavy oil, to be cracked down into light oil.
Then you do the same with light oil into petroleum.
And Viola! Your problem is solved.