Coolant problem, I have been having to add coolant every 2-3 days?

Hello, it seems like the dealership has really been through this entire vehicle. This might be a stupid question, but have they replaced the radiator or radiator cap? I'm just asking because when they do their pressure test, they are removing the radiator cap to put the pressure tester on, and I have seen in the past radiator caps leaking while driving but the coolant evaporating or just plain running out onto the ground while driving.
Your train of thought is correct though, but I would think if the coolant pump was the issue, you would get some type of warning, being that these are electronic coolant pumps. I can't believe they have replaced the head gasket 4 times, hopefully that was under warranty for you?
I don't see any technical bulletins or recalls on this issue either. It even looks like the hybrid coolant pump is on the CAN bus network, being able to control coolant flow at different rates. And that would definitely set a code in some module.
I would inspect the radiator cap, the hose that goes to the reservoir, as well as the reservoir itself. I know this all sounds very basic, but they have replaced everything else.
Is this the plug in Hybrid model? There's a listing for both, plug in or not
And have they found any codes ever set in any module at all?

I'm going to post this case study and see if there's anyone that's seen this before. So, I just need to know if it's the 2016 HYUNDAI SONATA HYBRID 2.0L or Plug in Hybrid?

Okay, did you hear this noise while you were sitting in the vehicle? I have a feeling it's not the engine, those bubbling/gurgling type noises usually come from the heater core when there is air in it. I'm trying to think about this logically since so much has been done to the vehicle already. I'm looking at diagram of the entire HVAC assembly, which houses the Evaporator core as well as the heater core, and a ton of actuator doors and such, when heater cores leak, they will cause the coolant to come into the vehicle and end up on the floor, making the carpets wet. But not knowing this exact design, I wonder if it leaks out the drain hose for the Evaporator condensation. I'll post this diagram I'm looking at. But all we really have left here is the Radiator or the Heater core. I think you have it right; pressure test it yourself. You can rent a cooling system pressure testing kit from AutoZone. you just have to put down the money and they will return it all when you bring the kit back undamaged. Hopefully they have not changed the policy. I rented one awhile back because I didn't have one with me at the time.
The coolant system will run anywhere from 15-18 PSI max when fully hot. So don't pump it up higher than that. I think you'll find a leak that way. I'm going to also post some of the replies I got from other techs that work on these.
One guy is stating there might be a heat exchanger running to the Catalytic Converter, which I've never heard of, we don't get too many hybrids on here as of yet. He stated to unbolt the heat exchanger going to the exhaust and then do the pressure test,
Honestly it sounds like you're losing a lot of coolant in a short period of time, Keep an eye under the vehicle when pressure testing. do it in the morning when the vehicle is cold to begin with.
This is a guide on pressure testing. but keep a flashlight with you so you can pressurize it and let it sit and hold the pressure for a while if possible. I don't think it will hold pressure too long,
Knowing there is already dye in the system should help. I don't know 100% if the heater core leaking on this vehicle will show up inside or leak out the Evap drain hose, so keep an eye on that. You should notice it hanging down under the vehicle about where the dashboard is. I'm sorry you're having such a difficult time with this. But that coolant is going somewhere, if this one tech is right, and it's leaking down the exhaust, it might not be happening until you're moving.
This diagram of the HVAC system is obviously expanded apart, but you can see the location of everything, and the list numbers it all. Please let us know what you find. I will keep looking through service info for anything relevant.

https://www.2carpros.com/articles/radiator-pressure-test

This is the hybrid side of the cooling system.

Part of the issue I think here, is you're losing coolant somewhere and where the coolant is lost air is going to be present. So, as it cools down over night or just when it's off, it's going to draw air in through this mystery spot. And the coolant temperature sensor cannot read air temps, it has to be in coolant to read accurately. Even though the small spots you're seeing may seem unlikely to be the source of the leak, that's going to be the area to focus on, unless you see one of these heat exchanger units running down to the Catalytic Converter, the tech that mentioned this said he wasn't sure if this model had it or not, but it would look like a couple of heater hoses running down to the Converter. That might be the coolant boiling off down at the Converter, you just can't see it.
Something else I came across was this diagram of the Inverter Radiator. Which runs along the lower front end, an inverter is what changes voltages from AC voltage to DC voltage, and it produces heat due to the high voltage levels that the Electric part of the engine runs on. So, there are multiple areas where coolant is being transferred to that wouldn't be on a conventional engine. With your lower radiator hose being cold after hours of running, either the coolant isn't being circulated through the radiator or the radiator itself is clogged.
I went through service info on the exhaust system for this vehicle and didn't see any kind of heat exchanger. So that's something you'll have to take a look at while the vehicle is up on the ramps, I think you should try a pressure test yourself and see what you come up with. The Dealership techs get paid a flat rate time usually so if they can't come up with a cause in a certain amount of time, they are going to start throwing parts at it as they have been. I wouldn't be surprised to find out it's the radiator and the coolant is leaking out onto something and boiling off, and that's why you're not seeing any in the driveway or leaking down.
That would explain the noises you hear too. Do you think the reservoir is where some of the noises could be coming from?
I also see this "Bleed air from the hybrid motor cooling system using GDS". So, using their factory scan tool to bleed air out the system. I'm wondering also if there were any codes stored in any modules, it should be on any work orders or receipts they gave you, I'm sure you have a mountain of paperwork from all this, but for them to replace the entire engine, along with 4 head gaskets, why would they not go after the radiator or Inverter radiator as well.
I doubt they got it very hot running in the shop while diagnosing the issue, it's going to get much hotter while you're out driving for longer periods of time.
This is their service info on bleeding the system after the EEWP (electric water pump) 5th diagram. Its the same way I would bleed a normal vehicle, when cold, leave the radiator cap off and start the vehicle, and the coolant level will drop while air is escaping during warm up, then refill and put the cap on. I don't recommend you doing the water pump on this, the high voltage sections of the motor can be fatal.
But get the pressure test kit and see what you come up, the leak is only going to get worse and has to show itself at some point here.

Okay, so what you are describing with the coolant tubes going to the exhaust manifold is probably a version of the heat exchanger that the dealer tech was mentioning, can you give me your vin number so I can make sure I'm looking at the correct service information. All Data will direct me straight to your vehicle by the vin. Because there are variations in these hybrid designs. If you're uncomfortable posting the vin here, email it to me at "MobileTechRh45@myyahoo com", that's my email address for work. It is possible that the coolant is being lost down the exhaust and being evaporated when it hits the exhaust pipes as well as burned up by the catalytic converter. We're limited on places it can be going with no external signs anywhere. Plus, with a hybrid, you'll be running on the battery system when they are charged enough and the combustion engine when needed, I know they are pretty quiet in either mode. But I want to find more information on any coolant tubing running to the manifold.

Burning coolant will not show up as hydrocarbons in the exhaust, raw gasoline will show up as hydrocarbons, and CO (carbon monoxide) which is partially burned fuel, along with other emissions gases that the catalyst system is supposed to burn off and convert to water.
There is a chemical test that we will do sometimes if we suspect a bad head gasket or cracked cylinder head or engine block that is pushing combustion gases into the coolant system. Below is a picture of that, the tube goes into the opening in the radiator or coolant reservoir and then the chemical testing part is added, and it will change colors if there are any combustion gases detected in the coolant system. These tests can be bought at any auto parts store. I'm not sure how much they cost now, but you could try it, additional testing never hurts. I would hope that the dealership would have found any issues with the amount of work they have done to it, but on the other hand, it sounds like they are not doing too much for diagnostics, if they have actually done all the head gasket work and such.

But leave your vin number or email it to me so I can be sure I'm on the correct service info. And how long has it been since you picked it up from the dealership last? Just wondering how fast it went through an entire gallon.

I had a coolant leak on a Honda CRV once that was not showing up anywhere like this, in fact it passed the 1st pressure test, the max on that system was 15psi if I remember correctly and it didn't show the leak until I tested it a 2nd time at 18psi, which turned out to be a tiny pinhole in one of the metal coolant pipes that had rubber coolant hoses attached to either end. There was this super tiny pinhole on the bottom of the tube that I never saw leak, but the vehicle was going through coolant all the time. It took a while to find that. I think a week or so.

Can you take a picture of the tubes running to the exhaust manifold for me? You can post it here. I'm looking at some different setups, but not sure which one you have.

Is this what you're seeing?
This is an EGR Cooler which cools the EGR exhaust gases with the engine coolant before its directed back into the intake manifold when the EGR valve is activated. Exhaust gas recirculation is used when the engine is under a heavier load, such as wide-open throttle pulls. It allows a small amount of exhaust gases to be metered back into the intake manifold which in turn, reduces in-cylinder temperatures so that NOX gases are reduced.

Okay, no rush, whenever you get time.

I did get the VIN; this engine does have an EGR cooler which is what I think is in your picture. So, I don't think the issue can be with the engine itself at this point, with a new engine and new head multiple times, it has to be something else external to the engine block itself. I also see a Water temperature control assembly, which is connected to the EGR valve. With all these extra components, being newer technology, I would think they should have replaced this EGR cooler (1st diagram) and the entire assembly to rule it out, they are already replacing everything else around it. The Water temperature control assembly is in the 2nd diagram, you can see it's located at the end of the cylinder head, it has a temperature sensor, and it looks like an electronic EGR valve on it as well.
I think your thought on it is leaking out the exhaust is correct, even though that is a ton of coolant to have gone through in a couple of weeks.
You could be hearing any number of solenoids shutting off after the vehicle is turned off. I mean it's nice you have a new engine at this point, but the dealership is going to have to shift their focus onto other areas here. They can't keep throwing cylinder heads and gaskets at it when that's not the problem.
When you first start it in the morning, does it first run off the gas engine until its warmed up and then switches over to electric mode, or is that something that's difficult to notice? Because wherever the coolant is going, it's still leaking into some area when you first shut the vehicle off,
The only things left that haven't been replaced are the EGR cooler system and the part of the coolant system that runs through the Inverter to cool that section of the electric motor. Besides that, the rest has been replaced. The 3rd diagram is just the EGR valve, and the 4th is where the coolant runs for the Inverter and electric water pump. They can replace those components. Or just give you a new vehicle honestly.
They should be doing a full system scan for codes in any other modules, which I'm sure they have at this point, but that usually doesnt show much when it comes to coolant leaks, except for coolant temperature sensor signals being off.

Wow, it's not cheap that's for sure. I hope they are covering all of this under warranty for you. I think along with the EGR cooler though, they should do this water temperature control assembly. It looks like the EGR valve is part of that, as well as it being the separating section for the coolant and the exhaust. I'm sure the Inverter is not where the coolant is leaking into, otherwise you would have all sorts of issues with the electric motor side of things. But I think you're on the right track here. I would have thought the dealership would have started looking in other places, after even just the new engine. I assume that it was a brand new one, it sounds like they replaced the engine block and cylinder head with all new.
I'm going to go through the Technical bulletins some more on this and see if there's anything on the EGR cooler section.

Well, I can see how they were able to replace the engine stating it was a bad lower end bearing, there's a recall on that, so even if it wasn't an actual bearing issue, they could have used that while trying to figure out this coolant issue. But there aren't any coolant issues I see at all. At least not listed on All Data's TSBs/Recalls.