After purge mussels 6 time in salt water 20 mins each, why they still exude much grime

The President's Choice mussels in sauce are (properly) fully cooked and then frozen in packages for your convenience. I can't find heating instructions for their products but, regardless of which method you use, they should be prepared from frozen with the goal being to heat them - not cook them.

Regarding the live PEI mussels, you are overcooking them. If the meat is shriveled, they are overcooked. You can't just assume that 5 minutes is the ticket for properly cooked mussels.

While there are different methods of cooking mussels and other shellfish such as grilling or baking, for steaming, there are some tips to help ensure that the mussels are fully cooked but not overdone.

• Use a wide base pan so that the mussels are not overcrowded in the pan. Cook in more than one batch if necessary.
• Use a proper amount of cooking liquid. (Personally, I usually aim for ~.5" - 1", depending on the size of the shellfish.)
• Bring your cooking liquid to a boil, add the mussels to the cooking liquid (no steamer basket), and reduce the heat so that the cooking liquid is simmering - NOT BOILING. You want a gentle steam.
• Cover the pan with a clear lid. That will allow you to see when they start to open and monitor the cooking.

• If you have uniformly sized mussels they will cook more evenly. So, two methods for finishing:

  1. If the mussels are not uniformly sized and smaller ones are opening before others, pluck them out as they open. When the last ones are open, remove the pan from the heat and put all of the mussels back in the pan and let them sit covered for a minute or two.

  2. If the mussels are uniformly sized and are pretty much opening at the same time, as soon as they are all open, leave the pan covered and remove from the heat. Let them sit for a minute or two in the residual heat and they will be ready to serve.

The reason for letting them sit for a minute or two in the residual heat is that some mussels will open very quickly, ~3 minutes. That typically is not considered enough time for them to be fully cooked. And if they take longer, an extra minute or two in the residual heat is not enough to ruin them.

Last but not least, remember that time can vary. Even with mussels that take longer, it's still a quick process. So it's important to keep your eye on things.

Where I come from (Portugal) it is quite common to see in most restaurants and establishments shellfish being soaked several hours to even days long before consumption, especially sand dwelling shellfish, which is not the particular case of mussels.

The reason for this is that it keeps them alive and fresh for longer, while also purging any remaining sand or debris naturally found inside them, which is very common in burrowing shellfish, quite unpleasant to find when eating and can virtually ruin the dish.

These are however always soaked in either salted tap water at worse, or at preferably clean natural sea water from where they came from at best. Never just unsalted tap water, because this would obviously kill them quickly, and remove any natural salt that acts as flavor enhancer. Chlorine based disinfectants commonly present in tap water will also slowly affect quality of any living creatures (including aquarium fish) and may eventually be fatal them in the long run.

From your provided examples, most against soaking either state that tap water will kill them quickly, or considerably affect quality (which are both true); or is not needed for farmed shellfish.

I can't speak much for farmed shellfish, they are not as common here and quality may vary with providers and techniques, but even farmed one can some times be quite sandy.

So I'd say that soaking with either salted water or ideally sea water is at at worst redundant or not needed, but can be quite beneficial in some situations.

For farmed shellfish, if you find them clean and edible it is probably not needed, for "free range" ones you probably have more to gain by soaking than not.