I am in process of doing an in depth study on the Biblical expression of Hell. There is so much non sense wrapped around this biblical doctrine. Great question!
One has to understand that when we look up the original greek first you have to check the word, what it means the majority of the times it is translated, which basically is the general translation of the word. Then you have to look at all the nuances of the term and build a case based on that. This term 'aion' the majority of the times it is translated by the best Greek scholars the NAS / lockman foundation could find is translated forever. The webster dictionary translates the term forever as - for a limitless time, continually. this is not to say eternally because it has a beginning. Eternity is from forever past to forever future, which is not fully correct either because eternity is outside of time all together. To have past and future in the same sentence as eternity is problematic at the least, but for our limited minds and for discussions sake let it be said this way. Second, relative to this answer, the nuance meaning of the term 'aion' is translated as age, ages. Out of 81 times the word is used in correlation to what we are looking at only 27 times the word is translated age/ages.
GOING A LITTLE DEEPER:
When I look at this passage what jumps out at me is the combination of the greek word 'aion' repeated 2x in a row. The text literally says
"...torment ascendeth up forever and ever (aion aion)". I know that when a biblical writer wants to make an emphatic point or extend the meaning of a term he would write it 2x's. In other words even if this word was translated ages it would be translated something like tho, "And the smoke of their torment ascendeth up for ages upon ages with no end". In order to make a case that this torment was only for ages and not for forever, the writer would need to remove one of the "aion" in order to try and make that pint. And even at that the case would be about 25% possible fact because the majority of the times this word is used it is translated forever.
Secondly, to put the final nail in this coffin, we have to look at the other NT passages that utilize the term 'aion' in repetition to see more precisely what it consistently is referring to see exactly what it means here in this particular passage.
All the passages that have the greek term 'Aion Aion' forever and ever back to back:
Ephesians 3:21 to Him be the glory in the church and in Christ Jesus to all generations forever and ever. Amen.
Philippians 4:20 Now to our God and Father be the glory forever and ever. Amen.
1 Timothy 1:17 Now to the King eternal, immortal, invisible, the only God, be honor and glory forever and ever. Amen.
2 Timothy 4:18 The Lord will rescue me from every evil deed, and will bring me safely to His heavenly kingdom; to Him be the glory forever and ever. Amen.
Hebrews 13:21 equip you in every good thing to do His will, working in us that which is pleasing in His sight, through Jesus Christ, to whom be the glory forever and ever. Amen.
1 Peter 4:11 Whoever speaks, is to do so as one who is speaking the utterances of God; whoever serves is to do so as one who is serving by the strength which God supplies; so that in all things God may be glorified through Jesus Christ, to whom belongs the glory and dominion forever and ever. Amen.
1 Peter 5:11 To Him be dominion forever and ever. Amen.
Revelation 1:6 and He has made us to be a kingdom, priests to His God and Father—to Him be the glory and the dominion forever and ever. Amen.
Revelation 4:9 And when the living creatures give glory and honor and thanks to Him who sits on the throne, to Him who lives forever and ever,
Revelation 4:10 the twenty-four elders will fall down before Him who sits on the throne, and will worship Him who lives forever and ever, and will cast their crowns before the throne, saying,
Revelation 5:13 And every created thing which is in heaven and on the earth and under the earth and on the sea, and all things in them, I heard saying, “To Him who sits on the throne, and to the Lamb, be blessing and honor and glory and dominion forever and ever.”
Revelation 7:12 saying, “Amen, blessing and glory and wisdom and thanksgiving and honor and power and might, be to our God forever and ever. Amen.”
Revelation 10:6 and swore by Him who lives forever and ever, who created heaven and the things in it, and the earth and the things in it, and the sea and the things in it, that there will be delay no longer,
Revelation 11:15 Then the seventh angel sounded; and there were loud voices in heaven, saying, “The kingdom of the world has become the kingdom of our Lord and of His Christ; and He will reign forever and ever.”
Revelation 14:11 And the smoke of their torment goes up forever and ever; they have no rest day and night, those who worship the beast and his image, and whoever receives the mark of his name.”
Revelation 15:7 Then one of the four living creatures gave to the seven angels seven golden bowls full of the wrath of God, who lives forever and ever.
Revelation 19:3 And a second time they said, “Hallelujah! Her smoke rises up forever and ever.”
Revelation 20:10 And the devil who deceived them was thrown into the lake of fire and brimstone, where the beast and the false prophet are also; and they will be tormented day and night forever and ever.
Revelation 22:5 And there will no longer be any night; and they will not have need of the light of a lamp nor the light of the sun, because the Lord God will illumine them; and they will reign forever and ever.
Do I need to say anything more?
I am absolutely 100% sure that there torment is from that time begins in Rev 14:11 to all eternity future - FOREVER!
SOME FINAL REMARKS:
This is a fearful subject, and one that needs to be dealt with sensitively, but also should be thoroughly discussed. I would like to speak openly regarding this subject but can't for fear that my post will be deleted. If the posting person "Brilliant" needs me to clarify anything please don't hesitate to ask. Again, great question!