Reference Map:
1). Use the Teleport Wizard to teleport to the Dense Essence Mines.
2). Use the Agility Shortcut to the South, then run South to the Mines. Mine a full inventory of Dense Essence Blocks.
3). Once you have a full inventory of Essence Blocks, run back to the shortcut you took (or teleport Home then use the Teleport Wizard to get back). Then run West and use the Dark Altar to convert your Essence Blocks.
*NOTE* Each Essence Block you convert requires 1 Prayer Point.
4). Use your chisel on all of the blocks to turn them into Fragments. Either run back East to the Agility Shortcut or teleport Home and use the Teleport Wizard to get back to the Shortcut. What I like to do is run back and take that run time to chisel all of the blocks.
4). Mine another full inventory of Dense Essence Blocks, then return the Dark Altar once again and convert them. Do not chisel the 2nd inventory.
5). Run all the way East/Southeast to the Soul Altar (it's a bit of a run). When there, craft your first bit of shards. Once they're crafted, begin chiseling the rest of the blocks in your inventory, then craft them as well.
6). Teleport to ::thieve. Once there, talk to the Nurse to restore your Run Energy, pray at the Altar to restore your Prayer, then use the Chest to bank your Soul Runes. Then use the Teleport Wizard to teleport back to the Essence Mines. Loop back to Step 1.