I successfully upgraded from the stock HDD to a K' SSD (2.5/7mm FF) this past Saturday, into my VPCEL13FD/W !
Utilized this Y'T' video for the similiar unit (240gb) ;
https://www.youtube.com/watch?v=OZowO5CyUTg&t=1s
The other (SSD manufacturers') 'corp.' videos I referred to;
https://www.youtube.com/watch?v=unXF5cpWMpk
https://www.youtube.com/watch?v=3e1ZzvTOuxI&t=14s
Good Luck,
D'
p.s. this sony model laptop is nicely designed for end users who are comfortable to upgrade, w/access panels to both RAM bay and HDD. And IF Sony still manufacturered and supplied their (contract) part dealers with batteries ..... easily removed/replaced battery ! A call to their Canadian contractor revealed no listing of Batt' availability ! Even if still available, stated pricepoint is a ridiculously over $250cdn !! yeeech, half of my original purchase $ for laptop !