If your vehicle is showing continuous blue smoke from the exhaust when accelerating, here are the most likely causes and the parts you'll need to fix each one.
A stuck or clogged PCV valve builds up excess crankcase pressure, forcing engine oil into the intake manifold where it burns continuously during acceleration.
Worn piston rings fail to seal the cylinder walls properly, allowing oil to bypass into the combustion chamber (blow-by) and burn when engine load and RPM increase.
On turbocharged vehicles, worn internal seals allow oil to leak into the intake or exhaust tract, which burns heavily under boost during acceleration.
Adding too much oil causes the crankshaft to whip the oil into a froth, which is then sucked into the intake through the PCV system and burned.
While bad valve seals typically cause smoke on startup or deceleration (high vacuum), completely failed seals can allow continuous oil burning under all driving conditions.
If the engine was recently rebuilt, piston rings installed upside down or with their end gaps aligned will allow massive oil blow-by under load.