The petroleum will dry up very soon.
Something that withers from thirst ends up drying up. If you let a plant dry up like this it might die if you don't water it soon.
This is a jukugo word that uses the on'yomi readings of the kanji. You didn't learn this reading for 渇 yet, so here's a mnemonic to help you:
If all of your plants are drying up you should just give them to your cats (かつ). Cats love to play with dried up plants. At least they won't go to waste.