Q: how much does bitcoin price need to increase to compete with aluminium smelting?
Aluminium smelting is the process of electrolizing aluminium oxide into aluminium. It uses a huge amount of energy, so much that it's usually much easier to bring the aluminium oxide to the power than the power to the oxide. So smelting plants are placed nearby sources of very cheap electricity, usually hydro or coal. The scale of an aluminium mining operation is so great that they probably have a very special deal to get their electricity really cheap. Find a country that has good potential for hydropower, and convince it's government to build a power station. An example is the Tiwai Point Smelter and the Manapouri Dam constructed especially for it. (building it involved removing 1.4 million tonnes of rock, and 16 deaths) The Tiwai Smelter uses 13% of all electricity in New Zealand.
Like bitcoin mining, smelting aluminium needs lots of cheap power. How does the aluminum industry compare to bitcoin? according to this site primary aluminium (primary meaning refining, not recycling) uses 804,375 GWh (as of 2016) and according to this site bitcoin mining uses 68TWh, or 68,000 GWh. So bitcoin mining only needs to go up 12 times to use as much power, world wide, as aluminium!
If the bitcoin price does go up 12 times, mining will become 12 times as profitable, and miners will expand their operations, currently unprofitable mines will become profitable. This would make the bitcoin price around 100k. If that happens, and bitcoin mining expands towards the marginal return, the electricity used will rival industry.
Currently, the profitablity of a bitcoin mine depends on having access to cheap power. However, since it's easy to put the bitcoin mine right next to the power station, and it's possible to just run the bitcoin mine in off peak times it's easy to make use of this cheap power for mining. But, if mining continues to expand, it could absorb the power oversupply, and if price continues to increase, it will drive up the cost of power, which will increase the costs for other things that need lots of power (such as aluminium), and your household energy costs.
That's if the price goes up ~10 times. If it goes up ~100 times... I'll leave imagining that as an exercise for reader. Normally, things going up in price 10 times is unusual, but these numbers are not conservative by the standards of bitcoin pundits! Even mainstream publications like forbes suggest 600k per bitcoin
Now might be a good time to buy a few solar panels.