There are many factors that indicate bitcoin will not only reach 20k, but also surpass it in the near future.
1. The bitcoin network is in its infancy still. First we must understand the potential size of the bitcoin network. The world population is around ~8 billion. If we take a smaller subset, restricted by internet users and age (15-64), we are left with ~2.4 billion. Currently, there are ~20M addresses associated with the bitcoin network. Each user can have multiple addresses, so in reality, the number of users could be much smaller (~2-20M users). This is between 0.083% - 0.83% of the 2.4 billion potential users. Of course not all 2.4B users are expected to use the network in the near future, but if we can even get 10% adoption (240 million users), then the expected price should rise to $120,000 - $1,200,000 (assuming it is a 1 to 1 function explained in the second point). Based on this we would need ~1.5-2% adoption to reach 20k with a 2m userbase (a very conservative estimate). More likely, if the userbase is somewhere in the middle (10M users), we would need 0.33% adoption.
2. The bitcoin network is growing rapidly. In the last 3 years the number of wallet addresses increased 20x and so did the price (1 to 1 function / linear). The number of wallet addresses each year increase by 30-115%. Based on the current growth rate, it will hit 1% adoption rate by the end of this year. Depending on the number of users we can estimate WHEN btc will hit 20k. My personal estimate would be between late 2018 - early 2019, but we have to wait for BTC to stabilize first (explained in the 4th point).
3. The overall marketcap is still very small and has a lot of room to grow. The US stock market is around 30 Trillion. Commdoities/Futures market is even bigger. The cryptoassets marketcap is currently ~250B and at its peak reached around 800B. This is still less than 1% of the US stock market and even smaller when compared to the global equities market. Due to the small size and illiquid market, retail investors (big hedge funds, banks, high net worth entities), have yet to enter the space. It is just a matter of time until this happens, as we have seen BTC futures introduced a couple months ago and potential ETF in the talks.
4. BTC follows a long term cycle. It can be shown that historically bitcoin decreases significantly after hitting all time highs. BTC hit an all time high (ATH) in June 2011 ($30) and then dropped 93% to $2. It then remained stable slowly increasing to $10. Then in April 2013, BTC again hit an all time high at around $213. 4 months later, price dropped to $60 (72% decrease). Then it remained stable until late 2014, when it spiked to a new ATH around $1000 per coin. Like the previous trends, BTC fell again over the next 4 months to $300 per coin (72% decrease). It then remained stable for almost an entire year, until Jan 2017 where the price started to increase more aggressively, reaching new all time high levels of 20k per coin (in Dec 2017 and Jan 2018). Now we are in the decline period, where BTC has declined to 5.5k (~70% decrease).
Following this long term cycle, I would expect BTC to hit new all time highs again, once the price has stabilized.