On-demand transit has become a common mode of transport with ride-sourcing companies like Uber, Lyft, Didi transforming the way we move. With the increase in popularity for such services, the supply needs to adapt according to the demand. For this, the demand needs to analyzed to examine if there are recurrent patterns in them; making it predictable and easily manageable. The identified demand patterns can then be used for optimized fleet management. In this paper, we propose three steps for extracting such demand patterns from travel requests (1) constructing the origin-destination zones by spatial clustering (2) calculating the hourly origin-destination matrix for each day, and (3) temporal clustering to extract the dynamic demand patterns. We demonstrate the three step approach on the open-source Didi taxi data. The data is composed of 1 month (November 2016) of travel requests data from a small area in Chengdu, China with approximately 200 000 rides for a single day on average. It can provide insight into the day-to-day regularity and within-day regularity of the demand patterns in Chengdu.