Compared to horizontal-axis wind turbines (HAWTs), vertical-axis wind turbines (VAWTs) exhibit a different behaviour when built in tight arrays. In this research we build a model based on a free vortex model and empirical wake models, which are the Jensen wake model and multiple wakes combination models. The Jensen wake model and multiple wakes combination models are used to calculate the power production of wind farms, where the power output of single turbine is calculated using the free vortex model at a given wind speed and wind direction. The simulation results are compared with the field test results from a literature. The goal is to investigate the main factors impacting the power density of wind farms of VAWT pairs. The results indicate that the power density of wind farms using VAWTs could be much higher than existing wind farms, mainly because of enhanced power performance of closely-spaced counter-rotating VAWT pairs and because of large height-diameter-ratio of VAWTs. However, wind direction has a crucial influence on the power production of wind farms using turbine pairs.