Ultradeep carbonate gas reservoirs have typical characteristics such as diverse storage media，strong heterogeneity，high temperature，and high pressure. They are generally developed using deviated wells，which complicates the evaluation of gas well productivity. Considering factors such as multiple storage media，stress sensitivity，nonlinear percolation，threshold pressure effect，and well deviation angle，a trinomial productivity prediction model was established based on the Forchheimer’s gas-phase differential equation，stress sensitivity and physical simulation experimental data of gas-phase flow. The gas well productivity of different types of carbonate reservoirs in different regions was predicted，and the effects of the above factors on gas productivity were analyzed.The results indicate that pore-type and low-permeability cavity-type reservoirs are affected by threshold pressure effects，while fracture-cavity type and high-permeability cavity-type reservoirs are influenced by nonlinear flow. Therefore，the trinomial productivity prediction model is more suitable for ultradeep carbonate gas reservoirs with diverse reservoir types. Different types of reservoirs exhibit different degrees of stress sensitivity and nonlinear flow characteristics. Physical simulation experiments on the cores from various reservoirs are necessary to determine the parameters required for the productivity equation. The well deviation angle creates a negative skin factor affecting gas well productivity. When the well deviation angle is greater than 55°，the gas well productivity of all types of reservoirs starts to increase rapidly， especially for fracture-cavity type reservoirs. The threshold pressure effect has a significant negative impact on productivity at low pressure differentials， whereas stress sensitivity and nonlinear flow mainly impact at high pressure differentials. Starting pressure gradient and nonlinear flow significantly inhibit gas well productivity when their coefficients are 0.01-0.048 MPa/m and 109-1012 m?1， respectively. In contrast， the productivity loss caused by stress sensitivity is relatively stable. The dominant factors affecting well productivity are the skin coefficient and formation coefficient. During the development stage， the impact of the nonlinear flow effect on high-permeability reservoirs and the threshold pressure effect on low-permeability reservoirs is also significant.