Modelling the full physics in the wellbore is very important for investigating the wellbore pressure drop on well productivity in reservoir simulation. The pressure drop along the wellbore includes a hydrostatic, a friction and an acceleration component. The acceleration component is generally small in comparison with the overall pressure drop, and in the majority of literature it is neglected. In certain circumstance, it was shown in the literature (Ozkan, Sarica, and Haci 1999) that the acceleration pressure drop can have a significant impact on productivity in a horizontal well.
In this paper, a new formulation of acceleration pressure is derived and the results are compared with those in a commercial reservoir simulator. The new model is derived from the material balance and momentum balance equations in a coupled wellbore and reservoir system. Due to the impact of inflow from the reservoir on the velocity in the well segments, an acceleration pressure drop is induced. The physics of acceleration pressure is implemented as part of complex wellbore model in a multimillion grid reservoir simulator in a massively parallel computational environment. Detailed formulation of acceleration pressure and its derivatives with regards to primary variables are derived. Its influence on wellbore performance is shown using reservoir simulation examples. The effect of acceleration pressure is investigated using sensitivity studies of parameters such as reservoir permeability, well completion and well configuration. Simulated results show that the magnitude of impact of acceleration component on wellbore performance can be large within horizontal wells in a high-porosity high-permeability reservoir. The observations can be used for better history match and more accurate forecast.