A calculation model for the bottom hole flowing pressure of nitrogen injector with coupled wellbore temperature and pressure

When nitrogen injection is used for enhancing oil recovery, the bottom hole flowing process is the important factor affecting oil displacement effect. And Cullender-Smith model is generally adopted to calculate borehole pressure distribution of gas wells. However, the physical property parameters of nitrogen vary with temperature and pressure. In order to accurately calculate the bottom hole flowing pressure of nitrogen injectors, the nitrogen injector transformed from the water injector was taken as the study object. The bottom hole flowing pressure calculation model for nitrogen injector with coupled wellbore temperature and pressure distribution was proposed according to the energy equilibrium equation of vertical conduit flow, combined with the calculation methods suitable for the physical property parameters of nitrogen (e.g. density, viscosity, deviation factor and friction resistance). Then, by means of the fourth order Runge-Kutta iteration, the bottom hole flowing pressure was calculated using the software MATLAB. Finally, the relationships of threshold injection pressure and injection speed of nitrogen vs. bottom hole flowing pressure were evaluated. The analysis on the logging data of nitrogen injection test in Hongqian well block shows that the calculation result of new pressure prediction model is accordant with the measured value. It is indicated that the injection pressure in the early stage of gas injection is less affected by the variation of injection rate and it is mainly dominated by the physical properties of reservoirs.