Pressure model and calculation of well test for gas wells with CO_2 injection considering thermal effect

CO2 is often injected into an oil well to explore for oil.After shutting the well and suspending the injection,the temperature of any location in the wellbore is different from that of the location in earth formation at the same level of depth.So there is heat exchange between the wellbore and earth formation,and the varying temperature and wellbore storage both have an influence on the pressure at the bottom hole of the wellbore.A pressure model and its calculation of well test for gas wells with CO2 injection considering thermal effect was presented to give correct numerical simulation to the profile of pressure,temperature,density and velocity in the wellbore at any time after shutting the well.In this model,a reservoir model was connected to the pipe flow model in the wellbore.The reservoir model was solved half-analytically and half-numerically,while the pipe flow model in wellbore was solved numerically with the method of PISO.The result of calculation shows that after shutting the well the thermal effect has an obvious influence on the shape of curve of the bottom hole pressure derivative in the early period,thus facilitating CO2 injection.