Unsteady model for wellbore pressure transmission of carbon dioxide fracturing considering limited-flow outlet

Abstract

The outlet flow rate is limited during CO2 fracturing, which significantly affects the CO2 property distribution and pressure transmission in the wellbore. In this paper, a transient wellbore flow model with a limited-flow outlet is developed to simulate the pressurization process of CO2 injection, which incorporates the compressible fluid flow governing equations, CO2 compressibility, and wellbore heat transfer. The calculation results show a good accordance with field data. The results show that the wellbore pressure and pressurization rate increase gradually with CO2 injecting under a constant inlet pump rate, and the variations in CO2 crucial properties are dominated by borehole pressurization with time increasing. Regarding the two injection patterns, a larger pressurization rate can be obtained under a lower inlet pump rate for tubing injection, while the friction pressure loss can be effectively reduced for commingled injection. Moreover, the pressurization rate increases with inlet pump rate, but also the frictional ratio and its growth rate, hence, the inlet pump rate should not be excessive. Furthermore, the inlet pressure must exceed a lower limit to prevent CO2 from gasifying, which is 4.52 MPa under the calculation condition. The model can provide more insights for the design, control, and optimization of CO2 fracturing.