Method to optimize the volume of nitrogen gas injected into the trapped annulus to mitigate thermal-expanded pressure in oil and gas wells

Trapped annular pressure caused by thermal-expand liquid greatly threatens well integrity, so its mitigation is very necessary and essential. Nitrogen gas has been proved as an effective and low-cost mitigation measure for thermal-expanded annular pressure, but few methods are available to design the injection volume while this is vital for its mitigation reliability. Hence, this paper aims to develop a design method of the optimal injection volume of nitrogen gas to mitigate trapped annular pressure. The design method is based on volume consistency law and volume compensation effect. The proposed design method takes annular pressure increment and optimal injection volume as mitigation aim. A solving process is proposed according to volume increment and error iteration. An index is defined to evaluate mitigation efficiency. The results indicate the mitigation would fail once the injection volume is lower than the optimal injection volume, but over-surplus injection volume reduces mitigation efficiency. Optimal injection volume increases as production time and rate increase. The mitigation efficiency decreases and optimal injection volume increases as water depth increases. The optimal volume increases as the geothermal gradient increases. More nitrogen gas is needed as the mitigation aim of annular pressure increment decreases. The optimal injection volume increases as the expand-compress ratio increase while mitigation efficiency changes little. This design method can be applied in deep-water and HPHT wells. Detailed production data should be obtained and the geothermal temperature should be measured accurately. The extra injection volume is recommended to overcome the unexpected change of production plan and error of geothermal temperature measurement. The mitigation aim should consider the change of well barriers’ strengths. The expand-compress ratio of annular liquid should be adjusted to prevent too large optimal injection volume. Compared with field experience or qualitative analysis, this method can provide an optimal injection volume as reference for the mitigation of thermal-expanded annular pressure, which can enhance the long-term reliability of mitigation by injecting nitrogen gas, thus promoting the popularization.