Mohammadpour Mobarakeh, Behnoud Parisa, Khorsand Movaghar Mohammad Reza
Department of Petroleum Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, P.O. Box 15875-4413, 1591634311, Iran.
Sci Rep. 2023 Oct 18;13(1):17726. doi: 10.1038/s41598-023-44678-3.
Well-test operation with a constant flow rate for long-time production is not typical in practice. Therefore, reservoirs frequently produce fluids with constant pressure at the wellhead, into a constant pressure separator or pipeline. During the production under this condition, the pressure drop at the wellbore varies as a function of the rate because of changes in the friction flow; therefore, the wellbore formation pressure is not constant. As a consequence, the wellbore storage effect emerges and should be incorporated in the modeling of fluid flow under production at a constant wellhead pressure. All available methods considering the wellbore storage effect can merely be applied for production under the constant rate condition. Moreover, well-test modeling under these circumstances needs a specific function for production rate, which made this type of well-testing less common. Even though there are exact solutions for production under the constant wellbore pressure in the Laplace domain, their inverse transform is quite complex and cannot be applied for modeling the wellbore storage effect. In this study, a new function is introduced as an approximate solution of the diffusivity equation, for a well that produces at a constant wellbore pressure, using multiple steps of the optimization process. Consequently, an efficient correlation is developed for flow rate about or concerning this condition. Next, the effect of the wellbore storage at constant pressure well-test operation was enumerated for the first time, which was commonly neglected in previous studies. This endeavor concentrated on modeling the two types of well-test operation, producing at constant wellhead pressure and, pressure build-up following the production at a constant wellhead pressure (constant pressure Build-up test). The results were also verified with numerical simulation as well as field data further confirming the excellent accuracy of developed solutions.
在实际生产中，长时间以恒定流量进行试井作业并不常见。因此，油藏通常在井口保持恒定压力，将流体输送到恒压分离器或管道中。在这种条件下生产时，由于摩擦流的变化，井筒处的压力降会随产量而变化；因此，井筒地层压力并不恒定。结果，井筒储存效应出现，并且在井口压力恒定的生产过程中的流体流动建模中应予以考虑。所有考虑井筒储存效应的现有方法仅适用于恒定产量条件下的生产。此外，在这些情况下进行试井建模需要特定的产量函数，这使得这种类型的试井不太常见。尽管在拉普拉斯域中对于井筒压力恒定的生产有精确解，但其逆变换相当复杂，不能用于井筒储存效应的建模。在本研究中，引入了一个新函数作为扩散方程的近似解，用于在井筒压力恒定的情况下生产的井，该函数通过多步优化过程得到。因此，针对这种情况开发了一个关于产量的有效关联式。接下来，首次列举了恒压试井作业中井筒储存的影响，这在以前的研究中通常被忽略。这项工作集中于对两种试井作业进行建模，即在井口压力恒定的情况下生产以及在井口压力恒定的生产之后进行压力恢复（恒压恢复测试）。结果还通过数值模拟以及现场数据进行了验证，进一步证实了所开发解的卓越准确性。
