Coupling Simulation of Longitudinal Vibration of Rod String and Multi-Phase Pipe Flow in Wellbore and Research on Downhole Energy Efficiency

Abstract

The wellbore of a sucker–rod pumping well experiences a multi–phase flow consisting of oil, gas, and water. The flow pattern and pump discharge pressure are greatly impacted by oil well production, which in turn significantly affects the simulation results of longitudinal vibration in the sucker–rod string. When calculating the discharge pressure in a hydrostatic column containing both oil and water (HC), the pressure is not affected by the oil well’s production. This thereby avoids interference between vibrations in the sucker–rod string’s longitudinal direction and the flow from the wellbore. Considering the coupling characteristics between the longitudinal vibration of the sucker–rod string and the wellbore flow, a mathematical model of the sucker–rod pumping system (CMSRS) and a mathematical model of the downhole energy efficiency parameters were established. In detail, the CMSRS comprises two parts: the discharge pressure mathematical models of multi–phase flow dynamics (MD) and the wave equation of the longitudinal vibration of the sucker–rod string. A numerical simulation model of the sucker–rod pumping system was constructed based on a mathematical model. We compared the experimental results, the simulation results of the CMSRS and the simulation results of the sucker–rod string based on the oil–water two–phase hydrostatic column (SMSRS) and found good agreement, indicating the feasibility of the CMSRS. The simulation details show the following: (1) The HC model’s discharge pressure exceeds that of the MD model by more than 33.52%. The polished rod load for the CMSRS is 18.01% lower than that of the SMSRS, and the pump input power for the CMSRS is 36.23% lower than that of the SMSRS. (2) The effective power simulation model based on the energy balance relationship is essentially the same as the effective power calculated by the model based on multi–phase flow effective power. This validates the accuracy of the multi–phase flow effective power model. (3) The limitations of the industry standard effective power model are that (i) the effective head is the net lift height of the fluid in the wellbore reduced to the oil and water phases rather than the effective lift height based on the energy balance relationship and (ii) the power of the gas phase delivered by the pumping pump is disregarded, and only the effective power of the pump delivering the oil–water mixture is considered. (4) The influence of the wellbore parameters on the wellbore efficiency and sub–efficiency is systematically analyzed. The analysis results have an important significance in the guidance of energy saving in pumping wells.