Geothermal energy is a sustainable and renewable source that can be extracted by circulating a single- or two-phase fluid through a geothermal well system. Two-phase flow and heat transfer models are required for predicting pressure and temperature profiles in oil, gas, and geothermal wells. We model fluid flow, thermodynamics and heat transfer in an idealised vertical well for single-(i.e., water) and two-phase fluid mixtures (CO₂-, and air-water) under a bubbly flow regime. First, we calibrated a Peng-Robinson Equation of State (PR-EOS) for CO₂-, and air-water systems. Second, we solved continuity, energy and momentum equations and modelled transient conductive heat transfer through the well. Third, we investigated the effects of mass flow rate, transient heat transfer, single- and two-phase fluid on the extracted power, temperature, and pressure profiles of the deep well bore heat exchanger.

The results show that the temperature of the hot fluid decreases as it flows to the surface both in the case of adiabatic flow and in cases with heat loss. The mass flow rate controls the fluid temperature drop during its ascent to the surface. The production pressure of a gas-liquid phase system is higher than that of a system with single liquid phase at the same injection pressure, temperature, and mass flow rate. Increasing mass flow rate up to a threshold value leads to an increase in the production pressure. Above the threshold mass flow rate (i.e., 7 kg/s in this study), the production pressure reduces because of the significant increase in the frictional pressure drop. Production temperature, production pressure, and total power increases over time due to the local heating around the production well and reduction of the heat loss.

地热能是一种可持续和可再生的能源，可以通过使单相或两相流体通过地热井系统循环来提取。需要两相流动和传热模型来预测石油，天然气和地热井中的压力和温度曲线。我们在气泡流状态下对单相（即水）和两相流体混合物（CO _2-和空气-水）的理想垂直井中的流体流动，热力学和传热进行建模。首先，我们针对CO ₂校准了Peng-Robinson状态方程（PR-EOS）-和空气-水系统。其次，我们求解了连续性，能量和动量方程，并对通过井的瞬态传导热进行了建模。第三，我们研究了质量流量，瞬态传热，单相和两相流体对深井筒热交换器的提取功率，温度和压力曲线的影响。

结果表明，在绝热流动和热损失的情况下，热流体的温度随着流向表面的温度而降低。质量流率控制着流体在上升到表面期间的温度下降。在相同的注射压力，温度和质量流量的情况下，气液相系统的生产压力要高于单液相系统的生产压力。将质量流量增加到阈值会导致生产压力增加。高于阈值质量流量（即本研究中为7 kg / s），由于摩擦压降的显着增加，生产压力降低。由于生产井周围的局部加热和热量损失的减少，生产温度，生产压力和总功率随时间增加。