Nonisothermal reservoir/wellbore flow modeling in gas reservoirs

Most analytical and numerical flow modeling presuppose isothermal flow behavior in the reservoir. However, for high rates and large consequent drawdown gas reservoirs, the nonisothermal behavior becomes the norm due to the Joule-Thomson (J-T) effect. Other factors, such as a fluid's adiabatic expansion (AE), heat convection, and the heat exchange with surrounding formations may also make contributions. Accounting for this nonisothermal flow behavior becomes a necessity for accurately estimating a well's performance due to changes in fluid properties. This paper starts with the general energy balance in the reservoir and presents a semianalytical solution to estimate the nonisothermal, single-phase gas temperature in the reservoir during production. This solution considers the J-T effect, adiabatic expansion effect, transient temperature behavior, heat convection, and heat exchange of fluid with over and under-burden formation. The variations of gas viscosity, density, J-T coefficient as a function of temperature and pressure are taken into consideration by making a small spatial step at each computational node. A field case study validates the time-variant wellbore temperature profiles with the coupled reservoir heat-transfer model. Distributed temperature measurements or DTS during a drillstem test (DST) made this validation feasible. The J-T effect dominates in the near wellbore region due to dramatic pressure change. The J-T induced cooling usually occurs for gas in the reservoir. However, for high-pressure systems, the gas behaves like a liquid and gets heated up. For some intermediate pressure intervals, the gas temperature slightly increases with expansion, reach a plateau, and then gradually decreases as the gas moves toward the wellbore with declining pressure. By coupling the reservoir heat-transfer model with the wellbore heat-transfer model, one can monitor more accurately.