An Analytical Heat Transfer Model in Oil Reservoir during Long-Term Production

Contrary to the assumption of previous researchers, the radial temperature in the petroleum reservoir during production is non-isothermal because several heat transfer mechanisms change the radial temperature in reservoirs. As there have been few studies, especially after long-term production, this work derives steady-state analytic solutions considering the long-term production. It also presents sensitivity analysis with the various production conditions to investigate heat transfer between the producing fluids and surrounding formations during fluids flowing (hereafter, system heat transfer) in a steady-state. For oil production, the system heat transfer induces a cooling effect on the radial temperature in the reservoir, reducing the temperature rise due to the Joule–Thomson (J–T) heating. This cooling effect increases with the larger Peclet number, however, the relative contribution of the cooling effect to the radial temperature change diminishes. The equations explain that the cooling effect is proportional to the temperature increase due to J–T heating. With a larger permeability, a more convective-dominant phase causes more heat transfer actively. Although the cooling effect itself is amplified with the larger permeability, its relative contribution to the temperature change decreases. From the analysis, the cooling effect of system heat transfer is significant in the low-permeability reservoirs with large drawdown. The system heat transfer is confirmed to be an essential factor in measuring the accurate productivity index of unconventional reservoirs.