This research presents an analytical 1D radial-flow model for estimating the transient flowing-fluid temperature in a single-phase oil reservoir. The model allows fluid density, viscosity, and the J-T coefficient to vary with pressure and temperature. A rigorous thermodynamic expression based on fluid PVT behavior underpins the proposed model. The usual assumption of isothermal flow may be unsuitable in low-conductivity formations where large drawdowns occur. The increase in fluid temperature associated with Joule-Thompson (J-T) heating triggers the consequent changes in oil viscosity and density. This model is also extended to estimate flowing fluid temperature for single-phase gas. In case of gas, Joule-Thomson cooling is observed. The Joule-Thomson coefficient for a low pressure gas is usually positive and so it results in a temperature reduction as pressure decreases.
A detailed sensitivity analysis has shown the effect of production rate on reservoir heating and consequent changes in fluid properties. Specifically, we observed that fluid temperature increase above the original formation temperature occurs with a decrease in formation permeability, an increase in oil viscosity, and a decrease in overall heat-transfer coefficient. Of course, J-T heating increases with increasing flow rate.
Changes in reservoir temperature occur within about 100 ft from the wellbore assuming 1D radial flow. Overall, the lessons learned from this study illuminates the need for reevaluating tubular design, flow-assurance issues related to dissolved solids, and assessment of well productivity index arising from J-T heating.
We coupled a wellbore temperature model with our reservoir model to get a complete picture of temperature during production. Results from reservoir model (bottomhole pressure and temperature) are used in the wellbore model as inputs. The model is then validated with field data. Coupled reservoir/wellbore model is useful for analysis of flowing fluid temperature of whole production system.