Temperature transient analysis for bounded oil reservoir under depletion drive

Abstract The significant pressure and temperature signals at wellbores associated with hydrocarbon production can be very useful for reservoir characterization and production analysis purposes. Temperature transient analysis is emerging partly due to the advancement of the downhole temperature monitoring system. Among different flow regimes encountered during the production of a vertical well, the long-lasting boundary dominated flow is crucial since most oil in conventional reservoirs are recovered during this period. The production induced temperature response behaves transient for boundary dominated pressure response and can be analyzed for reservoir property estimation. In this work, we derive a novel temperature transient analytical solution to model sandface temperature signal under boundary dominated flow. Our approach to obtaining the analytical solution from the governing energy balance equation uses Laplace transform with the input of pseudo-steady state pressure equation. This solution can be integrated with previous temperature transient analytical solutions to model the temperature signal from a depletion drived production well. The temperature modeling results acquired from this analytical solution are validated against those from numerical simulation in multiple cases and present distinct behavior under boundary dominated flow. Compared to the heating Joule-Thomson effect in the transient period near the production well, a cooling effect is observed throughout the reservoir after pressure transient reaches the reservoir outer boundary. The magnitude of this cooling effect is proportional to production time. This finding shows the potential of using temperature data at observation wells away from the production well during boundary dominated flow. Further parametric analyses are conducted on eight reservoir, production, and fluid properties to investigate their impacts on the temperature modeling results. These parameters are categorized based on their sensitivities on periods of transient and boundary dominated flow, in which total compressibility and production drainage area are sensitive to the temperature signals under boundary dominated flow only. Unlike the drawdown test, we find that the buildup temperature behavior under boundary dominated flow is identical to that during the transient period. After presenting the forward temperature modeling results, we extend existing reservoir characterization procedures to incorporate the boundary dominated flow. Drainage area and the distance to the closest boundary from the production well can be estimated from the measured temperature data acquired at both production and observation wells. Decent accuracies of the estimations are achieved for the examples presented in this work. The effects of thermal conduction and heat loss may not introduce significant errors in both forward and inverse thermal modeling for the long-lasting boundary dominated flow period. The temperature transient analytical solution under radial boundary dominated flow introduced in this paper considerably extends the scope for temperature transient analysis. This solution enables observation well temperature transient analysis, which seems promising for field application during the boundary dominated flow period. The analytical solution presented herein helps to advance the temperature transient analysis over the whole well production period and forms a basis for future studies on variable rate temperature transient analysis (rate-temperature transient analysis).