Transient Analysis of Sandface and Wellbore Temperature in Naturally Fractured Geothermal Reservoirs: Numerical and Analytical Approaches

Abstract

This work presents the numerical and analytical temperature solutions that couple the transient reservoir/wellbore thermal models to analyze the temperature measurements recorded at producing horizon or at a certain gauge depth above it for estimating the physical and thermal properties of naturally fractured geothermal reservoir (NFGR) during drawdown and buildup periods. The NFGR is replicated by a more general triple-porosity system adopted from Abdassah and Ershaghi model. We first develop numerical and analytical solutions to predict the sandface temperature in NFGRs, accounting for the Joule-Thomson (J-T) effect, adiabatic heat expansion/compression effect, heat convection and conduction. The developed numerical solution is verified and found to agree with the proposed analytical solutions. Then, the wellbore heat flow model adopted from Hasan and Kabir model is coupled with NFGR model to predict the wellbore temperature at a certain gauge depth above producing horizon. The results show that three heat radial flow regimes and two thermal inter-porosity regimes have been identified. It is demonstrated that the early-time heat flow is dominated by the adiabatic heat expansion/compression effect, and the intermediate- and late-time heat flows are dominated by J-T heating/cooling effect. It is demonstrated that thermal properties such as J-T coefficient, adiabatic heat expansion coefficient and fracture intrinsic porosity can be estimated through temperature transient analysis, which are not accessible by pressure data. The results also show that when the gauge location is near the producing horizon, the heat transfer regimes keep almost identical to sandface during drawdown period. As the distance between the gauge location and producing horizon increases, drawdown-wellbore temperatures are more dominated by wellbore heat loss, thereby may miss some information contents from reservoir. Moreover, buildup-wellbore temperatures are usually dominated by wellbore heat loss and do not exhibit any discernable flow regimes even though gauge location is near the producing horizon. It is demonstrated that wellbore temperature derivative exhibits unit slope at early times for drawdown and buildup periods. Finally, we develop an integrated semilog-straight-line analysis workflow of combining sandface pressure and temperature data to estimate NFGR properties. Synthetic test example is interpreted to demonstrate the applicability of the developed workflow.