Horner プロット法による平衡地層温度の信頼性

抄録

A static formation temperature (TBU) is estimated from bottom-hole temperature (BHT) circulating time (t_k) and the elapsed time after circulation stopped (Δt), using a Horner-plot method. TBU is compared with reservoir temperature measured in conjunction with bottom-hole pressure survey (TBHP) or with drill stem test (TDST) in the oil and gas fields with various geothermal gradients.
The Horner-plot method gives a reliable static formation temperature in regions of low geothermal gradient. The TBU in high temperature wells is lower than TDST and TBHP. The difference between TBU and TDST or TBHP in the regions of the high geothermal gradient is caused basically by the equation Eq. 1 of the Horner-plot method.
BHT=T_f-Clog(t_k+Δt)/Δt Eq. 1
Where, T_f is true formation temperature.
According to DOWDLE and COBB (1975), comparative analytical studies of the temperature buildup and pressure buildup using the diffusivity equation showed that the two method are not completely analogous. And, Eq 1 is not correct theoretically.
MIDDLETON (1982) has proposed that the temperature behavior at the bottom-hole was presented by the equation Eq. 2.
BHT=T_m+(T_f-T_m)〔exp(-a²/4κ•Δt)〕Eq. 2
Where, borehole of radius a, thermal diffusivity κ. As compared with Eq. 2, Eq. 1 does not include main factors of the thermal diffusivity and mud temperature (T_m) in BHT stabilization model.
However, the Horner-plot method is useful to estimate the reliable static formation temperature from BHT in the regions of low to middle geothermal gradient less than about 4°C/100m. A careful observation is necessary in approximating TBU at the high-temperature field.