A COMPARISON OF TWO METHODS OF ESTIMATING STATIC FORMATION TEMPERATURE FROM WELL LOGS*

Two methods for estimating the true formation temperature from well logs are compared. One method requires knowledge of the circulation time, whereas the other requires an estimate of the thermal diffusivity of the contents of the well. Both methods require three or more successive bottom-hole temperature measurements. Data from 157 wells have been analyzed, and the calculated formation temperatures from the two methods agree well. By an analysis of best matching of the two methods, it is found that 0.35 × 10^-6 m² s^-1 is a good estimate for the thermal diffusivity of the well contents.     

Thermal diffusivity of seasonal snow determined from temperature profiles

Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point measurements of thermal conductivity and density, which continually change due to snow metamorphism. Traditional methods for determining these two quantities are generally limited by temporal resolution. In this study we present a method to determine the thermal diffusivity of snow with high temporal resolution using snow temperature profile measurements. High resolution (between 2.5 and 10 cm at 1 min) temperature measurements from the seasonal snow pack at the Plaine-Morte glacier in Switzerland are used as initial conditions and Neumann (heat flux) boundary conditions to numerically solve the one-dimensional heat equation and iteratively optimize for thermal diffusivity. The implementation of Neumann boundary conditions and a t-test, ensuring statistical significance between solutions of varied thermal diffusivity, are important to help constrain thermal diffusivity such that spurious high and low values as seen with Dirichlet (temperature) boundary conditions are reduced. The results show that time resolved thermal diffusivity can be determined from temperature measurements of seasonal snow and support density-based empirical parameterizations for thermal conductivity.     

Long-term underground temperature measurements at Syowa Station, East Antarctica

Underground temperature measurements in two shallow boreholes have been carried out by the Japanese Antarctic Research Expedition at Syowa Station, East Antarctica from April, 1981 to January, 1985. Two quartz thermometers were installed in the first borehole at depths of 2 and 5 m and three were in the second one at depths of 1, 4 and 6.8 m. The mean underground temperatures in the first borehole were −8.181 and −8.843°C at depths of 2 and 5 m, and in the second one −8.242 and −8.220°C at depths of 4 and 6.8 m. As the mean air temperature at Syowa Station was −10.8°C, the underground temperature in the 2 −6.8 m depth range is about two degrees higher than the air temperature. The thermal diffusivities of the observation area are determined by the same principle of the Ångström method, using long-term underground temperature records. The thermal diffusivity around Syowa Station is established to be about two times larger than those of ordinary igneous and metamorphic rocks measured in the laboratory. The thermal conductivity of the drilled cores and surrounding outcropping rocks are also measured by the transient method with temperature conditions at +23°C and −20°C. The thermal conductivities measured in various samples at −20°C are about 7% larger than those at +23°C. Thes tendency is consistent with the results of holocrystalline rock experiments.     

Solutions of the heat conduction equation in a non-uniform soil

A class of analytic, periodic solutions of the heat conduction equation in a non-uniform soil is derived. The class may be characterized by the fact that the speed of the temperature wave varies according to the square root of the soil diffusivity (a function of soil depth). In addition it is shown that the constant soil solution is the limiting case when the rate of change with depth of diffusivity and thermal conductivity become very small. The solutions may be regarded as general whenever temperature analysis is restricted to small values of depth or whenever the soil parameters vary slowly. For all other cases the class of solutions possess the additional property that the rate of change of conductive capacity varies directly as the product of the bulk density and specific heat of the soil. A particular temperature profile is given for the case when the diffusivity varies as the nth power of depth.     

南海南部礼乐盆地礁体发育区的构造热演化特征

礼乐滩是礼乐盆地的重要组成部分,自晚渐新世礼乐地块裂离北部陆缘后开始发育礁灰岩.为认识这些长期浸没海水中的礼乐礁体及其下伏地层的热状态与热演化特征,在详细分析礼乐滩钻井测温数据和镜质体反射率数据的基础上,对一条穿过礁体的骨干剖面进行了构造热演化数值模拟.结果显示,礁体区钻井2000～4500 m深度范围内温度介于30～90℃之间,井底与海底之间的平均地温梯度仅10℃·km^-1左右,地温梯度随深度逐渐增加,3000～4000m深度段地温梯度介于32～37℃·km^-1;礁体下伏地层有机质曾经经历了比现今所处温度更高的古温度.进一步分析表明,高孔高渗的礁体上部因与周围低温海水发生热交换,导致地层温度降低、地温梯度和热流降低甚至为负值;与海水热交换作用随深度增加而减弱并最终停止,地层温度逐渐升高,地温梯度和热流值趋于正常;现今钻井3000～4000 m深度段地温梯度约为35℃·km^-1,基底热流可能介于65～75 mW·m^-2,平均约为70 mW·m^-2;礁体发育区有机质热成熟度主要是...     

Periodic heat conduction in a non-uniform soil

The one dimensional heat conduction equation is applied to a non-uniform soil in which harmonic boundary conditions are specified. The analytic solutions are derived for practical use and satisfy a law that the thermal diffusivity is proportional to the square of the speed of the temperature wave. Depending on the nature of this speed the solutions may be categorized as circular, parabolic, hyperbolic, or exponential. A practical example is given in which the damping depth and thermal capacity of the soil both vary with depth. It shows that there may be considerable differences between uniform and nonuniform soils as far as temperature is concerned. A case of a slowly varying soil layer is also examined and is compared with the constant soil solution.     

Exploration of regional surface average heat flow from meteorological and geothermal series

We attempt to compute the Surface Average Heat Flow （SAHF） from long-term temperature observations of one hundred seventy-seven observational points at the depths of 0.8, 1.6, and 3.2 m, which were relatively evenly distributed in mainland China. We first employ Fourier transformation to remove the influence of atmospheric temperature variations from the observation series, which are classified into the type of the steady-state temperature monotonously increasing with depth （type I） and other three types. Then we compare our results obtained from the data of type I, of which the values are thought to equal to those of the mean borehole heat flow, with those obtained from traditional heat flow observations mainly distributed in North China Craton. In computations of the SAHF at the observation stations, we deduce the thermal diffusivity and volumetric specific heat of the soil by employing harmonic solutions of the heat conduction equation for the same moisture group as the first step, and then we determine the SAHF using Fourier＇s law. Our results indicate that the SAHF derived from shallow earth geothermal data can reflect the heat flow field to a large extent.     

The thermal diffusivity of red sandy soil at Waltair

Summary The study of heat exchanges or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature change produced in any layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil from range and lag methods suggested byJohnson andDavies [15]²) andCoutis [7] respectively. The values of diffusivity cbtained from these methods agree well with each other. The effect of soil moisture on diffusivity has been studied. The diffusivity increases with the increase of moisture in the surface layers of the scil. The ratio of ranges of soil temperature at different depths is found to be approximately constant which is in agreement with the theory of heat flow into the soils. The results of diffusivity obtained from these methods agree well with those results of past workers. The mean value of the thermal diffusivity of red sandy soil at the experimental site of Waltair is found to be 6.336×10^–3 cm²/sec.     

中国大陆科学钻探靶区深部温度预测

依据中国大陆科学钻探(CCSD)两口先导孔中地热测量和岩石样品热物性参数,对5000m深钻的可能钻遇温度进行了预测.先导孔中地温梯度介于1-26℃/km;岩石热导率变化为2.64-8.81W/(m@K),平均(3.4±1.26)W/(m@K);实测热流值为76-80mW/m2;30块岩石样品放射性生热率变化为(0.0-2.17)μW/m3,450m深度以上层平均(0.76±0.5)μW/m3,以下层段平均(0.48±0.2)μW/m3,生热率随深度递减,但变化趋势难以明确判定.分别对热流和热导率取上、下限,采用不同的生热率随深度的分布函数,区分考虑或不考虑热导率的温度相关性,分别计算出5000m深度内可能的温度分布剖面.计算结果表明,超深井于5000m垂直深度上的温度将达到110-140℃,2000m深度的探井钻遇温度将介于54-64℃.此外,考虑热导率的温度效应后预测的温度一般高于未考虑热导率温度效应5-8℃.     

Impact of Groundwater Flow and Energy Load on Multiple Borehole Heat Exchangers

The effect of array configuration, that is, number, layout, and spacing, on the performance of multiple borehole heat exchangers (BHEs) is generally known under the assumption of fully conductive transport. The effect of groundwater flow on BHE performance is also well established, but most commonly for single BHEs. In multiple‐BHE systems the effect of groundwater advection can be more complicated due to the induced thermal interference between the boreholes. To ascertain the influence of groundwater flow and borehole arrangement, this study investigates single‐ and multi‐BHE systems of various configurations. Moreover, the influence of energy load balance is also examined. The results from corresponding cases with and without groundwater flow as well as balanced and unbalanced energy loads are cross‐compared. The groundwater flux value, 10^?7 m/s, is chosen based on the findings of previous studies on groundwater flow interaction with BHEs and thermal response tests. It is observed that multi‐BHE systems with balanced loads are less sensitive to array configuration attributes and groundwater flow, in the long‐term. Conversely, multi‐BHE systems with unbalanced loads are influenced by borehole array configuration as well as groundwater flow; these effects become more pronounced with time, unlike when the load is balanced. Groundwater flow has more influence on stabilizing loop temperatures, compared to array characteristics. Although borehole thermal energy storage (BTES) systems have a balanced energy load function, preliminary investigation on their efficiency shows a negative impact by groundwater which is due to their dependency on high temperature gradients between the boreholes and surroundings.     

Reconstruction of the surface temperature in the Kura depression (Azerbaijan) by the inversion of borehole data

In order to reconstruct the ground surface temperature history (GSTH) in the Kura depression from the data on borehole temperatures, we selected two thermal logs, which met the requirements of the well temperature inversion into the GSTH. The temperature gradients measured in these wells varied about 20 K/km, which is typical for the region of study. The borehole temperatures were inverted into the ground surface temperatures in the past in accordance with the program developed by Po Yu Shen. It was found that the ground surface temperature had increased by 1–2°C during the last century. The GSTH derived from the well temperature inversion agrees with the climate temperatures measured at the Ganca meteorological station, which has been operating since 1873. These results obtained for the Kura depression are consistent also with the results of similar studies in other regions in the world.     

Determination of the formation temperature from shut-in logs: Estimation of the radius of thermal influence

As a consequence of drilling and completion operations most wells have reduced permeability near the borehole (skin zone). This may result in a corresponding change of thermal conductivity of formations near the borehole. At the same time the mathematical models, which describe the process of thermal recovery of formations are based on the assumption that the thickness of the radius of heated zone (during circulation of the drilling mud) is significantly larger than the well radius (or skin zone). It is shown below that the radius of the heated zone (radius of investigation or radius of thermal influence) can be approximated by simple formulas. It is shown that for six field bottom-hole temperature surveys the radius of thermal influence (RTI) is too small, and for this reason, the duration of the drilling mud circulation period should increased.     

The thermal diffusivity of soil at tropical stations in southern hemisphere

Summary The study of heat transfer or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature changes produced in the layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil at the sites Arapongas (23.5°S, 51.7°W) and São José dos Campos (23.3°S, 45.8°W), in Brazil (South America), in accordance with the simple theory of periodic heat flow in a one dimensional, semiinfinite, homogeneous medium. The diffusivity increases with the increase of moisture content in the surface layers of the soil. The results of diffusivity obtained from these methods agree well with those of past workers obtained by other techniques.     

皖14井水温响应机理浅析

通过巢湖皖14井高精度水温观测环境及数字化改造以来的观测资料,分析不同深度(-160m、-195m)处水温变化特征。以2012年4月11日印尼8.6级地震为例,巢湖皖14井水温同震响应所获得的数据为分析基础,利用Ansys中的热分析模型进行数值模拟,研究了同震响应过程中井孔系统水温度变化与热量传递间的关系及机理。模拟结果显示:水温数值模拟曲线与实际测量数据曲线一致,该井水温同震响应表现为下降特征,主要是热对流所致。     

The effect of stratification and compressibility on anelastic convection in a rotating plane layer

We study the effect of stratification and compressibility on the threshold of convection and the heat transfer by developed convection in the nonlinear regime in the presence of strong background rotation. We consider fluids both with constant thermal conductivity and constant thermal diffusivity. The fluid is confined between two horizontal planes with both boundaries being impermeable and stress-free. An asymptotic analysis is performed in the limits of weak compressibility of the medium and rapid rotation (τ^?1/12???|θ|???1, where τ is the Taylor number and θ is the dimensionless temperature jump across the fluid layer). We find that the properties of compressible convection differ significantly in the two cases considered. Analytically, the correction to the characteristic Rayleigh number resulting from small compressibility of the medium is positive in the case of constant thermal conductivity of the fluid and negative for constant thermal diffusivity. These results are compared with numerical solutions for arbitrary stratification. Furthermore, by generalizing the nonlinear theory of Julien and Knobloch [Fully nonlinear three-dimensional convection in a rapidly rotating layer. Phys. Fluids 1999, 11, 1469–1483] to include the effects of compressibility, we study the Nusselt number in both cases. In the weakly nonlinear regime we report an increase of efficiency of the heat transfer with the compressibility for fluids with constant thermal diffusivity, whereas if the conductivity is constant, the heat transfer by a compressible medium is more efficient than in the Boussinesq case only if the specific heat ratio γ is larger than two.     

青藏高原北部活动层土壤热力特性的研究

利用2003年10月～2004年9月期间高原北部可可西里(QT01)、北麓河(QT02)、开心岭(QT05)、通天河(QT06)等地活动层土壤温度梯度、土壤热通量及土壤水分的观测资料,计算了高原北部活动层土壤的导热率、土壤容积热容量、导温率等土壤热力参数.结果显示,QT02、QT05、QT06三站导热率、导温率夏秋季节较大而冬季较小,容积热容量则相反,表现为秋冬季节大而夏季较小;QT01站导热率表现为春季大,夏季较小;表层土壤粒度较小及较低的土壤湿度是冬季导热率较小的可能原因;冻土的热力特征参量可描述为相应深度的温度、体积含冰量及土壤盐度的函数,土壤含水量是融土热特征参数的主要影响因子;土壤水分含量小于某一临界值时,导温率随土壤水分含量的增大而增大,反之则减小.     

An empirical test of helium diffusion in apatite: borehole data from the Otway basin, Australia

We have analyzed helium ages of apatites from several boreholes in the Otway basin, Australia, to evaluate whether laboratory helium diffusivity can be accurately extrapolated to conditions relevant in nature. Downhole apatite helium ages define a broad swath of values from 78–71 Ma at the surface (15°C) to nearly zero at depths corresponding to ambient temperatures of 80°C. The width of the swath results from uncertainties in corrected borehole temperatures, differences in the thermal history experienced by the various boreholes, and possibly from slightly different helium diffusivities among the detrital apatite grains studied. In the eastern Otway basin, the shape and position of the helium age profile is in good agreement with predictions based on the extrapolation of laboratory diffusivity data for Durango apatite coupled with published thermal histories for this part of the basin. In contrast, helium ages are much younger than predicted in the western Otway basin. Based on measured ages from Otway sediments, which have been essentially isothermal over the last few million years, an empirical diffusivity (D/a²) of 2×10⁻¹⁵ s⁻¹ can be assigned to apatites residing at downhole temperatures of 67–97°C. This empirical diffusivity is consistent with laboratory diffusion measurements, demonstrating that such measurements are reasonably accurate and can be applied with confidence to natural geologic settings. Given this confirmation of the laboratory diffusivity data, the discrepancy between the observed and modeled helium age profiles in the western Otway basin suggests that these sediments recently experienced higher temperatures than presently supposed.     

利用气象地温资料反演大地热流

利用气象台记录的深度为0.8m,1.6m和3.2m的月平均地温资料,进行Fourier频谱分析,得到定常波和子谐波（变化波）两部分.同时取地表以下为水平分层的均匀双层介质,建立数学模型,根据线性热传导和最优化理论对定常波以及子谐波的振幅谱和相位谱进行联合反演,计算气象台地表附近的定常地温梯度以及地表土壤的热扩散系数等物性参数,并据此计算该地的大地热流值.初步计算结果表明,上述方法得到的某些地区的大地热流值与传统的通过钻孔测量法得到的大地热流值符合得相当好.     

Use of shallow groundwater temperature profiles to infer climate and land use change: interpretation and measurement challenges

Temperature is often used to infer the effect of land use and climate conditions on aquifers. Reliable data are needed to examine the temperature behaviour in the subsurface; thus, the use of robust acquisition techniques is unavoidable. Three temperature measurement techniques were applied to assess the sources of bias that could occur during temperature logging in a shallow Quaternary coastal aquifer in Ferrara (Northern Italy). Open borehole temperature logging, multilevel sampling straddle packers isolated temperature measurements within a flow cell above ground and multilevel sampling straddle packers isolated temperature measurements via an in‐well level logger (MLS‐IW) were compared for several coastal monitoring wells to gain insights on the limitations of each technique. Results show that the source of bias between the three applied techniques are different: (i) the open borehole temperature logging method tends to record heat convection through the open borehole and is not representative of the aquifer temperature distribution; (ii) the multilevel sampling straddle packers isolated temperature measurements within a flow cell above ground method is swayed by the air temperature and the heating of the submersible pump used to lift groundwater above ground; and (iii) the MLS‐IW provides the most reliable vertical thermal profiling both in summer and winter, because groundwater temperature is directly measured at the selected monitoring depth. The implementation of a 1D flow model demonstrates that if precise temperature profiles are needed to infer the influence that land use and climate changes have on groundwater, the MLS‐IW method is a reliable method that could be applied to existing monitoring wells. Copyright © 2016 John Wiley & Sons, Ltd.     

盐水泥浆条件下定向井双侧向测井环境校正方法研究

在定向井中,双侧向测井数据由于受井眼、围岩、井斜、径向侵入等环境因素的影响,难以准确地估算储层的电阻率和更准确地识别储层流体.本文拟提出图版法和反演法相结合的思路来研究地层视电阻率的校正问题.首先,针对研究区的测井环境和钻井液电阻率,计算了不同尺寸井眼的双侧向测井响应,绘制了井眼校正图版;然后,针对斜度井地层模型,采用三维有限元方法计算了不同井斜、不同厚度地层的测井响应,构建了井斜-围岩/层厚图版,利用该图版实现了井眼校正和井斜-围岩/层厚的电阻率快速校正.最后,针对钻井液侵入的影响,采用反演方法计算了侵入半径和地层真电阻率,最终实现了双侧向测井的环境校正.利用上述理论与方法对海洋中定向井的双侧向测井资料进行了环境校正,提高了储层流体定性识别和定量评价的精度.