Heat flow rate at a bore-face and temperature in the multi-layer media surrounding a borehole

Assessment of the heat either delivered from high temperature rocks to the borehole or transmitted to the rock formation from circulating fluid is of crucial importance for a number of technological processes related to borehole drilling and exploitation. Normally the temperature fields in the well and surrounding rocks are calculated numerically by finite difference method or analytically by applying the Laplace-transform method. The former approach requires tedious and, in certain cases, non-trivial numerical computations. The latter method leads to rather bulky formulae that are inconvenient for further numerical evaluation. Moreover, in previous studies where the solution is obtained analytically, the heat interaction of the circulating fluid with the formation was treated on the condition of constant bore-face temperature. In the present study the temperature field in the rock formation disturbed by the heat flow from the borehole is modeled by a heat conduction equation, assuming the Newton model for the convective heat transfer on the bore-face, with boundary conditions that account for the thermal history of the borehole exploitation. The problem is solved analytically by the generalized heat balance integral method. Within this method the approximate solution of the heat conduction problem is sought in the form of a finite sum of functions that belong to a complete set of linearly independent functions defined at the finite interval bounded by the radius of thermal influence and that satisfy the homogeneous boundary conditions on the bore-face. In the present study first and second order approximations are obtained for the composite multi-layer domain. The numerical results illustrate that the second approximation is in a good agreement with the exact solution. The only disadvantage of this solution is that it depends on the radius of thermal influence, which is an implicit function of time and can only be found numerically by iterative algorithms. In order to eliminate this complication, in this study an approximate explicit formula for the radius of thermal influence and new close-form approximate solution are proposed on the basis of the approximate solution obtained by the integral-balance method. Employing the non-liner regression method the coefficients for this simplified solution are obtained. The accuracy of the approximate solution is validated by comparison with the exact analytical solution found by Carslaw and Jaeger for the homogeneous domain.     

The effect of a fluid-filled fracture on the temperature profile in a borehole

Fluid flow in fractures in crystalline rock can be detected by making temperature measurements in a borehole that intersects them. Analysis of the thermal anomaly allows a quantitative estimate of the rate of fluid flow. A characteristic anomaly that decays with time is produced when drilling fluid is forced into a fracture in which water does not normally flow. Models of a planar heat source with a strength that is uniform or that increases linearly during the drilling time adequately reproduce two examples from the Canadian Shield.     

The influence of the thermosiphon effect on the thermal response test

The issue of natural and forced groundwater movements, and its effect on the performance of ground heat exchangers is of great importance for the design and sizing of borehole thermal energy systems (BTESs). In Scandinavia groundwater filled boreholes in hard rock are commonly used. In such boreholes one or more intersecting fractures provide a path for groundwater flow between the borehole and the surrounding rock. An enhanced heat transport then occurs due to the induced convective water flow, driven by the volumetric expansion of heated water. Warm groundwater leaves through fractures in the upper part of the borehole while groundwater of ambient temperature enters the borehole through fractures at larger depths. This temperature driven flow is referred to as thermosiphon, and may cause considerable increase in the heat transport from groundwater filled boreholes. The thermosiphon effect is connected to thermal response tests, where the effective ground thermal conductivity is enhanced by this convective transport. Strong thermosiphon effects have frequently been observed in field measurements. The character of this effect is similar to that of artesian flow through boreholes.     

天然气水合物取样钻头及岩层温度场数值分析

为防止深海海底天然气水合物钻探取样过程中发生分解及钻头热磨损,运用摩擦学及传热学基本原理,以弹性库仑摩擦模型作为接触单元本构模型,建立具有刚柔接触的取样钻头和岩层摩擦生热及传热的瞬态动力学耦合数学模型,采用有限元方法进行计算分析.结果表明,钻头温度变化较大,岩层温度变化较小,且只在和钻头接触局部区域内较明显.不同钻速、摩擦系数以及侧壁压力下,钻头和岩层温度变化趋势不同.在实际钻探取样时,对应不同工况和地质条件,应合理选择钻井液循环速率及分布,选择合适钻速,防止取样失败.     

中深层同轴换热器充填材料热性能研究

地热能作为分布广、储量大的可再生能源,在节能减排和促进碳中和方面具有重要作用。同轴换热器在开采中深层岩土体热量方面优势明显,可以进行无干扰式“取热不取水”开发。作为换热器与地层岩土体的传热媒介,充填材料对热性能的影响至关重要。采用数值模拟方法分析5种充填材料对流体温度、岩土体温度和作用范围的影响。结果表明,充填材料水的热阻是细砂-膨润土的1.5倍;采用高导热的充填材料（细砂-膨润土）后,出口流体温度升高了1.81℃,环空流体随深度增加呈非线性演化;换热器短期（4个月）和长期（20年）运行模式下井底（2 000 m）影响范围分别是深度500 m的1.5倍和7倍;细砂-膨润土作为充填材料的换热器在短期和长期运行模式下,井底影响范围可分别达到5.2 m和36.5 m。     

Progress in hot dry rock exploitation

The term hot dry rock (HDR) has been used to describe the exploitation of the thermal energy contained in rocks that have a sufficiently high temperature but contain insufficient fluids to enable the heat to be extracted. The attraction of such a resource is that it is probably available everywhere, but at varying depths. International activity has focused on the problem of circulating fluids through the rock and extracting the heat by conduction from the rock to the fluid. The initial concepts were based on creating individual cracks to interlink two wells approximately 500 m apart. The necessary heat exchange area was to be achieved by using multiple systems of interconnections in parallel. The results from the field work have shown that the interlinking is dominated by stimulated natural joints and the degree of normal dilation that can be achieved is limited by the orientation of the natural discontinuity with the pre-existing stresses and, hence, the shear stress on the joint. The normal dilation is important because it controls the resistance to flow between the wells. The shear mechanism controls the far-field water losses and the direction of growth of the more permeable interwell region and has obvious implications for the proposed geometry of any system. The cost of drilling has been shown to be comparable to deep drilling for other purposes and the development of deviated holes in strong crystalline rocks has been shown to be possible. The progress of the stimulation has been mapped successfully by locating the microseismic events generated by shearing but the relationship of the microseismically active areas and the heat transfer region has yet to be identified. No adverse environmental problems have been identified; the produced fluids are generally benign and the microseismicity is well below any threshold of damage. The goal of a universally available heat source free of stack emissions and waste products that does not consume finite reserves of minerals and hydrocarbon demands substantial investment in the research to determine if it is attainable. The major field programmes should have reached their preliminary conclusions by the middle of 1986.     

The detection of groundwater flow by precise temperature measurements in boreholes

The flow of water is a very effective means for the transfer of heat, and one method of detecting such flow is to make precise temperature measurements at closely spaced intervals in a borehole that intersects a flow zone. Water can flow through permeable formations; within a borehole it can flow between two aquifers or fracture systems; it can flow into a fracture system during the drilling of a borehole; and it can flow up or down narrow, dipping fracture zones. Each of these phenomena produces a characteristic thermal signature on a borehole temperature log that can be modelled mathematically. Analysis of such thermal anomalies permits, therefore, a quantitative estimate to be made of the amount and rate of fluid flow. In principle, very small flow rates can be detected from their thermal effects, but in practice other factors, such as thermal conductivity variations, can cause variations in thermal gradients that limit the detectability. Anomalies that persist over large depth ranges compared with the diameter of the borehole can generally be interpreted unambiguously. Examples of each type of flow are given.     

Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers

Several models are available in literature to simulate ground heat exchangers. In this paper an approach based on electrical analogy is presented, for this reason named CaRM (CApacity Resistance Model). In some cases several information are needed during design: both the borehole and the surrounding ground are affected by thermal exchange. The model here presented allows to consider the fluid flow pattern along the classical vertical ground heat exchangers as a single U-tube, a double U-tube or coaxial pipes. Besides, ground temperature at different distances from borehole are calculated, taking into account also the thermal interference between more boreholes. Starting from the supply temperature to the heat exchanger, the outlet fluid temperature is calculated and the ground temperature in each node, step by step. The model has been validated by means of a commercial software based on the finite differences method. Further comparisons have been carried out against data from a ground thermal response test and from the survey of an office building equipped with a ground coupled heat pump and vertical double U-tube heat exchangers. The agreement of results validates the model here presented.     

同轴地埋管换热器岩土热响应试验研究

岩土热物理性质是影响地源热泵系统设计和运营的关键因素,对位于武汉市洪山区的2口不同深度的同轴地埋管换热孔分别进行48 h的热响应试验,并对同轴地埋管换热器内外管之间环形空间中的平均流体温度进行测试.根据同轴地埋管换热器的几何特性,以简便实用的方式测量同轴地埋管换热器环状空间传热流体的平均温度,结合同轴地埋管换热器钻孔热...     

太阳能地层钻孔贮热体夏季贮热过程的研究

建立太阳能地层钻孔（Ｂｏｒｅｈｏｌｅ）贮热单元体夏季贮热过程的理论模型，数值模拟贮热岩体在夏节贮存热量过程中的热特性，详细分析了加热流体温度、贮热单元体的贮热速率以及岩体内温度场在整个夏季贮热过程中的变化规律，揭示了岩层导热与加热体对流热交换之间的热耦合性。     

Heat extraction thermal response test in groundwater-filled borehole heat exchanger – Investigation of the borehole thermal resistance

In groundwater-filled borehole heat exchangers (BHEs) convective flow influences the heat transfer in the borehole. During heat extraction thermal response tests (TRTs) the effect of the changing convective flow is more dominant than during heat injection tests. Water is heaviest around 4 °C and when exceeding this temperature during the test, the convective flow is stopped and restarted in the opposite direction resulting in a higher borehole thermal resistance during that time. Just before 0 °C the convective flow is the largest resulting in a much lower borehole thermal resistance. Finally, during the freezing period phase change energy is released and material parameters change as water is transformed into ice, resulting in a slightly higher borehole resistance than at a borehole water temperature of 0 °C. The changes in borehole thermal resistance are too large for ordinary analysis methods of thermal response tests to work. Instead another method is introduced where the borehole thermal resistance is allowed to change between different time intervals. A simple 1D model of the borehole is used, which is matched to give a similar mean fluid temperature curve as the measured one while keeping the bedrock thermal conductivity constant during the whole test. This method is more time-consuming than ordinary TRT analyses but gives a good result in showing how the borehole thermal resistance changes. Also, a CFD-model with a section of a simplified borehole was used to further study the effect of convection and phase change while the temperature was decreased below freezing point. The test and the model show similar results with large variations in the borehole thermal resistance. If the knowledge of changing borehole thermal resistance was used together with a design program including the heat pump and its efficiency, a better BHE system design would be possible.     

Entropy generation minimization of a MHD (magnetohydrodynamic) flow in a microchannel

The dissipative processes that arise in a microchannel flow subjected to electromagnetic interactions, as occurs in a MHD (magnetohydrodynamic) micropump, are analyzed. The entropy generation rate is used as a tool for the assessment of the intrinsic irreversibilities present in the microchannel owing to viscous friction, heat flow and electric conduction. The flow in a parallel plate microchannel produced by a Lorentz force created by a transverse magnetic field and an injected electric current is considered assuming a thermally fully developed flow and conducting walls of finite thickness. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid-wall interfaces. Velocity, temperature and current density fields in the fluid and walls are used to calculate the global entropy generation rate. Conditions under which this quantity is minimized are determined for specific values of the geometrical and physical parameters of the system. The Nusselt number is also calculated and explored for different conditions. Results can be used to determine optimized conditions that lead to a minimum dissipation consistent with the physical constraints demanded by the microdevice.     

Transient conjugated heat transfer in thick walled pipes with convective boundary conditions

Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number.     

Influence on thermal response test by groundwater flow in vertical fractures in hard rock

In this paper different approaches to groundwater flow and its effect in the vicinity of a borehole ground heat exchanger are discussed. The common assumption that groundwater flow in hard rock may be modelled as a homogeneous flow in a medium with an effective porosity is confronted and models for heat transfer due to groundwater flow in fractures and fracture zones are presented especially from a thermal response test point of view. The results indicate that groundwater flow in fractures even at relatively low specific flow rates may cause significantly enhanced heat transfer, although a continuum approach with the same basic assumptions would suggest otherwise.     

套管式中深层地埋管换热器传热建模及取热分析

为了研究无干扰换热条件下,中深层地热能的实际取热性能,文章通过数值模拟方法模拟计算了套管式中深层地埋管换热器的名义取热量。模拟结果表明,套管式中深层地埋管换热器的名义取热量随着钻孔深度、大地热流、循环水流量、当地大气年平均温度的增加而增加。套管式中深层地埋管换热器周围土层的地质条件分布也影响着中深层地埋管换热器的名义取热量,具体表现为浅层土层的导热系数越小,中深层地埋管换热器的名义取热量越大;深层土层的导热系数越大,中深层地埋管换热器的名义取热量也越大。通过调整地埋管换热器的相关参数,并选择合适的地埋管埋设地点等优化措施,可使套管式中深层地埋管换热器达到可观的名义取热量。     

NUMERICAL SIMULATION OF TRANSIENT COOLING OF A HOT SOLID BY AN IMPINGING FREE SURFACE JET

This paper treats transient cooling of a hot solid by an impinging circular free surface liquid jet. The flow and thermal fields in the liquid as well as the temperature distributions in the hot solid have been predicted numerically. The Navier-Stokes equations for incompressible fluid flow in an axisymmetric coordinate system and the transient heat conduction equation for a solid have been solved by a finite difference method. The hydrodynamics of the liquid film and the heat transfer processes have been investigated to understand the physics of the phenomena.     

裂缝性储层水平井钻井井壁稳定模型研究

钻井井壁稳定是钻井过程中的复杂性问题。当水平井筒穿过储层天然裂缝时,天然裂缝可能在较小的井底流体压力下发生剪切破坏,造成井壁垮塌。为此,基于弹性力学和岩石力学理论,并考虑岩石孔隙弹性和热弹性效应影响,推导了井壁主应力计算式。视天然裂缝为地层中的结构弱面,基于主应力与天然裂缝法向的空间位置关系,得出了天然裂缝法向与井壁最大主应力夹角计算式,结合弱面结构剪切破坏准则,得到维持井壁稳定的最小井底流压数学求解模型,提出了模型求解和井壁稳定流压获取方法。通过公式推导及计算实例分析可知:天然裂缝倾角和走向、原地应力和水平井方位将影响钻井过程中防止井壁垮塌的最小井底流体压力的设计,也即影响安全钻井液密度的选择。     

Forced convection with viscous dissipation in the thermal entrance region of a circular duct with prescribed wall heat flux

The thermal entrance forced convection in a circular duct with a prescribed wall heat flux distribution is studied under the assumptions of a fully developed laminar flow and of a negligible axial heat conduction in the fluid, by taking into account the effect of viscous dissipation. The solution of the local energy balance equation is obtained analytically by employing the Laplace transform method. The effect of viscous dissipation is taken into account also in the region upstream of the entrance cross-section, by assuming an adiabatic preparation of the fluid. The latter hypothesis implies that the initial condition in the entrance cross-section is a non-uniform radial temperature distribution. Two special cases are investigated in detail: an axially uniform wall heat flux, a wall heat flux varying linearly in the axial direction.     

The combined effects of longitudinal heat conduction,flow nonuniformity and temperature nonuniformity in crossflow plate-fin heat exchangers

An analysis of a crossflow plate-fin compact heat exchanger, accounting for the combined effects of two-dimensional longitudinal heat conduction through the exchanger wall and nonuniform inlet fluid flow and temperature distribution is carried out using a finite element method. A mathematical equation is developed to generate different types of fluid flow/temperature maldistribution models considering the possible deviations in fluid flow. Using these models, the exchanger effectiveness and its deterioration due to the combined effects of longitudinal heat conduction, flow nonuniformity and temperature nonuniformity are calculated for various design and operating conditions of the exchanger. It was found that the performance variations are quite significant in some typical applications.