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Extracting thermal energy from medium-deep ground layer for building heating is a promising means for pushing forward cleaner heating initiative. There is no available analytical model that can provide fast, accurate and effective simulation of both fluid and soil temperature field of deep borehole heat exchanger (DBHE) under complex geothermal gradient and subsurface stratifications. In this study, a stratified segmented finite line source method (SS-FLS) is proposed as an main contribution and novelty. The proposed model is validated by comparing with finite element method, model degradation example, and actual engineering project data of DBHE. The accuracy and robustness of the SS-FLS is fully checked. Then the effects of stratification on soil temperature field and fluid temperature field are investigated. It is found that the shape of temperature contour and temperature distribution have direct link with stratification as well as heat extraction rate on the heat pump side. Moreover, two critical model parameters are discussed in details which poses an important guide for both model application and system analysis. [Display omitted] • Stratified segmented finite line source (SS-FLS) method is proposed. • SS-FLS model is accurate, fast and easy-implemented for DBHE applications. • Impacts radius of DBHE is enlarging from shallow to deeper layers. • The fluid in the coaxial tube of DBHE is cooled down at the same pace. [ABSTRACT FROM AUTHOR]

The geothermal heat pump system based on deep borehole heat exchanger (DBHE) is one of the important systems to realize cleaner heating. It is key to ensure that DBHE can make full use of the dynamic characteristics of deep heat extraction and recovery (HER) in a long period of time to maintain the stability of geothermal field as well as sustainable development of DBHE and geothermal energy. This study mainly has made contributions in the following four aspects: (1) Through numerical analysis with a "stratified segmented finite line source method" (S2-FLS) and its model analytical expression, the impacts of heating duration and heating load distribution on the long-term operation performance of DBHE is revealed, which provides a theoretical basis for the optimal operation of DBHE. (2) The numerical analysis explained how complex geological conditions affect the dynamic heat extraction and heat recovery of DBHE in intermittent operation mode, which provides a theoretical basis for DBHE drilling site selection. (3) The model robustness is fully checked and an initial investigation on DBHE array with HER is presented, which may lead to massive application of deep geothermal systems. • A robust, efficient and easy implemented model is proposed for deep borehole heat exchanger. • The long-term heat extraction/recovery ability of deep borehole heat exchanger is verified. • Analysis on geological conditions can provide guides for drilling site selection. • The deep borehole array with heat extraction and recover is demonstrated. [ABSTRACT FROM AUTHOR]

• A new analytical model is proposed for deep geothermal systems. • New observations in non-uniform insulated system in cooling mode. • Turning points are identified when non-uniformity of insulation is investigated. • Multi-factor based evaluation is performed based on orthogonal test design. Deep borehole heat exchanger (DBHE) based ground source heat pump (GSHP) is a promising system for geothermal energy application in medium-deep layer. In this study, DBHE with non-uniform pipe insulation is proposed and numerically investigated. An effective analytical model is built based on segmented finite line-source method and a newly derived water heat transfer model. The year-round field test data are used for model verification. In-depth analyses are given to a comparison between the uniform and non-uniform insulation cases in both heating and cooling modes, and sensitivity analysis on non-uniformity of insulation. A orthogonal test is conducted for energy performance evaluation and optimization. It is found that DBHE with non-uniform insulation can outperform the one with full insulation in cooling mode, which offers new insights. In addition, an optimum insulation length can be identified through the non-uniformity analysis on insulation. It shows that the order of influence factor is heating season duration ratio, flow rate of working fluid, material thermal resistance non-uniformity of the center pipe, pipe sizing ratio, borehole depth, and insulation length non-uniformity of the center pipe. By choosing the proper system design parameters, the system energy saving could be up to 21.8%. [ABSTRACT FROM AUTHOR]

• A new analytical model is proposed for deep borehole heat exchanger. • The model takes full consideration of seepage, stratification, and geothermal gradient. • The model is featured as high computational speed, robust, and flexibility. • An analysis on heat extraction and recover of single and multiple DBHE is offered. Deep geothermal energy can be used as space heating as an important sustainable, clean and efficient method through deep borehole heat exchanger (DBHE). However, the heat transfer of DBHE is much more complex than conventional shallow borehole and there is no available analytical modeling tool. This study fully considered the complex geological conditions of seepage, stratification, and geothermal gradient in the modeling. A S3-FLS with full name of "stratified-seepage-segmented finite line source method" is proposed and then verified through multi-facets comparison with numerical models and real project data. In addition, the unsteady heat transfer of water flow inside coaxial tube is established and incorporated with the S3-FLS model. The new model is featured as high computational speed, robustness, and flexibility. Those features are supported by the model analysis in this study, via investigating the impact of borehole segmentation, comparison between unsteady and steady water heat transfer and impact of complex geological conditions on system simulation. In addition, it is shown that the model can be easily used for dynamic heat extraction and recovery analysis, as well as DBHE array analysis, through some initial illustrations. [ABSTRACT FROM AUTHOR]