Impact of thermal dispersion on full-scale heat transfer of borehole heat exchangers

doi:10.11949/0438-1157.20201220

Abstract

Abstract:

Research on the heat transfer of borehole heat exchanger (BHE) is the key to enhance the heat transfer efficiency of the ground source heat pump(GSHP) system. Most of the BHE models proposed in the current literature ignore the influence of thermal dispersion, which is caused by spatial heterogeneity of underground aquifer. In order to consider thermal dispersion effect, an improved full-scale heat transfer model is developed by including thermal dispersion coefficient. The main findings are summarized as follows. The appropriate range of seepage velocity applied in the model is from 1×10^-8 m/s to 1×10^-6 m/s. The thermal dispersion effect is mainly reflected in the medium and long time scale. Seepage velocity, thermal dispersivity and porosity are the main factors affecting the heat transfer process. High values of the seepage velocity and thermal dispersivity of groundwater, as well as low values of the porosity, may lead to strong thermal dispersion effect. Seepage velocity has the strongest impact on the overall heat transfer around boreholes, followed by the thermal dispersivity, and the porosity has the weakest effect. As far as the borehole group is concerned, thermal dispersion has the greatest impact on the heat transfer process of the upstream borehole, followed by the middle reaches, and the downstream is the least. Within the parameters studied in this paper, thermal dispersion can increase the steady-state heat transfer capacity of the borehole by 5.52% to 49.93%.

Key words: ground source heat pump, borehole heat exchangers, groundwater seepage, full-time scale heat transfer, thermal dispersion

摘要：

开展地埋管换热器的传热研究是增强其传热性能以及提高热泵系统能效比的关键，现有的地埋管换热器传热模型多忽略了由地下含水层空间非均质性而产生的热弥散传热。因此，基于渗流影响下的全尺度模型和求解热弥散系数的速度一次方模型，提出了考虑热弥散影响的地埋管换热器全尺度传热模型。研究表明此模型所适用的地下水渗流速度范围为1×10^-8~1×10^-6 m/s；热弥散效应主要在中长时间尺度下体现，渗流速度、热弥散度以及孔隙率是影响传热过程的主要因素。地下水渗流速度和热弥散度越大，孔隙率越小，热弥散效应越强。综合考虑三类影响因素，渗流速度对钻孔传热的影响最大，热弥散度次之，孔隙率的影响最弱；对钻孔群而言，热弥散对上游钻孔传热过程的影响最大，中游次之，下游最小；在所研究的参数范围内，热弥散可使钻孔稳态传热能力提升5.52%~49.93%。

关键词: 地源热泵, 地埋管换热器, 地下水渗流, 全尺度传热, 热弥散

CLC Number:

TK 521.2

LI Xiaoyu, XU Hongyang, DAI Min, CAI Shanshan. Impact of thermal dispersion on full-scale heat transfer of borehole heat exchangers[J]. CIESC Journal, 2021, 72(5): 2547-2559.

李晓宇, 徐宏阳, 代敏, 蔡姗姗. 热弥散对地埋管换热器全尺度传热的影响[J]. 化工学报, 2021, 72(5): 2547-2559.

Figures/Tables 13

Table 1 G functions for predicting the wall temperature of borehole

模型	G函数
ILS	$G I L S t = 1 4 π λ ∫ r b 2 4 a t ∞ e x p ? - u u d u = 1 4 π λ E 1 r b 2 4 a t$	(1)
FLS	$G F L S t = 1 4 π H λ ∫ 0 H d z ∫ 0 H e r f c r b 2 + z - l 2 2 a t r b 2 + z - l 2 - e r f c r b 2 + z + l 2 2 a t r b 2 + z + l 2 d l$	(2)
MILS^[19]	$G M I L S t = 1 4 π 2 λ ∫ 0 π e x p P e 2 R' c o s φ ∫ 0 P e 2 F o / 4 1 ψ e x p - ψ - P e 2 R' 2 16 ψ d ψ d φ$	(3)
MFLS^[19]	$G M F L S t = 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ$ $f R, F o, P e = 1 4 R e x p - P e 2 R e r f c R - P e × F o 2 F o + e x p P e 2 R e r f c R + P e × F o 2 F o$	(4)
CMLS	$G C M L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u$ $φ = a * k * J n u r b J n' a * u r b - J n' u r b J n a * u r b$ $ψ = a * k * J n u r b Y n' a * u r b - J n' u r b Y n a * u r b$ $f = a * k * Y n u r b J n' a * u r b - Y n' u r b J n a * u r b$ $g = a * k * Y n u r b Y n' a * u r b - Y n' u r b Y n a * u r b$	(5)
CMLS-MFLS	$G C M L S - M F L S t = G C M L S t + G M F L S t - G I L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u + 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ - 1 4 π λ ∫ r b 2 4 a t + ∞ e x p - u u d u$	(6)

Table 1 G functions for predicting the wall temperature of borehole

模型	G函数
ILS	$G I L S t = 1 4 π λ ∫ r b 2 4 a t ∞ e x p ? - u u d u = 1 4 π λ E 1 r b 2 4 a t$	(1)
FLS	$G F L S t = 1 4 π H λ ∫ 0 H d z ∫ 0 H e r f c r b 2 + z - l 2 2 a t r b 2 + z - l 2 - e r f c r b 2 + z + l 2 2 a t r b 2 + z + l 2 d l$	(2)
MILS^[19]	$G M I L S t = 1 4 π 2 λ ∫ 0 π e x p P e 2 R' c o s φ ∫ 0 P e 2 F o / 4 1 ψ e x p - ψ - P e 2 R' 2 16 ψ d ψ d φ$	(3)
MFLS^[19]	$G M F L S t = 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ$ $f R, F o, P e = 1 4 R e x p - P e 2 R e r f c R - P e × F o 2 F o + e x p P e 2 R e r f c R + P e × F o 2 F o$	(4)
CMLS	$G C M L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u$ $φ = a * k * J n u r b J n' a * u r b - J n' u r b J n a * u r b$ $ψ = a * k * J n u r b Y n' a * u r b - J n' u r b Y n a * u r b$ $f = a * k * Y n u r b J n' a * u r b - Y n' u r b J n a * u r b$ $g = a * k * Y n u r b Y n' a * u r b - Y n' u r b Y n a * u r b$	(5)
CMLS-MFLS	$G C M L S - M F L S t = G C M L S t + G M F L S t - G I L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u + 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ - 1 4 π λ ∫ r b 2 4 a t + ∞ e x p - u u d u$	(6)

Fig.1 The heat transfer models of borehole heat exchanger

Fig.2 Elevation (a) and plane (b) diagram of borehole group

Table 2 Operation parameters of single hole buried pipe heat exchanger

相关参数	取值
单位长度热量(q_l)	28.85 W/m
U型管热导率(λ_p)	0.42 W/(m·K)
土壤热扩散率(a)	1.33 $×$ 10^-6 m²/s
回灌材料热扩散率(a_b)	4.84 $×$ 10^-6 m²/s
U型管内水流量(?)	0.563 kg/s
竖直钻孔长度(H)	100 m
U型管间距(x_u)	0.026 m
U型管内管径(r_i)	0.016 m
U型管外管径(r_o)	0.02 m
渗流速度(u_d)	1×10^-7 m/s
钻孔半径(r_b)	0.065 m
土壤初始温度(T₀)	15 $℃$
热弥散度(α_L)	0.5 m

Table 2 Operation parameters of single hole buried pipe heat exchanger

相关参数	取值
单位长度热量(q_l)	28.85 W/m
U型管热导率(λ_p)	0.42 W/(m·K)
土壤热扩散率(a)	1.33 $×$ 10^-6 m²/s
回灌材料热扩散率(a_b)	4.84 $×$ 10^-6 m²/s
U型管内水流量(?)	0.563 kg/s
竖直钻孔长度(H)	100 m
U型管间距(x_u)	0.026 m
U型管内管径(r_i)	0.016 m
U型管外管径(r_o)	0.02 m
渗流速度(u_d)	1×10^-7 m/s
钻孔半径(r_b)	0.065 m
土壤初始温度(T₀)	15 $℃$
热弥散度(α_L)	0.5 m

Fig.3 Comparisons between analytical and numerical models considering thermal dispersion

Fig.4 The prediction curve of fluid temperature response at different seepage velocity under unit load in two types of model

Fig.5 Temperature response of fluid at different seepage velocities

Fig.6 Temperature response of fluid with different thermal dispersivity

Fig.7 Temperature response of fluid with different porosity

Fig.8 Temperature response of fluid in borehole group at different seepage velocities

Fig.9 Temperature response of fluid in borehole group with different thermal dispersivity

Fig.10 Temperature response of fluid in borehole group with different porosity

Fig.11 Sensitivity analysis of impact factors on the fluid temperature response in the borehole

References 31

1	Wagner V, Blum P, Kübert M, et al. Analytical approach to groundwater-influenced thermal response tests of grouted borehole heat exchangers[J]. Geothermics, 2013, 46: 22-31.
2	Capozza A, De Carli M, Zarrella A. Investigations on the influence of aquifers on the ground temperature in ground-source heat pump operation[J]. Applied Energy, 2013, 107: 350-363.
3	Habibi M, Amadeh A, Hakkaki-Fard A. A numerical study on utilizing horizontal flat-panel ground heat exchangers in ground-coupled heat pumps[J]. Renewable Energy, 2020, 147: 996-1010.
4	Fahs M, Graf T, Tran T V, et al. Study of the effect of thermal dispersion on internal natural convection in porous media using Fourier series[J]. Transport in Porous Media, 2020, 131(2): 537-568.
5	Alcaraz M, García-Gil A, Vázquez-Suñé E, et al. Advection and dispersion heat transport mechanisms in the quantification of shallow geothermal resources and associated environmental impacts[J]. Science of the Total Environment, 2016, 543: 536-546.
6	Jouybari N F, Lundström T S, Hellström J G I. Investigation of thermal dispersion and intra-pore turbulent heat flux in porous media[J]. International Journal of Heat and Fluid Flow, 2020, 81: 108523.
7	Xue Y Q, Xie C H, Li Q F. Aquifer thermal energy storage: a numerical simulation of field experiments in China[J]. Water Resources Research, 1990, 26(10): 2365-2375.
8	倪龙. 同井回灌地下水源热泵源汇井运行特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2007.
	Ni L. Operation performance research on heat source/sink well of groundwater heat pump with pumping & recharging in the same well (GWHPPRSW)[D]. Harbin: Harbin Institute of Technology, 2007.
9	Park B H, Bae G O, Lee K K. Importance of thermal dispersivity in designing groundwater heat pump (GWHP) system: field and numerical study[J]. Renewable Energy, 2015, 83: 270-279.
10	Hidalgo J J, Carrera J, Dentz M. Steady state heat transport in 3D heterogeneous porous media[J]. Advances in Water Resources, 2009, 32(8): 1206-1212.
11	邓鼎兴. 地埋管地源热泵水热耦合模拟与浅层地温能适宜性评价[D]. 武汉: 中国地质大学, 2015.
	Deng D X. Thermo-hydro coupling simulation of BHE and shallow geothermal energy geological suitability assessment[D]. Wuhan: ChinaUniversity of Geosciences, 2015.
12	Metzger T, Didierjean S, Maillet D. Optimal experimental estimation of thermal dispersion coefficients in porous media[J]. International Journal of Heat and Mass Transfer, 2004, 47(14/15/16): 3341-3353.
13	Liu G Q, Zhou Z F, Li Z F, et al. Analysis and experimental study on thermal dispersion effect of small scale saturated porous aquifer[J]. Energy, 2014, 67: 411-421.
14	刘国庆, 周志芳, 李兆峰, 等. 小尺度含水层热量运移试验研究及热弥散效应评估[J]. 岩土力学, 2015, 36(1): 171-177.
	Liu G Q, Zhou Z F, Li Z F, et al. Experimental study of heat transfer and thermal dispersion effect assessment in small scale aquifer[J]. Rock and Soil Mechanics, 2015, 36(1): 171-177.
15	李世孝. 非饱和带在水源热泵工程中的导热特性研究[D]. 沈阳: 沈阳建筑大学, 2013.
	Li S X. Research of usaturated zone's thermal characteristic in the water source heat pump engineering[D]. Shenyang: Shenyang Jianzhu University, 2013.
16	魏炜, 王明众, 潘俊, 等. 非饱和多孔介质回灌过程中热弥散度特性试验[J]. 沈阳建筑大学学报(自然科学版), 2013, 29(5): 931-936.
	Wei W, Wang M Z, Pan J, et al. Experimental research on thermal dispersion degree properties of unsaturated porous media during recharge[J]. Journal of Shenyang Jianzhu University (Natural Science), 2013, 29(5): 931-936.
17	Lu X R, Ren T S, Gong Y S. Experimental investigation of thermal dispersion in saturated soils with one-dimensional water flow[J]. Soil Science Society of America Journal, 2009, 73(6): 1912-1920.
18	Rau G C, Andersen M S, Acworth R I. Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments[J]. Water Resources Research, 2012, 48(3): W03511.
19	Molina-Giraldo N, Blum P, Zhu K, et al. A moving finite line source model to simulate borehole heat exchangers with groundwater advection[J]. International Journal of Thermal Sciences, 2011, 50(12): 2506-2513.
20	陈红兵, 栾丹明, 牛浩宇, 等. 地下水渗流条件下土壤蓄热性能的数值研究[J]. 可再生能源, 2017, 35(3): 454-458.
	Chen H B, Luan D M, Niu H Y, et al. Numerical study on thermal property of underground heat exchanger under the influence of groundwater advection[J]. Renewable Energy Resources, 2017, 35(3): 454-458.
21	Gelhar L W, Welty C, Rehfeldt K R. A critical review of data on field-scale dispersion in aquifers[J]. Water Resources Research, 1992, 28(7): 1955-1974.
22	Zeng H Y, Diao N R, Fang Z H. A finite line-source model for boreholes in geothermal heat exchangers[J]. Heat Transfer—Asian Research, 2002, 31(7): 558-567.
23	Li M, Lai A C K. New temperature response functions (G functions) for pile and borehole ground heat exchangers based on composite-medium line-source theory[J]. Energy, 2012, 38(1): 255-263.
24	Cui T F, Cai S S, Guo H J, et al. Full-scale model to predict borehole fluid temperature with groundwater advection[C]//Proceedings of the IGSHPA Research Track 2018. International Ground Source Heat Pump Association, 2018.
25	Cai S S, Li X Y, Zhang M H, et al. An analytical full-scale model to predict thermal response in boreholes with groundwater advection[J]. Applied Thermal Engineering, 2020, 168: 114828.
26	Goldsztein G H. Solute transport in porous media: dispersion tensor of periodic networks[J]. Applied Physics Letters, 2007, 91(5): 054102.
27	Cheng P, Hsu C T. Applications of van Driest's mixing length theory to transverse thermal dispersion in forced convective flow through a packed bed[J]. International Communications in Heat and Mass Transfer, 1986, 13(6): 613-625.
28	Hsu C T, Cheng P. Thermal dispersion in a porous medium[J]. International Journal of Heat and Mass Transfer, 1990, 33(8): 1587-1597.
29	Doughty C, Hellström G, Tsang C F, et al. A dimensionless parameter approach to the thermal behavior of an aquifer thermal energy storage system[J]. Water Resources Research, 1982, 18(3): 571-587.
30	Molina-Giraldo N, Bayer P, Blum P. Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions[J]. International Journal of Thermal Sciences, 2011, 50(7): 1223-1231.
31	Saeid S, Al-Khoury R, Nick H M, et al. Experimental-numerical study of heat flow in deep low-enthalpy geothermal conditions[J]. Renewable Energy, 2014, 62: 716-730.

[1]	JI Yichen, QIAN Hua, ZHENG Xiaohong. Development and validation of three-dimensional model coupling heat and seepage for predicting ground temperature distribution [J]. CIESC Journal, 2016, 67(S2): 94-99.
[2]	ZHENG Xiaohong, QIAN Hua, LIANG Wenqing, ZHANG Lei. Impact of ground water seepage on ground temperature distribution and performance of GSHP [J]. CIESC Journal, 2014, 65(z2): 202-207.
[3]	CHEN Zhongshan, XIE Maozhao, LIU Hongsheng. Numerical simulation of thermal dispersion in porous media with large porosity [J]. CIESC Journal, 2014, 65(3): 870-878.