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Thermodynamic analysis of heat transfer in a wellbore combining compressed air energy storage

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Abstract

Compressed air energy storage (CAES) is a potential energy storage technology. The gas phase and short cycle period are two key factors affecting heat transfer loss in the wellbore of CAES. A semi-analytical solution was developed by using the convolution method considering gas movement in this study to describe the transient behavior of heat transfer with a short cycle period. The comparative analysis of the presented solution with two published solutions showed that the solution matched well with the previous solutions under steady state. Parametric studies were carried out to investigate the impact of injection rate, overall heat transfer coefficient and thermal diffusivity of the formation on heat loss in the wellbore. The results indicated that a low overall heat transfer coefficient and thermal diffusivity of the formation with an appropriate injection rate can efficiently reduce the heat loss. A hypothetical case study with a short cycle period of injection and production was conducted to demonstrate the applicability of the developed solution in CAES. The results suggest that the semi-analytical solution is applicable for heat transfer in the wellbore of CAES.

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Abbreviations

a :

Geothermal gradient, °C/m

b :

Surface temperature, °C

α :

Thermal diffusivity of the formation, m2/s

β :

Volume expansivity, 1/°C

r w :

Inner radius of inner tubing, m

r to :

Outside radius of inner tubing, m

r di :

Inner radius of outer tubing, m

r do :

Outside radius of outer tubing, m

r ci :

Inner radius of casing, m

r co :

Outside radius of casing, m

r h :

Radius of wellbore, m

T e :

Temperature of formation, °C

T inj :

Injection fluid temperature, °C

T ei :

Initial temperature of formation, °C

T w :

Fluid temperature in wellbore, °C

T out :

Production temperature at wellhead, °C

T bot :

Temperature in the bottom of well, °C

T tshut :

Wellhead temperature after shut-in

u :

Average flow velocity in borehole, m/s

c f :

Specific heat of fluid in wellbore, J/kg °C

λ e :

Thermal conductivity of the formation, W m−1 °C−1

P :

Pressure of fluid, MPa

ρ f :

Density of fluid in wellbore, kg/m3

U :

Overall heat transfer coefficient, W m−2 °C−1

q’:

The heat loss to formation per unit length of the wellbore, W/m

t :

Time, s

z :

Depth, m

s :

Laplace variable with respect to t

R loss :

Ratio of heat loss

H heat,out :

Total production enthalpy, J

H heat,in :

Total injection enthalpy, J

D w :

The length of the well, m

−:

Laplace transform

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Acknowledgements

This work was supported by “the Fundamental Research Funds for the Central Universities” (Grant Number. 2015KJJCB17),the National Natural Science Foundation of China (Grant Number: 41572220), and the Research and Development Project on Geological Disposal of High Level Radioactive Waste by the State Administration of Science, Technology and Industry for National Defense (Grant Number: 2012-240).

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Authors and Affiliations

  1. College of Water Sciences, Engineering Research Centre of Groundwater Pollution Control and Remediation of Ministry of Education, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Yi Li, Litang Hu & Jinsheng Wang

  2. School of Mechanical Engineering, Tongji University, Shanghai, 201804, People’s Republic of China

    Keni Zhang

Authors
  1. Yi Li
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  2. Keni Zhang
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  3. Litang Hu
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  4. Jinsheng Wang
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Correspondence to Litang Hu.

Additional information

This article is part of a Topical Collection in Environmental Earth Sciences on ‘‘Subsurface Energy Storage II’’. Guest edited by Zhonghe Pang, Yanlong Kong, Haibing Shao, and Olaf Kolditz.

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Li, Y., Zhang, K., Hu, L. et al. Thermodynamic analysis of heat transfer in a wellbore combining compressed air energy storage. Environ Earth Sci 76, 247 (2017). https://doi.org/10.1007/s12665-017-6552-6

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