Modeling of vertical ground heat exchangers

ABSTRACT

Below a certain depth, the ground temperature remains almost unchanged annually. This phenomenon can be exploited by coupling a ground heat exchanger to a heat pump, storing heat in the ground during summer for use in winter. The ground provides a better source/sink for heat than outside air for heat pump efficiency, as it is cooler than the outside air in the summer and warmer in the winter. Through increased efficiency, such systems also help avoid environmental impact. Much attention is now focused on utilizing ground heat pumps for heating and cooling buildings, as well as water heating, refrigeration and other thermal tasks. Modeling such systems is important for understanding, designing and optimizing their performance and characteristics. Several heat transfer models exist for ground heat exchangers, which usually consist of a series of vertical or horizontal underground pipes. Here, an introduction to ground heat exchanger types is provided, analytical and numerical models for heat transfer in vertical heat exchangers are reviewed and compared, recent related developments are described, and design software for vertical ground heat exchangers is discussed.

KEYWORDS:

• Ground source heat pump
• vertical borehole heat exchangers
• heat exchanger models

Acknowledgments

The support provided by the Ontario Ministry of Environment is gratefully acknowledged.

Nomenclature

cp	=	specific heat at constant pressure, J/kgK
d	=	borehole diameter, m
Fo	=	Fourier number
h	=	heat transfer coefficient, W/m2K
H	=	active borehole depth, m
k	=	thermal conductivity, W/mK
$\dot{m}$	=	mass flow rate of the circulating fluid, kg/s
Pr	=	Prandtl number
$\dot{q}$	=	heat flow per unit length of pipe, W/m
R	=	thermal resistance, mK/W
r	=	radial coordinate, m
Re	=	Reynolds number
t	=	temperature, K
z	=	axial coordinate, m

Greek Letters

α	=	thermal diffusivity, m2/s
β	=	shape factor
$\epsilon$	=	efficiency
$\tau$	=	time, s

Subscripts

0	=	initial
b	=	borehole
e	=	equivalent
f	=	circulating fluid
g	=	grout
p	=	pipe