Modeling of Ground Source Heat Pump System and Ground Heat Exchanger

This article discusses the mathematical modeling of ground source heat pump system and ground heat exchanger. It explains the vertical ground heat exchanger model and analytical models used in engineering applications. The article also highlights the need for further research to improve the models and make the system more cost-effective.

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2.4 Ground Source Heat pump system model and process of stimulation:
GSHP system has one significant component which is Ground Heat Exchanger. The
dependency of the effectiveness of the GHSP system is dependent on the GHX loop. GHX loop
provides connection between the ground and the heat pump (Luo et al.,2015). GHX is considered
as the most expensive component of the GHSP system. Hence, for the mitigation of the cost of
GSHP system for the installation and optimum design along with the reducing of the length of
GHX, it is essential to do further research about the performance of GHX(Soni, Pandey &
Bartaria,2016). In order to determine the temperature of the carrier fluid mathematical model is
essential(Sivasakthivel,Murugesan & Sahoo, 2014). This calculation helps to determine the
circulation between the heating pumps and GHE for different operational conditions. It also
helps to determine the evaluation of different GSHP systems.
2.4.1 Vertical Ground Heat Exchangers model:
Two different zones are used in the analysis of the heat transfer process of GHE. One of
them is using the rock or soil outside of GHE and other is the inside zone of GHE, which
includes grout, U-tub pipes and fluids circulating inside the pipe (Sivasakthivel et al., 2017).
There are many mathematical calculations have been implemented in order to determine the
transfer of the transient heat from the outside zone of GHE (Sivasakthivel,Murugesan & Sahoo,
2014). The classification of the models can be done in two ways- numerical models and
analytical models. The analytical model is generally based on cylindrical heat source theory and
infinite line sources theory (Culha et al.,2015). The complexity of the numerical models is high
and is implemented through the computer tools. Cylindrical source model and line source model
are widely used in the engineering application (Sarbu and Sebarchievici, 2016). The reason of

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using these two models are for their simplicity and accuracy. Both the theories allows to assume
infinite length in case of vertical GHE along with the resource of heat within the infinite medium
which is homogeneous. The various analytical models are described below.
7.2 Analytical Models:
The modeling of the heat transfer in GHE using the analytical modeling is complex as it
requires the time of month or the year to show the transit effects. The system requires large time
scale and the complexity of the system makes this process impossible to follow
(Sivasakthivel,Murugesan & Sahoo, 2014). Hence, the analysis of the heat transfer in GHE is done
in two separate regions. The inside of the borehole contains grout and u-tubes, the borehole
surrounds the ground(Soni, Pandey & Bartaria,2016). The wall temperature of the borehole is
important for stimulation of the system and engineering applications (Sivasakthivel et al., 2017).
The analysis of the heat transfer inside the borehole can VGHE model. Some of the cases , some
system conducts the ground heat outside the borehole. Cylindrical source model and line source
model are widely used in the engineering application (Sarbu and Sebarchievici, 2016). The
reason of using these two models are for their simplicity and accuracy. Both the theories allows
to assume infinite length in case of vertical GHE along with the resource of heat within the
infinite medium which is homogeneous. The various analytical models are described below.
7.3.1 Vertical Ground Heat Exchangers Model:
The time required for the stimulation of the system is less than a minute. Therefore, the
response of the grout material inside the borehole can be considered (Sarbu & Sebarchievici,2014).
The finite difference can be evaluated through the use two dimensional model along with the

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longitudinal and radical heat transfer(Sivasakthivel,Murugesan & Sahoo, 2014). The two
dimensional mode based on the fully implicit finite volume can be used for the heat exchanger
in the vertical ground(Soni, Pandey & Bartaria,2016). This model can be considered as the
extended version of Eskilson’s g-function model. This model describes the thermal response for
the short time, which is defined as the period of hour or less.
7.4 Closing Remarks:
The GHE modeling has been described in this phase. The study shows that the solutions
inside the borehole stays in a steady state. The transient effect outside the borehole should be
taken into account. In most cases, the thermal therapy outside the borehole does not taken into
account for most of the analytical models (Soni, Pandey & Bartaria,2016). Instead of that it is
assumed that the length of the borehole is infinite. However, these process is still used in most
of the cases for designing of GHE of the little computation time. The focus on the constant
ground heat load is followed for most of the analytical model(Sivasakthivel,Murugesan & Sahoo,
2014). However, further researches are needed for the improvisation of these models along with
the ground heat load which is periodic in nature (Buker & Riffat,2016). The solution for both inside
the borehole and outside the borehole can be determined through the use of analytical model
(Sarbu and Sebarchievici, 2016). In case, where the study regarding the full system is required ,
the analysis is done for inside and outside of BHE. In this case, the literature has the lack of
complete study. The simplifying assumptions while sizing the GHE is based on the line source
theory which contains ground properties, over sizing the GHE by increasing the length (Soni,
Pandey & Bartaria,2016). This results the evaluation of the system cost which makes it less
competitive compared to the other conventional heating g system(Sivasakthivel,Murugesan &
Sahoo, 2014). Migration of the moisture does not have the certain impact on the temperature or

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the flow of heat in the surrounded ground, which ahs the vertical heat exchangers (Sivasakthivel
et al., 2017). The flowing of the heat in the surrounding ground of VGHE is dependent on the
groundwater flow present. It has been seen that the application of the numerical methods are
often applied to the modeling of the larger system as the required computational time for the
large solution.

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