Systematic Renovation Design of Surface Water Source Heat Pump for a Hot Spring Center Based on Thermodynamic Analysis

2.1 Field survey of hot spring center

Our research team carried out a field survey. The survey results are the mean of multiple measurements: In the river, the water temperature was 14℃, and flow rate was 10,951m³/h; In the first hot spring pool at the source, the water temperature was 48.7℃, and flow rate was 4.6m³/h; In the second hot spring pool at the source, the water temperature was 51.6℃, and flow rate was 14. 6m³/h; For the raw water flowing out of the mountain to the inlet of the pools, the water temperature was 52℃, and flow rate was 14m³/h. After consulting the Engineering Department, it was confirmed that the water flows are constant throughout the year. Then, the flow rates and raw water temperatures of different seasons were derived (as shown in Table 1 below).

2.2 Outdoor and air conditioning design parameters

The outdoor and air conditioning design parameters are listed in Tables 2 and 3, respectively.

In the pools, the hot spring water could lose heat through the heat dissipation of surface evaporation, and the heat conduction via pool bottom, pool walls, equipment, and pipes. Due to the heat loss, the hot spring water will become cooler and cooler. To stabilize the pool water at a certain temperature, it is necessary to supplement an amount of heat equal to the heat loss.

4.1 Exergy analysis of WSHP system

(1) Exergy and exergy loss

The first law of thermodynamics was adopted to judge whether the energy utilization of the surface WSHP system has quantity and quality differences. This paper employs exergy to measure the availability S_EX of surface water energy. Any irreversible process at the hot spring center will reduce the working capability of the surface WSHP system. To obtain the enthalpy exergy, i.e., the maximum useful work, a series of reversible processes are needed to balance the system with the surrounding environment.

Let C(ε, φ, r, d) be the state of surface WSHP system; U(ε₀, φ₀, r₀, d₀) be the ambient environment state of the only heat source. The series of processes for the surface WSHP system to shift from state C to state U, i.e., the system reaches an equilibrium with the ambient environment, must be reversible. Therefore, the heat source should be isolated first, such that the system experiences the reversible adiabatic process of C→D. This ensures that φ_D equals the ambient temperature φ₀. Next, the system will exchange heat with the ambient environment, and thus go through the reversible constant temperature process of D→U, and thus reach an equilibrium with the ambient environment. Figure 1 shows the reversible processes of C→D→U.

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Figure 1. Reversible processes of C→D→U

Without considering the changes in the kinetic and potential energies at the inlet and outlet, the first law of thermodynamics was applied to the processes of C→D→U. Then, the system energy flowing through each unit mass of surface water can be described by:

$e={{d}_{0}}-d+{{p}_{h}}$                   (1)

Considering the two stages of the processes, formula (1) can be rewritten as:

$e={{e}_{C\to D}}+{{e}_{D\to U}}=0+{{\phi }_{0}}\left( {{r}_{0}}-r \right)$                   (2)

Thus, system exergy can be expressed by:

${{s}_{EX}}={{p}_{h\max }}=\left( d-{{d}_{0}} \right)-{{\phi }_{0}}\left( r-{{r}_{0}} \right)$                    (3)

where, p_hmax is the maximum useful work for the surface water to change from state 1 to state 2:

${{p}_{h\max }}={{s}_{EX1}}-{{s}_{EX2}}=\left( {{d}_{1}}-{{d}_{2}} \right)-{{\phi }_{0}}\left( {{r}_{1}}-{{r}_{2}} \right)$             (4)

Formula (4) shows that the enthalpy exergy of surface water is a state parameter dependent on the state of the water and the state of the ambient environment. The enthalpy exergy equals zero, when the system reaches an equilibrium with the ambient environment. If the environment is the only heat source, then p_hma is the exergy difference between the initial and final states of surface water.

(2) System exergy analysis

Exergy analysis was carried out on the surface WSHP system and its components. For the surface WSHP at the hot spring center, the working flow of refrigerant varies with seasons. The heating and cooling states between winter and summer are usually switched with four-way valves.

Let LO_C be the exergy loss of the compressor; P_EX be the theoretical power of the compressor; δ_E and P be the mechanical efficiency and input power of the compressor motor, respectively; q_L be the mass flow of refrigerant; φ₀ be the ambient temperature; S_EX-a and S_EX-b be the input and output exergies of the compressor, respectively. Then, the exergy balance of the compressor can be described by:

${{S}_{EX-a}}+{{P}_{EX}}={{S}_{EX-b}}+L{{O}_{C}}$                (5)

where, LO_C can be calculated by:

$\begin{align}  & L{{O}_{C}}=\left( {{S}_{EX-a}}-{{S}_{EX-b}} \right)+{{P}_{EX}} \\ & ={{q}_{L}}\left( {{d}_{a}}-{{d}_{b}} \right)+{{\phi }_{0}}{{q}_{L}}\left( {{r}_{a}}-{{r}_{b}} \right)+{{\delta }_{E}}P \\\end{align}$                     (6)

Let LO_N be the exergy loss of the condensers; q_WA2 be the secondary water flow; SH_ε,_W be the constant pressure specific heat of water; S_EX-g and S_EX-b be the input exergies of the condensers; S_EX-c and S_EX-h be the output exergies of the condensers. Then, the exergy balance of the condensers can be described by:

${{S}_{EX-b}}+{{S}_{EX-g}}={{S}_{EX-c}}+{{S}_{EX-h}}+L{{O}_{N}}$                      (7)

where, LO_N can be calculated by:

$L{{O}_{N}}=\left( {{S}_{EX-b}}-{{S}_{EX-c}} \right)+\left( {{S}_{EX-g}}-{{S}_{EX-h}} \right)$                    (8)

Formula (8) can be rewritten in the form of power:

$\begin{align}  & L{{O}_{N}}={{q}_{L}}\left[ \left( {{d}_{b}}-{{d}_{c}} \right)+{{\phi }_{0}}\left( {{r}_{b}}-{{r}_{c}} \right) \right] \\ & +{{q}_{SW}}\left[ \left( {{d}_{g}}-{{d}_{h}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{g}}/{{\phi }_{h}} \right) \right] \\\end{align}$                      (9)

There exists an equation:

${{q}_{L}}\left( {{d}_{b}}-{{d}_{c}} \right)={{q}_{WA2}}\left( {{d}_{h}}-{{d}_{g}} \right)$                      (10)

Combing formulas (9) and (10):

$L{{O}_{N}}={{\phi }_{0}}\left[ {{q}_{L}}\left( {{r}_{c}}-{{r}_{b}} \right)+{{q}_{WA2}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{h}}/{{\phi }_{g}} \right) \right]$                 (11)

Let S_EX-c and S_EX-d be the input and output exergies of the throttle valve, respectively; LO_T be the exergy loss of the throttle valve. Then, the exergy balance of the throttle valve can be described by:

${{S}_{EX-c}}={{S}_{EX-d}}+L{{O}_{T}}$                      (12)

where, LO_T can be calculated by:

$\begin{align}  & L{{O}_{T}}={{S}_{EX-c}}-{{S}_{EX-d}} \\ & ={{q}_{L}}\left[ \left( {{d}_{c}}-{{d}_{d}} \right)-{{\phi }_{0}}\left( {{r}_{c}}-{{r}_{d}} \right) \right] \\\end{align}$                      (13)

There exists an equation:

${{d}_{c}}={{d}_{d}}$                  (14)

Combing formulas (13) and (14):

$L{{O}_{T}}={{q}_{L}}{{\phi }_{0}}\left( {{r}_{d}}-{{r}_{c}} \right)$                    (15)

Let S_EX-d and S_EX-i be the input exergies of the evaporators; S_EX-a and S_EX-j be the output exergies of the evaporators. Then, the exergy balance of the evaporators can be described by:

${{S}_{EX-d}}+{{S}_{EX-i}}={{S}_{EX-a}}+{{S}_{EX-j}}+L{{O}_{EV}}$                   (16)

where, LO_EV can be calculated by:

$L{{O}_{EV}}=\left( {{S}_{EX-d}}-{{S}_{EX-a}} \right)+\left( {{S}_{EX-i}}-{{S}_{EX-j}} \right)$                (17)

Formula (17) can be rewritten in the form of power:

$\begin{align}  & L{{O}_{EV}}={{q}_{L}}\left[ \left( {{d}_{d}}-{{d}_{a}} \right)+{{\phi }_{0}}\left( {{r}_{d}}-{{r}_{a}} \right) \right] \\ & +{{q}_{WA3}}\left[ \left( {{d}_{i}}-{{d}_{j}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{i}}/{{\phi }_{j}} \right) \right] \\\end{align}$                (18)

There exists an equation:

${{q}_{L}}\left( {{d}_{a}}-{{d}_{d}} \right)={{q}_{WA3}}\left( {{d}_{i}}-{{d}_{j}} \right)$               (19)

Combing formulas (18) and (19):

$L{{O}_{EV}}={{\phi }_{0}}\left[ {{q}_{L}}\left( {{r}_{a}}-{{r}_{d}} \right)+{{q}_{WA3}}S{{H}_{\eta ,w}}ln\left( {{\phi }_{j}}/{{\phi }_{i}} \right) \right]$             (20)

Let S_EX-e and S_EX-h be the input exergies of the plate heat exchangers; S_EX-f and S_EX-g be the output exergies of the plate heat exchangers; LO_PH be the exergy loss of the plate heat exchangers; q_WA1 be the flow of surface water. Then, the exergy balance of the plate heat exchangers can be described by:

${{S}_{EX-e}}+{{S}_{EX-h}}={{S}_{EX-f}}+{{S}_{EX-g}}+L{{O}_{PH}}$             (21)

where, LO_PH can be calculated by:

$L{{O}_{PH}}=\left( {{S}_{EX-e}}-{{S}_{EX-f}} \right)+\left( {{S}_{EX-h}}-{{S}_{EX-g}} \right)$                (22)

Formula (22) can be rewritten in the form of power:

$\begin{align}  & L{{O}_{PH}}={{q}_{WA1}}\left[ \left( {{d}_{e}}-{{d}_{f}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{e}}/{{\phi }_{f}} \right) \right] \\ & +{{q}_{WA2}}\left[ \left( {{d}_{h}}-{{d}_{g}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{h}}/{{\phi }_{g}} \right) \right] \\\end{align}$                  (23)

There exists an equation:

${{q}_{WA1}}\left( {{d}_{f}}-{{d}_{e}} \right)={{q}_{WA2}}\left( {{d}_{h}}-{{d}_{g}} \right)$                  (24)

Combing formulas (23) and (24):

$L{{O}_{PH}}={{\phi }_{0}}\left[ \begin{align}  & {{q}_{WA1}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{f}}/{{\phi }_{e}} \right) \\ & +{{q}_{WA2}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{g}}/{{\phi }_{h}} \right) \\\end{align} \right]$                (25)

Let S_EX-j and S_EX-k be the input exergies of the fan coils; S_EX-i and S_EX-l be the output exergies of the fan coils; LO_WS be the exergy loss of the fan coils; q_g be the air flow processed by the fan coils; SH_D be the constant pressure specific heat of the air. Then, the exergy balance of the fan coils can be described by:

${{S}_{EX-j}}+{{S}_{EX-k}}={{S}_{EX-i}}+{{S}_{EX-l}}+L{{O}_{WS}}$                  (26)

where, LO_WS can be calculated by:

$L{{O}_{WS}}=\left( {{S}_{EX-j}}-{{S}_{EX-i}} \right)+\left( {{S}_{EX-k}}-{{S}_{EX-l}} \right)$                (27)

Formula (27) can be rewritten in the form of power:

$\begin{align}  & L{{O}_{WS}}={{q}_{WA3}}\left[ \left( {{d}_{j}}-{{d}_{i}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{j}}/{{\phi }_{i}} \right) \right] \\ & +{{q}_{g}}\left[ \left( {{d}_{k}}-{{d}_{l}} \right)+{{\phi }_{0}}S{{H}_{\varepsilon ,g}}ln\left( {{\phi }_{k}}/{{\phi }_{l}} \right) \right] \\\end{align}$                 (28)

There exists an equation:

${{q}_{WA3}}\left( {{d}_{i}}-{{d}_{j}} \right)={{q}_{g}}\left( {{d}_{k}}-{{d}_{l}} \right)$               (29)

Combing formulas (28) and (29):

$L{{O}_{WS}}={{\phi }_{0}}\left[ \begin{align}  & {{q}_{WA3}}S{{H}_{\varepsilon ,w}}ln\left( {{\phi }_{i}}/{{\phi }_{j}} \right) \\ & +{{q}_{g}}S{{H}_{\varepsilon ,g}}ln\left( {{\phi }_{l}}/{{\phi }_{k}} \right) \\\end{align} \right]$                   (30)

The exergy loss LO_HP of the surface WSHP system equals the sum of the exergy losses of different parts of the system:

$\begin{align}  & L{{O}_{HP}}=L{{O}_{C}}+L{{O}_{N}}+L{{O}_{T}} \\ & +L{{O}_{EV}}+L{{O}_{PH}}+L{{O}_{WS}} \\\end{align}$            (31)

In the cooling working condition, the exergy loss of the surface WSHP system can be calculated by:

$L O_{H P}=\delta_{E} P+q_{L}\left(d_{a}-d_{b}\right)$

$+\phi_{0}\left[\begin{array}{c}q_{w 1} S H_{\varepsilon, w} \ln \left(\phi_{f} / \phi_{e}\right) \\ +q_{g} S H_{\varepsilon, g} \ln \left(\phi_{k} / \phi_{l}\right)\end{array}\right]$          (32)

Formula (32) shows that the value of LO_HP is independent of any other intermediate state parameter, but related to such parameters of ambient temperature, inlet/output temperature of surface water, input power of the compressor, exergy difference of refrigerant, surface water flow, mass flow of refrigerant, and the temperature difference between supply and return airs.

The goal of exergy analysis is to improve the thermal efficiency of the surface WSHP system. However, the optimal setting for the thermal efficiency does not necessarily lead to the optimal economy of different parts of the system. Therefore, the systematic renovation design of the WSHP must be prepared combining thermodynamics with economy. Figure 2 resents the exergy dissipation model of the surface WSHP system, i.e., the thermo-economics model of the system.

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Figure 2. Thermo-economics model of the surface WSHP system

4.2 Optimal design for VIP section

As shown in Figure 3, the low-temperature hot spring water (39℃) in the VIP pool is filtered before flowing into the circulating water tank in the VIP section. From that tank, the low-temperature water is pumped to the WSHP by a circulating water pump. At the WSHP, the water is heated cyclically from 39℃ to 50℃. The work consumed for the heating is the energy loss during the 11℃ of temperature rise at the WSHP. After reaching 50℃, the hot spring water is transmitted by a lift pump to the front-end tank. From that tank, the high-temperature hot spring water flows under gravity to different pools to make up for their heat losses. In this way, the hot spring water in the system is utilized cyclically, without needing additional warmed spring water.

Figure 3. Constant temperature water replenishment of VIP section

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Figure 4. Constant temperature water replenishment of outdoor section

4.3 Systematic optimal design of outdoor section and indoor section

As shown in Figure 4, the low-temperature hot spring water (39℃) in the outdoor pool is filtered before flowing into the circulating water tank in the outdoor section. From that tank, the low-temperature water is pumped to the WSHP by a circulating water pump. At the WSHP, the water is heated cyclically from 39℃ to 50℃. The work consumed for the heating is the energy loss during the 11℃ of temperature rise at the WSHP. After reaching 50℃, the hot spring water is transmitted by a lift pump to the front-end tank. From that tank, the high-temperature hot spring water flows under gravity to different pools to make up for their heat losses. In this way, the hot spring water in the system is utilized cyclically, without needing additional warmed spring water. As shown in Figure 5, the constant temperature water replenishment of the indoor section is the same as that in the VIP section and the outdoor section.

Figure 5. Constant temperature water replenishment of indoor section

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Figure 6. Primary recycling of waste heat

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Figure 7. Secondary recycling of waste heat