Water pumping analysis and experimental validation of beach well infiltration intake system in a seawater source heat pump system

Abstract

Based on energy conservation equation and Darcy’s law, a model of beach well infiltration intake system applied in a seawater source heat pump system was established. The model consists of the seawater seepage and the heat transfer process. A porous medium model in a software named FLUENT was applied to simulate the seepage and the heat transfer process. This model was also validated by field experiment conducted on the seashore in Tianjin, China. The maximum relative error between simulation results and experimental results was 2.1% (less than 5%), which was acceptable in engineering application. The porosity and coefficient of thermal conductivity of the aquifer soil were determined to be 0.49 W/(m·K) and 1.46 W/(m·K), respectively in the simulation. In addition, the influencing factors of pumping water of beach well were also analyzed. The pumping water was found to increase when the distance between the beach well and the impervious boundary becomes longer, when the distance between the beach well and the supplying water source shortens, when the diameter of the beach well enlarges, and the drawdown enlarges.

Keywords

water pumping analysis / experimental validation / infiltration intake system / seawater source heat pump

Introduction

In recent years, there has been an increasing research focus on environmental protection and energy reduction. New energy, which is divided into two types, namely natural energy and recycled energy, becomes more popular in the field of study. Seawater is used as natural energy, and seawater source heat pump (SWHP) system has attracted many researchers’ interest and has been used in many heating systems at seaside in the world [ 1- 4] and in both residential and commercial buildings [ 5- 8].

SWHP is a technology that utilizes solar and geothermal energy absorbed by seawater to realize the transformation of thermal energy from low-grade to high-grade. There are many applications in using SWHP in which Europe and America are taking a leading role [ 9]. However, some problems like seawater corrosion and freezing in winter, to some extent, prevent the unit from proper operation. To solve these problems, the beach well infiltration intake system (BWIIS) is used in SWHP [ 10].

BWIIS, often applied to desalination technology in some countries and regions [ 11– 13], is usually classified into surface type and indirect type according to the intake mode. Figure 1 shows the common indirect BWIIS. Seawater is abstracted from the coast and sand layer of seafloor near the coast. This process can reduce the water pollution from sea creature and sediment. Then, the seawater is collected into the beach well and further processed in the factory [ 14]. Peters and Pintó [ 15] analyzed the indirect intake system of desalination on the environment. Compared with the surface type, the indirect type could get the stable seawater temperature and reduce the amount of chemical reagent in the desalination process. Li et al. [ 16] analyzed the influencing factors of intake scheme in detail and proposed the principles for selection of intake scheme.

Therefore, the technology of BWIIS in seawater-source heat pump was presented in this paper in order to make full use of ocean energy and geothermal energy, and to meet the requirements of energy reduction. Simulation models were established and experimental tests were conducted to verify the feasibility of this system. The thermal conductivity of aquifer was determined, and the accuracy of mathematical modeling was verified further based on the comparison between experimental value and simulation value. In addition, the water pumping analysis was performed.

Mathematical modeling

In a BWIIS, the pump draws the water from beach well. Seawater flows through a coastal aquifer driven by hydraulic gradients between the sea and beach well. It, then, exchanges heat with the refrigerant in the heat pump system.

BWIIS consists of the seawater seepage and the heat transfer process. It is, therefore, essential to establish a seepage and heat transfer model to study BWIIS. Seepage and heat transfer characteristics of BWIIS is affected by not only the design conditions of beach well but also the aquifer structure. In this model, the aquifer is supposed to be homogeneous and isotropous; the flow of aquifer is in accord with Darcy’s law; the natural convection in the process of groundwater heat migration is not considered; and the thermal properties of the pipe and seawater are constant.

There exists the heat migration in the heat transfer process between seawater and aquifer soil due to the difference in water level between seawater and beach well. Based on the energy conservation equation, the heat migration equation is [ 17- 19],

(1) {\displaystyle \frac{\partial T}{\partial \tau }}={\displaystyle \frac{\mathrm{1}}{c}}\mathrm{div}\left(\mu \mathrm{grad}T\right)-{\displaystyle \frac{c_{\mathrm{w}}}{c}}\mathrm{div}\left(Tv\right),

(2) \mu ={\mu }_e+{\mu }_v,

where T is the temperature (°C), τ is the time (s), c and c_w are the specific heat capacity of porous media and water, respectively (J/(kg⋅°C)), ν is seepage velocity (m/s), μ is the coefficient of thermal conductivity for the aquifer (W/(m⋅K)), and μ_e and μ_v are the coefficient of thermal conductivity and mechanical dispersion, respectively (W/(m⋅K)).

The seepage of seawater can be described by adopting Darcy’s law. The detailed analysis is shown in Section 3.3. And Darcy’s law is defined as

(3) Q=KA{\displaystyle \frac{\mathrm{\Delta }h}{L}}=KAJ,

(4) v=KJ,

where Q is the seepage flux (m³/s), K is the permeability coefficient (m/s), A is the cross-sectional area of flow (m²), Δh is the head loss between the top and the bottom of seepage (m), L is the length over which the drawdown is taking place (m), and J is the hydraulic slope.

FLUENT, the computational fluid dynamics simulation software, was applied to simulate this seepage and heat transfer model. A porous medium model was generated in FLUENT, and the energy equation for porous medium is expressed as

(5) {\displaystyle \frac{\partial }{\partial t}}\left[n{\rho }_{\mathrm{f}}{h}_{\mathrm{f}}+\left(1-n\right){\rho }_{\mathrm{s}}{h}_{\mathrm{s}}\right]+{\displaystyle \frac{\partial }{\partial x_i}}\left({\rho }_{\mathrm{f}}{u}_i{h}_{\mathrm{f}}\right) ={\displaystyle \frac{\partial }{\partial x_i}}\left(k_{\mathrm{eff}}{\displaystyle \frac{\partial T}{\partial x_i}}\right)-n{\displaystyle \frac{\partial }{\partial x_i}}{\displaystyle \sum _{j\prime }{h}_{j\prime }{J}_{j\prime }}+n{\displaystyle \frac{\mathrm{d}P}{\mathrm{d}t}}+n{\tau }_{ik}{\displaystyle \frac{\partial u_i}{\partial x_k}}+n{S}_{\mathrm{f}}^{\mathrm{h}}+\left(1-n\right)S_{\mathrm{s}}^{\mathrm{h}},

where h_f and h_s are the enthalpy of fluid and solid medium in porous medium region, respectively (J/kg); ρ_f and ρ_s are the density of fluid and solid medium in porous medium region, respectively (kg/m³); u_i is the fluid velocity subentry at i direction (m/s); P is the static pressure (Pa); τ_ik is the stress tensor (Pa); n is the porosity of porous medium; J_j′ is the diffusion flux of j′ (kg/(m²⋅s)); S_{\mathrm{f}}^{\mathrm{h}} and S_{\mathrm{s}}^{\mathrm{h}} are the enthalpy source item of the fluid and solid in the porous medium region, respectively (W/m³); and k_eff is the effective coefficient of thermal conductivity (W/(m⋅K)).

Experimental system

To validate the mathematic model established above, an experimental system for BWIIS, which is described in Figs. 2 and 3, was installed on December 15th, 2012, on the seashore in Tianjin, China. The experimental system mainly consists of the temperature measuring point, a pumping well and an observation well. The observation well is mainly used to observe the water level which can provide some basis for analyzing the flow condition of water in the aquifer.

Seawater and soil sample test

Some parameters of seawater and soil should be determined in the model when simulating the seawater seepage. Therefore, a test of seawater and soil sample was conducted. The coefficient of thermal conductivity of soil sample was measured by the line heat source method. And the coefficient of thermal conductivity λ is defined by

(6) \lambda ={\displaystyle \frac{q}{\mathrm{2}\pi \mathrm{\Delta }t}}\ln \left({\displaystyle \frac{{\tau }_{\mathrm{1}}}{{\tau }_{\mathrm{2}}}}\right),

(7) q={\displaystyle \frac{\mathrm{0.86}{I}^{\mathrm{2}}R}{l}}={\displaystyle \frac{\mathrm{0.86}{V}^{\mathrm{2}}}{lR}},

where q is the heat quantity emitted by the heater strip per unit length and time (kcal/(m·h)), Δt is the temperature difference between time τ₁ and time τ₂ (°C), l is the length of heater strip (m), R is the resistance of heater strip (Ω), I is the electric current through heater strip (A), and V is the voltage through heater strip (V).

The density of plain fill, silt clay, aquifer and seawater was 1160 kg/m³, 1850 kg/m³, 3050 kg/m³ and 1004 kg/m³, respectively. The heat capacity of the plain fill, silt clay, aquifer and seawater was 1260 J/(kg·K), 1092 J/(kg·K), 672 J/(kg·K) and 4217 J/(kg·K), respectively, while the thermal conductivity of the plain fill, silt clay and seawater was 0.75 W/(m·K), 1.39 W/(m·K) and 0.56 W/(m·K), respectively. The thermal conductivity of the aquifer is determined by the numerical method which will be shown in Section 3. 4. The kinetic viscosity of seawater was 0.829 × 10^-3 Pa·s.

Water quality analysis

Considering the corrosion of seawater on the heat exchanger, the water quality of the BWIIS was evaluated. Some indexes vary significantly. The conductivity varies from 57.9 MS/cm to 19.9 MS/cm, the salinity varies from 25200 mg/L to 17200 mg/L, and the turbidity varies from 10.32 NTU to 1.02 NTU. Some indexes, such as the PH value and dissolved oxygen vary slightly. Based on these results, the water quality was improved significantly by the action of soil. The improvement of water quality could contribute to reducing the corrosion of seawater on the heat exchanger greatly. Besides, it can reduce the handling expense for seawater and extend the life span of the system.

Water level analysis

The water level test was conducted by a scale, string and floating ball. The temperature test was performed by some constantan thermocouples and the multichannel data acquisition unit of FLUENT.

To identify the flow condition of water in the aquifer, water level tests were conducted at a flow of 30 m³/h and 40 m³/h. At the flow of 30 m³/h, the water level of seawater and beach well is 154 cm and 92 cm, while 149 cm and 61 cm at the flow of 30 m³/h. The water level of beach well decreases when the water was pumped. As the flow increases, the drawdown increases. Equation (8) was applied to judge the water flow in the aquifer.

(8) {\displaystyle \frac{Q_{\mathrm{1}}}{Q_{\mathrm{2}}}}={\displaystyle \frac{S_{\mathrm{1}}}{S_{\mathrm{2}}},}

where Q₁ and Q₂ denote the flow (m³/h), and S₁ and S₂ denote the drawdown at the flow of Q₁ and Q₂, respectively (m).

The experimental results conform to Eq. (8). Thus, the flow in the aquifer is considered as laminar flow, which means the model is in accord with the actual application of Darcy’s law.

The experimental data at the flow of 45 m³/h was applied to calculate the permeability coefficient K. In the process in which the water was pumped, the water quantity varied from 40 m³/h to 45 m³/h, with an average flow of 43 m³/h. It is seen from Fig. 4 that the variation of water is synchronous with the seawater, observation hole and beach well, which means that the aquifer soil has a powerful permeability. In addition, the seawater level is 0.44 m higher than the water level in the observation hole while it is 0.87 m higher than that of the beach well in average.

Equation (9) is used to determine the permeability coefficient K.

(9) K={\displaystyle \frac{\mathrm{0.366}{Q}_{\mathrm{0}}}{MS}}\lg {\displaystyle \frac{\mathrm{2}{l}_{\mathrm{1}}-l_{\mathrm{2}}}{l_{\mathrm{2}}}},

where Q₀ denotes the pumping water (m³/s), M denotes the thickness of the aquifer (m), S denotes the water level difference between seawater and the observation hole (m), and l₁ and l₂ denote the distance from the beach well to seawater and the observation hole, respectively (m).

Based on the experimental results and the location of the beach well, the average permeability coefficient K was calculated as 0.0029 m/s.

To further study the variation of pumping water temperature, a test of 66 h was performed. The pumping water quantity varies from 40 m³/h to 45 m³/h in the process of pumping due to the influence of tide. The results are described in Fig. 5.

Model validation

The model was validated against the detailed parameters listed in Table 1 and some important technical parameters calculated by numerical method in Section 2, including permeability coefficient K, porosity n, and coefficient of thermal conductivity λ. Additionally, an experimental test was implemented in the experimental system shown in Figs. 2 and 3.

Take the porosity changing at the start of the 42th hour as the porosity of aquifer soil, which is calculated by the numerical method according to pumping water and water level difference between seawater and the beach well. The value approximates to 0.49.

Seen from Fig. 6, the outlet water temperature of the beach well fluctuates around the soil initial temperature in the first 42 h of pumping water, because seawater migration is slower in the aquifer and soil heat conduction is smaller in this period. The main component of seawater is the water stored in the aquifer and seawater cannot reach the beach well. After the 42th hour, the outlet water temperature fluctuates slowly and begins to drop as seawater has reached the beach well. This period is divided into two parts, Part 1 and Part 2, to conveniently analyze the relationship between the experimental value and the simulation value.

Part 1 is used to determine the coefficient of thermal conductivity for the aquifer. Based on the outlet water temperature between the 42th and the 54th hour, the calibration for the seepage heat transfer model was conducted, and the coefficient of thermal conductivity was computed using Eq. (1), that is, 1.46 W/(m·K). To better describe the relationship in Part 1, three typical coefficient of thermal conductivity was chosen to observe the difference, as depicted in Fig. 7.

Part 2 is used to verify the accuracy of the model. As demonstrated in Fig. 6, the two values are very close. The maximum relative error is calculated to be equivalent to 2.1% (less than 5%) which is acceptable in engineering application. The simulation results coincide very much with the experimental data, which proves that the mathematical model proposed can effectively simulate the heat transfer process.

Results and discussion

The pumping water of the BWIIS is related to the drawdown, the hydrogeological parameters of the aquifer, and the design parameters of beach well including the location and diameter. But for a specific project, the hydrogeological parameters of the aquifer have been determined, and other parameters like drawdown and design parameters of the beach well should be analyzed.

Location of beach well

Combined with the experiment system, the single well with a diameter of 2 m was taken as an example while other parameters were kept constant when changing the location. When water level difference between seawater and well water was 1 m, the pumping water of the location at X= 20 m Y=4 m, X=100 m Y=4 m, X=100m Y=14 m was 67.1 m³/h, 70.7 m³/h, 102.1 m³/h, respectively. The results indicate that the longer distance from the beach well to the impervious boundary and the shorter distance from the beach well to the supplying water source can both increase the pumping water, while the latter has a greater influence on pumping water. The impervious boundary is defined as the boundary of the aquifer soil except for the seawater boundary. And it is estimated that the pumping water flow increases when X increases, and it will reach the maximum when the beach well is located at X = 100 m. The pumping water flow decreases if X increases. This is because the longer relative distance from the beach well to the impervious boundary can improve the permeability of the soil.

Diameter of beach well

The single well located at X = 20 m, Y = 4 m was chosen as an example to observe the influence of beach well diameter on pumping water. In addition, other parameters such as well location and drawdown were kept the same as those used in the simulation in Section 3. Figure 8 shows the pumping water of beach well with different diameters when water level difference between seawater and well water is 0.87 m. The pumping water of the well is increased greatly when the diameter changes from 0.4 m to 1 m, while slightly when the diameter changes from 1 m to 4 m. Based on these results, the pumping water can increase 13.2% when the well diameter changes from 1 m to 2 m, and it can just increase 31.2% when well diameter changes from 1 m to 4 m. The pumping water has no linear relationship with the well diameter, and the growth rate of pumping water decreases with well diameter increasing.

Drawdown

Taking the single well with a diameter of 2 m and location of X = 20 m, Y = 4 m as an example, the drawdown was changed to observe the variation of pumping water. Besides, other parameters such as flow rate and diameters of the beach well were kept the same as those used in the simulation conducted in Section 3. The relationship between pumping water and drawdown is displayed in Fig. 9. It is observed that the pumping water increases with the drawdown increasing. It can be estimated that the pumping water quantity can reach the maximum when the drawdown lowers to the top of the aquifer in order to insure that the flow condition in aquifer is saturated flow.

Conclusions

In this paper, a model of beach well infiltration intake system applied in the seawater source heat pump system was built based on the energy conservation equation and Darcy’s law. The porous medium model in simulation software FLUENT was applied to simulating the seepage and heat transfer process.

The water quality of BWIIS was improved significantly by the action of soil, which could greatly reduce the seawater corrosion on the heat exchanger. Water level analysis was conducted in order to determine the porosity and coefficient of thermal conductivity for the aquifer soil in the simulation, which are 0.49 W/(m·K) and 1.46 W/(m·K). The simulation value of pumping water temperature is very close to the temperatures measured from field experiment. The maximum relative error is 2.1% (less than 5%), proving that the model is validated. Besides, influencing factors of pumping water on the beach well infiltration intake system were analyzed. The pumping water increases when the distance between the beach well and the impervious boundary becomes longer, when the distance between the beach well and the supplying water source shortens, when the diameter of the beach well enlarges and drawdown enlarges.

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