Thermal analysis of cisterns/wells for air conditioning and heat pump

Abstract

The ever-increasing price of energy is driving improvements in the efficiency of many systems. Air-conditioning is one of the major sources of energy consumption in buildings. Several countries utilize the stability of ground temperature to improve the efficiency of air-conditioning systems. This idea can be transferred to using well water to exchange heat with the air-conditioning system. The success of such system depends on the thermal conductivity of the surrounding rock which is needed to extract or supply heat to the water. A numerical model was developed to find the thermal conductivity of a well, constructed from concrete bricks in an excavated pit in limestone rock. The model uses the energy change in water as the input for the numerical model. The same model was used to find the thermal conductivity by imposing the water temperature on the surface nodes. To validate the results a three-dimensional computational model was also developed. The results of these models were compared to analytical solutions available in textbooks for semi-infinite solids with different boundary conditions. The thermal conductivity of the well in consideration was found to be 1.4 W/mK when utilizing the numerical model. For the three-dimensional computation model, the thermal conductivity was found to be 2 W/mK when assuming an energy input caused by the change in water temperature, or 1.05 W/mK when the water temperature was imposed on the surface nodes. The results are comparable to handbook values for limestone and concrete. The analytical solution for exponential heat flux for a semi-infinite solid verified the numerical model. It was noted however, that the assumption of having linear flow of heat or one-dimensional flow of heat is not accurate since it overestimates the thermal conductivity of rock for the energy method. A work around to this problem was to assume an ever-increasing heat transfer area with increasing depth from the surface nodes. This improved the result considerably. Using the thermal conductivity found in this dissertation an example scenario was created to analyse if using well water as the source or sink of heat is beneficial when compared to using air. It was assumed that an air-conditioner of peak load 2.5 kW operated for 6 hours a day dumps heat into a well having a capacity of 45 m3 . In this scenario the improvement is minimal over the summer period, given the rate at which water temperature increases and does not justify the added capital cost of the system. The thermal conductivity of rock has to be higher to justify such a system.