Problem 4.11 - A Home Geothermal Heat-Pump

Introduction and Description

With the global quest for energy efficiency, there is renewed interest in geothermal heat pumps which have been in limited use for more than 70 years. Essentially this technology relies on the fact that a few meters below the surface of the earth the temperature remains relatively constant throughout the year, warmer than the air above it during winter, and cooler during summer. According to the Spring 2009 newsletter from David White, in Southeast Ohio this temperature is around 55°F (13°C). This means that we can design a heat pump which can combine hot water and space heating in winter in which the earth is used as a heat source (rather than the outside air) at a considerable increase in coefficient of performance COP. Similarly, with suitable valving, we can use the same system in summer for hot water heating and air conditioning in which the earth is used as a heat sink, rather than the outside air. This is achieved by using a Ground Loop in order to enable heat transfer with the earth, as described in the Popular Mechanics website: The Guide to Home Geothermal Energy.

Problem 4.11 - We wish to do a preliminary thermodynamic analysis of the following home geothermal heat pump system designed for wintertime hot water and space heating. Notice that with suitable valving this system can be used both in winter for space heating and in summer for air conditioning, with hot water heating throughout the year.

Notice that the condenser section includes both the hot water and space heater and station (3) is specified as being in the Quality region. Assume that 50°C is a reasonable maximum hot water temperature for home usage, thus at a high pressure of 1.6 MPa, the maximum power available for hot water heating will occur when the refrigerant at station (3) reaches the saturated liquid state. (Quick Quiz: justify this statement). Assume also that the refrigerant at station (4) reaches a subcooled liquid temperature of 20°C while heating the air.

Using the conditions shown on the diagram and assuming that station (3) is at the saturated liquid state

• a) On the P-h diagram provided below carefully plot the five processes of the heat pump together with the following constant temperature lines: 50°C (hot water), 13°C (ground loop), and -10°C (outside air temperature)

• b) Using the R134a property tables determine the enthalpies at all five stations and verify and indicate their values on the P-h diagram.

• c) Determine the mass flow rate of the refrigerant R134a. [0.0127 kg/s]

• d) Determine the power absorbed by the hot water heater [2.0 kW] and that absorbed by the space heater [0.72 kW].

• e) Determine the time taken for 100 liters of water at an initial temperature of 20°C to reach the required hot water temperature of 50°C [105 minutes].

• f) Determine the Coefficient of Performance of the hot water heater [COPHW = 4.0] (defined as the heat absorbed by the hot water divided by the work done on the compressor)

• g) Determine the Coefficient of Performance of the heat pump [COPHP = 5.4] (defined as the total heat rejected by the refrigerant in the hot water and space heaters divided by the work done on the compressor)

• h) What changes would be required of the system parameters if no geothermal water loop was used, and the evaporator was required to absorb its heat from the outside air at -10°C. Discuss the advantages of the geothermal heat pump system over other means of space and water heating.

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