Modeling of vertical ground loop heat exchangers for ground source heat pump systems

Abstract

The ability to predict both the long-term and short-term behavior of ground loop heat exchangers is critical to the design and energy analysis of ground source heat pump systems. For detailed analysis and accurate simulation of the transient heat transfer in vertical ground loop heat exchangers, a numerical model is developed. The model is based on the two-dimensional, fully implicit finite volume formulation and utilizes an automated parametric grid generation algorithm for different pipe sizes, shank spacing and borehole geometry. The numerical method and grid generation techniques have been validated against an analytical model. The numerical model has been developed with two main purposes in mind. The first application is the calculation of non-dimensional temperature response factors for short time scales that can be used in building simulation. The second application is use in a parameter estimation technique used to predict borehole ground formation thermal properties from short time scale test data.

The short-term behavior of ground-coupled heat pump systems is important for the design of ground loop heat exchangers, the energy analysis of ground source heat pump systems, and the design of hybrid ground source systems. Using short time-step response factors, a direct evaluation of system energy consumption and electrical demand in hourly or shorter time intervals becomes possible since a detailed assessment of the ground heat exchanger behavior on an hour-by-hour basis can be performed. This is important especially when dealing with strong short time-step system fluctuations due to building dynamics and for commercial buildings that have time-of-day electricity rates. The short time-step model is cast as a TRNSYS component model and validated using actual operating field data from an elementary school building located in Lincoln, Nebraska.

Furthermore, a short time-step ground loop heat exchanger model is crucial for analysis of hybrid ground source heat pump systems. Ground source heat pumps for cooling-dominated commercial buildings utilize supplemental heat rejecters such as cooling towers, fluid coolers or surface heat rejecters to reduce system first cost and to improve system performance. The use of supplemental heat rejecters for cooling dominated buildings allows the design of smaller borehole fields. Heat pump performance degradation is avoided by offsetting the annual load imbalance in the borefield and the resulting long-term temperature rise. Utilizing the short time-step model, a parametric study is presented to investigate the advantages and the disadvantages of various system operating and control strategies in a hybrid ground source heat pump application under different climate conditions. An actual office building located in Stillwater, Oklahoma is used as the example building. A preliminary life cycle cost analysis is conducted to compare each operating and control strategy to determine the lowest cost alternative for a given climate.

The numerical model is also used as part of parameter estimation algorithm that is developed to predict borehole ground formation thermal properties from short time scale test data. Determination of the ground's thermal conductivity is a significant challenge facing designers of Ground Source Heat Pump (GSHP) systems applied in commercial buildings. The number of boreholes and the depth and cost of each borehole are highly dependent on the ground thermal prope11ies. Hence, depending on the geographic location and the local drilling costs, the ground thermal properties strongly influence the initial cost to install a GSHP system. In order to be able to predict ground thermal properties, a parameter estimation technique is employed that minimizes the sum of the squares error between experimentally measured temperature responses and the temperature predictions of the numerical model. An experimental apparatus has been built capable of imposing a heat flux on a test borehole, and measuring its temperature response. The downhill simplex method of Nelder and Mead (1969) in conjunction with the two-dimensional numerical model is used to determine the thermal conductivity of the surrounding ground. In order to validate the procedure, independent measurements of the soil conductivity test results are reported for several test boreholes and a laboratory experiment. A detailed uncertainty analysis of the thermal conductivity prediction is conducted to assess the impact of uncertainty of a series of input parameters.