A New Method to Determine the Thermal Properties of Soil Formations from In Situ Field Tests

Abstract

The geothermal or ground-source heat pump (GHP) has been shown to be a very efficient method of providing heating and cooling for buildings. GHPs exchange (reject or extract) heat with the earth by way of circulating water, rather than by use of circulating outdoor air, as with an air-source heat pump. The temperature of water entering a GHP is generally cooler than that of outdoor air when space cooling is required, and warmer than that of outdoor air when space heating is required. Consequently, the temperature lift across a GHP is less than the lift across an air-source heat pump. The lower temperature lift leads to greater efficiency, higher capacity at extreme outdoor air temperatures, and better indoor humidity control. These benefits are achieved, however, at the cost of installing a ground heat exchanger. In general, this cost is proportional to length of the heat exchanger, and for this reason there is an incentive to install the minimum possible length such that design criteria are met. The design of a ground heat exchanger for a GHP system requires, at a minimum, the operating characteristics of the heat pumps, estimates of annual and peak block loads for the building, and information about the properties of the heat exchanger: the size of the U-tubes, the grouting material, etc. The design also requires some knowledge of the thermal properties of the soil, namely thermal conductivity, thermal diffusivity, and undisturbed soil temperature. In the case of a vertical borehole heat exchanger (BHEx) these properties generally vary with depth; therefore, in the design, effective or average thermal properties over the length of the borehole are usually sought. When the cost of doing so can be justified, these properties are measured in an in situ experiment: a test well is drilled to a depth on the same order as the expected depth of the heat pump heat exchangers; a U-tube heat exchanger is inserted and the borehole is grouted according to applicable state and local regulations; water is heated and pumped through the U-tube (using a field generator to power the equipment, or line voltage where available); and the inlet and outlet water temperatures are measured as a function of time. Data on inlet and outlet temperature, power input to the heater and pump, and water flow rate are collected at regular intervals--typically 1 to 15 min--for the duration of the experiment, which may be as long as 60 h. Two common methods for determining soil thermal properties from such measurements are the line source method and the cylinder source method. Both are based on long-term approximate solutions to the classical heat conduction problem of an infinitely long heat source in an infinite homogeneous medium. Although there are some differences in the way the two methods are implemented, the only difference between the two models is whether the heat source is considered to be a line or a cylinder. In both methods, power input to the water loop is assumed to be constant. The simplicity of these methods makes them attractive, but they also have some disadvantages. First of all, because the line source and cylinder source approximations are inaccurate for early time behavior, some of the initial data from the field test must be discarded. The amount of data discarded can affect the property measurement. Also, both methods assume that the heat transfer to the ground loop is constant. In practice, heat input to the loop may vary significantly over the course of a field test due to rough operation of the generator or short-term sags and swells in power line voltage. Presumably, this variation affects the accuracy of the thermal property measurement, but error analysis is rarely performed. This report presents a new method for determining thermal properties from short-term in situ tests using a parameter estimation technique. Because it is based on numerical solutions to the heat conduction equation, the new method is not affected by short-term variations in heat input. Also, since the model is accurate even for short times, there is no need to discard initial data. The parameter estimation technique used to determine the properties is based on statistical principles that provide quantitative estimates of measurement accuracy. The parameter estimation method has now been tested with a laboratory test rig at Oklahoma State University and in field tests at two elementary schools in Lincoln, Nebraska. Using our estimation algorithms, and building on the validation achieved during testing, we have developed a computer program, the Geothermal Properties Measurement (GPM) model, that allows users to determine thermal properties from short-term in situ field tests. This program is currently available free of charge.