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Equivalent time for interrupted tests on borehole heat exchangers.

Article Excerpt
INTRODUCTION

By exchanging heat with the ground (or surface water), ground-source heat pump systems efficiently heat and cool buildings. These systems often use vertical ground loops for the heat exchange with the ground (Bose 1988; Kavanaugh and Rafferty 1997). The vertical ground loop consists of a high-density polyethylene (HDPE) U-tube inserted into a vertical borehole (Figure 1a). With the U-tube in place, a grout mixture is pumped into the borehole to fill the space between the U-tube and the borehole wall. Low-permeability grout prevents water and contaminants from traveling along the vertical borehole.

[FIGURE 1 OMITTED]

The design of the ground loops depends on the thermal conductivity of the surrounding soil and rock. A larger soil thermal conductivity allows the heat to be exchanged at a larger rate for a given borehole. For a given set of heat input rates during an annual cycle, the required borehole length decreases as the soil thermal conductivity increases.

Because the soil thermal conductivity is such an important parameter, in-situ tests are often performed on a test borehole for larger commercial installations. Reviews of the history and status of in-situ thermal conductivity tests have been written by Gehlin and Spitler (2003) and Sanner et al. (2005). Morgensen (1983) proposed an in-situ test as a viable method to determine soil thermal conductivity. Early portable test rigs were described by Eklof and Gehlin (1996) and Austin et al. (2000).

During an in-situ test, an above-ground electric heater usually provides heat to the fluid circulating through the ground loop, while the inlet and outlet fluid temperatures are measured. The average of these two instantaneous temperature readings is usually taken to represent the average temperature in the vertical ground loop at a given time. In an ideal test, the measured circulating flow rate and the heat input rate remain constant throughout the test. A semilog plot of loop temperature versus the logarithm of time is often used to estimate the soil thermal conductivity. If the borehole loop is represented by a line-source of heat, a model by Carslaw and Jaeger (1959) reveals that the soil thermal conductivity is related to the slope of the late-time temperature rise in the semilog plot (Figure 2).

[FIGURE 2 OMITTED]

Because the cost of a test increases with increasing test duration, there is a desire to have a prior estimate of the minimum test duration that yields valid results. Austin et al. (2000) recommend a minimum duration of 50 hours based on their experiences with field data sets. Gehlin (1998) suggests a minimum duration of 60 hours, but recommends using 72 hours. Smith and Perry (1999) suggest that 12 to 20 hours may sometimes be sufficient, partly because if the test duration is too short, the estimated soil thermal conductivity is too low, which is a conservative estimate for the design of ground heat exchangers. Beier and Smith (2003a) argue no simple rule for minimum duration applies to all cases. They propose a method to estimate the minimum test duration based on the borehole and soil properties.

Electrical power outages, electric heater failures, or other unexpected events sometimes interrupt borehole tests before the test duration is sufficient to estimate soil thermal conductivity. One would like to restart the test immediately after the equipment problems are fixed, but the temperature distribution in the ground has been changed. Most analysis methods assume a spatially uniform ground temperature at the start of the test, and this assumption is invalid if the test is restarted quickly.

To return to the initially undisturbed ground conditions, Martin and Kavanaugh (2002) recommend a 10- to 12-day waiting period before retesting a borehole after a completed 48-hour test. For an interrupted test, they suggest the waiting period can be reduced in proportion to the reduced test time (Kavanaugh et al. 2001). Such time delays cost time and money when the equipment is on location and ready for restarting the test.

If the duration of the interruption is no more than a few hours, the best course of action may be to restart the test immediately after the problem is repaired, even with only standard analysis methods. As an example, Figure 2 illustrates temperature rise curves from both uninterrupted and interrupted tests in a large laboratory sandbox. Information about the sandbox is given later in this paper. During the interrupted test (open symbols), electric power was shut off for a two-hour period, starting at approximately nine hours into the test. The loop temperature is greatly distorted immediately after startup, but the rising temperature eventually overlays on the uninterrupted curve with nearly the same late-time slope. The estimated thermal conductivity values from each test are within 2% of each other. In this case, the cumulative test time is 51 hours, including the interruption. Thus, restarting the test immediately after the power is restored is the best strategy in this case. Beier and Smith (2005) describe a method to estimate the time it takes for the temperature curve to recover from the interruption. For longer interruptions in the sandbox, the recovery time becomes substantially longer; an 8-hour interruption requires a recovery time of about 190 hours after the beginning of the initial test. Therefore, analysis methods are needed to shorten the required test time for longer interruptions and still provide an accurate estimate of the soil thermal conductivity.

Some previous methods for geothermal boreholes handle variable rates, but their applications to interrupted tests have not been reported in the literature. For instance, Shonder and Beck (1999, 2000) and Austin et al. (2000) have numerical parameter estimation methods to estimate soil thermal conductivity in variable-rate tests, but they have not reported applications to tests in which the heat input rate goes to zero. A deconvolution method by Beier and Smith (2003b) requires a complete temperature and heat input rate data set, but the missing data during the interrupted period make this method inapplicable to interrupted tests.

Preliminary attempts to apply the computer program developed by Shonder and Beck (1999) revealed some shortcomings in the program's present form for handling interrupted tests. The parameter estimation algorithm uses an objective function, which is the sum of squared differences between the calculated and measured loop temperatures. The algorithm minimizes this objective...

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