1、782 2009 ASHRAEABSTRACTGeothermal heat pumps exchange heat with the ground through the use of ground heat exchangers where the heat transfer rate depends on the thermal conductivity of the surrounding soil. An in-situ test is often performed on a verti-cal borehole to estimate soil thermal conductiv
2、ity, but the test must have sufficient duration in order to obtain an accurate estimate. Conventional analysis methods usually do not check to see if the test duration is sufficient. This paper validates a procedure to perform this check as a supplement to current methods. The procedure uses an anal
3、ytical composite model of borehole heat transfer to estimate the minimum test duration necessary to determine soil thermal conductivity within 5% of the estimated value from a very long test. Data sets from 16 field tests are used in the validation process. The minimum test dura-tion ranges from app
4、roximately 10 to 53 hours among the tests when a simplified line-source model is used for evaluating soil thermal conductivity. The results indicate no simple rule for minimum duration applies to all cases. Instead, the proposed procedure based on the analytical composite model can deter-mine if tes
5、t duration is sufficient. INTRODUCTIONIn geothermal heat pump (GHP) systems heat is extracted or rejected to the ground to take advantage of the relatively constant temperature of the ground. The design of ground-loop heat exchangers for GHP systems requires an estimate of soil thermal conductivity.
6、 Often prior to the final design of a large installation, in-situ tests are performed on vertical test boreholes to estimate soil thermal conductivity. The vertical ground-loop heat exchanger has a U-tube inserted into a bore-hole, as illustrated in Figure 1a. Grout is placed in the borehole to fill
7、 the space that is not occupied by the U-tube. The low-permeability grout prevents water and contaminants from migrating along the vertical borehole. Gehlin and Spitler (2003) and Sanner et al. (2005) have reviewed the history and status of in-situ thermal conductivity tests. Early portable test rig
8、s have been described by Eklf and Gehlin (1996) and Austin et al. (2000). A typical equipment setup for an in-situ test uses an electric heater at the surface as a controlled heat source. Water is pumped through the U-tube and exchanges heat with the ground. In the ideal test the heat input rate is
9、constant during the test. Transient temperatures of the circulating water are recorded at the supply and return connections of the ground loop. The average of these two temperatures is used to approximate the average temperature Required Duration For Borehole Test Validated by Field DataYedi D. Liu
10、Richard A. Beier, PhDAssociate Member ASHRAEYedi D. Liu is an associate professor and senior engineer in the College of Mechanical Engineering, Tongji University, Shanghai, P.R. China. Richard A. Beier is an associate professor in the Department of Mechanical Engineering Technology, Oklahoma State U
11、niversity, Stillwater, OK.LO-09-027 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2. For personal use only. Additional reproduction, distribution, or transmission in either print or digita
12、l form is not permitted without ASHRAEs prior written permission.Figure 1 a) Geometry of actual borehole; (b) Composite model of borehole.ASHRAE Transactions 783along the loop. This average temperature is often plotted in a semilog plot similar to Figure 2. For a given heat input rate, the recorded
13、temperature rise will be steeper for soil with lower thermal conductivity, because the soil does not conduct heat away from the borehole as quickly as in the case of higher soil thermal conductivity. Thus, the transient temperature of the borehole contains information about the soil thermal conduc-t
14、ivity. Two techniques to analyze test data use line-source (Carslaw and Jaeger, 1959; Ingersoll and Plass, 1948) and cylindrical models (Deerman and Kavanaugh, 1991) of the borehole geometry in treating conduction heat transfer. The line-source model (Equation A-1 in Appendix A) ignores the finite d
15、iameter of the borehole and treats the U-tube as a verti-cal line. An additional mathematical approximation gives a simplified line-source model (Equation A-3), which forms a straight line in Figure 2. The cylindrical model captures the finite diameter of the borehole and replaces the U-tube with a
16、single vertical pipe. The advantage of these relatively simple analytical solutions is the ease of applying them to a borehole test data set. The fit of each model to a loop temperature curve from borehole test #1 in Stillwater, Oklahoma is shown in Figure 2. Each of these models ignores the thermal
17、 storage of the fluid circulating through the loop, the detailed geometry of the borehole, and the difference in the thermal properties of the grout and soil. Thus, these three models do not fit the early-time data (Figure 2), which are strongly influenced by near borehole effects. The models match
18、the late-time data, which are dominated by the soil properties. The line-source model reveals that the late-time temperature curve should have a linear trend in Figure 2. The soil thermal conductivity is inversely proportional to the late-time slope (Equation A-4).The above models have been applied
19、to test #1 without any account for heat input rate variations. Variations in heat input rate may cause significant scatter in the loop temperature curve (Figure 2), which adversely affects the estimate for soil thermal conductivity. A few techniques have been developed to handle variations in the he
20、at input rate. Shonder and Beck (1999, 2000) have taken into account rate variations in their parameter estimation technique for estimating soil thermal conductivity. Their technique uses a numerical method to eval-uate a composite model for the borehole. The actual borehole is represented by the si
21、mplified, radially symmetric geometry in Figure 1b where the U-tube is replaced by a single pipe with an effective radius rp. An annular region between the single pipe and the soil is filled with grout, which has different ther-mal properties from the soil. The entire loop temperature curve is used
22、in the parameter estimation fits in Figure 3. Austin et al. (2000) have also reported results from a parameter estima-tion technique tied to a detailed numerical model of the bore-hole geometry.Whichever method is used to analyze a field test, the dura-tion of the test must be sufficient in order to
23、 get an accurate estimate of soil thermal conductivity. If a test is interrupted by an electrical power outage or other unexpected event, the ques-tion becomes whether the test duration was sufficient prior to the interruption. The first 20 hours of data from two field tests are shown in Figure 3. A
24、 linear fit based on the simplified line-source-model overlays on each data set. The linear fit is applied to the data between 10 and 20 hours for each test. The Figure 2 Comparisons of borehole models to loop temperature measurements in borehole test #1.Figure 3 Fits of simplified line-source model
25、 and parameter estimation technique to loop temperature curves from test #2 and test #3. 784 ASHRAE Transactionsparameter estimation fit (Shonder and Beck, 1999) is also shown. The model fits look good but they raise some ques-tions. Are 20 hours of data sufficient to determine an accurate estimate
26、of soil thermal conductivity for each test? Although each data set shows an apparent late-time linear trend, how can one confidently say the soil thermal conductivity estimate would remain unchanged if the test duration was extended? These questions apply to both the line-source and parameter estima
27、tion methods. The main purpose of this paper is to provide and verify a procedure that answers these questions. As in many applications, the duration of the test must be chosen to balance opposing issues. A shorter duration reduces the cost of a field test. Yet the duration must be sufficient to giv
28、e an accurate estimate of soil thermal conductivity. As shown later in this paper, the 20 hours of data in Figure 3 provide an accurate estimate of soil thermal conductivity for one of the tests but not the other. Although past authors provide guidelines for the required test duration, their recomme
29、ndations do not agree. Austin et al. (2000) recommend a minimum duration of 50 hours based on their experiences with field data sets. Kavanaugh et al. (2001) recommend tests durations between 36 to 48 hours. Gehlin (1998) suggests a minimum duration of 60 hours but recommends using 72 hours. Smith a
30、nd Perry (1999) suggest that 12 to 20 hours may sometimes be sufficient, partly because if the test duration is too short the estimated soil ther-mal conductivity is too low, which is a conservative estimate for the design of ground heat exchangers.Signorelli et al. (2007) conclude there is no strai
31、ghtforward and general guideline for the test duration needed by the line-source model. They perform a sensitivity analysis for the line-source model by comparing results with a very detailed 3-D finite-element model of the borehole. Under perfect simulated conditions with little unwanted noise, the
32、y conclude a test dura-tion of 50 hours generally provides good results from the line-source analysis. A method to estimate the minimum duration of a test was proposed by Beier and Smith (2003a) based on an analytical solution of the composite model in Figure 1b. However, the verification of the mod
33、el was based more on data sets from a laboratory sandbox rather than field tests. The model does not take into account fluctuations in the heat input rate and other unwanted noise, which occur in nearly every field test. Furthermore, both the test duration to reach the late-time linear trend and the
34、 soil thermal conductivity depend on the slope of the loop temperature curve. The effects of unwanted noise in the loop temperature curve become amplified when evaluating the slope of the curve. The present paper determines whether this composite model method is robust enough to consistently work on
35、 field data. Also, the method outlined by Beier and Smith (2003a) relies on a cumbersome set of graphs to use, but the corre-sponding calculations in the present paper are made in an easy-to-use spreadsheet, which is available from one of the authors (R. A. Beier). Because the parameter estimation t
36、echnique fits the entire loop temperature curve (Figure 3), one would hope the tech-nique could get by with shorter test duration than the line-source model. A secondary purpose of this paper is to evaluate if the use of the parameter estimation technique shortens the required test duration. Althoug
37、h Gehlin and Hellstrm (2003) and Kavanaugh et al. (2001) have compared various models, they have not addressed the requirements for the test duration among the different models. MINIMUM TEST DURATION ESTIMATEThe analytical solution to the composite model (Beier and Smith, 2003a) allows one to predic
38、t the minimum test duration of a thermal conductivity test. The composite model (Figure 1b) can match the entire loop-temperature curve by treating the soil and grout separately with different thermal properties. The soil and the grout are treated as internally homogenous regions. The model does not
39、 explicitly account for the thermal resistance due to the U-tube pipe walls or any contact resis-tances at the pipe/grout or grout/soil interfaces. Instead, these resistances are implicitly rolled into the value of rp. In order to develop an analytical solution, heat is added or removed from the cir
40、culating fluid at a constant rate. The composite model fits the entire loop temperature curve in Figure 2 including the early-time data. The composite model is formulated in terms of dimen-sionless variables and parameters, which are listed in Appen-dix B. Some of the advantages of using dimensionle
41、ss variables are seen in identifying the beginning of the late-time trend for a typical loop temperature plot. A dimensionless temperature derivative is related to the late-time slope of the curve in Figure 2. The dimensionless temperature derivative is calculated from the composite model solution u
42、sing Equation B-7 in Appendix B. In Figure 4 the dimensionless derivative always takes on a value of at large test times. This value of corresponds to the late-time linear trend in Figure 2. The derivative curves in Figure 4 provide a way to estimate the required test duration for the semilog plot (
43、Figure 2) to reach a slope within a certain percentage of its final slope. For instance a 5% window around the final slope corresponds to an interval between 0.475 and 0.525 on the vertical axis in Figure 4. One identifies the smallest value of dimensionless time after which the curve remains inside
44、 this window. The dimensionless parameters in Figure 4 are defined in Appendix B.For any of the analytical or numerical models applied to the borehole test, the composite model can be used to verify the test has sufficient duration to reach the late-time linear trend on the semi-log plot. Thus one c
45、an answer the question of whether the duration for each test in Figures 2 and 3 is suffi-cient. The conventional analysis methods by themselves do not answer this question. A spreadsheet has been written to carry out the calculations with Visual Basic Applications (VBA) subroutines. To perform this
46、check one follows these steps in the proposed procedure:ASHRAE Transactions 785Step 1. Apply one of the models (e.g. line-source model or parameter estimation model) to the loop temperature curve (Figure 2) and estimate the soil thermal conduc-tivity and borehole resistance.Step 2. Enter the estimat
47、ed soil thermal conductivity and borehole resistance in the spreadsheet to help evalu-ate the dimensionless groups in Appendix B for the composite model.Step 3. Other parameters for the composite model must be evaluated from other information besides the loop temperature curve and entered in the spr
48、eadsheet. The grout thermal conductivity and volume heat capacity can be estimated for a given grout type. Knowledge of soil types that are penetrated by the borehole aids in estimating the volumetric heat capacity of the soil. The volume of water in the loop can be calculated along with its heat ca
49、pacity based on the U-tube inner diameter and length. These values are needed to evaluate the dimen-sionless parameters in Appendix B. Step 4. The spreadsheet identifies the smallest value of dimensionless time (Equation B-3) for which the dimen-sionless derivative curve (Figure 4) remains inside a 5% window around the final value of .Step 5. The spreadsheet calculates the test time (in hours) to reach within 5% of the semilog final slope from the definition of dimensionless time (Equation B-3). Step 6. Compare the test time from the spreadsheet to the actual duration of the
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