ASHRAE Journal - August 2010 - 74

contact, centered in the bore) and B (tubes centered in the bore but separated) and Hellström’s configuration B and C (tubes in contact with opposite outer walls). Comparisons of other TP test results indicate most of the bore resistances fall within the range predicted by configurations B and C for smaller U-tubes in typical bore diameters of 4 to 6 inches (10 to 15 cm).
Bore Resistance Calculator From Formation Thermal Property (k, T, α) Test Data Houston, TX Bore Resistance Calculation Using Remund and Hellstrom Methods with Added BC Arrangement Remund Hellstrom GroutThermCond 0.85 Btu/hr-ft-ºF U-Tube Arrangement Sb Res Grout Res Pipe Res Bore Res Bore Pipe Resistance for HDPE DR 11 & 9 Configuration A 5.974 0.1969 0.0714 0.2683 0.2950 TubeOD 1.315 inches 8.017 0.1468 0.0714 0.2181 0.2599 Configuration B Configuration C DimRatio 11 13.456 0.0874 0.0714 0.1588 0.2150 Configuration BC 0.1766 FlowRate 7.7 gpm

hr-ft-ºF/Btu hr-ft-ºF/Btu hr-ft-ºF/Btu hr-ft-ºF/Btu

Bore Resistance Calculation From Thermal Property Test Data Using Line Source & Cylindrical Source Methods Ground and Loop Information Thermal Conductivity Test Results & Calculation Mid Range Bore Resist = Rtotal - Rground BoreLength 300 feet time (hrs) Temp (ºF) Power (W) Ln(time) slope therm.cond. Resistances (hr-ft-ºF/Btu) BoreDiameter 4.75 inches 8 103.8 6750 2.079 Btu/hr-ft-ºF FO (mid) Rgrn(mid) Rtot (mid) Rbore (mid) GroundTemp 70.3 ºF 12 106 6756 2.485 5.426 1.126 11.779 0.237 0.467 0.230 16 107.7 6756 2.773 5.909 1.035 15.706 0.256 0.489 0.233 Properties from Formation Type 20 108.8 6747 2.996 4.930 1.240 19.632 0.270 0.503 0.233 CpLow 0.2 Btu/lb-ºF 24 109.7 6726 3.178 4.936 1.235 23.559 0.282 0.515 0.233 CpHigh 0.22 Btu/lb-ºF 28 111 6706 3.332 8.433 0.721 27.485 0.292 0.532 0.240 3 32 111.6 6712 3.466 4.493 1.351 31.411 0.300 0.540 0.239 DensityLow 130 lb/ft 3 36 112.1 6712 3.584 4.245 1.431 35.338 0.308 0.546 0.238 DensityHigh 155 lb/ft RhoCpLow 26 40 112.7 6709 3.689 5.695 1.066 39.264 0.315 0.554 0.239 RhoCpHigh 34.1 PowerAvg 6728 TCAvg 1.151 For Avg ρ×cp Value RboreAvg 0.236 RhoCpAvg 30.05 Check 5.518 1.103

Table 1: Calculated bore resistances and field test results—Houston.7

From Figure 2 G-factor (Fo = 28.8) ≈ 0.34 and Rg = G-factor/kg = 0.34/1.17 Btu/h·ft·°F = 0.291 h·ft·°F/Btu (0.168 m·K/W) Equation 2 is used to compute bore resistance

− Rg q (72.7°F− 56°F)×244 ft = − 0.291h⋅ft ⋅°F/Btu . 3.41Btu/W ⋅h×2606 W = 0.167 h⋅ft ⋅°F/Btu (0.096 m⋅K/W)
Bore Resistance Equations for Design and Simulation Tools

Rb =

(t w − t g )× Lb

resistance from the thermal property test results and Equations 1, 2 and 3 at four hour increments. In this case the field test bore resistance falls between the values computed from Remund’s configuration A (tubes in contact, centered in the bore) and B (tubes centered in the bore but separated) and Hellström’s configuration B and C (tubes in contact with opposite outer walls). Comparisons of other TP test results indicate most of the bore resistances fall within the range predicted by configurations B and C for smaller U-tubes in typical bore diameters of 4 to 6 in. (100 to 150 mm). Table 2 compares results for a larger U-tube bore (1.25 in. (32 mm]) and a relatively low thermal conductivity grout (0.4 Btu/h · ft · °F [0.69 W/m · K]). This indicates the correlations may provide a conservative bore resistance and under predict the value when larger diameter U-tubes are used.
Summary

Bore resistance is an important component in the design and simulation of vertical ground source heat pumps. Tables and equations have been used that account for the bore diameter, tube dimensions and conductivity, grout/fill conductivity, and assumed location of the tubes. Since it is difficult to predict the location of the tubes, these correlations have a degree of uncertainty, which is unavoidable given the nature of field installations. The bore resistance field test can be used to verify and improve these correlations while providing an indication of the degree of uncertainty. Two sets of equations developed by Remund5 and Hellström6 can be applied to three assumed locations of U-tubes (A: centered in the bore and touching, B: tubes centered in the bore but separated, and C: tubes in contact with opposite outer walls). A more likely location is that the tubes are touching the outer wall and in near contact (B/C), which was not addressed by Remund5 or Hellström.6 However, a data base could be developed and published to improve this estimate if more field test results of bore resistance become available. The upper portion of Table 1 shows a spreadsheet tool to calculate bore resistance using the methods suggested by Remund5 and Hellström.6 The lower portion of the table calculates the bore
74 ASHRAE Journal

Computation of the bore resistance of vertical ground heat exchangers can be accomplished using the results of standard thermal property tests. This is a valuable tool for verifying thermal and economic effectiveness of grouts and ground heat exchangers, ensuring loops have been properly installed, and improving the accuracy of correlations for system design and simulation. It is important to note, that although bore resistance is important, the dominate resistance to heat flow is the ground itself. Sufficient loop lengths and bore separation distances are critical to ensure acceptable liquid temperatures are returned to the equipment for efficient operation.
References
1. ASHRAE. 2001. “Investigation of the Methods for Determining Soil and Rock Formation Thermal Properties From Short-Term Field Tests.” RP-1118. 2. Ingersoll, L.R., O.J. Zobel, and A.C. Ingersoll. 1954. Heat Conduction with Engineering, Geological and Other Applications, 2nd Ed. Madison, Wis.: University of Wisconsin Press. 3. Kavanaugh, S.P. and K.D. Rafferty. 1997. Ground Source Heat Pumps: Design of Geothermal Systems for Commercial and Industrial Buildings. ASHRAE. ashrae.org August 2010

ASHRAE Journal - August 2010

Table of Contents for the Digital Edition of ASHRAE Journal - August 2010