Geothermal Grout Calculator
Determine borehole thermal resistance (R_b), total drilling footage savings from thermally enhanced grout, silica sand blending ratios, and 50-lb grout bag quantities.
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Borehole Thermal Resistance (R_b) & Enhanced Grouting
Heat transferred between the circulating geothermal fluid and the surrounding ground must conduct across three resistances in series: fluid convective resistance, the HDPE pipe wall conduction resistance, and the grout annulus resistance. Standard pure bentonite grout has poor thermal conductivity ($k approx 0.40 ext{ BTU/hr-ft-}^circ ext{F}$), acting as a thermal choke.
Grout Thermal Physics & Paul Formulas
- Borehole Thermal Resistance ($R_b$):
R_b = (1 / k_grout) × β_0 × (r_bore / r_pipe)^β_1
Whereβ_0andβ_1are shape factors dependent on U-tube leg spacing (Class A, B, or C). - Silica Sand Blending:
Blending 50-70 mesh high-purity silica sand (typically 150 to 250 lbs of sand per 50-lb bag of bentonite) increases thermal conductivity up to 1.0 to 1.2 BTU/hr-ft-°F. - Economic Payback:
Drilling costs $14 to $22 per foot. Reducing required total borehole depth by 20% to 30% yields net project savings thousands of dollars greater than the modest cost of silica sand additives.
Frequently Asked Questions
What is borehole thermal resistance (R_b)?
Borehole thermal resistance (R_b) is the thermal resistance between the fluid inside the HDPE U-tube pipes and the borehole rock boundary wall. Lower R_b allows much higher heat transfer per foot of bore.
How much drilling footage does thermally enhanced grout save?
Using thermally enhanced grout (k = 1.0 to 1.2 BTU/hr-ft-°F) instead of plain bentonite (k = 0.40) reduces required total borehole drilling footage by 20% to 30%.
What kind of sand is mixed with bentonite for thermal grout?
High-purity rounded quartz silica sand (typically 50-70 mesh) is blended into bentonite slurry at ratios of 150 to 250 pounds of sand per 50-pound bag of dry bentonite.