Ground-Source Heat Pumps: Design & Performance

Ground-source heat pumps (GSHP) extract thermal energy from shallow geothermal resources, exploiting the earth’s relatively constant subsurface temperature (10-20°C at depths below 3-6 m) to provide highly efficient space conditioning. GSHP systems achieve coefficient of performance (COP) values of 3.5-5.0 in heating mode and energy efficiency ratios (EER) of 15-25 in cooling mode, significantly exceeding air-source heat pump performance.

Physical Principles

The earth functions as a thermal reservoir with temperature stability derived from:

Heat Storage Capacity: Soil and rock possess substantial thermal mass, maintaining temperatures near the annual average air temperature at depths exceeding the frost line.

Thermal Inertia: Underground temperatures lag seasonal variations by approximately 3 months due to soil thermal diffusivity:

$$\alpha = \frac{k}{\rho c_p}$$

where $\alpha$ is thermal diffusivity (m²/s), $k$ is thermal conductivity (W/m·K), $\rho$ is density (kg/m³), and $c_p$ is specific heat capacity (J/kg·K).

Temperature Profile: Subsurface temperature varies with depth according to:

$$T(z,t) = T_m + A_s e^{-z\sqrt{\frac{\omega}{2\alpha}}} \cos\left(\omega t - z\sqrt{\frac{\omega}{2\alpha}}\right)$$

where $T_m$ is mean annual surface temperature, $A_s$ is surface temperature amplitude, $z$ is depth, $\omega$ is annual frequency (2π/365 days), and $t$ is time.

Ground Loop Configurations

graph TB
    subgraph "GSHP System Configurations"
        A[Ground Loop Types]
        A --> B[Closed Loop - Vertical]
        A --> C[Closed Loop - Horizontal]
        A --> D[Closed Loop - Pond/Lake]
        A --> E[Open Loop]
        A --> F[Hybrid Systems]

        B --> B1[Single U-Tube<br/>50-150m depth]
        B --> B2[Double U-Tube<br/>75-200m depth]
        B --> B3[Coaxial<br/>100-250m depth]

        C --> C1[Horizontal Trenches<br/>1.5-2.5m depth]
        C --> C2[Slinky Configuration<br/>1.8-3m depth]
        C --> C3[Spiral Coils<br/>2-3m depth]

        D --> D1[Submerged Coils<br/>2-6m depth]
        D --> D2[Grid Pattern<br/>Min 0.5 acre]

        E --> E1[Supply Well]
        E --> E2[Discharge Well/Surface]

        F --> F1[Ground Loop + Cooling Tower]
        F --> F2[Ground Loop + Solar Thermal]
    end

    style A fill:#1e3a8a,color:#fff
    style B fill:#2563eb,color:#fff
    style C fill:#2563eb,color:#fff
    style D fill:#2563eb,color:#fff
    style E fill:#2563eb,color:#fff
    style F fill:#2563eb,color:#fff

Vertical Borehole Systems

Vertical closed-loop systems employ U-tube heat exchangers installed in boreholes ranging from 50-200 m depth, spaced 4-6 m apart. This configuration minimizes land area requirements and accesses more stable ground temperatures.

Borehole Heat Transfer: Heat exchange rate per unit length:

$$q’ = \frac{T_g - T_f}{R_b}$$

where $q’$ is heat transfer rate per meter (W/m), $T_g$ is undisturbed ground temperature, $T_f$ is fluid temperature, and $R_b$ is borehole thermal resistance (m·K/W).

Thermal Resistance Components:

$$R_b = R_{pipe} + R_{grout} + R_{contact}$$

Grout thermal conductivity significantly impacts performance: enhanced thermally-conductive grout (k = 1.5-2.5 W/m·K) reduces borehole length requirements by 15-30% compared to standard bentonite grout (k = 0.7-1.0 W/m·K).

Horizontal Loop Systems

Horizontal loops require larger land areas (0.3-0.5 acres per ton of cooling capacity) but involve lower drilling costs. Installation depth typically ranges from 1.5-2.5 m, below frost depth but within the zone of seasonal temperature variation.

Slinky Configuration: Overlapped coils increase heat transfer surface area per trench length:

$$L_{slinky} = \frac{L_{straight}}{2.5 \text{ to } 3.5}$$

This configuration reduces trench length by 60-70% while maintaining equivalent heat transfer performance.

Pond and Lake Loops

Submerged coils in bodies of water exploit natural convection and high water thermal conductivity (0.6 W/m·K). Minimum requirements:

• Water depth: 2-3 m minimum to prevent freezing
• Surface area: 0.5 acre minimum per 12,000 BTU/h (3.5 kW) capacity
• Coil placement: 1.5-2 m depth with ballast anchoring

Open Loop Systems

Direct groundwater systems pump water through a heat exchanger and discharge to a secondary well or surface water body. Key considerations:

• Groundwater flow rate: 1.5 gpm (5.7 L/min) per ton of capacity
• Water quality: minimize fouling, scaling, and corrosion
• Regulatory compliance: discharge permits and well construction codes
• Screen sizing: prevent sand migration (maximum velocity 0.05-0.1 ft/s)

Ground Loop Sizing Methodology

Heat Extraction/Rejection: Annual heat balance must prevent long-term ground temperature degradation:

$$Q_{annual,heating} \approx Q_{annual,cooling}$$

IGSHPA Sizing Equation: Required borehole length:

$$L = \frac{Q_a R_{ga} + Q_h R_{gh} - W_c(COP-1)R_{gh}}{T_g - (T_{wi} + T_{wo})/2}$$

where:

• $L$ = total borehole length (m)
• $Q_a$ = annual average heat transfer (W)
• $Q_h$ = peak heat transfer (W)
• $R_{ga}$ = effective ground thermal resistance for annual pulse (m·K/W)
• $R_{gh}$ = effective ground thermal resistance for short-term pulse (m·K/W)
• $W_c$ = compressor power (W)
• $T_g$ = undisturbed ground temperature (°C)
• $T_{wi}, T_{wo}$ = inlet/outlet fluid temperatures (°C)

Thermal Conductivity Values:

Performance Metrics

Coefficient of Performance:

Loop Type Comparison:

| Configuration | Installed Cost | Land Required | COP Range | Applications | |—|—|—|—| | Vertical borehole | $15-30/ft depth | Minimal | 3.8-5.0 | Limited land, high performance | | Horizontal trench | $6-12/ft length | 0.3-0.5 acre/ton | 3.5-4.5 | Available land, lower budget | | Slinky horizontal | $8-15/ft length | 0.15-0.25 acre/ton | 3.6-4.6 | Moderate land area | | Pond/lake | $4-8/ft coil | Water body required | 3.7-4.8 | Existing water resources | | Open loop | $8-18/gpm | Well field area | 4.0-5.2 | Adequate aquifer, water quality |

Hybrid System Configurations

Hybrid GSHP systems integrate supplemental heat rejection or source equipment to optimize performance and reduce ground loop size:

Cooling Tower Hybrid: Reduces peak cooling load on ground loop by 20-40%, preventing thermal saturation in cooling-dominated climates.

Solar Thermal Hybrid: Solar collectors recharge ground temperature during heating season, maintaining long-term thermal balance.

Boiler/Chiller Hybrid: Conventional equipment handles peak loads beyond GSHP capacity, downsizing ground loop investment.

Design Standards and Guidelines

IGSHPA Standards: International Ground Source Heat Pump Association provides:

• Closed-loop/geothermal heat pump systems design and installation standards
• Grouting procedures and materials specifications
• Thermal conductivity testing protocols

ASHRAE References:

• ASHRAE Handbook - HVAC Applications, Chapter 34: Geothermal Energy
• ASHRAE Standard 90.1: minimum efficiency requirements for water-source heat pumps
• ASHRAE Guideline 14: measurement of energy and demand savings

Thermal Response Testing: In-situ testing determines actual ground thermal conductivity and borehole resistance for projects exceeding 20 tons capacity. Test duration: 48-72 hours minimum with constant heat injection rate 50-80 W/m.

System Longevity and Maintenance

Ground loop lifespan: 50+ years for HDPE piping (ASTM D3350, PE4710 specification). Heat pump equipment lifespan: 20-25 years with proper maintenance. Annual maintenance includes filter replacement, refrigerant charge verification, and antifreeze concentration testing (25-30% propylene glycol maintains freeze protection to -15°C).